5.60 Thermodynamics & Kinetics Spring 2008

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1 MIT OpenCourseWare Therodynaics & Kinetics Spring 2008 For inforation about citing these aterials or our Ters of Use, visit:

2 1 Enzye Catalysis Readings: SAB, pp Enzyes are biological catalysts, consisting of proteins, that greatly accelerate reaction rates and do so with exquisite specificity. That is, a cheical reaction involving one reactant goes uch faster, but other cheical reactions involving the sae reactant or the sae cheical reaction perfored on an analogous reactant are soeties largely unaffected. S A E P A (accelerated) (not accelerated) P C S B P B (not accelerated) The reactant in an enzyatic process is called a substrate. Exaples: invertase 1) Sucrose + H 2 O(C 12 H 22 O 11 ) glucose (C 6 H 12 O 6 ) + fructose (C 6 H 12 O 6 ). O OH HO lactase 2) lactose (a C 12 ilk sugar) glucose + galactose (lactose intolerant: unable to produce lactose. LactAid and other products contain a for of lactase)

3 2 3) H COO H H C COO C +H 2 O fuarase OOC H OOC fuarate OH L-alate Key features: rate accelerated product specificity substrate selectivity [invertase does not work on splenda which is chlorinated sucrose.] stereospecificity (1) Michaelis-Menten Mechanis C C H One echanis that describes the behavior of any enzyes is known as the Michaelis-Menten echanis. k E + S 1 ES (1) k 1 k 2 ES E + P (2) S P (overall) In the first step of this echanis (1), enzye binds substrate, creating a Michaelis coplex (ES). This step is readily reversible. In the second step (2) the substrate is converted to product and is released fro the enzye. Frequently this step ay be considered irreversible because the concentrations, [E] and [P], are quite sall.

4 3 Because [E] is so sall and k 2 is usually large, the Michaelis coplex (ES) is generally present at low concentration. Treating ES as a steady-state interediate, we can derive an expression for the reaction rate. d[es] = k1 [E] k 1 [ES] k 2 [ES] = 0. dt At this point it is convenient to also replace [E], because it is often difficult to easure accurately. This is done by expressing the total enzye concentration as a su of free enzye [E] and enzye bound to substrate [ES]. = [E] + [ES] [E] = [ES]. Although [ES] is sall, the approxiation [E] is not valid, because is usually very sall as well. Substituting for [E], one obtains 0 = ( [ES] ) k 1 [ES]+ k 2 [ES] = 0 k [ES] SS = 1 [E] = 0 + k 1 + k 2 + k 1 + k 2 d[p] k = k2 [ES] = 2 dt + k 1 + k 2 This expression is traditionally written d[p] v = dt initial = + K Michaelis-Menten equation where v stands for reaction velocity, k 2 has been replaced by, and k 1 + k 2 has been replaced by K, the Michaelis constant. One typically easures the initial value of v (rate of appearance of P) at a series of initial values of. Two kinds of plots are convenient.

5 4 (i) v vs., v = d[p] dt initial v = v ax saturated All E tied up in ES v ax 2 initial slope = = v ax, when << K K K = K The initial slope ust not be confused with the initial rate. The initial slope is obtained by easuring the initial rate for several reaction ixtures at initial values of. This illustrates two iportant liits: (i) = K v linear in K (ii) [ S ] >> K v [ E ] 0 constant with respect to. v ax is the axiu reaction rate for a given quantity of enzye. It is achieved at a saturating concentration of substrate, at which every enzye olecule is busy carrying out a reaction (ES E + P) and there are no free enzye olecules waiting to find substrate.

6 5 is soeties called the turnover nuber, because it represents the rate at which each enzye olecule produces products under these saturating conditions. Maxiu nuber of product olecules fored per unit tie Turnover nuber = Nuber of enzye olecules = Maxiu rate of product foration = k ax = = Total concentration of enzye (2) Lineweaver-Burk plot A second useful plot for enzye kinetics is called the Lineweaver-Burk plot. It is useful because it is linear in 1/. 1 + K 1 K 1 = = + v K cat 1/v K K slope = = v ax 1 1 = v ax 1 K 1/ Notice that with this type of plot, it is possible to obtain K and v ax without easuring. However, in order to deterine = v ax /, one needs an accurate easureent of. To find accurate values of the slope and intercept, it is necessary to saple a wide range of values spaced roughly equally in 1/. One usually sets up reactions with a variety of initial substrate concentrations and easures the initial rate for each to obtain the data for this plot.