Evaluation of Michaelis-Menten Parameters

Kinetic parameters for several enzymes It is important to have a feel for the magnitudes of the kinetic constants, k and 1/K M, for certain enzymes. The table in the net slide sho!s the range of values encountered for several di"erent enzymes. #otice that almost all the eperiments reported !ere performed at moderate temperatures and p$ values. The eception is pepsin, !hich has the task of hydrolyzing proteins in the acid environment of the stomach. %onse&uently, the enzyme has the greatest activity under the acidic conditions employed in the eperimental determination of its kinetic parameters.

Kinetic parameters for several enzymes Enzyme 'epsin

Trypsin

%hymotryp sin

Substrate

Temp, C

pH

k3, s – 1

1/K, 

%arbobenzoy()( tyrosine ethyl ether

*1.+

.-

-.--1-

*-

%arbobenzoy()(

*1.+

.-

-.--11

+-

glutamyl()(tyrosine 0enzoyl()( argininamide

.

2.

2.-

-

%hymotrypsinogen

13.+

2.

,3--

422-

5aturin

.

2.

1*,1--

--

0enzoyl()(arginine ester

.-

.-

+.2

1,--

Methyl hydrocinnamate

.-

2.

-.-+

+

Methyl dl(α(chloro(β( hen l ro ionate

.-

2.

-.1*

*.*

– 1

Kinetic parameters for several enzymes Enzyme

Substrate Methyl l(β( phenyllactate

Temp, C

pH

.-

2.

k3, s – 1

1/K,  – 1

1.*

1--

6valuation of Michaelis(Menten 'arameters 7 series of batch runs !ith di"erent levels of substrate concentration is made in order to estimate the values of the kinetic parameters. The results are plotted graphically so that the validity of the kinetic model can be tested and the values of the kinetic parameters can be estimated.

The most straightfor!ard !ay is to plot r against %5

The asymptote for r !ill be rma and KM is e&ual to %5 !hen r 8 -.rma. $o!ever, this is an unsatisfactory plot in estimating rma and KM because it is di9cult to test the validity of the kinetic model. Therefore, the Michaelis(Menten e&uation is usually rearranged so that the results can be plotted as a straight line.

The Michaelis(Menten e&uation is rearranged to be epressed in linear form. 5ome of the better kno!n methods are: ;a< plot ;b< )angmuir )ine!eaver(0urk plot ;c< 6adie($ofstee plot

)7#=M>I? ')@T • 7lso kno!n as Hanes!"oolf plot • 'roponents of this method are: – %harles 5amuel $anes – 0arnet Aoolf

• This e&uation !as given by )angmuir for the treatment of data from the adsorption of gas on a solid surface.

CS r

=

KM rmax

+

1

rmax

CS

• ?efer to Bigure ., p. , Cames )ee

5lope: 1/rma and intercept: KM/rma

)I#6A67D6?(0>?K ')@T • 7lso kno!n as #ouble reciprocal plot • 'roponents are: – $ans )ine!eaver – Eean 0urk

1

r

=

1

rm ax

+

KM

1

rm ax C S

• ?efer to Bigure ., p. , Cames )ee – 5lope: KM/rma – Intercept: 1/rma

67EI6($@B5T66 EI7=?7M • 7lso kno!n as: – Aoolf(6adie(7ugustinsson($ofstee – 6adie(7ugustinsson

r

= rmax − K M

r CS

• ?efer to Bigure .+, p. , Cames )ee – 5lope: −KM – Intercept: rma

@bservations: • The )ine!eaver(0urk plot is more often employed than the other t!o plots because it sho!s the relationship bet!een the independent variable %5 and the

dependent variable r. $o!ever, 1/r approaches inFnity as %5 decreases, !hich gives undue !eight to inaccurate measurements made at lo! substrate concentrations, and insu9cient !eight to the more accurate measurements at high substrate concentrations. The points on the line in Bigure . represent seven e uall s aced substrate concentrations.

@bservations • The 6adie($ofstee plot gives slightly better !eighting of the data than the )ine!eaver(0urk plot. 7 disadvantage of

this plot in is that rate of reaction appears boththe coordinates !hile itris usually regarded as a dependent variable. • 0ased on the data distribution, the )angmuir plot is the most satisfactory of the three, since the points are e&ually spaced.

ummary$ In conclusion, the values of MM kinetic parameters, rma and KM can be estimated as follo!s: 1. Make a series of batch runs !ith di"erent levels of substrate concentration at a constant initial enzyme concentration and measure the change of product or substrate !ith respect to time. . 6stimate the initial rate of reaction from the %5 or %' versus time curves for di"erent initial substrate concentrations.

ummary$ In conclusion, the values of MM kinetic parameters, rma and KM can be estimated as follo!s:

*. 6stimate the kinetic parameters by plotting one of the three plots eplained in this section. It is important to eamine the data points so that you may not include the points !hich deviate systematically from the kinetic model.

6ample .* Brom a series of batch runs !ith a constant enzyme concentration, the follo!ing initial rate data !ere obtained as a function of initial substrate concentration. CS %mmol/ &'

1

(

3

)

*

1+

1)

(+

Initial rn rate, r ;mmol/) Gmin<

-.-

-.

-.*-

-.

-.1

-.-

-.-

-.**

a. 6valuate the Michaelis(Menten kinetic parameters by employing the )angmuir plot, the )ine!eaver(0urk plot, the 6adie($ofstee plot. In evaluating the kinetic parameters, do not include data points !hich deviate systematically from the Michaelis(Menten model and eplain the reason for deviation. b. Ahich of the three methods employed gives the best estimate of the kinetic parametersH c. ?epeat part ;a< by using all data.

'roblem . 6adie ;13< measured the initial reaction rate of hydrolysis of acetylcholine ;substrate< by dog serum ;source of enzyme< and obtained the follo!ing data:

Substrate Concn %mol/&'

+ ++3(

+ ++-.

+ ++(

+ ++0+

+ ++.)

Initial ?n ?ate ;mmol/)∙mi n)

-.111

-.1

-.1*

-.1++

-.--

'roblem .1 6adie ;13< measured the initial reaction rate of hydrolysis of acetylcholine ;substrate< by dog serum ;source of enzyme< in the absence and presence of prostigmine ;inhibitor