Enzymatic Catalysts 3

K_M

michealis constant

higher enzyme binding affinity

higher K_m=

weaker affinity

k_cat (turnover number or catalytic constant)

speed of catalysis

measures product formation (substrate turnover)

higher k_cat →

higher speed

V_max

related to K_cat and [E_t]

V_max=

k_cat[E_t]

higher V_max →

higher max rate

k_cat/K_M

measure of catalytic efficiency of enzyme

Michaelis constant (k_m)

enzyme binding affinity unit in M

enzyme conservation equation

[E]=[E_t]-[ES]

Michaelis-Menten equation

V=V_max[S]/(K_m+[S])

substrate constant

K_S

K_M=

(k_-1+k₂)/k₁

higher K_m=

weaker binding between E and S

The rate is half-maximal when

[S]=K_M

Association of E+S only limited by

diffusion (k₁=10⁹ M^-1sec^-1)

weak binding affinity has a high

off rate (k_-1=10⁴ sec^-1)

Lineweaver-Burk Plot

(1/v_o)=(K_M/V_max)((1/[S])+(1/V_max))

Slope of lineweaver-burk plot

K_M/V_max

X-intercept of lineweaver-burk plot

-1/K_M

Y-intercept of lineweaver-burk plot

1/V_max

cluster of points at high [S] in the lineweaver-burk plot

easy to introduce experimental errors

Lineweaver-burk plot is also known as the

double reciprocal plot

k_cat is the 

turnover number or catalytic constant

measure of enzyme’s maximal catalytic activity

k_cat

V_max=k_cat[E_t] →k_cat=

V_max/[E_t]

in a simple reaction k_cat=

k₂

k_cat/K_M describes the efficiency of E when

[S] not saturated

[k₂/(k₂+k_-1)] cannot exceed

1

upper limit of k_cat/K_M<k₁ is the

rate of diffusion of S into the enzyme’s active site

rate constant for diffusion in water

10⁸-10⁹ (M^-1sec^-1)

many enzymes have k_cat/K_M ratios of

10⁸-10⁹

enzymes that have k_cat/K_M ratios of 10⁸-10⁹ mean that

they have achieved catalytic perfection

Examples of drugs that are enzymatic inhibitors

penicillin

lovastatin

ritonavir

how does penicillin inhibit enzymes

inhibits enzyme cross-linking peptidoglycan stands in bacterial cell walls

how does lovastatin inhibit enzymes

inhibits HMG-CoA reductase, a key enzyme in cholesterol biosynthesis

how does ritonavir inhibit enzymes

inhibits HIV protease

“statin”

blocks sterols

types of enzyme inhibition

irreversible or reversible

Irreversible inhibition

stable, covalent, permanent alteration of enzyme

reversible enzyme inhibition

noncovalent association with enzyme or enzyme-substrate complex or both

3 main types of reversible inhibition

competitive inhibition, uncompetitive inhibition, noncompetitive inhibition

competitive inhibition

reduces the steady state [ES]

effect of inhibitor can be overcome by adding excess substrate.

competitive inhibition is structurally similar to S competes with S for

for active site binding

reduces the steady state [ES]

fraction of enzymes trapped in EI

Enzyme conservation equation

[E_t]=[E]+[ES]+[EI]

K_eq for EI complex

K_I=[E][I]/[EI] and then [EI]=[E][I]/K_I

at equilibrium (V_{(ES formation)}=V_{(ES disappearance)})

[E]=[ES]K_M/[S]

competitive inhibitor

no change to V_max

Alters K_M→K_M(1+[I]/K_I)

More [S] → outcompetes inhibitor →

achieves the same V_max at higher [S]

for competitive inhibitors- [S]>K_M to reach

½ V_max

competitive inhibitors make the lineweaver-burk plot

slope steeper

competitive inhibitor moves X-intercept towards

axis intersection

Competitive Inhibitor Y-intercept for Lineweaver-Burk plot

Stays the same

Competitive inhibitor for lineweaver-burk plot when apparent K_M rises but

V_max stays the same

Competitive inhibition binds only __ but not free enzyme

ES

Uncompetitive inhibition

V₀=(V_max/α’)/(K_M/α’ +[S])

uncompetitive inhibition α’=

1+([I]/K_I’)

uncompetitive inhibitor changes both K_M and

V_max

Uncompetitive inhibitor alters the positions of ___ for lineweaver-burk plot

X and Y intercepts

uncompetitive inhibitor for lineweaver-burk plot is a series of

parallel lines

lineweaver-burk plot for uncompetitive inhibitor ___ change

K_M and V_max

lineweaver-burk plot for uncompetitive inhibitor (does/doesn’t) change the slope

doesn’t

noncompetitive (mixed) inhibition binds to ___

E and ES

noncompetitive inhibition

V₀=((V_max/α’)[S])/((α/α’)K_m+[S])

Noncompetitive inhibition α=

1+([I]/K_I

noncompetitive inhibition α’=

1+([I]/K_I’)

(noncompetitive inhibition) if α=α’, 

NI does not change K_M but alters V_max

NI changes the slope

steeper

(lineweaver-burk plot) NI: when K_I=K_I’

Y int. moves up

V_max ↓