Complexes encounter

The introductory remarks about unimolecular reactions apply equivalently to bunolecular reactions in condensed phase. An essential additional phenomenon is the effect the solvent has on the rate of approach of reactants and the lifetime of the collision complex. In a dense fluid the rate of approach evidently is detennined by the mutual difhision coefficient of reactants under the given physical conditions. Once reactants have met, they are temporarily trapped in a solvent cage until they either difhisively separate again or react. It is conmron to refer to the pair of reactants trapped in the solvent cage as an encounter complex. If the unimolecular reaction of this encounter complex is much faster than diffiisive separation i.e., if the effective reaction barrier is sufficiently small or negligible, tlie rate of the overall bimolecular reaction is difhision controlled. 

The reason for this enliancement is intuitively obvious once the two reactants have met, they temporarily are trapped in a connnon solvent shell and fomi a short-lived so-called encounter complex. During the lifetime of the encounter complex they can undergo multiple collisions, which give them a much bigger chance to react before they separate again, than in the gas phase. So this effect is due to the microscopic solvent structure in the vicinity of the reactant pair. Its description in the framework of equilibrium statistical mechanics requires the specification of an appropriate interaction potential. 

R), i.e. there is no effect due to caging of the encounter complex in the common solvation shell. There exist numerous modifications and extensions of this basic theory that not only involve different initial and boundary conditions, but also the inclusion of microscopic structural aspects [31]. Among these are hydrodynamic repulsion at short distances that may be modelled, for example, by a distance-dependent diffiision coefficient... 

In many instances tire adiabatic ET rate expression overestimates tire rate by a considerable amount. In some circumstances simply fonning tire tire activated state geometry in tire encounter complex does not lead to ET. This situation arises when tire donor and acceptor groups are very weakly coupled electronically, and tire reaction is said to be nonadiabatic. As tire geometry of tire system fluctuates, tire species do not move on tire lowest potential energy surface from reactants to products. That is, fluctuations into activated complex geometries can occur millions of times prior to a productive electron transfer event. 

In tills weakly coupled regime, ET in an encounter complex can be described approximately using a two-level system model [23]. As such, tlie time-dependent wave function is... 

Interactions between nonpolar compounds are generally stronger in water than in organic solvents. At concentrations where no aggregation or phase separation takes place, pairwise hydrophobic interactions can occur. Under these conditions, the lowest energy state for a solute molecule is the one in which it is completely surrounded by water molecules. However, occasionally, it will also meet other solute molecules, and form short-lived encounter complexes. In water, the lifetime of these complexes exceeds that in organic solvents, since the partial desolvation that accompanies the formation of these complexes is less unfavourable in water than in organic solvents. 

The next step in the calculations involves consideration of the allylic alcohol-carbe-noid complexes (Fig. 3.28). The simple alkoxide is represented by RT3. Coordination of this zinc alkoxide with any number of other molecules can be envisioned. The complexation of ZnCl2 to the oxygen of the alkoxide yields RT4. Due to the Lewis acidic nature of the zinc atom, dimerization of the zinc alkoxide cannot be ruled out. Hence, a simplified dimeric structure is represented in RTS. The remaining structures, RT6 and RT7 (Fig. 3.29), represent alternative zinc chloride complexes of RT3 differing from RT4. Analysis of the energetics of the cyclopropanation from each of these encounter complexes should yield information regarding the structure of the methylene transfer transition state. 

For the reason given above and for other reasons, it is unlikely that the encounter complex is a n complex, but just what kind of attraction exists between Y+ and ArH is not known, other than the presumption that they are together within a solvent cage (see also p. 694). There is evidence (from isomerizations occurring in the alkyl group, as well as other observations) that n complexes are present on the pathway from substrate to arenium ion in the gas-phase protonation of alkylbenzenes. ... 

Not only are there substrates for which the treatment is poor, but it also fails with very powerful electrophiles this is why it is necessary to postulate the encounter complex mentioned on page 680. For example, relative rates of nitration of p-xylene, 1,2,4-trimethylbenzene, and 1,2,3,5-tetramethylbenzene were 1.0, 3.7, and 6.4, though the extra methyl groups should enhance the rates much more (p-xylene itself reacted 295 times faster than benzene). The explanation is that with powerful electrophiles the reaction rate is so rapid (reaction taking place at virtually every encounter between an electrophile and substrate molecule) that the presence of additional activating groups can no longer increase the rate. ... 

All enzymatic reactions are initiated by formation of a binary encounter complex between the enzyme and its substrate molecule (or one of its substrate molecules in the case of multiple substrate reactions see Section 2.6 below). Formation of this encounter complex is almost always driven by noncovalent interactions between the enzyme active site and the substrate. Hence the reaction represents a reversible equilibrium that can be described by a pseudo-first-order association rate constant (kon) and a first-order dissociation rate constant (kM) (see Appendix 1 for a refresher on biochemical reaction kinetics) ... 

The binary complex ES is commonly referred to as the ES complex, the initial encounter complex, or the Michaelis complex. As described above, formation of the ES complex represents a thermodynamic equilibrium, and is hence quantifiable in terms of an equilibrium dissociation constant, Kd, or in the specific case of an enzyme-substrate complex, Ks, which is defined as the ratio of reactant and product concentrations, and also by the ratio of the rate constants kM and km (see Appendix 2) ... 

As we have just seen, the initial encounter complex between an enzyme and its substrate is characterized by a reversible equilibrium between the binary complex and the free forms of enzyme and substrate. Hence the binary complex is stabilized through a variety of noncovalent interactions between the substrate and enzyme molecules. Likewise the majority of pharmacologically relevant enzyme inhibitors, which we will encounter in subsequent chapters, bind to their enzyme targets through a combination of noncovalent interactions. Some of the more important of these noncovalent forces for interactions between proteins (e.g., enzymes) and ligands (e.g., substrates, cofactors, and reversible inhibitors) include electrostatic interactions, hydrogen bonds, hydrophobic forces, and van der Waals forces (Copeland, 2000). 

Although fccat is a composite rate constant, representing multiple chemical steps in catalysis, it is dominated by the rate-limiting chemical step, which most often is the formation of the bound transition state complex ES from the encounter complex ES. Thus, to a first approximation, we can consider kCM to be a first-order rate constant for the transition from ES to ES ... 

Equations (2.10) and (2.12) are identical except for the substitution of the equilibrium dissociation constant Ks in Equation (2.10) by the kinetic constant Ku in Equation (2.12). This substitution is necessary because in the steady state treatment, rapid equilibrium assumptions no longer holds. A detailed description of the meaning of Ku, in terms of specific rate constants can be found in the texts by Copeland (2000) and Fersht (1999) and elsewhere. For our purposes it suffices to say that while Ku is not a true equilibrium constant, it can nevertheless be viewed as a measure of the relative affinity of the ES encounter complex under steady state conditions. Thus in all of the equations presented in this chapter we must substitute Ku for Ks when dealing with steady state measurements of enzyme reactions. 

We can now relate the kinetic constants kCM, Ku, and kcJKM to specific portions of the enzyme reaction mechanism. From our discussions above we have seen that the term kCM relates to the reaction step of ES conversion to ES. Hence experimental perturbations (e.g., changes in solution conditions, changes in substrate identity, mutations of the enzyme, and the presence of a specific inhibitor) that exclusively affect kCM are exerting their effect on catalysis at the ES to ES transition step. The term KM relates mainly to the dissociation reaction of the encounter complex ES returning to E + S. Conversely, the reciprocal of Ku (1IKU) relates to the association step of E and S to form ES. Inhibitors and other perturbations that affect the... 

For the enzyme isomerization mechanism illustrated in scheme C of Figure 6.3, there are two steps involved in formation of the final enzyme-inhibitor complex an initial encounter complex that forms under rapid equilibrium conditions and the slower subsequent isomerization of the enzyme leading to the high-affinity complex. The value of kohs for this mechanism is a saturable function of [/], conforming to the following equation ... 

In a two-step enzyme isomerization mechanism, as in scheme C, the affinity of the inhibitor encounter complex and the affinity of the final E I complex are reflected in the diminutions of v, and of vs, respectively, that result from increasing concen-... 

On the other hand, when K Kf, the concentration of inhibitor required to observe slow binding inhibition would be much less than the value of K, for the inhibitor encounter complex. When, for example, the inhibitor concentration is limited, due to solubility or other factors, and therefore cannot be titrated above the value of Kif the steady state concentration of the El encounter complex will be kinet-ically insignificant. Under these conditions it can be shown (see Copeland, 2000) that Equation (6.6) reduces to... 

For compounds that conform to the mechanism of scheme C, an alternative method for defining inhibition modality is to measure progress curves (or preincubation effects vide supra) at varying inhibitor and substrate concentrations, and to then construct a double reciprocal plot of 1/v, as a function of l/[.Sj. Using the analysis methods and equations described in Chapter 3, one can then determine the modality of inhibition for the inhibitor encounter complex. Similarly, for inhibitors that conform to the mechanism of scheme B, a double reciprocal plot analysis of l/vs as a function of 1/[S] can be used to define inhibition modality. 

Addition of the L-732,531 FKBP binary complex to a calcineurin activity assay resulted in increasingly nonlinear progress curves with increasing binary complex concentration. The htting of the data to Equation (6.3) revealed an inhibitor concentration effect on v-, as well as on vs and obs, consistent with a two-step mechanism of inhibition as in scheme C of Figure 6.3. Salowe and Hermes analyzed the concentration-response effects of the binary complex on v, and determined an IC50 of 0.90 pM that, after correction for I.S I/A (assuming competitive inhibition), yielded a A) value for the inhibitor encounter complex of 625 nM. 

Figure 6.20 Concentration-response plot for the initial inhibitor encounter complex between COX1 open circles) and COX2 closed circles) and DuP697. For COX1, the data were taken from steady state velocity measurements. For COX2, the data were obtained from the y-intercept values of the data fits in Figure 6.19.

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