Complex molecules, diffusion

The dynamics of a supramolecular system are defined by the association and dissociation rate constants of the various components of the system. The time-scale for the dynamic events is influenced by the size (length-scale) and by the complexity of the system. The fastest time for an event to occur in solution is limited by the diffusion of the various components to form encounter complexes. This diffusion limit provides an estimate for the shortest time scale required for kinetic measurements. The diffusion of a small molecule in water over a distance of 1 nm, which is the length-scale for the size of small host systems such as CDs or calixarenes, is 3 ns at room temperature. In general terms, one can define that mobility within host systems can occur on time scales shorter than nanoseconds, while the association/dissociation processes are expected to occur in nanoseconds or on longer time scales. The complexity of a system also influences its dynamics, since various kinetic events can occur over different time scales. An increase in complexity can be related to an increase in the number of building blocks within the system, or complexity can be related to the presence of more than one binding site. 

The presence of a covalent acyl-enzyme intermediate in the catalytic reaction of the serine proteases made this class of enzymes an attractive candidate for the initial attempt at using subzero temperatures to study an enzymatic mechanism. Elastase was chosen because it is easy to crystallize, diffracts to high resolution, has an active site which is accessible to small molecules diffusing through the crystal lattice, and is stable in high concentrations of cryoprotective solvents. The strategy used in the elastase experiment was to first determine in solution the exact conditions of temperature, organic solvent, and proton activity needed to stabilize an acyl-enzyme intermediate for sufficient time for X-ray data collection, and then to prepare the complex in the preformed, cooled crystal. Solution studies were carried out in the laboratory of Professor A. L. Fink, and were summarized in Section II,A,3. Briefly, it was shown that the chromophoric substrate -carbobenzoxy-L-alanyl-/>-nitrophenyl ester would react with elastase in both solution and in crystals in 70 30 methanol-water at pH 5.2 to form a productive covalent complex. These... 

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 ... 

An additional condition may be imposed, even when a cofactor-independent enzyme is used, if a mediator molecule is involved in the electron transfer process, as is often the case with oxidases. Laccases, for example, may employ small-molecule diffusible mediator compounds in their redox cycle to shuttle electrons between the redox center of the enzyme and the substrate or electrode (Scheme 3.1) [1, 2]. Similarly, certain dehydrogenases utiHze pyrroloquinoline quinone. In biocatalytic systems, mediators based on metal complexes are often used. 

Several different types of this dust are distinguished by astronomers. On average, interstellar dust resides in widely separated diffuse clouds. But there are also dense regions of gas and dust into which little ultraviolet radiation can penetrate, thereby providing an environment for the formation of complex molecules these are referred to as molecular clouds. Clouds of particles expelled by cooler stars into the regions around them are called circumstellar... 

Firstly, reactions of hydrocarbons will be discussed. Vehicle exhaust contains a complex mixture of hydrocarbons (ICubo et al., 1993). These will have different reactivity and their different molecular masses lead to different propensities for mass transport, the larger molecules diffusing more slowly to the catalyst coating. While the full (vast) range of hydrocarbons in the exhaust could not practically be included in a model, it is desirable to include a small number of representative hydrocarbons to emulate the range of activity and transport properties of the full mixture. 

The equilibrium constant for Eq. 9-102, calculated from the pKa of 7.0 for imidazole, is 10 7 M. Since Keq is also the ratio of the overall rate constants for the forward and reverse reactions, we see that for the forward reaction kj = 10 7 x 1.5 x 1010 = 1.5 x 103 s . This slow rate results from the fact that in the intermediate complex (in brackets in Eq. 9-102) the proton is on the imidazole group most of the time. For a small fraction of the time it is on the coordinated molecule HzO but reverts to being on the imidazole many times before the imidazole and OH3+ separate (see also Eqs. 9-97 and 9-98). Because of this unfavorable equilibrium within the complex, the diffusion-controlled rate of proton transfer from a protonated imidazole to water is far less than for proton transfer in the reverse direction. 

The relatively new method of fluorescence correlation spectroscopy (FCS) is based on the fact that molecules with different molecular weights (usually) exhibit different diffusion times in solution. Thus, small molecules diffuse faster than larger ones. To determine K- values, one component must be labeled with a fluorescent dye. Due to the different molecular weights of the uncomplexed, labeled component and the complex, the diffusion times of the free and complexed molecule differ. This fact allows determining the distribution of free and complexed molecules in the solution. After measuring the distribution in different mixtures with varying ligand concentrations, the K- value can be calculated [44]. 

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