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Enzymes

  • Enzymes are biological catalysts essential for accelerating chemical reactions under physiological conditions.

  • Without enzymes, metabolic reactions would require millions of years, rendering life impossible.

  • Enzymes:

    • Increase rates of chemical reactions.

    • Not consumed by reactions.

    • Do not alter the equilibrium concentration ratio of substrates and products.

  • Most enzymes are proteins, while some, known as ribozymes, are composed of RNA.

Enzyme Kinetics

  • Enzyme kinetics refers to the quantitative analysis of enzyme function, aiding in understanding reaction mechanisms and comparing enzyme efficiency under various conditions.

Module 6 Overview

Topics and Readings

  • Module 6 Topics:

    1. Overview of Enzymes

    2. Enzyme Function

    3. Enzyme Mechanisms

    4. Enzyme Reactions

    5. Enzyme Kinetics

  • Textbook Chapters:

    • Chapter 7.1: Overview of Enzymes

    • Chapter 7.2: Enzyme Function & Mechanisms

    • Chapter 7.3: Enzyme Reactions

    • Chapter 7.4: Enzyme Kinetics

Enzyme Kinetics

Characteristics of First-Order Reactions

  • A plot of initial velocity ($v_0$) versus substrate concentration ($[S]$) produces a hyperbolic curve if the enzyme reaction follows Michaelis–Menten kinetics.

  • The plot of product formation ($[P]$) versus time for different substrate concentrations can determine the initial velocity by calculating the slope of the tangent during the initial phase (0-50 seconds).

Definition

  • Enzyme kinetics quantitatively studies the rates of chemical reactions catalyzed by enzymes under controlled laboratory conditions.

  • Understanding enzyme kinetics helps determine the following:

    • Reaction mechanisms.

    • Effects of regulatory molecules.

    • Effects of mutations.

Michaelis-Menten Enzyme Kinetics

  • It is used to study first-order reactions where a substrate is converted to a product ($S
    ightarrow P$) under steady-state conditions.

Rate Constants and Reaction Velocity

Relation to Activation Energy

  • The initial substrate concentration ([S]) is related to the activation energy ($ riangle G^{ullet}$) for first-order reactions.

  • The velocity ($v$) of the reaction is defined as: v=k[S]v = k[S]

    • Where:

    • $k$: rate constant with units of $s^{-1}$ for first-order reactions.

    • $v$: amount of product formed per unit time in molarity per second ($M s^{-1}$).

Bimolecular Reactions

  • Many metabolic reactions involve two substrates or molecules and are second-order reactions.

  • The rate is proportional to the product of the concentrations of the substrates: v=k[S][Y]v = k[S][Y]

    • Where:

    • $S$ and $Y$ are substrates.

Michaelis-Menten Kinetics

Substrate Concentration Changes

  • The substrate concentration is not constant as it is consumed to generate product, affecting reaction rates over time.

  • Initial velocity ($v_0$) is measured at the beginning of the reaction, where substrate concentration changes only minimally, allowing approximation.

  • Under high substrate concentration ($[S] >> [E]$), the initial velocity approaches maximal velocity ($v_{max}$).

Initial Velocity and Michaelis Constant ($K_m$)

Defining $K_m$

  • The Michaelis constant ($Km$) relates to the rate constants ($k1, k{-1}, k2$) for an enzyme reaction.

  • It can be experimentally determined from a plot of initial velocity versus substrate concentration under conditions where $[S] >> [E]$.

  • The value of $Km$ is defined as the substrate concentration at which the reaction rate is half of $v{max}$.

Properties of $K_m$

  • A low $K_m$ indicates high catalytic activity at low substrate concentrations.

  • $K_m$ is independent of enzyme concentration when the enzyme is limiting.

Michaelis-Menten Equation

  • The Michaelis-Menten equation describes the hyperbolic curve using $[S], v{max}, Km$ to define $v0$: v</em>0=racv<em>max[S]K</em>m+[S]v</em>0 = rac{v<em>{max}[S]}{K</em>m + [S]}

Lineweaver-Burk Plot

  • Parameters can be obtained from a Lineweaver-Burk plot:

    • Slope = $Km/v{max}$

    • Y-axis intercept = $1/v_{max}$

    • X-axis intercept = $-1/K_m$

  • The x-axis intercept for different enzyme reactions remains consistent, indicating that $K_m$ is unaffected by enzyme concentration under certain conditions.

Catalytic Efficiency of Enzymes

Turnover Number ($k_{cat}$)

  • Turnover number ($k_{cat}$) defines maximum catalytic activity under saturating substrate levels.

  • Catalytic efficiency requires evaluating $k{cat}/Km$ (specificity constant).

Case Study: Fumarase

  • Example: The $Km$ for fumarate is five times lower than that for malate, yet $k{cat}$ values for both substrates are nearly identical.

  • This contrasts leads to a specificity constant for fumarate that is approximately four times higher than that for malate, demonstrating that fumarate is the preferred substrate for the enzyme.

Effects of pH and Temperature on Enzyme Activity

  • Seven amino acids have ionizable side chains which can gain or lose protons depending on local environment and effective pKa.

  • Changes in pH can alter active site chemistry, affecting enzyme efficiency.

  • Temperature changes can impact both catalytic properties and protein structure.