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I R Epstein

Publications and source records attributed to I R Epstein.

27 records · Page 2Linked to original sources
PubMed1987

Kinetics of actin-myosin binding. I. An exactly soluble one-variable model.

To treat the kinetics of actin-myosin binding as simply as possible, a one-variable model is developed and the notion of effectivity factors is introduced. An effectivity factor is a ratio of the reaction rate in the presence of cooperativity to that in the noncooperative case and is calculated by averaging cooperativity factors over all sites belonging to one seven-site actin unit. The technique is applicable to a variety of models involving cooperative association and dissociation processes. This averaging assumes the equivalence of all regulated actin units. The model may be solved exactly for arbitrary degrees of "preloading" of subfragment 1 (S1) on the regulated actin.

Actins↗
PubMed1987

Kinetics of actin-myosin binding. II. Two-variable model and actin gelation.

We consider a model of actin-myosin interaction in which the sites belonging to each seven-site regulated actin unit are subdivided into two classes, "internal" and "external." The time evolution of each class of sites is considered separately, leading to a pair of coupled differential equations that may be integrated numerically. We also consider the critical sol-gel transition point for actin filaments crosslinked by two-headed heavy meromyosin (HMM). The possibility of new types of chemical oscillation and pattern formation arising from periodic sol-gel transitions is discussed.

Actins↗
PubMed1983

Kinetic model for the interaction of myosin subfragment 1 with regulated actin.

A one-dimensional kinetic Ising model is developed to describe the binding of myosin subfragment 1 (SF-1) to regulated actin. The model allows for cooperative interactions between individual actin sites with bound SF-1 ligands rather than assuming that groups of actin monomer sites change their state in a cooperative fashion. With the triplet closure approximation, the model yields a set of 16 independent differential (master) equations which may be solved numerically to yield the extent of binding as a function of time. The predictions of the model are compared with experiments on the transient binding of SF-1 to regulated actin in the presence of Ca2+ and in the absence of Ca2+ with varying amounts of SF-1 prebound to the actin filament and on the equilibrium binding of SF-1 X ADP to regulated actin in the absence of Ca2+. In all cases, the calculations fit the data to within the experimental errors. In the case of SF-1 X ADP, the results suggest that a repulsive interaction exists between adjacently bound SF-1 at the ends of two neighboring seven-site actin units.

Actins↗
PubMed1979

Coexistence, competition and hypercyclic interaction in some systems of biological interest.

Systems of differential equations which describe the selective behavior of self-replicating macromolecules or species under the constraint of constant organization are classified according to their coexistent and competitive behavior as well as the cooperative and/or hypercyclic nature of the inter-species interactions. Two theorems are proved which relate the possibilities for coexistence and competition among species to the presence or absence of hypercyclic linkages.

Journal Article↗
PubMed1979

Selection and self-organization of self-reproducing macromolecules under the constraint of constant flux.

We investigate the dynamic behavior of a set of self-reproducing macromolecules (e.g., polynucleotides) under conditions such that the fluxes of all monomer units into the system are kept constant. Such conditions might prevail in an evolution reactor or in certain naturally occurring situations. A general set of equations is developed to describe the behavior of both the macromolecule and the monomer concentrations. The question of how the rate of macromolecule synthesis varies with the monomer levels is discussed briefly. With the help of several physically reasonable approximations, we obtain an exact solution for a simplified constant flux system. Comparison with the corresponding system under the constraint of constant overall organization reveals important similarities, most notably in the existance and composition of quasispecies. Given the same set of physical and chemical parameters, a system subject to constant flux will always evolve toward selective equilibrium more slowly than under the constraint of constant organization.

Kinetics↗
PubMed1978

Cooperative and non-cooperative binding of large ligands to a finite one-dimensional lattice. A model for ligand-oligonucleotide interactions.

A combinatorial approach is employed to calculate exact expressions for the extent of binding to a finite one dimensional lattice of ligands which cover more than one lattice site. The binding may be either cooperative or non-cooperative. It is found that the assumption of an effectively infinite lattice is generally a good one, except with relatively low concentrations of strongly cooperative ligands. An approach to analyzing experimental data is suggested which makes explicit use of the lattice length dependence of binding to extract more information about the binding parameters than can be obtained using the infinite lattice approximation. It is shown that irreversible binding cannot be viewed as a limiting case of reversible binding. The reasons for this difference are discussed, and expressions for the extent of irreversible binding are derived.

Binding Sites↗