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:
- A.P.Lyubartsev and L.Nordenskiöld
"Computer Simulations of Polyelectrolytes",
in Handbook of Polyelectrolytes and Their Applications,
S. K. Tripathy, J. Kumar and H. S.Nalwa, Eds.,
American Scientific Publishers, Los Angeles (2002),
Volume 3, Chapter 11, pp. 309-326.
- A. P. Lyubartsev
"Molecular Simulations of DNA Counterion Distributions"
Dekker Encyclopedia of Nanoscience and Nanotechnology,
pp. 2131 - 2143 Dekker (2004)
PDF text
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.
-
P.N.Vorontsov-Velyaminov, A.P.Lyubartsev. "Self consistent field - Monte
Carlo method in the polyelectrolyte theory. Calculation of the electrostatic
potential for the symmetrical polyions". Molekulyarnaya Biologia (Moscow),
v.21, p.654-662 (1987); in Rissian (Engl. Transl: Molek.Biol, v.21,p.545
(1987))
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P.N.Vorontsov-Velyaminov, A.P.Lyubartsev. "Monte Carlo - self consistent
field method in the polyelectrolyte theory" J.Biomol.Struct. and Dyn.,
v.7., p.739-747 (1989)
-
A.P.Lyubartsev, V.P.Kurmi, P.N.Vorontsov-Velyaminov. "Monte Carlo -
self consistent field simulation of the interaction of single- and divalent
ions with DNA"Molekulyarnaya Biologia (Moscow), v.24, p.1533-1540 (1990)
(in
Russian)
-
P.N.Vorontsov-Velyaminov, A.P.Lyubartsev. "Monte Carlo - self consistent
field study of the symmetrical models of polyelectrolytes" Molecular
Simulations, v.9, p.285-306 (1992).
-
A.P.Lyubartsev, V.P.Kurmi, P.N.Vorontsov-Velyaminov "Numerical experiment
study of the ionic surroundings of symmetrical models of polyelectrolytes"
Rus.J.Phys.Chem, v.66,p.179-182 (1992)
Flexible polyelectrolytes
This paper describes results of simulation of
lattice model of flexible polyelectrolyte with explicit ions at different
temperatures and concentrations:
-
A.P.Lyubartsev, P.N.Vorontsov-Velyaminov. "Monte Carlo simulation of
flexible polyelectrolytes" Vysokomolekulyarnye Soedineniya (Moscow;
in Russian), v.32A, p.721-726 (1990)
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.
-
A.P.Lyubartsev, L. Nordenskiöld. "A Monte Carlo Simulation Study
of Ion Distribution and Osmotic Pressure in Hexagonally Ordered DNA."
J.Phys.Chem., v.99, p.10373 (1995). Abstract
-
A. P. Lyubartsev, J. X. Tang, P. A. Janmey, and L. Nordenskiöld
"Electrostatically induced polyelectrolyte association of rodlike
virus particles". Phys. Rev. Lett., v.81, p.5465-5468
(1998)
Abstract
and full PDF text from the AIP Web site
- J. X.Tang, P.A.Janmey, A.P.Lyubartsev and L.Nordenskiöld, "
Metal ion induced lateral aggregation of filamentous viruses fd and M13
", Biophys. J. ,v. 83: pp. 566-581 (2002)
Abstract and full text
from the Biophys.J. Web site.
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:
-
A.P.Lyubartsev, L.Nordenskiöld "Monte Carlo Simulation Study of
DNA Polyelectrolyte Properties in the Presence of Multivalent Polyamine
Ions" J.Phys.Chem, v.101,p.4335 (1997). Abstarct;
Paper
(HTML).
-
N.Korolev, A.P.Lyubartsev, A.Rupprecht and L.Nordenskiöld, "Experimental
and Monte Carlo simulation studies on the competitive binding of Li+,
Na+, and K+ ions to DNA in oriented DNA fibers",
J. Phys. Chem. B, v.103, pp. 9008-9019 (1999)
-
N.Korolev, A.P.Lyubartsev, A.Rupprecht and L.Nordenskiöld, "Competitive
binding of Mg2+, Ca2+, Na+, and K+
ions to DNA in oriented DNA fibers: Experimental and Monte Carlo simulation
results", Biophys. J, v.77, pp. 2736-2749 (1999)
-
N. Korolev, A.P.Lyubartsev, A.Rupprecht and L.Nordenskiöld,
"Competitive
Substitution of Hexammine Cobalt(III) for Na+ and K+ Ions in Oriented DNA
Fibers" Biopolymers, v. 58, pp. 268-278 (2001)
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.
-
N. Korolev, A. P. Lyubartsev, L. Nordenskiöld. "Application of
the polyelectrolyte theories for description of DNA melting in the presence
of Na+- and Mg2+-ions". Biophys. J., v.75, pp.3041-3056
(1998)
- N. Korolev, A. P. Lyubartsev and L. Nordenskiöld
Application of the Poisson-Boltzmann polyelectrolyte model for analysis of
equilibtia between single-, double-, and triple-stranded polynucleotides
in the presence of K+, Na+, and Mg2+ ions,
J. Biomol. Struct. and Dynamics, v.20(2), pp.275-290 (2002)
Abstract from the JBSD Web site
- N. Korolev, A. P. Lyubartsev and L. Nordenskiöld
Application of the Poisson Boltzmann polyelectrolyte model for analysis
of thermal denaturation of DNA in the presence of Na+ and polyamine cations
Biophysical Chemistry, v.104, pp.55-66 (2003)
Abstract and full text
In this paper, electrostatic contribution to the force nesessary to release
DNA from the nucleosome, is evaluated within the mean field
(Poisson-Boltzmann) theory:
- N. Korolev, A. P. Lyubartsev and A. Laaksonen
"Electrostatic Background of Chromatin Fiber Stretching"
J. Biomol. Struct. and Dyn., v. 22(2), pp. 215-226 (2004)  
Abstract
PDF text
Molecular Dynamics of DNA
-
A.P.Lyubartsev and A.Laaksonen "Molecular Dynamics
Simulations of DNA in Solution with Different Counterions". J.Biomol.Struct.
and Dyn., v.16, pp.579-587 (1998) Abstract;
Supplementary
material
-
N. Korolev, A.P.Lyubartsev, L. Nordenskiöld
and A. Laaksonen, "Spermine: An "invisible" component in the crystals
of B-DNA: A grand canonical Monte Carlo and
Molecular Dynamics simulation study" J. Mol. Biol., 308, 907-917
(2001) Abstract
and full text from the Ideal Library
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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