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How concentration of each molecular species change over time
Course:- Chemical Engineering
Reference No.:- EM131383213




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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 kcat, and the Michaelis Menten constant Km. This equation is:

r = (kcat [E]tot [S]) / (Km + [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 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 kcat of hexokinase and the Km 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 first 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 reaction rate r to the substrate concentration [S], the inhibitor concentration [I], the total enzyme concentration [E]tot, the enzyme turnover number kcat, the substrate's Michaelis Menten constant Km, and the inhibitor's equilibrium disassociation constant, Ki. The Ki has units of mM. You must also define the kinetic constants that appear in your definition of Km and Ki.

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 steady-state.

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 kcat, the substrate's Michaelis Menten constant Km, and the inhibitor's equilibrium disassociation constant, Ki.




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