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Enzyme Kinetics…
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
Enzymatic catalysis
Role of enzymes
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serve the same role as any other catalyst in chemistry
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act with a higher specificity
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acid and base catalyst possible due to proximal locations of amino acids
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alter the structure location of quantity of the enzyme and you have regulated the formation of product - try that
in organic chemistry !
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Don't lose sight of what enzymes do. catalyze reactions – nothing more
reactants -> products.
What do Enzyme ACTUALLY do?
Naming Enzymes
•Enzyme commission for each enzyme based on the type of reactions. Kind of like
IUPAC
•Yeah right - the mother of invention – he/she who finds/discovers/purifies/clones the
enzyme, names if. Trivial names rule…
• First recognition of an enzyme and naming – 1833: alcohol precipitate of malt extract converted starch into sugar – called diatase (first use of suffix –ase)
• Proteases traditionaly are the only enzymes w hich don’t end in ‘ase’ and use ‘-­‐in’ • Enzyme is coined after the Greek for “in yeast”
• 1050s started need to use a standardized naming: Otto Hofmann-­‐Ostenhof and Dixon & W ebb – common, non-­‐systematic names still rule.
Enzyme Nomenclature Provides a Systematic Way of Naming Metabolic Reactions
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Enzyme reaction types: Enzymes are classified into six major classes based on the reaction they catalyze.
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Enzyme specificity
- One of the most powerful actions of enzymes.
Group complementation - the ability to recognize specific regions of the substrate to align reactants with catalytic site.
Based on non-covalent molecular interactions.
Lock and key vs. induced fit - both occur. Induced fit takes place when binding of one part of the substrate to the
enzyme alters the conformation of the enzyme to make a true "fit"
Binding does not mean activity
Enzyme specificity
An enzyme can bind and react stereo-specifically with chiral compounds
This can happen due to a three point attachment
– Binding can then only occur in one way and therefore the products are not a mixture.
General Information on Enzymology
Enzyme nomenclature
• Active site
Substrate vs. reactant
• Prosthetic groups, coenzyme and cofactors
• Activity vs. reaction
Suffix -ase
Another important reminder - not all activity is on or off. Many times the enzyme has a low or constitutive activity that
can be increased many times. It is a common mistake to think of enzymes being on or off.
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Cofactors
Group transfer, redox and some acid base reactions need additional components, aa alone is not sufficient for
reaction
• Cofactors – metals (Cu, Fe, Zn),
• Cofactors – organics molecs (coenzymes) often converted from vitamins
Job of Enzyme Catalysts
Specifically bind substrate(s) (reactants), decrease transition state energy to increase the rate (NOT
thermodynamics) of a favorable reaction:
• High specificity
• Low side reactions
• Ability to be regulated: Active site – amino acids and cofactors binding and “doing” the reaction, are regulated
by the rest of the protein
How do enzymes work?
• By reducing the energy of activation
• This happens because the transition state is stabilized by a number
of mechanisms involving the enzyme/protein
• Without enzymes reactions occur by collisions between reactants or
addition of various organic catalysts
• The energy barrier between the reactants and product, is the free
energy of activation.
• The free energy (ΔG) of the reaction is what determines if a reaction
is spontaneous.
The overall free energy of a reaction, ΔG, is independent of the free
energy of activation. So if the ΔG is less than zero the reaction will proceed once a catalyst is added (the enzyme).
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But the converse is also true - the reverse reaction is also able to proceed depending on the ΔG. Some
reactions have very little changes free energy and are freely reversible. Availability of enzyme (catalyst) and
the relative concentrations of products and reactants will decide which direction these reactions will go.
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Enzyme Kinetics
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 the 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
Rates of a reaction…
Molecularity – the number of molecules that must collide/interact for a reaction to occur.
• For enzymes, molecules that are involved at the active site for a step of the reaction.
• Unlike non-enzyme catalyzed reactions, the rate is too complex but often initially described as unimolecular or
bimolecular
• Remember, order – refers to rate equation, while molecularity defines the mechanism
Gen Chem – Rates of Reaction…
Quick Review – MOST enzymes catalyze reactions in a first or second order reaction.
- Less about collisions of freely moving molecules than binding and reacting on a surface of a catalyst (enzyme
active site):
For single/uni-molecularity reactions –
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1 order A->P
The rate is proportional to the concentration of substrate
Simple rate laws don’t easily apply
• 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
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nd
order reaction (bimolecular)
A + B -> P + Q
2A -> P + Q
Typical biochemical reaction – few if any enzyme catalyzed reactions are higher than second-order
Rate of reaction is dependent on concentration of both A and B.
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Enzyme Kinetics
Kinetic defn.: Of or relating to or produced by motion.
Kinetics defn.: the branch of chemistry or biochemistry concerned with measuring and studying the rates of
reactions.
Enzyme kinetics are defined differently than basic chemistry kinetics because of the large catalyst…
Measuring Rates of Enzyme Catalyzed Reactions
Louis Michaelis and Maud Menten's theory
assumes the formation of an enzyme-substrate complex
assumes that the ES complex is in rapid equilibrium with free enzyme
assumes that the breakdown of ES to form products is slower than
1) formation of ES and
2) breakdown of ES to re-form E and S
Enzyme Kinetics
An enzyme-catalyzed reaction of substrate S to product P, can be written
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Actually, the enzyme and substrate must combine and E recycled after the reaction is finished, just like any catalyst.
Because the enzyme actually binds the substrate the reaction can be written as:
The simplest reaction is a single substrate going to a single product.
Rate or velocity of the reaction depends on the formation of the ES
•The P -> ES is ignored
•The equilibrium constant Keq is based on the idea that the reaction is limited to the formation of the ES complex
and that only K1 and K-1 are involved because the thermodynamics of the reversal of K2 cause it to be minimal
How fast an enzyme catalyzes a reaction is it's rate. The rate of the reaction is in the number of moles of product
produced per second
[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.
Enzyme-Catalyzed Reactions
• The relationship between the concentration of a substrate and the rate of an
enzymatic reaction is described by looking at the concentration of S and v
• 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
Psuedo First Order Kinetics
For the most part enzyme reactions are treated as if there is only one
substrate and one product.
If there are two substrates, one of them is held at a high concentration (0 order) and
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the other substrate is studied at a lower concentration
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so that for that substrate, it is a first order reaction.
This leads us to the M and M equation.
•Mathematical model of the representation of the M&M eq. For the reaction:
1) The Michaelis constant Km is:
Think of what this means in terms of the equilibrium.
Large vs. a small Km
2) When investigating the initial rate (Vo) the Michaelis-Menten equation is:
Graphical representation is a hyperbola. Think of the difference between O2 binding of myoglobin and hemoglobin.
•When [S] << Km, the velocity is dependent on [S]
•When [S] >> Km, the initial velocity is independent of [S]
•When [S] = Km, then Vo = 1/2 V max
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
Understanding KmThe "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
Conditions for Michaelis -Menten
Two assumptions must be met for the Michaelis-Menten equation
1) Equilibrium -the association and dissociation of the substrate and
enzyme is assumed to be a rapid equilibrium and Ks is the
enzyme:substrate dissociation constant.
Two Assumptions…
2) Steady state - the enzyme substrate complex ES is at a constant value.
That is the ES is formed as fast as the enzyme releases the product. For
this to happen the concentration of substrate has to be much higher than
the enzyme concentration. That is why we only study the initial velocity.
Later in the reaction the substrate concentration is relatively lower and the
rate of product starts to be limited by diffusion and not the mechanism of
the enzyme.
Don't for get the two assumptions - They both lead to the same equation,
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the michaelis-menten equation.
What is this awe inspiring equation? The Michaelis-Menten kinetic model explains several aspects of the behavior of
many enzymes. Each enzyme has a Km value that is characteristic of that enzyme under certain conditions.
Determining Km and Vmax
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Must be done experimentally/emperically
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Measure rate of enzyme vs different concentrations of substrate
BUT YOU CAN’T GET THERE FROM HERE
Create a secondary plot to determine kinetic constants
Linear Plots Can Be Derived from the Michaelis-Menten EquationLineweaver-Burk:
Begin with v = Vmax[S]/(Km + [S]) and take the reciprocal of both sides
Rearrange to obtain the Lineweaver-Burk equation:
A plot of 1/v versus 1/[S] should yield a straight line
Linear Plots Can Be Derived from the Michaelis-Menten Equation
Hanes-Woolf:
Begin with Lineweaver-Burk and multiply both sides by [S] to obtain:
Hanes-Woolf is best - why?
Because Hanes-Woolf has smaller and more consistent errors across the
plot
Other uses of Km
The Turnover Number Defines the Activity of One Enzyme Molecule
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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 Turnover Number Defines the Activity of One Enzyme Molecule
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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 well 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
The Ratio kcat/Km Defines the Catalytic Efficiency of an Enzyme
So What? Or WDIC?
Km
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Km - relates to affinity ; Vmax relates to efficiency
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Km tell how much substrate to use in an assay
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If more than one enzyme share the same substrate, KM also will determine how to decide which
pathway the substrate will take
Vmax tells about pathways
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Rate limiting enzyme in pathway
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Km and Vmax can be used to determine effectiveness of inhibitors and activators for enzyme studies and
clinical applications
Enzyme Inhibitors
Molecules which bind and act to alter the reaction kinetics of an enzyme. By binding to enzyme reducing the affinity,
velocity, catalytic turnover or all of the above. - examples include poisons and drugs
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Some inhibitors reversibly bind directly to active site competing with normal substrate (competitive inhibitor)
Some inhibitors reversibly bind to the protein away from active site – altering structure of protein so the
enzyme does not function (either won’t bind or won’t react substrate). Non and Un-competitive and
allosteric…
Other inhibitors bind covalently (irreversibly) to the active site, leaving the enzyme “dead”. Suicide Inhibitor
Competitive Inhibitors Compete With Substrate for the Same Site on the Enzyme
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Lineweaver-­‐Burk plot of competitive inhibition, showing lines for no I, [I], and 2[I].
Km is reduced but Vmax is unchanged
Uncompetitive Inhibition, where I combines only with E, but not with ES
Note that both intercepts change but the slope (K /V
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the presence of I.
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max
) remains constant in 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 K but that it decreases V .
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max
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.
Enzymes Can Be Inhibited Irreversibly
Penicillin is an irreversible inhibitor of the enzyme glycoprotein peptidease, which catalyzes an essential step in
bacterial cell all synthesis.
Note the similarities in the structures of cGMP (left) and Viagra (right). Viagra produces an increase in [cGMP] in
penile vascular tissue, allowing vascular muscle relaxation, improved blood flow, and erection.
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Kinetic Behavior of Bimolecular Reactions?
Enzymes often catalyze reactions involving two (or more) substrates
Bisubstrate reactions may be sequential or single-displacement reactions or double-displacement (ping-pong)
reactions
Single-displacement reactions can be of two distinct classes:
1. Random, where either substrate may bind
first, followed by the other substrate
2. Ordered, where a leading substrate binds first, followed by the other substrate
Conversion of AEB to PEQ is the Rate-Limiting Step in Random, Single-Displacement Reactions
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In this type of sequential reaction, all possible binary enzyme-substrate and enzyme-product complexes are
formed rapidly and reversibly when enzyme is added to a reaction mixture containing A, B, P, and Q.
In an Ordered, Single-Displacement Reaction, the Leading Substrate Must Bind First
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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
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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.
How Can Enzymes Be So Specific?
Are All Enzymes Proteins?
Mostly – The answer is YES. BUT….
Ribozymes - segments of RNA that display enzyme activity in the absence of protein
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Examples: RNase P and peptidyl transferase
Abzymes - antibodies raised to bind the transition state of a reaction of interest
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