6.1 Enzyme Kinetics: Substrate Concentration & Reaction Rate

Enzyme Kinetics

Enzyme Kinetics: rate of a chemical rxn can be measured by the appearance of product (or disappearance of substrate)

• enzymes DONT affect thermodynamics

• overtime [product] will increase until equilibrium

For a simple isomerization rxn:

→ rate of product appearance will depend on [enzyme:substrate complex]

• rate: v = k [ES]

• under steady state conditions: [ES] is relatively constant

  • after substrate binds to enzyme the [ES] doesn’t change much, THUS theres a steady state after initial binding

• substrate can dissoc. or be converted to product after binding to enzyme

note:

Rxn rate at start of Reaction: Initial Velocity (V0)

Initial velocity (V0) = rxn rate (rate of product formation) at the START of a rxn

• rate at the beginning, BEFORE product accumulates - thus NO reverse rxn is occurring form product buildup

• rate is dependent on [substrate]

  • adding more [substrate] increase initial velocity of rxn (1st order

→ described by the Michaelis-menten equation

Ligand Binding vs. Enzyme system for Kinetics

Ligand Binding: focus on Kd (dissoc constant)

Enzyme System: includes 4 rate constants

• focus on:

  • k1 = association of E + S

  • k-1 = breakdown of ES to E + S

  • k2/Kcat = formation of products from ES

• has assumptions

Assumptions of the Enzyme System

1. steady state conditions apply: [ES] is UNchanging overtime → rate of making ES = rate of breaking ES

2. NO [product] at beginning of rxn

• initial conditions: [P] = 0, thus we can ignore k-2

3. relative concentrations: always more [substrate] than enzyme, so we’re only concerned with substrate in solution

• [S] » [E] , thus we can ignore the change in [S] with formation of ES complex

4. formation of product: v0 = k2 [ES]

• 1st order rate equation

• k2 = kcat

Michaelis-Menten Kinetics

M-M Kinetics = derives a relationship b/w [ES] & [S] to find the rate of product formation

• says initial velocity (v0) depends on [ES]

  • v0 = kcat [ES]

• says rate of [ES] formation must equal rate of breakdown to be at steady state

  

  • thus at steady state: [ES] is unchanging so

→ total enzyme (E Total) = [E] + [ES]

• can be used to find [ES]

Derivation of Michaelis-Menten equation

1. defines [ES] by [S]

2. defines michale’s constant (Km) to simply the rate constant of the rxn

3. replaces rate constants with Km, so the rate of rxn (V0) equals:

• this is the equation at actual [ES]

4. defines maximum rate (Vmax) at the max [ES]

5. simples Kcat x [E total] to Vmax in equation to get the final M-M equation

→ Final Michaelis-Menten equation: for the rate of rxn

Michaelis-Menten Equation Components

M-M equation: V0

• Vmax ISNT a constant, it changes w amount of enzyme present

• Km is a constant

• M-M enzymes have a hyperbolic curve

→ Max velocity (Vmax) = determined by the total amount of enzyme in the system

• NOT a constant

→ Michaelis constant (Km) = reflects the balance b/w formation & breakdown of the ES complex

• k1 = association of E + S

• k-1 = breakdown of ES to E + S

• k2/Kcat = formation of products from ES

M-M Kinetics: Hyperbolic Curve

for: Km, [S], V0, Vmax

• measures initially velocity (V0) against [substrate]

• M-M equation generates a hyperbolic relationship b/w [S] & V0

Km = [Substrate] to get to 50% max velocity of enzyme rxn

• increase Km = pushes curve to right, thus need MORE [S]

• decreased Km = pushes curve to left, thus need LESS [S]

note: this ISNT when 50% of substrate is bound, as [S] » [E]

Q. Considering the Michaelis-menten equation, what is the [S] (in terms of Km) when the velocity of the reaction is 80% of Vmax?

1. M-M equation

   

2. 
   

   

3. multiply 0.80 by (Km + [S])

4. isolate for [S] again

answer: [S] = 4Km

• Km = [Substrate] to get to 50% max velocity of enzyme rxn

  • thus at 4Km, the enzyme is operating at 80% of max velocity

  • note: if rate/velocity is greater than 50%, then its greater than Km

sorta like: [S] for M-M equation = km x (V0/ 1- V0) → _Km

Rearranging the M-M equation so its linear: Lineweaver-Burk Plots

→ hyperbolic curves are bad at going to infinity, thus we can rearrange the equation so its linear (create reciprocal)

• get Double-Reciprocal plot

slope:

y-int:

x-int: