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Question: problem4enzymekinetics enzymes act as catalysts to speed up the rate...

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Problem4-Enzyme_Kinetics: Enzymes act as catalysts to speed up the rate of chemical reactions in living cells. In most cases, they convert one chemical, the substrate, into another, the product. The Michaelis-Menten equation is commonly used to describe such reactions: mS] k, [S] V- where v the initial reaction velocity, the maximum initial reaction velocity, [S]- substrate concentration, and ka half-saturation constant. As in Fig.3, the equation describes a saturating relationship which levels off with increasing [S. The graph also illustrates that the half-saturation constant correspond to the substrate concentration at which the velocity is half the maximum. Second-order Michaelis-Menten model 0.5 Michaelis-Menten model k, [S Fig.3. Two versions of Michaelis-Menten model of enzyme kinetics Although the Michaelis-Menten model provides a nice starting point, it has been refined and extended to incorporate features of enzyme kinetics. One simple extension involves so-called allosteric enzymes, where the binding of a substrate molecule at one site leads to enhancedbinding of subsequent molecules at other sites. For cases with two interacting bonding sites, the following second-order version often results in a better fit: VE This model also describes a saturating curve but, as depicted in Fig.3, the squared concentrations tend to make the shape more sigmoid, or S-shaped. Suppose that you are provided with the following data: [S 1.3 1.8 4.5 6 9 v 0.07 0.13 .275 0.335 0.35 0.36 0.22 Employ linear regression to fit this data with linearized versions of Eqs. (1) and (2). Aside from estimating the model parameters, asses the validity of the fits calculating the error for each fitting and make the graph of v vs. [S] (for each model) together with the experimental data shown in table above.

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