The proposed work is intended to contribute to the statistical mechanical theory of biological macromolecules and macromolecular systems, and occasionally to make such other contributions to related statistical mechanical inquiry as may seem timely and opportune by virtue of special knowledge and interests. A distinguishing characteristic of the methods is the interplay between simulations and theoretical analysis, which will become increasingly prominent in the proposed work on polyelectrolytes in external fields. The first objective is to develop algorithms for Brownian and molecular dynamics simulations of a polyelectrolyte molecule and the surrounding salt solution in the presence of external, time dependent electric fields of arbitrary amplitude. The polyelectrolyte chain and a near layer of salt solution will be simulated as a system of particles. The distant salt solution will be simulated by continuous fields that satisfy linear or quasi-linear equations that are solved numerically. Boundary conditions will merge the continuum and molecular descriptions at the open interface between the two subsystems and allow a simultaneous computer solution of the equations of motion for both subsystems. Potential applications of the work are to the theory of analytical and separative techniques such as pulsed electrophoresis, and biological issues such as the response of living tissue to weak electromagnetic fields, the passage of ions across membranes, and electrically modified growth. The second objective is to explore and amplify the recent discovery that the stress in concentrated polymer solution is due primarily to the interaction force that one chain exerts on another, rather than to local orientational entropy. The discovery, if confirmed, will reconcile the apparent paradox that the mechanical properties of polymers require rationalization of a persistent elasticity, while computer simulations show that polymers in concentrated solutions and melts retain considerable flexibility. Verification of the revised picture of concentrated polymer solutions may have some impact on the related problems of gel electrophoresis and, in a more qualitative way, on intuitive views of quaternary structure in biopolymers.
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