Download Advanced Kinetic Analysis Using a LAMBDA Series Spectrometer

Advanced Kinetic Analysis
Using a Lambda Series Spectrometer
and the UV KinLab Software Module
HansWilly Müller
PerkinElmer Instruments
Advanced Kinetic Analysis using a Lambda Series Spectrometer
and the UV KinLab Software Module
HansWilly Müller
PerkinElmer Instruments
1. Introduction
1.1 Kinetics
Kinetics defines the course of chemical reactions with time. Knowledge of kinetics of chemical reactions
is important for the understanding of the biochemical processes in living organisms. The driving force of
these chemical reactions are the rules of thermodynamics, which are the same for “in vitro” processes as
for “in vivo” processes. Biochemical reactions occur enzyme controlled, as a part of a complex reaction
cycle. Enzyme kinetics is the systematic analysis of enzyme catalyzed reactions, involving the study of
the dependence of reaction rates on substrate concentration, pH, temperature, and other variables.
The rate (ν) of an enzyme catalyzed or any other chemical reaction is defined as the change of the concentration of the participating reaction partners with time. It is defined with the unit Mole . Liter-1 . s-1.
It is the product of the rate constant (k) and the concentration (c).
v=
− dc
= k •c
dt
ν = Rate of an enzyme catalyzed reaction (moles/L.s), c = initial concentration of one reaction partner, t = time,
k = rate constant (s-1).
The rate constant (k) is a measure of the probability of a chemical reaction occurring between the
molecules involved.
The reaction rate may change significantly with time during the chemical reaction. Therefore we
distinguish between several orders of reaction.
The order of a chemical reaction is defined after the number of the partners involved:
When the reaction rate is independent on c, it means that same amount of substance is reacting per unit
of time - the reaction rate does not change with time. This is defined as a zero order reaction. This is the
case, for example, when a reagent A reacts to P independently from the concentration
of A or P, and the reaction velocity is constant.
1.
k0
v=
⎯→ P
Reaction: A ⎯⎯
− d [ A] d [P ]
=
= k0
dt
dt
When this zero order reaction is integrated to the time, this results in a linear relation.
[A] = [A0 ] − k0t
Reactions obeying zero order show typically linear increase of product and linear decrease of substrate
with time. A reaction is zero order, when a catalyst is involved, the concentration of which is constant and
extremely low, compared to the concentration of the other partners. A catalyzed zero
order reaction is independent on the number of reacting partners.
2 . When the rate is dependent on c, it changes with increasing or decreasing amount of remaining sub-
stance. This is valid for a reaction where only molecules of the same kind are involved. This would be
a spontaneous transformation of a reagent A to the product P, as, for example, it is happens in radioactive decay. This monomolecular reaction is defined as a first order reaction:
k
1
Reaction: A ⎯⎯
⎯
→P
v=
− d [ A] d [P ]
=
= k1 • [ A]
dt
dt
The velocity ν of a first order reaction can be measured from the decrease of reactant A or the increase
of product P.
3.
A reaction where two different types of molecules react is called bimolecular reaction. The reaction
type is second order. This is the case, when two chemicals react to a product:.
A + B ⎯⎯2 → P
k
the reaction rate is proportional to the decrease of A and B and to the increase of P.
v=
− d [ A] − d [B] d [P]
=
=
= k2 [ A][B ]
dt
dt
dt
Theoretically all chemical reactions are reversible. Therefore it is possible to specify reaction rates for
both directions, forwards and reverse. The forwards reaction is usually defined as k+1, the backwards reaction is defined as k-1.
The equilibrium constant (Keq) defines the concentration ratio of the reactants in the equilibrium under
standard conditions (25°C, 1 molar concentration). In the equilibrium state the reaction rates in both directions are the same. The concentration of the reactants does not change:
k +1
= K eq
k −1
A reaction
A+B↔ C+D
or
[C ] • [D ] = K
[A] • [B] eq
can only occur, when the change of free energy ΔG of the system is negative (exergonic reaction) - when
energy is released.
According to
ΔG = ΔG° + RT . In
[C ] • [D]
[A] • [B]
this free energy depends on the equilibrium constant of the reaction and on the concentration on the reactants. ΔG corresponds to the free energy, which is released under standard conditions and is proportional
to the equilibrium constant:
ΔG = − RT . In Keq
In the state of equilibrium ΔG = 0. When ΔG is positive, the reaction is endergonic and can only happen
when coupled to an exergonic reaction. In biological systems this energy is supplied by energy-rich substances, for example ATP, which release an amount of energy > 7 kcal per mole during hydrolysis.
2
1.2 Kinetic Reactions in Enzyme Systems
Chemical reactions in living systems would be extremely slow without the catalytic activity of
enzymes. Biological processes use reaction chains and reaction cycles where several reactions are combined in sequence and the product of the first reaction is used up by the next reaction. There is a continuous flow of substances from one open system into another open system, while -at the same time- reaction
products are removed. The system permanently tries to reach an unattainable equilibrium. In such a system, enzymes may change the local concentrations, while converting more substrate than the surrounding
sources can supply. These reaction chains usually drive into one direction.
In such a combination of different reactions the concentration of a substrate A is continuously kept constant and the last product Z of the metabolism is continuously removed. Then the concentration of the
intermediate products (B through Y) will reach a “stationary concentration”. In these kind of processes we
talk about steady state not about an equilibrium. This steady state depends on the activity of the enzymes
and is characteristic for the individual situation of the metabolism.
The kinetics of enzyme reactions have Enzyme/Substrate complexes as intermediate products. For the
simplest case of a single enzyme/single substrate reaction, the following equation is valid:
S+E
k 1→
⎯⎯
←⎯
⎯⎯
k −1
ES
k2
⎯⎯
⎯→
P+E
S=Substrate, E=Enzyme, ES=Enzyme substrate complex, P=Product
The enzyme combines with the substrate to an Enzyme substrate complex which then is cleaved into Enzyme and Product. This is a cyclic, usually very fast process, where the enzyme is released again and is
able to react with another substrate molecule.
From above equation we can derive the following differential equations:
d[S ]
= − k1 [S ] • [E ] + k −1 • [ES ]
dt
(a)
d[E ]
= −k1 [S ] • [E ] + (k −1 + k 2 ) • [ES ]
dt
(b)
d [ ES ]
= k1 [S ] • [E ] − (k −1 + k 2 ) • [ES ]
dt
(c)
d [ P]
= k 2 [ES ]
dt
(d)
The second reaction, when the enzyme substrate complex is converted to enzyme and product, is much
slower than the reaction, where this complex is formed; k2<<k1. This means the reaction:
k2
ES ⎯⎯
→ P + E determines the velocity of the total reaction and equation (d) simplifies to:
d [ P]
= k2 [ES] = v
dt
(e)
3
When we make the assumption that in a steady state the concentration of the enzyme substrate complex
is constant and the concentration of the enzyme is constant:
d [ ES ] d [ E ]
=
= 0,
dt
dt
Now equations (b) and (c) can be simplified to:
[ E ][ S ]
[ ES ]
=
k 2 + k−1
,
k1
where we can combine the expression with all 3 velocity constants to another constant (Km):
Km =
[ E ][ S ]
k 2 + k1
,=
k1
[ ES ]
(f)
The initial, total enzyme concentration is the sum of the free and the bound enzyme:
[E0 ] = [E ] + [ES ]
With this, equation (f) can be expressed as:
( [E0 ] − [ES ])[S ]
(g)
Km
after rearranging of equation (g) it is:
[ES ] =
[E0 ][S ]
K m + [S ]
(h)
Together with equation (e) this can be combined to:
v = k 2 [E0 ] •
[S ]
K m + [S ]
(i)
We can define k 2 [E 0 ] = Vmax , the maximal velocity, because the whole amount of enzyme participates on
the reaction. Now equation (i) can be expressed as:
V =
Vmax [S ]
K m + [S ]
(j)
This equation is of fundamental importance for enzyme kinetic measurement, showing the relation between
reaction velocity and substrate concentration.
The Michaelis constant is the substrate concentration, which produces half maximum reaction rate:
K m = [S ] where v =
Vmax
2
Vmax = k 2 [E0 ]
A graphical plot of the Michaelis-Menten kinetics (equation (j) ) gives a hyperbolic reaction curve
(Figure 1).
4
Because Vmax is seldom reached in practice, the linearized plot according to Lineweaver and Burk is
preferred for graphical determination of the constants (Figure 2). The respective equation is the reciprocal
expression of (j):
Km
1
1
1
=
+
•
v V max V max [ S ]
1
1
is plotted versus
. In this diagram Km and Vmax can be determined
v
[S ]
1
1
is the intersection of the line with the abscissa,
is the intersection of the line with
graphically: −
Vmax
Km
In the Lineweaver Burk diagram
the ordinate.
Figure 1. Michaelis-Menten kinetics.
Figure 2. Lineweaver-Burk kinetics.
Legend:
S = Substrate
v = Reaction rate dS/dt
E = Enzume
Vmax = Maximum reaction rate
ES = Enzyme Substrate complex
P = Product
[ ] = Concentration
[ 0] = Initial concentration
kn = Rate constant for reaction n
Km = Michaelis-Constant =
k 2 + k −1
k1
5
2. Practical Enzyme Activity Determination
2.1 Data Collection and Routine Enzyme Activity Determination
If the reaction is zero order, concentration of product will increase linearly with respect to time. This is
the ideal condition for an enzyme assay, and the assay should be set up so that the reaction is at or near
zero order during the entire measurement period.
k
S ⎯⎯0 → P
v=
− d [ S ] d [ P]
=
= k0
dt
dt
[P ] = k0 • t
An accurate enzyme assay requires the proper control of pH and temperature, usually a small volume of
sample (often only between 10 and 100 µL), and the use of optimized data collection interval for the concentration range being studied: high reaction rates require smaller data intervals on the time axis, low
reaction rates may be recorded with larger data intervals.
In simple routine tests in practice often only 2 - 5 data points are collected per experiment. In more sophisticated enzyme studies it is recommended to take between 10 and 20 data points, which will allow a
more precise linear regression analysis, when using a computerized system.
For example, when the expected slope (ΔA/min) is only around 0.01 A/min it would be recommended to
follow this reaction for about 15 minutes with 60s time intervals. For a faster reaction, with a expected
slope (ΔA/min) of about 0.1 A/min a measurement time of only 3 minutes would be sufficient, but absorbance reading should be collected at least every 15s.
Enzymes are measured in units of activity, not in concentration. The standard unit of enzyme activity is
defined as “the amount of enzyme that will catalyze the conversion of one micromole of substrate per
minute under defined conditions.” The conditions that should be specified are temperature (often 25°C),
optimum pH and substrate concentration. The specific activity of an enzyme is the enzyme activity related to the enzyme concentration (protein content).
According to Beer Lambert’s law the concentration of a substance is, within certain limits, proportional to
its absorbance. Therefore, in a photometric test, the decrease of the substrate or the increase of the product
can be monitored. With kinetic methods you can monitor an enzymatic reaction, and from this calculate
enzyme activity.
6
A special type of enzyme
assay (for oxidoreductases) system involves the oxidation and
reduction of the pyridine
nucleotides NAD(P)+ or
NAD(P)H respectively.
This reaction is followed
at 340 nm where
NAD(P)+ has no absorbance, but the product
NAD(P)H absorbs
strongly. The molar absorbance coefficient of
NADH is at 340 nm: ε =
6.3 [l * mmole-1 * cm-1].
Figure 3. Repetitive scan where the enzymatic reduction of NAD+ to NADH
is followed. Absorbance maximum of NADH is at 340 nm.
A typical example for this
type of reaction is the determination of alcohol dehydrogenase (ADH). In this reaction, the substrate acetaldehyde is enzymatically reduced according to the reaction scheme:
ADH
Acetaldehyde + NAD+ ⎯⎯
⎯→ Ethanol + NADH + H +
Figure 3 shows the increase in absorbance between 295 nm and 420 nm (maximum at 340 nm) during
this reaction using repetitive wavelength scans at one minute intervals. When we observe this reaction at a
single wavelength (340 nm) then the plot of absorbance versus time is linear.
Other enzymatic tests (for hydrolases) often
include a non-colored compound,
(e.g. p-nitrophenyl - derivative) which is
enzymatically converted to a colored product
(e.g. p-nitrophenol). A typical example for this
type of test is the determination of the activity
of alkaline phosphatase (AP). Here the substrate
(p-nitrophenyl-phosphate) is cleaved by the
enzyme AP to the product p-nitrophenolate.
7
This type of reaction is not followed by recording the whole absorbance spectrum (as shown in Figure 3).
Usually the reaction is followed at a single wavelength to obtain a plot of absorbance versus time, as can be
seen in Figure 4. In this case the enzymatic formation of the product can be monitored by measuring the
change of absorbance with time. Beer Lambert’s law states, that the absorbance of a substance at a specific
wavelength (A(λ)) is proportional to its concentration (c) and the pathlength (d):
A(λ ) = ε (λ )• d • c
In a kinetic test the absorbance of product (or substrate, respectively) is measured in certain time intervals. The product concentration [P] at a certain time depends itself on the rate constant of the enzymatic
reaction:
[P ] = c = k • t
Combining both equations gives:
A(λ ) = ε (λ ) • d • k • t
In a zero order reaction the term (ε(λ) . d . k) is constant. This allows us to simplify above equation to
A( λ ) = F • t
→
A( λ )
=F
t
This enzyme specific factor (F) consists (at substrate saturation) of the specific rate constant (k), molar
absorbance coefficient (ε (λ)) and the pathlength of the cell (d). These specific enzyme factors are usually
documented for existing enzyme tests and can be found in literature.
This means that the slope of a linear absorbance versus time plot is proportional to the product concentration at the time and thus to enzyme activity. The slope (ΔA/min) multiplied by a factor gives the enzyme
activity in U/L.
Figure 4. Enzyme activity determination of α-amylase in 2 samples of saliva, measured at 546 nm for
3,5 minutes using UV KinLab software. The enzyme test uses starch as substrate, which is
hydrolized to reducing oligosaccarides by α-amylase. The oligosaccharides are detected with 3,5dinitrosalicylic acid, giving a colored dye.
8
The result of a routine enzyme test, appears as shown in Figure 5, when using the statistics option:
Date: 25.07.1996 Time: 08:48:26
Method: KIN1.MKI
Sample
Type
Range [Sec] dA/min Activity (U/μL) Resid.Err Corr.Coeff Comments
--------------------------------------------------------------------------------------------------------------------------MALTASE1 Blank
0 - 240 0.0013
0.0000
0.0080 0.99844 Batch 08-15
MALTASE2 Average1 0 - 240 0.0111
0.0087
0.0087 0.99954 Sample 1,low
MALTASE3 Average1 0 - 240 0.0223
0.3978
0.0094 0.99889 Sample 1,low
MALTASE4 Average2 0 - 240 0.0334
0.5966
0.0102 0.99891 Batch 35-16
MALTASE5 Average2 0 - 240 0.0445
0.7955
0.0109 0.99908 Batch 35-16
MALTASE6 Average3 0 - 240 0.0557
0.9944
0.0116 0.99051 Sample 2, hi
MALTASE7 Average3 0 - 240 0.0668
1.1933
0.0123 0.99897 Sample 2, hi
MALTASE8 Average4 0 - 240 0.0779
1.3922
0.0131 0.99843 Batch 88-15
MALTASE9 Average4 0 - 240 0.0891
1.5910
0.0138 0.99991 Batch 88-15
Average1
Mean: 0.2983
0.1406
Average2
Mean: 0.6961
0.1329
Average3
Mean: 1.0938
0.1544
Average4
Mean: 1.4916
0.1431
Figure 5. Results page of a routine enzyme test with statistics, automatic blank subtraction and duplicate
measurement with automatic mean value calculation.
2.2 Enzyme Activity Determination with KinLab Software Package
The PerkinElmer UV WinLab
instrument control and data
evaluation software package
includes a special application
program for easy kinetics data
evaluation: UV KINLAB. This
is a very powerful program
which allows flexible determination of enzyme activity from
kinetic runs, recorded with the
Lambda series UV/Vis spectrometers. UV KinLab is designed both for routine kinetic
analyses, where many samples
have to be analyzed in the same
way, and for the research type of
analysis with extensive post run
evaluation possibilities.
On the general information page
you can select the type of data
evaluation mode (Figure 6). For
routine enzyme determinations
you can choose the “Total
Range” or the “Fixed Range,” or
even the “Automatic” Mode.
Figure 6. First UV KÌnLab page for selecting the evaluation
mode to determine enzyme activity.
9
When you select “Total Range” or “Fixed Range” the software will always calculate the enzyme activity
in the defined time range, just as routine users in clinical chemistry or simple biochemical applications
need it. The “Total Range” mode will evaluate the curve over the total, selected time range. In the fixed
range it is possible to define a “time window” in which the evaluation will then be done. For example “lag
times” may be entered there so that the enzyme activity determination begins after a certain waiting time.
In the “Automatic Mode” the software will automatically search and select the most linear range of the
kinetics run and will calculate the enzyme activity only from this linear range. When selected this mode,
the software tests the entire range and evaluates the linearity. It then narrows the range intelligently to see
if the evaluation criterion for linearity can be improved. In this way non linear portions, lag-phase, exceptional interruptions (like opening the sample compartment cover) are ignored and the maximum number of
data points showing the highest correlation to linearity are used to compute the slope.
The most flexible evaluation is the
“Interactive Mode” with extensive
possibilities for post-run result calculation. An example for this mode will
be shown later in this paper.
On the second page the number of
samples is defined together with filenames. It is possible to define a blank
and to group samples together calculations of average values from different
samples (Figure 7).
The blank sample will be measured
like a real sample. The slope of this
measurement will be subtracted from
the slopes of the real samples. This
will correct for non-enzymatic and
non-specific reactions taking place in
the blank sample (without enzyme) as
well as in the real samples.
The “average option” allows to get
mean values for multiple tests of the
same sample. Mean value then will be
given as it was shown already in Figure 5.
Figure 7. Second UV WinLab page for sample list including
blank and average definition.
On the next method page the instrument parameters are defined. Most important parameters are measurement wavelength and the duration of the kinetic run, the total time (Figure 8). The measurement time
interval should always stand in relation to the total measuring time. For very fast kinetic measurements it
is possible to measure in time intervals of 25 ms. In this case, the total time normally will not exceed 5 s,
which, for example, would result in 200 data points. A fast kinetic reaction normally will be terminated
in this time frame.
On the other hand a very slow reaction do not need short time intervals, because the absorbance changes
will be relatively slow. For example in an 2 hour reaction a interval time of 60 s is normally more than
sufficient. This will give 120 data points which is enough for reliable and precise slope calculation. For
normal enzymatic tests, which usually last between 5 and 15 minutes, a time interval of 30 s gives plenty
of data points for reliable slope and enzyme activity determination.
10
Slit width selection is only possible with
instruments with variable slits and normally will not affect the kinetic results.
Usually kinetic experiments are measured
with 2 nm slit.
The parameter “response time” is used
to smooth the detector raw data. A high
response time results in less noisy kinetic
runs involving, however, longer measurement and data integration time. The raw
absorbance data will be averaged over a
longer time. A short response time on the
other hand will result in more “noisy”
kinetic runs. In normal single cuvette measurements, between 0 and 2 A, the parameter “Response time” is of minor importance, a response time of 0.5 s is
optimal in all cases.
When working with an automatic cell
Figure 8. Instrument and timing page.
changer, the response time, and with this
the measurement time per cell position, is
optimized for fast measurement cycles. One measurement cycle of an 8 position cell holder is done within
15 s when response time is set to 0 s. The user does not need to care about the relation between response
time and measurement time.
When measuring with an automatic cell changer the interval time (page 1) should stand in relation to the
expected measurement time. It is recommended to select a interval time which allows the measurement of
a complete cell changer cycle. As
mentioned above, shortest cycle time
would be 15 s, when measuring 8
positions of the automatic cell
changer. If the cycle time is shorter
than the time required to complete a
sequence, the next sequence starts as
soon as the previous one is finished.
The 4th page is for the definition of
cell changer functions. Here the cells
are defined (first/last cell), where samples will be positioned in the experiment. Position number 1 is often used
as autozero position, where a cuvette
filled with buffer is normally placed.
When a Peltier thermostatted cell
changer is installed, it is also possible to
set the cell holder temperature (Figure
9).
Figure 9. Accessory page to define cell changer position and
temperature of the Peltier controlled cell holders.
11
On the last page the parameters
are set for data output. It can be
defined which data are going to
be printed or stored. Also the
report format can be selected.
KinLab contains several default
results templates for the output
of data, like the standard result
template giving rate, enzyme
activity and factor (used for the
result, shown in Figure 12).
Another template will output
slope, intercept and standard
deviation (used for the result,
shown in Figure 12). Other
available templates are used for
data export to GraFit™ or other
spreadsheet calculation programs or for dedicated applications. You can modify the default templates and create new
individual templates.
Figure 10. Method Output Page.
2.3 Result Calculation and Presentation
After a method has been defined, the kinetic experiments can be started. Data will be collected from the
spectrometer and will be displayed on-line on the monitor. You can toggle between graphic or tabular
presentation of the actual readings.
After completion of the run, reaction rate and enzyme activity is calculated according to the set parameters.
In Figure 12 it can be seen, that evaluation of all curves is in the range between 20 and 160s. The corresponding section of the kinetic data is then highlighted on the screen with a green background. Numerical
results will be presented as shown in Figures 5 and 13.
It is possible to select replicate measurement for automatically averaging several sets of the same sample.
The software will calculate the mean values of each set of replicates together with standard deviation
(Figure 14).
To correct for a nonspecific background kinetic reaction, usually a blank is recorded with each batch of
samples. The sample, defined in the method as a “blank” will in practice not contain enzyme. Although no
enzyme is present, this blank still may have some background rate which will also be present in the real
samples. These background reactions may result from non-enzymatic reactions or impurities in buffer or
substrate solutions.
The blank is measured in the same way as the other samples. If a multicell transport is being used, the
blank can be recorded in real-time along with the sample assays. It is very useful when the blank rate is
subtracted automatically. KinLab software will subtract this “blank” rate from the rate of the samples
and will give corrected values (Figure 14). The raw data, however, remain unchanged in any case for
later evaluations.
12
The correlation between sample
blank and Autozero in kinetic experiments is shown in Figure 11:
Cuvette is filled with buffer solution and substrate is added. Then
the cuvette is inserted into the sample beam of the spectrometer. Usually this solution shows low absorbance (Figure 11a). Then it is
recommended to perform an
Autozero on the spectrometer. The
Autozero is not absolutely required,
the kinetic results are not depending on the start absorbance of the
solution; after Autozero, however
the kinetics starts at zero absorbance and makes it easier to
compare different kinetic runs
(Figure 11b).
a)
A
b)
A
Autozero
Blank / Sample
Blank / Sample
time
0.0
time
0.0
Start
A
d)
c)
A
Calculate
da/dt
Blank
time
0.0
0.0
time
Figure 11. Measurement of blank, sample and corrected sample.
After Autozero, the enzyme is
added and the kinetic experiment is started. To one of the samples in a batch, the same volume of buffer
will be added instead of enzyme. This is the blank solution, which often shows, despite of the absence of
enzyme, some sloping increase of absorbance with time. This small slope is a nonspecific background
kinetic reaction, which also occurs in the sample solutions and there it adds a certain amount to the enzyme activity (Figure 11c).
After the experiment the
slope of the blank will be
subtracted from all sample
slopes. This will give the
pure enzyme activity as result. The KinLab program
will do this calculation automatically, when the respective sample position is defined as a “blank” in the
sample list (Figure 11d).
Figure 12. Result page, showing graphic display of the kinetic
run and the numerical results.
13
In double beam spectrometers it is also possible, to
measure the blank solution in
the reference beam. In this
case, the background kinetic
slope of the blank is subtracted on-line, optically. The
resulting sample slopes and
enzyme activities will be
corrected, without further
mathematical manipulations.
Date: 14.05.1996
Method: KIN1.MKI
Time: 14:01:26
Range
Rate
Activity
Sample
Type
Sec
dA/min Factor U/μL
Comments
---------------------------------------------------------------------------------------------------------------POD1
Sample
20 - 160 0.1283 17.860 2.291 Activity after 2.0 hours
POD2
Sample
20 - 160 0.1400 17.860 2.500 Activity after 2.5 hours
POD3
Sample
20 - 160 0.1516 17.860 2.708 Activity after 3.0 hours
POD4
Sample
20 - 160 0.1633 17.860 2.917 Activity after 3.5 hours
POD5
Sample
20 - 160 0.1749 17.860 3.124 Activity after 4.0 hours
POD6
Sample
20 - 160 0.1866 17.860 3.333 Activity after 4.5 hours
POD7
Sample
20 - 160 0.1983 17.860 3.542 Activity after 5.0 hours
POD8
Sample
20 - 160 0.2099 17.860 3.749 Activity after 5.5 hours
POD9
Sample
20 - 160 0.2216 17.860 3.958 Activity after 6.0 hours
Figure 13. Kinetic Numerical Results. Here the “fixed time range” mode for evaluation between
20 s and 160 s had been selected in the method. Results show the increase of
Phenol-oxidase activity during a 6hr fermentation.
For complex kinetic runs, it is often necessary to select the right, linear part of the curve for enzyme
activity determination. In this case a single calculation mode can be selected and each curve can be evaluated individually. This is done by moving the green highlighted background (as shown in
Figure 12) into the desired range of the curve and sizing it to the linear range. When you are satisfied,
just click on the “calculate” button and the curve is evaluated only in the selected time window (see
Figure 14).
As can be seen from Figure 14 it will also be possible to use another report type, which gives more statistical information, residual error and correlation coefficient.
Residual error is calculated as: RE =
[∑ (Δy)
2
]
/ ( n − p) ,
where n = number of data points and p = number of parameters in the curve equation. The residual error
serves to compare the linearity of different kinetic curves. The smaller the value is, the better is the curve
fit.
Correlation coefficient is calculated as: CC =
∑(y
1−
∑(y
i
i
−~
y)
− y)
2
2
,
y = calculated function value. The correlation coefficient is a
where yi = reading, y = mean of yi , and ~
measure for the linearity of the curve fit. The closer it is to 1, the better is the curve fit.
It is also possible to average different samples and to subtract a blank (Figure 14).
14
Date: 14.05.1996
Method: KIN1.MKI
Time: 14:09:23
Rate Activity
Sample
Type
Range [Sec] dA/min U/µL Resid.Err Corr.Coeff
Comments
-------------------------------------------------------------------------------------------------------------------------------AMYLASE1 Blank
0 - 180 0.0009 0.0000 0.0014 0.99982 Kinetic demo sample
AMYLASE2 Average1 16 - 180 0.0162 1.6224 0.0038 0.99940 Kinetic demo sample
AMYLASE3 Average1
0 - 164 0.0321 3.2087 0.0048 0.99924 Kinetic demo sample
AMYLASE4 Average2
0 - 199 0.0393 3.9326 0.0070 0.99899 Kinetic demo sample
AMYLASE5 Average2 33 - 232 0.0409 4.0872 0.0070 0.99903 Kinetic demo sample
AMYLASE6 Average3
5 - 232 0.0563 5.6334 0.0102 0.99867 Kinetic demo sample
AMYLASE7 Average3
5 - 196 0.0734 7.3422 0.0077 0.99911 Kinetic demo sample
AMYLASE8 Average4
5 - 196 0.0849 8.4933 0.0081 0.99911 Kinetic demo sample
AMYLASE9 Average4 79 - 227 0.0778 7.7821 0.0052 0.99934 Kinetic demo sample
Average1
Mean: 2.4156 1.1217
Average2
Mean: 4.0099 0.1093
Average3
Mean: 6.4878 1.2084
Average4
Mean: 8.1377 0.5029
Figure 14. Statistics result page with flexible slope ranges and blank correction. Average calculation
of two successive samples.
Another very useful feature of UV WinLab is the automatic linear range detection. In this mode the software will find automatically and calculate instantly the linear range of a kinetic curve and will take this
for enzyme activity
determination.
An example for this
is shown in Figure
15. Here a typical
kinetic curve (over
60 min) is shown.
This curve shows a
linear part. However, after about 30
minutes, the reaction gets slower due
to depletion of substrate and accumulation of product. The
software then is able
to detect the linear
part of the curve.
Figure 15. Automatic linear range detection.
This is highlighted
with a green background and will be taken for enzyme activity determination. In addition, the ideal linear curve fit is
shown. Together with this, the correlation coefficient is also displayed. This is to prove, that the linear
range is optimally found and still allows modification by the user.
KinLab allows to customize the report format in a individual way. You will get your kinetics report exactly in the way as you define it. Figure 16 shows a typical customized report of a 9 sample kinetic run
together with the graphics and results.
15
Perkin-Elmer UV Application Lab
Biochemical Analyses
Date: 19.02.97
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Time: 13:34:14
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A
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0,1
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0,0
20
40
60
80
100
120
Sec
140
160
180
200
220
240,0
0,84
Data recorded with LAMBDA Bio 20 UV Vis Spectrometer
Operator: Annelore Meissner
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KinLab allows to customize the report format in a individual
way. You will get your kinetics report exactly in the way
as you define it. Figure 15 shows a typical customized
report of a 9 samples kinetic run together with the graphics
and results.
A
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UV/Vis Spectrum of Indicator -->
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200,0
400
600
NM
Kinetic Results
_______________
Date:
Method:
20.09.96
KIN1.MKI
Time: 17:40:26
Range
Rate
Activity
Sample
Type
Sec
dA/min Factor U/L
Comments
----------------------------------------------------------------------------------MALTASE1 Blank
0 240 0.1225 122.09 0.0000
Blank
MALTASE2 Sample
0 240 0.0111 122.09 1.3595
Kinetic demo sample
MALTASE3 Sample
0 240 0.0223 122.09 2.7191
Kinetic demo sample
MALTASE4 Sample
0 240 0.0334 122.09 4.0786
Kinetic demo sample
MALTASE5 Sample
0 240 0.0445 122.09 5.4382
Kinetic demo sample
MALTASE6 Sample
0 240 0.0557 122.09 6.7977
Kinetic demo sample
MALTASE7 Sample
0 240 0.0668 122.09 8.1572
Kinetic demo sample
MALTASE8 Sample
0 240 0.0779 122.09 9.5168
Kinetic demo sample
MALTASE9 Sample
0 240 0.0891 122.09 10.876
Kinetic demo sample
Figure 16. Example for a user-defined, customized report.
16
700,0
3. Enzyme Mechanism Studies
UV KinLab allows easily to export data into other software package for further data evaluation. For example kinetic results can be transferred to a special software package for Enzyme mechanism studies,
called GraFit.
First we determine the slopes
from tests, where we vary the
substrate concentration and
keep all other parameters constant. Figure 17 shows the
schematics of an enzyme
mechanism study to describe
the v versus [S] curve, so that
vmax and Km can be determined.
Then the v versus [S] equation
is linearized by the method of
choice in GRAPHIT and the
Figure 17: Schematics of an enzyme mechanism study. Several enenzyme constants are
zyme tests are performed, where only the substrate concomputed.
centration is varied. The slope in the test increases with
increasing substrate concentration, to finally reach vmax
the maximum slope (a)). Then the slopes (reaction velocities) are plotted against substrate concentration (b).
0,06
R
a
t
e
Rate
0,04
Curve 1
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Results
Results
0
0
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1
[Substrate]
File : GPT01
Friday 26.07.96 10:57
Simple weighting
Enzyme Kinetics
Reduced Chi squared = 8,427e-007
___________________________________________________
Variable
Value Std. Err.
___________________________________________________
V max
Km
0.0637
0.2573
0.0011
0.0109
Figure 18: Michaelis Menten plot and result calculation,
performed with GraFit software from data
created with UV KinLab.
17
A realistic example is shown in Figure
18. In this case 25 triplicate kinetic runs
had been evaluated in UV KinLab. In
these 25 runs the enzyme activity (rate)
was determined each with a different
substrate concentration using UV
KinLab. UV KinLab itself allows to arrange the used substrate concentration
and the reaction rate in a way, that these
data are accepted by GraFit software.
Transfer is done with a mouse-click.
GraFit is a spreadsheet and data fitting
program, which is specialized for biochemical applications. A typical example
is a
Michaelis Menten plot which is easily
performed with GraFit, from data
recorded and evaluated with UV
KinLab. Other plots according to
Lineweaver Burk, Eadie Hofstee,
Hill etc. are also possible as well as
calculation of inhibitor constants and
many more.
4. Instrumental Requirements
Quality of kinetic data can only be as good as the raw data, produced by the spectrometer. Therefore it is
important to use a stable, high quality UV/Vis spectrometer for kinetics measurement. Below is a list of
some of the most important specifications, related to instrument requirements with respect to kinetic
measurements. These are the required specifications for biochemical kinetic analyses, as provided by the
PerkinElmer Lambda series UV/Vis spectrometers. These instrument systems including spectrometer,
intelligent software and accessories are ideal for precise and comfortable analysis in biochemistry and
biotechnology.
• Stability. The spectrometer for kinetic data collection must be stable, to avoid interference of the instrument drift with the actual absorbance changes from the sample. Most recommended would be a
double beam spectrometer with a drift specification smaller than 0.0002 A/h. With such a spectrometer
long term kinetic experiments can be performed without any interference from instrument drift.
• Reference compensation: In kinetic experiments often a blank is used, which itself shows a certain
change of absorbance during the experiment. In a double beam spectrometer this change of the blank
is automatically compensated, when putting the blank into the reference beam of the spectrometer.
• Straylight: Often it is difficult to predict, which final absorbance is reached during a kinetic experiment. In addition it is often the case, that the sample is opaque and thus shows high absorbance.
Therefore it is important that the UV/Vis Spectrometer is capable to measure linearily up to high absorbance range. This gives you the security, that you get linear kinetic plots, also when measuring at
higher absorbances, in microcells or with turbid samples. The straylight specification will give you an
estimation up to which absorbance levels it is possible to measure. A spectrometer with a straylight
specification < 0.01%T is very well suitable to measure up to about 3 absorbance units.
• Noise: When measuring at very low absorbance levels to detect small enzyme activities a spectrometer
with low noise specification is required. Noise specifications of
< 0.001 are sufficient to detect the
extremely low enzyme activities.
• Wavelength range: A monochromator based spectrometer with a wavelength range from 190-1100 nm will
allow to measure all types of enzyme
tests. In addition it will be possible to
record spectra and do protein and
DNA quantitations.
• Data interval: For fast kinetic analysis short measurement times with very
short cycle times are required. A
spectrometer with a data interval of
25 ms will be able to collect 40 data
per second.
MASSTAB
4:5
Figure 19: Water thermostated automatic 8-cell changer
for Lambda series spectrometers.
• Temperature control: Enzyme tests are very temperature sensitive. Therefore it is absolutely necessary to thermostat the sample during measurement. Sample and economical water thermostatted cell
holders should be available. Another possibility for cell thermostatting are Peltier controlled cell holders, which do not require an external water circulator.
18
Cell changer accessories: Enzyme tests are often time consuming. Normally a typical enzymatic test
will last about 10-15 minutes. Automated, thermostatted cell changers will help to reduce the measurement time for multiple samples, because they will accommodate up to 9 samples which can be
measured simultaneously. Water thermostatted 8-cell holders (see Figure 19) or Peltier thermostatted
9-cell changer systems are available for the PerkinElmer Lambda series of instruments.
19
PerkinElmer Instruments
761 Main Avenue, Norwalk, CT 06859-0010 U.S.A.
Tel: (800) 762-4000 or (203) 762-1000. Fax: (203) 762-6000
Internet: http://www.perkinelmer.com.
All analytical instruments and systems manufactured by PerkinElmer
are developed and produced under the quality requirements of ISO 9001.
PerkinElmer is a registered trademark of The PerkinElmer Corporation.
PerkinElmer Instruments © 2000
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August 2000
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