Enzyme Kinetics

Reaction Progress Curve

• Reaction progress is determined by changes in the free energy of the substrates (S), transition state, and products (P).
• Free energy can be calculated via the Gibbs free energy equation: ΔG = ΔH – TΔS
  • ΔG = Change in free energy: Lower values mean that the reaction is more likely to occur. Negative values mean that the reaction will occur spontaneously.
  • ΔH = Change in enthalpy: associated with changes in heat of a reaction in which exothermic reactions have high enthalpy and release heat and endothermic reactions have low enthalpy and require heat
  • T = Current temperature of the environment
  • ΔS = Change in entropy:
    • Entropy is a measure of the disorder of a system, which is dependent on the number of possible microstates.
    • Example: systems with a ↑ number of possible microstates → ↑ entropy
• The transition state represents the most unstable point of interactions between the enzyme and the substrate(s) and is the highest energy point of the reaction.
• Enzymes stabilize the transition state and lower the activation energy (ΔG⁰) of the reaction, making the reaction significantly easier to achieve.
• Once the transition state is attained, the reaction must proceed to a lower energy state. This is accomplished by either converting the substrates to products or reverting back to the substrate form.

Dependence of the Reaction Rate on Temperature

• A ten-degree Centigrade rise in temperature will increase the activity of most enzymes by 50 to 100%, and variations as small as 1 or 2 degrees may increase the activity by 10 to 20%.
• This can only take place within a limited range of temperatures since enzymes have an optimum temperature and they become denatured (irreversibly degraded) at temperatures that are too high.
• Common body temperatures:
  • 36–38^oC: Optimum body temperature; allows enzymes to function properly.
  • < 36^oC: Hypothermia causes dramatic slowing of enzyme function.
  • > 38^oC: Fever can initially allow enzymes to function better.
  • > 40^oC: Hyperthermia causes enzymes to begin to denature and lose function (heat exhaustion and heat stroke).

Dependence of the Reaction Rate on pH

• Enzymes operate at an optimum pH. Changes in the pH value cause changes within the functional groups of the enzyme or of its substrate.
• Changes in pH lead to changes in the ionic or hydrophobic forces that affect the spatial structure at the active center and improve or deteriorate the enzyme’s ability to bind its substrate.
• Stronger pH changes in either direction may even denature the enzyme. Pepsin, for example, works effectively at a pH of about 2, where other enzymes would long have been denatured.
• Enzymes in different areas of the body operate at the most common pH values of those areas.
• Common pH values:
  • Bloodstream: 7.35–7.45
  • Stomach: < 2 when full; 2–6 when fasting
  • Duodenum: 5–7
  • Jejunum: 6-7
  • Ileum: 7-8

Dependence of the Reaction Rate on Substrate Concentration

Steady state conditions

Early changes in concentrations of S, enzyme (E), enzyme-substrate complex (ES), and P change dramatically and are difficult to measure. Steady state occurs when changes in E and ES are relatively small.

• E and S are high early in the reaction, while ES and P are low.
• ES and P increase as the reaction proceeds, decreasing E and S.
• As S decreases, so does the formation of ES late in the reaction. At this point, a reverse reaction becomes likely.

Initial reaction rate (V_o)

The initial rate of the reaction is used to avoid the measurement of the reverse reaction once enough product has been made.

• Higher substrate concentrations increase V₀ until the reaction approaches V_max.
• V₀ = V_max[S] / K_M + [S]
• As [S] goes up, V₀ approaches V_max.
• As [S] goes down, V₀ approaches K_M.
• K_cat = the amount of product produced when the reaction achieves V_max. This allows for the measurement of concrete results of a reaction instead of rates.

Michaelis-Menten graph

Plotting the initial reaction rate (V₀) on the y-axis against the substrate concentration on the x-axis on a graph results in a hyperbolic curve, which approaches the maximum velocity V_max at high substrate concentrations due to saturation of the enzyme with substrate.

Michaelis-Menten constant (K_M)

K_M is the substrate concentration at which half-maximal velocity (½ V_max) is reached (K_M is measured on the x-axis while ½ V_max is measured on the y-axis).

• Indicates the affinity of an enzyme for its substrate in an inverse manner and is characteristic for the particular enzyme-substrate complex
• If the K_M value is low, the enzyme has a strong affinity for the substrate and less is needed to reach ½ V_max.
• If the K_M value is high, the enzyme has less affinity for the substrate and more is needed to reach ½ V_max.
• Dependent on the temperature and pH value, but independent of the enzyme concentration

Lineweaver-Burke plot

1/V₀ is plotted on the y-axis and 1 / [S] is plotted on the x-axis, resulting in a linear plot of the same data used in Michaelis-Menten kinetics.

• The slope of the line is equal to K_M / V_max.
• The y-intercept is equal to 1 / V_max.
• The x-intercept is equal to -1 / K_M.