Assignment Help >> Chemical Engineering
Assignment: Introduction to Biomolecular Engineering
1. The Michaelis 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:
r = (k_{cat} [E]_{tot} [S]) / (K_{m} + [S])
A member of your 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 Dglucose and measured the resulting production rate of Dglucose 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 LineWeaver Burke plot) or nonlinear regression. You must show all work, including any graphs, calculations, or necessary code.
Dglucose, mM

Dglucose 6phosphate 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 enzymesubstrate complex (ES). In the first case, the inhibitor forms an enzymeinhibitor complex (EI). In the second case, the inhibitor forms an enzymesubstrateinhibitor complex (ESI). This is called noncompetitive inhibition.
Derive an expression that relates the enzymecatalyzed reaction 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}.
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. Write down a mole conservation equation for the free enzyme and enzyme complexes.
D. Then solve for the enzyme complex concentrations by assuming that their concentrations have reached steadystate.
E. Finally, employ these expressions to determine the reaction rate r, which is equal to the production 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}.