Most processes occurring in a system are determined by the relative free energy between two or more states because the free energy is a measure of the probability of finding the system in a given state. When the two states of interest are connected by a pathway, usually called reaction coordinate, along which the free-energy profile is determined, this profile or potential of mean force (PMF) will also yield the relative free energy of the two states. Twelve different methods to compute a PMF are reviewed and compared, with regard to their precision, for a system consisting of a pair of methane molecules in aqueous solution. We analyze all combinations of the type of sampling (unbiased, umbrella-biased or constraint-biased), how to compute free energies (from density of states or force averaging) and the type of coordinate system (internal or Cartesian) used for the PMF degree of freedom. The method of choice is constraint-bias simulation combined with force averaging for either an internal or a Cartesian PMF degree of freedom.

A new charge-on-spring (COS) model for water is introduced (COS/D). It includes a sublinear dependence of the induced dipole on the electric field for large field strength to include the effect of hyperpolarizability by damping the polarizability. Only two new parameters were introduced to define the damping of the polarizability. In the parametrization procedure, these two damping parameters, the two Lennard-Jones parameters, the charge on the oxygen, and the distance between the virtual site and the oxygen atom were varied to reproduce the density, the heat of vaporization, the dielectric permittivity, and the position of the first peak in the radial distribution function of liquid water at room temperature and pressure. In this way, a model was obtained that correctly describes a variety of thermodynamic, dynamic, and dielectric properties of water while still preserving the simplicity of the COS model, which allows a straightforward introduction of explicit polarization into (bio)molecular force fields.

Since the most recent description of the functionalities of the GROMOS software for biomolecular simulation in 2005 many new functions have been implemented. In this article, the new functionalities that involve modified forces in a molecular dynamics (MD) simulation are described: the treatment of electronic polarizability, an implicit surface area and internal volume solvation term to calculate interatomic forces, functions for the GROMOS coarse-grained supramolecular force field, a multiplicative switching function for nonbonded interactions, adiabatic decoupling of a number of degrees of freedom with temperature or force scaling to enhance sampling, and nonequilibrium MD to calculate the dielectric permittivity or viscosity. Examples that illustrate the use of these functionalities are given.

Methodology to compute the relative static dielectric permittivity and dielectric relaxation time of molecular liquids is reviewed and explicit formulas are given for the external field method in the case of simulations using a spherical cutoff, in which the background dielectric permittivity (εcs) can be larger than one, in combination with a Poisson-Boltzmann reaction-field approximation for long-range electrostatic interactions. The external field method is simple to implement and computationally efficient. It is particularly suitable for polarizable molecular models with zero permanent dipole moment and for coarse-grained molecular models with εcs > 1. The dielectric permittivities and relaxation times of water (H2O), dimethylsulfoxide (DMSO), methanol (MeOH), and chloroform (CHCl3), which range from 2 to 80 and from 5 ps to 50 ps, respectively, were calculated as an illustration.

For the understanding of cellular processes the molecular structure of biomolecules has to be accurately determined. Initial models can be significantly improved by structure refinement techniques. Here, we present the refinement methods and analysis techniques implemented in the GROMOS software for biomolecular simulation. The methodology and some implementation details of the computation of NMR NOE data, (3)J-couplings and residual dipolar couplings, X-ray scattering intensities from crystals and solutions and neutron scattering intensities used in GROMOS is described and refinement strategies and concepts are discussed using example applications. The GROMOS software allows structure refinement combining different types of experimental data with different types of restraining functions, while using a variety of methods to enhance conformational searching and sampling and the thermodynamically calibrated GROMOS force field for biomolecular simulation.

A method to enhance sampling of a small subset of N(h) particular degrees of freedom of a system of N(h) + N(l) degrees of freedom is presented. It makes use of adiabatically decoupling these degrees of freedom by increasing their mass followed by either increasing their temperature or reducing their interaction or the force acting on them. The appropriate statistical-mechanical expressions for use of these methods in simulation studies are derived. As long as the subset of mass-increased degrees of freedom is small compared to the total number of degrees of freedom of the system, sampling of this subset of degrees of freedom can be much enhanced at the cost of a slight perturbation of the configurational distribution. This is illustrated for a test system of 1000 SPC, simple point charge, water molecules at 300 K and a density of 997 kg m(-3). Various fractions N(h)/(N(h) + N(l)) of water molecules were adiabatically decoupled to different degrees. The size of the diffusion coefficient of these decoupled water molecules was used as a measure for how much the sampling was enhanced and the average potential energy per water molecule was used as a measure of how much the configurational distribution of the system gets distorted. A variety of parameter values was investigated and it was found that for N(h)/(N(h) + N(l)) ≤ 0.1 the diffusion of the N(h) molecules could be enhanced by factors up to 35 depending on the method, the ratio N(h)/(N(h) + N(l)), the extent of adiabatic decoupling, and the temperature or force scaling factors, at the cost of a slight perturbation of the configurational distribution.

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