Simulations of Charged Polymers

Significant Achievements, Anticipated Outcomes and Future Work

Our major development is a novel and highly efficient method for studying the complex conformation of molecular systems. Preliminary results using this method show a speed-up by a factor of 40 and even larger speed improvements are possible. Using this method we are able to investigate problems which where earlier prohibited by their computational cost. We have investigated the mechanical stability of charged polymers and can for example explain why DNA shows a totally different response to external stress then more flexible polymers. We expect to develop the method further and use it as an highly effective general optimization tool.

We have performed parallel simulations of charged polymers. Both of polyelectrolytes which have one kind of charge, as for example in DNA, and of so-called polyampholytes which have both positive and negative charges. Polyampholytes can be used as crude analogies to proteins. Of specific interest has been the condensation phenomena found for charged polymers and how these collapsed structures respond to an external force. We have found that for polyelectrolytes the stiffness of the chain has a major influence on both the condensed structure and the force response. Flexible polyelectrolytes form regular globules and unfold easily when an external force is applied. Stiff polyelectrolytes as DNA, form toroidal condensed structures and have a very different response to external force. The intrinsic chain stiffness results in a co-existence of toroidal and elongated conformations, which leads to an instability when an external force is applied to the polymer. This is something reflected in experimental single molecule experiments.

The behavior of polyelectrolytes can be understood by simple theoretical reasoning. When turning towards compact polyampholytes the results are very different. Although the condensed conformations resemble that of polyelectrolytes, the response to external force is very different. Polyampholytes have a marked plateau phase in which a constant force can lead to very different polymer sizes. In this region the polymer takes on a pearl-necklace structure in which compact, locally collapsed, parts of the chain are connected by longer, stretched parts, of the chain. Although direct experimental evidence of pearl-necklace structures does not exist, the force expansion curves indicate a way of detecting these exotic conformational behaviors.

Computational Techniques Used

During the project we have implemented and tested various methods to speed up molecular simulations using the well known Monte Carlo algorithm.

Cluster moves - For Monte Carlo simulations, statistically independent configurations are reached faster by employing global moves. A well-known example is the pivot move, which is found to speed up polymer simulations substantially. When electrostatic interactions, with explicit salt particles, are included, these global moves have a low acceptance rate since the energetic penalty for leaving the small ion cloud behind is large. This is significant when the electrostatic interactions become large, e.g. when multivalent ions are present. By including the small ions in the pivot, i.e. by doing a clothed pivot, we have shown that the efficiency of the pivot move can be increased by between 150% (for monovalent counterions) to 20000% (for trivalent counterions).

Parallel ensemble techniques - When the free energy landscape is complex, e.g. at low temperature, the convergence time of a simulation may become large since the simulation gets stuck in local minimas. By adding an extra dimension, e.g. temperature, it is possible to escape local minimas by moves in the temperature instead of conventional moves. In order for the moves in temperature to be acceptable the energy distributions, at different temperatures, need to overlap and thus the different temperatures must by closely spaced. This can be achieved by running several instances of the simulation, on parallel processors, at different temperatures. Our implementation of a parallel ensemble technique, used to study compact polyelectrolytes, does in some situations show linear scaling up to 8 processors.

Parallel free energy simulations - We have developed a method of parallelizing flat histogram Monte Carlo simulations, which give the free energy of a molecular system as an output. In the serial version, a constant probability distribution, as a function of any system parameter, is calculated by updating an external potential, which is added to the system Hamiltonian. This external potential is related to the free energy. In the parallel implementation, the simulation is distributed on to different processors. With regular intervals the modifying potential is summed over all processors and distributed back to every processor, thus spreading the information of which parts of parameter space have been explored. For a relatively small problem, with 84 particles, this implementation is shown to decrease the execution time linearly with added number of processors up to 32 processors on both the VPAC and APAC National Facility linux clusters. We expect the method to show linear scaling up to even more processors, for larger and more realistic problems.

Publications, Awards and External Funding

External Funding and Awards

DP0209690 Static and Dynamic Forces in Colloidal and Fluid Systems (2002-2004), $300k
Investigators: Prof Franz Grieser , Prof Derek Y Chan, Prof Geoff W Stevens, Dr John Elie Sader

DP0343786 Spectroscopy of Complex Fluids in Flow (2003-2005), $433k
Investigators: A/Prof David Edwin Dunstan , Prof Derek Y Chan

ARC Special Research Centre – Particulate Fluid Processing Centre (2003-2005), $2691k

Publications

[1] M. O. Khan and D. Y. C. Chan, Monte Carlo simulations of stretched charged polymers, J. Phys. Chem., 107, 2003, 8131-8139.
[2] M. O. Khan and D. Y. C. Chan, The effect of chain stiffness on polyelectrolyte condensation, Manuscript in preparation
[3] M. O. Khan, G. Kennedy and D. Y. C. Chan, An effective parallel Monte Carlo algorithm for free energy calculations of molecular systems, Submitted to J. Chem. Phys.