Molecular dynamics simulations of water and biomolecules with a Monte Carlo constant pressure algorithm
Introduction
It is often desirable to carry out molecular dynamics simulations at constant pressure rather than constant volume for direct comparison with experimental data. A need for doing simulations in the (N,P,T) ensemble also arises because the ‘correct’ volume of the simulation system is initially unknown when one is dealing, e.g., with solvated proteins or other non-trivial solutions. With periodic boundary conditions (PBC) [1], [2] constant pressure simulations are in principle straightforward, while spherical boundary models generally employ surface restraints to attain correct densities [3], [4], [5], [6]. Among several different algorithms available for carrying out MD simulations at constant pressure [1], [7], [8], [9], [10], the one that is probably most often used in biomolecular simulations is due to Berendsen et al. [9]. In this algorithm the (isotropic) pressure is calculated at each time step from the kinetic energy and virial of the systemwhere V is the volume of the periodic box and the virial is obtained from the intermolecular forces throughAs intramolecular forces do not contribute to the pressure, the sum in Eq. (2) is often taken over molecules and the forces act on their centers of mass. The boxlengths and molecular center of mass coordinates are then scaled in each time step according to l→μl and x→μx, whereHere, κ is formally identified as the isothermal compressibility, while τp is an arbitrary coupling parameter, or relaxation time, that is chosen to attain ‘reasonable’ density fluctuations in the system. While the Berendsen algorithm may appear somewhat ad hoc it can be shown to correspond to the assumption of a simple exponential decay of pressure fluctuations, which intuitively seems reasonable.
In this Letter we wish to explore an alternative to the above type of ‘pressure bath’ or ‘piston’ methods, where the viral needs to be evaluated in each MD step, by considering the combination of regular (PBC) constant temperature MD with Monte Carlo sampling of volume fluctuations at a given constant external pressure. A search of the literature on this topic revealed that this idea has indeed been tried by Chow and Ferguson in 1995 [11], albeit only using liquid neon as a test case. Here, we describe the implementation of a MC constant pressure algorithm within the MD program Q [6] and report its initial testing on simulations of liquid water and of chemical reactions in proteins using the empirical valence bond (EVB) model.
Section snippets
Methods
The combined MD/MC algorithm propagates trajectories according to the standard leap-frog Verlet scheme with temperature scaling in each MD time step through the Berendsen thermostat [9]. Usually it will not be meaningful or efficient to do trial moves on the volume of the periodic box in each time step but rather at some fixed interval. This interval can, e.g., be chosen to be equal to the nonbonded list update interval in cases where cutoffs are used. A volume move is then tried after the
Liquid water simulations
We start by examining constant pressure MD/MC simulations of liquid water at ambient temperature and pressure using the SPC [12] and TIP3P [13] water models. Results for the different systems and computational setups are given in Table 1. For comparison some results from Jorgensen and Jenson [18] and van der Spoel et al. [19] are also given in the table. We can see that the results regarding density and potential energy obtained for the smaller systems containing 216 water molecules are
Conclusions
We have presented a combined MD/MC approach for carrying out simulations of arbitrary molecular systems at constant pressure that follows the idea of Chow and Ferguson [11]. Application of this method to liquid water simulations with the SPC and TIP3P models shows that earlier results from both MD simulations with standard pressure coupling schemes and MC simulations are well reproduced. We also find that isothermal compressibilities calculated for the SPC model with the present method are in
Acknowledgments
Support from the Swedish Research Council (VR) and the Swedish Foundation for Strategic Research (SSF/Rapid) to J.Å. and from the Norwegian Reserach Council (NFR) to B.O.B. is gratefully acknowledged. We thank Dr. David van der Spoel for useful discussions.
References (31)
- et al.
Chem. Phys. Lett.
(1984) - et al.
J. Mol. Graph. Model
(1998) - et al.
Comput. Phys. Commun.
(1995) - et al.
FEBS Lett.
(1999) - et al.
Biochim. Biophys. Acta
(1997) - et al.
Biochim. Biophys. Acta
(2000) - et al.
Biochim. Biophys. Acta
(2002) Biochim. Biophys. Acta
(2002)J. Biol. Chem.
(2003)Biochim. Biophys. Acta
(2002)
Computer Simulation of Liquids
J. Chem. Phys.
J. Comput. Chem.
J. Chem. Phys.
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