U.S. patent application number 11/302993 was filed with the patent office on 2006-10-26 for determination of light absorption pathlength in a vertical-beam photometer.
This patent application is currently assigned to Molecular Devices Corporation. Invention is credited to Calvin Y. Chow, Dean G. Hafeman.
Application Number | 20060238764 11/302993 |
Document ID | / |
Family ID | 22822393 |
Filed Date | 2006-10-26 |
United States Patent
Application |
20060238764 |
Kind Code |
A1 |
Hafeman; Dean G. ; et
al. |
October 26, 2006 |
Determination of light absorption pathlength in a vertical-beam
photometer
Abstract
Disclosed are photometric methods and devices for determining
optical pathlength of liquid samples containing analytes dissolved
or suspended in a solvent. The methods and devices rely on
determining a relationship between the light absorption properties
of the solvent and the optical pathlength of liquid samples
containing the solvent. This relationship is used to establish the
optical pathlength for samples containing an unknown concentration
of analyte but having similar solvent composition. Further
disclosed are methods and devices for determining the concentration
of analyte in such samples where both the optical pathlength and
the concentration of analyte are unknown. The methods and devices
rely on separately determining, at different wavelengths of light,
light absorption by the solvent and light absorption by the
analyte. Light absorption by the analyte, together with the optical
pathlength so determined, is used to calculate the concentration of
the analyte. Devices for carrying out the methods particularly
advantageously include vertical-beam photometers containing samples
disposed within the wells of multi-assay plates, wherein the
photometer is able to monitor light absorption of each sample at
multiple wavelengths, including in the visible or UV-visible region
of the spectrum, as well as in the near-infrared region of the
electromagnetic spectrum. Novel photometer devices are described
which automatically determine the concentration of analytes in such
multi-assay plates directly without employing a standard curve.
Inventors: |
Hafeman; Dean G.;
(Hillsborough, CA) ; Chow; Calvin Y.; (Portola
Valley, CA) |
Correspondence
Address: |
David J. Brezner;Dorsey & Whitney LLP
Intellectual Property Department
555 California Street, Suite 1000
San Francisco
CA
94104-1513
US
|
Assignee: |
Molecular Devices
Corporation
Sunnyvale
CA
94089
|
Family ID: |
22822393 |
Appl. No.: |
11/302993 |
Filed: |
December 13, 2005 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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10316707 |
Dec 10, 2002 |
6995844 |
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11302993 |
Dec 13, 2005 |
|
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|
09220177 |
Dec 23, 1998 |
6496260 |
|
|
10316707 |
Dec 10, 2002 |
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Current U.S.
Class: |
356/433 ;
356/319 |
Current CPC
Class: |
G01J 3/1804 20130101;
G01N 21/314 20130101; G01N 21/253 20130101; G01N 21/6452 20130101;
G01N 21/31 20130101; G01J 3/08 20130101 |
Class at
Publication: |
356/433 ;
356/319 |
International
Class: |
G01N 21/00 20060101
G01N021/00; G01J 3/427 20060101 G01J003/427 |
Claims
1-77. (canceled)
78. A multi-channel photometric analysis device for determining
optical characteristics of analytes in sets of liquid containing
samples having unknown optical pathlengths, the device comprising:
a. a first sample holder for holding the sets of liquid containing
samples in one or more substantially vertical channels; b. a means
for positioning the sets of samples in the optical channels; and c.
a light source means, a wavelength selection means, and a light
distribution means which cooperate to transmit substantially
vertically through the samples, wherein the light comprises a fist
calibration wavelength, a second calibration wavelength and
analyte-measuring wavelength, wherein the first and second
calibration wavelengths are different and within the near infrared
wavelength region of from 750 to 2500 nanometers and provide
characteristic light signal values for each liquid sample, wherein
there exists a predetermined relationship between the light signal
values and the optical pathlength through the samples and wherein
the analyte-measuring wavelength provides a characteristic analyte
light signal value related to the concentration of analyte present
in each sample.
Description
BACKGROUND OF THE INVENTION
[0001] 1. Field of the Invention
[0002] This invention relates to the field of photometry. In
particular, the invention relates to spectrophotometric methods and
apparatus capable of determining the light absorption pathlength
for various samples to be analyzed with a spectrophotometer.
[0003] 2. Description of the Related Art
[0004] The problem of an undefined light absorption pathlength in
vertical-beam photometers has existed since the advent of
vertical-beam photometers, i.e., for over 20 years. Substantial
errors in determination by vertical-beam photometry of either
relative optical pathlength or the concentration of analytes in a
solvent contained in a sample-retaining device of unknown optical
pathlength by prior art methods occur because of 1) substantial
variation in solvent temperature, 2) substantial variation in the
solvent composition, 3) substantial presence of materials in the
samples which absorb light in the wavelength region where the
optical pathlength of the solvent is being monitored and 4) optical
aberrations which occur upon passing analysis light though the
variable curved meniscus of samples having a liquid-gas
interface.
[0005] Photometry is a common measurement technique employed to
monitor optical characteristics of samples. Customarily, samples
contain an analyte species dissolved in a solvent at an unknown
concentration. The concentration of the analyte in a sample may be
determined by using a photometric device to measure the fraction of
light absorbed by the sample at a specific wavelength (.lamda.).
The value of .lamda. is usually chosen to be near the wavelength of
light where the analyte absorbs maximally. According to the
Beer-Lambert law, equation 1, absorbance is determined as follows:
Absorbance .times. .times. ( A .lamda. ) = log .times. I o I =
.lamda. 1 C ( 1 ) ##EQU1##
[0006] where I.sub.o is the incident radiation intensity, I is the
intensity of light emerging from the sample, .epsilon..sub..lamda.
is the molar extinction coefficient of the analyte dissolved in the
solvent, I is the light absorption pathlength, and C is the
concentration of absorbing analyte in the solvent. The value of I
customarily is measured with a photometric apparatus, such as a
photometer or spectrophotometer, equipped with a fixed light path
sample-retaining device called a cuvette, such as a 1 cm light
absorption pathlength cuvette. The sample-retaining device contains
a sample comprised of analyte dissolved in a solvent. The value of
I.sub.o is ordinarily measured with the same system (photometric
apparatus, sample-retaining device and solvent except that no
analyte is present in the solvent. Alternatively, I.sub.o may be
measured in the absence of both the sample and the sample-retaining
device (this value of I.sub.o is called an "air blank"). When an
"air blank" is employed, a separate A.sub..lamda. measurement of
the solvent and sample-retaining device gives a "solvent blank"
absorbance value. A "corrected absorbance" value related to
absorbance of the analyte is then obtained by subtracting the
"solvent blank" from each absorbance measurement made on the
samples comprised of analyte dissolved in solvent and contained in
the sample-retaining device. These two alternative procedures and
combinations thereof give mathematically equivalent results.
Absorbance measurements made by either procedure allows unknown
concentrations of the analyte to be determined by calculation
according to Eq. 1, provided that .epsilon..sub..lamda. and I are
known.
[0007] A spectrophotometer is a photometric apparatus which employs
an adjustable means to pre-select a desired portion of the
electromagnetic spectrum as incident radiation. Usually
spectrophotometers employ a monochrometer having a dispersive
means, such as a prism or diffraction-grating, to provide
continuously selectable, narrow, bands of light centered about the
desired wavelength .lamda.. Most conventional photometers and
spectrophotometers employ a horizontal light beam that traverses
the liquid sample so as to avoid passing through a liquid-gas
interface that is typically above the sample. With such
horizontal-beam photometers, the geometry and optical pathlength
within the sample is fixed for any given cuvette. Cuvettes for
visible and ultraviolet light absorption measurements customarily
have a 1 cm pathlength. Cuvettes with pathlengths between 0.1 cm
and 10 cm are also common, however. With any such fixed pathlength
cuvette in a horizontal-beam photometers, unknown concentrations C
of the analytes may be calculated from absorbance measurements
provided that the values of .epsilon..sub..lamda. and l are
known.
[0008] When either .epsilon..sub..lamda. and I is not known, values
of C may be determined readily by employing known concentrations of
the analyte dissolved in the same solvent (i.e., "standards") and
performing similar light-absorbance measurements on unknown
concentrations of analyte dissolved in the same solvent and on the
standards. The most common procedure comprises plotting
A.sub..lamda. versus concentration of analyte in the standards
(i.e., a "standard curve") and then comparing the results obtained
with the unknown concentrations of analyte to the standard curve.
This procedure allows determination of the unknown concentrations
of analyte from the "standard curve".
[0009] Vertical-beam photometers also measure light absorption in
order to determine the unknown concentrations of analyte in
samples. In vertical-beam, photometers, however, the light beam
usually passes only through one wall of the sample-retaining
device, through the sample, and then through the interface between
the sample a surrounding gas atmosphere (which is usually air). The
latter liquid-gas interface, the meniscus, is usually curved, the
specific shape depending upon the interactions between the liquid
sample and the gas and the side-walls of the sample retaining
device. Depending upon the design of a particular vertical-beam
photometer, the light beam may traverse the meniscus either before
or after passing through the sample. In either case, the optical
pathlength through the sample is not a constant value. Instead, the
optical pathlength is related to the sample volume and the meniscus
shape. The nature of the sample, the sample-retaining device
surfaces, and gas each contributes to the shape of the meniscus,
quantitatively affecting the optical pathlength through the sample.
Thus, in vertical beam photometers, the value of l in Eq. 1 usually
is unknown and is difficult to control reproducibly.
[0010] Vertical-beam photometry has become a popular technique
despite the disadvantage of not having a fixed optical pathlength
through the sample. This popularity stems from the fact that the
optical characteristics of a large multiplicity of samples may be
analyzed with a vertical-beam photometer in a small period of time.
Typically, vertical-beam photometers monitor the optical
characteristics of samples disposed in the wells of, for example,
96 well multi-assay plates. The optical characteristics, such as
light absorption or light scattering, of the samples contained
within each well of such multi-assay plates may be monitored,
typically, in 10 seconds or less, and generally in one minute or
less. Vertical-beam photometers also allow repetitive measurements
of such a multiplicity of samples to be made typically with
intervals of 10 seconds or less (and generally in one minute or
less) between each of a series of measurements. In such a way the
kinetic properties, such as the rate of change in absorbance, of a
plurality of samples may be monitored in a very short time.
[0011] In vertical-beam photometry of the prior art, an
approximated constant value of l is used for standards and
unknowns. Concentrations of unknown analytes are determined, often
with acceptable precision, by plotting "standard curves" using the
approximated value of l and comparing the absorbance results
obtained with unknown concentrations of analyte to the standard
curve, as mentioned previously.
[0012] The fact that a value of C may not be calculated directly
from Eq. 1, but instead must be determined from a standard curve
constructed for each analytical measurement, severely hinders the
ability of vertical-beam photometric techniques. The additional
time and expense required for preparing such standard curves for
each analysis is often an onerous disadvantage to vertical-beam
photometry. Thus, convenient, accurate, and precise methods and
apparatus for determining optical pathlength of samples in
vertical-beam photometers would be of great utility.
[0013] Japanese Kokai Patent Application number Sho58[1983]-1679Y2
discloses that the unknown optical pathlength of vessels may be
determined by dispensing a colored solution, with a known
relationship between optical pathlength and color absorbance, into
the vessels and determining the color absorbance of this solution.
A similar method is taught in U.S. Pat. No. 5,298,978, issued Mar.
29, 1994.
[0014] Additionally Japanese Kokai Patent Application numbers Sho
60(1985]-183560 and Sho 61[1986]-82145 disclose methods of
determining relative optical pathlength of aqueous samples within
different reactor vessels (contained in a common reactor) by
measuring the optical density of the samples at two different
wavelengths in the near-infrared wavelength region from 900 to 2100
nanometers. With clear quartz reaction vessels, the reference
teaches that (A.sub.975-A.sub.900), (A.sub.1195-A.sub.1070), or
(A.sub.1260-A.sub.1070) may be used to determine the relative
optical pathlength through aqueous samples. For reactors made of
synthetic acryl resins, where the resin has interfering absorption
bands, the prior art teaches that (A.sub.970-A.sub.1070) or
(A.sub.1280-A.sub.1070) may be used to determine relative optical
pathlength of the samples. Once relative optical pathlength is
known for each of the vessels of the reactor, then optical density
values of analyte (measured at a third wavelength) may be
normalized for variation in optical pathlength to obtain the
relative concentration of analyte in each reactor vessel. Employing
vessels with known concentrations of analyte allows one to
determine the absolute concentrations of analyte within other
vessels.
[0015] There also exists need for methods and apparatus that may be
utilized with samples that are dissolved in a variety of different
solvents or in mixtures of different solvents. Because analytes are
extremely diverse and may have diverse light-absorption properties,
there exists no apparatus capable of determining concentration and
optical pathlength of any analyte dissolved in various solvents or
mixtures of solvents. Further complicating this situation is the
extreme variability of concentrations of analytes from one sample
to the next.
SUMMARY OF THE INVENTION
[0016] The instant invention provides a solution to the problem of
undefined light absorbance pathlength in vertical-beam photometers.
The invention provides methods and devices that are convenient to
employ and that require minimal additional measurement apparatus.
Thus, the cost associated with making such measurement is kept to a
minimum.
[0017] The invention further provides methods and apparatus for
determining optical pathlength and sample concentration that
furnish accurate and reproducible results. The results, determined
by using the invention in vertical-beam photometers, are
essentially interchangeable and indistinguishable from those
obtained in horizontal-beam photometry.
[0018] The invention also provides methods and apparatus for
determining optical pathlengths between 1 millimeter and 1
centimeter in aqueous samples within vertical-beam photometers. The
inventive methods and apparatus may be utilized with samples that
are dissolved in a variety of different solvents or in mixtures of
different solvents.
[0019] Thus, in one embodiment of the invention, optical pathlength
is determined in vertical-beam photometers by analyzing an optical
property of the sample solvent which is dependent upon optical
pathlength but independent of all relevant concentrations of all
analytes which may possibly be contained within a sample
solvent.
[0020] In one aspect, the invention provides multi-channel
photometric analysis devices for determining optical
characteristics of analytes in sets of liquid-containing samples
having unknown optical pathlengths. These devices comprise [0021]
a. a first sample holder for holding the sets of liquid-containing
samples in one or more substantially vertical optical channels;
[0022] b. a means for positioning the sets of samples in the
optical channels; [0023] c. a light source means, a wavelength
selection means, and a light distribution means which cooperate to
transmit light substantially vertically through the samples,
wherein the light comprises a first calibration wavelength, a
second calibration wavelength and an analyte-measuring wavelength,
wherein the first and second calibration wavelengths are different
and within the near infrared wavelength region of from 750 to 2500
nanometers and provide characteristic light signal values for each
liquid sample, wherein there exists a predetermined relationship
between the light signal values and the optical pathlength through
the samples and wherein the analyte-measuring wavelength provides a
characteristic analyte light signal value related to the
concentration of analyte present in each sample; [0024] d. a
detector for determining measured light signal values from light
transmitted through each sample at the first and second calibration
wavelengths and the analyte-measuring wavelength; [0025] e. a means
for determining a measured relationship between the light signal
values; [0026] f. a means for determining from the measured
relationship and the predetermined relationship a correction factor
related to the optical pathlength through each sample; [0027] g. a
means for determining from the correction factor and the analyte
light signal value, a ratio relating the analyte signal value to
the optical pathlength in each of the samples.
[0028] The invention also encompasses vertical-beam photometric
devices for measuring the rate of change in optical characteristics
of samples contained in sample sites disposed on an assay plate,
the device comprising:
[0029] a wavelength selection means for selecting a first
wavelength band of light from a first wavelength range ad for
selecting a second and a third wavelength bands of light from
within a second wavelength range;
[0030] a sample-retaining means for retaining one, or more,
samples, and
[0031] a light-transmitting means for transmitting the light from
the light source to the wavelength selection means and through the
one, or more, sample;
[0032] a photodetector means for detecting the first, second and
third bands of light transmitted through a selected sample, and for
providing a first, a second and a third signal in respective
relationship to the first, second and third bands of light so
transmitted;
[0033] a means for determining the optical pathlength of the first
band of light transmitted through the selected sample from the
difference of the second and third signals; and
[0034] a means for relating the first signal to the optical
pathlength so determined so as to determine and automatically
indicate optical parameters including either the absorbance or the
fraction of incident light transmitted through the selected sample
per unit optical pathlength of the selected sample.
[0035] and additionally a means for kinetic analysis of the signal
of the photodetector means relating to the selected site so as to
determine the rate of change of the optical parameters.
[0036] In another aspect, the invention provides multi-channel
photometric analysis devices for determining optical
characteristics of analytes in sets of liquid-containing samples
having unknown optical pathlengths. In this aspect, the devices
comprise: [0037] a. a first sample holder for holding the sets of
liquid-containing samples in one or more substantially vertical
optical channels; [0038] b. a means for positioning the sets of
samples in the optical channels; [0039] c. a light source means, a
wavelength selection means, and a light distribution means which
cooperate to transmit light substantially vertically through the
samples, wherein the light comprises a first calibration wavelength
and a second calibration wavelength, wherein the first and second
calibration wavelengths are different and within the near infrared
wavelength region of from 750 to 2500 nanometers and provide
characteristic light signal values for each liquid sample, wherein
there exists a predetermined relationship between the light signal
values and the optical pathlength through the samples; [0040] d. a
detector for determining measured light signal values from light
transmitted through each sample at the first and second calibration
wavelengths; [0041] e. a means for determining a measured
relationship between the light signal values; [0042] f. a means for
determining from the measured relationship and the predetermined
relationship a correction factor related to the optical pathlength
through each sample; [0043] g. a means for determining from the
correction factor the optical pathlength in each of the
samples.
[0044] In another aspect, the invention provides methods for
determining the vertical optical pathlength through a
liquid-containing sample comprising
[0045] a. placing the liquid-containing sample in a sample holder
which provides a substantially vertical light path through the
sample, said vertical light path having an unknown optical
pathlength through the sample;
[0046] b. transmitting light through the sample along the vertical
light path, the light comprising a first calibration wavelength and
a second calibration wavelength,
[0047] the first calibration wavelength and the second calibration
wavelength having different near infrared wavelengths within the
range of from 750 nanometers to 2500 nanometers to provide two
characteristic light signal values for the liquid with a
predetermined relationship between the values and the vertical
optical pathlength through the sample;
[0048] c. determining measured light signal values at the first
calibration wavelength and at the second calibration
wavelength;
[0049] d. determining from the measured light signal values, and
the predetermined relationship, the vertical optical light path
pathlength through the sample.
[0050] In yet another aspect, the invention provides methods for
determining the amount of analyte in a liquid-containing sample
comprising
[0051] a. placing the liquid-containing sample in a sample holder
which provides an unknown, substantially vertical, optical light
path through the sample;
[0052] b. transmitting light through the sample along the vertical
light path, the light comprising a first calibration wavelength, a
second calibration wavelength, and an analyte-measuring
wavelength,
[0053] the first calibration wavelength and the second calibration
wavelength having different near infrared wavelengths within the
range of from 750 nanometers to 2500 nanometers to provide two
characteristic light signal values for the liquid with a
predetermined relationship between the values and the vertical
optical pathlength through the sample;
[0054] and the analyte-measuring wavelength providing a
characteristic analyte light signal value related to the quantity
of analyte present in the vertical optical light path;
[0055] c. determining measured light signal values at the first
calibration wavelength, the second calibration wavelength and at
the analyte-measuring wavelength, said measured light signal values
resulting from the passage of the light through the sample;
[0056] d. determining a measured relationship between the measured
light signal values at the first and second calibration
wavelengths;
[0057] e. determining from the measured relationship and the
predetermined relationship a correction factor related to the
pathlength of the vertical light path through the sample;
[0058] f. determining from the correction factor and the measured
light signal value at the analyte-measuring wavelength the amount
of analyte in the sample.
[0059] In a further aspect, the invention provides photometric
analysis systems for determining the vertical optical pathlength
through a liquid-containing sample comprising
[0060] a. a sample holder into which the liquid-containing sample
is placed and which provides a vertical light path through the
sample where the vertical optical light path is unknown;
[0061] b. a light source which transmits light through the sample
along the vertical light path, the light comprising a first
calibration wavelength and a second calibration wavelength
wherein
[0062] the first and second calibration wavelengths are different
and within the near infrared wavelength region of from 750 to 2500
nanometers and provide two characteristic light signal values for
the liquid with a predetermined relationship between the values and
the vertical optical pathlength through the liquid;
[0063] c. a detector for determining measured light signal values
at the first and second calibration wavelengths,
[0064] d. means for determining a measured relationship between the
measured light signal values at the first and second calibration
wavelengths; and
[0065] e. means for determining the vertical optical pathlength
through the sample from the measured relationship.
[0066] In still another aspect, the invention provides a
photometric analysis system for determining the amount of an
analyte in a liquid-containing sample the system comprising
[0067] a. a sample holder into which the liquid-containing sample
is placed and which provides a vertical light path through the
sample where the vertical optical light path is unknown; and
[0068] b. a light source which transmits light through the sample
along the vertical light path, the light comprising a first
calibration wavelength, a second calibration wavelength and an
analyte-measuring wavelength, wherein
[0069] the first and second calibration wavelengths are different
and are within the near infrared wavelength region of from 750 to
2500 nanometers and provide two characteristic light signal values
for the liquid with a predetermined relationship between the
signals and the vertical optical pathlength through the liquid, the
analyte-measuring wavelength providing a characteristic analyte
light signal value related to the quantity of analyte present in
the vertical optical light path;
[0070] c. detector for determining measured light signal values at
the first and second calibration wavelengths and the
analyte-measuring wavelength;
[0071] d. means for determining a measured relationship between the
light signal values measured at the first and second calibration
wavelengths;
[0072] e. means for determining from the measured relationship and
the predetermined relationship a correction factor related to the
vertical optical pathlength through the sample; and
[0073] f. means for determining the amount of the analyte in the
sample from the correction factor and the measured light signal
value at the analyte-measuring wavelength.
BRIEF DESCRIPTION OF THE DRAWINGS
[0074] FIG. 1 is a graph showing calibration of pathlength versus
volume in a NUNC 96-well microplate.
[0075] FIG. 2 is a graph showing the results of measuring the
optical density of fractions at 490 nm in a vertical-beam
photometer.
[0076] FIG. 3 is a graph of the results of measuring the optical
density of fractions at 490 nm in a vertical-beam photometer where
the results have been corrected for the light absorption pathlength
of each fraction so as to indicate optical density per unit (cm)
optical pathlength of each fraction.
[0077] FIG. 4 is a plot of total elution volume versus the optical
density measured at 490 nm for the combined volumes of the wells in
a NUNC 96-well microplate.
[0078] FIG. 5 is a graph showing the absorption spectrum of pure
water between 750 nm and 1100 nm at four different
temperatures.
[0079] FIG. 6 is a graph of the near infrared (NIR) portions of the
electromagnetic spectrum for a biological buffer solution,
Dulbecco's phosphate-buffered saline (PBS).
[0080] FIG. 7 is a graph of the results of the near infrared (NIR)
portion of the electromagnetic spectrum for pure water and 0.1M,
0.5M and 1.0M citric acid solutions in pure water.
[0081] FIG. 8 is a graph of the results of the near infrared (NIR)
portion of the electromagnetic spectrum, between 750 nm and 1100
nm, of either pure water, 0.1M, 0.5M or 1.0M sucrose solutions in
pure water.
[0082] FIG. 9 is a schematic representation of the device of the
present invention.
[0083] FIG. 10 is a schematic representation of a preferred
embodiment of the present invention.
[0084] FIG. 11 is a schematic representation of a more preferred
embodiment of the present invention.
DESCRIPTIONS OF THE PREFERRED EMBODIMENTS
[0085] The disclosed invention comprises photometric methods and
devices for determining Light Absorption Pathlength of liquid
samples containing analytes dissolved or suspended in a solvent.
The methods and devices rely on determining a relationship between
the light absorption properties of the solvent and the optical
pathlength of liquid samples containing the solvent. This
relationship is used to establish the Light Absorption Pathlength
for samples having an unknown Light Absorption Pathlength, but
having a similar solvent composition. Such samples, for example,
may be contained within a plurality of wells disposed in a
multiassay plate, such as a 96-well microplate, in a vertical-beam
photometer. Such vertical-beam photometers are able to measure
absorbance of analytes within such samples at predetermined
wavelengths of light. According to the invention such vertical-beam
photometers may automatically determine and indicate, to an analyst
carrying out a chemical measurement, the concentration of an
analyte. The automatic determination is made, according to Equation
(1), from (a) the absorbance of the analyte in the sample, (b) the
Light Absorption Pathlength determined according to the invention,
and (c) a predetermined "extinction coefficient of the analyte. In
such a way novel photometer devices automatically determine and
indicate the concentration of analytes in such multi-assay plates
directly without employing a standard curve.
[0086] Generally, the methods and devices of the invention rely on
separately determining light absorption by the solvent and, at a
different wavelength, light absorption by the analyte. Devices for
carrying out the methods particularly advantageously include
vertical-beam absorbance photometers with sample retaining means
for containing samples disposed within the wells of multi-assay
plates, wherein the photometer is able to monitor light absorption
of each sample at multiple wavelength bands, including bands in the
visible or UV-visible region of the spectrum, as well as bands in
the near-infrared region of the electromagnetic spectrum.
[0087] The invention, however, is not limited to photometers that
measure light absorption solely. Rather the invention is useful
generally in vertical-beam photometers that measure optical
characteristics in samples where the optical pathlength through a
sample is not known but where it is desirable to know such optical
pathlength. The invention will find general utility in
vertical-beam photometers that, additionally, measure other optical
properties of liquid samples, including, but not limited to
fluorescence, phosphorescence, chemiluminescence, or light
scattering. Thus the invention is useful for chemical measurement
by vertical-beam photometers where the measurement is made by
either light absorptivity, fluorometry, phosphorometry,
chemiluminometry, turbidimetry (where the loss of light from the
optical pathlength is measured as optical density) and nephelometry
(where the light scattered off the optical axis is measured). When
utilizing the invention to measure optical properties of samples
other than light absorbance, the invention will monitor light
absorbance, of the solvent in the sample, in combination with
optical properties of the sample other than light absorbance.
[0088] As used herein, A indicates an absorbance value measured
according to Eq. 1 and a subscripted value following A indicates
the center of the bandpass spectrum of light (given in nanometers)
that is used to make the light-absorbance measurement. For example,
(A.sub.1770-A.sub.1310) is the mathematical difference between
absorbance measurements, made on the same sample with the same
optical pathlength, with 1770 nanometer and 1310 nanometer center
bandpass incident light respectively. In certain situations the
fraction of incident light transmitted (I/I.sub.o) may be employed
rather than the amount of light absorbance (log I.sub.o/I) after
accounting for the mathematical relationship between these two
parameters.
[0089] The solvents suitable for use in the invention and apparatus
of the invention may be any solvent although those absorbing light
in the near-infrared region are preferred. Particularly preferred
solvents are those having low ultraviolet and visible absorbance
spectra. Such solvents are those typically having low electronic
transition probabilities at energy levels corresponding to light of
180 to 750 nanometer wavelength. For electronic transition
probabilities of various solvents, see "High Purity Solvent Guide,"
James T. Przybytek, ed., 1992, Burdick & Jackson Laboratories,
Inc., Muskegon, Mich.
[0090] As used herein, the near-infrared portion of the
electromagnetic spectrum is that portion extending from about 750
to 2500 nanometers (i.e., from about 0.750-2.5 microns wavelength
or, in wavenumbers, about 13,300-4000 cm.sup.-1). Liquid water
absorbs light with values of .epsilon..sub..lamda..cndot.C between
0.01 and 60 cm.sup.-1 at absorption bands located within the near
infrared region. At room temperature, the values of
.epsilon..sub..lamda..cndot.C for pure water is about 0.18
cm.sup.-1 near 970 nanometers and is about 0.58 cm.sup.-1 near 1200
nanometers wavelength. These values may be found in Luck, Berichte
der Bunsengesellschaft 67: 186-189, 1963; and Thomas et al., The
Journal of Physical Chemistry 69: 3722-2726, 1965.
[0091] The light absorption pathlength customarily employed in
vertical-beam photometry is between 1 millimeter and 1
centimeter.
[0092] According to Eq. 1, the values of A.sub..lamda. at
wavelengths of about 970 nanometers and about 1200 nanometers are
0.018 or 0.058, respectively, for a 1 millimeter light absorption
pathlength and 0.18 or 0.58, respectively, for a pathlength of 1
centimeter in pure water at room temperature. These values are well
within the range of 0.01 to 4.0 absorbance units which is generally
desirable for precise optical density measurements in vertical-beam
photometers.
[0093] It has been unexpectedly discovered that near-infrared
analysis of water at selected wavelengths is sufficiently robust to
give an inaccuracy of less than 5% variation from the true
pathlength value in vertical-beam photometry. This discovery is
surprising since: (1) absorption of light by molecules in the
near-infrared region (NIR) of the electromagnetic spectrum is due
to overtones or combinations of overtones originating from
fundamental absorption bands in the mid-infrared region extending
from 4000 to 600 cm.sup.-1; (2) absorbance in the mid-infrared
region is due to intra-molecular bond stretching and bending
vibrational motions and is highly dependent upon the extent of
hydrogen bonding in aqueous solutions; and (3) physical parameters
such as temperature or ionic strength, for example, influence the
absorption coefficient and wavelength of maximum absorption. In
addition, analytes present in water may potentially influence
hydrogen bonding within the solvent, thus changing the light
absorption properties of the water solvent. These problems are
discussed in the Handbook of Near-Infrared Analysis, Donald A.
Burns, Emil W. Ciurczak, eds., Marcel Dekker, Inc. 1992. See also,
G. L. Kemeny and D. L. Wetzel, "Moisture: Study of a Lively
Near-Infrared Diffuse Reflectance Spectrum," Paper 117, FACSS
13.sup.th Annual Meeting, Sept. 28-Oct. 3, 1986, St. Louis Mo.; and
G. L. Kemeny and D. L. Wetzel, "Differences in the Spectrum of
Water," AACC Annual Meeting, Nov. 1-6, 1987, Nashville, Tenn.
Furthermore, samples analyzed by vertical-beam photometry
customarily have a curved meniscus and no single unique pathlength
exists for all rays of light passing through the sample.
[0094] The methods and apparatus of the invention may be used to
determine various light absorption pathlengths within vertical-beam
photometers containing samples, preferably light absorption
pathlengths between about 1 millimeter and 1 centimeter. Further,
the invention may be used with a variety of solvents and analytes.
Disclosed herein are four embodiments suitable for determining
light absorption pathlengths. These methods and apparatus each
utilize measurement of absorbance of the sample solvent in the
near-infrared region of the electromagnetic spectrum (NIR).
[0095] The first embodiment is especially well suited for use in
determining optical pathlength in purely aqueous solvents within a
moderate temperature range. This embodiment may be used at
temperatures from about room temperature to the temperature of the
human body (i.e., from about 20 to 40.degree. C.).
[0096] The second embodiment may be used to determine light
absorption pathlength for samples having an analyte in aqueous
solvents over a broader range of temperatures, i.e., from about 0
to 100.degree. C.
[0097] The third embodiment is suitable for determining light
absorption pathlength in mixtures of aqueous and non-aqueous
solvents.
[0098] Finally, the fourth embodiment is preferred for use with
nonaqueous solvents having values of .epsilon..sub..lamda..cndot.C
of from about 0.05 to 5 cm.sup.-1 for absorption bands located
within the near infrared to infrared regions of the electromagnetic
spectrum from about 800 to 6000 nanometers.
[0099] Vertical-beam photometers suitable for carrying out the
invention will have the following:
[0100] 1. a light source, such as tungsten halogen, xenon flash
lamp, mercury arc lamp, or the like;
[0101] 2. a wavelength selection means capable of selecting bands
of light in the ultraviolet-visible region of the electromagnetic
spectrum from between 180 to 750 nanometers. (These
ultraviolet-visible bands will normally be used for analysis of
concentration of analytes in samples comprised of at least one
analyte dissolved in a solvent);
[0102] 3. a wavelength selection means capable of selecting bands
of light in the infrared region of the electromagnetic spectrum
greater than 750 nanometers;
[0103] 4. a light-distribution means, such as optical lenses and
mirrors for directing light, or a system of fiber optics for
directing the light;
[0104] 5. a sample-retaining means for retaining samples disposed
on a multi-assay plate, such as the NUNC 96-well microplate;
and
[0105] 6. a light detection means, such as photo-diodes,
photo-conduction cells, a photo-multiplier, photo-Darlington cells,
a diode-array, or the like capable of detecting both the bands of
the light in the ultraviolet visible region and the bands of light
in the infrared region.
[0106] 7. a means for determining the optical pathlength of the
samples, as described above.
[0107] Suitable wavelength selection means for both the
ultraviolet-visible region and the infrared region of the
electromagnetic spectrum include optical filters of colored glass,
or the like, interference filters, or monochromators for dispersing
the light and selecting a band of light. With either filters or a
monochrometer the bands of light desirably will be narrow in the
range of 1 to 25 nanometers bandwidth. Preferably the bands will be
even narrower, but not so narrow as to unduly limit the amount of
light provided, generally in the 5-10 nanometer range. Usually the
wavelength selection means capable of selecting bands of light in
the infrared region will need to select bands of light only in the
near-infrared region of the electromagnetic spectrum from 750
nanometers to 2500 nanometers wavelength. Alternatively, a laser,
such as a helium-neon, argon ion, carbon dioxide, or solid state
laser, e.g. a GaAlAs laser, could be used to fulfill both the
requirement for a light source and a wavelength selection means.
When more than one band of wavelengths is desired, two, or more,
lasers or light-emitting diodes may be combined as the light source
and the desired wavelength range may be supplied by turning on the
light source emitting the desired wavelength band of light. Such
lasers have the advantage of having high light intensity at
extremely narrow bandwidth. Alternatively, light-emitting diodes
(LEDs) may be used to supply light of the desired wavelength range.
A variety of LEDs may be used selectively to provide the desired
wavelength bands of light when switched from on to off.
Alternatively, the LEDs or laser sources of light may be used in
conjunction with a white light source, together with optical
filters or a monochrometer. In this way, the wavelength range and
intensity of the white light source may be extended at a desired
wavelength.
[0108] A vertical-beam photometer suitable for monitoring the
absorbance of liquid samples in the ultraviolet-visible and the
near-infrared portions of the electromagnetic spectrum when fitted
with the appropriate interference filters, is described in U.S.
Pat. Nos. 4,968,148 and 5,112,134. A vertical-beam photometer
disclosed in pending U.S. patent application Ser. No. 08/228,436
also would be suitable when fitted with a monochrometer capable of
providing bands of light in the near-infrared portion of the
electromagnetic spectrum. Such a monochomater is Part No. 36-0504
available from Optometrics Inc., Ayer, Mass. All documents, e.g.,
patents and journal articles, cited above or below are hereby
incorporated by reference in their entirety.
[0109] All documents, e.g., patents and journal articles, cited
above or below are hereby incorporated by reference in their
entirety.
[0110] A particularly preferred instrument and software for
carrying out the present invention is the SPECTRAmax.RTM.PLUS
microplate spectrophotometer. In the following examples a
SPECTRAmax.RTM.PLUS microplate spectrophotometer was used and is
available commercially from Molecular Devices Corporation.
[0111] A schematic representation of the optical design of an
apparatus of the invention, as embodied in a SPECTRAmax.RTM.PLUS
microplate spectrophotometer is shown in FIG. 11. Such a microplate
spectrophotometer has a xenon flash lamp as a light source 102.
Light produced by source 102 is dispersed by a monochrometer 110,
having a diffraction grating 112, onto a monochrometer exit slit
114. The selected light exiting through the exit slit 114 is
resolved into wavelength bands of 2 run (full width at half-height)
which are selectable in 1 nm increments between 190 and 1000
nanometers by moving the angle of the grating 112 with respect to
the exit slit 114.
[0112] As shown in FIG. 11, nine optical fibers 120 are arranged
linearly at the exit slit to collect the selected light into 9
optical fiber channels 122. Eight of the fiber channels 122 are
used to direct the selected light to 8 individual channels of a
vertical-beam photometer chamber 130 which is adapted to hold
multi-assay plates 132. The plates are retained by a multi-assay
plate housing 131 (not shown). The housing accommodates multi-assay
plates 135 such as standardized 96-well microplates with sample
wells in a 8.times.12 rectangular array, or alternatively,
multi-well, linear, sample strips, such as standardized 8-well
strips. The optics 133 (not shown) of the vertical-beam photometer
chamber are adapted to allow the light to pass substantially
vertically through fluid samples in the multi-assay plate 135 so as
to pass through a gas/liquid interface in each sample (i.e. passing
through a meniscus) as is customary for vertical-beam
photometry.
[0113] The remaining optical fiber is used to carry the selected
light to a cuvette housing 134 which is adapted to hold a
rectangular cuvette 140 or a rounded tube (e.g. a standard 1 cm
pathlength optical cuvette or test tube). The optics of the cuvette
housing are adapted to allow the light to pass through fluid
samples in the cuvette without passing through a gas/liquid
interface (i.e. without passing through a meniscus) as is customary
for horizontal-beam photometry.
[0114] A first silicon photodetector 150 related to each optical
fiber channel is positioned to collect light diverted by a
beam-splitter 152 positioned to reflect light before it has passed
through the space where the fluid samples are placed (i.e., the
sample position). A second silicon photodetector 154 related to
each optical fiber channel is positioned to collect the light after
it has passed through the sample position. The ratio of
photocurrents from the two photodetectors in each channel is used
to compute the optical density of (or % transmission of light
passing through) the fluid samples (relative to a reference such as
air only in the sample position). This arrangement of
photodetectors is utilized both in cuvette housing 134 and the
vertical-beam photometer chamber 130.
[0115] Cuvettes 140 are placed manually in cuvette housing 134 and
fluid samples are placed one-at-a-time in a cuvette 140 for optical
density measurements. In contrast, multiple samples may be placed
in the wells of multi-assay plates 132. Light from each of the 8
parallel optical fiber channels passes simultaneously through up to
8 wells of a multi-assay plate allowing 8 simultaneous optical
density measurements in 8 different wells of the plate. A motorized
plate carrier repositions the multi-assay plate so that subsequent
groups of 8 wells are interrogated by the 8 optical channels. In
sequence, this process is repeated until all samples have been
interrogated, 8 at a time. For example, when a standard 96-well
multi-assay plate with samples arranged in a 8 rows.times.12
columns in a rectangular array is used, the plate carrier
repositions the multi-assay plate 12 times sequentially, so as to
interrogate simultaneously the 8 samples in each of the 12
columns.
[0116] For determination of optical pathlength of aqueous samples,
near-infrared interference filters 160, mounted on a motor-driven
filter wheel 162 (not shown) in monochrometer 110, are individually
selected and placed in the optical path of the microplate
spectrophotometer. The interference filters are 1/2 inch diameter
and have a 10 nanometer bandpass (nominally centered within 5
nanometers of 1000 nanometers and near 900 nanometers,
respectively). Light from the flash lamp passes through the filters
and reflects off the optical grating and into the exit slit 114
having the optical fibers. Maximal light throughput is achieved
when the optical grating 112 is placed at its "zero order" angle
where light originating from the flash lamp is reflected into the
monochrometer exit slit 114 without diffraction. The optical fibers
120 direct the light to the individual channels of a vertical-beam
photometer chamber 130 and to the cuvette housing 134 as described
above.
[0117] Alternatively, the grating 112 of monochrometer 110 may be
positioned so that bands of light centered within 5 nanometers of
1000 nanometer center wavelength or 900 nanometer wavelength are
diffracted onto exit slit 114 having optical fibers 122. In this
alternative embodiment, optical filters 160 and filter wheel 162
are not needed. Also in this alternative embodiment, the nominally
900 nanometer and 1000 nanometer bands of light directed into
optical fibers 122 will have similar bandpass as other UV, visible
and near infrared light diffracted by grating 112 onto
monochrometer exit slit 114 (in this example 2 nanometers).
[0118] In still another alternative embodiment, the width of the
monochrometer slit may be adjusted, either manually or
automatically by an electrical apparatus such as a motor or
solenoid, to provide a selected bandpass of light. In this way a
bandpass value may be selected for each center wavelength of light.
Generally bandpass values will be between 1 nanometer and 10
nanometers. More generally bandpass values can be between 0.25 and
25 nanometers.
[0119] Optionally solvent (e.g. water) contained in a reference
cuvette of known optical pathlength is used to calibrate the
instrumental determination of solvent pathlength. Cuvette 140 in
cuvette housing 134 may be used for this purpose. For example,
light from the flash lamp is passed through the 1000 nm
interference filter and absorption by the solvent in the reference
cuvette is measured. Customarily, the combined effects of light
reflectance and absorption are measured by comparison of the light
intensity transmitted through the solvent and the light intensity
transmitted through air (with neither the sample nor the sample
retaining device, i.e. the cuvette, present). Next light from the
flash lamp is passed through the 900 nm interference filter and
absorption by the solvent in the reference cuvette again is
measured. Again, the combined effects of both light reflectance and
absorption are measured by comparison of the light intensity
transmitted through the solvent and the light intensity transmitted
through air (with neither the sample nor the sample retaining
device, i.e., the cuvette, present). Loss of transmitted light due
to reflection and absorption by the cuvette is approximately the
same at the two wavelengths, thus the difference in (calculated
absorbance) values obtained in the two measurements gives the
differential absorbance of substantially only the solvent at the
two wavelengths of light. The difference in absorbance values
observed divided by the optical pathlength of the reference cuvette
employed is the calibration value for this specific pair of
filters. An experimental value of 0.1433 absorbance units/cm
optical pathlength was found for a specific 1000 nm/900 nm filter
pair where water, between 15.degree. C. and 37.degree. C., is used
as the solvent. This value is used in the examples described below.
See Example 11.
[0120] One skilled in the art will recognize that modifications may
be made in the present invention without deviating from the spirit
or scope of the invention. The invention is illustrated further by
the following examples which are not to be construed as limiting
the invention or scope of the specific procedures described
herein.
[0121] Experimental Measurements:
a) Instrumentation:
[0122] A Theromax.TM. microplate reader, commercially available
from Molecular Devices Corporation, Menlo Park Calif., USA, is used
to make all vertical-beam photometry measurements. Nominally 1000,
900, and 970 nanometer (center bandpass wavelength) inference
optical filters may be obtained from Andover Corporation, Salem,
N.H. Also, in this instance, the nominally 900 nanometer filter
(Cat. No. 900FS10-25) is centered at 902.6 nanometers with 11.5
nanometer bandpass (bandwidth at half maximal transmittance). Also
in this instance, the nominally 970 nanometer filter (Cat. No.
970FS10-25) is centered at 970.0 nanometers and has 8.5 nanometer
bandwidth at half maximal transmittance. Other optical filters were
obtained as catalog items from Molecular Devices Corporation.
Horizontal-beam photometric measurements, made for comparative
purposes, are made in a Hewlett-Packard Model 8451A diode array
spectrophotometer equipped with a 1 cm light path cuvette.
b) Reagents:
[0123] The following reagents may be obtained form Aldrich Chemical
Co., Milwaukee, Wisc.: Acid Orange 8 (Cat. No. 21,453-1), Acid
Orange 74 (Cat. No. 20, 181-2), Azure B (Cat. No. 86,105-7), Direct
Yellow 62 (Cat. No. 20,206-1), Naphthal Green B (Cat. No.
11,991-1). Bromocresol Purple was obtained from Sigma Chemical Co.
(Cat. No. B-4263). The spectra of these compounds in the
ultraviolet and visible regions of the electromagnetic spectrum is
given in, The Sigma-Aldrich Handbook of Stains, Dyes and
Indicators, by Floyd J. Green, 1990 Aldrich Chemical Co., Inc.,
Milwaukee, Wisc. Durkee Yellow Food Color may be obtained from
Durkee Famous Foods SCM Corporation, Westlake, Ohio. Schilling Blue
Food Color was obtained from McCormick & Co., Inc., P.O. Box
208, Hunt Valley, Md. Obtainable from Sigma Chemical Co. is PIPES
(Piperazine-N,N'-bis[2-ethanesulfonic acid]), sodium salt, Cat. No.
P-6757.
c) Multi-Assay Plates:
[0124] For vertical-beam photometry, samples are contained within
wells of a 96-well microplate multi-assay plate. The microplates
are Nunclon.RTM. Delta 96-well, flat-bottom plates which may be
obtained from VWR Scientific, Brisbane, Calif.
d) Experimental Conditions:
[0125] Measurements reported in the below example were made at room
temperatures between 20 and 25 degrees centigrade.
EXAMPLE 1
[0126] In this example a vertical-beam photometer was also used as
a horizontal-beam photometer in the near infrared at wavelengths
greater than 800 nm. For these horizontal-beam measurements, a 1.00
cm pathlength quartz cuvette is filled with water and capped with a
Teflon.RTM. stopper which is taped to the cuvette. The capped
cuvette was placed horizontally in a vertical-beam photometer so
that a selected band of incident light is passed through one clear
(transparent) wall of the cuvette, next through the water sample,
and finally through the opposite clear (transparent) wall of the
cuvette before being measured by the photodetector of the
photometer. The results of such measurements are equivalent to
measurements made by horizontal-beam photometry. The band of
incident light is first selected by passing through either the
nominally 900 nanometer center-band or the 970 nanometer
center-band interference filter (each of which have approximately a
10 nanometer bandpass). The resulting photometric values were used
as I. Values of I.sub.o for each optical filter were obtained with
neither the water sample nor the cuvette in the incident light path
(air blank). Absorbance values are calculated by the photometer at
each pre-selected wavelength by using Eq. 1. The difference in
absorbance values of the 1.00 cm optical pathlength cuvette filled
with water measured with the nominally 970 nanometer center-band
filter used to provide incident light and the 900 nanometer
center-band filter used to provide incident light (i.e.
A.sub.970-A.sub.900) was found to be 0.180. Horizontal beam
photometry at wavelengths less than 800 nm was performed with the
Hewlett-Packard Model 8451A spectrophotometer.
[0127] Next, similar measurements of (A.sub.970-A.sub.900) were
performed on six different samples containing chromophoric
analytes. Prior to measurement, the analytes were dissolved in the
de-ionized water at concentrations sufficient to yield samples
having absorbance values of between 1.0 and 3.0 absorbance units at
their respective maximal light absorption wavelengths in the
visible spectral region when placed in the same 1 cm optical
pathlength cuvette. The analytes are Acid Orange 8, Acid Orange 74,
Azure B, Direct Yellow 62, Durkee Yellow Food Color. The values of
A.sub.970-A.sub.900 obtained experimentally for each of the
analytes in aqueous solution range from 0.180 to 0.183. A similar
measurement for another analyte comprising Bromocresol Purple in a
solvent mixture of 12 mM PIPES (Piperazine-N,N-bis[2-ethanesulfonic
acid]) and 38 mM Sodium Phosphate Buffer (1.0 parts 0.05 M PIPES:
3:14 parts 0.05 M Sodium Phosphate Buffer by volume, final pH=5.8),
similarly was found to be 0.183. From Eq. 1, and employing two
absorbance measurements, A.sub..lamda.1 and A.sub..lamda.2, at two
different wavelengths, (.lamda..sub.1) and (.lamda..sub.2), we have
(A.sub..lamda.1-A.sub..lamda.2)=(.epsilon..sub..lamda.2-.epsilon..sub..la-
mda.1)lC. The value of
(.epsilon..sub..lamda.2-.epsilon..sub..lamda.1)C for these aqueous
analytes at room temperature, is about 0.182 cm.sup.-1. Based upon
this result, values of (.epsilon..sub.970-.epsilon..sub.900)C
within this range, predictably might be employed generally to
calculate light absorption pathlength from measured values of
(A.sub.970-A.sub.900) for a variety of aqueous samples (referred to
as Sample A.sub.970-A.sub.900) at room temperature. According to
this prediction obtained from a small number of experimental
samples, light absorption pathlength may be determined for aqueous
samples at temperatures ranging from about 15 to 40.degree. C.,
preferably about 23.degree. C, according to Eq. 2 with less than
about 5% error as follows: Light .times. .times. Absorption .times.
.times. Pathlength = Sample .times. .times. ( A 970 - A 900 ) 0.182
.times. .times. cm - 1 ( 2 ) ##EQU2##
[0128] Absorbance of samples per unit pathlength may be found by
measuring the absorbance, A.sub.x, of samples at a preselected
wavelength, x, preferably near the absorbance maximum of the
analyte. The resulting values are referred to as Sample A.sub.x
Light Absorbance per unit Pathlength in aqueous samples is
calculated using equation 3, as follows: Light .times. .times.
Absorbance .times. per .times. .times. Unit .times. .times.
Pathlength = Sample .times. .times. A .chi. .function. ( 0.182
.times. .times. cm - 1 ) Sample .times. .times. A 970 - A 900 ( 3 )
##EQU3##
[0129] From these results and the temperature data provided in
Berichte der Bunsengesellschaft, supra, even greater precision may
be obtained by a) measuring the temperature of the sample, or
alternatively of the sample compartment enclosing the aqueous
sample, and b) adjusting the 0.182 cm.sup.-1 value [i.e.,
(.epsilon.970-.epsilon..sub.900)C] in the denominator of the right
side of Eq. 2 and the numerator of Eq. 3 for the estimated
temperature of the sample. For example, for aqueous samples at
2.degree. C., the adjusted 0.182 cm.sup.-1 value would be about
0.157 cm.sup.-1, for 10.degree. C. about 0.168 cm.sup.-1, for
20.degree. C. about 0.180 cm-1, for 30.degree. C. about 0.190
cm.sup.-1, for 40.degree. C. about 0.200 cm.sup.-1, for 50.degree.
C. about 0.210 cm.sup.-1, for 60.degree. C. about 0.220 cm.sup.-1,
for 70.degree. C. about 0.230 cm.sup.-1, for 80.degree. C. about
0.240 cm.sup.-1 and for 90.degree. C. about 0.250 cm.sup.-1.
Intermediate values of (.epsilon..sub.970-.epsilon..sub.900)C for
intermediate temperatures may be obtained by interpolation.
[0130] In this example, the cuvette, filled with aqueous sample and
sealed at the top, was placed horizontally in the light beam of the
vertical-beam photometer without the use of any fixed retaining
means. These horizontal-beam photometric measurements made at the
individual 970 and 900 nanometer wavelengths varied by as much as
.+-.0.050 absorbance units from measurement to measurement. The
differential A.sub.970-A.sub.900 values, however, varied by no more
than .+-.0.002 absorbance units. Thus, the A.sub.970-A.sub.900
value is relatively independent of the angle of the incident test
light with respect to the sample cuvette in horizontal-beam
photometry. Differential measurements, such as the
A.sub.970-A.sub.900 value, therefore function to eliminate errors
due to variation of cuvette angle with respect to the beam of test
light in horizontal-beam photometry. Alternatively a fixed
sample-retaining means would also help to reduce such errors.
[0131] Next the same sample solutions were dispensed into the wells
of a 96-well microplate at sample volumes of 350, 300, 250, 200,
150, or 100 .mu.l per well. Each sample composition and volume
combination was tested in 8 replicate wells of the microplate.
Absorbance values for each well within the microplate, with
incident light passing substantially vertically through the wells,
were measured in the vertical-beam photometer at the same
center-band wavelengths employed for the respective samples in the
horizontal-beam spectrophotometer measurements. "Solvent blank,"
absorbance values of the pure water solvent were also measured in
the vertical-beam vs. an "air blank" at each measurement
wavelength. The appropriate "solvent blank" at each center-band
wavelength of incident light is subtracted from the experimental
absorbance measurements, which employed "air blank" values of
I.sub.o according to Eq. 1 above. These individual, "solvent
blank"-corrected absorbance values are determined for each analyte
near its wavelength of maximal absorbance in each well of the
microplate. Also, the optical pathlength (i.e. the light absorption
pathlength) is calculated from sample A.sub.970-A.sub.900 data
obtained from each well in the microplate according to Eq. 2 above.
The individual, "solvent blank"-corrected absorbance values
determined for each analyte near its wavelength of maximal
absorbance are then divided by the optical pathlength for each well
of the microplate. These values are termed specific absorbance
values. The specific absorbance values of each analyte (i.e., the
absorbance per unit pathlength, reported in units of cm.sup.-1) are
shown in Table I, below. TABLE-US-00001 TABLE I Optical Density/Cm
Pathlength Measured In A Vertical-Beam Photometer vs. A
Spectrophometer A/cm Microplate A/cm Absorbance per Centimeter
Pathlength 150-350 .mu.l Horizontal- Microplate vs. [A/cm
(cm.sup.-1)] Mean .+-. S.D. Beam Spectrophotometer Chromophore
Microplate Volume (cm.sup.-1) Spectrophotometer Difference
(cm.sup.-1); (wavelength) 350 .mu.l 300 .mu.l 250 .mu.l 200 .mu.l
150 .mu.l 100 .mu.l (CV in %) (cm.sup.-1) (% diff.) Acid Orange 8
2.37 2.33 2.32 2.33 2.34 2.37 2.34 .+-. 0.019 2.28 0.06 (2.5%) (490
nm) CV = 0.00% Acid Orange 74 1.59 1.59 1.59 1.59 1.59 1.61 1.59
.+-. 0.000 1.54 0.05 (3.2%) (480 nm) CV = 0.00% Azure B (650 nm)
1.43 1.44 1.44 1.46 1.45 1.47 1.44 .+-. 0.000 1.46 0.02 (1.0%) CV =
0.76% Blue Food Color 1.67 1.67 1.67 1.67 1.66 1.68 1.67 .+-. 0.004
1.66 0.01 (0.6%) (630 nm) CV = 0.24% Bromocresol 1.15 1.15 1.17
1.16 1.16 1.18 1.155 .+-. 0.008 1.10 0.05 (4.8%) Purple (420 nm) CV
= 0.52% Bromocresol 0.996 0.992 1.008 0.999 1.001 1.019 0.999 .+-.
0.006 0.955 0.04 (4.6%) Purple (590 nm) CV = 0.60% Direct Yellow 62
1.70 1.70 1.70 1.70 1.73 1.76 1.71 .+-. 0.013 1.70 0.01 (0.4%) (340
nm) CV = 0.76% Yellow Food 2.67 2.62 2.59 2.59 2.59 2.61 2.61 .+-.
0.019 2.62 0.01 (0.3%) Color (420 nm) CV = 0.73%
[0132] As shown in Table I, the coefficient of variation (CV) for
the measurement of specific absorbance values, made at the five
greatest sample volumes, for each of the seven different analytes,
and made at eight different wavelenghts, was less than 1%. Further,
even lowest volume (100 .mu.l) samples yielded acceptable specific
absorbance results. The CV of the specific absorbance measurements
for the 100 .mu.l samples, however, slightly exceeded 1%. The
reason for this increase in CV at the lowest volume (100 .mu.l) is
that optimal precision in vertical-beam photometers requires an
optical density of 0.100, or greater. As shown in FIG. 1, in a
typical 96-well microplate, a 100 .mu.l volume only gives about 0.2
cm optical (light absorption) pathlength. Employing the
relationship shown in equation 2 above, we see that a 100 .mu.l
aqueous volume in these microplates will produce only about 0.036
absorbance units in A.sub.970-A.sub.900 which is substantially less
than the 0.100 required for optimal precision.
[0133] Because there is diminished precision with such small sample
volumes (between 10 and 100 .mu.l) for example, in preferred
embodiments, precision of better than 1% may be obtained in
determination of light absorption pathlength by averaging multiple
measurements of A.sub.970-A.sub.900.
[0134] Absorbance values measured in a horizontal-beam
spectrophotometer with identical sample solutions in a 1 cm light
path cuvette are similar to those obtained with the vertical-beam
photometer, after correcting for the determined optical (light
absorption) pathlength.
[0135] Particularly preferred results are obtained when the
concentration of solvent is relatively unchanged by the analyte.
For example, the concentration of water in one (1) molar sodium
chloride aqueous solution, at 0.degree. C., is about 55.6,
substantially the same (within 1%) as for pure water at the same
temperature. Thus, any optical property of water that is dependent
upon the light absorption pathlength within the water, as well as
the water concentration, may be used to monitor the optical
pathlength within aqueous samples containing analytes, provided
that the optical property is otherwise unaffected by such
analytes.
[0136] It is preferred, in most aqueous samples to maintain a high
concentration of the water solvent relative to the concentration of
the dissolved analytes.
[0137] It is further preferred that absorbance measurements of the
solvent not be made exactly at the wavelength of maximal absorbance
of the solvent. Instead, absorbance measurements are preferably
made at a center-band wavelength selected to be between a local
maximum and a local temperature isosbestic or "pseudo-isosbestic"
point in absorbance of the solvent in the NIR. Such temperature
"pseudo-isosbestic" wavelengths exist for light absorbance by
solvents such as water. At such temperature "pseudo-isosbestic"
wavelengths absorbance by the solvent is nearly independent of
temperature.
[0138] In general, the wavelength where two absorbing chemical
species in equilibrium have identical absorptive optical properties
is called an isosbestic point. Such isosbestic points are often
taken as evidence for the existence of at least two
inter-convertible absorbing forms of a species and which forms have
overlapping absorption spectra. For example, the absorption spectra
of simple pH indicator dyes, (e.g. Phenol Red) show isosbestic
points as a function of pH. Phenol red, for example, has an
isosbestic point at 495 nanometers, where the protonated form
absorbs optimally close to 420 nanometers, and unprotonated form of
the dye absorbs maximally at 560 nanometers wavelength. The
equilibrium between the protonated and unprotonated forms of the
dye shifts as a function of temperature due to a non-zero
ionization enthalpy of the dye. Thus, at this (wavelength)
isosbestic point of Phenol Red will also be observed a temperature
isosbestic point because although the relative ratio of
unprotonated and protonated forms of the dye are temperature
dependent, the light absorptive properties of both forms of the dye
are substantially unaffected by temperature variation.
[0139] In contrast, when two inter-convertible absorbing forms of a
species with overlapping spectra exist but the measured optical
property of at least one of the individual chemical species is
affected by a variable, the "perfect" isosbestic is destroyed. For
example spectral narrowing or broadening of an individual chemical
species with temperature variation will result in such a
phenomenon. If the variation from a perfect isosbestic is slight, a
"pseudo-isosbestic" is said to exist. Such pseudo-isosbestic points
are, in fact, observed in the near-infrared absorptive properties
of water, as a function of both temperature and ionic strength
variation.
[0140] At both isosbestic and "pseudo-isosbestic" wavelengths the
absorbance values of solvents are nearly unaffected by temperature
or hydrogen-bonding influences. Water, for example, has multiple
"pseudo-isosbestic" wavelengths, with respect to temperature
variations, which occur between about 980-1010 nanometers, again
near 1080-1120 nanometers, again near 1180-1200 nanometers, again
near 1280-1320 nanometers, again near 1440-1460 nanometers, and
again near 1750-1800 nanometers. Therefore, when the optical
pathlength for aqueous samples is determined from NIR absorbance
measurements in these spectral regions, the variation in the
results due to temperature and hydrogen-bonding variations from
sample-to-sample, is minimized. It is further preferred that the
following absorbance differences for water, (A.sub.1000-A.sub.900),
(A.sub.1190-A.sub.1100), (A.sub.1440-A.sub.1310), or
(A.sub.1770-A.sub.1310) will be measured in order to determine the
optical pathlength of aqueous samples. It is preferred that the
center bandpass wavelength be within 10 nanometers of the
pseudo-isosbestic or isosbestic wavelengths given above. It may be
sufficient, however, for the center bandpass wavelength in most
cases to be within 20 nanometers.
[0141] The (A.sub.1000-A.sub.900) absorbance differences are
preferred NIR wavelengths for measuring absorbance with the silicon
photodetectors present in the "Theromax" microplate reader employed
for these measurements. Since silicon photodetectors do not provide
reasonable detectivity at wavelengths substantially greater than
1100 nanometers, the (A.sub.1000-A.sub.900) absorbance difference
is selected as the absorbance difference of choice to monitor the
absorbance of water to obtain suitable absorbance values at the
preselected wavelength with samples as small as 150 .mu.l and to
ensure that the CV of the measurements are less than 1%.
Alternatively, greater precision and less sensitivity to
temperature and sample variations can be obtained by providing
vertical-beam photometers with light detectors having good
detectivity in the NIR region longer than 1100 nanometers
wavelength. Suitable detectors include, for example, thermal-type
detectors, such as thermocouples, thermistor or pneumatic devices.
Alternatively, NIR semiconductor photodetectors, such as InGaAs,
PbS, InAs, or Ge detectors, could be used. With these infrared
photo-detectors, any of the above other disclosed
"pseudo-isosbestic pairs," (A.sub.1185-A.sub.1100),
(A.sub.1440-A.sub.1310), or (A.sub.1770-A.sub.1310), could be used
directly to monitor the light absorbance pathlength of water. With
such alternative photodetectors, the (A.sub.1185-A.sub.1100) pair
is most optimal because the absorbance of water at 1185 nanometers
is about 0.545 per cm of pathlength, which is very nearly optimal
for maximum signal-to-noise ratios in vertical-beam photometers
employing light-absorbance pathlengths of from 0.2 cm to 1.0
cm.
[0142] A suitable wavelength bandpass (wavelength bandwidth at
half-maximal intensity) for these measurements is about 10
nanometers. Bandpass values of from 0.5 to 15 nanometers are
acceptable, narrower bandpass values restrict the intensity of
available light unduly. Wider bandpass values result in undue loss
in amplitude of differential absorbance measurements.
[0143] The isosbestic center bandpass wavelengths given in this
example are preferred. In practice, a range of center bandpass
wavelengths, is acceptable for practice of the invention.
Generally, for the 900 nm wavelength the acceptable center bandpass
range is quite broad, from about 750 nm to about 925 nanometers.
Generally, for the 1000 nm isosbestic wavelength, the acceptable
center bandpass range is from about 980 nm to about 1020
nanometers. For the 1100 nm isosbestic wavelength, the acceptable
center bandpass range is from about 980 nm to about 1150
nanometers. For the 1190 isosbestic wavelength, the acceptable
center bandpass range is from about 1175 nam to about 1210
nanometers. For the 1310 nm isosbestic wavelength, the acceptable
center bandpass range is from about 1175 nm to about 1350
nanometers. For the 1440 nm isosbestic wavelength, the acceptable
center bandpass range is from about 1430 nm to about 1465
nanometers. For the 1700 nm isosbestic wavelength, the acceptable
center bandpass range is from about 1720 nm to about 1820
nanometers. Further, the differences in absorbances at the given
pairs of isosbestic wavelengths are preferred. It should be
recognized, however, that any of the isosbestic wavelengths may be
paired with any other isosbestic wavelength in order to determine a
difference in absorbance that is related to the pathlength of the
solvent (and which difference will be approximately independent of
temperature).
EXAMPLE 2
[0144] The method described in this example allows measurements of
optical pathlength with mixtures of aqueous and nonaqueous
solvents. It also provides for correction when substances, other
than water (that may absorb at the NIR wavelengths selected to
monitor optical pathlength in vertical-beam photometry) are present
in the solvent. In this example the differential NIR absorbance
(A.sub.970-A.sub.900) is used to monitor pathlength in aqueous
samples. Alternatively, the "pseudo-isosbestic pairs," described
above provide superior results under certain conditions. For
example, the (A.sub.1000-A.sub.900) pair will provide superior
results with silicon photodetectors when the temperature is highly
variable. The (A.sub.1185-A.sub.1100) pair will provide superior
results when the temperature is variable and when a vertical-beam
photometer is used which employs photodetectors sensitive to light
at wavelengths of 1100 and 1185 nanometers in the NIR because
larger absorbance values may be obtained with smaller light
absorbance pathlengths. This method is as follows:
[0145] 1. Load the solvent employed (to dissolve the analyte) into
a cuvette of known optical pathlength, for example, a 1 cm optical
pathlength cuvette. This pathlength is known as the Solvent
Pathlength. Place the cuvette in a photometer and measure
(A.sub.970-A.sub.900) This parameter is referred to as Solvent
(A.sub.970-A.sub.900) (The cuvette may be stoppered and placed on
its side in the incident light path of vertical-beam photometers in
order to accomplish this step.)
[0146] 2. Repeat part 1 in the same known optical pathlength
cuvette, now with the analyte of interest in the solvent. The
resulting parameter is referred to as Reference
(A.sub.970-A.sub.900) Also, measure, approximately, the absorbance,
A.sub.x, of the analyte at the wavelength which will be used for
subsequent measurements of analyte concentration. This parameter is
referred to as Reference A.sub.x. Preferably, the concentration of
the analyte should be adjusted so that the absorbance of the
analyte is a value between 1.0 and 2.0.)
[0147] 3. Measure the values of A.sub.x in samples with the
vertical-beam photometer as is customary. These parameters are
referred to as Sample A.sub.x. Also, measure (A.sub.970-A.sub.900)
values of the samples with the vertical-beam photometer. The later
parameter is referred to as Sample (A.sub.970=A.sub.900) The light
absorption pathlength in each of the samples is determined using
equation 4 as follows: Light .times. .times. Absorption Pathlength
= Sample .times. .times. ( A 970 - A 900 ) - { Sample .times.
.times. A .chi. Reference .times. .times. A .chi. [ Reference
.times. .times. ( A .times. 970 - A .times. 900 ) - Solvent .times.
.times. ( A .times. 970 - A .times. 900 ) ] } Solvent .times.
.times. ( A 970 - A 900 ) Solvent .times. .times. Pathlength ( 4 )
##EQU4## Light Absorbance per unit Pathlength for the samples is
determined from equation 5 as: Light .times. .times. Absorbance
.times. .times. per unit .times. .times. Pathlength = Sample
.times. .times. A .chi. Solvent .times. .times. ( A 970 - A .times.
900 ) Solvent .times. .times. Pathlength Sample .times. .times. ( A
970 - A 900 ) - { Sample .times. .times. A .chi. Reference .times.
.times. A .chi. [ Reference .times. .times. ( A 970 - A 900 ) -
Solvent .times. .times. ( A 970 - A 900 ) ] } ( 5 ) ##EQU5##
[0148] Preferably, the means for determining optical pathlength and
automatically determining and indicating light absorbance per unit
pathlength (i.e., specific absorbance) are included in a
vertical-beam photometric device capable of monitoring the optical
density of samples contained in a multi-assay plate at a minimum of
three (3) different center-band wavelengths of incident light. The
device preferably will include means for determining and indicating
if the analyte presents significant interference with a simple,
uncorrected, determination of Optical Pathlength. An Interference
Parameter is determined from equation 6 as follows: Interference
Parameter = Sample .times. .times. A .chi. .function. [ Reference
.times. .times. ( A 970 - A 900 ) - Solvent .times. .times. ( A 970
- A 900 ) ] Reference .times. .times. A .chi. Sample .times.
.times. ( A 970 - A 900 ) ( 6 ) ##EQU6##
[0149] Significant interference is deemed to be absent when the
Interference Parameter given by Eq. 6 is between 0.05 and -0.05,
for example. Thus, the interference of the analyte creates less
than a 5% error in determination of Optical Pathlength. The device
preferably will include automatic means for determining and
indicating when any of the parameters Sample A.sub.x, Sample
(A.sub.970-A.sub.900), Reference A.sub.x, Reference
(A.sub.970-A.sub.900) or Solvent (A.sub.970-A.sub.900) are less
than 0.05 and, thus, too low to provide an accurate estimation of
interference or specific absorbance.
[0150] Shown in Table II are the measurements of absorbance of
Napthal Green B in aqueous solvent samples determined according to
the method set forth in this example above. For comparison purposes
the results are determined according to Eq. (3) and according to
Eq. (5). The Light Absorbance per unit Pathlength measurements made
(as described in Example 1) according to Eq. (3) in the
vertical-beam photometer (microplate reader) were greater than the
results obtained in the spectrophotometer by 101% (i.e. more than
2-fold greater). Eq. 5, however, provides results from the
vertical-beam measurements with the vertical-beam photometer that
are substantially identical to those from the horizontal-beam
spectrophotometer. TABLE-US-00002 TABLE II Light Absorbance/Cm
Pathlength of an Interfering Analyte Determined with and without
correction for the Optical Interference of Napthal Green B A/cm
Microplate A/cm Absorbance per Centimeter Pathlength 150-350 .mu.l
Horizontal- Microplate vs. ie. A/cm (cm.sup.-1) Mean .+-. S.D. Beam
Spectrophometer Naphthal Green B Microplate Volume (cm.sup.-1)
Spectrophotometer difference (cm.sup.-1) (725 nm) 350 .mu.l 300
.mu.l 250 .mu.l 200 .mu.l 150 .mu.l 100 .mu.l (CV in %) (cm.sup.-1)
(% diff.) Uncorrected A/cm 2.40 2.39 2.40 2.41 2.44 2.51 2.41 .+-.
0.019 1.2 1.21 (+101%) (Eq. 3) CV = 0.08% Corrected A/cm 1.21 1.20
1.21 1.21 1.22 1.23 1.21 .+-. 0.07 1.20 0.01 (+0.8%) (Eq. 5) CV =
0.06%
[0151] The procedure described in this example also allows Light
Absorption Pathlength and Light Absorbance per unit Pathlength to
be determined for mixtures of aqueous and nonaqueous solvents. Such
mixture may include, for example, water, methanol, ethanol,
propanol, acetone, acetonitrile, pyridine, glycerol,
tetrahydrofuran, di- and trichlorobenzenes, or derivatives thereof,
and organic esters such as methyl- or ethyl-acetate. Any mixture of
a nonaqueous, i.e., organic, and aqueous solvent may be employed.
Multi-assay plates that are resistant to such solvents include
multi-assay plates made of glass, quartz, or other polymeric
material resistant to nonaqueous solvents. Suitable quartz 8- or
96-well multi-assay plates are available from Hellena Laboratories,
Beaumont Tex. and from Molecular Devices Corporation, Menlo, Park,
Calif. (Part Nos. R1077 or R1076).
[0152] It should be readily apparent that absorbance of the aqueous
solvent may be measured at any of the isosbestic center bandpass
wavelength pairs described in example. #1 above. For example,
(A.sub.1000-A.sub.900), or any other suitable isosbestic center
bandpass wavelength, could be used advantageously to eliminate
temperature effects in the determination of Light Absorption
Pathlength, Light Absorbance per unit Pathlength, or Interference
Parameter. The acceptable center bandpass ranges are the same as
described in example #1 above.
EXAMPLE 3
[0153] The method described in this example may be employed with
any solvent, including solvents substantially free of water. For
this method the absorbance spectrum of the desired solvent is
determined in the NIR. Two wavelengths are then selected, a first
wavelength near an absorbance maximum, denoted as A.sub.max, of the
solvent; and a second wavelength near an absorbance minimum denoted
as A.sub.min, of the solvent. The difference in absorbance of
samples at the first and second wavelengths, (A.sub.max-A.sub.min,)
should preferably be selected to be between 0.050 and 5.0. It is
particularly preferred that the value of (A.sub.max-A.sub.min) be
selected to be between 0.1 and 1.0. The method is conducted as
follows: [0154] 1A. Load the solvent employed to dissolve the
analyte into a cuvette of known (pre-determined) optical
pathlength, for example, a 1 cm optical path cuvette. This optical
pathlength is known as the Solvent Pathlength. Place the cuvette in
a photometer and measure (A.sub.max-A.sub.min.) This parameter is
referred to as Solvent (A.sub.max-A.sub.min.) (The cuvette may be
stoppered and placed on its side in the light path of a
vertical-beam photometer in order to make this measurement.) [0155]
2A. Repeat step 1A, as described above in the same known optical
pathlength cuvette with the analyte of interest now in the solvent.
This parameter is referred to as Reference (A.sub.max-A.sub.min.)
Also measure, approximately, the absorbance, A.sub.x, of the
analyte at the wavelength which will be used for subsequent
measurements of analyte concentration. This parameter is referred
to as Reference A.sub.x. Preferably, absorbance of the analyte is
between about 0.5 and 2.0) [0156] 3A. Measure the values of A.sub.x
in samples with the vertical-beam photometer. These parameters are
referred to as Sample A.sub.x. Also measure (A.sub.max-A.sub.min)
values of the samples with the vertical-beam photometer. The later
parameter is referred to as Sample (A.sub.max-A.sub.min). The light
absorption pathlength in each of the samples is determined from
equation 7 as follows: Light .times. .times. Absorption Pathlength
= Sample .times. .times. ( A max - A min ) - { Sample .times.
.times. A x Reference .times. .times. A x [ Reference .times.
.times. ( A max - A min ) - Solvent .times. .times. ( A max - A min
) ] } Solvent .times. .times. ( A max - A min ) Solvent .times.
.times. Pathlength ( 7 ) ##EQU7## Light Absorbance per unit Optical
Pathlength for samples is determined using equation 8: Light
.times. .times. Absorbance .times. .times. per unit .times. .times.
Pathlength = Sample .times. .times. A .chi. Solvent .times. .times.
( A max .times. - A .times. min ) Solvent .times. .times.
Pathlength Sample .times. .times. ( A max - A min ) - { Sample
.times. .times. A .chi. Reference .times. .times. A .chi. [
Reference .times. .times. ( A max - A min ) - Solvent .times.
.times. ( A max - A min ) ] } ( 8 ) ##EQU8##
[0157] In general, this method provides for determining the
absorbance of an analyte per unit light absorption pathlength (or
fraction of light transmitted by an analyte per unit light
absorption pathlength) wherein the analyte is suspended or
dissolved in a liquid solvent such that a relationship between
light absorption of the analyte and the light absorption pathlength
of the analyte are unknown. This method also provides for
determination of the concentration of the analyte according to
Equation (1) from (a) the absorbance of an analyte in the sample,
(b) the light absorption pathlength of sample, and (c) a
predetermined extinction coefficient of the analyte. If the analyte
interferes with determination of the light absorption pathlength,
or if solvents other than water are present, the relationship
between absorbance of the solvent and absorption pathlength (or the
amount of interference) may be quantitated, thus allowing a correct
light absorption pathlength to be determined.
[0158] In general, a first, a second and a third light signal
resulting from, respectively, a first, second, and third
predetermined wavelength of light transmitted through substantially
identical optical pathlength within a sample and wherein a
difference between the first and the second light signals (e.g.
A.sub.970-A.sub.910) is related to the light absorption pathlength
and the third light signal (e.g. A.sub.490 where Acid Orange 8 is
the analyte) is related to both the light absorption pathlength and
the concentration of the analyte. The light absorption properties
of the sample solvent may be determined, independently of the
analyte by measuring a forth and fifth light signal (e.g. A.sub.970
and A.sub.910) resulting from, respectively, the first and the
second wavelength of light transmitted through a predetermined
optical pathlength (e.g. 1 cm) of the solvent which is employed as
a first reference liquid. Comparison of the difference in the first
and second light signals (e.g. A.sub.970-A.sub.910 of the sample)
and the forth and fifth light signals (e.g. A.sub.970-A.sub.910 of
the solvent) allows the known light absorption pathlength of the
solvent to be compared directly to the unknown light absorption
pathlength of the sample.
[0159] Provided that the sample does not interfere with
determination of the light absorption pathlength, the concentration
of the analyte may be determined form absorbance of the sample at
the third wavelength (e.g. A.sub.490, where Acid Orange 8 is the
analyte) or the fraction of light transmitted at the third
wavelength per unit light absorption pathlength, from the
predetermined light pathlength, the third light signal, the
difference in the first and second light signal and the difference
in the fourth and fifth light signals.
[0160] When the sample interferes with determination of the light
absorption pathlength, the concentration of the analyte may be
determined by measuring a relationship between absorbance of the
analyte at the third wavelength and its (interfering) absorbance at
the first and second predetermined wavelengths. Thus, a second
reference liquid, containing the analyte, is prepared and used to
measure a sixth and a seventh light signal resulting from,
respectively, the first and second predetermined wavelengths of
light transmitted through a predetermined light pathlength of the
second reference liquid (e.g. A.sub.970-A.sub.910 of the second
reference solution). The second reference liquid also is used to
measure an eight light signal at the third predetermined wavelength
(e.g. A.sub.490, where Acid Orange 8 is the analyte) in a
predetermined pathlength. The effect of sample interference may be
eliminated substantially from determination of light absorption
pathlength according to the example as shown in equation 7.
Similarly the effect of sample interference may be eliminated
substantially from determination of light absorption per unit
pathlength according to the example shown in Equation 8. Thus, the
light absorption pathlength, light absorption per unit pathlength,
fraction of light transmitted per unit pathlength, or concentration
of analyte (according to Equation 1) may be determined from the
predetermined optical pathlength and from the first, second, third,
fourth, fifth, sixth, seventh and eighth light signals.
[0161] Preferably, the means for determining Light Absorption
Pathlength and for determining and indicating Light Absorbance per
unit Optical Pathlength automatically are included in a
vertical-beam photometric device capable of monitoring the optical
density of samples contained in a multi-assay plate at a minimum of
three (3) different center-band wavelengths of light. The device
preferably will include means for determining and automatically
indicating if the analyte presents significant interference with a
simple, uncorrected, determination of Light Absorption Pathlength.
An Interference Parameter, is determined using equation 9 as
follows: Interference p .times. arameter = Sample .times. .times. A
x .function. [ Reference .times. .times. ( A max - A min ) -
Solvent .times. .times. ( A max - A min ) ] Reference .times.
.times. A x Sample .times. .times. ( A max - A min ) ( 9 )
##EQU9##
[0162] There are a variety of uses for the methods and devices of
the invention. For example, the volume of samples collected from a
fraction-collector in the wells of a multi-assay plate may be
desired. In such a determination, the relationship between Sample
Volume and Light Absorption Pathlength would be first determined
according to any one of the methods provided above. This procedure
is carried out in the following example.
EXAMPLE 4
[0163] The data established in Example 1 above were used to
determine the relationship between Light Absorption Pathlength and
Sample Volume in the Nunclon.RTM. Delta 96-well, flat-bottom
multi-assay plates utilized in that Example. Measurements of
A.sub.970-A.sub.900 were performed on six different chromophoric
analytes, Acid Orange 8, Acid Orange 74, Azure B, Direct Yellow 62,
Durkee Yellow Food Color, and Schilling Blue Food Color, in aqueous
solvent. The sample solutions were dispensed into the wells of the
multi-assay plate at either 350, 300, 250, 200, 150, or 100 .mu.l
sample volume per well. Each sample and volume combination was
tested in 8 replicate wells of the microplate.
[0164] The values of Sample (A.sub.970-A.sub.970) obtained
experimentally were used to determine Light Absorption (i.e.,
optical) Pathlength for each well according to. Eq. 2. FIG. 1 shows
the volume of sample pipetted into each well vs. the mean Light
Absorption Pathlength so determined and averaged for all of a given
volume. The result shows that, for the 96-well NUNC microplate, the
linear relationship described by equation 10 is observed: Light
Absorption Pathlength=[(2.82 cm/ml) (Sample Volume)]-9.0612 cm
(10)
[0165] The correlation coefficient for this linear relationship was
0.9999. The inverse of this relationship is described by equation
11 for a 96-well NUNC microplate as follows: Sample .times. .times.
Volume = ( Light .times. .times. Absorption .times. .times.
Pathlength + 0.0612 .times. .times. cm ) .times. ml 2.82 .times.
.times. cm ( 11 ) ##EQU10##
[0166] Equation 11 may be used to determine the approximate volume
contained within the wells of such a multi-assay plate upon
determining the Light Absorption Pathlength of the samples.
Further, with suitable calibration, this procedure may be used to
determine the volume contained in the wells of any type of assay
plate. The wells of the microassay plates may be of various
geometric shape, including flat-bottom, round-bottom (U-bottom),
V-bottom, or any other shape. Any geometry or shape of wells in the
multi-assay plate may be employed as long as the relationship
between sample volume from the Light Absorption Pathlength is
substantially reproducible (generally within 5%). The relationship
need not be linear, as is shown above for NUNC microplates which
have cylindrical (flat-bottom) wells. It is only necessary to
determine this relationship utilizing a multiplicity of known
volumes of samples, and then determining Light Absorption
Pathlength for the samples of known volume. This relationship may
be used subsequently, together with Light Absorption Pathlength
determinations in individual wells of multi-assay plates to
estimate the liquid volume present within such plates.
EXAMPLE 5
[0167] This example demonstrates utility of the invention in the
field of chromatography Chromatography is used, generally, to
separate analyte components in a sample mixture. Generally in
chromatography, there exists a mobile phase and a stationary phase.
The sample is applied in the mobile phase at the input of a means
of retaining the stationary phase, e.g. a tubular column with a
mesh support at the output of the column. As the mobile phase
passes over the stationary phase the analytes bind to the
stationary phase for more, or less time, depending on their
affinity for the stationary phase, and therefore appear at
different times at the output of the column. Separation of analytes
in a sample is thereby accomplished when, "fractions" of the mobile
phase, at the output of the column, are collected over time. In
chromatography, generally, one wishes to analyze the amount, or
concentration, of analyte present in each fraction collected.
Furthermore, for reproducible chromatographic systems, carried out
under constant conditions, (e.g. constant temperature, constant
stationary phase, constant mobile phase, constant flow rate,
constant column volume, etc.,) the same analyte will usually appear
at the same "elution volume," (i.e. after the same volume of mobile
phase has passed through the column). For such reproducible
systems, one generally wishes to have a plot of the relative
concentration of each analyte as a function of elution volume. The
below example discloses utility of the instant invention in
obtaining such "chromatograms" simply and conveniently while
employing a vertical-beam photometer.
[0168] Certain, commercially-available fraction collectors may be
employed conveniently to collect fractions directly in the wells of
96-well microplates such as the NUNC microplate employed above. For
example, one such fraction collector is manufactured by the Gilson
Corporation, Middleton, Wisc. Generally, such fraction collectors
collect fractions for a given time interval, or alternatively, such
fraction collectors may count the droplets at the output of the
chromatographic column and each fraction may contain a certain
predetermined number of droplets. One problem is that each fraction
contains a different, and unknown volume whenever the flow rate is
not maintained constant for the time interval method, and whenever
the surface tension of the mobile phase is not maintained constant
for the drop-counting method. Therefore, analysis of the fractions
collected in a multi-assay plate by vertical-beam photometry will
give absorbance values for each fraction that will be influenced
both by the concentration of analyte present and by the volume of
analyte present in the sample. The two variables, concentration and
volume, thereby are confounded and a method for determining the two
variables separately is needed. One method of the prior art is to
manually measure the volume of each fraction, to withdraw a known
volume from each well to transfer the withdrawn volume into a
second multi-assay plate and to measure the optical density of each
well in the second multi-assay plate. This prior art procedure
suffers from the disadvantage that it is tedious, cumbersome, and
prone to errors made during the volume-measuring and transferring
steps. The method described below provides for a less tedious and
cumbersome procedure and may be automated so as substantially to
avoid errors.
[0169] In the present example, immunoglobulin (IgG) protein
molecules were covalently-labeled with a fluorescent, fluorescein
moiety. The reagent for labeling the protein was an NHS ester of
fluorescein as provided in the Immuno-Ligand Assay Labeling Kit,
Cat. No. R9002, Molecular Devices Corp., Menlo Park, Calif. The IgG
was reacted with the labeling reagent at 40:1 molar ratio of
reagent to protein in pH 7.0 phosphate-buffered saline (PBS)
according to the instructions provided by the commercial supplier
of the reagent. The reaction product, in 0.3 ml volume, was applied
to a PD-10 column containing G-25 Sephadex.RTM. gel filtration
media (Pharmacia, Uppsula Sweden) as the solid phase. The column
was eluted with 0.1 ml aliquots of PBS applied successively to the
top of the column. Each fraction was collected, into a separate
well of a NUNC 96-well microplate, from the time of application of
each 0.1 ml aliquot of PBS until the column ceased to flow. After
the flow ceased, the output of the column was switched to a new
well of the microplate and the next aliquot of 0.1 ml of PBS was
applied and the next fraction collected, etc.
[0170] FIG. 2 shows the results of measuring the optical density of
each fraction at 490 nanometer wavelength in a Spectramax 250
vertical-beam photometer (Molecular Devices Corporation, Menlo
Park, Calif.). The first fraction was collected for analysis after
discarding the first 1.5 ml of PBS collected from the column. As
seen in FIG. 2, a maximum in OD.sub.490 was observed at fraction 17
where the labeled protein eluted from the column, as determined by
similarly measuring the optical density of the fractions at 280
nanometers, which also shows a maximum in absorption of fraction
17. Unreacted labeling reagent eluted from the column in subsequent
fractions are not shown in the figures. The shape of the curve
shown in FIG. 2 is somewhat irregular. This irregularity,
apparently, is not due to irregular variation in the concentration
of IgG but is due to irregularity in the optical pathlength of the
individual fractions. Shown in FIG. 3 are the same data corrected
for light absorption pathlength of each fraction. The shape of the
elution pattern of the labeled protein appears much more regular in
FIG. 3, where the OD.sub.490 per cm pathlength (i.e., the specific
OD.sub.490) is plotted for each fraction compared to FIG. 2 where
only the OD.sub.490 is shown. The light absorption pathlength in
each fraction was determined by monitoring the difference in
absorbance at 970 and 900 nanometer center-band pass wavelengths of
near-infrared light in the Theromax vertical-beam photometer and
calculated according to equation 2.
[0171] Further shown in FIG. 4 are the same data shown in FIG. 3,
except that the cumulative volume (after the first 1.5 ml. eluted
from the column) appears on the ordinate of the plot. The
cumulative volumes were determined by employing the relationship of
Equation 11, established for PBS in NUNC 96-well flat bottom
microplates, to determine the volume of each fraction from the
measured optical density difference at 970 and 900 nanometer
center-band pass wavelength and the light absorption pathlength
values calculated from these data and equation 2. The volumes of
each subsequent fraction then were summed to determine the
cumulative elution volume. Each OD.sub.490 per cm optical
pathlength point is plotted at the mean cumulative elution volume
of an individual fraction.
EXAMPLE 6
[0172] Elimination of Error in Determination of Optical Pathlength
Due to Variation in Solvent Temperature
[0173] Data have been gathered for a series of aqueous biological
buffer solutions, which now permit further optimization of
wavelength selection in the near infrared portion of the
electromagnetic spectrum ("NIR") for use in determining optical
pathlength of samples dissolved in such aqueous buffers. The NIR
portion of the electromagnetic spectrum extends from 750 to 2500
nanometers wavelength. In this NIR range, light detection means may
be detectors made of indium-gallium arsenide; gallium arsenide,
germanium, cadmium sulfide, lead sulfide, or the like. Preferably
the measurement wavelengths will be between 750 and 1100 nanometers
so that silicon photodetectors may be used as a light detection
means. Silicon photodiodes generally are useful in the range of 180
nanometers to 1100 nanometers wavelength.
[0174] The following reagents were prepared: One-tenth molar (0.1
M) N-[2-Hydroxyethyl]piperazine-N'-[2-ethanesulfonic acid] (HEPES)
was prepared from HEPES (1.0M) obtained from Sigma Chemical Co.,
St. Louis Mo. (Cat. No. H0887), by dilution into de-ionized water.
One-tenth molar (0.1 M) Tris(hydroxymethyl) aminomethane (TRIS), pH
7.12, was prepared from 1.0 M TRIS obtained from BioRad
Laboratories, Hercules, Calif. (Cat. No. 161-0719) by dilution into
de-ionized water. The 0.1 M sodium phosphate was prepared by mixing
61 ml of 1.0 M sodium phosphate monobasic, (Cat. No. S369-1) and 39
ml of sodium phosphate dibasic, (Cat. No. S374-500) each from
Fisher Scientific Pittsburgh, Pa. and diluting into de-ionized
water. Threshold Assay Buffer was prepared by dilution of
Concentrated (10.times.) Threshold Assay Buffer obtained from
Molecular Devices Corporation, Sunnyvale, Calif. (Cat. No. R3030-1)
and diluted to 1.times. (pH 57.02) in de-ionized water. Dulbecco's
phosphate buffered saline solution, pH 7.3 (PBS), was obtained from
Irvine Scientific (Cat. No. 9236). One-tenth molar (0.1M)
2[N-Morpholino]ethanesulfonic acid (MES) buffer, pH 6.14, was
prepared from MES obtained from Sigma Chemical Company (Cat. No.
M-8250) in deionized water.
[0175] FIG. 5 shows the absorption spectrum of pure water between
750 and 1100 nanometers at 4 different temperatures, i.e.
14.degree. C., 23.degree. C., 35.degree. C. and 44.degree. C. The
spectra were taken in an ATI Unicam UV-2-100 Double Beam Scanning
UV-Visible Spectrometer with a 2.0 nanometer fixed bandwidth. The
data were taken under the control of a Compaq 386 computer running
ATI Vision software set to take spectral data in the "Survey" mode
at "Intelliscan" speed. Approximately 3 ml samples were placed in
Spectro Clear.TM. Acrylic precision spectrophotometer cuvettes,
with a light absorption pathlength of 1.00 cm, obtained form
Centaur Science, Inc., Stamford, Conn., (Cat. No. SCA-20) in the
sample beam of the spectrophotometer. The reference beam contained
no sample or cuvette. (Measurements made in this configuration are
said to employ an "air blank").
[0176] FIG. 5 also shows that between 900 and 917 nanometers there
is relatively little absorbance of the water sample. Between 960
and 980 nanometers there is a peak of maximal absorbance of the
water sample. The wavelength of maximal absorbance
(.lamda..sub.max), as well as the absorbance at .lamda..sub.max,
changes as a function of temperature. For example, at 974
nanometers which is near .lamda..sub.max, the absorbance changes by
about 0.4% per degree centigrade. Thus, in order to obtain .+-.1%
precision in determination of optical pathlength, the temperature
must vary by no more than .+-.2.50.degree. C.
[0177] In contrast, at about 998 nanometers pure water gave
constant optical density of about 0.14 at all four temperature
values. Thus, the wavelength region near 998 nanometers (e.g. the
wavelength region from 988 to 1008 nanometers) is a region where
optical properties of pure water are nearly independent of
temperature. For the present, we shall call such a wavelength
region an "isosbestic wavelength region" which for pure liquid
water occurs near 998 nanometers as a function of temperature.
[0178] FIG. 6 similarly shows the NIR absorption spectrum of
Dulbecco's phosphate-buffered saline (PBS) containing 200 mg/l
potassium chloride, 200mg/l potassium phosphate monobasic, 8000
mg/l sodium chloride and 1158 mg/l sodium phosphate dibasic, pH
7.23 which is a commonly-used biological buffer solution. The
absorption spectrum is strikingly similar to that of pure water
seen in FIG. 5. The NIR absorption spectrum for isotonic (0.155 M)
sodium chloride; 0.1 M phosphate, pH 7.0 and 0.1 M TRIS, 0.1 M
HEPES, 0.1 M MES and Threshold Assay Buffer similarly were recorded
at 14.degree. C., 23.degree. C., 35.degree. C. and 44.degree. C. In
each case the NIR absorption spectra (not shown) are virtually
indistinguishable from that of pure water (i.e. less than 3%
different in relative absorption intensity any wavelength). The
isosbestic behavior, as a function of temperature, in each case is
observed near 998 nanometers.
[0179] Table III shows optical density values, determined at
several selected wavelengths, each at the 4 selected temperature
values, for each aqueous buffer solution. Also shown in Table III
are the results of taking the difference in optical density
measured at 998 nanometers and optical density measured at either
900 or 910 nanometers, i.e., (OD.sub.998-OD.sub.900) or
(OD.sub.998-OD.sub.910) for each aqueous buffer solution at each
temperature. The results show that for the 8 different samples, the
(OD.sub.998 and OD.sub.900) and (OD.sub.998-OD.sub.910) were
remarkably constant at all temperature values. The
(OD.sub.998-OD.sub.900) values ranged from 0.138 to 0.133, i.e. a
range of 3.6%. The (OD.sub.998-OD.sub.910) values ranged from 0.135
to 0.132. i.e. a range of 2.9%. Thus interference or inaccuracies
in determining optical pathlength though liquid samples can be
eliminated substantially by:
[0180] 1.) measuring a first optical density value of the samples
in a first "isosbestic wavelength region",
[0181] 2.) measuring a second optical density value of the samples
in a second "isosbestic wavelength region", and
[0182] 3.) determining the difference in the first and second
optical density values.
[0183] Preferably, the absorption coefficient of the sample is
substantially different in the first and second wavelength regions.
For example, as shown in FIGS. 5 and 6 and Table III, for aqueous
samples a "isosbestic wavelength region" occurs about 998
nanometers (generally from 993 to 1002 nanometers, and more
generally from 988 to 1008 nanometers). A second isosbestic
wavelength region occurs about 910 nanometers (generally from 900
to 910 nanometers, and more generally from 750 to 930 nanometers).
Alternatively, a second isosbestic wavelength region occurs near
1090 nanometers (generally from 1080 to 1100 nanometers and more
generally from 1050 to 1150 nanometers). TABLE-US-00003 TABLE 3 0.1
M 0.9% NaCl 1.times. Threshold Phosphate dH20 (Saline) 0.1 M HEPES
Assay Buffer 0.1 M TRIS 1.times. PBS Buffer 0.1 M MES 14.degree. C.
900 0.075 0.072 0.072 0.070 0.074 0.072 0.071 0.076 910 0.075 0.073
0.073 0.071 0.075 0.073 0.072 0.077 974 0.240 0.237 0.235 0.236
0.238 0.238 0.236 0.239 976 0.241 0.239 0.236 0.237 0.239 0.239
0.237 0.240 978 0.242 0.239 0.236 0.237 0.239 0.239 0.237 0.241 980
0.241 0.239 0.236 0.237 0.239 0.240 0.237 0.240 982 0.240 0.238
0.235 0.236 0.239 0.239 0.237 0.240 998 0.222 0.220 0.218 0.217
0.221 0.220 0.218 0.222 1000 0.219 0.216 0.214 0.214 0.218 0.217
0.215 0.219 998-900 0.147 0.148 0.146 0.147 0.147 0.148 0.147 0.146
998-910 0.147 0.147 0.145 0.146 0.146 0.147 0.146 0.145 23.degree.
C. 900 0.073 0.072 0.072 0.069 0.073 0.072 0.071 0.075 910 0.075
0.072 0.073 0.070 0.074 0.073 0.072 0.076 974 0.250 0.248 0.245
0.246 0.248 0.248 0.247 0.249976 976 0.250 0.248 0.245 0.246 0.249
0.249 0.247 0.250 978 0.250 0.248 0.245 0.245 0.249 0.248 0.246
0.249 980 0.249 0.247 0.244 0.245 0.247 0.247 0.245 0.248 982 0.247
0.245 0.243 0.243 0.246 0.246 0.244 0.247 998 0.223 0.220 0.218
0.218 0.222 0.221 0.219 0.222 1000 0.219 0.216 0.214 0.214 0.218
0.216 0.215 0.219 998-900 0.150 0.148 0.146 0.149 0.149 0.149 0.148
0.147 998-910 0.148 0.148 0.145 0.148 0.148 0.148 0.147 0.146
35.degree. C. 900 0.073 0.071 0.072 0.069 0.073 0.071 0.071 0.074
910 0.075 0.072 0.073 0.070 0.074 0.072 0.073 0.076 974 0.262 0.259
0.256 0.258 0.260 0.260 0.260 0.262 976 0.262 0.259 0.256 0.257
0.260 0.260 0.259 0.261 978 0.260 0.258 0.255 0.256 0.259 0.258
0.258 0.260 980 0.258 0.256 0.253 0.254 0.256 0.256 0.255 0.257 982
0.256 0.253 0.250 0.251 0.254 0.253 0.253 0.255 998 0.223 0.220
0.218 0.218 0.222 0.220 0.220 0.222 1000 0.218 0.215 0.213 0.213
0.217 0.216 0.215 0.217 998-900 0.150 0.149 0.146 0.149 0.149 0.149
0.149 0.148 998-910 0.148 0.148 0.145 0.148 0.148 0.148 0.147 0.146
44.degree. C. 900 0.073 0.070 0.071 0.069 0.072 0.071 0.071 0.074
910 0.075 0.072 0.072 0.071 0.074 0.072 0.072 0.076 974 0.271 0.268
0.265 0.266 0.269 0.268 0.268 0.270 976 0.269 0.266 0.264 0.265
0.267 0.267 0.267 0.269 978 0.267 0.264 0.262 0.263 0.266 0.265
0.264 0.267 980 0.265 0.262 0.259 0.260 0.263 0.262 0.261 0.264 982
0.261 0.258 0.256 0.257 0.259 0.259 0.258 0.260 998 0.222 0.220
0.218 0.218 0.222 0.220 0.219 0.222 1000 0.217 0.214 0.212 0.212
0.216 0.215 0.214 0.216 998-900 0.149 0.150 0.147 0.149 0.150 0.149
0.148 0.148 998-910 0.147 0.148 0.146 0.147 0.148 0.148 0.147
0.146
[0184] When employing (OD.sub.998-OD.sub.910) values to measure
optical pathlength, a value of 0.135 cm.sup.-1 (generally from
0.140 to 0.130 cm.sup.-) may be used to calculate optical
pathlength through substantially aqueous samples. For example, if a
(OD.sub.998-OD.sub.910) value of 0.135 is determined for aqueous
samples with an unknown optical pathlength, the unknown optical
pathlength is calculated to be 0.135/0.135 cm.sup.-1, i.e. 1 cm.
Similarly, if an (OD.sub.998-OD.sub.910) value of 0.100 is
determined, then the unknown optical pathlength is 0.100/0.135
cm.sup.-1, i.e. 0.741 cm. As another example, optical pathlengths
through substantially aqueous samples may be determined from any
measured (OD.sub.998-OD.sub.900) value by employing the constant
0.137 cm.sup.-1 (instead of 0.135 cm.sup.-1) in a similar fashion.
As a third example, optical pathlengths through substantially
aqueous samples may be determined from any measured
(OD.sub.998-OD.sub.1090) value by employing the constant 0.110
cm.sup.-1 in a similar fashion. It will be recognized by those
skilled in the art of photometry that any constant so determined
for any predetermined mixture of aqueous and nonaqueous solvents,
may be used (together with measurement of the NIR absorbance
properties of the predetermined mixture) for determination of any
unknown optical pathlength for the mixture.
EXAMPLE 7
[0185] Elimination of Error in Determination of Optical Pathlength
Due to Variation in Solvent Composition
[0186] In this example, NIR absorption spectra, between 750 and
1100 nanometers, were acquired as described in Example 6. The
samples were maintained near room temperature (at about 20 to
25.degree. C.).
[0187] FIG. 7 shows the NIR absorption spectra of pure water, 0.1
M, 0.5 M , and 1.0 M citric acid solutions (in water). The citric
acid solutions show relatively insignificant deviation from the
spectrum of water at the lowest, 0.1 M concentration. The deviation
however increases with increasing concentration and is greatest at
the highest (1.0 M) citrate concentration.
[0188] FIG. 8 similarly shows the NIR absorption spectra, between
750 and 1100 nanometers, of either pure water, 0.1 M, 0.5 M, or 1.0
M sucrose solutions (in pure water). Similar to the citric acid
solutions, the sucrose solutions show relatively insignificant
deviation from the spectrum of pure water for the lowest, 0.1 M
concentration. As for citrate, however, the deviation increases
with increasing solute concentration and is greatest at the highest
(1.0 M) concentration. The deviation caused by sucrose is slightly
more pronounced than that caused by citrate. The value of
(OD.sub.970-OD.sub.910) is about 20% less for 1.0 M sucrose
compared to pure water. Significantly better, the value of either
(OD.sub.998-OD.sub.910) or (OD.sub.998-OD.sub.900) are only about
9% less for 1.0 M sucrose compared to pure water. While significant
improvement in determining optical pathlength is obtained by
measuring absorption of light in the "isosbestic wavelength region"
near 998 nanometers, substantially complete elimination of error in
such determinations, with all aqueous samples, however, is not
possible.
EXAMPLE 8
[0189] Incorporation of a Reference Solvent Liquid of Known Optical
Pathlength
[0190] In order to substantially eliminate errors in determination
of unknown optical pathlength of sample solutes dissolved at high
concentration in a solvent liquid, an improved method with the
following steps is employed: [0191] 1. Place a reference comprising
a reference sample solvent in a known optical pathlength, and a
sample, comprising a sample in the sample solvent, in an unknown
optical pathlength, and [0192] 2. Measure: [0193] a) a first
optical density value (A.sub.REF.lamda.1) of the reference sample
solvent at a first preselected wavelength in the NIR where the
sample analyte does not absorb light substantially and where
absorption of light by the sample solvent is near a local maximum
(for example in the region of 950 to 1000 nanometers for an aqueous
solvent), and [0194] b) a second optical density value
(A.sub.REF.lamda.2) of the reference sample solvent at a second
preselected wavelength in the NIR where neither the sample analyte
nor the reference sample solvent absorb light substantially (for
example in the region of 900 to 910 nanometers, or the region from
1060 to 1080 nanometers, for an aqueous solvent), and [0195] c) a
third optical density value (A.sub.SMP.lamda.1) of the sample at
the first preselected wavelength, and [0196] d) a fourth optical
density value (A.sub.SMP.lamda.2) of the sample at the second
preselected wavelength, and [0197] 3. Calculate the optical
pathlength as: Sample .times. .times. Light .times. .times.
Absorption .times. .times. Pathlength = Reference .times. .times.
Light .times. .times. Absorption .times. .times. Pathlength .times.
.times. ( A SMP .times. .times. .lamda.1 - A SMP .times. .times.
.lamda.2 ) ( A REF .times. .times. .lamda.1 - A REF .times. .times.
.lamda.2 ) ( 12 ) ##EQU11##
EXAMPLE 9
[0198] A Device Incorporating A Reference Solvent Liquid of Known
Optical Pathlength
[0199] Advantageously, a device will enclose both the reference and
the sample so that the temperature of the reference and the sample
will be substantially the same temperature, generally within a
range of 2.degree. C. and more generally with a range of 5.degree.
C. Also advantageously, the device will enclose a multiplicity of
samples, e.g. an 8.times.12 array of samples in a 96-well
multiassay plate, at a multiplicity of sample sites maintained at
substantially the same temperature as the reference. A preferred
embodiment of the present invention is herein described. The device
was used in following method steps 1-3 and Equation 4 and 5 in
Example 2. The device measures unknown optical pathlengths of a
multiplicity of assay sites with the aid of an incorporated
reference liquid of known optical pathlength. In operation, a user
performs the following operations: [0200] (a.) The reference liquid
is placed in a cuvette, of known optical pathlength, within the
device. The reference liquid is preselected to be similar in
solvent composition and temperature to the samples. (Optimally but
not required, the sample analyte will be present in the reference
liquid.) [0201] (b.) Next, the samples on a multiassay plate, are
placed in the device so that the samples and the reference liquid
are maintained at substantially the same temperature (to within
1-2.degree. C.). [0202] (c.) The device measures the transmission
of NIR light through each of the liquid samples and through the
reference liquid of known optical pathlength. [0203] (d.) The
device compares the transmission of light through both the samples
and the reference liquid and calculates the optical pathlength of
the samples.
[0204] Having determined the optical pathlength through each of the
samples in a multi-assay plate, the device also may be used to
determine the concentration of analytes in such samples by
determining the absorbance of the analytes at a preselected
wavelength. The results of such determinations, therefore, may now
be expressed in terms of optical density per unit pathlength, e.g.
A.cndot.cm.sup.-1. Customarily the results will be expressed in
optical density per 1 cm pathlength. For example, if the sample
material absorbs at 405 nanometers wavelength and the optical
density of the sample at 405 nanometers, A.sub.405, if determined
by the device to be 0.150 O.D. units; and the optical pathlength of
the sample, determined by steps a-d above is determined to be 0.5
cm, then the calculated A.sub.405.cndot.cm.sup.-1 value will be
0.300.
[0205] Once the optical pathlength is known, the concentration of
analyte may be determined by Beer-Lambert Law given in equation
(1), from the extinction coefficient .epsilon..sub..lamda. at a
preselected wavelength .lamda..
[0206] Shown in FIG. 9 is a photometric measuring system 10 for
monitoring the optical characteristics of a multiplicity of samples
contained on a multiassay plate 12 having multiplicity of sample
sites with variable optical pathlength. The system has at least one
reference site of known optical pathlength. The system 10 is
comprised of a light source means 22 which directs light to a
wavelength selection means 23, which causes a substantially
monochromatic band of light to pass into a light distribution means
24. The light distribution means 24 directs light to:
[0207] a) a means for retaining a reference optical pathlength of
known pathlength, shown in FIG. 9 as a cuvette means 40. Light
transmitted through the reference optical pathlength is detected by
a photodetector means 26, and
[0208] b) a chamber means 16 which encloses the multiplicity of
sample sites.
[0209] The multi-assay plate 12 is carried by a plate carrier means
20 so as to position the sample sites so that light directed by the
light distribution means 24, and transmitted by the samples is
detected by the photodetector means 26. A temperature control means
28 controls the temperature within the chamber means 16 and the
cuvette means 40.
[0210] Electrical signals from the photodetector means 26 are sent
to an acquisition and control processor means 14 which is in
electrical communication with a central processor unit means 15.
The central processor means 15 may send data directly to a printer
and be controlled by a user. Advantageously, however, the central
processor means 15 will be interfaced to a user interface computer
30, which enables the user to control the system 10, acquire data,
visualize data, compute data parameters from the acquired data, and
ultimately to export the data or parameters to an external printing
device.
[0211] FIG. 10 is a detailed description of a preferred embodiment
of the photometric measuring system 10. Except for the disclosure
given below, the preferred embodiment is identical to the preferred
device disclosed in U.S. patent application Ser. No. 08/228,436
filed Apr. 15, 1994 which is incorporated herein by reference. The
system 10 produces a beam of substantially monochromatic light, in
the form of flashes, and delivers this light sequentially to a
plurality of light channels, eight in the preferred embodiment, to
sequentially illuminate the fluid sample in the multiassay plate
12.
[0212] An excitation light source 50, such as a xenon flash lamp,
emits light flashes containing wavelengths between at least 200
nanometers and 1100 nanometers. Light from the excitation light
source 50 beams through an aperture 51 limiting the light arc (61)
to approximately ten degrees (10.degree.). This light then passes
through a source lens 52, which focuses the light through one of a
series of filters 55, included on a filter wheel 56, upon a
monochrometer, generally designated 54. The excitation light source
50, aperture 51, and source lens 52 cooperate to define the lights
source means 22.
[0213] The source lens 52, in this preferred embodiment is a fused
silica plano-convex lens with a 12.7 millimeter diameter, a 16
millimeter focal length, and an optical magnification of 1.times..
The source lens 52 is spaced 32 millimeters from the excitation
light source 50 and 32 millimeters from the entrance slit 53 where
light enters the monochrometer 54. A collimating/focusing mirror 57
reflects and collimates the light beam onto a rotatable diffraction
grating 59. There the light is dispersed at an angle with respect
to the grating. This angle is dependent upon the wavelength of
light striking the grating. The dispersed light falls back on the
collimating/focusing mirror 57 which focuses substantially
monochromatic light, within a narrow wavelength band, upon an exit
slit 63. Thus, the wavelength range (bandpass) of substantially
monochromatic light passing through exit slit 63 is dependent upon
the wavelength of light and the angle of the grating 59 with
respect to the collimated light beam. The wavelength of maximal
intensity of light passing through the exit slit may be preselected
by rotating the grating 59 with respect to the incident light
coming from mirror 57. The bandpass of monochromatic light passing
through exit slit 63 is dependent principally upon the optical
distance from grating 59 to exit slit 63, as well as the widths of
exit slit 63, entrance slit 53 and aperture 51.
[0214] Exit slit 63 preferably, 0.7 in width and 1.3 millimeters in
height, is formed by a metal end cap forming the end of a bundle of
optical fibers 58 which accepts the substantially monochromatic
light. Cooperating to define the wavelength selection means 23 are
filter wheel 56, optical filters 55, and monochrometer 54. The
output of monochromator 54 provides light having a predetermined,
continuously selectable, second wavelength range within the first
wavelength range provided by light source 50. In the preferred
embodiment disclosed herein, the second wavelength range has a
predetermined bandpass width, defined as the wavelength width at
one-half maximum light transmission, of about 2 nanometers for all
center-band wavelengths continuously selectable by the user between
250 and 750 nanometers. The bandpass width may be predetermined
within a range of about 1 to 20 nanometers by changing the width of
the exit slit 63, e.g. by employing a mechanically adjustable slit
as the exit slit 63.
[0215] In the preferred embodiment optical fiber bundle 58 includes
nineteen (19) optical fibers each 200 microns in diameter with a
numerical aperture of 0.22, each arranged at the input in three (3)
rows of six (6), seven (7), and six (6) fibers. This effectively
defines a 0.7 millimeter by 1.3 millimeter rectangular exit slit
63. The output of the optical fiber 58 is configured as a circle
with a diameter of 1.3 millimeters. Light from the output of fiber
58, which is emitted over a solid angle of about ten degrees, is
split by a beam splitter 60, a sapphire window in this preferred
embodiment. The beam splitter 60 splits the fight into a test light
that passes through the beam splitter 60 to a rotor assembly 70 and
a reference light that reflects from the beam splitter 60 to a flat
reference mirror 62. The reference mirror 62 reflects the reference
light through a reference lens 66 to a reference photodetector 64
of the photodetector means 26. The reference lens 66 is a bi-convex
lens, is made of fused silica, has a focal length of 6.8
millimeters, and has a diameter of 6.8 millimeters.
[0216] The intensity of light flashes emitted by the Xenon flash
light 50 may vary by as much a 50% between successive flashes due
to variations in the energy and position of the flash arc within
the flash lamp. The reference photodetector 64 outputs an
electrical signal; representative of the amplitude of the
monochromatic light carried by the optical fiber 58 for each flash
of the light excitation source 50. This electrical signal is used
as an intensity reference for the reading of sample light
transmitted through samples in the multi-assay plate 12.
[0217] The rotor assembly 70 includes two substantially identical
rotor mirrors 71 and 72 to redirect the light by 180.degree.
(degrees) (each mirror reflects light by 90.degree.) and a rotor
lens 74 to focus the light beam between the rotor mirrors 71 and
72. The rotor mirrors 71 and 72 and rotor lens 74 act to reduce the
spot size of the light beam from 1.3 millimeter diameter at the
input of the rotor assembly 70, which is the output of the optical
fiber 58, to 0.65 millimeters at the output, which is the input of
a selected one of nine (9) receiving optical fibers 76 or the input
of a reference distribution optical fiber 90. The reduction in
light beam diameter within the rotor 70 allows substantially all of
the light to be launched at a solid angle or about 20.degree. into
the receiving fibers 76 of the light distribution means 24, greatly
enhancing efficiency of sample light transmitted through the rotor
70. Care is taken so that the sample light is not focused in such a
way that it exceeds the numerical aperture of the receiving optical
fibers 76 and 90 which will accept light over a solid angle of
about 24.degree..
[0218] The optical distribution channels are defined by the
receiving optical fibers 76 and 90, made of solid silica or quartz,
1 millimeter in diameter, with a numerical aperture of 0.22. Light
from the sample distribution optical fibers 76 reflects off a
sample light mirror 78, made of MgF.sub.2 with a flat surface, into
a substantially vertical sample light distribution direction. A
sample light aperture 80 further limits the numerical aperture of
the light beam. A sample light lens 82 and a sample light
photodetector lens 86, each a biconvex lens made of fused silica
with a 6.8 millimeter focal length and a 6.8 millimeter diameter,
further focus the sample light. For ease of illustration, FIG. 10
shows only one of a series of eight substantially identical sample
light distribution optical fibers 76, sample light mirrors 78,
sample light apertures 80, sample light lenses 82 and sample light
photodetector lenses 86.
[0219] A reference pathlength distribution optical fiber 90 directs
reference pathlength light from optical rotor 70 to reference
pathlength lens 92, through a reference cuvette of known optical
pathlength 94, which is retained in place by a cuvette holder 96.
Customarily photometric measuring system 10 provides cuvette holder
96 without cuvette 94. During use of the invention, the user
selects an appropriate reference cuvette which may be made of
quartz, glass, polystyrene, polymethacylate or other suitable
transparent material. Cuvette 94 and cuvette holder 96 cooperate to
define cuvette means 40. Reference pathlength light transmitted
through cuvette 94 is detected by reference pathlength
photodetector 98.
[0220] In operation, first a reference sample solvent is placed in
the reference cuvette of known optical pathlength (e.g. a 1.00 cm
optical pathlength) and samples in the sample solvent are placed in
one, or more, wells of the multi-assay plate 12. The multi-assay
plate is then placed on a plate carrier means 20 within chamber
means 16. The user instructs the system 10 to "read" one-or-more
preselected samples. The plate carrier means positions the
preselected samples between the sample light lenses 82 and sample
light photodetector lenses 86 so that light from the sample
distribution optical fibers 76 will pass substantially vertically
through the samples without striking the side-walls of the
multi-assay plate, which contains the samples.
[0221] In a reading cycle the rotor assembly 70 first rotates so as
to distribute light to a dark channel, so that no light falls upon
sample photodetectors 88 or pathlength reference photodetector 98
when light source 50 emits a flash of light. Electrical signals
from sample photodetectors 88 and pathlength reference
photodetector 98 provide a zero light baseline value for each
photodetector when the light is distributed to a dark channel. The
rotor assembly 70 secondly rotates so as to distribute reference
pathlength light through the reference cuvette 94, which contains
reference sample solvent in a known optical pathlength. The
reference cuvette is retained in place by a cuvette holder 96.
Reference pathlength light transmitted through cuvette 94 is
detected by reference pathlength photodetector 98 which, in turn,
sends an electrical signal related to the intensity of detected
light to acquisition and control processor means 14.
[0222] The rotor assembly 70 next rotates to sequentially
illuminate the series of eight sample light distribution optical
fibers 76 so as to sequentially illuminate the fluid samples in the
multiassay plate 12. The multiplicity of samples receives sample
light having a substantially identical spectral distribution of
light intensity provided by monochrometer 54. The photometric
device 10 described provides the above sample light characteristics
to a multiplicity of samples in a multi-assay plate within short
periods of times so that the optical properties of 96 samples
contained in a conventional 8.times.12 microplate may be determined
within approximately 9 seconds (generally from 8 to 10 seconds).
Determination of optical pathlength requires measurement at, at
least 2 different wavelengths, .lamda.1 and .lamda.2. Thus, in
order to measure optical pathlength through the samples the
measurement procedure is first performed at .lamda.1 and then
repeated at .lamda.2, thus the measurements is completed within 18
seconds (generally from 16 to 20 seconds). Optionally, the reading
process may be adjusted to proceed at a slower prace (for example
over 10 minutes or more) when there is no need for rapid
determinations.
EXAMPLE 10
[0223] Elimination of Error in Determination of Absorbance of
Samples per Unit Optical Pathlength
[0224] The device disclosed in Example 9 may be used to
substantially eliminate error in the determination of the ratio of
absorbance of analytes within liquid samples and the optical
pathlength. These ratiometric measurements are given as "Light
Absorbance per Unit Pathlength" in Examples 2 and 3 above.
[0225] In order to perform such ratiometric measurements, the
device additionally monitors the absorbance of an analyte, in the
one or more samples sequentially, at a preselected wavelength. This
value is given as "Sample A.sub.x" in examples 2 and 3 above. The
device then computes the ratio of Sample A.sub.x and the optical
pathlength, for each sample, to give "Light Absorbance per Unit
Pathlength".
[0226] The examples below show further methods resulting in
improved precision in determination of light absorbance by an
analyte dissolved in a solvent by using vertical-beam
photometry.
EXAMPLE 11
[0227] Methods for Improving Precision of Optical Pathlength
Determination in a Vertical-Beam Photometer
[0228] 1. Evaluation of precision was carried out with
SPECTRAmax.RTM.PLUS microplate spectrophotometer. For these
evaluations 200 .mu.l of 0.05 M potassium phosphate buffer,
adjusted to pH 7.00 with NaOH (and containing yellow food coloring
as the test analyte) was dispensed in the wells of a quartz,
96-well microplate (available from Molecular Devices as Part Number
R8024). The test analyte solution is available from Fisher
Scientific as Catalog Number SB107-500 (pH 7.00 Buffer
Solution).
[0229] The test analyte solution has a broad spectral absorption
maximum between 420 and 440 nanometers which returns close to a
baseline value between 510 to 520 nanometers. The wavelength for
determining analyte absorbance was selected to be 420 nanometers
near the absorption maximum. Precision absorbance studies were
performed in 96 replicate wells of the quartz microplate. The test
analyte was dispensed into the microplate wells and analyte
absorbance per unit solvent pathlength was measured in each well.
Two method variables were evaluated in all four possible
combinations for effect on measurement precision. The first
variable was to determine the absorbance of the analyte at a single
wavelength (A.sub.420) (single wavelength mode) or at dual
wavelengths (A.sub.420-A.sub.520) (dual wavelength mode). In the
dual wavelength mode, the second absorbance value (A.sub.520) is
used as a reference absorbance measurement. In all cases,
absorbance of the solvent was measured at two wavelengths (1000 and
900 nanometers) in order to determine optical pathlength of the
solvent. Thus, at least three absorbance values are always
determined at at least three different wavelengths. Light
Absorbance per Unit Pathlength is then calculated as:
0.1433(A.sub.420)/(A.sub.1000-A.sub.900) or alternatively
0.1433(A.sub.420-A.sub.520)/(A.sub.1000-A.sub.900).
[0230] In practice, the absorbance of each sample in the
multi-assay plate (in this case a 96-well microplate) was measured
at 420, 520, 900 and 1000 nanometers A second method variable was
to (A) measure all absorbances values in each individual sample at
all preselected (in this case three or four) wavelengths without
moving the samples (a "Stationary Read"). This was accomplished, in
this example, by selecting 420, 520, 900 and 1000 nanometers
bandpass light, sequentially, with monochrometer 54 for each sample
before moving the microplate 12 with plate carrier means 20.
Alternatively, other methods of spectral scanning without sample
movement, such as emplying a diode-array detector together with a
spectral dispersion means such as a prism, grating, tunable optical
fillers, array of optical fillers, etc., may be used. In the
alternative (B) of the second method variable, absorbance values
are measured on all samples at a first wavelength (by moving the
samples), switching to a second wavelength by adjusting the
monochrometer and measuring absorbances values on all samples at
the second wavelength (again by moving the samples), and repeating
the process until all absorbance values, at all selected wavelength
values, have been determined. In both cases repositioning of the
multi-assay is performed by the motorized plate carrier which
centrally positions the sample wells under the light paths of the
fiber optic channels.
[0231] Table IV gives the results of a precision test using the
four combinations of the two method variables. Dual wavelength
absorbance measurements gave greater precision (less error) than
single wavelength absorbance measurements. Also, absorbance
measurements using multiple wavelengths gave the greatest precision
when measurements were made at all the wavelengths prior to moving
the fluid samples ("Stationary Read"). The lowest error was
observed when dual wavelength absorbances were carried out in
combination with a Stationary Read. In that case, the standard
deviation of Absorbance/cm Pathlength measurements was 0.003
absorbance units per cm (coefficient of variation=0.8%). In
contrast when single wavelength absorbance measurements were made
and the samples were not stationary, the standard deviation of
Absorbance/cm Pathlength measurements was 0.008 absorbance units
per cm (coefficient of variation=2.1%). TABLE-US-00004 TABLE IV
Error in Determination of Analyte Absorbance per Unit Optical
Pathlength Stationary Non Stationary A.sub.420-A.sub.520 *0.003
*0.006 A.sub.420 *0.006 *0.008 *Standard Deviation (Absorbance
units/cm optical pathlength) for measurement of a single well. Data
taken with 200 .mu.l sample volumes in a quartz 96 well microplate
in a SPECTRAmax .RTM. Plus microplate spectrophotometer. N = 96.
Mean pathlength = 0.522 cm. Mean A.sub.420 and
(A.sub.420-A.sub.520) per cm pathlength = 0.380.
[0232] The difference in absorbance at 1000 and 900 nanometers was
used to compute the optical pathlength through the aqueous test
analyte solution. As shown in FIGS. 5 and 6, the absorbance of
solvent in dilute aqueous solutions of analytes is substantially
independent of temperature within 20 nanometers of the temperature
isosbestic wavelength near 1000 nanometers; within 40 nanometers of
another temperature isosbestic wavelength near 1110 nanometers; and
in the region of 750 to 940 nanometers encompassing the temperature
isosbestic wavelength near 920 nanometers. The difference in
absorbance between any two temperature isosbestic wavelength
regions may be utilized for monitoring the pathlength of the
solvent. The temperature isosbestic points near 1000 and 920
nanometers were selected to determine the optical pathlength
through the aqueous test analyte solution because the difference in
absorbance for any given optical pathlength is greatest with these
two wavelengths, yet these two wavelength values all relatively
close, one to another. Further, it is advantageous to select the
wavelengths to be as long as possible to a) minimize possible
interference from substances which absorb strongly in the visible
wavelengths and b) minimize interferences from light scattering
phenomena (e.g. Raleigh Scattering, which is inversely proportional
to wavelength raised to the fourth power).
[0233] As a consequence of selecting a temperature isosbestic
wavelength and not wavelength at an absorbance maximum or minimum,
the slope of change in absorbance with change in wavelength is
quite large. Wavelength selection precision, thus is very important
for reproducibly and accurately measuring optical pathlength.
Further accuracy is realized when all channels of a multi-channel
vertical-beam photometer are exactly matched, or alternatively,
separately calibrated. The following example shows that additional
precision may be obtained by separately calibrating each channel of
a multiple- (8) channel-microplate spectrophotometer.
[0234] 2. Separate calibration of each optical channel of a
vertical-beam photometer may be performed by placing a cuvette of
constant optical pathlength in each channel the sample compartment
of a vertical-beam photometer and separately measuring the
differential absorbance of sample solvent (in this case water) in
each channel. For example (A.sub.1000-A.sub.900) may be measured
for water in a 1 cm pathlength cuvette. The differential absorbance
values measured respectively for each optical channel are stored
and subsequently recalled to calculate optical pathlength from
differential absorbance values measured on aqueous samples of
unknown optical pathlength.
[0235] Alternatively, separate calibration of each optical channel
may be performed by employing a horizontal-beam reference cuvette
(as shown in FIG. 10) and measuring the absorbance of an analyte
dissolved in a reference solution which is contained in the
reference cuvette. (This is called the reference analyte
calibration method.) In this measurement, absorbance by the cuvette
containing a reference solvent (without the reference analyte) is
subtracted from the absorbance value taken with the reference
analyte dissolved in the reference solvent to obtain a calibration
absorbance value for the reference analyte. Next, the same
reference solution is placed into the sample wells of a multi-assay
plate in a housing enclosing the multi-assay plate in the optical
path of the vertical-beam photometer. Again, absorbance of the
multi-assay plate containing a reference solvent (without the
reference analyte) is subtracted from the absorbance values taken
with the reference analyte dissolved in the reference solvent to
obtain a calibration absorbance value for the reference analyte in
the multi-assay plate. In addition, differential absorbance of the
sample solvent is measured in each channel. For example,
(A.sub.1000-A.sub.900) may be measured when the sample solvent is
water. This measurement is repeated with the same reference
solution for each optical channel of the vertical-beam photometer.
From the results of reference analyte absorbance and differential
absorbance of the sample solvent in each channel, a calibration
value is calculated for each optical channel so that the absorbance
of the analyte per unit optical pathlength for each vertical-beam
photometer channel is identical to the result obtained in the
reference cuvette.
[0236] The reference analyte calibration method described above was
applied to each channel of a SPECTRAmax.RTM.PLUS microplate
spectrophotometer. Next error analysis for determination of Analyte
Absorbance per Unit Optical Pathlength was determined for the same
analyte, under similar conditions as were used to generate the data
shown in Table IV. Analyte absorbance was measured as
(A.sub.420-A.sub.520) under conditions giving optimal precision.
When an average calibration value was used for all 8 channels of
the vertical-beam photometer a standard deviation of 0.0021 (0.55%
coefficient of variation) was observed. When eight (8)
separately-determined calibration values were used for the
respective 8 channels of the SPECTRAmax.RTM.PLUS microplate
spectrophotometer, a standard deviation of 0.0011 (0.29%
coefficient of variation) was observed. In each case, the results
were the mean of 3 multi-assay plates, each containing 96 samples
(N=288). Thus, measurement precision was approximately doubled by
employing solvent pathlength calibration values individually
determined for each optical channel.
EXAMPLE 12
[0237] Measurement of Solvent Absorbance at NIR Wavelengths Greater
than 1100 Nanometers.
[0238] In vertical-beam photometry, optical pathlengths generally
vary from about 0.05 cm to about 2.0 cm. Most frequently the sample
volumes are between 2 millimeters and 1.0 cm. For precise analysis
of Analyte Absorbance per Unit Optical Pathlength on very small
sample volumes, precise measurement of Optical Pathlength on short
pathlengths between 0.05 cm and 0.5 cm is advantageous. As shown in
FIGS. 5-8, the differential absorbance of aqueous solutions, at any
two wavelengths between 750 nanometers and. 1100 nanometers is less
than 0.2 for a 1 cm pathlength. For a 0.1 cm pathlength, for
example, this results in a differential absorbance less than 0.020.
The precision of individual absorbance measurements in
vertical-beam photometers is generally about 0.001 absorbance
units. Thus, significant error (in this case about 7% coefficient
of variation) will be inherent in measurement of 0.1 cm optical
pathlengths in aqueous solutions. Increasing the amplitude of
absorption of the solvent, or alternatively, increasing the
precision of absorbance measurements is necessary to improve
analytical precision.
[0239] The amplitude of the absorbance of solvents generally
employed in analytical chemistry, such as alcohols, ketones,
aromatic hydrocarbons (e.g. benzenes, toluenes and anilines),
alkanes, furans, sulfoxides, as well as aqueous media, are
generally quite small in the region between 770 nanometers and 1100
nanometers. The amplitude of absorbance of these solvents increases
at wavelengths longer than 1100 nanometers. These wavelengths
generally will be within the near infrared region (750-2500 nm
wavelength) or the infrared region of the electromagnetic spectrum
(2.5 micron to 1000 micron wavelength).
[0240] Analyte Absorbance, Optical Pathlength and Analyte
Absorbance per Unit Optical Pathlength of three different analytes
(at three different analyte analysis wavelengths) were determined
by vertical-beam photometry. In each case, optical pathlength by
measuring light absorption by a sample solvent is determined both
at temperature isosbestic wavelengths less than 1100 nanometers and
at temperature isosbestic wavelengths greater than 1100 nanometers.
For wavelengths less than 1100 nm, differential absorbance of water
at the temperature isosbestic wavelengths of 900 and 1000
nanometers preferably is used to determine solvent pathlength (as
described above). For wavelengths greater than 1100 nm,
differential absorbance of water at the temperature isosbestic
wavelengths of 1100 and 1200 nanometers preferably is used to
determine solvent pathlength. For absorbance measurements employing
wavelengths longer than 1100 nanometers, the silicon photodetectors
(both the reference and sample measurement silicon photodiodes) in
one optical channel of a SPECTRAmax.RTM.PLUS vertical-beam
spectrophotometer (1 sample and 1 reference photodetector) were
replaced with InGaAs PIN Photodiodes (Type No. G5832-03, obtained
from Hamamatsu Corporation, Hamamatsu City, Japan). For comparison
purposes, the absorbance of each analyte also was measured in a 1
cm fixed optical pathlength cuvette by horizontal-beam
photometry.
[0241] The results of the absorbance measurements are summarized in
TABLE V. Vertical-beam photometry in each case was performed at 6
different optical pathlengths. The first analyte listed is bovine
serum albumin (BSA) at 2 mg/ml in phosphate-buffered saline (0.05 M
sodium phosphate, 0.1M NaCl, pH 7.2 (PBS)). Absorbance of the BSA
analyte was determined at 280 nm. When analyzed in the 1 cm fixed
optical pathlength cuvette, A.sub.280 was 0.995. When analyzed by
vertical-beam photometry employing 900 nm and 1000 nm differential
absorbance to determine optical pathlength of the PBS solvent,
A.sub.280 (per cm optical pathlength) ranged from 1.033, at 350
.mu.l sample volume, to 1.054 at 100 .mu.l sample volume. The later
value is 5.9% greater than the 0.995 A.sub.280 reference value
determined in the 1.0 cm fixed pathlength cuvette. In contrast,
when analyzed by vertical-beam photometry employing 1200 nm and
1100 nm differential absorbance to determine optical pathlength of
the PBS solvent, A.sub.280 (per cm optical pathlength) ranged from
1.007, at 350 .mu.l sample volume, to 1.017 at 100 .mu.l sample
volume. The later value is only 2.2% greater than the 0.995
A.sub.280 reference value. Thus, the accuracy at the 100 .mu.l
sample volume was substantially improved by employing 1200 nm and
1100 nm differential absorbance to determine optical pathlength of
the PBS solvent.
[0242] The second analyte shown in TABLE V was yellow food coloring
in 0.05 M potassium phosphate buffer, adjusted to pH 7.00 with
NaOH. The test analyte solution is available from Fisher Scientific
as Catalog Number SB107-500 (pH 7.00 Buffer Solution). Absorbance
of the yellow food coloring analyte was determined at 420 nm. When
analyzed in the 1 cm fixed optical pathlength cuvette, A.sub.420
was 0.389. When analyzed by vertical-beam photometry employing 900
nm and 1000 nm differential absorbance to determine optical
pathlength of the PBS solvent, A.sub.420 (per cm optical
pathlength) ranged from 0.395 at 350 .mu.l sample volume, to 0.403
at 100 .mu.l sample volume. The later value is 4.0% greater than
the 0.389 A.sub.420 reference value determined in the 1.0 cm fixed
pathlength cuvette. In contrast, when analyzed by vertical-beam
photometry employing 1200 nm and 1100 nm differential absorbance to
determine optical pathlength of the 0.05 M potassium phosphate
buffer solvent, A.sub.420 (per cm optical pathlength) ranged from
0.384, at 350 .mu.l sample volume, to 0.385 at 100 .mu.l sample
volume. The later value is only about 0.3% less than the 0.389
A.sub.420 reference value. Thus, the accuracy at the 100 .mu.l
sample volume again is greatly improved by employing 1200 nm and
1100 nm differential absorbance to determine optical pathlength of
the PBS solvent.
[0243] The third analyte shown in TABLE V was Napthol Green B dye
(Aldrich Chemical Co., Milwaukee, Wisc.) dissolved in water (50
.mu.g/ml). Absorbance of the Napthol Green B dye analyte was
determined at 720 nm. When analysed in the 1 cm fixed optical
pathlength cuvette, A.sub.720 was 0.569. When analysed by
vertical-beam photometry employing 900 nm and 1000 nm differential
absorbance to determine optical pathlength of the PBS solvent,
A.sub.720 (per cm optical pathlength) ranged from 0.917 at 350
.mu.l sample volume, to 0.904 at 100 .mu.l sample volume. All of
these values are approximately 60% greater than the 0.569 A.sub.720
reference value determined in the 1.0 cm fixed pathlength cuvette.
This very large error is attributed to significant differential
absorbance of the Napthol Green B dye at 900 and 1000 nanometers.
In contrast, when analysed by vertical-beam photometry employing
1200 nm and 1100 nm differential absorbance to determine optical
pathlength of the water solvent, A.sub.720 (per cm optical
pathlength) ranged from 0.569, at 350 .mu.l sample volume, to 0.560
at 100 .mu.l sample volume. The later value is about 1.6.% less
than the 0.569 A.sub.720 reference value. Thus, the accuracy at the
100 .mu.l sample volume again is greatly improved by employing 1200
nm and 1100 nm differential absorbance to determine optical
pathlength of the (aqueous) solvent. The considerable interference
of the Napthol Green B dye is removed by performing the optical
pathlength determination at the 1100 and 1200 temperature
isosbestic wavelengths of the (aqueous) solvent. In general,
employing absorbance measurements at temperature isosbestic
wavelengths greater than 1000 nanometers to determine optical
pathlength will provide considerable increased accuracy.
TABLE-US-00005 TABLE V Absorbance/(Cm Optical Pathlength) With
Optical Pathlength Measured at Different NIR Wavelengths in Aqueous
Samples Absorbance Solvent Pathlength Sample Volume in Microplate 1
cm Sample/Wavelength Wavelengths 350 .mu.L 300 .mu.L 250 .mu.L 200
.mu.L 150 .mu.L 100 .mu.L Cuvette BSA, 2 mg/ml 1200/1100 nm 1.007
1.019 1.032 1.021 1.026 1.017 0.995 A.sub.280 nm 1000/900 nm 1.033
1.030 1.030 1.033 1.044 1.054 Fisher pH 7.0 1200/1100 nm 0.384
0.386 0.386 0.385 0.385 0.385 0.389 (yellow) Buffer 1000/900 nm
0.395 0.396 0.398 0.398 0.396 0.403 A.sub.420 nm Napthol Green B,
1200/1100 nm 0.569 0.571 0.577 0.566 0.573 0.560 0.569 50 ug/ml
1000/900 nm 0.917 0.913 0.914 0.915 0.916 0.904 A.sub.720 nm
[0244] From the foregoing it will be appreciated that, although
specific embodiments of the invention have been described herein
for purposes of illustration, various modifications may be made
without deviating from the spirit and scope of the invention.
* * * * *