Chemical master versus chemical langevin for first-order reaction networks

Markov jump processes are widely used to model interacting species in circumstances where discreteness and stochasticity are relevant. Such models have been particularly successful in computational cell biology, and in this case, the interactions are typically rst-order. The Chemical Langevin Equation is a stochastic dierential equation that can be regarded as an approximation to the underlying jump process. In particular, the Chemical Langevin Equation allows simulations to be performed more eectively. In this work, we obtain expressions for the rst and second moments of the Chemical Langevin Equation for a generic rst-order reaction network. Moreover, we show that these moments exactly match those of the under-lying jump process. Hence, in terms of means, variances and correlations, the Chemical Langevin Equation is an excellent proxy for the Chemical Master Equation. Our work assumes that a unique solution exists for the Chemical Langevin Equation. We also show that the moment matching re- sult extends to the case where a gene regulation model of Raser and O'Shea (Science, 2004) is replaced by a hybrid model that mixes elements of the Master and Langevin equations. We nish with numerical experiments on a dimerization model that involves second order reactions, showing that the two regimes continue to give similar results

Mathematical and computational modelling of post-transcriptional gene relation by micro-RNA

Mathematical models and computational simulations have proved valuable in many areas of cell biology, including gene regulatory networks. When properly calibrated against experimental data, kinetic models can be used to describe how the concentrations of key species evolve over time. A reliable model allows ‘what if’ scenarios to be investigated quantitatively in silico, and also provides a means to compare competing hypotheses about the underlying biological mechanisms at work. Moreover, models at different scales of resolution can be merged into a bigger picture ‘systems’ level description. In the case where gene regulation is post-transcriptionally affected by microRNAs, biological understanding and experimental techniques have only recently matured to the extent that we can postulate and test kinetic models. In this chapter, we summarize some recent work that takes the first steps towards realistic modelling, focusing on the contributions of the authors. Using a deterministic ordinary differential equation framework, we derive models from first principles and test them for consistency with recent experimental data, including microarray and mass spectrometry measurements. We first consider typical mis-expression experiments, where the microRNA level is instantaneously boosted or depleted and thereafter remains at a fixed level. We then move on to a more general setting where the microRNA is simply treated as another species in the reaction network, with microRNA-mRNA binding forming the basis for the post-transcriptional repression. We include some speculative comments about the potential for kinetic modelling to contribute to the more widespread sequence and network based approaches in the qualitative investigation of microRNA based gene regulation. We also consider what new combinations of experimental data will be needed in order to make sense of the increased systems-level complexity introduced by microRNAs

Dynamical quarks effects on the gluon propagation and chiral symmetry restoration

We exploit the recent lattice results for the infrared gluon propagator with light dynamical quarks and solve the gap equation for the quark propagator. Chiral symmetry breaking and confinement (intimately tied with the analytic properties of QCD Schwinger functions) order parameters are then studied.Comment: Contribution to QCD-TNT-III: "From quarks and gluons to hadronic matter: A bridge too far?