5. Kinetics of Allosteric Enzymes. Sigmoidal Kinetics. Cooperativity Binding Constant

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1 5. Kinetics of Allosteric Enzymes Sigmoidal Kinetics Cooperativity Binding Constant

2 Kinetics of Allosteric Enzymes Contents Definitions Allosteric enzymes Cooperativity Homoallostery Heteroallostery Biphasic effect The Sigmoidal Plot and the Hill Equation Effects of substrate cooperativity on Linear Plots The Hill Plot

3 Allosteric enzymes Allosteric Enzymes multisubunit proteins with multiple topologically distinct binding sites which interact functionally with each other interactions between the subunits can be influenced by binding of the substrate (homoallostery) binding of effectors on regulatory sites (heteroallostery). Action of effectors Alter affinity of E for its substrate Change catalytic activity Change in tertiary and quaternary structure of allosteric protein upon effector binding Rate-limiting enzymes subject to allosteric regulation

4 Cooperativity Cooperativity: intro Modification in the binding constant of a protein for a substrate by the prior binding of an effector I.E.: when a substrate binds to one enzymatic subunit, the rest of the subunits are stimulated and become active Homoallostery: Binding of S influences affinity of E for S Noncooperative: Hyperbolic curve Cooperative : + Cooperativity: Binding of S - Cooperativity: Binding of S Sigmoidal curve affinity of E for S affinity of E for S V max is never reached [S] 0.5 = [S] at ½V max

5 Reciprocal Plot T ( TENSE ) High K m Binds S weakly R ( RELAXED ) Low K m Binds S strongly Binding of S increases affinity of enzyme for the S, i.e. equilibrium shifts from T R

6 Cooperativity: mechanisms Two models hypothesized: MWC model and KNF model. The Monod-Wyman-Changeux (MWC) model was advanced by Jacques Monod, Jeffries Wyman and Jean- Pierre Changeux in It posits that the protein has only two states, a lowaffinity state T and a high-affinity state R, where the T state is thermodynamically favored. - At low amounts of bound ligand, protein prefers the low-affinity T state; as the amount of bound ligand increases, protein prefers the high-affinity state. - Structural studies have supported the MWC model and elucidated the R and T states; however, the model cannot explain negative cooperativity.

7 An alternative model is the sequential or "induced fit" model of Daniel Koshland, George Némethy and Filmer (KNF model): - Ligand binding at one site causes a local conformational change ("induced fit") that causes small conformational changes at nearby binding sites, affecting their affinity for the ligand. - Thus, according to the KNF model, the protein has many slightly different conformational states, corresponding to all possible modes of ligand binding. In reality: usually MWC or combination. Current theory: pre-existing states, no conformational change, cooperativity driven by entropy, enthalpy or both

8 From Mathews Ch 7 (Hb oxygen-binding example):

9 Physiological function of sigmoidal kinetics Effect of extreme homoallostery Cooperative substrate binding maintains homeostasis of a dynamic system by keeping [S] within narrow margins. A small change in [S] causes a large change in enzyme activity. Examples: hemoglobin and glucokinase

10 Effectors bind at alternative regulatory sites of a multisubunit enzyme Binding of effectors influences the affinity of the enzyme for the S, i.e. the equilibrium between the T and R states In the absence of effectors, the V vs. [S] curve is sigmoidal Heteroallostery Activators affinity of enzyme for substrate. The equilibrium shifts from T R Inhibitors affinity of enzyme for substrate The equilibrium shifts from R T

11 Biphasic Effect In addition to allosteric inhibitors (which bind to binding sites distinct from the catalytic site), allosteric enzymes may be influenced by Competitive inhibitors Competitive inhibitors are substrate analogues that binds to the same catalytic site as the S Low [I] would increase the ability of the E to bind S and thus increase reaction velocity High [I] would block S binding in the usual way

12 The Sigmoid Plot and the Hill Equation Non-allosteric enzyme Hyperbolic plot MM Kinetics v 0 = V max [S] K m + [S] Allosteric enzyme Sigmoidal plot Non MM kinetics v 0 = V max [S] n K n [S] n n = Hill coefficient (sometimes written as n H ) Value gives a measure of cooperativity n = 1: No cooperativity, graph is hyperbolic n > 1: + ve Cooperativity, sigmoidal curve n < 1: - ve Cooperativity, sigmoidal curve

13 Effect of n on V vs [S] plot

14 Effect of n on linear plots The linear plots, such as the Lineweaver-Burk plot, commonly used in kinetic analysis are based on an algebraic conversion of the Michaelis equation. Since enzymes showing substrate cooperativity do not obey the Michaelis equation they do not show straight lines with these "linear" plots

15 The Hill Plot The Hill equation is rearranged as follows: v 0 = V max [S] n K n [S] n v 0 = [S] n V max - v 0 K n 0.5 log v 0 = n log [S] n log K 0.5 V max - v 0 A plot of log [v 0 /(V max v 0 )] vs log [S] is thus a straight line with slope n and y-intercept = n log K 0.5

16 Drawing the Hill Plot: Log S

17 The Hill Plot: problem Need V max for Hill Plot: 1. Get this from direct linear or Hanes plot using only higher [S]. 2. Use this V max to draw a Hill plot and calculate a (rough) estimate of n 3. Use this estimated n to redraw the original linear plot but replace the substrate concentration with S n. 4. Should now give a better straight line. Recalculate V max from this and redraw the Hill plot with the new value. This should give you a reasonable measure of n. ALTERNATIVELY: use software to do curve-fitting but with Hill equation instead of M-M equation!!

18 Allosteric enzymes.. are multi-subunit To summarise: bind other ligands at sites other than the active site (allosteric sites) can be either activated or inhibited by allosteric ligands exist in two major conformational states, R and T often control key reactions in major pathways, which must be regulated. Examples of these enzymes include glycogen phosphorylase (breaks down intracellular glycogen reserves) and aspartate transcarbamyolase, which catalyzes the first step in the synthesis of pyrimidine nucleotides.