We introduce an alternative formulation of the exact stochastic simulation algorithm (SSA) for sampling trajectories of the chemical master equation for a well-stirred system of coupled chemical reactions. Our formulation is based on factored-out, partial reaction propensities. This novel exact SSA, called the partial-propensity direct method (PDM), is highly efficient and has a computational cost that scales at most linearly with the number of chemical species, irrespective of the degree of coupling of the reaction network. In addition, we propose a sorting variant, SPDM, which is especially efficient for multiscale reaction networks.

Using NMR, we measure the proton chemical shift ␦, of supercooled nanoconfined water in the temperature range 195 K < T < 350 K. Because ␦ is directly connected to the magnetic shielding tensor, we discuss the data in terms of the local hydrogen bond geometry and order. We argue that the derivative ؊(٢ ln ␦/٢T)P should behave roughly as the constant pressure specific heat CP(T), and we confirm this argument by detailed comparisons with literature values of CP(T) in the range 290 -370 K. We find that ؊(٢ ln ␦/٢T)P displays a pronounced maximum upon crossing the locus of maximum correlation length at Ϸ240 K, consistent with the liquid-liquid critical point hypothesis for water, which predicts that CP(T) displays a maximum on crossing the Widom line.configurational specific heat ͉ nuclear magnetic resonance ͉ proteins ͉ proton chemical shift U nlike most fluids, water displays anomalies in thermodynamical properties such as compressibility, isobaric heat capacity, and thermal expansion coefficient, and their explanation on molecular basis remains a challenge (1-3). One hypothesis that has received support from various theoretical studies (4-7) is the liquid-liquid (LL) critical point hypothesis, but a proper test can be obtained only by studying the properties of liquid water well below its homogeneous nucleation temperature, T H ϭ 231 K. This is made possible by confining water inside nanoporous structures so small that the liquid cannot freeze.Among recent findings concerning water's dynamical properties at these low temperatures are (8-13): a fragile-to-strong crossover and the violation of the Stokes-Einstein relation, related to the crossing of the Widom line and to the existence of a low-density-liquid-like (LDL-like) local structure. The Widom line is the locus of maximum correlation length in the one-phase region beyond the liquid-liquid critical point, where thermodynamic response functions take their maximum values (12, 13). Scattering experiments (using neutrons and x-rays) have given precise values of the pair correlation function (PCF), providing important benchmarks for testing models of its structure. The PCF represents only an isotropically averaged measure of structure. Thus, in many cases, PCFs may not faithfully reproduce the subtle hydrogen bond geometry responsible for water's thermal anomalies. Our goal in this study is to provide additional information on the local hydrogen bond geometry and, in particular, the average number of the possible configurations of the local molecular hydrogen bonding geometry, by measuring the NMR proton chemical shift ␦. If a water molecule in a dilute gas is taken to be an isolated-state reference, the chemical shift ␦ accounts for the change of the value of the magnetic shielding with respect to that of such a reference. Hence the chemical shift is related to the ''non-dilute'' or ''virial'' interaction of a water molecule with its surroundings, providing a picture of the intermolecular geometry (14-19). Originally, it has been proposed, especially in the high ...

We use a modified Shan-Chen, noiseless lattice-BGK model for binary immiscible, incompressible, athermal fluids in three dimensions to simulate the coarsening of domains following a deep quench below the spinodal point from a symmetric and homogeneous mixture into a two-phase configuration. The model is derivable from a continuous-time Boltzmann-BGK equation in the presence of an intercomponent body force. We find the average domain size grows with time as t(gamma), where gamma increases in the range 0.545+/-0.014q(4) crossover in the scaled structure function, which disappears when the dynamical scaling reasonably improves at later stages (Re=37). This excludes noise as the cause for a q(2) behavior, as analytically derived from Yeung and proposed by Appert et al. and Love et al. on the basis of their lattice-gas simulations. We also observe exponential temporal growth of the structure function during the initial stages of the dynamics and for wave numbers less than a threshold value, in accordance with the diffusive Cahn-Hilliard Model B. However, this exponential growth is also present in regimes proscribed by that model. There is no evidence that regions of parameter space for which the scheme is numerically stable become unstable as the simulations proceed, in agreement with finite-difference relaxational models and in contradistinction with an unconditionally unstable lattice-BGK free-energy model previously reported. Those numerical instabilities that do arise in this model are the result of large intercomponent forces which turn the equilibrium distribution negative.

Incoming Simian Virus 40 particles bind to their cellular receptor, the glycolipid GM1, in the plasma membrane and thereby induce membrane deformation beneath the virion leading to endocytosis and infection. Efficient membrane deformation depends on receptor lipid structure and the organization of binding sites on the internalizing particle. To determine the role of receptor diffusion, concentration and the number of receptors required for stable binding in this interaction, we analyze the binding of SV40 to GM1 in supported membrane bilayers by computational modeling based on experimental data. We measure the diffusion rates of SV40 virions in solution by fluorescence correlation spectroscopy and of the receptor in bilayers by single molecule tracking. Quartz-crystal microbalance with dissipation (QCM-D) is used to measure binding of SV40 virus-like particles to bilayers containing the viral receptor GM1. We develop a phenomenological stochastic dynamics model calibrated against this data, and use it to investigate the early events of virus attachment to lipid membranes. Our results indicate that SV40 requires at least 4 attached receptors to achieve stable binding. We moreover find that receptor diffusion is essential for the establishment of stable binding over the physiological range of receptor concentrations and that receptor concentration controls the mode of viral motion on the target membrane. Our results provide quantitative insight into the initial events of virus-host interaction at the nanoscopic level.

By means of a three-dimensional amphiphilic lattice-Boltzmann model with short-range interactions for the description of ternary amphiphilic fluids, we study how the phase separation kinetics of a symmetric binary immiscible fluid is altered by the presence of the amphiphilic species. We find that a gradual increase in amphiphile concentration slows down domain growth, initially from algebraic to logarithmic temporal dependence, and, at higher concentrations, from logarithmic to stretched-exponential form. In growth-arrested stretched-exponential regimes, at late times we observe the self-assembly of sponge mesophases and gyroid liquid-crystalline cubic mesophases, hence confirming that (a) amphiphile-amphiphile interactions need not be long-ranged in order for periodically modulated structures to arise in a dynamics of competing interactions, and (b) a chemically specific model of the amphiphile is not required for the self-assembly of cubic mesophases, contradicting claims in the literature. We also observe a structural order-disorder transition between sponge and gyroid phases driven by amphiphile concentration alone or, independently, by the amphiphile-amphiphile and the amphiphile-binary fluid coupling parameters. For the growth-arrested mesophases, we also observe temporal oscillations in the structure function at all length scales; most of the wave numbers show slow decay, and long-term stationarity or growth for the others. We ascribe this behavior to a combination of complex amphiphile dynamics leading to Marangoni flows.

molecular discreteness is apparent in small-volume chemical systems, such as biological cells, leading to stochastic kinetics. Here we present a theoretical framework to understand the effects of discreteness on the steady state of a monostable chemical reaction network. We consider independent realizations of the same chemical system in compartments of different volumes. Rate equations ignore molecular discreteness and predict the same average steadystate concentrations in all compartments. However, our theory predicts that the average steady state of the system varies with volume: if a species is more abundant than another for large volumes, then the reverse occurs for volumes below a critical value, leading to a concentration inversion effect. The addition of extrinsic noise increases the size of the critical volume. We theoretically predict the critical volumes and verify, by exact stochastic simulations, that rate equations are qualitatively incorrect in sub-critical volumes.

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We present the first simulations of the self-assembly kinetics of the gyroid cubic mesophase using a Boltzmann transport method. No macroscopic parameters are included in the model and three-dimensional hydrodynamics is emergent from the microscopic conservation laws. The self-assembly arise from local inter-particle interactions in an initially homogeneous, phase segregating binary fluid with dispersed amphiphile. The mixture evolves in discrete time according to the dynamics of a set of coupled Boltzmann-BGK equations on a lattice. We observe a transient microemulsion phase during self-assembly, the structure function peaks and direct-space imaging unequivocally identifying the gyroid at later times. For larger lattices, highly ordered subdomains are separated by grain boundaries. Relaxation towards the ordered equilibrium structure is very slow compared to the diffusive and microemulsion-assembling transients, the structure function oscillating in time due to a combination of Marangoni effects and long-time-scale defect dynamics.Block copolymer melts or dispersions, and homopolymer-block copolymer blends are examples of systems that self-assemble into regular, liquid-crystalline structures when subjected to the appropriate temperature or pressure quenches [1][2][3][4]. These structures, called mesophases due to their features being intermediate between those of a solid and a liquid, are also found in fluid mixtures of a surfactant in a solvent, binary immiscible fluids containing a third, amphiphilic phase, and lipidic biological systems [1,5]. They all form due to the competing attraction-repulsion mechanism between the species. The morphology of these mesophases is defined by the spatial loci where most of the amphiphile concentrates, forming multi-or mono-layer sheets of self-assembled amphiphile. Common equilibrium mesophases include lamellae, hexagonal columnar arrays, and the primitive "P", diamond "D" and gyroid "G" cubic phases [1,2]. The sheets of these cubic phases are surfaces or labyrinths of zero mean curvature, the skeletons of which form double (inter-weaving), chirally symmetric bicontinuous cubic lattices which are 6-, 4-and 3-fold coordinated, respectively. The gyroid is the phase which exhibits the least surface area per unit cell among those, and is ubiquitous in nature; we show in this paper that it can spontaneously self-assemble from a purely microscopic, kinetic-theoretical lattice model with hydrodynamic interactions.