1) Enzyme kinetics with non-productive binding [80pts]. Consider a kinetic scheme where the substrate can bind an enzyme in two orientations. One state (ES) can proceed to product and another state (ES') is in a non-productive conformation: E+Sk1k1ESk2E+Pk3k3ES a) [30 pts] Derive a rate equation for this reaction. Your answer should take the form: Vobs=(c2+[S])c1[E]0[S] Where c1 and c2 are constants that are functions of the individual rate constants. c1 is the observed value of kcat and c2 is the observed value of KM. Your answer will be in the general form of the Michaelis-Menten equation and you should be able to write expressions for kcat (i.e., c1 - the observed value of kcat ) and KM (i.e., c2 - the observed value of KM ) in terms of the individual rate constants above. Hint: this and subsequent steps of the problem will be much easier if you group rate constants together in apparent equilibrium constants like the way we define KM in the simple Michaelis-Menten scheme. *Note: your answer must take the form exactly as indicated above. c1 and c2 are constants with no dependence on [S] or any other variables. You still have more algebra to do (and parts c-d will be extremely difficult) if your answer looks like this: Vobs=(cy+cz[S])+[S]cx[E]0[S]