Conditional entropy contracted

This quantity averages the Shannon entropies conditional on the Gamma and lognormal models, with weights given by their posterior probabilities. In Appendix B, we show that the average entropy is a concave function on the space of probability distributions which is monotone under contractive maps (Sebastiani and... 

The magnitudes of entropies of activation have provided valuable information regarding the details of the interactions between enzymes and substrates. The process of muscular contraction involves an interaction between the muscle enzyme myosin and adenosine triphosphate (ATP). Myosin is an enzyme which catalyzes the hydrolysis of ATP, a process which we have seen (p. 246) to be more exergonic than is the case for many other phosphates, and this hydrolysis contributes energy for contraction. Because of its catalytic action, myosin is also referred to as adenosine triphosphatase (ATP-ase). When the activated complex is formed from ATP ase and its substrate ATP, the entropy of activation is about 41 cal K" mol under approximately normal physiological conditions. We saw on p. 400, on the basis of a very simple electrostatic theory of AS values for ionic reactions in aqueous solution, that there will be a positive contribution of about 10 cal mol for each unit of the product [ [ % ( The long myosin molecules bear a series of positive... 

Description of the mechanics of elastin requires the understanding of two interlinked but distinct physical processes the development of entropic elastic force and the occurrence of hydrophobic association. Elementary statistical-mechanical analysis of AFM single-chain force-extension data of elastin model molecules identifies damping of internal chain dynamics on extension as a fundamental source of entropic elastic force and eliminates the requirement of random chain networks. For elastin and its models, this simple analysis is substantiated experimentally by the observation of mechanical resonances in the dielectric relaxation and acoustic absorption spectra, and theoretically by the dependence of entropy on frequency of torsion-angle oscillations, and by classical molecular-mechanics and dynamics calculations of relaxed and extended states of the P-spiral description of the elastin repeat, (GVGVP) . The role of hydrophobic hydration in the mechanics of elastin becomes apparent under conditions of isometric contraction. 

Figure 9. Mechano-chemical coupling by 20Mrad y-irradiation cross-linked of poly[0.8(GVGVP), 0.2(GEGVP)] under isotonic (A) and isometric (B) conditions. In part B under isometric contraction conditions there occurs an increase in entropic elastic force resulting from a decrease in entropy of...

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