Chemical Engineering: Biomolecular Engineering Homework

ChE 340 Introduction to Biomolecular Engineering Homework Set # 1. January 23 th , 201 7 DUE: February 3rd , 201 7 1. The Michael is Menten equation quantifies the relationship between reaction rate r, substrate concentration [S], total enzyme concentration [E] tot, the turnover rate k cat, and the Michaelis Menten constant K m. This equation is: A member of y our team has performed a series of experiments to measure enzyme reaction rates. They have added 10 µM of hexokinase and excess ATP to varying concentrations of D -glucose and measured the resulting production rate of D -glucose 6 - phosphate. The data from these experiments is listed below. Using this experimental data, determine the k cat of hexokinase and the K m of glucose in this reaction. You may use either graphing techniques (e.g. a Line -Weaver Burke plot) or non -linear regression. You must show all work, including any graphs, calculations, or necessary code. D-glucose, mM D-glucose 6 -phosphate production rate, mM/second 0.200 0.0130 0.500 0.0312 1.000 0.0589 10.00 0.2846 100.0 0.4683 2. Consider an enzyme that catalyzes the conversion of a single substrate, S, to a product, P, while also being inhibited by an inhibitor I. The inhibitor binds to either the enzyme (E) or the enzyme -substrate complex (ES). In the fi rst case, the inhibitor forms an enzyme -inhibitor complex (EI). In the second case, the inhibitor forms an enzyme -substrate -inhibitor complex (ESI). This is called non -competitive inhibition. Derive an expression that relates the enzyme -catalyzed reactio n rate r to the substrate concentration [S], the inhibitor concentration [I], the total enzyme concentration [E] tot, the enzyme turnover number k cat, the substrate's Michaelis Menten constant K m, and the inhibitor's equilibrium disassociation constant, K i. The K i has units of mM. You must also define the kinetic constants that appear in your definition of K m and K i. ] [ ] [ ] [ S K S E k r m to t ca t   A. Begin your derivation by writing down all chemical reactions occurring in the system. B. Then employ mass action kinetics to derive a system of ordinary differential equations that describes how the concentrations of each molecular species change over time. C. W rite down a mole conservation equation for the free enzyme and enzyme complexes. D. Then solve for the enzyme complex concentrations by assum ing that their concentrations have reached steady -state. E. Finally, employ these expressions to determine the reaction rate r, which is equal to the product ion rate of the product species, in terms of the substrate concentration [S], the inhibitor concentration [I], the total enzyme concentration [E] tot, the enzyme turnover number k cat, the substrate's Michaelis Menten constant K m, and the inhibitor's equilibrium disassociation constant, K i.