Enzyme Kinetics

• Enzyme kinetics involves studying the rates of enzymatic reactions and how those rates change due to external factors
• Chemical kinetics is the study of the rates of chemical reactions, the influences upon them, and the mechanisms behind their progression including how fast they proceed and what impacts their rate

First-Order Reactions

• Focus on reactions where A is converted to B
• The reaction velocity (V) measures the amount of product formed over a period
• V is proportional to the decreasing concentration of A or the increasing concentration of B
• k is the rate constant, indicating the proportionality

Enzymatic Reaction Factors

• The key factor affecting rate is [S]
• Measuring the initial rate, V₀, simplifies things as [S] is considered constant at the beginning of the reaction, when [S]>>>[E]
• V₀ increases alongside [S], with the increase being linear at lower [S] and dropping at higher [S], approaching Vmax but not reaching it

Overall Reaction Stages

• Analyzing enzymatic reactions can be done by considering two main stages for the overall reaction
• Fast, reversible substrate binding allows [ES] to be considered constant, known as the "steady-state assumption"
• The Rate-limiting step allows k₂ to be ignored as at t = 0, [P] is 0 (and assuming rapid release of EP)

Catalytic Process

• The overall reaction is controlled by k₂
• k₂ = kcat, the rate constant that defines the catalytic process
• The rate depends on [S] in a first-order reaction; at high [S], the rate is zero order because the enzyme reaches saturation

Michaelis-Menten Kinetics

• Enzyme kinetics based on the steady-state approximation was studied by Michaelis and Menten
• The enzyme binds a single substrate and the model assumes cofactors are already bound
• There are two distinct steps, quick and reversible substrate binding, but slow and irreversible product formation
• During the reaction, [ES] is constant

Steady-State Approximation Details

• Soon after the reaction starts, a 'steady state' situation is reached, where [ES] remains constant
• The rate of formation of ES equals the rate of breakdown of ES, expressed as k₁ [E] [S] = k₂ [ES] + k₋₁ [ES]
• Total enzyme concentration [E]tot = [ES] + [E]
• In the initial phase, [E] decreases and [ES] increases
• [ES] and [E] remain steady during much of the reaction
• [ES] declines only at the end when [S] is exhausted

Michaelis Menten Equation

• Describes the kinetics of the enzyme-catalyzed reaction, based on the previous assumptions
• Initial velocity increases non-linearly
• Vmax is the maximum achievable reaction velocity
• Km, is the Michaelis constant, which equals [S] required to achieve half the maximum velocity

Michaelis Constant

• Km, is measured in units of M
• It is the rate of ES breakdown over its formation, defining the equilibrium between E+S and ES
• Km is related to binding affinity, where lower values mean tighter binding and higher affinity, and vice versa

Maximal Velocity Details

• In practice, Vmax only occurs at very high substrate concentrations, saturating the active site
• Vmax indicates the maximum moles of substrate processed per unit of time
• Vmax measured in mol/s (units)
• Saturating conditions exist and give order zero when Vmax is reached

Turnover Number Details

• kcat defines how the overall reaction is controlled
• kcat indicates Vmax, and if its a high or low value can be used as measurement of capacity and efficiency
• Vmax is reached when the enzyme is saturated, and [ES] = [E]tot then Vmax = k₂ [E]tot
• Turnover number indicates substrate molecules converted to product per unit of time when the enzyme is fully saturated
• k₂ is the turnover number, measured in s⁻¹
• Example turnover numbers, Carbonic anhydrase = 600,000 s⁻¹, Acetylcholine Esterase = 14,000 s⁻¹, Lactate dehydrogenase = 1000 s⁻¹, Chymotrypsin = 100 s⁻¹

Michaelis Constant Details

• Km is [S] concentration when reaction initial velocity is half of Vmax (Vmax/2), derived from combining all rate constants
• Km indicates how tightly the enzyme binds its substrate, a weak substrate has high [S]
• Km has low [S] when it is a good and strong substrate
• Substrate binding depends on shape complementarity, and interactions (e.g., H-bonds, hydrophobic effects)
• Lower Km indicates better substrate, while higher Km indicates weaker substrate

Lineweaver-Burk Equation

• Used to analyze kinetic data and experimentally determine Michaelis-Menten parameters like Vmax and Km
• Lineweaver and Burk proposed a linear equation in terms of initial rate V₀ and [S]
• The reciprocal of the Michaelis-Menten equation gives a Lineweaver-Burk equation of a straight line with y= mx+c
• Using y and x axis intercepts, important kinetic Vmax and Km terms can be measured
• Measured from easily measured properties, for both the rate and substrate concentration