Competing reaction processes on a lattice as a paradigm for catalyst deactivation.

We mobilize both a generating function approach and the theory of finite Markov processes to compute the probability of irreversible absorption of a randomly diffusing species on a lattice with competing reaction centers. We consider an N-site lattice populated by a single deep trap, and N-1 partially absorbing traps (absorption probability 0

Surface site diffusion and reaction on molecular "organizates" and colloidal catalysts: A geometrical perspective.

We study surface-mediated, diffusion-controlled reactive processes on particles whose overall geometry is homeomorphic to a sphere. Rather than assuming that a coreactant can diffuse freely over the surface of the particle to a target site (reaction center), we consider the case where the coreactant can migrate only among N - 1 satellite sites that are networked to the reaction site by means of a number of pathways or reaction channels. Five distinct lattice topologies are considered and we study the reaction efficiency both for the case where the satellite sites are passive and for the case where reaction may occur with finite probability at these sites. The results obtained for this class of surface problems are compared with those obtained by assuming that the reaction-diffusion process takes place on a planar, two-dimensional surface (lattice). The applicability of our results to surface-mediated processes on "organizates" (cells, vesicles, micelles) and on colloidally dispersed catalyst particles is brought out in the Introduction, and the correspondence between the lattice-based, Markovian approach developed here and Fickian models of surface diffusion, particularly with regard to the exponentiality of the decay, is discussed in the concluding section.

Stochastic flows in integral and fractal dimensions and morphogenesis.

The effect of dimensionality and spatial extent on the dynamics of an irreversible reaction confined to a finite system was studied by a Monte Carlo simulation. Stochastic flows on surfaces of integral and fractal dimensions and the consequences of reducing the dimensionality of the reaction space are described. As regards the timing and efficiency of chemical reactions in small systems, our simulations show that placing the reactive site at a central location may be favored at an early stage of growth but, as the system evolves in size, a location on the boundary becomes favored. The possible relevance of these calculations to the problem of morphogenesis is brought out.

Isopiestic determination of water binding by fish antifreeze glycoproteins.

The effectiveness of water binding of antifreeze glycoproteins relative to hemoglobin, cytochrome c and polyvinylpyrrolidone was determined by analyzing results obtained in an isopiestic study at 25 degrees C. The net weight of water which moved from a protein/NaCl aqueous sample to a saturated NaCl reference solution increased in the order: antifreeze glycoprotein, hemoglobin, polyvinylpyrrolidone and cytochrome c. Since the glycoproteins were least effective in transporting water we conclude that, of the proteins studied, the glycoprotein was most effective in binding water under equilibrium conditions at 25 degrees C.

Spectator-ion effect on the passage of ions through membranes.

In this paper, we investigate the interplay between geometric and dielectric factors in influencing the image force acting on an ion passing through a membrane, for a system having the approximate dimensions of Escherichia coli. We also study the effect of one ion in a membrane on the passage of a second ion through the membrane, by calculating the radial and angular forces experienced by the second ion due to the presence of the "spectator ion." Our conclusions follow from numerical studies on expressions obtained by solving (exactly) Laplace's equation for the model assumed in this paper. The conclusions are: (i) small changes in the dielectric constant of the membrane are far more significant in determining the image force acting on an ion in a membrane than dramatic changes in the dielectric character of the regions interior and/or exterior to the cell; (ii) a spectator ion in a membrane situated near a boundary may influence in a significant way the passage of a second ion through the middle third of the membrane. We suggest that this latter result should be taken into account in discussing the mechanism of ion migration across membranes.

Denaturation: an example of a catastrophe.

We show that a "phase diagram" for the conformational states of proteins can be constructed using the mathematical theory of singularities of functions developed recently by René Thom. For proteins subjected to the disruptive influences of temperature and/or concentration of denaturing agent, this theory can be used as a predictive tool to account for the shape, sense, and changes in the curves that result when the optical rotatory dispersion is plotted as a function of these two constraints. The mathematical model is found to be in accord with known experimental data on collagen, lysozyme, and ribonuclease.