Enzyme CatalysisEnzyme: a biological catalystwith the exception of some RNAs that catalyze their own splicing (Section 10.4), all enzymes are proteinsenzymes can increase the rate of a reaction by a factor of up to 1020 over an uncatalyzed reactionsome enzymes are so specific that they catalyze the reaction of only one stereoisomer; others catalyze a family of similar reactionsThe rate of a reaction depends on its activation energy, DGan enzyme provides an alternative pathway with a lower activation energy

Enzyme Catalysis (Contd)For a reaction taking place at constant temperature and pressure, e.g., in the body

the change in free energy is

Difference in energies between initial state and final state

The change in free energy is related to the equilibrium constant, Keq, for the reaction by

Enzyme Catalysis (Contd)Consider the reaction

Temperature dependence of catalysis Temperature can also catalyze reaction (increase rate)

This is dangerous, why?

Increasing temperature will eventually lead to protein denaturation

Enzyme KineticsFor the reaction

The rate of reaction is given by rate equation

Where k is a proportionality constant called the specific rate constantOrder of reaction: the sum of the exponents in the rate equation

Enzyme Kinetics (Contd)Consider the reaction

Whose rate equation is given by the expression

Determined experimentally, not always from balanced equations The reaction is said to be first order in A, first order in B, and second order overall Consider this reaction of glycogen with phosphate

How Enzymes bind to SubstrateIn an enzyme-catalyzed reactionSubstrate, S: a reactantActive site: the small portion of the enzyme surface where the substrate(s) becomes bound by noncovalent forces, e.g., hydrogen bonding, electrostatic attractions, van der Waals attractions

Binding ModelsTwo models have been developed to describe formation of the enzyme-substrate complex

Lock-and-key model: substrate binds to that portion of the enzyme with a complementary shape

Induced fit model: binding of the substrate induces a change in the conformation of the enzyme that results in a complementary fit

2 Modes of E-S Complex Formation

Formation of Product

An Example of Enzyme CatalysisChymotrypsin catalyzes The selective hydrolysis of peptide bonds where the carboxyl is contributed by Phe and Tyr

It also catalyzes hydrolysis of the ester bonds

An Example of Enzyme Catalysis (Contd)

Non-Allosteric Enzyme Behavior Point at which the rate of reaction does not change, enzyme is saturated, maximum rate of reaction is reached

ATCase: An Example of Allosteric Behavior Sigmoidal shape- characteristic of allosterism Again Max. velocity reached, but different mechanism

Michaelis-Menten KineticsInitial rate of an enzyme-catalyzed reaction versus substrate concentration

Michaelis-Menten ModelFor an enzyme-catalyzed reaction

The rates of formation and breakdown of ES are given by these equations

At the steady state

Michaelis-Menten Model (Contd)When the steady state is reached, the concentration of free enzyme is the total less that bound in ES

Substituting for the concentration of free enzyme and collecting all rate constants in one term gives

Where KM is called the Michaelis constant

Michaelis-Menten Model (Contd)It is now possible to solve for the concentration of the enzyme-substrate complex, [ES]

Or alternatively

Michaelis-Menten Model (Contd)In the initial stages, formation of product depends only on the rate of breakdown of ES

If substrate concentration is so large that the enzyme is saturated with substrate [ES] = [E]T

Substituting k2[E]T = Vmax into the top equation gives

Michaelis-Menten Model (Contd)When [S]= KM, the equation reduces to

Linearizing The Michaelis-Menten EquationIt is difficult to determine Vmax experimentallyThe equation for a hyperbola

Can be transformed into the equation for a straight line by taking the reciprocal of each side

Lineweaver-Burk PlotThe Lineweaver-Burke plot has the form y = mx + b, and is the formula for a straight line

a plot of 1/V versus 1/[S] will give a straight line with slope of KM/Vmax and y intercept of 1/Vmaxsuch a plot is known as a Lineweaver-Burk double reciprocal plot

Lineweaver-Burk Plot (Contd)KM is the dissociation constant for ES; the greater the value of KM, the less tightly S is bound to E

Vmax is the turnover number

Turnover Numbers Vmax is related to the turnover number of enzyme:also called kcat

Number of moles of substrate that react to form product per mole of enzyme per unit of time

Enzyme InhibitionReversible inhibitor: a substance that binds to an enzyme to inhibit it, but can be releasedcompetitive inhibitor: binds to the active (catalytic) site and blocks access to it by substratenoncompetitive inhibitor: binds to a site other than the active site; inhibits the enzyme by changing its conformation

Irreversible inhibitor: a substance that causes inhibition that cannot be reversedusually involves formation or breaking of covalent bonds to or on the enzyme

Competitive InhibitionSubstrate must compete with inhibitor for the active site; more substrate is required to reach a given reaction velocity

We can write a dissociation constant, KI for EI

Competitive Inhibition

Competitive Inhibition

In a Lineweaver-Burk double reciprocal plot of 1/V versus 1/[S], the slope (and the x intercept) changes but the y intercept does not change

A Lineweaver-Burke Plot for Competitive Inhibition

Noncompetitive Inhibition (Contd)Several equilibria are involved

The maximum velocity Vmax has the form

Noncompetitive Inhibition (Contd)

A Lineweaver-Burke Plot for Noncompetitive InhibitionBecause the inhibitor does not interfere with binding of substrate to the active site, KM is unchangedIncreasing substrate concentration cannot overcome noncompetitive inhibition

A Lineweaver-Burke Plot for Noncompetitive Inhibition (Contd)

Other Types of InhibitionUncompetitive- inhibitor can bind to the ES complex but not to free E. Vmax decreases and KM decreases.

Mixed- Similar to noncompetitively, but binding of I affects binding of S and vice versa.