Kinetics: Enzymatic Reactions and Rate Laws

Kinetics: Rate of Enzymatic Reactions

• Enzymatic reactions involve a substrate binding to an enzyme.
• Multistep reactions have rate-limiting steps that determine the overall reaction rate.
• Chemical reactions are represented by A → P, where I symbolizes intermediates.
• Reaction rates are calculated as the change in reactant or product concentration per unit time (v = -∆[A]/∆t or +∆[P]/∆t).

Reaction Rates

• Reaction rates measure the change in concentration of reactants or products over time.
• The graph showing the change of molecules against time shows how the number of molecules of a specific reactant decreases as time increases and the number of molecules of the product increases.

Rate Law = Rate Equation

• The rate of a reaction is proportional to the concentrations of reactants raised to certain powers (Rate = K [A]^m [B]ⁿ).
• The proportionality constant 'k' is the rate constant.
• Reaction orders (m and n) must be determined experimentally.

Reaction Order

• The order of a reaction is the sum of the exponents in the rate equation (m + n).
• Order is also referred to as molecularity, which is the number of molecules that collide simultaneously in the elementary reaction.
• Zero-order reactions have a rate independent of reactant concentration (rate=k).
• First-order reactions have a rate directly proportional to the concentration of one reactant (rate = k[A]).
• Second-order reactions involve the rate proportional to the concentration of two reactants (rate = k [A]² or k[A][B])

Half-time (t_1/2)

• Half-life is the time required for half of the reactant to be consumed.
• For zero-order reactions, t_1/2= [A]₀ / 2k
• For first-order reactions, t_1/2= ln2/k.
• For second-order reactions, t_1/2= 1 / k[A]₀.

Michaelis-Menten Equation

• Michaelis-Menten proposed a model to explain enzyme kinetics.
• One substrate, one intermediate and one product are considered.
• This model considers that the catalytic step is the rate-limiting step.

Graphical Relationships

• Vo is reaction velocity and [S] is substrate concentration. A plot of Vo against [S] gives a hyperbolic curve.
• At low [S], the reaction is first order, and increases with [S].
• At high [S], the reaction approaches a maximum velocity (V_max), after which it is not affected by [S].

Derivation of the Michaelis-Menten Equation

• The Michaelis constant (K_M) is the substrate concentration at which the reaction velocity is half of its maximum.
• The relationship Vo = V_max [S]/ (K_M + [S]) represents the Michaelis-Menten equation.

Analysis of Kinetic Data

• V₀ vs [S] plots, require extrapolation to determine V_max and K_M.
• 1/V₀ vs 1/[S] plots (Lineweaver-Burk plots) yield a straight line.
• Eadie–Hofstee plots is also used to analyze kinetic data.

Catalytic Efficiency

• k_cat is a catalytic constant (turnover number).
• High k_cat means fast enzyme activity.

Enzyme Catalysis

• Enzymes are biological catalysts that bind to substrates, forming temporary complexes that stabilize reaction transitions.
• Enzymes lower the activation energy needed to begin a reaction by properly orienting and changing the substrate’s shape.
• Enzymes are capable of catalyzing a reaction many times in one encounter with the substrate.

Enzyme Kinetics

• Enzyme kinetics is the study of the rates of enzyme-catalyzed reactions.
• It is involved with determining how different aspects of conditions influence the reaction rate.

Explore the principles of kinetics focusing on enzymatic reactions and the determination of reaction rates. This quiz covers topics such as rate laws, the significance of rate-limiting steps, and the mathematical representation of reaction rates. Test your understanding of how these concepts apply in biochemical contexts.