Part 3

• The three dimensional structure of the protein


  • Provides important information
  • Enhanced by traditional protein chemistry and modern methods of site directed mutagenesis
• Mutagenesis


  Changing the amino acid sequence of a protein by genetic engineering
• These technologies permit enzymologists to examine the role of individual amino acids in enzyme structure and action
• Enzyme kinetics

  Determining the rate of reaction and how it changes in response to changes in experimental parameters
• Substrate Concentration Affects the Rate of Enzyme Catalyzed Reaction
• Enzyme catalyzed reaction


  At a given instant, the enzyme exists in two forms: the free or uncombined form E and the substrate combined form ES
• Pre-steady state

  1. Initial transient period when the concentration of ES builds up

  2. Very brief, often microseconds, required to convert one molecule of substrate to product
• Steady state


  The reaction achieves a state where [ES] (and the concentration of any other intermediates) remains approximately constant for the remainder of the reaction
• As most of the reaction reflects steady state, the traditional analysis of reaction rates is referred to as steady state kinetics
• Initial rate (V_0)

  Measured at the beginning of the reaction when only a small percentage of substrate is converted to product, so [S] can be regarded as constant
• At relatively low concentrations of substrate

  V_0 increases by smaller and smaller amounts in response to increases in [S]
• At high [S]

  A plateau is reached where increases in V_0 are vanishingly small as [S] increases
• ES complex

  The key to understanding the kinetic behavior of enzymes
• The kinetic pattern led to the proposal that the combination of an enzyme with its substrate molecule to form an ES complex is a necessary step in enzymatic catalysis
• Michaelis and Menten

  Postulated that the enzyme first combines reversibly with its substrate to form the enzyme substrate complex ES in a relatively fast reversible step, which then breaks down in a slower second step to yield the free enzyme and the reaction product P
• The overall rate must be proportional to the concentration of the species that reacts in the second step, ES
• At low [S]


  The rate is proportional to [S] because the equilibrium of E + S (k_1) (k_-1) ES is pushed toward formation of more ES as [S] increases
• At high [S]


  Virtually all the enzyme is present as the ES complex and [E] is vanishingly small, so the enzyme is saturated with the substrate and further increases in [S] have no effect on the rate
• After the ES complex breaks down to yield the product, P, the enzyme is free to catalyze the reaction of another molecule of substrate, and will do so rapidly under saturating conditions
• Saturation kinetics

  The saturation effect observed in enzymatic catalysts
• Michaelis-Menten equation


  Expresses the relationship between [S], V_0 and V_max, related through the constant K_m
• Derivation of the Michaelis-Menten equation

  1. Starts with the two basic steps of the formation and breakdown of ES

  2. Introduces the steady state assumption

  3. Solves for [ES] in terms of [E_t], [S] and K_m

  4. Expresses V_0 in terms of V_max, [S] and K_m
• K_m is defined as (k_-1 + k_2) / k_1
• When V_0 = 1/2 V_max, K_m = [S]
• Lineweaver-Burk equation

  A linear transformation of the Michaelis-Menten equation, used to determine V_max and K_m from a plot of 1/V_0 vs 1/[S]
• Nonlinear regression is more commonly used to derive V_max and K_m directly from the V_0 vs [S] plot
• Kinetic parameters V_max and K_m

  Used to compare enzymatic activities, but do not necessarily provide mechanistic insight
• The Michaelis-Menten equation applies to all enzymes that exhibit a hyperbolic dependence of V_0 on [S], even if their reaction mechanisms differ from the simple two-step model
• Interpreting K_m and V_max

  • Their meaning can vary greatly depending on the specific aspects of the reaction mechanism
  • K_m does not always represent substrate affinity
  • V_max depends on the rate limiting step of the reaction
• k_cat


  A more general rate constant used to describe the limiting rate of any enzyme catalyzed reaction at saturation
• the enzyme still apply, but K_m cannot be considered a simple measure of substrate affinity
• Even more common are cases in which the reaction goes through several steps after the formation of ES; K_m can then become a very complex function of many rate constants
• V_max

  The quantity that depends on the rate limiting step of the enzyme catalyzed reaction
• Two step Michaelis-Menten mechanism


  E + S (k_1) (k_-1) ES (k_2) (k_-2) EP (k_3) E + P
• If an enzyme reacts by the two step Michaelis-Menten mechanism, V_max = k_2 [E_t], where k_2 is rate limiting
• However, the number of reaction steps and the identity of the rate limiting step(s) can vary from enzyme to enzyme
• Reaction where product release, EP E + P is rate limiting


  E + S (k_1) (k_-1) ES (k_2) (k_-2) EP (k_3) E + P
• Early in the reaction, when [P] is low, the overall reaction can be adequately described by the scheme
• k_cat


  A more general rate constant to describe the limiting rate of any enzyme catalyzed reaction at saturation
• If the reaction has several steps, one of which is clearly rate limiting, k_cat is equivalent to the rate constant for that limiting step