Transition state dissociation constants

The signature of proton transfer in solution is the red-shifted fluorescence of the deprotonated chromophore [4-7], From the transition frequencies of absorption and emission and the ground-state dissociation constant, the dissociation constant in the excited state can be calculated [4-7], The time scales of proton transfer processes generally are very short, of the order of picoseconds or below [7], Only recently has it become possible to detect the photoinduced proton transfer dynamics in solution in real time [9,10],... 

A situation that arises from the intramolecular dynamics of A and completely distinct from apparent non-RRKM behaviour is intrinsic non-RRKM behaviour [9], By this, it is meant that A has a non-random P(t) even if the internal vibrational states of A are prepared randomly. This situation arises when transitions between individual molecular vibrational/rotational states are slower than transitions leading to products. As a result, the vibrational states do not have equal dissociation probabilities. In tenns of classical phase space dynamics, slow transitions between the states occur when the reactant phase space is metrically decomposable [13,14] on the timescale of the imimolecular reaction and there is at least one bottleneck [9] in the molecular phase space other than the one defining the transition state. An intrinsic non-RRKM molecule decays non-exponentially with a time-dependent unimolecular rate constant or exponentially with a rate constant different from that of RRKM theory. 

Fast transient studies are largely focused on elementary kinetic processes in atoms and molecules, i.e., on unimolecular and bimolecular reactions with first and second order kinetics, respectively (although confonnational heterogeneity in macromolecules may lead to the observation of more complicated unimolecular kinetics). Examples of fast thennally activated unimolecular processes include dissociation reactions in molecules as simple as diatomics, and isomerization and tautomerization reactions in polyatomic molecules. A very rough estimate of the minimum time scale required for an elementary unimolecular reaction may be obtained from the Arrhenius expression for the reaction rate constant, k = A. The quantity /cg T//i from transition state theory provides... 

There are important consequences for this statement. The enzyme must stabilize the transition-state complex, EX, more than it stabilizes the substrate complex, ES. Put another way, enzymes are designed by nature to bind the transition-state structure more tightly than the substrate (or the product). The dissociation constant for the enzyme-substrate complex is... 

Thus, the enzymatic rate acceleration is approximately equal to the ratio of the dissociation constants of the enzyme-substrate and enzyme-transition-state complexes, at least when E is saturated with S. 

This is illustrated in Figure 1.6 for the dissociation of CO [3]. As a consequence of the high value of a, the proportionality constant of recombination is usually approximately 0.2, reflecting a weakening of the adatom surface bonds in transition state by this small amount. It implies that typically one of the six surface bonds is broken in the transition state compared to the adsorption state of the two atoms before recombination. 

A case similar to the slow, practically irreversible inhibition of jack bean a-D-mannosidase by swainsonine is represented by the interaction of castanospermine with isomaltase and rat-intestinal sucrase. Whereas the association constants for the formation of the enzyme-inhibitor complex were similar to those of other slow-binding glycosidase inhibitors (6.5 10 and 0.3 10 M s for sucrase and isomaltase, respectively), the dissociation constant of the enzyme-inhibitor complex was extremely low (3.6 10 s for sucrase) or could not be measured at all (isomaltase), resulting in a virtually irreversible inhibition. Danzin and Ehrhard discussed the strong binding of castanospermine in terms of the similarity of the protonated inhibitor to a D-glucosyl oxocarbenium ion transition-state, but were unable to give an explanation for the extremely slow dissociation of the enzyme-inhibitor complex. 

Consider the enzyme-catalyzed and noncatalyzed transformation of the ground state substrate to its transition state structure. We can view this in terms of a thermodynamic cycle, as depicted in Figure 2.4. In the absence of enzyme, the substrate is transformed to its transition state with rate constant /cM..M and equilibrium dissociation constant Ks. Alternatively, the substrate can combine with enzyme to form the ES complex with dissociation constant Ks. The ES complex is then transformed into ESt with rate constant kt , and dissociation constant The thermodynamic cycle is completed by the branch in which the free transition state molecule, 5 binds to the enzyme to form ESX, with dissociation constant KTX. Because the overall free energy associated with transition from S to ES" is independent of the path used to reach the final state, it can be shown that KTX/KS is equal to k, Jkail (Wolfenden,... 

Miller and Wolfenden, 2002). This latter ratio is the inverse of the rate enhancement achieved by the enzyme. In other words, the enzyme active site will have greater affinity for the transition state structure than for the ground state substrate structure, by an amount equivalent to the fold rate enhancement of the enzyme (rearranging, we can calculate KJX = Ksik Jk, )). Table 2.2 provides some examples of enzymatic rate enhancements and the calculated values of the dissociation constant for the /A binary complex (Wolfenden, 1999). 

The equilibrium constant of hexaphenylethane dissociation, in striking contrast to the rate constant for dissociation, varies considerably with solvent. The radical with its unpaired electron and nearly planar structure probably complexes with solvents to a considerable extent while the ethane does not. Since the transition state is like the ethane and its solvation is hindered, the dissociation rate constants change very little with solvent.12 13 From an empirical relationship that happens to exist in this case between the rate and equilibrium constants in a series of solvents, it has been calculated that the transition state resembles the ethane at least four times as much as it resembles the radical. These are the proportions that must be used if the free energy of the transition state in a given solvent is to be expressed as a linear combination of the free energies of the ethane and radical states.14... 

For the low-spin t2g aqua ions [Ru(H20)6]2+, [Rh(H20)6]3+, and [Ir(H20)e]3+ a d-activation mode would a priori be predicted. The approach of a seventh water molecule towards a face or edge of the coordination octahedron is electrostatically disfavored by the filled t2g orbitals which are spread out between the ligands. Rate constants for anation reactions of Cl-, Br-, and I- on [Ru(H20)e]2+ are very similar, indicating identical steps to reach the transition state, namely the dissociation of a water molecule (130). An extension of this study to a large variety of ligands demonstrated clearly that the rate determining... 

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