enzyme inhibits plots
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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.
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