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Determination of Enzyme Kinetics Using Stopped-Flow Spectroscopy (SX Series Application Note)















Abstract: This study describes the use of an SX20 spectrometer to measure the presteady state kinetics of a well-studied enzymatic reaction. The hydrolysis of p-Nitrophenyl acetate catalysed by the enzyme α-chymotrypsin is studied. Kinetic parameters such as rate constants and the Michaelis-Menten constant are evaluated.




Author: James Law, PhD


Introduction

Stopped-fl ow systems manufactured by Applied Photophysics

Ltd have been used to determine enzyme kinetics for over three

decades as can be seen from the thousands of references in the

scientific literature. This study demonstrates the application of an

SX20 stopped-fl ow spectrometer to measure the pre-steady state

kinetics of a well-known enzymatic reaction. The reaction was

one of the first to be characterised by the stopped-fl ow technique

over 50 years ago. This is the hydrolysis of p-Nitrophenyl acetate

catalysed by the enzyme α-chymotrypsin.1 Extensive research over

the years has established the mechanistic details of this reaction.

α-chymotrypsin is a member of the serine protease enzyme family;

these proteins are ubiquitous throughout life where they carry

out their essential function in peptide bond hydrolysis. All serine

proteases execute their catalytic role at an active site consisting

of a catalytic triad. The triad invariably contains a Histidine, Serine,

and an Aspartic acid residue (Figure 1). The Serine residue acts as

a nucleophile on the target carbonyl group whereas the Histidine

and Aspartic acid residues involve themselves in hydrogen transfer

and hydrogen bonding. The steps in the catalysed hydrolysis of

p-Nitrophenyl acetate by α-chymotrypsin and trypsin are shown in the figure below


This reaction can be summarised in three steps by the following

reaction scheme:









Step (A) of the reaction is a pre-equilibrium that occurs much

faster than the subsequent two steps. The formation of acylated

enzyme intermediate is accompanied by the loss of the fi rst product

p-Nitrophenolate. It is this step that can be observed in the stoppedfl

ow experiment due to the intense absorption of light at 400 nm by

p-Nitrophenolate [P].


MATERIALS AND METHODS


Reactions were carried out using an SX20 fi tted with a 20μL optical

cell (2mm pathlength). The light source used was a 150W ozonefree

xenon lamp. Absorbance was measured at 400nm using the

standard SX20 photomultiplier tube. For each reaction, 1000 points

were recorded over a 60s time period. All drive volumes were 100μL.

All chemicals and reagents were purchased from Sigma-Aldrich.

60μM α-chymotrypsinin (20% Isopropyl alcohol, 20mM Phosphate

bu er, pH7.3) was mixed with p-Nitrophenolate (250μM to 8mM,

20% Isopropyl alcohol). The drive volumes were 200μL and 6

repeats were performed for each reaction with the averaged trace

being taken. The non-catalysed reaction was also recorded for

each concentration and subtracted from the equivalent catalysed

spectrum.

Results


The figure above shows the trace observed when α-chymotrypsin, 60μM,

is rapidly mixed with a 100-fold excess of p-Nitrophenyl acetate

in a SX20 spectrophotometer. The curve shows some interesting

features. Initially (i.e. 0-5s into the reaction), the rate of production

is relatively quick. This initial “burst” of p-Nitrophenolate formation

is followed by a linear steady state rate of production.

The shape of the curve can be explained if step (B) occurs rapidly

compared to the final deacylation step (C) which is ‘rate limiting’.

The pre-equilibrium in step (A) occurs too quickly to be observed

in the stopped-fl ow trace and therefore the initial observed rate

occurs when [ES] is at its highest concentration. At this point, the

rate of formation of p-Nitrophenolate depends only on step (B) of

the mechanism. This gives rise to the initial observable ‘burst phase’

of the reaction.

Like most enzymes, serine proteases display saturation kinetics;

that is, the initial rate of reaction approaches a hypothetical

maximum velocity, Vmax, as [S] is increased. Vmax is therefore the rate

of reaction when the enzyme is fully saturated i.e. all the enzyme

is in the form of [ES]. The above mechanism therefore follows the

Michaelis-Menten model of enzyme kinetics and the initial rate of

reaction (v0) can be describe by equation (1):


Vmax [S]

ν n = ____________

KM + [S]

Where KM represents the Michaelis-Menten constant. KM is defined as the concentration of substrate at which the initial rate of reaction is half that of Vmax and is a commonly used parameter for comparing substrate a nities in enzyme-substrate systems. The initial rate of reaction can be described by a rate constant, kobs, which represents the rate constant of the initial exponential phase of the reaction.

This constant can be easily obtained by fitting the observed trace to the equation (2) using the SX’s Pro-Data Viewer’s fitting function. (Single exponential plus slope)

Ae - k t + bt+ c

Figure below shows how kobs varies with substrate concentration, exemplifying the enzymes saturation kinetics, i.e. kobs approaches a maximum value (that of which would be obtained at Vmax and is equal to k2).

It can be shown that under these conditions ([S]>>[E]) the value of

kobs can be described by equation (3): note the similarity to equation (1).

k2 [S]

kobs = _________

KM + [S]

We can fit the data to this equation using non-linear least squares

regression to obtain parameters for k2 and KM. This was performed

using the Solver Add in in Microsoft ExcelTM. The values extracted

are shown in Table 1.

Alternatively, this equation can be rearranged to the following:

1 Km 1 1

____ = __ __+ __

K obs k2 [S] k2


The values of KM and k2 can be evaluated by measuring the fi rst order rate constant at increasing initial substrate concentrations. Plotting a graph of 1/kobs against 1/[S] gives a straight line graph with slope equal to KM/k2 and intercept equal to 1/k2. 3,4 Figure 5 shows this plot obtained with α-chymotrypsin (30μM with p-Nitrophenolacetate concentrations ranging from 125μM to 4mM.


Although it is generally considered that non-linear regression is a

more accurate method for analysis, in this case we obtain similar

values using both fitting methods.5

Once the reaction has reached the steady state, the rate of reaction

depends only on step C in Figure 3. This is because it is much slower

than the preceding two steps and is thus rate-determining. We can

determine the steady state rate of reaction from the linear part of

the trace in Figure 4 because we can relate the absorbance change

to the change in p-Nitrophenolate concentration according to Beer-

Lambert Law. From the mechanism of this reaction, it is clear that

the amplitude of the burst phase, i.e. point at which an extrapolation

of the linear phase touches the y-axis, is approximately equal to the

amount of active enzyme; this gives us a value for [Ea] from which

we can determine k3 via equation (5) (implied from Figure 3).3 The

value of k3 was therefore assessed from each trace and the average

value was calculated to be 0.016s-1.

k3 = d [Q] / dt

_________

[Ea]








Conclusion

Applied Photophysics Ltd’s SX20 stopped-flow spectrometer can be used to study the pre-steady state kinetics of enzymatic reactions. Here, kinetic parameters of the enzymatic hydrolysis of p-Nitrophenolacetate were obtained. Although this is a relatively

slow reaction, SX20 stopped-flow spectrometers have the capacity to measure kinetics from 0.5ms after mixing.


References

1. Gutfreund, H. & Sturtevant, J.M. The mechanism of the reaction of chymotrypsin with p-nitrophenyl acetate. The Biochemical Journal 63, 656-61 (1956).

2. Hedstrom, L. Serine protease mechanism and specificity. Chemical Reviews 102, 4501-24 (2002).

3. Bender, M., Kezdy, F. & Wedler, F. α-Chymotrypsin : Enzyme Concentration and Kinetics. Journal of Chemical Education 44, 84-88 (1967).

4. Gutefreund Kinetics For The Life Sciences. (Cambridge University Press: Cambridge, 1995).

5. Leatherbarrow, R.J. Using linear and non-linear regression to fit biochemical data. Trends in Biochemical Sciences 15, 455-8 (1990).