02_-_Enzyme_Kinetics - Quantitative Physiology I /...

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Quantitative Physiology I / Molecular and Cellular Systems, BMEN E4001x Notes 02 - Enzyme kinetics Glycolysis is a key step in carbohydrate metabolism. This is the breakdown of glucose into pyruvate, which goes into the citric acid cycle, yielding two energy stores, ATP and NADH. Here are the first few steps, for which enzyme regulation plays a key role. This process takes some ATP, converting it to the lower energy ADP, but ATP is replenished later in metabolism. In this scheme, consider phosphofructokinase (PFK1) adds a second phosphate group (from ATP) to fructose, leading later to splitting of this molecule ATP is a substrate for this enzyme ATP is also an inhibitor of PFK1, leading to feedback regulation of this enzyme and metabolism Enzyme Kinetics In an enzymatic relation, something happens after the binding. So, our equations need to include this conversion. However, measured kinetics show a slightly different kinetics than would be alluded to using our bimolecular model. Note that for the initial A+B->C reaction, the initial rate reaction, assuming [C](t=0)=0 is: 1 1 k ] B ][ A [ dt ] C [ d abk dt dc = = In contrast, enzymatic systems often show saturation. A simple mechanism to express simple enzyme kinetics, Michaelis Menten (1913): E P C E S 2 1 1 k k k + →   → + - This system allows regeneration of E. It is also recognized that P+E-> C can conceptually happen, but it is assumed here that P gets removed immediately. G l u c o s e F r u c t o s e 6 - P F r u c t o s e 1 , 6 - P P y r u v a t e P F K 1
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0 2 2 1 1 2 1 1 1 1 e c e ck dt dp ck ck sek dt dc ck ck sek dt de ck sek dt ds = + = - - + = + + - = + - = - - - Equilibrium Approximation In this original form, Michaelis and Menten assumed fast equilibrium between the S,E and C. Thus: k 1 se=k -1 c and by using e+c=e 0 , with a similar chain of algebra as for biomolecular binding, they got: 1 1 s s 0 s 0 k k K ; ] S [ K ] S [ ] E [ ] C [ ; s K s e c - = + = + = Quite reasonable, when it is recognized that this is the same form as biomolecular binding. Put another way, this is bimolecular binding leading to a slow evolution of C into P + E. As the next step is ] [ ] [ 2 C k dt P d = we can say that the rate of reaction is proportional to [C], or 1 1 S S 0 2 k k K ; ] S [ K ] S [ ] E [ k V - = + =
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This note was uploaded on 12/21/2010 for the course BMEN 4001 taught by Professor Kam during the Fall '10 term at Columbia.

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02_-_Enzyme_Kinetics - Quantitative Physiology I /...

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