1993 Free Response Calculus Bc Solution
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Ionic solutions do not resemble the ideal solutions of elementary textbooks. Indeed, ions such as Na+ and K+ have specific properties, and can be selected by biological systems, because they are nonideal and have highly correlated behavior. Screening69 and finite size effects33, 34, 35, 37, 38, 70 produce the correlations more than anything else. Solvent effects enter (mostly) through the dielectric coefficient. Ionic solutions do not resemble a perfect gas71 of noninteracting uncharged particles. Indeed, because of screening,69, 72 the activity (which is a measure of the free energy) of an ionic solution is not an additive function as concentration is changed (Fig. 3.6 of Ref. 37; Fig. 4.2.1 of Ref. 38) and so does not easily fit some definitions (p. 6 of the book of international standards for physical chemistry73) of an extensive quantity.
These simulations and theories of simple models of ions in crowded confined spaces allow understanding of one of the most important properties of proteins, selectivity, because they compute the nonideal properties of ions that depend on screening, the finite size of the ion, the shape and size of the confining space, and on the concentration of all species of ions.33, 35, 37, 38, 70 The quite different sodium channels of nerve and calcium channels of the heart are both described well by a single model with the same two fixed parameters in a wide range of solutions of different composition and content.15, 112, 133 Each channel type is represented only by spheres taking the place of its characteristic amino acid side chains that produce selectivity143, 144 (Glu Glu Glu Glu for calcium channels; Asp Glu Lys Ala for sodium channels). The simulations are confined to thermodynamic equilibrium, where there are no flows of any kind. The model is subject to all sorts of appropriate objections mostly because of its evident lack of the atomic detail of the protein. The simulations are surprisingly successful, nonetheless.15, 52, 112 Reduced models seem to describe the kinds of energy used by these channels to create selectivity, probably because they allow the concentrations of every ionic species to change the activity (i.e., free energy per mole) of every other ion. Of course, evolution is likely to use other forms of energy as well in other situations. 2b1af7f3a8