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Enzyme Kinetics: Screencasts

Derives the rate expression for an enzyme reaction with a substrate to make a product using the rate-determining step approximation.

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Describes the three types if inhibition of enzyme reactions: competitive, noncompetitive, uncompetitive. 

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Important Equations:

Enzyme reactions with no inhibition

E+Sk1ES        (1)

ESk2E+S        (2)

ESk3P+E        (3)

E = enzyme, S = substrate (i.e., reactant), ES = enzyme-substrate complex, P = reaction products

The rate of consumption of substrate (rs) = rate of formation of products (rp)

Michaelis-Menten equation

rp=rs=k3[Et][S][S]+KM=Vmax[S][S]+KM     (a)

where [S] = substrate concentration

[Et] = total enzyme concentration = [E]+[ES]

[E] = concentration of enzyme

[ES] = concentration of enzyme-substrate 

KM=k2k1 = Michaelis-Menten constant

Vmax=k3[Et] = maximum rate of reaction

A linear plot is obtained by inverting eqn. (a) to yield the Lineweaver-Burke equation

1rs=1Vmax+KMVmax[S]    (b)

A plot of 1rs versus 1[S] is a straight line with an intercept of 1Vmax and a slope of KMVmax.

Although a linear plot can be obtained, nonlinear regression may be a better way to measure enzyme kinetic parameters (M. Marasovic, T. Marasovic, M. Milos, Robust Nonlinear Regression in Enzyme Kinetic Parameters Estimation, Journal of Chemistry, Vol 2017, Article ID 6560983.)

Enzyme reactions with competitive inhibition

E+Sk1ES        (1)

ESk2E+S        (2)

ESk3P+E        (3)

I+Ek4EI (inactive)       (4)

EIk5E+I          (5)

I = inhibitor, EI = enzyme-inhibitor complex

[EI] = concentration of an enzyme-inhibitor complex

rs=rp=Vmax[S][S]+KM(1+[I]KI)  (c)

1rs=1[S]KMVmax(1+[I]KI)+1Vmax   (d)

where [I] = inhibitor concentration

[EI] = concentration of enzyme-inhibitor complex

[Et] = total enzyme concentration = [E]+[ES]+[EI]

[KI]=k5k4 = inhibition constant

A plot of 1rs versus 1[S] is a straight line with an intercept of 1Vmax and a slope of KMVmax(1+[I]KI).

Enzyme reactions with uncompetitive (anti-competitive) inhibition: The inhibitor binds to the enzyme-substrate complex forming an inhibitor-enzyme-substrate complex.

E+Sk1ES                  (1)

ESk2E+S                  (2)

ESk3P+E                  (3)

I+ESk6IES (inactive)       (6)

IESk7I+ES       (7)

where IES = complex with both I and S bound to E

rs=rp=Vmax[S]KM+[S](1+[I]KI)      (e)

1rs=1[S](KMVmax)+1Vmax(1+[I]KI)    (f)

where KI=k7k6

A plot of 1rs versus 1[S] is a straight line with an intercept of 1Vmax(1+[I]KI) and a slope of KMVmax.

[Et] = total enzyme concentration = [E]+[ES]+[IES]

Enzyme reactions with noncompetitive (mixed) inhibition: The inhibitor can bind to the enzyme or enzyme-substrate complex. The substrate can also bind to the inhibitor-enzyme complex.

E+Sk1ES                  (1)

ESk2E+S                  (2)

ESk3P+E                  (3)

I+Ek4EI (inactive)   (4)

EIk5E+I                    (5)

I+ESk8IES (inactive)     (8)

IESk9I+ES       (9)

S+IEk10IES (inactive)    (10)

IESk11S+IE       (11)

where KI=k5k4=k9k8   KM=k2k1=k11k10

rs=rp=Vmax[S](KM+[S])(1+[I]KI)  (g)

1rs=1[S](KMVmax)(1+[I]KI)+1Vmax(1+[I]KI)   (h)

A plot of 1rs versus 1[S] is a straight line with an intercept of 1Vmax(1+[I]KI) and a slope of KMVmax(1+[I]KI).

Substrate inhibition: The substrate reacts with an enzyme-substrate complex to form an inactive substrate-enzyme-substrate complex.

E+Sk1ES                  (1)

ESk2E+S                  (2)

ESk3P+E                  (3)

S+ESk12SES (inactive)       (12)

SESk13S+ES                   (13)

rs=rp=Vmax[S](KM+[S]+[S]2KI)         (i)

1rs=1[S](KMVmax)+1Vmax(1+[S]KI)   (j)

where KI=k13k12

This plot is not linear because the y-intercept depends on the substrate concentration [S].