enzyme_kinetics1

enzyme_kinetics1 - Enzyme Kinetics: Part A General...

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Enzyme Kinetics: Part A General Formulation of Ligand Binding Professor Steinman has already covered the analysis of ligand binding to macromolecules. For the biochemist not working on enzyme mechanisms, this is possibly the most important physical analysis to understand. It applies to any binding reaction of the type, E + S ES K d k 1 k -1 or more complicated variations with more than one ligand molecule binding to the enzyme (or other macromolecule). Remember that K d = k 1 k 1 = [E] free [S] free [ES] The "free" subscripts are important. We are interested in the fraction of total enzyme bound by substrate, f b : f b = [ES] [E] free + [ES] since [E] total = [E] free + [ES] In his lecture 4 notes, Professor Steinman shows that, using the relation for K d above, one can easily arrive at the relationship: f b = [S] free K d + [S] free Here, in calculating the fraction of enzyme bound by S, f b , one assumes that [S] free = [S] total . For enzyme kinetics, this is generally a very good assumption since we often use nanomolar
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2 enzyme concentrations and millimolar substrate concentrations. In this case, the concentration of S bound by E is insignificant compared to the total concentration of S. This is not always the case. When one deals experimentally with complexes that have very low K d values (e.g. low nM), frequently it is necessary to work under conditions where [Ligand] • [Macromolecule]. This is not uncommon when studying, for example, hormones binding to receptors or antibodies binding to proteins. In these cases, the general solution for a binding reaction must be employed to extract the correct K d value from your data. This equation is: f b = ([ E] t + [S] t + K S ) ([ E] t + [S] t + K S ) 2 4[E] t [S] t 2[E] t Basic Equations of Enzyme Kinetics When working with enzyme catalyzed reactions, generally [E] << [S] tot so that it is a valid assumption that [S] free = [S] tot . We will use this assumption throughout the discussion of enzyme kinetics. Most frequently one takes the phrase "enzyme kinetics" refers to the analysis of the "steady state" kinetics of enzymatic reactions. The term "steady state" has a specific meaning. The steady state is the phase of a reaction in which reactive intermediates are both formed and decomposed at the same rate so that their concentrations are essentially constant. Analogies are always helpful for an intuitive understanding. A good analogy is that an animal population can be in a "steady state". This occurs when the rate of birth and death are equal. The "reactive intermediates" (the live animals in the population) are then in the steady state, with the most "stable" states being those of pre-birth and death.
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3 Consider the following chemical reaction: A + B AB* C + D If the AB * complex is a high energy species relative to the A + B and C + D ground states then, as a good approximation, as soon as it is formed it will either go to A + B or C + D. This means that it's concentration will be very low and
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enzyme_kinetics1 - Enzyme Kinetics: Part A General...

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