Previous Class. Today. Michaelis Menten equation Steady state vs pre-steady state

Transcription

1 Previous Class Michaelis Menten equation Steady state vs pre-steady state Today Review derivation and interpretation Graphical representation Michaelis Menten equations and parameters

2 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]

3 The Michaelis Menten Equation

4 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

5 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

6 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?

7 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 ES with the effectiveness of productive substrate binding kcat/km can be obtained directly from steady state expts

8 Units v 0 = initial velocity of Product formation = moles Product formation (moles substrate loss)/litre x time = mm s -1 Vmax = represents the maximum rate the enzyme reaction can achieve. Vmax occurs when all of the enzyme is in the ES complex. Km = [S] at Vmax/2 = µm kcat = first order rate constant = s -1 # of catalytic cycles active site undergoes per unit of time kcat/km = second order rate reaction of E and S = M -1 s -1

9 Plotting kinetic data Michaelis-Menten kinetics (steady state kinetics) Measure Initial rates (v 0 ) at different substrate concentrations by detecting the absorbance difference over time and obtaining the slope of the line Obtain various initial rates at different substrate concentrations and plot Use Lineweaver-Burke plots to obtain kcat, Km, kcat/km

10 Plotting kinetic data Measuring initial rates: The initial velocity is the amount of product produced per minute Assay involves adding all of the components including substrate first Once enzyme is added the absorbance is continually monitored and recorded with respect to time Abs vs time can be plotted Determine slope of tangent Absor. Enzyme added time

11 Plotting kinetic data Measuring initial rates: The slope of tangent = Abs/unit of time (min) Recall A = εcl, therefore A = ε cl (change in conc of Product) When c occurs in a known time period then c min -1 = v 0 v 0 = A min -1 / εl = c min -1 Has M/min after multiplying by vol. of enzyme assay solution the units change to mol/min.

12 Plotting kinetic data Determine v 0 at different substrate concentrations and plot

13 The Michaelis Menten Equation

14 Lineweaver-Burke transformation of the Michaelis-Menton equation. Velocity vs substrate plots are useful for visually estimating kinetic parameters Hyperbolic curves cannot properly determine the upper limit of the curve (Vmax) Transforming the data to a form that can be plotted as a line may improve accuracy.

15 Lineweaver-Burke transformation of the Michaelis-Menton equation. v = Vmax [S] Km + [S] Reciprocal of the equation is: 1 Km + [S] = v Vmax [S] Express reciprocal in the familiar form y = mx + b

16 Lineweaver-Burke transformation of the Michaelis-Menton equation. y = mx + b 1 Km = + V Vmax [S] 1 Vmax

17 1 Km = + V Vmax [S] 1 Vmax Lineweaver-Burke equation represents a straight line with slope = Km/Vmax, y intercept = 1/Vmax, and x intercept = -1/Km A 0.6 B 0.5 1/v (mm/min) /[S] (mm)

18 Lineweaver-Burke transformation of the Michaelis-Menton equation. Most commonly used Magnitude of errors can become distorted Furthest point to the right (lowest [S]) influences where line is drawn e.g. small error in v = large error in 1/v Good for observing enzyme inhibition

19 Eadie-Hofstee Plot Multiply both sides of L.B. by Vmax Multiply both sides by v Rearrange for v v 0 Km Vmax v 0 = - [S] Plot v 0 vs v 0 [S]

20 Eadie-Hofstee Plot Vmax v 0 -Km = slope Vmax Km v 0 /[S]

21 Eadie-Hofstee Plot Best for controlling slight deviations from linearity One disadvantage is that the least precise parameter (v 0 ) is expressed in both sides of the equation and plot

22 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)

23 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