Diffusional encounter complex

The Brownian Dynamics (BD) simulation technique can be used to simulate the diffusion and the association of molecules in solution. BD simulations have been widely used to simulate protein-small molecule and protein-protein association (62). This method may be exploited to simulate the hrst step of molecular recognition when two molecules diffuse from a distance. From such simulations, it is possible to compute the structure and the diffusional encounter complex ensemble and to calculate the bimolecular association rate constant for two diffusing proteins or enzymes and their substrates or inhibitors. In these calculations, the effects of mutations and variations in ionic strength, pH, and viscosity can be investigated (63). 

Eor simulation of molecular recognition by BD to compute association rate constants and for the generation of the structures of diffusional encounter complexes, the following setup may be used. One solute, which usually is the larger one, is positioned... 

The deduced preselection of the dipolar species in the electric field of the receptor may be assumed to enormously accelerate the diffusional approach of dipolar ligands [153]. The resulting formation of a diffusional encounter complex Figure 4.8) represents the initial step in molecular recognition and selection which is followed by a sequence of consecutive steps, during which more and more substructures make contact with the subsites of the receptor cleft, which eventually may fully encompass an inhibitor molecule when being complementary. 

As a result of the solvent-cage effect, any slow reaction occurring between two or more species in solution may be divided into two steps. The first step involves a diffusional encounter and the second step is a rearrangement of the encounter complex in the first step to yield a product [1,2]. If the overall rate is more than an order of magnitude slower than the diffusion-controlled limit, the first step may be treated as a pre-equilibrium process. The steps involved may be written as... 

How may these measured functions be related to the rate coefficients of reactions of the excited species It is useful to consider how the excitation arises and the various ways in which the excited species may dissipate its excess energy. Suppose A is excited to A which reacts with B to give products. There are two distinct mechanisms which may be considered for such a fluorescence quenching process. Before the transfer of energy from A to B is possible the species must form an encoimter complex in which the solvent cages of A and B have been sufficiently modified to allow significant chemical interaction between the two reactants. By the dynamic, or diffusional, pathway A is formed in comparative isolation from B, and the encounter complex is produced as a second step... 

This phenomenon was first identified and explained by Forster.120 The structureless emission is attributed to an excited pyrene dimer (1P - P) that is formed by collisional association of singlet excited pyrene P with a pyrene molecule P in the ground state. It was subsequently found that many aromatic molecules exhibit similar behaviour. The expression excimer (excited dimer) was proposed by Stevens to distinguish such species from the excited state of a ground-state complex. Excimer formation is prominent at relatively low concentrations of pyrene (Figure 2.22, left), because of its unusually long fluorescence lifetime, 1t = 650 ns, which allows for diffusional encounters of P with P even at low concentration. 

Spatio and Spatio-Temporal Patterns. An exotic form of diffusional encounter should be mentioned, which arises from sets of reaction-diffusions equations (48). In 1952, the mathematician Alan Turing postulated the existence of two-dimensional and three-dimensional spatio and spatio-temporal patterns for certain classes of reactive systems (49). The physical realization of these mathematical solutions has been observed in a variety of systems (50). It suffices to say that since these patterns have been observed in both simple chemical systems and complex biological systems, their possibility in homogeneous catalysis should certainly not be ruled out. In this regard, static spectroscopic cells may be particularly prone to such spatial variation because of the lack of mixing. 

These reactions are modelled in terms of a diffusional step or kd[ff), resulting in the formation of a bimolecular encounter complex. This is followed by competing pathways for dissociation of the complex or or energy transfer k or k ). Deactivation of the excited quencher is described by p. The observed CPL is directly proportional to the difference in excited state concentrations of the two enantiomers, and this may be related to the specific rate constants introduced above. If, for example, we make the reasonable assumption that the diffusion and deactivation are independent of chirality, one can derive the following expression for AN t)... 

As illustrated in Fig. 9.13 the Fe(II), forming complexes with these hydroxy and carboxyl ligands, encounter in their upward diffusion the settling of Fe(III)(hydroxides and interact with these according to the catalytic mechanism, thereby dissolving rapidly the Fe(III)(hydr)oxides. The sequence of diffusional transport of Fe(II), oxidation to insoluble Fe(OH)3 and subsequent settling and reduction to dissolved Fe(II) typically occurs within a relatively narrow redox-cline. 

The haphazard rotational motions of molecules or one or more segments of a molecule. This diffusional process strongly influences the mutual orientation of molecules (particularly large ones) as they encounter each other and proceed to form complexes. Rotational diffusion can be characterized by one or more relaxation times, t, describing the motion of a molecule or segment of volume, V, in a medium of viscosity, 17, as shown in the following equation ... 

The photosensitized electron transfer process involves two successive steps (eq. 5) In the primary event an encounter cage complex of the photoproducts is formed. This can either recombine to yield the original reactants or dissociate into separated photoproducts. The separated photoproducts can then recombine by a diffusional back electron transfer reaction to form the original reactants. We have introduced two conceptional approaches as a means for assisting the separation of the encounter cage complex and for the stabilization... 

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