Internal equilibrium constant

Equihbria involving the productively bound substrates and the products formed during an enzyme-catalyzed reaction. These equihbria can be treated in terms of internal equilibrium constants (i mt) between these enzyme-bound species. 

Phosphorus-31 NMR has been used to measure internal equilibrium constants within enzyme-substrate (ES) complexes.663 685 687 By having both substrate and product concentrations high enough to saturate the enzyme, all of the enzyme exists as ES and enzyme-product (EP) complexes in equilibrium with each other. For a phosphotransferase at least one substrate and one product contain phosphorus. Although the NMR resonances are broadened by binding to the large, slowly tumbling protein, their areas can be measured satisfactorily and can be used to calculate an equilibrium constant such as that for Eq. 12-32 ... 

Balancing internal equilibrium constants sequestration of unstable intermediates12... 

Dahlberg, M. E., and Benkovic, S. J. (1991). Kinetic mechanism of DNA polymerase I (Klenow fragment) Identification of a second conformational change and evaluation of the internal equilibrium constant. Biochemistry 30, 4835-4843. 

Perform equilibrium measurements to establish the overall free energy of the reaction in solution, and, if possible, the internal equilibrium constants for reactions occurring at the active site. In addition, it is often possible to measure the equilibrium dissociation constants for the binding of any substrates that, by themselves, will bind and not react, such as the first substrate to bind in a multiple-substrate mechanism. 

The net overall equilibrium constant for the reaction in solution (Kna) and the internal equilibrium constant for reaction at the active site (/fmi) can be measured most easily using radiolabeled substrates. Thus the problem becomes one of separating substrate and product chromatographically and then quantitating the ratio of /fnet = P]/[S] following incubation of the substrate with a trace of enzyme for a time sufficient for the reaction to come to equilibrium. The equilibration time can be estimated from the magnitude of kcJKm in the forward and reverse reactions. If the substrate and product concentrations are below their Km values, then the rate of approach to equilibrium can be approximated by... 

The internal equilibrium constant can be measured after finding conditions under which all of the substrate and product will be bound to the enzyme. This is done by working at concentrations of enzyme in 5- or 10-fold excess of the dissociation constants for each substrate. Accordingly, the ratio of [P]/[S] measured will reflect the ratio of [E-P]/[E-S] = Kim- The time required for the reaction to come to equilibrium can be approximated from the relationship /tobs itcai + kai to provide a minimum estimate of the rate of reaction at the active site. Usually the time calculated will be in the millisecond domain, but incubation for S sec is more convenient for manual mixing and usually no side products are formed on this time scale. Although in some cases it may be difficult to obtain concentrations of enzyme in excess of the dissociation constants for the substrates and products, the quantitation of the product/substrate ratio can be done quite accurately thanks to the fundamental property of enzyme catalysis that leads to an internal equilibrium constant close to unity for most enzymes (78-20). 

There have been extensive discussions in the literature regarding maximization of the catalytic efficiency of enzymes and the value of their internal equilibrium constants is the equilibrium constant between substrates and products of the enzyme when all are bound productively) (98-102). For example, the value of A int is near unity for both liver alcohol dehydrogenase (78) and lactate dehydrogenase (103) when measured with their natural substrates. The ability of these same enzymes to function with alternative substrates with widely differing external equilibrium constants raises important questions regarding the relationships of the internal thermodynamics of such reactions. 

Shifts in AE° on complex formation reflect a difference between the internal equilibrium constant K2 and the overall equilibrium constant Attention has focused on the relationship between K2 and in connection with the optimal free energy profile for an enzyme-catalyzed reaction (117, 118). In a sequential reaction mechanism, the greatest flux of material occurs along pathways lacking both large kinetic barriers and highly stable intermediates (119). in terms of a... 

A complete kinetic scheme has been established for the enzyme from both sources. The L. casei dihydrofolate reductase followed a reaction sequence identical to the E. coli enzyme (Scheme I) moreover, none of the rate constants varied by more than 40-fold Figure 20 is a reaction coordinate diagram comparing the steady-state turnover pathway for E. coli and L. casei dihydrofolate reductase, drawn at an arbitrary saturating concentration (1 mM) of NADPH at pH 7. The two main differences are (i) L. casei dihydrofolate reductase binds NADPH more tightly in both binary (E-NH, -2 kcal/mol) and tertiary (E NH-H2F, - 1.4 kcal/mol E-NH-H4F, - 1.8 kcal/mol) complexes, and (ii) the internal equilibrium constant (E-NH H2F E-N-H4F) for hydride transfer is less favorable for the L. casei enzyme (1 kcal/mol). These changes, as noted later, are smaller than those observed for single amino acid substitutions at the active site of either enzyme. Thus, the overall kinetic sequence as well as the... 

The equilibrium between intermediates EA and EP, EA zz EP, is characterized by the free energy change A5 in Fig. 3, corresponding to -RT Inf/fpr) KfT is the dimensioneless internal equilibrium constant (i.e., fcforward/fcreverse) (Bimbaum et al, 1989). The simplest way to determine the internal equilibrium constant would be to incubate a low level of substrate with increasing amounts... 

---