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Enzyme Kinetics

Enzyme Kinetics is a sub-branch of the discipline Chemical Kinetics, it deals with the measurement of reaction rates of chemical reactions catalysed by enzymes. In this discipline, we explore the mechanisms which make an enzyme function as a catalyst, it's role in metabolism, how it's activity can be controlled.

Basic Enzyme Catalysis Mechanism

In enzyme catalysis, we say that a substrate binds to an enzyme's active site and on binding due to a series of steps called the 'Enzymatic Mechanism' a product is formed. To measure the reaction rates of reactions catalysed by enzymes, laboratory methods called "Enzyme assays" are implemented. The mechanisms followed by Enzymes to catalyse a reaction can be of 2 types: • Single Substrate Mechanisms : Kinetics of Enzymes that bind only to a single substrate. Eg. Kinetics of Hexokinase • Multiple Substrate Mechanism : Kinetics of Enzymes that bind to or produce multiple substrates and products. Eg. Kinetics of DNA Polymerase.

The General Principles followed in Enzyme Kinetics

For a reaction catalysed by enzymes, these principles are always followed:

Enzyme catalysed reactions follow saturation kinetics

• Reactions catalysed by enzymes use the same reactants and produce the same products as in the uncatalyzed reaction.
• They do not alter the equilibrium between the substrate (reactant) and the product
• For a given enzyme concentration, and low substrate concentration, the reaction rate increases with substrate concentration till at high substrate concentration the reaction rate reaches a maximum asymptotically. Thus Enzyme kinetics follow Saturation Kinetics.

The substrate concentration, when the rate is halfway till the theoretical asymptote is called the Michaelis-Menton Constant denoted by KM.

Enzyme assays

Progress Curve we get on Enzyme Assays

Enzyme assays are laboratory methods used to measure reaction rates of enzyme catalysed reactions. The goal of Enzyme assays is to make a graph called the "progressive curve" which theoretically portrays how the rate of the reaction changes with substrate or product concentration. Enzyme assays can be grouped into 3 categories:

• Spectrophotometric Methods - which measure the change in absorbance of reactants and products
• Radiometric assays - which involve release of radioactivity
• Mass Spectrometry - which monitor the addition and release of stable isotopes

Each of these methods are arranged in the order of increased sensitivity.

Modes of Catalysis

At present the most widely accepted model of Enzyme Catalysis is the "Induced Fit Model" which replaced the earlier "Lock and Key Hypothesis".

The "Induced Fit Model" proposes that the enzyme and substrate bind with weak interactions that induces a conformational change in the structure of the enzyme to strengthen the bond, this change in conformation, brought catalytic centres in the enzyme and substrate closer together to bring about the reaction. The "Lock and Key Hypothesis" however, proposed that the enzyme had rigid sites on it called the "active site" that could accommodate only that specific substrate the enzyme acts upon.

Enzyme kinetics cannot prove which mode of catalysis is used by an enzyme, however its data can be used to predict the mode of catalysis followed by a particular enzyme.

Mechanisms of Enzyme Catalysis

Enzymes catalyse a tremendous variety of reactions using different combinations of five basic catalytic mechanisms. Some enzymes act on only a single substrate molecule (Single Substrate Mechanism); others act on two or more different substrate molecules whose order of binding may or may not be obligatory (Multiple Substrate Mechanism).

Single Substrate Mechanism

Enzymes that bind to only one substrate at a time follow the enzyme kinetics mechanism called the Single Substrate Mechanism. Isomerases, Hammer-head Ribozymes, and RNA lyase all fall under enzymes that follow this mechanism

Michaelis-Menton Equation

The Michaelis–Menten equation describes the rate of the enzymatic reaction as a function of substrate concentration. For an enzymatic reaction,

${\ce {E + S <=>[k_1][k_0] ES ->[k_2] E + P}}$

The Michaelis–Menten Equation Assumes that Enzyme substrate complex (ES) maintains a Steady State i.e. the rate of formation and consumption of ES is the same. In this reaction, the product formation from ES is a first order reaction. Thus the rate here can be given as,

$r={d[P] \over dt}=k_{2}[ES]$

Formation of ES from the enzyme and substrate interaction is a second order reaction. Thus, the rate here can be given as,

$r={d[ES] \over dt}=k_{1}[E][S]$

Thus, due to the steady state approximation,

$k_{2}[ES]+k_{0}[ES]=k_{1}[E][S]$

thus,

${[E]+[S] \over [ES]}={k_{0}+k_{2} \over k_{1}}$

The value, ${k_{0}+k_{2} \over k_{1}}$is condensed to K_M called the Michaelis-Menton Constant, which is that substrate concentration where half of the enzyme concentration is used to make the Enzyme- Substrate complex. On further simplification, the reaction rate simplifies to,

$V={V_{M}[S] \over K_{M}+[S]}$, where V_M is the maximum rate of the reaction

This equation called the Michaelis-Menton equation is the basic equation of Enzyme Kinetics. It describes a regular hyperbola.

KM can also be calculated using the equation,

Michaelis Menton plot

$K_{M}=K_{S}+{k_{2} \over k_{1}}$, where K_S is the Dissociation constant of the enzyme.

Thus, the Michaelis-Menton constant can also be used as a measure of "affinity" of an enzyme to its substrate provided k2/k1 is small compared to KS. Steady state reaction kinetics however cannot reveal the number of intermediates or the nature of the ES in the reaction.

Multiple Substrate Mechanism

Ternary Mechanism

Multi-substrate reactions follow complex rate equations as many substrates bind to the enzyme. To analyse these reactions the concentration of substrate A is kept constant and substrate B varied. Under these conditions, the enzyme behaves just like a single-substrate enzyme and a plot of v by [S] gives apparent KM and VM constants for substrate B. Similarly, on keeping substrate B constant and substrate A varied, apparent KM and VM for substrate A can be found. Catalysis of more than one substrate can occur via 2 ways:

• Substrate binding one at a time - Ping Pong Mechanism
• Substrates binding at once - Ternary Complex Mechanism

Enzyme Inhibition

Many substances alter the activity of an enzyme by combining with it in a way that influences the binding of substrate or product formation. Substances that reduce an enzyme’s activity in this way are known as inhibitors. A large part of the modern medicine consists of enzyme inhibitors. Based on whether the binding of the inhibitor is reversible or irreversible, inhibition is also classified as Reversible inhibition and Irreversible Inhibition.

Enzyme Inhibition

Reversible Inhibition

Inhibitors whose activity on an enzyme can be reversed are called reversible inhibitors. Reversible inhibitors inhibit enzyme activity in 3 ways:

• Competitve Inhibition :

Inhibitors compete directly with a normal substrate for an enzyme’s substrate-binding site.

• Uncompetitve Inhibition :

The inhibitor binds directly to the enzyme–substrate complex

• Noncompetitive Inhibition :

Inhibitor binds to both the Free Enzyme and the Enzyme–Substrate Complex

Irreversible Inhibition

Inhibitors whose activity on an enzyme cannot be reversed are called irreversible inhibitors. They are sometimes also called "suicide inhibitors". Inhibition done by these inhibitors is called Irreversible Inhibition