Exact results and mean field approximation for a model of molecular aggregation

We present a simple one-dimensional model with molecular interactions favouring the formation of clusters with a defined optimal size. Increasing the density, at low temperature, the system goes from a nearly-ideal gas of independent molecules to a system with most of the molecules in optimal clusters, in a way that resembles the formation of micelles in a dilution of amphiphilic molecules, at the critical micellar concentration. Our model is simple enough to have an exact solution, but it contains some basic features of more realistic descriptions of amphiphilic systems: molecular excluded volume and molecular attractions which are saturated at the optimal cluster. The comparison between the exact results and the mean field density functional approximation suggests new approaches to study the more complex and realistic models of micelle formation; in particular it addresses the long-standing controversy surrounding separation of internal degrees of freedom in the formulation of cluster association phenomena.Comment: 7 pages, 5 figures, some minor correction

Analysis of nucleotide diversity of NAT2 coding region reveals homogeneity across Native American populations and high intra-population diversity.

N-acetyltransferase 2 (NAT2), an important enzyme in clinical pharmacology, metabolizes antibiotics such as isoniazid and sulfamethoxazole, and catalyzes the transformation of aromatic and heterocyclic amines from the environment and diet into carcinogenic intermediates. Polymorphisms in NAT2 account for variability in the acetylator phenotype and the pharmacokinetics of metabolized drugs. Native Americans, settled in rural areas and large cities of Latin America, are under-represented in pharmacogenetics studies; therefore, we sequenced the coding region of NAT2 in 456 chromosomes from 13 populations from the Americas, and two from Siberia, detecting nine substitutions and 11 haplotypes. Variants *4 (37%), *5B (23%) and *7B (24%) showed high frequencies. Average frequencies of fast, intermediate and slow acetylators across Native Americans were 18, 56 and 25%, respectively. NAT2 intra-population genetic diversity for Native Americans is higher than East Asians and similar to the rest of the world, and NAT2 variants are homogeneously distributed across native populations of the continent

Bulk inhomogeneous phases of anisotropic particles: A fundamental measure functional study of the restricted orientations model

The phase diagram of prolate and oblate particles in the restricted orientations approximation (Zwanzig model) is calculated. Transitions to different inhomogeneous phases (smectic, columnar, oriented, or plastic solid) are studied through minimization of the fundamental measure functional (FMF) of hard parallelepipeds. The study of parallel hard cubes (PHC's) as a particular case is also included motivated by recent simulations of this system. As a result a rich phase behavior is obtained which include, apart from the usual liquid crystal phases, a very peculiar phase (called here discotic smectic) which was already found in the only existing simulation of the model, and which turns out to be stable because of the restrictions imposed on the orientations. The phase diagram is compared at a qualitative level with simulation results of other anisotropic particle systems.Comment: 11 pages, 10 figure

Lattice density-functional theory of surface melting: the effect of a square-gradient correction

I use the method of classical density-functional theory in the weighted-density approximation of Tarazona to investigate the phase diagram and the interface structure of a two-dimensional lattice-gas model with three phases -- vapour, liquid, and triangular solid. While a straightforward mean-field treatment of the interparticle attraction is unable to give a stable liquid phase, the correct phase diagram is obtained when including a suitably chosen square-gradient term in the system grand potential. Taken this theory for granted, I further examine the structure of the solid-vapour interface as the triple point is approached from low temperature. Surprisingly, a novel phase (rather than the liquid) is found to grow at the interface, exhibiting an unusually long modulation along the interface normal. The conventional surface-melting behaviour is recovered only by artificially restricting the symmetries being available to the density field.Comment: 16 pages, 6 figure

Condensation of Hard Spheres Under Gravity: Exact Results in One Dimension

We present exact results for the density profile of the one dimensional array of N hard spheres of diameter D and mass m under gravity g. For a strictly one dimensional system, the liquid-solid transition occurs at zero temperature, because the close-pakced density, $\phi_c$, is one. However, if we relax this condition slightly such that $phi_c=1-\delta$, we find a series of critical temperatures T_c^i=mgD(N+1-i)/\mu_o with \mu_o=const, at which the i-th particle undergoes the liquid-solid transition. The functional form of the onset temperature, T_c^1=mgDN/\mu_o, is consistent with the previous result [Physica A 271, 192 (1999)] obtained by the Enskog equation. We also show that the increase in the center of mass is linear in T before the transition, but it becomes quadratic in T after the transition because of the formation of solid near the bottom

Newton black films as wetting systems

Newton black films (NBFs) can appear under a wide range of experimental conditions. NBFs define the adhesive states of foams and emulsions, showing their formation is a very general physical phenomenon. We show that the existence of NBFs and their whole experimental behavior can be understood within the theory of wetting transitions. NBFs are experimental realizations of partial wetting or pre-wetting states. Hence, they provide experimental systems to investigate the pre-wetting transition, and the spreading behavior under conditions that are very difficult to realize in other experimental systems. We also introduce two new computational approaches to obtain the disjoining pressure isotherm from canonical simulations, and to estimate the contact angles of droplets of nanoscopic dimensionsFinancial support for this work was provided by The Royal Society project “Intrinsic Structure of Aqueous Interfaces” and the Dirección General de Investigación, Ministerio de Ciencia y Tecnología of Spain, under Grant No. FIS2010-22047-C05, and by the Comunidad Autónoma de Madrid under the R&D Program of activities MODELICOCM/ S2009ESP-1691. H.M. would like to thank the Universidad Autonoma de Madrid for the award of a FPU-UAM doctoral grant. F.B. would like to thank the EPSRC for the award of a Leadership Fellowship (EP/J003859/1

Density Functional for Anisotropic Fluids

We propose a density functional for anisotropic fluids of hard body particles. It interpolates between the well-established geometrically based Rosenfeld functional for hard spheres and the Onsager functional for elongated rods. We test the new approach by calculating the location of the the nematic-isotropic transition in systems of hard spherocylinders and hard ellipsoids. The results are compared with existing simulation data. Our functional predicts the location of the transition much more accurately than the Onsager functional, and almost as good as the theory by Parsons and Lee. We argue that it might be suited to study inhomogeneous systems.Comment: To appear in J. Physics: Condensed Matte

Schwinger Boson Formulation and Solution of the Crow-Kimura and Eigen Models of Quasispecies Theory

We express the Crow-Kimura and Eigen models of quasispecies theory in a functional integral representation. We formulate the spin coherent state functional integrals using the Schwinger Boson method. In this formulation, we are able to deduce the long-time behavior of these models for arbitrary replication and degradation functions. We discuss the phase transitions that occur in these models as a function of mutation rate. We derive for these models the leading order corrections to the infinite genome length limit.Comment: 37 pages; 4 figures; to appear in J. Stat. Phy

A computer simulation approach to quantify the true area and true area compressibility modulus of biological membranes

We present a new computational approach to quantify the area per lipid and the area compressibility modulus of biological membranes. Our method relies on the analysis of the membrane fluctuations using our recently introduced coupled undulatory (CU) mode [Tarazona et al., J. Chem. Phys. 139, 094902 (2013)], which provides excellent estimates of the bending modulus of model membranes. Unlike the projected area, widely used in computer simulations of membranes, the CU area is thermodynamically consistent. This new area definition makes it possible to accurately estimate the area of the undulating bilayer, and the area per lipid, by excluding any contributions related to the phospholipid protrusions. We find that the area per phospholipid and the area compressibility modulus features a negligible dependence with system size, making possible their computation using truly small bilayers, involving a few hundred lipids. The area compressibility modulus obtained from the analysis of the CU area fluctuations is fully consistent with the Hooke's law route. Unlike existing methods, our approach relies on a single simulation, and no a priori knowledge of the bending modulus is required. We illustrate our method by analyzing 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine bilayers using the coarse grained MARTINI force-field. The area per lipid and area compressibility modulus obtained with our method and the MARTINI forcefield are consistent with previous studies of these bilayersWe acknowledge the support of the Spanish Ministry of Science and Innovation (Grant Nos. FIS2010-22047-C05 and FIS2013-47350-C5). We would also like to acknowledge the Imperial College High Performance Computing Service for providing computational resources. F.B. would like to thank the EPSRC (No. EP/J003859/1) for the award of a Leadership Fellowshi