Medicinal Chemistry Applet

Michaelis-Menten kinetics

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Introduction

Enzymes catalyze reactions in physiological systems.  In an equilibrium, an enzyme (E) binds a substrate (S) to form an enzyme-substrate complex (E-S).  The E-S complex can dissociate or irreversibly convert the substrate to a product (P) (Scheme 1).  The Michaelis-Menten equation describes the relationship between the rate of substrate conversion by an enzyme to the concentration of the substrate (Equation 1).  In this equation, V is the rate of conversion, V_max is the maximum rate of conversion, [S] is the substrate concentration, and K_m is the Michaelis constant.  The Michaelis constant is equivalent to the substrate concentration at which the rate of conversion is half of V_max.  K_m approximates the affinity of enzyme for the substrate.  A small K_m indicates high affinity, and a substrate with a smaller K_m will approach V_max more quickly.  Very high [S] values are required to approach V_max, which is reached only when [S] is high enough to saturate the enzyme.  While the derivation is not shown in this discussion, V_max is equivalent to the product of the catalyst rate constant (k_cat) and the concentration of the enzyme.

Scheme 1 - enzyme-substrate complex and product formation model

     (1)

Applet

This applet plots V vs [S] data for up to three compounds/situations.  For each compound, K_m and V_max must be specified.  The units of K_m and [S] are concentration, e.g. mM or µM.  The units of V_max and V are amount of product over time, typically µmol/min or similar.

Problem information

Some enzymes are extremely specific while others accept a broad range of substrate structures.  Chymotrypsin, a digestive enzyme that hydrolyzes proteins, is a fairly general enzyme.  Although chymotrypsin will react with a range of substrates, the various substrates will not react equally well.  Three esters of amino acids are shown below with their corresponding K_m and V_max values.

Problems

1. Using the applet, generate V_max vs time plots for the three chymotrypsin substrates.  With this type of graph, which is easier to distinguish visually - a difference in K_m or V_max?
2. Substrates 1, 2, and 3 are very similar and are drawn to highlight their resemblance.  The Michaelis-Menten plots for these compounds also are very similar.  However, just because two compounds look the same in their structure does not mean that they will behave the same with an enzyme.  Compound 4 below looks much like the other three.  Drop the data for compound 3, replace it with the data for compound 4, and generate a new graph.  Does the enzyme treat compound 4 in the same way as the other three?

   

3. Stereochemistry is another important aspect of structure.  Generate a new graph including compounds 2 and 5.  The number of structural aspects that must be considered and accounted for in studying enzyme kinetics makes this field extremely challenging.

   

Reference

Hein, G. E.; Neimann, C. J. Am. Chem. Soc. 1962, 84, 4487.

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