Math 183. Shtylla Spring 2014 1 Assignment #1 Due on Wednesday, January 29, 2014 Name: Meliss a M. Hernandez Instr uctio ns: Soluti ons must be written clearly and stapled to this prob lem sheet. Scor es will depend not only on being able to provide the correct answer, but also on your ability to presen t yo ur though ts in an orga nized and clear wa y . An y outsi de sources must be cited and also anyone you worked on this set with must be acknowledged. Read Section 1.2, Biochemic al Kinet icsin the class lectur e notes. 1. Enzyme Kinetics. The react ion scheme shown below is central to the study ofenzyme -mediated reactions in biochemistry. The reaction scheme is E + S k 1 k −1 C k 2 E + P . (1) E is the concentration of an enzyme that catalyzes the transformation of the substrate of the reaction (S) into the product (P). An enzyme-substrate complex (C), where the enzyme and complex are bound together. a) Based on the law of mass action and examples in Chapter 1, write a dif- ferential equation system corresponding to the scheme. Solution: dSdt = −k 1 ES+k −1 CdEdt = −k 1 ES+ ( k −1 +k 2 )CdCdt =k 1 ES− (k −1 +k 2 )CdPdt =k 2 Cb) From the differential equation system verify that the following conserv ation statements hold: E(t) +C(t) =E0 (2) S(t) +C(t) +P(t) =S0 (3) Interpret the conservation statements in terms of the amount of the reac- tants and enzyme. Solution:
