CLIN. CHEM.
19/10, 1128-1134
(1973)
Kinetics of the Cholesterol-Sulfuric Acid Reaction:
A Fast Kinetic Method for Serum Cholesterol
Thomas E. Hewitt and Harry L. Pardue1
We studied the kinetics of the reaction between cholesterol and sulfuric acid in acetic acid-acetic
anhydride medium.
Results have been used to establish
near-optimal
conditions
for the fast kinetic determination of cholesterol
in serum. The reaction
rate
measured during the first 20 s of the reaction is proportional to cholesterol
concentration.
There is good
agreement
(<2%
deviation)
between
pseudo-f irstorder rate constants
for cholesterol
standards
and
sera. Recoveries
of standard
cholesterol
added to
sera range from 99% to 104% (average,
100.7%).
Values for serum cholesterol
by this kinetic determination tend to be somewhat
lower than equilibrium
values
reported
by local
hospital
laboratories.
Whether
bilirubin
interferes
depends
on reaction
conditions;
under optimal conditions,
each milligram
of bilirubin
is kinetically
equivalent
to about
1
mg of apparent cholesterol.
Kinetic data are included
to show how results
are degraded
by operating
under nonoptimal
conditions,
and considerations
involved in changing experimental
conditions
are discussed.
Additional Keyphrases: optimal analytical
conditions
#{149}
bilirubin interference
#{149} analytical
implications
of kinetic data #{149}Liebermann-Burchard
reaction
#{149}molar
absorptivity
#{149}
equilibrium and kinetic values compared
Several reports have emphasized
the potential
improvements
in speed
and selectivity
to be gained
when kinetic methods
are applied
to analytical
reactions that approach
equilibrium
slowly (1-3).
The
Liebermann-Burchard
reaction
for cholesterol
is an
example
of a reaction
that potentially
can be significantly
improved
by use of kinetic
measurements.
Equilibrium
applications
of this reaction
have been
studied
extensively
(4); however,
there are no reports
of kinetic
applications
of the reaction.
We have carried out an extensive
study
of the kinetics
of this
reaction
system and of the analytical
implications
of
the kinetic data. We conclude
that the reaction
can
be used for the fast kinetic determination
of cholesterol in serum,
and we report data to demonstrate
the advantages
and limitations
of the suggested
method.
The reaction
is monitored
by measuring
the absorption
of the reaction
product
at 615 nm. The
From the Department
of Chemistry,
ette, md. 47907.
1 Correspondence
should be directed
Received
1128
June
CLINICAL
6, 1973; accepted
CHEMISTRY,
July
Purdue
University,
to this author.
10, 1973.
Vol. 19, No. 10, 1973
reaction
exhibits
an induction
period,
the length of
which
decreases
with increasing
acetic
anhydride
concentration
and temperature.
After
the initial
delay time, the reaction
is first order in cholesterol
concentration
over a wide range of concentrations.
The pseudo-first-order
rate constant
increases
with
increasing
sulfuric acid and acetic anhydride
concentrations
and with increasing
temperature,
and decreases with increasing
water content
of the reagent
or sample.
Analytical
conditions
depend
on the characteristics one chooses to optimize.
For example,
sensitivity
and speed are favored by high values for sulfuric acid
and acetic
anhydride
concentrations
and temperature, selectivity
over bilirubin
is favored by high acetic anhydride
concentration,
and reagent
stability
is favored
by low acetic
anhydride
concentration.
Our suggested
conditions
(37 #{176}C,
and the following
amounts
of reagents
per kg: 221 g of H2SO4, 94 g of
acetic
acid, 677 g of acetic
anhydride
and 8 g of
Na2SO4)
optimize
speed, sensitivity,
and selectivity
at the expense
of reagent
stability.
Sufficient
data
are included
to permit the potential
user to evaluate
the nature
and magnitudes
of compromises
that
must be accepted
in adapting
the method
to his particular needs.
In our analytical
procedure,
10 jsl of sample
is
added to 3 ml of the above-mentioned
reagent
in a
reaction
cell controlled
at 37 #{176}C,
and the rate of
change of absorbance
at 615 nm is measured
within
about 20 s after the sample
and reagent
are mixed.
Cholesterol
concentration
is calculated
by using a
proportionality
constant
determined
for a 2.00 g/liter
standard.
Quantitative
data from many sera indicate
that normal sample matrix variations
have relatively
small effects (1-3%) on the reaction
rate constant
or
the molar absorptivity
of the reaction
product,
and
subsequently
on the recovery of cholesterol
added to
sera. Linear regression
data indicate
that kinetic results are somewhat
lower (1-5%)
than results
obtained
by a conventional
equilibrium
method
in a
local hospital
laboratory.
Bilirubin
contributes
a
positive
error that is kinetically
equivalent
to 1 mg
of apparent
cholesterol
for each milligram
of bilirubin
that is present.
These and other observations
are discussed in more detail in the text.
Lafay-
General Considerations
Equations
1 and
2 show
the
reactions
involved
in
the Liebermann-Burchard
Cholesterol
method
H2SO4
bis-cholestadienyl
+
for cholesterol
(5).
-
bis-cholestadienyl
monosulfonic
monosulfonic
acid
bis-cholestadienyl
+
disulfonic
acid
(1)
acid
-
-kC
(differential
form)
is proportional
then Equation
ln(A
H2S04
(2)
The sulfuric
acid concentration
is high enough that
it does not change
significantly
during the reaction,
but low enough that reaction
2 is slow in comparison
with reaction
1. Reaction
1 is monitored
continuously by the change in absorbance
at 615 nm.
Figure 1 represents
a typical tracing of absorbance
vs. time for a 200 mg/dl solution
of cholesterol.
This
figure points
out some of the differences
between
equilibrium
and kinetic methods.
The sharp spike at
zero time represents
the point at which the cholesterol sample
is added to the reagent
in the cell. The
reaction
passes through
an induction
period during
which it accelerates
toward an inflection
point, after
which it follows apparent
first-order
kinetics.
The
length
of the induction
period
and the apparent
first-order
rate constant
depend
on reaction
conditions as discussed
below.
The apparent
first-order
behavior
can be expressed
mathematically
as
dC
the absorbance
of the product,
the form
-
A,)
to the concentration
5 can be rewritten
= -kt +lnA,,
in
(6)
where A and A
represent
the absorbance
of the
product
at any time t and at infinite
time, respectively (see Figure 1). It follows that a plot of ln (A.
A) vs. t is linear for a first-order
reaction
and that
the slope of the plot is proportional
to the rate constant as indicated
in Equation
7.
-
k =
-[
ln(A,.
-
A,)/t]
(7)
One of the most significant
observations
to make
here is the fact that the rate constant
determined
in
this fashion
is independent
of the concentration
of
the rate-limiting
species. This fact, and the relationship expressed
in Equation
4, makes the apparent
first-order
rate constant
a unique
diagnostic
tool in
the evaluation
of sample-to-sample
variation
to be
expected
from a kinetic
method
based on a first-
(3)
0
x.
where C is the time-dependent
cholesterol
concentration,
t is the time,
and k is the apparent
firstorder rate constant.
In the area of the inflection
point,
the response
curve
appears
to be linear,
suggesting
apparent
zero-order
behavior.
In other
words, this means that measurable
response
is being
observed
while an insignificant
amount
of the ratelimiting
reactant
(cholesterol
in this case) is being
used up. Mathematically,
this means that the concentration
term in Equation
3 is approximated
by
the initial concentration
(C
C0) and that the derivative
term is estimated
from measurable
values
for absorbance
and time [dc/dt
-(1/eb)M/it}
obtained
from a line drawn
through
the apparent
linear portion of the curve. Substituting
these quantities into Equation
3 and rearranging,
we have
C0
1
=
keb
A
4
C,
C
C
o
Time 1mm)
Fig. 1. Absorbance
vs. time response for cholesterol-sulfuric acid reaction
Conditions: H2S04, 22.1 9/100 g; acetic anhydride, 47.7 9/100 g; acetic
acid, 29.4 g/100
g; Na2SO4. 0.8 g/100
g; 25 #{176}C;
20-M1 Sample
(4)
it
where
and b represent
the molar absorptivity
of the
absorbing
product
and the cell pathlength,
respectively. Figure 2 represents
a plot of M/t
vs. cholesterol concentration
for two sets of conditions
to be
discussed
later,
and demonstrates
the validity
of
Equation
4.
The integrated
form of Equation
3 is useful
in
evaluating
the apparent
first-order
rate constant
and
in demonstrating
a unique
feature
of the rate constant determined
in this fashion. The expression
is
Cholesterol
Ct
ln
--
=
-kt
(integrated
form)
Fig. 2. Rate
(5)
If it is assumed
that each mole of cholesterol
is converted
to one mole of absorbing
product,
and that
1mg / dl)
vs. cholesterol
concentration
Both curves,
22.1 g/100
g H2S04; 0.8 g/100
g/100 g acetic anhydride;
9.4 g/100 g acetic
F, 47.7 g/100 g acetic anhydride;
29.4 g/100
g Na2SO4. Curve A. 67.7
acid; 37 C; n = 4. Curve
g acetic acid; 25 #{176}C;
n =
5
CLINICAL
CHEMISTRY,
Vol. 19, No. 10. 1973
1129
order reaction.
It is surprising
that few if any reported kinetic methods
make use of this simple test.
Materialsand Methods
Instrumentation
Photometer.
A specially
designed
filter photometer
featuring
photometric
drift of about
0.02% T per
hour was used in this work. The photometer
is similar in principle
to that described
earlier (6) in that
optical feedback
is used for source stabilization;
but
it is different
from previous
designs in that it utilizes
an inexpensive
triac-controlled
power supply to drive
a high wattage
tungsten-halogen
lamp (Model EHT
-250-W
projector
bulb;
General
Electric
Co., Nela
Park, Cleveland,
Ohio 44112). A 20-nm bandpass
interference
filter (lot No. 1677; Optics
Technology,
Inc., Palo Alto, Calif. 94304) is used to isolate
an
energy
band centered
at 615 nm. The photometer
circuitry
converts
percent
transmittance
to absorbance.
Data recorder-processor.
Two options were used in
the collection
and processing
of data on absorbance
vs. time. One option involved
a strip-chart
recorder
for recording
data and subsequent
manual extraction
of slope (.A /zt values).
The other option involved
an on-line digital computer
(PDP-12;
Digital Equipment Corp., Maynard,
Mass. 01754). The computer
processes
data on percent transmittance
vs. time and
yields a print-out
of cholesterol
concentration,
the
first-order
rate constant,
statistical
parameters,
and
other pertinent
data.
Reagents
Sulfuric
acid.
Reagent-grade
sulfuric
acid (No.
2876; Mallinckrodt
Chemical
Works, St. Louis, Mo.
63160) is used without further treatment.
Acetic
acid. Glacial
acetic acid is prepared
by refluxing
reagent-grade
acetic
acid (No. 2504, Mallinckrodt)
with potassium
permanganate
and then
distilling.
Acetic
anhydride.
Technical-grade
acetic
anhydride
(Union
Carbide
Chemical
Co., Indianapolis,
md. 46220) is fractionated
from sodium acetate
(7).
Sodium
sulfate.
Anhydrous
reagent-grade
sodium
sulfate
(No.
3891;
J. T. Baker
Chemical
Co.,
Phillipsburg,
N. J. 08865) is used without
further
treatment.
Color reagent.
A stock color reagent is prepared
by
carefully
mixing the desired amounts
of sulfuric and
acetic
acids, acetic
anhydride,
and sodium
sulfate
following
the procedure
described
by Huang
et al.
(4). This reagent
is divided into several portions
and
stored at 4 #{176}C
in glass-stoppered
reagent bottles;
it is
dispensed
with either a 4-ml syringe with Teflon needle or a reagent
dispenser
(3005 A-L Repipet;
Lab
Industries,
Berkeley,
Calif. 94710).
Cholesterol
samples.
A commercial
cholesterol
standard
(No. 179, 0.2 g/100 g cholesterol
standard;
Hycel Inc., Houston,
Tex. 77000) was used throughout this work. Solid standards
(No. 911; National
Bureau of Standards,
Washington,
D. C. 20000) were
1130
CLINICAL
CHEMISTRY.
Vol. 19, No. 10, 1973
stored
desiccated
in a freezer
compartment.
Standard solutions
were prepared
by weighing
appropriate amounts
and dissolving
them in glacial
acetic
acid.
Control sera were prepared
as directed
by the suppliers and test sera were run without
any prior treatment. All samples
and standards
were dispensed
into
the reaction
vessel with a 50-1il syringe (Model 705CH; Hamilton
Co., Reno, Nev. 89502).
Procedure
The photometer
and its associated
circuitry
are
permitted
to warm up for an hour and the circulating water bath is adjusted
to the desired
working
temperature.
The samples
and color reagent
are immersed in the water bath and adjusted
to the working temperature.
The reaction
cell is rinsed with small portions
of
the color reagent
and then 3.00 ml of this reagent
is
dispensed
into the cell. The stirrer is started
and 10
sl of the cholesterol
sample
is injected
into the color
reagent.
Data are obtained
on absorbance
vs. time
and processed
by any desired method(s).
Results and Discussion
All rate data are reported
as rates of change of absorbance
with
time
(A/zt,
_1)
rather
than
changes
of concentration
with time so that the potential
user will know the magnitudes
of absorbance
that must be measured.
Reaction
rates can be calculated from wolar
absorptivities
and (or) apparent
first-order
rate constants
given later for the different
conditions
studied.
Cholesterol
concentrations
are
expressed
as milligrams
per 100 grams;
all other
concentrations
are expressed
as g/100 g (“wt %“).
Preliminary
work yielded
similar
results
for the
solution
from Hycel and solutions
prepared
from the
National
Bureau
of Standards
reagent.
Except
for
calibration
curves
involving
serial
dilutions,
the
Hycel standard
was used throughout
the remainder
of this work.
Equation
4 identifies
the rate constant
and molar
absorptivity
as the chemically
related
parameters
that must be characterized.
We show here how these
parameters
depend
on experimental
variables
that
can be controlled
as well as sample
matrix
effects
that are not so easily controlled.
Kinetic
Dependencies
Sulfuric
acid dependency.
Figure
3 shows
how
reaction
rate is related to sulfuric acid concentration
under different
conditions.
Curves A, B, and C represent the sulfuric acid dependency
at 25 #{176}C
and 120,
240, and 320 mg/dl
cholesterol.
All data were normalized
to the same acetic anhydride
concentration
(47.7 g/100 g) before being plotted.
These data were
also normalized
to 200 mg of cholesterol
per deciliter
and plotted
as curve D. Curve E represents
the sulfuric acid dependency
at 37 #{176}C,
67.7 g of acetic anhydride per 100 g, and 200 mg cholesterol
per deciliter. Curve F is the log-log plot of the normalized
8
C
Time (min)(absorbonce
Fig. 4. Effects of temperature
centration
on response
ordinate)
and acetic anhydride con-
curves
All curves, 22.1 g/100 g H2S04; 0.8 9/100 g Na2SO4; 200 mg/dl cholesterol. Curves A, C, E, 67.7 9/100 g acetic anhydride; 9.4 9/100 g acetic
acid; 37, 30, and 25 C,
tic anhydride;
29.4 g/100
respectively.
Curves B, 0. F. 47.7 9/100 g aceg acetic acid; 37, 30, and 25 C. respectively
Sulfuric Acid Iwt ‘/.)
Fig.
3. Effect
of sulfuric
acid on reaction
Linear coordinates:
Curves A-D; data normalized to
anhydride:
25 #{176}C;
cholesterol,
120. 240, 320, and
A-D,
respectively);
n = 5. Curve E - 67.7 9/100 g
#{176}C;
cholesterol, 200 mg/dl; n = 4
Log coordinates:
Curves F and G, Data taken from
rate
g acetic
200 mg/dI
(curves
acetic anhydride;
37
curves 0 and E. re-
spectively
0
x
data at 25 #{176}C
(curve D) and curve G is the log-log
plot of the data at 37 #{176}C
(curve E). The slopes of the
two lines are virtually
the same and show that the
reaction
rate increases
with the 1.5th power of the
sulfuric
acid concentration
(rate
[H2S04]1.5).
The
operating
value of’ 22.1 g of sulfuric
acid per 100 g
represents
a compromise
between
increased
sensitivity and increased
viscosity
of the reagent
as the sulfuric acid concentration
is increased.
Temperature
dependency.
Effects
of temperature
on the reaction
at two different
acetic
anhydride
concentrations
are included
in Figures 4 and 5. The
traces of response
curves in Figure 4 show that the
shapes
of absorbance
vs. time curves as well as the
reaction
rates are dependent
upon temperature.
The
induction
period, which lasts for more than one minute at 25 #{176}C,
is virtually
eliminated
at 37 #{176}C.
On the
other hand,
the product
of reaction
1 is much less
stable at 37 #{176}C
than at either 25 or 30 #{176}C.
The plots
of -ln
(A
A,) vs. time show that the reaction
eventually
reaches pseudo-first-order
behavior
for all
conditions
examined,
and that the time required
to
reach this condition
decreases
with increasing
temperature.
Equation
4 is valid for data collected
as
soon as 20 s after mixing at 37 #{176}C,
while this time increases to about 1 mm at 30 #{176}C
and more than 2 mm
at 25 #{176}C.
Temperature
also affects the rate constant
and the
sensitivity
of the method.
Apparent
first-order
rate
constants
obtained
from the slopes of the -ln (A
A,) vs. time are plotted
as a function
of temperature in Figure
5. Log-log plots of these data show
that the rate is proportional
to the third power of
-
-
Acetic Anhydride (wt %)
47.7 9/100
C
C
0
C-)
0
IC,
TemperaturelC)
Fig. 5. Effects of temperature,
rubin on reaction rate constant
acetic
anhydride,
and bili-
Temperature,
rate constant
ordinate.
A, data taken from curves
B. 0,
and F of Figure 4. B. data taken from curves A, C. and E of Figure 4.
Acetic
anhydride.
rate-constant
ordinate.
C. cholesterol standard; 0,
serum sample.
Both curves,
37 0C; 22.1 9/100
g H2S04; 0.8 9/100
g
Na2SO4; acetic acid by difference.
Bilirubin,
acetic anhydride
abscissa,
error ordinate. Error contributed by 1 mg/dl bilirubin in 200 mg/dI cholesterol sample
temperature
(rate
T3) when the temperature
is expressed in degrees centrigrade.
Acetic anhydride
dependency.
Effects of acetic anhydride on the reaction
are also included
in Figures 4
and 5. Both the length of the induction
period and
the rate constant
depend
on acetic anhydride
concentration.
The delay time decreases
and the rate
constant
increases
with increasing
acetic anhydride
concentration.
Figure 5 also shows that the rate constant reaches
a maximal
value at about 70% acetic
anhydride.
The behavior
of serum samples
and standards prepared
in acetic acid are observed
to be very
similar.
The
vertical
displacement
between
the
curves results from a depression
of the rate by water
added with the sera. The data in Figure 5 also show
that the error caused by bilirubin
decreases
with increasing
acetic
anhydride
concentration.
Thus,
the
higher acetic anhydride
concentration
not only leads
CLINICAL
CHEMISTRY,
Vol.
19, No.
10, 1973
1131
Table 1. Molar Absorptlvitiesof the Sulfuric AcidCholesterolReaction Product
z
Acetic
anhydride,
9/100 a
+
‘I
‘O
-J
Water Added
lIl
Fig. 6. Effect of water on reaction rate
All curves. 22.1 g/100 g H2S04; 0.8 g/100 g Na2SO4; 200 mg/dI cholesterol. Linear coordinates:
-0- 47.7 g/100 g acetic anhydride; 29.4 g/100
g acetic acid; 25 #{176}C;
n = 4. -U-, 67.7 g/100
g acetic anhydride;
9.4
g/100 g acetic acid: 37#{176}C;
n = 3.
Log coordinates:
x, data taken from -0-. +. data taken from -U-
to shortest
measurement
times and highest sensitivity, but also improves
the selectivity
of the method
over bilirubin
and minimizes
the effects of fluctuations in acetic anhydride
concentration.
On the other
hand,
the higher
acetic
anhydride
concentration
leads to an accelerated
decrease
in absorbance
at 615
nm after the reaction
has reached equilibrium
(compare curves A and B).
Water dependency.
Cholesterol
standards
usually
are prepared
in glacial acetic acid while serum samples obviously
contain
high water
concentrations.
Therefore,
it is necessary
to determine
what effect
water has on the reaction
rate. Figure 6 shows the
effects of various amounts
of water added to 3.00 ml
of reagent
containing
10 microliters
of a 200 mg/dl
cholesterol
standard.
The effect of water on the reaction is observed
to be smaller
at 37 #{176}C
and 67.7 g of
acetic anhydride
per 100 g than at 25 #{176}C
and 47.7
g of acetic anhydride
per 100 g. Slopes of the loglog plots
show
the relationships,
rate
l/(zl
H2O)#{176}#{176}44
and rate
1/(sl H20)#{176}’#{176}76
at the high and
low conditions
of temperature
and acetic anhydride,
respectively.
The water effect can be handled
either by adding
an amount
of water equal to the sample
size in the
standardization
step or by computing
a correction
factor from the data in Figure 6. We have used both
procedures
with equal
success.
This point
is discussed in more detail below under “matrix
effects.”
Reagent
stability.
The stability
of the color reagent
depends
on the temperature
at which
it is
stored
and its composition.
Table
1 presents
some
stability
data. The rate constant
for the reagent containing
68 g of acetic
anhydride
per 100 g decreases
by about
20% during
a two-week
period at
room temperature
while the rate constant
for the 48
g/100 g acetic
anhydride
preparation
decreases
by
only 3% during the same period. Reagent
stability
is
improved
markedly
by storage
at 4 #{176}C.
In either
case, the reagent
can be used for several weeks if it is
restandardized
for each day’s operation.
Biliru bin. Bilirubin
reacts
with sulfuric
acid to
produce
a product
which absorbs
at 615 nm. The
reaction
kinetics
are somewhat
more complex
than
1132
CLINICALCHEMISTRY,
Vol. 19, No. 10, 1973
Molar
absorptivlty,
llter/mol cm
Temperature,
Rate
constant
X 102
_1
67.7
25
2139
1.35
67.7
67.7
67.7#{176}
2146
2151
2.37
2234
4.19
47.7
30
37
37
25
1960
0.95
47.7
47.7
30
37
477#{176}
37
2014
2025
2014
1.72
3.72
3.62
5.23
Reagent stored 14 days at room temperature.
H2S04. 22.1 g/100 g; Na2SO4, 0.8 g/100 g; acetic
wavelength
= 615 nm.
a
acid,
by difference;
of Rate Constants for Sera
and Standards Containing Water
Table 2. Comparison
Rate constant (s’
Acetic
anhydrlde
9/1009
No.
sera
Value
67.7
67.7
20
10
3.94
4.27
0.086
0.034
4.03
4.29
0.049
0.12
1.024
1.005
0.035
0.076
1.00
0.99
Sera’#{176},t
Ratio
SD
Value
SD
Sera/std.
67.7
3
10
4.56
2.98
0.11
47.7
0.027
4.58
2.95
47.7
10
2.97
0.010
2.90
0.03
0.98
2.40
0.047
...
0.031
2.28
2.74
0.104
0.048
1.00
0.013
1.84
0.026
1.02
47.7
47.7
37.7
27.7
a
Std. + H2O
X 102)
4
6
3
2
...
.
...
..
..
2.74
1.80
.
...
10zl of water or serum used in each case.
Cholesterol
concentrations
bilirubin concentrations
H2S04, 22.1 g/100
temp., 37#{176}C.
ranged
from
110
to
340
mg/dl
and
ranged from 0.1 to 1.6 mg/dl in the sera.
g; Na2SO4, 0.8 g/100 g; acetic acid, by difference;
for cholesterol
in that
the reaction
is not easily
forced into pseudo-first-order
behavior.
Accordingly,
it is not possible to quote meaningful
apparent
firstorder rate constants
for the reaction.
However,
it is
possible
to compare
initial rates (.A/zt)
for cholesterol and bilirubin.
The reaction
rate increases
linearly with bilirubin
concentration
up to 40 mg/dl
(the highest value examined).
One milligram
of bilirubin gives a rate equivalent
to what would be given
by about 1.6 mg of cholesterol
at 25 #{176}C
and 48 g of
acetic
anhydride
per 100 g, and about
0.6 mg of
cholesterol
at 37 #{176}C
and 68 g of acetic anhydride
per
100 g. These
values
correspond
to 0.8% and 0.3%
errors, respectively,
at 200 mg/dl
of cholesterol
(see
Figure
5). Variations
in apparent
first-order
rate
constants
for serum samples
in Table
1 include
effects of variable amounts
of bilirubin.
Molar Absorptivity
Dependencies
Table 1 lists molar absorptivities
measured
at 615
nm for a variety of conditions.
Absorptivity
increases
slightly with both temperature
and acetic anhydride
concentration.
Also, there appears
to be a slight increase in this constant
with time at the high acetic
anhydride
concentration.
Other data
not included
520
here show a small depression
of the molar absorptivity by 20 al of water added
with a standard.
In all
cases, the changes
in molar absorptivity
are small
compared
to the kinetic
effects and as such do not
play a significant
role in the selection
of reaction
conditions.
4
38
0
0
‘C
a
x 28
E
MatrixEffects
The sample
matrix
could affect either
the rate
constant
or the molar absorptivity
and each of these
parameters
must be examined
separately.
Rate constants.
Equation
7 was used to evaluate
rate constants
for a large number
of serum samples
under a variety
of conditions.
Results
are summarized in Table
2. Note first the last column
in the
Table,
in which the ratio of the average
rate constant for several sera to that of a standard
plus water
is tabulated.
In every case, the ratio is close to unity,
showing
that for these sera, the sample
matrix
has
little or no influence
on the rate constant
for any of
the conditions
examined.
The Table includes
the actual averages
and standard
deviations,
which can be
used to predict
variations
expected
with any desired
degree of confidence.
The individual
data points for
the first entry of 20 samples
in the Table are plotted
as an inset in the lower right-hand
corner of Figure
7. The data in this Table were collected
over many
months,
with use of different
reagent
preparations,
and agreement
among rate constants
down any column is not expected.
Molar absorptivity.
It is somewhat
more difficult
to evaluate
the effect of sample
matrix on the molar
absorptivity,
because
one needs to know the concentration
of the analyte
in the sample to calculate
this
constant.
Our approach
was to add known amounts
of cholesterol
to samples
that had first been analyzed
without
added cholesterol
and to measure
the differ-
.220
C.
w
12
40
120
40
2(X)
28)
360
440
520
Kinetic Method
Fig. 7. Comparison
of equilibrium
and kinetic
results
for
sera
#{149},
25 #{176}C;
47.7 g/100 g acetic anhydride; 0, 30#{176}C;
67.7 g/100 g acetic
anhydride; X, 37#{176}C;
67.7 g/100 g acetic anhydride. Regression equation:
y = 0.953x + 16.1: SD of slope = 0.025
ence in absorbance.
Results of these experiments
are
included
in Table 3, which includes
recovery data for
both equilibrium
and kinetic
methods.
Results
are
quoted
as cholesterol
concentration
rather
than
molar absorptivities,
to permit
a direct comparison
with kinetic
values.
Because
absorbance
is proportional to both concentration
and molar absorptivity,
percentage
recoveries
reported
for our equilibrium
method
represent
the deviation
of the molar absorptivity from the expected
value based on standards.
The data suggest a positive
bias of about 3% in the
equilibrium
recovery
values.
Kinetic
recoveries
average very nearly 100%. We are unable to explain
the
bias in the equilibrium
values.
In any event, these studies suggest that on the average, matrix effects will be limited
to a few percent
at most.
Table 3. Recovery of Cholesterol Standard Added to Sera Obtained from Local Hospital
Cholesterol concentration, mg/dI
Equilibrium
Kinetic
%d
Equilib.
Kinetic
163
200
126
463
504
358
412
324
103
102
100
104
105
186
397
103
101
103
99
103
99
103
208
193
426
141
200
107
105
103
101
104
387
338
395
257
134
457
332
99
108
100
103.3
100.7
Foundb
Sera + Std.’
247
315
264
296
476
509
257
288
178
222
120
173
205
127
373
422
342
190
225
191
214
401
442
200
198
416
135
228
292
140
145
206
260
135
355
412
456
362
Reported”
Recovery,
Found#{176}
Sera + Std.c
Av
99
99
99
99
Conditions; 30#{176}C;
22.1 g/100 g H2S04, 9.4 g/100 g acetic acid, 67.7 g/100 g acetic anhydride, 0.8 g/100 g Na2SO4; 1O-pI sample.
a
C
d
Values reported by local hospital laboratory.
Values found in this laboratory by equilibrium and kinetic methods.
Values found for lO-pI sample plus lO-pI of 200 mg/dl standard.
Calculated as 100 X quotient of “Sera + Std” values divided by “Found”
values + 200.
- -- CLINICAL
CHEMISTRY,
___________
Vol. 19, No. 10, 1973
1133
Table 4. Comparison of Equilibrium and
Kinetic Values for Cholesterol in Control Sera
concentration, mg/dl
‘Cholesterol
Sample
no.
Reported
1
2
3
4
5
Equilibrium”
Kinetic
200
248
207
260
200
240
140
129
140
131
290
351
360
362
165
169
170
186
200
264
Values obtained by two independent laboratories.
H2S04, 22.1 g/100 g, Na2504, 0.8 9/100 g; aceticanhydrlde,47.7
g/1 00 g; acetic acid, 29.4 9/100 g; temp. 25#{176}C.
a
The reader
should
note that the cholesterol
concentrations
determined
in the recovery
experiments
are equivalent
to sample
concentrations
ranging
from 120 to 509 mg/dl. The good recoveries
obtained
for cholesterol
added
to the higher
concentrations
suggest linearity
into the abnormal
range.
Analysis
Data
Three types of experiments
were conducted
to test
the validity
of the kinetic
method
for cholesterol.
These experiments
included
control sera run by the
equilibrium
and kinetic methods,
recovery of cholesterol added to sera and comparison
of kinetic values
for several
sera with equilibrium
values determined
in a local hospital
laboratory.
The recovery
experiments
were presented
in Table
3 and discussed
above; other results are summarized
below.
Control
sera. Results
for five control
sera run by
two independent
laboratories
and by the kinetic
method
are shown in Table 4. There are differences
among
the several
values,
but the agreement
between individual
kinetic results and either equilibrium result usually
is as good as the agreement
between the equilibrium
results.
Similar
experiments
performed
on standards
prepared
by us gave similar
results.
Sample
number
4 is an interesting
example
in which all three methods
gave results much higher
than that reported
by the supplier.
We are unable to
explain this result.
Clinical samples.
Samples
of serum in which cholesterol
had been determined
were collected
from a
local hospital
and assayed
by the kinetic
method.
Figure 7 is a plot of equilibrium
vs. kinetic
values.
Data are included
for three sets of conditions.
The
slope of the regression
line is 0.95 ± 0.05 (at 95%
confidence
level) and the intercept
is 16.1 on the ordinate.
This
suggests
that
the below 300 mg/dl
results are somewhat
lower than reported
equilibrium
values. We are unable to explain this difference
fully;
however, the water correction,
which is applied to the
kinetic
method
but not to the equilibrium
method,
could account for much of the difference.
The data collected
under different
conditions
yield
slightly
different
regression
equations.
The equation
at 25 “C is y = 0.92 x + 22.4, that at 30 “C is y =
1134
CLINICAL CHEMISTRY, Vol. 19, No. 10, 1973
1.14 x
15.5, and that at 37 #{176}C
is y = 0.92 x + 19.2.
We think these differences
represent
day-to-day
variations rather than differences
imposed
by the different conditions.
In conclusion:
These results
demonstrate
that kinetic measurements
can be used for fast determinations of cholesterol
in sera and show how reaction
conditions
can be varied to optimize
different
performance characteristics.
The data also indicate
sources
and magnitudes
of errors to be expected.
The successful application
of the proposed
method
depends
on the availability
of a stable
photometer,
careful
control
of reagent
composition,
efficient
mixing
of
sample
and reagent,
and careful
temperature
control. If one uses an acetic anhydride
concentration
of
68 g/100 g and a temperature
of 37 “C, stirring
and
temperature
equilibrium
must be established
within
a few seconds.
Decreasing
either
or both of these
variables
will lengthen
the analysis
time but will
place less stringent
requirements
on the stirring
efficiency and temperature
control system.
Possibly
the
requirements
placed on the photometer
could be relaxed somewhat
by the use of larger sample sizes. Although
we have obtained
some data with 50- and
lO0-jl
samples,
we suggest
that
any attempts
to
modify the procedure
in this manner
be accompanied by a thorough
consideration
of the effects on
other variables.
One commercial
cholesterol
reagent
that has a composition
similar
to our 47.7 g/100 g
acetic anhydride
reagent gives rates much lower than
we observe
for reagents
prepared
by us. Potential
users who choose to use a commercial
reagent for the
kinetic
analysis
should evaluate
the reagent
carefully. Finally,
we think this and other kinetic
methods
place demands
on photometric
instrumentation
that
are only partially
met by the commercial
instrumentation now commonly
used, and point to a need for a
new generation
of photometers
for the clinical laboratory.
-
This investigation
was supported
in part by PHS
Research
Grant No. GM 13326-07 from the NIH. We are grateful
for technical assistance
from several staff members
in the clinical
chemistry laboratory
at St. Elizabeth
Hospital
Medical
Center
in Lafayette, Indiana.
References
1. Moss, D. W., The relative
merits and
and fixed-incubation
methods
of enzyme
mology. Gun. Chem. 18, 1449 (1972).
applicability
of kinetic
assay in clinical
ezizy-
2. Fabiny,
D. L., and Ertingshatisen,
G., Automated
reactionrate method
for determination
of serum creatinine
with the CentrifiChem.
Clin. Chern. 17,696(1971).
3. Malmstadt,
H. V., Cordos,
E. A., and Delaney,
C. J., Automated reaction-rate
methods
of analysis.
Anal. Chem. 44, No. 12,
26A (1972).
4. Zak, B., Weiner,
L. M., and Welsh,
B.,
study of bilirubin
interference
in the Huang
terol. Clin. Chirri. Acta 30, 697 (1970).
5. Tietz,
N. W., Fundamentals
of Clinical
Saunders
Co., Philadelphia,
Pa., 1970, p 353.
Spectrophotometric
reaction
for cholesChemistry,
W.
B.
6. Pardue,
H. L., and Deming,
S. N., High-stability
low-noise
precision
spectrophotometer
using optical feedback.
Anal. Chem.
41,986(1969).
7. Fieser, L. F., and Fieser, M., Reagents
for Organic
John Wiley and Sons, New York, N. Y., 1967, p3.
Synthesis,