Previous Class Cosubstrates (cofactors) Today Proximity effect Basic equations of Kinetics Steady state kinetics Michaelis Menten equations and parameters
Enzyme Kinetics Enzyme kinetics implies characterizing the rate or velocity of an enzyme catalyzed reaction Key to studying enzyme kinetics is to understand that reaction velocity is altered by changes in the substrate concentration which is displayed using mathematics To begin we will deal with a simple enzyme system consisting of one substrate and no allosteric cofactors. E + S ES E + P k 1 k 2 k -1
Progress of reaction as a velocity Without enzyme expect rate to be proportional to [S] With enzyme curve line is observed (1) First order kinetics similar to non catalyzed (substrate binding rate limiting) (2) Rate rising with [S] but not proportional (3) Zero order kinetics increase of [S] having little effect on rate of reaction saturated enzyme rate limiting step is conversion to product Velocity/Concentration Curve v (rate) (1) S (2) k 1 [S] P (3) + enzyme k 1 k 2 E + S ES E + P k -1 No enzyme
Velocity/Concentration Curve Analysis of curve addresses: How fast enzyme operates How efficiently enzyme converts substrates to products How enzyme responds to various inhibitors or stimuli This may reveal: If a reaction will likely occur in vivo What factors regulate enzyme Strategy for drug design v (rate) [S] k 1 k 2 E + S ES E + P k -1
The Michaelis Menten Equation Derivation k E + S 1 k ES 2 E + P k -1 v 0 = d[p]/dt = k 2 [ES] Steady State Approximation assumes that [ES] remains constant during the velocity (rate) measurement. d[es]/dt = 0
Steady State kinetics Steady state conditions: Enzyme is fully saturated with substrate (Forming reaction intermediate). When the concentration of the intermediate reaches steady state the reaction rates change slowly Therefore, more feasible to obtain rate experimentally under steady state conditions Pre-steady state: Enzyme is not saturated with substrate ([intermediates] still increasing)
Steady State vs Pre-Steady State -Analyze at low enzyme concentration -Easily obtained data -Macroscopic rate constants can be obtained -Little information about mechanism -Can be coupled to other methods to gain mechanistic details -High enzyme concentrations needed -Sophisticated equipment needed -Microscopic rate constants can be obtained -Detailed mechanistic information can be obtained -Intermediates can be directly observed
The Michaelis Menten Equation Derivation k 1 k E + S ES 2 E + P k -1 d[es] dt = k 1 [E][S] k -1 [ES] k 2 [ES] = 0 Steady state pg106
The Michaelis Menten Equation Derivation k 1 k 2 E + S ES E + P k -1 d[es] dt = k 1 [E][S] k -1 [ES] k 2 [ES] = 0 (approx) [E][S] [ES] = k -1 + k 2 = Km Eqn 1 k 1 [E T ] = [E] + [ES] = Km [ES] + [ES] = [ES] (Km + 1) = [ES] (Km + [S]) [S] [S] [S] [ES] = [E T ][S] Km + [S]
The Michaelis Menten Equation Derivation k 1 k 2 E + S ES E + P k -1 [ES] = [E T ][S] d[p] dt Km + [S] = k 2 [E T ][S] Km + [S] v 0 = d[p]/dt = k 2 [ES] d[p] dt => k 2 [E T ] = Vmax max d[p] dt = v 0 = Vmax [S] Km + [S]
The Michaelis Menten Equation v = Vmax [S] Km + [S] Km = Michaelis constant: Concentration of Substrate needed to reach half maximum velocity measure of substrate affinity Vmax = maximum velocity directly proportional to enzyme concentration
The Michaelis Menten Equation
The Michaelis Menten Equation Interpretation Obtain kinetic behaviour of an enzyme k 1 k 2 E + S ES E + P k -1 k 2 = kcat Catalytic constant of the reaction (first order) kcat is also known as the turnover number of the enzyme defining the maximum number of substrate molecules converted to product per unit of time How is kcat determined experimentally?
The Michaelis Menten Equation Km k 1 k 2 E + S ES E + P k -1 [E][S] [ES] = k -1 + k 2 = Km Eqn 1 k 1 Km represents the [S] when v = ½ Vmax (sub into eqn) Therefore, a lower Km value indicates a higher affinity for the substrate
The Michaelis Menten Equation kcat/km The constant part kcat/km is referred to as the catalytic efficiency of the enzyme: A direct measure of the efficiency of the enzyme in transforming Subst. kcat/km combines: the effectiveness of transformation of bound product with the effectiveness of productive substrate binding kcat/km can be obtained directly from steady state expts
Proximity Effects of Intramolecular Catalysis Proximity Effect-is defined as a rate increase due to two reactants being brought out of a dilute environment and placed closer together Catalyst only: Large loss of entropy would be experienced by substrate Enzymes (because they bind substrate; ES) provide a docking site and a micro environment allowing proper substrate orientation for reaction (induced fit, strain, binding energy) Increase in Effective Concentration of Catalytic Groups: Increases chances of reaction --molecules are closer together within an ES complex (becomes an intramolecular process)
Proximity Effects of Intramolecular Catalysis As an ES complex, substrate does lose freedom of movement (loss of entropy) upon fixation into active site. However, binding energy gained by positioning substrate with respect to catalytic residues overcomes loss of entropy Proximity Effect accounts for only part of rate enhancement Desolvating the substrate from water (or other solvent) eliminates energy barrier imposed by ordered solvent molecules (get some entropy back) accelerating reaction Remember: substitution of catalytic residues-not completely dead
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