Inverse Monte Carlo

Bridging the length- and time- scale gap in computer simulations

An obvious dilemma in molecular computer modelling is the fact that as the system is described in more details and more rigorously, the number of atoms that can be included becomes smaller. While the quantum ab-initio molecular dynamics may be based on a high quality, controllable approximation of the fundamental quantum theory, in practical terms it can be applied only to relatively small, typically a few dozens atoms, molecular systems, which can be simulated during a few picosecond. Classical molecular dynamics simulations can deal with tens of thousand atoms and cover a time scale of many nanosecond, but they typically use empirical potential functions with many adjustable parameters. When we go to mesoscale phenomena, the number of atoms and simulation time becomes unaffordable even for the classical molecular dynamics, and more simplified models becomes necessary. There is obvious need in developing methods which use information, obtained at a more fundamental and more accurate  level for a small system,  to construct an effective classical model to be used in simulations of bigger systems on longer time scale.

 Suggested recently inverse Monte Carlo approach may be used to link together different levels of molecular modelling.
The inverse Monte Carlo method solves the inverse problem of the statistical mechanics - reconstruct interaction potential between molecules if the distribution function is known.  If we know from some source the radial distribution function between particles, we can calculate the corresponding pair interaction potential. It is possible to prove that solution of the inverse problem is unique, but until recently there were no practically realisable way to find it.

The general scheme is the following.  First, detailed simulation on a more fundamental, "ab initio" level. Then, construction of a simplified (coarse-grained) model. Next, using the inverse MC to compute effective interaction potentials for the simplified model, based on distribution functions, calculated during the first step. Finally, simulation of the simplified model on a longer time- and length scale.  Below is the list of papers describing applications of the inverse Monte carlo method to different problems.
 

Effective solvent-mediated potentials

In this case radial distribution functions between ions in solution are calculated from all-atomic molecular dynamics simulations. Then, the inverse MC method is used to the obtain effective solvent-mediated potentials between the ions which can be used in Monte-Carlo simulations of the same system without explicit account for water molecules. This approach is described in the following papers:
 
  1. Alexander P. Lyubartsev and Aatto Laaksonen "Calculation of Effective Interaction Potentials from Radial Distribution Functions: A Reverse Monte Carlo Approach" Phys.Rev.E, v.52, p.3730 (1995). Abstract ; Paper (PostScript file)
  2. Alexander P. Lyubartsev and Aatto Laaksonen. Osmotic and Activity Coefficients from effective potentials for Hydrated Ions. Phys. Rev. E,  v.55(5),p.5689 (1997). Abstract ; Paper (Postscript file) .
  3. A.P.Lyubartsev, A.Laaksonen. "Reconstruction of pair interaction potentials from radial distribution functions." Computer Physics Communucations, v. 121-122, p.57-59 (1999). Paper (postscript file)
  4. A.P.Lyubartsev, A.Laaksonen. "Effective Potentials for Ion-DNA Interactions" J. Chem. Phys., v.111, p.11207-11215 (1999). Abstract
  5. R.Kjellander, A.P.Lyubartsev, and S.Marcelja, "McMillan Theory for Solvent Effects in Inhomogeneous Systems: Calculation of Interaction Pressure in Aqueous Electrical Double Layers" J. Chem. Phys., 114(21), 9565-9577 (2001) Abstract and full text from the JCP Web site
  6. A. P. Lyubartsev and S. Marcelja Evaluation of effective ion-ion potentials in aqueous electrolytes  Phys.Rev.E, v.65(4), 041203 (2002) Abstract and full text from the APS Web site
                Supplementary information: raw data on radial distribution functions and effective potentials in NaCl aqueous solution

Effective potentials for coarse-grained models

Larger groups of molecules can be united in single interaction centres. For example, lipid molecule may be presented as about 10 interaction centers, instead of about 100 atoms. Effective potentials for coarse-grained model may be built in a similar manner, as the solvent-mediated potentials, from all-atomic molecular dynamics simulations. See more information here:
  1. A.P. Lyubartsev "Multiscale modeling of lipids and lipid bilayers" Eur. Biophys. J., (2005) + Supplementary information

Ab-initio effective potentials

In this case radial distribution functions between atoms are calculated from ab-initio (usually Car-Parrinello) molecular dynamics simulations.  Calculated by the inverse MC effective potentials may be then used in classical molecular dynamics simulations.
  1. A.P.Lyubartsev and A.Laaksonen, "Determination of pair potentials from ab-initio simulations: Application to liqid water" Chem.Phys.Lett., v. 325, pp.15-21 (2000)  Abstract
  2. A.P Lyubartsev, K. Laasonen and A. Laaksonen "Hydration of Li+ ion. An ab-initio molecular Dynamics Simulation" J. Chem. Phys., v. 114, p.3120-3126 (2001) Abstract and full text from the JCP Web site

Other cases

  1. V. Lobaskin, A. Lyubartsev and P. Linse "Effective macroion-macroion potentials in asymmetric electrolytes" Phys. Rev. E, v. 63, 020401 (2001) Abstract and full text from the PRE Web site

This project has been supported by the Swedish Natural Sciences Research Council (NFR)

Software:


MagiC

by Alexander Mirzoev and Alexander Lyubarstev

A universal code to perform Inverse Monte Carlo calculation of effective potentials from results of more detailed ("atomistic") simulations.

MagiC download area

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Alexander Lyubartsev