Biochemistry - Lesson 6: Enzyme Kinetics and Inhibition

Enzyme kinetics quantifies how rapidly enzymes convert substrates into products and how different factors—substrate concentration, enzyme concentration, inhibitors—impact reaction rates. By modeling these behaviors, biochemists glean insights into enzyme mechanisms and regulatory strategies. This lesson covers the Michaelis–Menten equation, graphical methods (Michaelis–Menten plots, Lineweaver–Burk plots), and reversible inhibition types, culminating in a discussion of how enzymes adjust to cellular conditions and allosteric effectors.

Michaelis–Menten Kinetics

The Michaelis–Menten model assumes a rapid, reversible interaction between enzyme (E) and substrate (S) to form an enzyme–substrate complex (ES), which then produces product (P). Below is a flowchart illustrating this scheme:

flowchart LR A["E + S"] <--> B["ES"] B --> C["E + P"]

Under steady-state conditions, the rate of ES formation and breakdown reach equilibrium. The resulting equation:

v = (V_max [S]) / (K_m + [S])

• v: Initial reaction velocity
• V_max: Maximal rate at saturating [S]
• K_m: Substrate concentration at which v = 1/2 V_max

K_m provides an indication of substrate affinity—lower K_m often means stronger substrate binding.

Michaelis–Menten Plot

Below is a line chart illustrating how reaction velocity (v) changes with increasing substrate concentration ([S]). The curve plateaus near V_max, and K_m is identifiable where v = V_max/2.

From this plot, V_max is the upper plateau. K_m is the [S] giving half-maximal velocity, indicating how much substrate is required for substantial catalytic turnover.

Lineweaver–Burk Plot

Another way to extract V_max and K_m is the double-reciprocal or Lineweaver–Burk plot:

1/v = (K_m/V_max) * (1/[S]) + (1/V_max)

By plotting 1/v vs. 1/[S], one obtains a straight line, where intercepts yield 1/V_max and −1/K_m. While this approach can amplify errors at low [S], it provides a convenient linear representation of kinetic data.

Intercepts from the best-fit line provide 1/V_max (y-axis) and −1/K_m (x-axis). This linearization often helps diagnose different inhibition patterns.

Reversible Inhibition

Enzyme activity can be reduced by reversible inhibitors that bind noncovalently. Key types include:

Common Patterns of Reversible Inhibition

Inhibition Type	Binding Site	Effect on Km	Effect on Vmax
Competitive	Active site (competes with substrate)	Km increases	Vmax unchanged
Noncompetitive	Allosteric site (binds E or ES complex)	Km unchanged	Vmax decreases
Uncompetitive	Binds only to ES complex	Km decreases	Vmax decreases

Competitive inhibitors often resemble the substrate, blocking the active site. Noncompetitive inhibitors bind elsewhere on the enzyme, impacting catalytic function regardless of substrate presence. Uncompetitive inhibitors stabilize the ES complex, preventing product release. Observing changes in K_m and V_max can reveal which inhibition mode is at play.

Allosteric Enzymes and Sigmoidal Kinetics

Certain enzymes deviate from Michaelis–Menten hyperbolic behavior and exhibit sigmoidal kinetics instead—indicative of allosteric regulation. These enzymes possess multiple subunits and binding sites whose occupancy affects others:

• Positive Effectors: Bind an allosteric site, enhancing substrate affinity or catalytic turnover (activators).
• Negative Effectors: Bind allosteric sites to reduce enzyme activity (inhibitors).

A classic example is aspartate transcarbamoylase (ATCase), which shifts between T (tense) and R (relaxed) states, modulated by negative effectors like CTP or positive effectors like ATP, ensuring precise regulation of metabolic pathways.

Summary

By measuring velocity changes with substrate concentration and inhibitor presence, scientists characterize an enzyme’s catalytic efficiency (V_max, K_m), reveal mechanistic clues, and discern regulatory strategies. Michaelis–Menten plots show a hyperbolic rise to saturation, while Lineweaver–Burk transformations enable linear parameter determination. Inhibitors selectively modulate enzyme function—competitive, noncompetitive, or uncompetitive— each impacting K_m and V_max differently. Finally, allosteric enzymes display subunit cooperativity and sigmoidal kinetics, tailoring metabolic flux to cellular demands.

Suggested Reading:
Lehninger Principles of Biochemistry (chapters on enzyme kinetics, inhibition, and allosteric regulation)
Biochemistry by Berg, Tymoczko, and Stryer (sections on Michaelis–Menten derivations, Lineweaver–Burk plots, and regulatory enzymes)