Discreteness-Induced Slow Relaxation in Reversible Catalytic Reaction Networks

Slowing down of the relaxation of the fluctuations around equilibrium is investigated both by stochastic simulations and by analysis of Master equation of reversible reaction networks consisting of resources and the corresponding products that work as catalysts. As the number of molecules $N$ is decreased, the relaxation time to equilibrium is prolonged due to the deficiency of catalysts, as demonstrated by the amplification compared to that by the continuum limit. This amplification ratio of the relaxation time is represented by a scaling function as $h = N \exp(-\beta V)$, and it becomes prominent as $N$ becomes less than a critical value $h \sim 1$, where $\beta$ is the inverse temperature and $V$ is the energy gap between a product and a resource

Counter Chemotactic Flow in Quasi-One-Dimensional Path

Quasi-one-dimensional bidirectional particle flow including the effect of chemotaxis is investigated through a modification of the John-Schadschneider-Chowdhury-Nishinari model. Specifically, we permit multiple lanes to be shared by both directionally traveling particles. The relation between particle density and flux is studied for several evaporation rates of pheromone, and the following results are obtained: i) in the low-particle-density range, the flux is enlarged by pheromone if the pheromone evaporation rate is sufficiently low, ii) in the high particle-density range, the flux is largest at a reasonably high evaporation rate and, iii) if the evaporation rate is at the level intermediate between the above two cases, the flux is kept small in the entire range of particle densities. The mechanism of these behaviors is investigated by observing the spatial-temporal evolution of particles and the average cluster size in the system.Comment: 4 pages, 9 figure

Discreteness-induced Transition in Catalytic Reaction Networks

Drastic change in dynamics and statistics in a chemical reaction system, induced by smallness in the molecule number, is reported. Through stochastic simulations for random catalytic reaction networks, transition to a novel state is observed with the decrease in the total molecule number N, characterized by: i) large fluctuations in chemical concentrations as a result of intermittent switching over several states with extinction of some molecule species and ii) strong deviation of time averaged distribution of chemical concentrations from that expected in the continuum limit, i.e., $N \to \infty$. The origin of transition is explained by the deficiency of molecule leading to termination of some reactions. The critical number of molecules for the transition is obtained as a function of the number of molecules species M and that of reaction paths K, while total reaction rates, scaled properly, are shown to follow a universal form as a function of NK/M

Segregation and Phase Inversion in a Simple Granular System

The segregation and the phase inversion are investigated through a simple granular system which consists of only two inelastic hard spheres in a square box with an energy source. With the variation of the coefficient of restitution, the mass ratio between two spheres or the box size, we show that two types of segregated states and crossover between them are realized in such a small simple system.Comment: 7 pages, 3 figure

Size Segregation and Convection of Granular Mixtures Almost Completely Packed in the Rotating Thin Box

Size segregation of granular mixtures which are almost completely packed in a rotating drum is discussed with an effective simulation and a brief analysis. Instead of a 3D drum, we simulate 2D rotating thin box which is almost completely packed with granular mixtures. The phase inversion of radially segregated pattern which was found in a 3D experiment are qualitatively reproduced with this simulation, and a brief analysis is followed. Moreover in our simulation, a global convection appears after radial segregation pattern is formed, and this convection induces axially segregated pattern.Comment: 9 pages, 5 figures, PACS number(s): 45.70.-n, 45.70.M

Liquid-Solid Phase Transition of the System with Two particles in a Rectangular Box

We study the statistical properties of two hard spheres in a two dimensional rectangular box. In this system, the relation like Van der Waals equation loop is obtained between the width of the box and the pressure working on side walls. The auto-correlation function of each particle's position is calculated numerically. By this calculation near the critical width, the time at which the correlation become zero gets longer according to the increase of the height of the box. Moreover, fast and slow relaxation processes like $\alpha$ and $\beta$ relaxations observed in supper cooled liquid are observed when the height of the box is sufficiently large. These relaxation processes are discussed with the probability distribution of relative position of two particles.Comment: 6 figure

Quality Control and Performance of HIV Rapid Tests in a Microbicide Clinical Trial in Rural KwaZulu-Natal

Background Quality control (QC) and evaluation of HIV rapid test procedures are an important aspect of HIV prevention trials. We describe QC and performance of two rapid tests, Determine™ and Uni-Gold™ used in a microbicide clinical trial in rural KwaZulu-Natal, South Africa. Methods/Results Internal QC of both HIV rapid tests was conducted at the trial site using a Uni-Gold control kit (Uni-Gold™Recombigen® HIV). Both assays produced the expected results for a total of 4637 QC tests. Study participants were tested for HIV at screening and, if enrolled, at regular time points throughout the study. Positive or discordant results were confirmed by a double HIV immunoassay testing strategy at a local laboratory. Overall, 15292 HIV rapid test were performed. Sensitivity and specificity of Determine was 98.95% (95% CI: 97.72–99.61) and 99.83% (95% CI: 99.70–99.91) respectively [positive predictive value (PPV) 97.91% (95% CI: 96.38–98.92)], for Uni-Gold it was 99.30% (95% CI: 98.21–99.81) and 99.96% (95% CI: 99.88–99.99) respectively [PPV 99.47% (95% CI: 98.46–99.89)]. Conclusions The results suggest that a Uni-Gold control kit can be used for internal QC of both Uni-Gold and the HIV-1 component of the Determine rapid tests. Both rapid tests performed proficiently in the trial population

Influences of Excluded Volume of Molecules on Signaling Processes on Biomembrane

We investigate the influences of the excluded volume of molecules on biochemical reaction processes on 2-dimensional surfaces using a model of signal transduction processes on biomembranes. We perform simulations of the 2-dimensional cell-based model, which describes the reactions and diffusion of the receptors, signaling proteins, target proteins, and crowders on the cell membrane. The signaling proteins are activated by receptors, and these activated signaling proteins activate target proteins that bind autonomously from the cytoplasm to the membrane, and unbind from the membrane if activated. If the target proteins bind frequently, the volume fraction of molecules on the membrane becomes so large that the excluded volume of the molecules for the reaction and diffusion dynamics cannot be negligible. We find that such excluded volume effects of the molecules induce non-trivial variations of the signal flow, defined as the activation frequency of target proteins, as follows. With an increase in the binding rate of target proteins, the signal flow varies by i) monotonically increasing; ii) increasing then decreasing in a bell-shaped curve; or iii) increasing, decreasing, then increasing in an S-shaped curve. We further demonstrate that the excluded volume of molecules influences the hierarchical molecular distributions throughout the reaction processes. In particular, when the system exhibits a large signal flow, the signaling proteins tend to surround the receptors to form receptor-signaling protein clusters, and the target proteins tend to become distributed around such clusters. To explain these phenomena, we analyze the stochastic model of the local motions of molecules around the receptor.Comment: 31 pages, 10 figure

Required Levels of Catalysis for Emergence of Autocatalytic Sets in Models of Chemical Reaction Systems

The formation of a self-sustaining autocatalytic chemical network is a necessary but not sufficient condition for the origin of life. The question of whether such a network could form “by chance” within a sufficiently complex suite of molecules and reactions is one that we have investigated for a simple chemical reaction model based on polymer ligation and cleavage. In this paper, we extend this work in several further directions. In particular, we investigate in more detail the levels of catalysis required for a self-sustaining autocatalytic network to form. We study the size of chemical networks within which we might expect to find such an autocatalytic subset, and we extend the theoretical and computational analyses to models in which catalysis requires template matching