Dr. Riddhi Datta

ENZYMES

Dr. Riddhi Datta

How Enzymes Work

• An enzyme provides a specific environment within which a given reaction can occur more rapidly.
• An enzyme-catalyzed reaction takes place within the confines of a pocket on the enzyme called the active site.
• The molecule that is bound in the active site and acted upon by the enzyme is called the substrate.
• The surface of the active site is lined with amino acid residues with substituent groups that bind the substrate and catalyze its chemical transformation. These residues are called the catalytic groups.

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E:enzyme

S:substrate

P: product

ES: transient enzyme-substrate complex

EP: transient enzyme-product complex

Enzymes increase the rate of a reaction and do not affect reaction equilibria.

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Active sites of enzymes have some common features

• The active site is formed by groups that come from different parts of the amino acid sequence.

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• The active site takes up a relatively small part of the total volume of an enzyme.

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• Active sites are three-dimensional clefts or crevices.

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• Substrates are bound to enzymes by multiple weak attractions like electrostatic interactions, hydrogen bonds, van der Waals forces, and hydrophobic interactions.

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• The specificity of binding depends on the precisely defined arrangement of atoms in an active site.

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• The enzyme and the substrate possess specific complementary geometric shapes that fit exactly into one another.

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• The model was proposed by Emil Fischer in 1890.

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• It does not explain the stabilization of the transition state that the enzymes achieve.

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• It is an obsolete model.

Lock-and-key model of enzyme-substrate binding

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Induced-Fit Model of Enzyme-Substrate Binding

• The enzyme undergoes a change in conformation when the substrate binds, induced by multiple weak interactions with the substrate.

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• The active site forms a shape complementary to the substrate only after the substrate has been bound.

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• The induced fit model shows that enzymes are rather flexible structures. 

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• It was proposed by Daniel Koshland in 1958.

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The starting point for either the forward or the reverse reaction is called the ground state.

The free-energy change for this reacting system is expressed as standard free energy change (∆G°).

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Biochemical standard free-energy change (∆G’°) is the standard free-energy change at pH 7.0.

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• A reaction can occur spontaneously only if ∆G’° is negative: exergonic reactions

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• A system is at equilibrium and no net change can take place if ∆G’° is zero.

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• A reaction cannot occur spontaneously if ∆G’° is positive and input of free energy is required: endergonic reactions

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Here, the free energy of the ground state of P is lower than that of S.

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So ∆G’° for the reaction is negative and the equilibrium favors P.

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The position and direction of equilibrium are not affected by enzyme .

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• There is an energy barrier between S and P: the energy required for alignment of reacting groups, formation of transient unstable charges, bond re-arrangements, etc.

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• To undergo reaction, the molecules must overcome this barrier and must be raised to a higher energy level.

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• At the top of the energy hill is a point at which decay to the S or P state is equally probable. This is called the transition state.

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• The difference between the energy levels of the ground state and the transition state is the activation energy, ∆G^‡.

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• The rate of a reaction reflects this activation energy: a higher activation energy corresponds to a slower reaction.

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• Reaction rates can be increased by raising the temperature, thereby increasing the number of molecules with sufficient energy to overcome the energy barrier.

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• Catalysts (enzymes) enhance reaction rates by lowering activation energies.

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• Enzymes accelerate the inter-conversion of S and P.

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• The enzyme is not used up in the process, and the equilibrium point is unaffected.

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• Any reaction may have several steps, involving the formation and decay of transient chemical species called reaction intermediates (has a finite chemical lifetime).

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When several steps occur in a reaction, the overall rate is determined by the step (or steps) with the highest activation energy; this is called the rate-limiting step.

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Reaction equilibrium is linked to the standard free-energy change for the reaction (∆G’°)

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Reaction rate is linked to the activation energy(∆G^‡)

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An equilibrium such as S ⇌ P is described by an equilibrium constant, K’_eq under standard conditions:

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From thermodynamics, the relationship between K’_eq and ∆G’° can be described by the expression

∆G’° = -RT ln K’_eq

where R is the gas constant, 8.315 J/mol . K, and T is the absolute temperature, 298 K (25°C)

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• The study of mechanism of an enzyme-catalyzed reaction, determining the rate of the reaction and how it changes in response to experimental cues is called enzyme kinetics.

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• Substrate concentration [S] affects the rate of enzyme-catalyzed reactions.

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• At relatively low concentrations of substrate, initial velocity of reaction (V₀) increases almost linearly with an increase in [S].

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• At higher substrate concentrations, V₀ increases by smaller and smaller amounts in response to increases in [S].

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• Finally, a point is reached beyond which increases in V0 are vanishingly small as [S] increases. This plateau-like V₀ region is close to the maximum velocity, V_max.

Enzyme kinetics

Dr. Riddhi Datta

k₁: Equilibrium constant of forward reaction

k_-1: Equilibrium constant of reverse reaction

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k₂: Equilibrium constant of forward reaction

k_-2: Equilibrium constant of reverse reaction

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Dr. Riddhi Datta

In an enzyme-catalyzed reaction, the enzyme exists in two forms: free form [E] and substrate-combined form (ES).

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At low [S], most of the enzyme is in free form and the reaction rate is proportional to [S] because more ES is formed as [S] increases.

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The maximum initial rate of the catalyzed reaction (V_max) is observed when virtually all the enzyme is present as the ES complex.

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Now the enzyme is “saturated” with its substrate, so that further increases in [S] have no effect on rate.

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This condition exists when [S] is sufficiently high.

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After the ES complex breaks down to yield the product P, the enzyme is free to catalyze reaction of another molecule of substrate.

Dr. Riddhi Datta

When the enzyme is mixed with a high substrate concentration, there is an initial period, the pre–steady state, during which the concentration of ES builds up.

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The reaction quickly achieves a steady state in which [ES] remains approximately constant over time.

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The concept of a steady state was introduced by G. E. Briggs and Haldane in 1925.

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The measured V₀ generally reflects the steady state, and analysis of these initial rates is referred to as steady-state kinetics.

Dr. Riddhi Datta

Michaelis and Menten derived their equation starting from their basic hypothesis that the rate-limiting step in enzymatic reactions is the breakdown of the ES complex to product and free enzyme.

V0: Initial velocity

Vmax: Maximum velocity

[S]: Substrate concentration

Km: Michaelis constant

Michaelis-Menten equation

Derivation of this equation includes the steady-state assumption introduced by Briggs and Haldane

Dr. Riddhi Datta

k₁: Equilibrium constant of forward reaction

k_-1: Equilibrium constant of reverse reaction

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k₂: Equilibrium constant of forward reaction

k_-2: Equilibrium constant of reverse reaction

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Dr. Riddhi Datta

Early in the reaction, the product concentration, [P], is negligible, and it is assumed that the reverse reaction can be ignored. The overall reaction is simplified to:

V0 is determined by the breakdown of ES to form product, which is determined by [ES]:

Let [Et] is the total enzyme concentration (the sum of free and substrate-bound enzyme)

Therefore, free enzyme concentration = [Et] - [ES]

Also, [S] is far greater than [Et], so the amount of substrate bound by the enzyme at any given time is negligible compared with the total [S].

Dr. Riddhi Datta

At steady state, the rate of formation of ES is equal to the rate of its breakdown (Steady-state assumption). Therefore,

Simplifying,

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k₁[E_t][S] = (k_-1 + k₂)[ES] + k₁[ES][S]

k₁[E_t][S] = [ES](k_-1 + k₂ + k₁[S])

[ES] =

(k_-1 + k₂ + k₁[S])

k₁[E_t][S]

Solving for [ES],

[ES] =

[E_t][S]

(k_-1 + k₂)/k₁ + [S]

Dr. Riddhi Datta

(k_-1 + k₂)/k₁ is called Michaelis constant, K_m. Therefore,

[ES] =

[E_t][S]

K_m+ [S]

Substituting [ES] from the equation V₀ = k₂[ES],

V₀ =

k₂[E_t][S]

K_m+ [S]

Because the maximum velocity occurs when the enzyme is saturated (that is [ES] = [Et]), V_max can be defined as k₂[Et].

Dr. Riddhi Datta

The Michaelis-Menten equation is a statement of the quantitative relationship between the initial velocity V₀, the maximum velocity V_max, and the initial substrate concentration [S], all related through the Michaelis constant K_m.

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When V₀ is exactly one-half V_max,

On dividing by V_max,

Solving for K_m, we get K_m + [S] = 2[S], or

K_m is equivalent to the substrate concentration at which V₀ is one-half V_max.

K_m has unit of concentrations.

Dr. Riddhi Datta

Assumptions of Michaelis-Menten equation:

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• Single substrate is involved and a single product is formed

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• The process proceeds essentially to completion

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• Concentration of substrate is far greater than enzyme concentration

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• Enzyme-substrate complex is formed

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• Steady state is assumed

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The Double-Reciprocal Plot

The Michaelis-Menten equation states,

Taking the reciprocal of both sides,

Separating the components of the numerator on the right side of the equation gives,

Simplifying,

This form of the Michaelis-Menten equation is called the Lineweaver-Burk equation.

Dr. Riddhi Datta

For enzymes obeying the Michaelis-Menten relationship, a plot of 1/V₀ versus 1/[S] (the “double reciprocal” of the V₀ versus [S] plot) yields a straight line.

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This line has a slope of K_m/V_max, an intercept of 1/V_max on the 1/V₀ axis, and an intercept of -1/K_m on the 1/[S] axis.

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This double reciprocal plot allows a more accurate determination of V_max.

Dr. Riddhi Datta

Enzymes inhibitors

• Enzyme inhibitors are molecular agents that interfere with catalysis, slowing or halting enzymatic reactions.

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• Example: aspirin (acetylsalicylate) inhibits the enzyme that catalyzes prostaglandins synthesis which produce pain.

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• Enzyme inhibition can be either reversible or irreversible.

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• An irreversible inhibitor dissociates very slowly from its target enzyme

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• It binds tightly to the enzyme, either covalently or non-covalently.

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• Some irreversible inhibitors are important drugs.

• Reversible inhibition is characterized by a rapid dissociation of the enzyme inhibitor complex.

Irreversible inhibitors

Reversible inhibitors

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Competitive Inhibition

• A competitive inhibitor competes with the substrate for the active site of an enzyme.

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• The inhibitor (I) resembles the geometry of the substrate.

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• It occupies the active site forming EI complex and prevents substrate binding to the enzyme.

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• A competitive inhibitor diminishes the rate of catalysis by reducing the proportion of enzyme molecules bound to a substrate.

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• At any given inhibitor concentration, competitive inhibition can be relieved by increasing the substrate concentration.

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Uncompetitive Inhibition

• An uncompetitive inhibitor binds at a site distinct from the substrate active site.

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• It binds to the ES complex forming the ESI complex.

• An uncompetitive inhibitor acts by decreasing the turnover number.

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• Uncompetitive inhibition cannot be overcome by increasing the substrate concentration.

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• A mixed inhibitor binds at a site distinct from the substrate active site.

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• It binds to either E or ES.

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• A single inhibitor both hinders the binding of substrate and decreases the turnover number of the enzyme.

Mixed Inhibition

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• When [S] far exceeds [I], the probability that an inhibitor molecule will bind to the enzyme is minimized and the reaction exhibits a normal V_max.

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• However, the [S] at which V₀ = 1/2 V_max, the apparent K_m, increases in the presence of inhibitor by the factor α.

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• In the presence of a competitive inhibitor, the Michaelis-Menten equation becomes:

where

Competitive Inhibition

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• Three double-reciprocal plots are considered: one obtained in the absence of inhibitor and two at different concentrations of a competitive inhibitor.

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• Increasing [I] results in a family of lines with a common intercept on the 1/V₀ axis but with different slopes.

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• Because the intercept on the 1/V₀ axis equals 1/V_max, we know that V_max is unchanged by the presence of a competitive inhibitor.

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• The value of α can be calculated from the change in slope at any given [I].

Competitive Inhibition

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Uncompetitive Inhibition

• In the presence of an uncompetitive inhibitor, the Michaelis-Menten equation is altered to

where

• At high concentrations of substrate, V₀ approaches V_max/α’ .

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• Thus, an uncompetitive inhibitor lowers the measured V_max.

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• Apparent K_m also decreases, because the [S] required to reach ½ V_max decreases by the factor α’.

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• Three double-reciprocal plots are considered: one obtained in the absence of inhibitor and two at different concentrations of an uncompetitive inhibitor.

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• Changes in axis intercepts signal changes in V_max and K_m.

Uncompetitive Inhibition

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Mixed Inhibition

• In the presence of a mixed inhibitor, the Michaelis-Menten equation is altered to

where

• When α = α’, it is defined as noncompetitive inhibition.

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• A noncompetitive inhibitor would affect the V_max but not the K_m.

Dr. Riddhi Datta

• Three double-reciprocal plots are considered: one obtained in the absence of inhibitor and two at different concentrations of a mixed inhibitor.

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• Changes in axis intercepts signal changes in V_max and K_m.

Mixed Inhibition

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Effects of reversible inhibitors on apparent V_max and apparent K_m

Dr. Riddhi Datta

Regulatory Enzymes

• Each metabolic pathway includes one or more regulatory enzymes that exhibit increased or decreased catalytic activity in response to certain signals.

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• Adjustments in the rate of reactions catalyzed by regulatory enzymes alters the rate of entire metabolic sequences.

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• Such regulations allow the cell to meet changing needs for energy and for biomolecules required in growth and repair.

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• In most multienzyme systems, the first enzyme of the sequence is a regulatory enzyme.

Dr. Riddhi Datta

• Allosteric enzymes function through reversible, noncovalent binding of regulatory compounds called allosteric modulators or allosteric effectors to a site other than active site.

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• Allosteric modulators are generally small metabolites or cofactors.

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• The conformational changes induced by the modulator(s) interconvert more-active and less-active forms of the protein.

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• The modulators for allosteric enzymes may be inhibitory or stimulatory.

Allosteric enzymes

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• The substrate binding site is on the catalytic subunit (C) and the modulator binding site is on the regulatory (R) subunits

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• Binding of the positive (stimulatory) modulator (M) to its specific site on the regulatory subunit is communicated to the catalytic subunit through a conformational change.

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• This change renders the catalytic subunit active and capable of binding the substrate (S) with higher affinity.

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• On dissociation of the modulator from the regulatory subunit, the enzyme reverts to its inactive or less active form.

Dr. Riddhi Datta

• When the substrate and the modulator are identical, the interaction is termed homotropic. It is typically an activator of the enzyme.

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• When the modulator is a molecule other than the substrate the interaction is heterotropic. It may be either an activator or an inhibitor of the enzyme.

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• Some proteins have two or more modulators and therefore can have both homotropic and heterotropic interactions.

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• Cooperative binding of a ligand to a multimeric protein (or substrate to enzyme), is a form of allosteric binding often observed in multimeric proteins.

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• Allosteric enzymes show relationships between V₀ and [S] that differ from Michaelis-Menten kinetics.

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• For some allosteric enzymes, plots of V₀ versus [S] produce a sigmoid saturation curve, rather than the hyperbolic curve typical of non regulatory enzymes. K_0.5 is used instead of K_m in these cases.

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Dr. Riddhi Datta

The sigmoid curve of a homotropic enzyme.

The effects of a positive modulator (+) and a negative modulator (-) on an allosteric enzyme, where K_0.5 is altered without a change in V_max. The central curve is without modulator.

Less common type of modulation, in which V_max is altered and K_0.5 is nearly constant.

Homotropic

Heterotropic

Substrate-activity curves for representative allosteric enzymes

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Feedback inhibition

• In some multienzyme systems, the regulatory enzyme is specifically inhibited by the end product of the pathway whenever the concentration of the end product exceeds the cell’s requirements.

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• This type of regulation is called feedback inhibition.

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• Buildup of the end product ultimately slows the entire pathway.

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Reversible Covalent Modification of Regulatory Enzymes

• Activities of some regulatory enzymes can be modulated by covalent modification of the enzyme molecule.

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• Modifying groups include:
• Phosphoryl group
• Adenylyl group
• Uridylyl group
• Methyl group
• adenosine diphosphate ribosyl group

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• These groups are generally linked to and removed from the regulatory enzyme by separate enzymes.

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Methylation

• Enzymes can be regulated by addition or removal of methyl group.

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• The methylating agent is S-adenosylmethionine (adoMet)

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• Example: methyl-accepting chemotaxis protein of bacteria

ADP-ribosylation

• Sometimes enzymes are regulated by ADP-ribosylation.

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• The ADP-ribose is derived from nicotinamide adenine dinucleotide (NAD).

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• Example: bacterial enzyme dinitrogenase reductase

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Phosphorylation

• It is the most common type of regulatory modification.

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• One-third to one-half of all proteins in a eukaryotic cell are phosphorylated at one or more residues.

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• The attachment of phosphoryl groups to specific amino acid residues of a protein is catalyzed by protein kinases.

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• The removal of phosphoryl groups is catalyzed by protein phosphatases.

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• Phosphoryl group can be attached to a Ser, Thr, or Tyr residues

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• Phosphorylation can have dramatic effects on protein conformation and thus on substrate binding and catalysis.

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• Example: glycogen phosphorylase of muscle and liver

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Regulation by Proteolytic Cleavage of an Enzyme Precursor

• For some enzymes, an inactive precursor called a zymogen is cleaved to form the active enzyme.

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• Specific cleavage causes conformational changes that expose the enzyme active site and activates it.

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• Chymotrypsin and trypsin are initially synthesized as chymotrypsinogen and trypsinogen.

Enzymes at important metabolic intersections may be regulated by complex combinations of effectors, allowing coordination of the activities of interconnected pathways.

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Isozymes

• Isozymes are different proteins that catalyze the same reaction.

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• May occur in the same species, in the same tissue, or even in the same cell.

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• The different forms of the enzyme generally differ in:
• Kinetic properties
• Regulatory properties
• Cofactors
• Subcellular distribution

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• Isozymes may have similar, but not identical, amino acid sequences, and in many cases they clearly share a common evolutionary origin.

Dr. Riddhi Datta

The distribution of different isozymes of a given enzyme reflects at least four factors:

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• Different metabolic patterns in different organs
• Example: glycogen phosphorylase, the isozymes in skeletal muscle and liver have different regulatory properties.

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• Different locations and metabolic roles for isozymes in the same cell.
• Example: isocitrate dehydrogenase isozymes of the cytosol and the mitochondrion

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• Different stages of development
• Example: LDH in fetal liver and adult liver

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• Different responses of isozymes to allosteric modulators to fine-tune metabolic rates
• Hexokinase IV (glucokinase) of liver and the hexokinase isozymes of other tissues differ in their sensitivity to inhibition by glucose 6-phosphate.

Isozymes

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Recap!

• Enzymes are catalysts enhancing reaction rates by a factor of 10⁵to 10¹⁷.

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• Enzyme-catalyzed reactions are characterized by the formation of a enzyme-substrate complex.

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• Substrate binding occurs in a pocket on the enzyme called the active site.

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• The enzyme undergoes a change in conformation when the substrate binds, induced by multiple weak interactions with the substrate (Induced-fit Model).

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• Enzymes lower the activation energy, ∆G^‡, for a reaction and thereby enhance the reaction rate.

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• The equilibrium of a reaction is unaffected by the enzyme.

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V0: Initial velocity

Vmax: Maximum velocity

[S]: Substrate concentration

Km: Michaelis constant

• When substrate is added to an enzyme, the reaction rapidly achieves a steady state in which the rate at which the ES complex forms balances the rate at which it reacts.

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• As [S] increases, the steady-state activity of a fixed concentration of enzyme increases in a hyperbolic fashion to approach a characteristic maximum rate, V_max, at which essentially all the enzyme has formed a complex with substrate.

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• The substrate concentration that results in a reaction rate equal to one-half Vmax is the Michaelis constant K_m.

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• Michaelis-Menten equation (Steady-state kinetics) states:

Recap!

Dr. Riddhi Datta

• Enzyme inhibitors are molecular agents that interfere with catalysis, slowing or halting enzymatic reactions.

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• Reversible inhibition of an enzyme is competitive, uncompetitive, or mixed.

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• Competitive inhibitors compete with substrate by binding reversibly to the active site, forming EI complex.

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• Uncompetitive inhibitors bind only to the ES complex, at a site distinct from the active site.

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• Mixed inhibitors bind to either E or ES, again at a site distinct from the active site. In irreversible inhibition an inhibitor binds permanently to an active site by forming a covalent bond or a very stable noncovalent interaction.

Recap!

Dr. Riddhi Datta

Recap!

• The activities of metabolic pathways in cells are regulated by control of the activities of certain enzymes.

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• In feedback inhibition, the end product of a pathway inhibits the first enzyme of that pathway.

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• The activity of allosteric enzymes is adjusted by reversible binding of a specific modulator to a regulatory site.

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• Modulators may be the substrate itself or some other metabolite, and the effect of the modulator may be inhibitory or stimulatory.

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• The kinetic behavior of allosteric enzymes reflects cooperative interactions among enzyme subunits.

Dr. Riddhi Datta

Recap!

• Other regulatory enzymes are modulated by covalent modification of a specific functional group necessary for activity. The phosphorylation of specific amino acid residues is a particularly common way to regulate enzyme activity.

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• Many proteolytic enzymes are synthesized as inactive precursors called zymogens, which are activated by cleavage of small peptide fragments.

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• Isozymes are different proteins that catalyze the same reaction.

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• The different forms of the enzyme generally differ in:
• Kinetic properties
• Regulatory properties
• Cofactors
• Subcellular distribution