Solute-solute interactions in aqueous solutions of nonelectrolytes are interpreted using both lattice and distribution function theories of the dissolved state. Experimental activity data of high precision can be obtained from the literature for aqueous solutions of many nonelectrolytes. If the logarithm of the solvent activity coefficient (γ1) is expressed as a power series in the mole fraction of the solute (x2), lnγ1 = Bx22 + Cx23 + ···, then the coefficients B and C can be determined analytically from the experimental measurements. Values of B were obtained for 52 aqueous mixtures; values of C were obtained for 39 of these mixtures. The solutes considered include aliphatic alcohols, amines, amides, ketones, fatty acids, amino acids, and sugars. In some cases, experimental data were available from which the temperature dependence of the quantities B and C could also be determined. The effect of solute size on the coefficients B and C was investigated using the lattice theories of Flory, Huggins, and Guggenheim and McGlashan. More detailed conclusions concerning solute-solute interactions can be drawn by using experimental activity data in conjunction with the McMillan-Mayer theory of solutions. The minimum attractive contributions to the second virial coefficient of the osmotic pressure were estimated for most of the systems studied in this paper. Pairwise attractions seem to increase with (1) increasing aliphatic chain length (from the temperature dependence of the coefficient B it is also found that pairwise association due to aliphatic chains increases with increasing temperature); (2) an increase in the number of solute functional groups capable of participating in hydrogen-bond formation; (3) increasing dipole moment of the solute molecule for a series of amino acids and peptides. The minimum attractive contributions to the third virial coefficient were determined and interpreted for 12 of the systems. Finally, the relative importance of pairwise versus triplet interactions in aqueous solution was investigated.

The exact analytic expression for the mean time to absorption (or mean walk length) for a particle performing a random walk on a finite Sierpinski gasket with a trap at one vertex is found to be T((n))=[3(n)5(n+1)+4(5(n))-3(n)]/(3(n+1)+1) where n denotes the generation index of the gasket, and the mean is over a set of starting points of the walk distributed uniformly over all the other sites of the gasket. In terms of the number N(n) of sites on the gasket and the spectral dimension d of the gasket, the precise asymptotic behavior for large N(n) is T((n))-->1/3(2N(n))(2/d)-N1.464. This serves as a partial check on our result, as it is (a) intermediate between the known results T-N2 (d=1) and T-N ln N (d=2) for random walks on d-dimensional Euclidean lattices and (b) consistent with the known result for the asymptotic behavior of the mean number of distinct sites visited in a random walk on a fractal lattice.

Tertiary contact formation rates in alpha-synuclein, an intrinsically disordered polypeptide implicated in Parkinson's disease, have been determined from measurements of diffusion-limited electron-transfer kinetics between triplet-excited tryptophan:3-nitrotyrosine pairs separated by 10, 12, 55, and 90 residues. Calculations based on a Markovian lattice model developed to describe intrachain diffusion dynamics for a disordered polypeptide give contact quenching rates for various loop sizes ranging from 6 to 48 that are in reasonable agreement with experimentally determined values for small loops (10-20 residues). Contrary to expectations, measured contact rates in alpha-synuclein do not continue to decrease as the loop size increases (>/=35 residues), and substantial deviations from calculated rates are found for the pairs W4-Y94, Y39-W94, and W4-Y136. The contact rates for these large loops indicate much shorter average donor-acceptor separations than expected for a random polymer.

We consider an unbiased random walk on a finite, nth generation Sierpinski gasket (or "tower") in d = 3 Euclidean dimensions, in the presence of a trap at one vertex. The mean walk length (or mean number of time steps to absorption) is given by the exact formulaThe generalization of this formula to the case of a tower embedded in an arbitrary number d of Euclidean dimensions is also found, and is given byThis also establishes the leading large-n behavior T (n) ∼ N 2/d n that may be expected on general grounds, where N n is the number of sites on the nth generation tower and d = ln(d + 1) 2 / ln(d + 3) is the spectral dimension of the fractal.

We continue the study of a particle (atom, molecule) undergoing an unbiased random walk on the Sierpinski gasket, and obtain for the gasket and tower the eigenvalue spectrum of the associated stochastic master equation. Analytic expressions for recurrence relations among the eigenvalues are derived. The recurrence relations obtained are compared with those determined for two Euclidean lattices, the closed chain with an absorbing site and a finite chain with an absorbing site at one end. We check and confirm the internal consistency between the smallest eigenvalue and the mean walklength in each of the cases studied. Attention is drawn to the relevance of the results obtained to a problem of electron transfer in proteins.

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