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Overview of Kinetics
Velocity of reaction
∆[𝑃]
= ν = 𝑘[𝑆]
∆𝑡
Rate of reaction
M/sec
1st order reaction-rate depends on
concentration of one reactant
S  P
∆[𝑃]
= ν = 𝑘[𝑆]
∆𝑡
Conc. of reactant(s)
Rate constant
sec-1, M-1 sec-1
2nd order reactions may
Depend on two reactants
S1 + S2  P
∆[𝑃]
= ν = 𝑘[𝑆1 ] 𝑆2
∆𝑡
Review of Kinetics
Most of the time reactions obtain equilibrium
k1 and k-1 are the rate constants for forward
And reverse reactions
𝐾𝑒𝑞
[𝑃]𝑒𝑞
𝑘1
=
=
[𝑆]𝑒𝑞 𝑘−1
Kinetic rate constants
are useful in determining
equilibrium chemistry
When equilibrium is reached: rate of forward and reverse reactions are the same.
Determination of rates and rate constants
Method of initial rates (Vo) at different [S]o to determine
rate constants
-measure Vo very early in the reaction
-very little product has formed (equilibrium is not a factor)
Figure 7.2
[S]o
Enzyme Kinetics
E = enzyme
S = substrate
P = product
ES = enzyme–substrate complex
k1 = rate constant for ES binding
-IF k1 is very large, binding is very favorable
k2 = rate constant for P formation from ES
- IF k2 is very large, conversion to product is fast.
This enzymatic reaction depends upon both the [E] and [S]
Enzyme Kinetics
- A more common reaction scheme or mechanism
involves a reversible binding of E and S.
Define a dissociation constant (Kd), measure
of S binding to E.
𝑘−1
𝐾𝑑 =
𝑘1
If k1 >> k-1, S binding is
very favorable.
A small value for Kd means binding is favorable
Enzyme kinetics terminology
[S] – substrate concentration
Vo – initial velocity of a reaction. A significant amount of
substrate has not yet been converted to product.
Vmax – maximal velocity of a reaction. Addition of more
substrate will not increase the rate of the reaction.
KM – The concentration of substrate at which the rate
of the reaction is half-maximal
A commonly observed behavior for enzyme catalyzed reactions
showing the change in Vo as [S] is changed
This region is zero order in [S]
This region is 1st order in [S]
This behavior can be described mathematically by the
Michaelis-Menten equation
Vmax [S]
Vo =
K M +[S]
k2 (called kcat) is a measure of the number of substrate molecules
converted to product per second per enzyme molecule
kcat is called catalytic constant
and is determined at high [S]
kcat/KM is a rate measure of catalytic efficiency for the
conversion of E + S  E + P
Turnover numbers (kcat)
CO2 + H2O HCO3(1.7 microseconds (ms) per reaction)
Chymotrypsin catalyzes peptide cleavage
(0.01 sec per cleavage)
Experimental method for determining Vmax and KM
Figure 7.5
Plot the reciprocal of
The Michaelis-Menten
Equation.
A linear equation
is generated
Allosteric enzymes and regulation
Figure 7.7
These complex metabolic pathways must be regulated.
Regulation of metabolic pathways
In Feedback Inhibition, high concentration of the product of a pathway
controls the rate of its own synthesis by inhibiting an early step
Flux through the pathway is regulated depending on the
concentration of Product (K below)
In Allosteric Activation, high concentration of a metabolite early in the
pathway activates enzymes for synthesis of the final product.
Flux through the pathway is regulated depending on the
concentration of Metabolites (F and I below)
Feed-Forward Activation
- Metabolite early in the pathway activates an enzyme further
down the pathway
B is an allosteric activator
Figure 7.11 Effect of regulators on aspartate transcarbamoylase
CTP
ATP relaxes the enzyme (R state favored)
Binding of substrates more favored
CTP makes enzyme more “tense” (T state
favored) binding of substrates less favored
Regulation by covalent modification
Enzyme activity can be modified by covalent attachment
and removal of groups on the polypeptide chain
 reversible phosphorylation
Pyruvate dehydrogenase
catalyzes a reaction that link
glycolysis and the citric acid cycle.
Phosphate is removed
from serine residue
 reactivated form
Phosphate is attached
to serine residue
 Inactive form
Assignment
Read Chapter 7
Read Chapter 8
Topics not covered:
Concerted and Sequential models
Section 7.4 Enzymes can be studied one molecule at a time.