Forward commitment

Using the various simplifications above, we have arrived at a model for reaction 11.9 in which only one step, the chemical conversion occurring at the active site of the enzyme characterized by the rate constant k3, exhibits the kinetic isotope effect Hk3. From Equations 11.29 and 11.30, however, it is apparent that the observed isotope effects, HV and H(V/K), are not directly equal to this kinetic isotope effect, Hk3, which is called the intrinsic kinetic isotope effect. The complexity of the reaction may cause part or all of Hk3 to be masked by an amount depending on the ratios k3/ks and k3/k2. The first ratio, k3/k3, compares the intrinsic rate to the rate of product dissociation, and is called the ratio of catalysis, r(=k3/ks). The second, k3/k2, compares the intrinsic rate to the rate of the substrate dissociation and is called forward commitment to catalysis, Cf(=k3/k2), or in short, commitment. The term partitioning factor is sometimes used in the literature for this ratio of rate constants. 

Equation 11.36 recognizes that Hk3/Hk4 corresponds to the equilibrium isotope effect, hK3/4 for the step containing rate constants k3 and k4. The rate ratio k4/k.5 is the commitment for catalysis for the reaction that proceeds from products to substrates, and therefore is called the reverse commitment to catalysis, Cr. Also cf = k3/k2 is the forward commitment to catalysis. Since we have assumed that these steps are the only isotope sensitive ones, HK3/4 corresponds to the overall equilibrium isotope effect, HK. 

If k3[B]/k2 is much larger than unity, then the forward commitment is given by Equation 11.42 ... 

As mentioned in Section 11.3.5 for the case where the rate determining step is sensitive to both isotopic species, elucidation of the intrinsic isotope effects is not possible using the equations given thus far (if neither the reverse nor the forward commitment is zero). Even then, however, it is possible to solve for the intrinsic iso-... 

Selected entries from Methods in Enzymology [vol, page(s)] Add-base catalysis [with site-directed mutants, 249, 110-118 altered pH dependencies, 249, 110] commitment to [in determination of intrinsic isotope effects, 249, 343, 347-349 in interfacial catalysis, 249, 598-599 equilibrium isotope exchange in, 249, 443-479 hydrogen tunneling in, 249, 373-397] interfacial [competitive inhibitors, kinetic characterization, 249, 604-605 equilibrium parameters, 249, 587-594 forward commitment to, 249, 598-599 interpretation, 249, 578-586 (constraining variables for high processivity, 249, 582-586 kinetic variables at interface,... 

The observed change in the apparent CKIE for the reaction in the presence of pyridine supports this mechanism. Since the catalyst cannot affect kj, the increase results from a change in the balance between k i and subsequent steps that increases the forward commitment of the reaction. If we use the standard assumption that the transition state for C-C bond-breaking (associated with ki) is the point on the reaction coordinate where the C-C bond is completely broken, the CKIE will be comparable for all three compounds, regardless of the activation barrier. Therefore, a change in the observed CKIE can only result from changes in k and k2. 

The c r value is calculated for the first product released in a direct comparison or internal competition study, but for the perturbant in an equilibrium perturbation experiment. For example, with isocitrate dehydrogenase when deuterated isocitrate was used, (V/K) was near unity at neutral pH because the forward commitment for isocitrate is large, and certainly much larger than the reverse commitment for CO2, the first product released. In an equilibrium perturbation experiment, however, the perturbant on the right-hand side of the reaction is NADPH, which has an even higher reverse commitment than the forward one for isocitrate, so that the observed isotope effect of 1.15 was nearly equal to... 

Equation (84) can be converted to the comparable equation for the back reaction by dividing both sides by Cf and c, now become reverse and forward commitments in the back reaction, and is the intrinsic isotope effect in... 

We do not mean to imply that kg is an intrinsic isotope effect it will be given by an equation similar to Eq. (84) but containing only the internal portion of the forward commitment (cf.i ). The level of B will affect as long as is as big or bigger than ks- If k is zero (an ordered mechanism), becomes infinite at very high B, and no isotope effect is seen on WA itself. At very low B, on the other hand, cr.ex = kg/k. The level of B at which the isotope effect is half-suppressed is KaKJK. For a random mechanism, Cf.ex varies from kg/ik + its) at low B to kg/ki at high B. 

A forward commitment for a given reactant is defined as the ratio of the rate constant for the isotope-sensitive step to the net rate constant for release of that reactant from the enzyme, where a net rate constant corresponds to the net flux through a series of steps. 

If either substrate is rapidly released from the ternary complex, that is, either k4 or ks is large, the forward commitment factor simplifies to... 

At very low [B], the expression approaches the Mmiting isotope effect on V/K, that is, tends to (V/Kb), where the forward commitment factor reduces to... 

Thus, it is possible for a substrate to have a finite external commitment and stiU not be sticky, if Cr is larger than the external forward commitment (Qeland, 1977). 

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