Alexander P. Lyubartsev

New approach to Monte Carlo calculation of the free energy: Method of expanded ensembles

We propose a new effective Monte Carlo (MC) procedure for direct calculation of the free energy in a single MC run. The partition function of the expanded ensemble is introduced including a sum of canonical partition functions with a set of temperatures and additive factors (modification). Random walk in the space of both particle coordinates and temperatures provides calculation of free energy in a wide range of T. The method was applied to a primitive model of electrolyte including the region of low temperatures. In similar way other variants of expanded ensembles are constructed (e.g., over the number of particles N or volume V). Its facilities in quantum statistics (path integral Monte Carlo) and some other applications are also discussed.

The inhomogeneous structure of water at ambient conditions

Small-angle X-ray scattering (SAXS) is used to demonstrate the presence of density fluctuations in ambient water on a physical length-scale of ≈1 nm; this is retained with decreasing temperature while the magnitude is enhanced. In contrast, the magnitude of fluctuations in a normal liquid, such as CCl4, exhibits no enhancement with decreasing temperature, as is also the case for water from molecular dynamics simulations under ambient conditions. Based on X-ray emission spectroscopy and X-ray Raman scattering data we propose that the density difference contrast in SAXS is due to fluctuations between tetrahedral-like and hydrogen-bond distorted structures related to, respectively, low and high density water. We combine our experimental observations to propose a model of water as a temperature-dependent, fluctuating equilibrium between the two types of local structures driven by incommensurate requirements for minimizing enthalpy (strong near-tetrahedral hydrogen-bonds) and maximizing entropy (nondirectional H-bonds and disorder). The present results provide experimental evidence that the extreme differences anticipated in the hydrogen-bonding environment in the deeply supercooled regime surprisingly remain in bulk water even at conditions ranging from ambient up to close to the boiling point.

M.DynaMix – a scalable portable parallel MD simulation package for arbitrary molecular mixtures

A general purpose, scalable parallel molecular dynamics package for simulations of arbitrary mixtures of flexible or rigid molecules is presented. It allows use of most types of conventional molecular-mechanical force fields and contains a variety of auxiliary terms for inter- and intramolecular interactions, including an harmonic bond-stretchings. It can handle both isotropic or ordered systems. Besides an NVE MD ensemble, the simulations can also be carried out in either NVT or NPT ensembles, by employing the Nose–Hoover thermostats and barostats, respectively. If required, the NPT ensemble can be generated by maintaining anisotropic pressures. The simulation cell can be either cubic, rectangular, hexagonal or a truncated octahedron, with corresponding periodic boundary conditions and minimum images. In all cases, the optimized Ewald method can be used to treat the Coulombic interactions. Double time-step or constrained dynamics schemes are included. An external electric field can be applied across the simulation cell. The whole program is highly modular and is written in standard Fortran 77. It can be compiled to run efficiently both on parallel and sequential computers. The inherent complexity of the studied system does not affect the scalability of the program. The scaling is good with the size of the system and with the number of processors. The portability of the program is good, it runs regularly on several common single- and multiprocessor platforms, both scalar and vector architectures included.

Derivation and systematic validation of a refined all-atom force field for phosphatidylcholine lipids.

An all-atomistic force field (FF) has been developed for fully saturated phospholipids. The parametrization has been largely based on high-level ab initio calculations in order to keep the empirical input to a minimum. Parameters for the lipid chains have been developed based on knowledge about bulk alkane liquids, for which thermodynamic and dynamic data are excellently reproduced. The FFs ability to simulate lipid bilayers in the liquid crystalline phase in a tensionless ensemble was tested in simulations of three lipids: 1,2-diauroyl-sn-glycero-3-phospocholine (DLPC), 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC), and 1,2-dipalmitoyl-sn-glycero-3-phospcholine (DPPC). Computed areas and volumes per lipid, and three different kinds of bilayer thicknesses, have been investigated. Most importantly NMR order parameters and scattering form factors agree in an excellent manner with experimental data under a range of temperatures. Further, the compatibility with the AMBER FF for biomolecules as well as the ability to simulate bilayers in gel phase was demonstrated. Overall, the FF presented here provides the important balance between the hydrophilic and hydrophobic forces present in lipid bilayers and therefore can be used for more complicated studies of realistic biological membranes with protein insertions.

An extension and further validation of an all atomistic force field for biological membranes

Biological membranes are versatile in composition and host intriguing molecular processes. In order to be able to study these systems, an accurate model Hamiltonian or force field (FF) is a necessity. Here, we report the results of our extension of earlier developed all-atomistic FF parameters for fully saturated phospholipids that complements an earlier parameter set for saturated phosphatidylcholine lipids (J. Phys. Chem. B, 2012, 116, 3164-3179). The FF, coined Slipids (Stockholm lipids), now also includes parameters for unsaturated phosphatidylcholine and phosphatidylethanolamine lipids, e.g., POPC, DOPC, SOPC, POPE, and DOPE. As the extended set of parameters is derived with the same philosophy as previously applied, the resulting FF has been developed in a fully consistent manner. The capabilities of Slipids are demonstrated by performing long simulations without applying any surface tension and using the correct isothermal-isobaric (NPT) ensemble for a range of temperatures and carefully comparing a number of properties with experimental findings. Results show that several structural properties are very well reproduced, such as scattering form factors, NMR order parameters, thicknesses, and area per lipid. Thermal dependencies of different thicknesses and area per lipid are reproduced as well. Lipid diffusion is systematically slightly underestimated, whereas the normalized lipid diffusion follows the experimental trends. This is believed to be due to the lack of collective movement in the relatively small bilayer patches used. Furthermore, the compatibility with amino acid FFs from the AMBER family is tested in explicit transmembrane complexes of the WALP23 peptide with DLPC and DOPC bilayers, and this shows that Slipids can be used to study more complex and biologically relevant systems.

Hydration of Li+ ion. An ab initio molecular dynamics simulation

Ab initio Car–Parrinello molecular dynamics simulations of a Li+ ion in water have been carried out using the density-functional theory with Becke–Lee–Yang–Parr (BLYP) functional and ultrasoft Vanderbildt pseudopotentials. Both structural and dynamical properties of Li+ have been studied in detail and compared with available neutron scattering and spectroscopic data. Excellent agreement is obtained with the existing experimental data for the structure of the first hydration shell around the Li+ ion. Spectral features of bound water are compared to those of bulk water. Reasonable agreement is obtained with IR and Raman experiments. The ab initio simulation results have also been used to derive a Li+–water interaction potential. The best fit of the data gave a simple single-exponential potential function, which reproduces very well the liquid structure from the original ab initio simulations. This potential model, together with the simple point charge (SPC) water model, was applied to calculate the hydratio...

Multiscale modeling of lipids and lipid bilayers

A multiscale modeling approach is applied for simulations of lipids and lipid assemblies on mesoscale. First, molecular dynamics simulation of initially disordered system of lipid molecules in water within all-atomic model was carried out. On the next stage, structural data obtained from the molecular dynamics (MD) simulation were used to build a coarse-grained (ten sites) lipid model, with effective interaction potentials computed by the inverse Monte Carlo method. Finally, several simulations of the coarse-grained model on longer length- and time-scale were performed, both within Monte Carlo and molecular dynamics simulations: a periodical sample of lipid molecules ordered in bilayer, a free sheet of such bilayer without periodic boundary conditions, formation of vesicle from a plain membrane, process of self-assembly of lipids randomly dispersed in volume. It was shown that the coarse-grained model, developed exclusively from all-atomic simulation data, reproduces well all the basic features of lipids in water solution.

Recent development in computer simulations of lipid bilayers

Rapid development of computer power during the last decade has made molecular simulations of lipid bilayers feasible for many research groups, which, together with the growing general interest in investigations of these very important biological systems has lead to tremendous increase of the number of research on the computational modeling of lipid bilayers. In this review, we give account of the recent progress in computer simulations of lipid bilayers covering mainly the period of the last 5 years, and covering several selected subjects: development of the force fields for lipid bilayer simulations, studies of the role of lipid unsaturation, the effect of cholesterol and other inclusions on properties of the bilayer, and use of coarse-grained models.

Another Piece of the Membrane Puzzle: Extending Slipids Further.

To be able to model complex biological membranes in a more realistic manner, the force field Slipids (Stockholm lipids) has been extended to include parameters for sphingomyelin (SM), phosphatidylglycerol (PG), phosphatidylserine (PS) lipids, and cholesterol. Since the parametrization scheme was faithful to the scheme used in previous editions of Slipids, all parameters are consistent and fully compatible. The results of careful validation of a number of key structural properties for one and two component lipid bilayers are in excellent agreement with experiments. Potentials of mean force for transferring water across binary mixtures of lipids and cholesterol were also computed in order to compare water permeability rates to experiments. In agreement with experimental and simulation studies, it was found that the permeability and partitioning of water is affected by cholesterol in lipid bilayers made of saturated lipids to the largest extent. With the extensions of Slipids presented here, it is now possible to study complex systems containing many different lipids and proteins in a fully atomistic resolution in the isothermic-isobaric (NPT) ensemble, which is the proper ensemble for membrane simulations.

On the Competition between Water, Sodium Ions, and Spermine in Binding to DNA: A Molecular Dynamics Computer Simulation Study

The interaction of DNA with the polyamine spermine(4+) (Spm(4+)), sodium ions, and water molecules has been studied using molecular dynamics computer simulations in a system modeling a DNA crystal. The simulation model consisted of three B-DNA decamers in a periodic hexagonal cell, containing 1200 water molecules, 8 Spm(4+), 32 Na(+), and 4 Cl(-) ions. The present paper gives a more detailed account of a recently published report of this system and compares results on this mixed Spm(4+)/Na(+)-cation system with an molecular dynamics simulation carried out for the same DNA decamer under similar conditions with only sodium counterions (Korolev et al., J. Mol. Biol. 308:907). The presence of Spm(4+) makes significant influence on the DNA hydration and on the interaction of the sodium ions with DNA. Spermine pushes water molecules out of the minor groove, whereas Na(+) attracts and organizes water around DNA. The major binding site of the Spm(4+) amino groups and the Na(+) ions is the phosphate group of DNA. The flexible polyamine spermine displays a high presence in the minor groove but does not form long-lived and structurally defined complexes. Sodium ions compete with Spm(4+) for binding to the DNA bases in the minor groove. Sodium ions also have several strong binding sites in the major groove. The ability of water molecules, Spm(4+), and Na(+) to modulate the local structure of the DNA double helix is discussed.