Switching and diffusion models for gene regulation networks

We analyze a hierarchy of three regimes for modeling gene regulation. The most complete model is a continuous time, discrete state space, Markov jump process. An intermediate 'switch plus diffusion' model takes the form of a stochastic differential equation driven by an independent continuous time Markov switch. In the third 'switch plus ODE' model the switch remains but the diffusion is removed. The latter two models allow for multi-scale simulation where, for the sake of computational efficiency, system components are treated differently according to their abundance. The 'switch plus ODE' regime was proposed by Paszek (Modeling stochasticity in gene regulation: characterization in the terms of the underlying distribution function, Bulletin of Mathematical Biology, 2007), who analyzed the steady state behavior, showing that the mean was preserved but the variance only approximated that of the full model. Here, we show that the tools of stochastic calculus can be used to analyze first and second moments for all time. A technical issue to be addressed is that the state space for the discrete-valued switch is infinite. We show that the new 'switch plus diffusion' regime preserves the biologically relevant measures of mean and variance, whereas the 'switch plus ODE' model uniformly underestimates the variance in the protein level. We also show that, for biologically relevant parameters, the transient behaviour can differ significantly from the steady state, justifying our time-dependent analysis. Extra computational results are also given for a protein dimerization model that is beyond the scope of the current analysis

Almost sure and moment exponential stability in the numerical simulation of stochastic differential equations

Relatively little is known about the ability of numerical methods for stochastic differential equations (SDEs) to reproduce almost sure and small-moment stability. Here, we focus on these stability properties in the limit as the timestep tends to zero. Our analysis is motivated by an example of an exponentially almost surely stable nonlinear SDE for which the Euler-Maruyama (EM)method fails to reproduce this behavior for any nonzero timestep. We begin by showing that EM correctly reproduces almost sure and small-moment exponential stability for sufficiently small timesteps on scalar linear SDEs. We then generalize our results to multidimensional nonlinear SDEs. We show that when the SDE obeys a linear growth condition, EM recovers almost surely exponential stability very well. Under the less restrictive condition that the drift coefficient of the SDE obeys a one-sided Lipschitz condition, where EM may break down, we show that the backward Euler method maintains almost surely exponential stability

Numerical simulation of a linear stochastic oscillator with additive noise

The ability of numerical methods to reproduce long-time features of a linear stochastic oscillator is examined. It is shown that certain, widely-used, methods fail to capture the correct second moment growth rate, whereas a customized extension of the partitioned Euler method behaves well in this respect. It is also shown that the partitioned Euler method inherits an infinite-oscillation property. A weaker oscillation result is proved for a wide class of numerical methods

On the galaxy-halo connection in the EAGLE simulation

Empirical models of galaxy formation require assumptions about the correlations between galaxy and halo properties. These may be calibrated against observations or inferred from physical models such as hydrodynamical simulations. In this Letter, we use the EAGLE simulation to investigate the correlation of galaxy size with halo properties. We motivate this analysis by noting that the common assumption of angular momentum partition between baryons and dark matter in rotationally supported galaxies overpredicts both the spread in the stellar mass–size relation and the anticorrelation of size and velocity residuals, indicating a problem with the galaxy–halo connection it implies. We find the EAGLE galaxy population to perform significantly better on both statistics, and trace this success to the weakness of the correlations of galaxy size with halo mass, concentration and spin at fixed stellar mass. Using these correlations in empirical models will enable fine-grained aspects of galaxy scalings to be matched

Chemical master equation and Langevin regimes for a gene transcription model

Gene transcription models must take account of intrinsic stochasticity. The Chemical Master Equation framework is based on modelling assumptions that are highly appropriate for this context, and the Stochastic Simulation Algorithm (also known as Gillespie's algorithm) allows for practical simulations to be performed. However, for large networks and/or fast reactions, such computations can be prohibitatively expensive. The Chemical Langevin regime replaces the massive ordinary dierential equation system with a small stochastic dierential equation system that is more amenable to computation. Although the transition from Chemical Master Equation to Chemical Langevin Equation can be justied rigorously in the large system size limit, there is very little guidance available about how closely the two models match for a xed system. Here, we consider a transcription model from the recent literature and show that it is possible to compare rst and second moments in the two stochastic settings. To analyse the Chemical Master Equation we use some recent work of Gadgil, Lee and Othmer, and to analyse the Chemical Langevin Equation we use Ito's Lemma. We nd that there is a perfect match|both modelling regimes give the same means, variances and correlations for all components in the system. The model that we analyse involves 'unimolecular reactions', and we nish with some numerical simulations involving dimerization to show that the means and variances in the two regimes can also be close when more general 'bimolecular reactions' are involved

Annexin II-binding immunoglobulins in patients with lupus nephritis and their correlation with disease manifestations

Correspondence: Tak Mao Chan ([email protected]) and Susan Yung ([email protected]) Annexin II on mesangial cell surface mediates the binding of anti-dsDNA antibodies and consequent downstream inflammatory and fibrotic processes. We investigated the clinical relevance of circulating annexin II-binding immunoglobulins (Igs) in patients with severe proliferative lupus nephritis, and renal annexin II expression in relation to progression of nephritis in New Zealand Black and White F1 mice (NZBWF1/J) mice. Annexin II-binding Igs in serum were measured by ELISA. Ultrastructural localization of annexin II was determined by electron microscopy. Seropositivity rates for annexin II-binding IgG and IgM in patients with active lupus nephritis were significantly higher compared with controls (8.9%, 1.3% and 0.9% for annexin II-binding IgG and 11.1%, 4.0% and 1.9% for annexin II-binding IgM for patients with active lupus nephritis, patients with non-lupus renal disease and healthy subjects respectively). In lupus patients, annexin II-binding IgM level was higher at disease flare compared with remission. Annexin II-binding IgG and IgM levels were associated with that of anti-dsDNA and disease activity. Annexin II-binding IgG and IgM levels correlated with histological activity index in lupus nephritis biopsy samples. In NZBWF1/J mice, serum annexin II-binding IgG and IgM levels and glomerular annexin II and p11 expression increased with progression of active nephritis. Annexin II expression was present on mesangial cell surface and in the mesangial matrix, and co-localized with electron-dense deposits along the glomerular basement membrane. Our results show that circulating annexin II-binding IgG and IgM levels are associated with clinical and histological disease activity in proliferative lupus nephritis. The co-localization of annexin II and p11 expression with immune deposition in the kidney suggests pathogenic relevance

Proximity effect at superconducting Sn-Bi2Se3 interface

We have investigated the conductance spectra of Sn-Bi2Se3 interface junctions down to 250 mK and in different magnetic fields. A number of conductance anomalies were observed below the superconducting transition temperature of Sn, including a small gap different from that of Sn, and a zero-bias conductance peak growing up at lower temperatures. We discussed the possible origins of the smaller gap and the zero-bias conductance peak. These phenomena support that a proximity-effect-induced chiral superconducting phase is formed at the interface between the superconducting Sn and the strong spin-orbit coupling material Bi2Se3.Comment: 7 pages, 8 figure

Heavy Quarks and Heavy Quarkonia as Tests of Thermalization

We present here a brief summary of new results on heavy quarks and heavy quarkonia from the PHENIX experiment as presented at the "Quark Gluon Plasma Thermalization" Workshop in Vienna, Austria in August 2005, directly following the International Quark Matter Conference in Hungary.Comment: 8 pages, 5 figures, Quark Gluon Plasma Thermalization Workshop (Vienna August 2005) Proceeding

Production of phi mesons at mid-rapidity in sqrt(s_NN) = 200 GeV Au+Au collisions at RHIC

We present the first results of meson production in the K^+K^- decay channel from Au+Au collisions at sqrt(s_NN) = 200 GeV as measured at mid-rapidity by the PHENIX detector at RHIC. Precision resonance centroid and width values are extracted as a function of collision centrality. No significant variation from the PDG accepted values is observed. The transverse mass spectra are fitted with a linear exponential function for which the derived inverse slope parameter is seen to be constant as a function of centrality. These data are also fitted by a hydrodynamic model with the result that the freeze-out temperature and the expansion velocity values are consistent with the values previously derived from fitting single hadron inclusive data. As a function of transverse momentum the collisions scaled peripheral.to.central yield ratio RCP for the is comparable to that of pions rather than that of protons. This result lends support to theoretical models which distinguish between baryons and mesons instead of particle mass for explaining the anomalous proton yield.Comment: 326 authors, 24 pages text, 23 figures, 6 tables, RevTeX 4. To be submitted to Physical Review C as a regular article. Plain text data tables for the points plotted in figures for this and previous PHENIX publications are (or will be) publicly available at http://www.phenix.bnl.gov/papers.htm