Properties of some three-state, steady-state Ising systems, according to the Bragg-Williams approximation

Three-state, steady-state Ising systems: Monte Carlo and Bragg-Williams treatments

In two earlier papers, the steady-state critical and phase-transition properties of a lattice of three-state enzyme molecules were studied by using the "closed" Bragg-Williams (BW), or mean field, approximation. The "open" BW and Monte Carlo methods are applied to the same problem in this paper by using finite lattices. The open BW treatment provides a way of locating the cut across a van der Waals type of loop encountered in a phase transition in the closed BW system. Thermodynamic-like methods cannot be used for this purpose as they can with two-state, steady-state systems.

Nonantagonistic interactions between the sexes revealed by the ecological consequences of reproductive traits

In addition to the obvious role reproductive traits play in mating-system evolution, reproductive characters can also have critical ecological or life history consequences. In this study we examine the ecological consequences of mating for female cactophilic Drosophila to test different hypotheses about the processes driving divergence in reproductive characters. Comparisons between intra- and interpopulation matings suggest that population differences in mating benefits, namely increased desiccation resistance in mated females, is not solely attributable to either a male or female-specific reproductive trait. Instead, the results indicate that increased desiccation resistance is a product of a male-female postmating-prezygotic interactions. The results underscore that postmating-prezygotic interactions can serve as an arena for the evolution of male characters that confer substantial benefits to females, not just costs arising from sexual conflict. Variation in the relative benefits conferred by mating between intra- and interpopulation matings also suggests that the relationship between speciation and divergence in reproductive characters via male-female interaction will be difficult to predict.

The effects of modifiers on enzyme catalysis: a non-classical nearest neighbor approach

We present a nearest neighbor lattice model of the effects of modifiers on two-state enzyme catalysis of the reaction S in equilibrium with p. We do not in general make the assumptions of the classical approach to cooperative catalysis that yield (1) adsorption isotherms of the same form as those for the corresponding equilibrium system and (2) a rate of the catalyzed reaction proportional to the number of occupied catalytic sites. Closed form results are obtained for two approximations, the Bragg-Williams and the quasi-chemical. The latter requires (1), but is exact for several simple cases, including the concerted model, under this condition. Under (1) it is found that an interaction between modifier and catalytic sites, whether attractive or repulsive, increases the magnitudes of the slopes of the adsorption isotherms but that interactions between identical sites (catalytic or modifier) increase these magnitudes if attractive and decrease them if repulsive. Thus, the former interaction allows for phase transitions if sufficiently attractive or repulsive, but the latter only if sufficiently attractive. Herein also lies the explanation for why the concerted model displays only "positive cooperativity". It is further seen that it is not possible to classify a modifier as an activator or inhibitor of the catalyzed reaction solely on the basis of the sign of the interaction energy between catalytic and modifier sites. For a given energy, the rate of the reaction may increase or decrease in response to the modifier, or it may respond biphasically. Similarly, the rate may respond biphasically to the activities of s or p, leading to instabilities. Thus, possibilities of multiple nonequilibrium stationary states or spatio-temporal patterns are raised.

Theoretical models for cooperative steady-state ATPase activity of myosin subfragment-1 on regulated actin

Recent theoretical work on the cooperative equilibrium binding of myosin subfragment-1-ADP to regulated actin, as influenced by Ca2+, is extended here to the cooperative steady-state ATPase activity of myosin subfragment-1 on regulated actin. Exact solution of the general steady-state problem will require Monte Carlo calculations. Three interrelated special cases are discussed in some detail and sample computer (not Monte Carlo) solutions are given. The eventual objective is to apply these considerations to in vitro experimental data and to in vivo muscle models.

Theoretical model for the cooperative equilibrium binding of myosin subfragment 1 to the actin-troponin-tropomyosin complex

Recent experimental data on the equilibrium binding of myosin subfragment 1 (S-1) to regulated actin filaments in the presence and in the absence of Ca(2+) are analyzed by using a linear Ising model. In the model, each tropomyosin-troponin unit (including seven sites on the actin filament) can be in one of two possible states, which have different intrinsic free energies and different binding constants for S-1. Bound S-1 molecules do not interact with each other. There are nearest-neighbor (pair) interactions between these units that depend on the state of each member of the pair and on the number of Ca(2+) bound to one member of the pair. There are two sources of positive cooperativity in this system: the fact that seven actin sites change state together as part of a single unit; and the existence of attractive nearest-neighbor interactions between units. Parameters in the model are evaluated by fitting the data, both in the presence and in the absence of Ca(2+). Several extensions of this model are discussed.