Random collapsing

Random collapsing interactions have been used to model the effect of the environment (understood in a broad sense that could include the measurement apparatus) on the decaying particle [13,113]. For example, it is argued that as an unstable elementary particle decays in a bubble chamber, each bubble is a measurement indicating that the particle has not yet decayed (has survived), so that a reduction takes place, resetting the system into the initial undecayed state. The decay law that should be observed in experiment will be therefore an environment-affected F(t) rather than P(t). The probability that the system is not subjected to any measurement in a time interval St is taken to be exp (-kSf). The survival probability f(f) resulting from these measurements satisfies [13]... 

The basic features of folding can be understood in tenns of two fundamental equilibrium temperatures that detennine tire phases of tire system [7]. At sufficiently high temperatures (JcT greater tlian all tire attractive interactions) tire shape of tire polypeptide chain can be described as a random coil and hence its behaviour is tire same as a self-avoiding walk. As tire temperature is lowered one expects a transition at7 = Tq to a compact phase. This transition is very much in tire spirit of tire collapse transition familiar in tire theory of homopolymers [10]. The number of compact... 

The random-bond heteropolymer is described by a Hamiltonian similar to (C2.5.A3) except that the short-range two-body tenn v.j is taken to be random with a Gaussian distribution. In this case a tliree-body tenn with a positive value of cu is needed to describe the collapsed phase. The Hamiltonian is... 

In the collapse phase the monomer density p = N/R is constant (for large N). Thus, the only confonnation dependent tenn in (C2.5.A1) comes from the random two-body tenn. Because this tenn is a linear combination of Gaussian variables we expect that its distribution is also Gaussian and, hence, can be specified by the two moments. Let us calculate the correlation i,) / between the energies and E2 of two confonnations rj ]and ry jof the chain in the collapsed state. The mean square of E is... 

The collapse of the unfolded state to generate the molten globule embodies the main mystery of protein folding. What is the driving force behind the choice of native tertiary fold from a randomly oriented polypeptide chain ... 

If it is assumed that ionization would result in complete randomization of the 0 label in the caihoxylate ion, is a measure of the rate of ionization with ion-pair return, and is a measure of the extent of racemization associated with ionization. The fact that the rate of isotope exchange exceeds that of racemization indicates that ion-pair collapse occurs with predominant retention of configuration. When a nucleophile is added to the system (0.14 Af NaN3), k y, is found to be imchanged, but no racemization of reactant is observed. Instead, the intermediate that would return with racemization is captured by azide ion and converted to substitution product with inversion of configuration. This must mean that the intimate ion pair returns to reactant more rapidly than it is captured by azide ion, whereas the solvent-separated ion pair is captured by azide ion faster than it returns to racemic reactant. 

Correlated or geminate radical pairs are produced in unimolecular decomposition processes (e.g. peroxide decomposition) or bimolecular reactions of reactive precursors (e.g., carbene abstraction reactions). Radical pairs formed by the random encounter of freely diffusing radicals are referred to as uncorrelated or encounter (P) pairs. Once formed, the radical pairs can either collapse, to give combination or disproportionation products, or diffuse apart into free radicals (doublet states). The free radicals escaping may then either form new radical pairs with other radicals or react with some diamagnetic scavenger... 

The presence in these copolymers of hetero-substituted monomeric units randomly dispersed along the phosphazene skeleton brings about the extreme difficulty of the polymeric chains to be packed in regular structures. They lose, therefore, the original stereo-regularity of the parent phosphazene homopolymers (microcrystalline materials), and show only amorphous structures, with sharp decrease in the values of the Tg (collapsed up to about -90 °C) and with the onset of remarkable elastomeric properties [399,409,457]. 

An excluded-volume random-coil conformation will be achieved when the solvent quality exceeds the theta point, the temperature or denatu-rant concentration at which the solvent-monomer interactions exactly balance the monomer—monomer interactions that cause the polymer to collapse into a globule under more benign solvent conditions. A number of lines of small-angle scattering—based evidence are consistent with the suggestion that typical chemical or thermal denaturation conditions are good solvents (i.e., are beyond the theta point) and thus that chemically or thermally unfolded proteins adopt a near random-coil conformation. 

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