Kinetic parameter distribution theory

Presently, the quantitative theory of irreversible polymeranalogous reactions proceeding in a kinetically-controlled regime is well along in development [ 16,17]. Particularly simple results are achieved in the framework of the ideal model, the only kinetic parameter of which is constant k of the rate of elementary reaction A + Z -> B. In this model the sequence distribution in macromolecules will be just the same as that in a random copolymer with parameters P(Mi ) = X =p and P(M2) = X2 = 1 - p where p is the conversion of functional group A that exponentially depends on time t and initial concen-... 

One possible option is to adopt a statistical description of the kinetic parameters and to ask how likely it is for the quasi-species to be localized about the wild type. This undertaking requires an analysis beyond the second order in perturbation theory since a distant mutant with a selective value very close to that of the wild type may jeopardize the stability of the latter in the population. We were however encouraged by the progress that had been made with a problem of similar difficulty in the very different area of electron or spin localization in disordered solids. Indeed, it turns out that an expression of the form of Eqn. (III.5) may be obtained, with an explicit expression for the superiority parameter Oq, dependent on the distribution of replication rates but not on any average involving population variables. 

The kinetic parameters for desorption from the monohydride phase on Si(100)-2 X 1 have been controversial, but consensus has now been reached on the reaction order and Arrhenius parameters. The rotational and vibrational energy distributions are also well-characterized. Almost everything else about this reaction requires clarification. In this section, some of the remaining issues for theory and experiment are outlined. The motivations for these issues have been addressed in more detail in the main body of this chapter. 

Clearly, the procedure outlined above is complex. It requires solution of the flow fleld, in conjunction with the determination of the distribution of the electrostatic potential and of all species concentrations within the cell. In addition to the mathematical complexity, the transport properties (diffusivities, mobility) for all species must be given. This is further complicated by the fact that most practical electrolytes are concentrated and hence transport interactions between the species must be accounted for, requiring the application of the more complex concentrated electrolyte theory. Additionally, the electrode kinetics parameters must be known. However, as discussed below, simplifications are often possible, since most operating cells are typically controlled by either the electric potential distribution or by the concentration distribution (in conjunction with the electrode kinetics), and only a few systems are influenced about equally by both. 

Keilson-Storer kernel 17-19 Fourier transform 18 Gaussian distribution 18 impact theory 102. /-diffusion model 199 non-adiabatic relaxation 19-23 parameter T 22, 48 Q-branch band shape 116-22 Keilson-Storer model definition of kernel 201 general kinetic equation 118 one-dimensional 15 weak collision limit 108 kinetic equations 128 appendix 273-4 Markovian simplification 96 Kubo, spectral narrowing 152... 

This theory clearly predicts that the shape of the polymer length distribution curve determines the shape of the time course of depolymerization. For example Kristofferson et al. (1980) were able to show that apparent first-order depolymerization kinetics arise from length distributions which are nearly exponential. It should also be noted that the above theory helps one to gain a better feeling for the time course of cytoskeleton or mitotic apparatus disassembly upon cooling cells to temperatures which destabilize microtubules and effect unidirectional depolymerization. Likewise, the linear depolymerization kinetic model could be applied to the disassembly of bacterial flagella, muscle and nonmuscle F-actin, tobacco mosaic virus, hemoglobin S fibers, and other linear polymers to elucidate important rate parameters and to test the sufficiency of the end-wise depolymerization assumption in such cases. 

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