Enzymes Continued

Lecture 3

Fall 2007

Experimental Determination of Rate Parameters

• Non-linear equation – goal is to linearize it

• Double Reciprocal or Line-Weaver Burke Plot

• Eadie- Hofstee Plot

• Hanes Wolf Plot

SV

K

VvM 111

maxmax

S

vKVv M max

SVV

K

v

S M

maxmax

1

Plot 1/v vs 1/S Separates v and S Low S bias

Plot v vs v/S

Less bias on low S

Plot S/v vs S

More accurate Vmax

Example Plots

Line Weaver Burke

Eadie Hofstee

Hanes Wolf

More Complex Enzyme Models

• MM does not describe every substrate enzyme rxn, although it does a great job for many.

• Allosteric enzymes - more than one substrate binding site, binding of one substrate facilitates binding of another substrate molecule - cooperative binding.

• n = cooperativity coeff. and n > 1 indicates positive cooperativity.

nM

n

SK

Sv

dt

dSv

max

More Complex Enzyme Models

• Reversible Product Formation

S + E <----------> ES <-----------> E + P

• More than one Substrate

• Enzyme Inhibition– metal ions– high concentrations of substrate or product– other organic molecules

Enzyme Inhibition ModelsCompetitive

Competitive Inhibition - substrate and inhibitor compete for the enzymeS + E <------------> ES -----------> E + P (1)

E + I <--------> EI (2)

then = KM and = KI dissociation constants - check ratio for Ki

"KM" is effected in competitive inhibition KM, app = KM (1 + i/KI)

k1

k2k4

k3

k5

1

2

k

k

3

4

k

k

IM K

iKS

Svv

1

max

Enzyme Inhibition ModelsNon-competitive

Noncompetitive Inhibition - inhibitor and substrate bind simultaneously to enzyme, binding of one does not influence the affinity of either species to complex with the enzyme.

S + E <------------> ES -----------> E + P

E + I <--------> EI dissociation constant KI

EI + S <--------> EIS dissociation constant KM

ES + I <--------> EIS dissociation constant KI

KI

KM

KM

KI

Enzyme Inhibition ModelsNon-competitive

M

I

I

M

KS

KISv

v

ESI

IES

EI

IEK

ESI

SEI

ES

SEK

/1

][

]][[

][

]][[

][

]][[

][

]][[

max

Iapp KI

Svv

/1max

max,

The maximum velocity is affected

Enzyme Inhibition ModelsUncompetitive

Uncompetitive Inhibition - inhibitors bind to the enzyme substrate complex but not the enzyme itself.

S + E <------------> ES -----------> E + P

ES + I <--------> ESI dissociation constant KI

KI

KM

SK

SV

SKI

K

SKI

V

vappm

app

I

M

I

m

,

max,

/1

/1

Enzyme Inhibition ModelsSubstrate Inhibition

Substrate Inhibition - too much substrate

S + E <------------> ES -----------> E + P

ES + S <---------> ES2 dissociation constant KS1

1

max

1

2max

S

MM

SM K

SS

KK

Sv

KS

SK

Svv

Enzyme Inhibition ModelsSubstrate Inhibition

• Low substrate concentration S2/KS1 << 1 no inhibition observed

• High substrate concentration KM/S << 1 where inhibition dominates

SK

Svv

M max

1

max

1SK

S

vv

Enzyme Inhibition

• Can have any combination of effects.

• The "Mixed" case on Handout is a combination of noncompetitive and competitive inhibition.

Class ExerciseProblem 3.5 in textAn Inhibitor is added to the enzymatic reaction at a level of 1.0 g/L. The following data were obtained for KM= 9.2 g S/Lv S0.91 200.66 100.49 6.670.4 50.33 40.29 3.330.23 2.5

A) Is the inhibitor competitive or noncompetitive?

B) Find KI.

Other Things that Affect Enzymes – Focus on Binding Site

Other Things that affect enzymes

• pH

• Temperature

• Fluid forces - hydrodynamic forces, hydrostatic pressure and interfacial tension

• Chemical agents (alcohol, urea and hydrogen peroxide)

• Irradiation (light, sound, ionizing radiation)

pH

pH = log10(1/[H+]) = - log10[H+]

Ionization equilibrium of an acid

HA <-----> H+ + A-

Equilibrium constant

The pK of an acid is defined as

pK = - log K = log (1/K)

][

]][[

HA

AHK

pH Effects• Variations in pH effect the ionic form of the active site, changing the enzyme

activity and thus the reaction rate.Since enzymes contain amino acids they possess basic, neutral, or acid side groups which

can be positively or negatively charged at a given pH. For an acidic amino acid:

COOH COO-

(CH2)2 (CH2)2

-HN --- C --- CO- <-----> -HN --- C --- CO - Glutamic acid

H H

A <-----> A- + H+

At equilibrium pH = pK = 4.5

k1

k2

k2

k1

pH Effects

For a basic amino acid:

NH3+ NH2

(CH2)4 (CH2)4

-HN --- C --- CO- <-----> -HN --- C --- CO- Lysine

H H

Similarly the pK = 10

• So if the active site of an enzyme contains lysine and glutamine, the enzyme will be most active between 4.5 < pH < 10.

k1

k2

pH Effects

• a.     Each stage of deprotonation corresponds to a functional group

• (i)  First one on left is acid group• (ii) Second one is amino group• b.    Half-way through titration of

each group is point of inflection• (i)  pH = pKa• (ii) pKa is measure of tendency to

give-off proton• (iii) maximum buffer capacity

when pH = pKa

pH Effects

• pH may alter the 3-D shape of an enzyme

• pH may affect the maximum reaction rate Km

• pH may affect the stability of the enzyme

• pH may affect the affinity of the substrate to the enzyme if the substrate contains ionic groups.

• Examples - pepsin (stomach) 2< pH < 3.3, amylase (saliva) optimum 6.8

• Reaction Scheme and Rate Expression - Section 3.3.5.1 in text

Temperature Effects - activation• Acending part of graph -

temperature activation - rate varies according to Arrhenius equation:

v = k2 [E]

k2 = Ae-Ea/RT

• Ea - activation energy (kcal/mol) • [E] - enzyme concentration. • Plot of ln(v) versus 1/T straight

line with slope -Ea/R.

Temperature Effects - Inactivation

• Decending part of graph is the temperature inactivation or thermal denaturation.

•

• [E] = [E0]e-kdt

• [E 0] initial enzyme concentration

• kd denaturation constant, function of T

kd = Ade-Ed/RT

• Ed deactivation energy• v = Ae-Ea/RT [E0]e-kdt 

][][

Ekdt

Edd

Energy

• Ea = 4 to 20 kcal/mol

• Ed = 40 to 130 kcal/mol.

• Enzyme denaturation by temperature is much faster than enzyme activation.

• Increase T from 30 to 40 C, 1.8 fold increase in enzyme activity but 41 fold increase in enzyme denaturation.