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Aulani " Biokimia Enzim Lanjut" Presentasi 5 Basic enzyme kinetics Aulanni’am Biochemistry Laboratory Brawijaya University

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Aulani " Biokimia Enzim Lanjut" Presentasi 5 Enzymes Enzymes are catalysts, that speed up the rate of a reaction, without changing the extent of the reaction. They are (in general) large proteins and are highly specific, i.e., usually each enzyme speeds up only one single biochemical reaction. They are highly regulated by a pile of things. Phosphorylation, calcium, ATP, their own products, etc, resulting in extremely complex webs of intracellular biochemical reactions.

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Aulani " Biokimia Enzim Lanjut" Presentasi 5 Law of mass action Given a basic reaction A + B C k1k1 k -1 we assume that the rate of forward reaction is linearly proportional to the concentrations of A and B, and the back reaction is linearly proportional to the concentration of C.

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Aulani " Biokimia Enzim Lanjut" Presentasi 5 Equilibrium Equilibrium is reached when the net rate of reaction is zero. Thus or This equilibrium constant tells us the extent of the reaction, NOT its speed.

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Aulani " Biokimia Enzim Lanjut" Presentasi 5 Basic problem of enzyme kinetics Suppose an enzyme were to react with a substrate, giving a product. S + EP + E If we simply applied the law of mass action to this reaction, the rate of reaction would be a linearly increasing function of [S]. As [S] gets very big, so would the reaction rate. This doesn’t happen. In reality, the reaction rate saturates.

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Aulani " Biokimia Enzim Lanjut" Presentasi 5 Michaelis and Menten In 1913, Michaelis and Menten proposed the following mechanism for a saturating reaction rate S + E k1k1 k -1 C k2k2 P + E Complex. product Easy to use mass action to derive the equations. There are conservation constraints.

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Aulani " Biokimia Enzim Lanjut" Presentasi 5 Equilibrium approximation And thus, since Thus reaction velocity

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Aulani " Biokimia Enzim Lanjut" Presentasi 5 Pseudo-steady state approximation And thus, since Thus reaction velocity Looks very similar to previous, but is actually quite different!

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Aulani " Biokimia Enzim Lanjut" Presentasi 5 Basic saturating velocity s V V max KmKm V max /2

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Aulani " Biokimia Enzim Lanjut" Presentasi 5 Lineweaver-Burke plots Plot, and determine the slope and intercept to get the required constants.

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Aulani " Biokimia Enzim Lanjut" Presentasi 5 Cooperativity S + E k1k1 k -1 C1C1 k2k2 P + E S + C 1 k3k3 k -3 C2C2 k4k4 P + E Enzyme can bind two substrates molecules at different binding sites. or EC1C1 C2C2 E E SS S S P P

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Aulani " Biokimia Enzim Lanjut" Presentasi 5 Pseudo-steady assumption Note the quadratic behaviour

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Aulani " Biokimia Enzim Lanjut" Presentasi 5 Independent binding sites EC1C1 C2C2 E E SS S S P P 2k + k+k+ 2k - k-k- Just twice the single binding rate, as expected

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Aulani " Biokimia Enzim Lanjut" Presentasi 5 Positive/negative cooperativity Usually, the binding of the first S changes the rate at which the second S binds. If the binding rate of the second S is increased, it’s called positive cooperativity If the binding rate of the second S is decreased, it’s called negative cooperativity.

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Aulani " Biokimia Enzim Lanjut" Presentasi 5 Hill equation In the limit as the binding of the second S becomes infinitely fast, we get a nice reduction. Hill equation, with Hill coefficient of 2. This equation is used all the time to describe a cooperative reaction. Mostly use of this equation is just a heuristic kludge. VERY special assumptions, note.

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Aulani " Biokimia Enzim Lanjut" Presentasi 5 Another fast equilibrium model of cooperativity EC1C1 C2C2 E E SS S S P P Let C=C 1 +C 2 k -1 k1k1 k3k3 k -3 k2k2 k4k4 S + E k1k1 k -1 C s) P + E

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Aulani " Biokimia Enzim Lanjut" Presentasi 5 Monod-Wyman-Changeux model A more mechanistic realisation of cooperativity.

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Aulani " Biokimia Enzim Lanjut" Presentasi 5 Equilibrium approximation Don’t even think about a pseudo-steady approach. Waste of valuable time. which gives occupancy fraction and so on for all the other states Note the sigmoidal character of this curve

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Aulani " Biokimia Enzim Lanjut" Presentasi 5 Reversible enzymes Of course, all enzymes HAVE to be reversible, so it’s naughty to put no back reaction from P to C. Should use S + E k1k1 k -1 C k2k2 P + E k -2 I leave it as an exercise to calculate that

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Aulani " Biokimia Enzim Lanjut" Presentasi 5 Allosteric modulation substrate binding inhibitor binding at a different site this state can form no product (Inhibition in this case, but it doesn’t have to be) X Y Z

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Aulani " Biokimia Enzim Lanjut" Presentasi 5 Equilibrium approximation X YZ Could change these rate constants, also. Inhibition decreases the V max in this model

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