Polyelectrolytes

Polyelectrolytes may widely be defined as highly charged macromolecules or aggregates formed in aqueous solution by dissociation of charged units of these macromolecules. Many important biological macromolecules are polyelectrolytes. The most important example is DNA and RNA molecules, which dissociate in solution forming a strongly negatively charged polyion surrounded by atmosphere of small mobile counterions. Protein molecules in solution usually contain polar groups of the both signs. There exists also many synthetical polyelectrolytes with important technological applications.

Virtually all the properties of polyelectrolyte systems are critically dependent on electrostatical interactions. Our ability to describe and predict effects arising due to electrostatic forces is a key element of our understanding of general behaviour of polyelectrolytes. Accurate theoretical description of electrostatic forces is however difficult. For many actual problems, computer simulations are in fact the only way to obtain information on behaviour of polyelectrolyte systems.

My work on computer simulation of polyelectrolytes began during my PhD studies and continued afterwards in cooperation with Pavel Vorontsov-Velyaminov, Lars Nordenskiöld, Nikolai Korolev, Aatto Laaksonen, Jay Tang. Below is the summary of our research in this area.

Reviews on computer simulation of polyelectrolytes:

Monte Carlo - Self Consistent Field Method in the Polyelectrolyte Theory

This series of papers discribes the Monte-Carlo - self consistent field method for studies of ionic environment of polyelectrlyte models as well as its application to DNA and some other models. The method implies explicit Monte-Carlo simulation of ions in a close vicinity of the polyion and accounting for the other ions by a self-consistent field. Considerable saving of the CPU time can be achieved comparing to the usual Monte Carlo simulations, without loosing the accuracy.

Flexible polyelectrolytes

Effective forces between polyelectrolytes

Though charges of the same sign normally repeal each other, polyions of the same sign in solution at some curcumstances may attract each other. Effective attractive forces between polyelectrolytes of the same sign are responsible for many important processes in living cells. In the following papers, effective forces between polyelectrolytes are computed using expanded ensemble method for free energy calculation, using the fact that effective force may be expressed as volume derivative of the free energy.

Ion Competition

Ions of higher valence are attracted to DNA stronger, but their concentrations in cells are usually smaller than concentration of monovalent ions like Na+ or K+. There is competition between ions of different (and even of the same) valencies for binding to DNA. The papers below describe different aspect of ion competition:

Conformational transitions in DNA

Stability of different forms of DNA may be qualitatively evaluated by computations of electrostatic free energy within the mean field Poisson-Boltzmann theory. In this paper, electrostatic contribution to the force nesessary to release DNA from the nucleosome, is evaluated within the mean field (Poisson-Boltzmann) theory:

Molecular Dynamics of DNA

Software

The computer program SFMK on Monte Carlo - self consistent field simulation of cylindrical and spherical polyelectrolytes is on CCP5 server in Daresbury Lab.


Alexander Lyubartsev

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