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.

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Small-angle X-ray scattering (SAXS) is used to demonstrate the presence of density fluctuations in ambient water on a physical length-scale of Ϸ1 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.density fluctuations ͉ liquid-liquid hypothesis ͉ small angle X-ray scattering ͉ water structure ͉ X-ray spectroscopy L iquid water shows many anomalies in its thermodynamic properties such as compressibility, density variation and heat capacity (1-4). In the low-temperature regime, below the freezing point, these properties deviate strongly from normal and theories, related to a liquid-liquid phase transition between high and low density water, have been proposed to account for these anomalies (5). Although the anomalies are extreme in the supercooled region they are also present at ambient conditions where most of waters' physical, chemical and biological processes of importance occur. In contrast, water at ambient conditions has traditionally been considered as a homogeneous distribution of near-tetrahedral hydrogen-bonded (H-bonded) structures with thermal fluctuations increasing with temperature. This picture has been challenged by recent studies based on X-ray Raman (XRS) and conventional X-ray absorption spectroscopy (XAS) (6), and X-ray emission spectroscopy (XES) (7), suggesting two distinct local structures with tetrahedral as a minority and a highly hydrogen-bond (H-bond) distorted asymmetrical as the majority. In particular the proposed predominant asymmetrical structure has caused intense debate in the last years (see refs. 7 and 8 for detailed discussion).SAXS and small-angle neutron scattering (SANS) provide the most direct probes of density variations or fluctuations on large length scales in a liquid. Through an enhancement of the structure factor at low momentum transfer, Q, small deviations from the average electron density at different length scales can be reliably identified (9). Previous SAXS studies of w...

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.

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.