Download Enzymes 1 and 2

Enzyme Kinetics
Lectures 1 and 2
August 21st 2009
Champion CS Deivanayagam
Center for Biophysical Sciences and Engineering
University of Alabama at Birmingham
Birmingham, AL 35294-4400
 What are enzymes, and what do they do?
 What characteristic features define enzymes?
 Can the rate of an enzyme-catalyzed reaction be defined in a
mathematical way?
 What equations define the kinetics of enzyme-catalyzed
reactions?
 What can be learned from the inhibition of enzyme activity?
 What is the kinetic behavior of enzymes catalyzing bimolecular
reactions?
 How can enzymes be so specific?
 Are all enzymes proteins?
 Is it possible to design an enzyme to catalyze any desired
reaction?
What are you supposed to know from the lecture: (for your exam )
1. Definitions of :
A. An Enzyme (catalytic power, specificity and regulation)
B. Co-enzyme, co-factors, holoenzyme, apoenzyme
C. Active site
2. How do enzymes affect the thermodynamics of a reaction ?
3. Understanding the Michaelis-Menten constants (Km, Vmax)
4. Define turn-over rate
5. Define catalytic efficiency
6. What are single and double displacement reactions ?
7. The lock and key as well as induced fit hypothesis as related to the specificity of enzymes
Virtually All Reactions in Cells Are Mediated by
Enzymes
• Enzymes catalyze thermodynamically favorable reactions,
causing them to proceed at extraordinarily rapid rates
• Enzymes provide cells with the ability to exert kinetic
control over thermodynamic potentiality
• Living systems use enzymes to accelerate and control the
rates of vitally important biochemical reactions
• Enzymes are the agents of metabolic function
Reaction profile showing the large free energy of activation for glucose
oxidation. Enzymes lower ΔG‡, thereby accelerating rate.
What Characteristic Features Define Enzymes?
• Catalytic power is defined as the ratio of the enzymecatalyzed rate of a reaction to the uncatalyzed rate
• Specificity is the term used to define the selectivity of
enzymes for their substrates
• Regulation of enzyme activity ensures that the rate of
metabolic reactions is appropriate to cellular
requirements
•
•
Enzyme nomenclature provides a systematic way of naming metabolic reactions
Coenzymes and cofactors are nonprotein components essential to enzyme activity.
Catalytic power
The ratio of the Enzyme-catalyzed rate of reaction to the
uncatalyzed rate
Enzymes can accelerate reactions as much as 1016 over
uncatalyzed rates
Urease is a good example:
O
||
H2N –C-NH2 + 2H2O + H+  2NH4+ + HHCO3Catalyzed rate: 3x104/sec
Uncatalyzed rate: 3x10 -10/sec
Ratio is 1x1014
Specificity
• Enzymes selectively recognize proper substrates over other
molecules
• Enzymes produce products in very high yields - often much greater
than 95%
• Specificity is controlled by structure - the unique fit of substrate
with enzyme controls the selectivity for substrate and the product
yield
Regulation
• Regulation of enzyme activity is essential to the integration and
regulation of metabolism.
• Availability of substrates and co-factors determines how fast the
reaction goes
• Genetic regulation of enzyme synthesis and decay determines the
amount of enzyme present at any moment.
Enzyme Nomenclature Provides a Systematic Way of
Naming Metabolic Reactions
• Suffix –ase added to the substrate is the traditional way of naming
enzymes
• Examples: Phosphotase, protease.
• Outliers: Trypsin, pepsin, catalase
• International commission on Enzymes
• Six classes of reactions (Oxidoreductases, Transferases,
Hydrolases, Lyases, Isomerases, Ligases).
• Each class has subclasses
• Depending on the type of reactions
Coenzymes and Cofactors are Nonprotein components
essential to Enzyme Activity
Co-factors: are generally metal ions
Co-Enzymes: Vitamins, NAD, TPP, FAD
Tightly bound co-enzymes are referred to as ‘Prosthetic groups’ of the enzyme, and such a
combination is called a ‘Haloenzyme’ and in the absence of the co-enzyme the protein is
referred to as ‘Apo-enzyme’
Can the Rate of an Enzyme-Catalyzed Reaction Be
Defined in a Mathematical Way?
• Kinetics is the branch of science concerned with the rates of
reactions
• Enzyme kinetics seeks to determine the maximum reaction velocity
that enzymes can attain and binding affinities for substrates and
inhibitors
• Analysis of enzyme rates yields insights into enzyme mechanisms
and metabolic pathways
• This information can be exploited to control and manipulate the
course of metabolic events
Several kinetics terms to understand
•
•
•
•
•
rate or velocity
rate constant
rate law
order of a reaction
molecularity of a reaction
Exploring Enzyme Kinetics
• Consider a reaction of overall stoichiometry as shown:
A P
d [ P ]  d [ A]
v

dt
dt
[ A]
v
 k [ A]
dt
• The rate is proportional to the concentration of A
Enzyme Kinetics
• The simple elementary reaction of A→P is a first-order reaction
• Figure shows the course of a first-order reaction as a function of time
• .
The half-time, t1/2 is
the time for one-half
of the starting amount
of A to disappear
•
•
•
•
•
This is a unimolecular reaction
For a bimolecular reaction, the rate law is:
v = k[A][B]
Kinetics cannot prove a reaction mechanism
Kinetics can only rule out various alternative hypotheses because they don’t fit
the data
Catalysts Lower the Free Energy of Activation for a Reaction
•
•
•
•
•
•
A typical enzyme-catalyzed reaction must pass through a transition state
The transition state sits at the apex of the energy profile in the energy diagram
The reaction rate is proportional to the concentration of reactant molecules with the
transition-state energy
This energy barrier is known as the free energy of activation
Decreasing ΔG‡ increases the reaction rate
G / RT
The activation energy is related to the rate constant by:
k  Ae
Understand the difference between G and G‡
• The overall free energy change for a reaction is related to the equilibrium constant
• The free energy of activation for a reaction is related to the rate constant
• It is extremely important to appreciate this distinction
What Equations Define the Kinetics of Enzyme-Catalyzed Reactions?
• Simple first-order reactions display a plot of the reaction rate as a function of
reactant concentration that is a straight line
• Enzyme-catalyzed reactions are more complicated
• At low concentrations of the enzyme substrate, the rate is proportional to S, as in
a first-order reaction
• At higher concentrations of substrate, the enzyme reaction approaches zeroorder kinetics
• This behavior is a saturation effect
[ES] Remains Constant Through Much of the Enzyme Reaction
Time Course in Michaelis-Menten Kinetics
Time course for a typical enzyme-catalyzed
reaction obeying the Michaelis-Menten,
Briggs-Haldane models for enzyme kinetics.
The early state of the time course is shown
in greater magnification in the bottom
graph.
d[ES]/dt = 0 defines a steady state
The Michaelis-Menten Equation is the Fundamental Equation of Enzyme Kinetics
•
Louis Michaelis and Maud Menten's theory
k1
E + S  ES
k-1
k-1[ES] = k1 [E][S]
Ks= k-1/ k1 = [E][S]/[ES]
Ks – enzyme:substrate dissociation constant
• The second step defines the formation of the product P
k1
k2
E + S  ES  E + P
k-1
Km = (k-1 + k2)/k1
Km is the Michaelis constant
ET = E + ES
k1
k2
E + S  ES  E + P
k-1[ES] = k1 [E][S]
k-1
ET = E + ES or alternatively E = ET -ES
Rate of formation
vf = k1 ([ET] – [ES]) [S)
Rate of disappearance
vd = (k-1 + k2)[ES]
Assume that the ES complex is in rapid equilibrium with free enzyme
At steady state d[ES]/dt = 0 then, Vf = Vd then
k1 ([ET] – [ES]) [S] / [ES] = (k-1 + k2)/k1 = Km or alternatively [ES] = [ET] [S]/ Km + [S]
Product formation: v = d[P]/dt = k2 [ES]
v= k2 [ET] [S] / Km + [S]
At saturation [ES] complex is equal to the total enzyme concentration ET , then
[S] >> [ET] (and Km), [ET] = [ES] and therefore
v = Vmax = k2 [ET] = Vmax [S] / Km + [S] -Michealis-Menton Equation
When [S] = Km, then V = Vmax / 2
Understanding Km
The "kinetic activator constant"
• Km is a constant
• Km is a constant derived from rate constants
• Km is, under true Michaelis-Menten conditions, an estimate of
the dissociation constant of E from S
• Small Km means tight binding; high Km means weak binding
The Km values for some enzymes and their substrates
Understanding Vmax
The theoretical maximal velocity
• Vmax is a constant
• Vmax is the theoretical maximal rate of the reaction - but it is NEVER
achieved in reality
• To reach Vmax would require that ALL enzyme molecules are tightly
bound with substrate
• Vmax is asymptotically approached as substrate is increased
The dual nature of the Michaelis-Menten equation
Combination of 0-order and 1st-order kinetics
• When S is low, the equation for rate is 1st order in S
• When S is high, the equation for rate is 0-order in S
• The Michaelis-Menten equation describes a rectangular hyperbolic
dependence of v on S
The Turnover Number Defines the Activity of One
Enzyme Molecule
A measure of catalytic activity
• kcat, the turnover number, is the number of substrate molecules
converted to product per enzyme molecule per unit of time, when
E is saturated with substrate.
• If the M-M model fits,
k2 = kcat = Vmax/Et
• Values of kcat range from less
than 1/sec to many millions per sec
The Ratio kcat/Km Defines the Catalytic Efficiency of an Enzyme
The catalytic efficiency: kcat/Km
An estimate of "how perfect" the enzyme is
• kcat/Km is an apparent second-order rate constant
• It measures how the enzyme performs when S is low
• The upper limit for kcat/Km is the diffusion limit - the rate at which E and S diffuse
together
Linear Plots Can Be Derived from the Michaelis-Menten Equation
derive these equations
• Lineweaver-Burk:
• Begin with v = Vmax[S]/(Km + [S]) and take the reciprocal of both sides
• Rearrange to obtain the Lineweaver-Burk equation:
1  Km

v  Vmax
 1  1


  [S ]  Vmax
• A plot of 1/v versus 1/[S] should yield
a straight line
• Hanes-Woolf:
• Begin with Lineweaver-Burk and divide both sides by [S] to obtain:
[S ]  1

v  Vmax

Km
[
S
]


Vmax

• Hanes-Woolf is best - why?
• Because Hanes-Woolf has smaller and more consistent errors across the plot
Enzymatic Activity is Strongly Influenced by pH
• Enzyme-substrate recognition and catalysis are greatly dependent on pH
• Enzymes have a variety of ionizable side chains that determine its secondary and
tertiary structure and also affect events in the active site
• Substrate may also have ionizable groups
• Enzymes are usually active only over a limited range of pH
• The effects of pH may be due to effects on Km or Vmax or both
The Response of Enzymatic Activity to Temperature is Complex
• Rates of enzyme-catalyzed reactions generally increase with increasing
temperature
• However, at temperatures above 50° to 60° C, enzymes typically show a decline
in activity
• Two effects here:
– Enzyme rate typically doubles in rate for ever 10°C as long as the enzyme is
stable and active
– At higher temperatures, the protein becomes unstable and denaturation
occurs
What Can Be Learned from the Inhibition of Enzyme Activity?
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•
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Enzymes may be inhibited reversibly or irreversibly
Reversible inhibitors may bind at the active site or at some other site
Enzymes may also be inhibited in an irreversible manner
Penicillin is an irreversible suicide inhibitor
Competitive Inhibitors Compete With Substrate for the Same Site on
the Enzyme
Lineweaver-Burk plot of competitive inhibition, showing lines for no I, [I], and 2[I].
The Vmax is unaffected, but the Km’s are affected by the inhibitor.
Pure Noncompetitive Inhibition – where S and I bind to different sites
on the enzyme
Lineweaver-Burk plot of pure noncompetitive inhibition. Note that I does not alter Km
but that it decreases Vmax.
Mixed Noncompetitive Inhibition: binding of I by E influences binding
of S by E
Lineweaver-Burk plot of mixed noncompetitive inhibition. Note that both
intercepts and the slope change in the presence of I.
Uncompetitive Inhibition, where I combines only with E, but not with ES
Lineweaver-Burk plot of uncompetitive inhibition. Note that both intercepts
change but the slope (Km/Vmax) remains constant in the presence of I.
What Is the Kinetic Behavior of Enzymes Catalyzing Bimolecular
Reactions?
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•
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Enzymes often catalyze reactions involving two (or more) substrates
Reactions may be sequential or single-displacement reactions
These can be of two distinct classes:
Random, where either substrate may bind first, followed by the other
substrate
• Ordered, where a leading substrate binds first, followed by the other substrate
Kinetic Behavior of Enzymes Catalyzing Bimolecular Reactions?
E + A + B  AEB  PEQ  E + P + Q
Single-deplacement bisubstrate mechanism.
Conversion of AEB to PEQ is the Rate-Limiting Step in Random, SingleDisplacement Reactions
In this type of sequential reaction, all possible binary enzyme-substrate and enzymeproduct complexes are formed rapidly and reversibly when enzyme is added to a
reaction mixture containing A, B, P, and Q.
Creatine Kinase Acts by a Random, Single-Displacement Mechanism
The overall direction of the reaction will be determined by the relative concentrations
of ATP, ADP, Cr, and CrP and the equilibrium constant for the reaction.
The structures of creatine and creatine phosphate,
guanidinium compounds that are important in muscle
energy metabolism.
In an Ordered, Single-Displacement Reaction, the Leading Substrate
Must Bind First
The leading substrate (A) binds first, followed by B. Reaction between A and B occurs
in the ternary complex and is usually followed by an ordered release of the products,
P and Q.
The Double Displacement (Ping-Pong) Reaction
Double-Displacement (Ping-Pong) reactions proceed via formation of a covalently
modified enzyme intermediate. Reactions conforming to this kinetic pattern are
characterized by the fact that the product of the enzyme’s reaction with A (called P
in the above scheme) is released prior to reaction of the enzyme with the second
substrate, B.
The Double Displacement (Ping-Pong) Reaction
Double-displacement
(ping-pong)
bisubstrate
mechanisms are
characterized by
parallel lines.
Glutamate:aspartate Aminotransferase
An enzyme
conforming to a
double-displacement
bisubstrate
mechanism.
How Can Enzymes Be So Specific?
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•
•
•
The “Lock and key” hypothesis was the first explanation for specificity
The “Induced fit” hypothesis provides a more accurate description of specificity
Induced fit favors formation of the transition-state
Specificity and reactivity are often linked. In the hexokinase reaction, binding of
glucose in the active site induces a conformational change in the enzyme that
causes the two domains of hexokinase to close around the substrate, creating
the catalytic site
A drawing, roughly to scale, of H2O, glycerol, glucose, and an idealized hexokinase molecule. Binding of glucose in the
active site induces a conformational change in the enzyme that causes the two domains of hexokinase to close around
the substrate, creating the catalytic site.
Are All Enzymes Proteins?
•
Ribozymes - segments of RNA that display enzyme activity in the absence of
protein
– Examples: RNase P and peptidyl transferase
• Abzymes - antibodies raised to bind the transition state of a reaction of interest
Is It Possible to Design An Enzyme to Catalyze Any Desired Reaction?
• A known enzyme can be “engineered” by in vitro mutagenesis, replacing active
site residues with new ones that might catalyze a desired reaction
• Another approach attempts to design a totally new protein with the desired
structure and activity
– This latter approach often begins with studies “in silico” – i.e., computer
modeling
– Protein folding and stability issues make this approach more difficult
– And the cellular environment may provide complications not apparent in the
computer modeling