Phase Transitions and superuniversality in the dynamics of a self-driven particle

We study an active random walker model in which a particle's motion is determined by a self-generated field. The field encodes information about the particle's path history. This leads to either self-attractive or self-repelling behavior. For self-repelling behavior, we find a phase transition in the dynamics: when the coupling between the field and the walker exceeds a critical value, the particle's behavior changes from renormalized diffusion to one characterized by a diverging diffusion coefficient. The dynamical behavior for all cases is surprisingly independent of dimension and of the noise amplitude.Comment: 14 pages, 4 figure

Multiscale modeling in biology

The 1966 science-fction film Fantastic Voyage captured the public imagination with a clever idea: what fantastic things might we see and do if we could minaturize ourselves and travel through the bloodstream as corpuscles do? (This being Hollywood, the answer was that we'd save a fellow scientist from evildoers.

Analytical study of non Gaussian fluctuations in a stochastic scheme of autocatalytic reactions

A stochastic model of autocatalytic chemical reactions is studied both numerically and analytically. The van Kampen perturbative scheme is implemented, beyond the second order approximation, so to capture the non Gaussianity traits as displayed by the simulations. The method is targeted to the characterization of the third moments of the distribution of fluctuations, originating from a system of four populations in mutual interaction. The theory predictions agree well with the simulations, pointing to the validity of the van Kampen expansion beyond the conventional Gaussian solution.Comment: 15 pages, 8 figures, submitted to Phys. Rev.

Steady-state fluctuations of a genetic feedback loop:an exact solution

Genetic feedback loops in cells break detailed balance and involve bimolecular reactions; hence exact solutions revealing the nature of the stochastic fluctuations in these loops are lacking. We here consider the master equation for a gene regulatory feedback loop: a gene produces protein which then binds to the promoter of the same gene and regulates its expression. The protein degrades in its free and bound forms. This network breaks detailed balance and involves a single bimolecular reaction step. We provide an exact solution of the steady-state master equation for arbitrary values of the parameters, and present simplified solutions for a number of special cases. The full parametric dependence of the analytical non-equilibrium steady-state probability distribution is verified by direct numerical solution of the master equations. For the case where the degradation rate of bound and free protein is the same, our solution is at variance with a previous claim of an exact solution (Hornos et al, Phys. Rev. E {\bf 72}, 051907 (2005) and subsequent studies). We show explicitly that this is due to an unphysical formulation of the underlying master equation in those studies.Comment: 31 pages, 3 figures. Accepted for publication in the Journal of Chemical Physics (2012

On the Mechanical Properties of Graphyne, Graphdiyne, and Other Poly(Phenylacetylene) Networks

This is the author accepted manuscript. The final version is available from Wiley via the DOI in this recordWe simulate, analyse and compare the mechanical properties of a number of molecular sheet-like systems based on fully substituted, penta-substituted, tetra-substituted and tri-substituted poly(phenylacetylene) using static force-field based methods. The networks are modeled in a 3D environment with and without inter-layer interactions in analogy to graphite and graphene respectively. It is shown that by varying the type of substitution and the length of the acetylene chain, one may control the mechanical properties of such systems. In particular, it is shown that poly(phenylacetylene) systems can be specifically designed to exhibit negative Poisson's ratio, and that the stiffness can be controlled in an independent manner from the Poisson's ratios. This is significant as it highlights the fact that such systems can be tailored to exhibit a particular set of mechanical properties.The research work disclosed in this publication is funded by the ENDEAVOUR Scholarship Scheme (Malta). The scholarship may be part-financed by the European Union − European Social Fund (ESF) under Operational Programme II − Cohesion Policy 2014–2020, “Investing in human capital to create more opportunities and promote the well being of society.” JNG acknowledges the support of the University of Malta research grant

On the Compressibility Properties of the Wine-Rack-Like Carbon Allotropes and Related Poly(phenylacetylene) Systems

This is the author accepted manuscript. The final version is available from Wiley via the DOI in this record.Poly(phenylacetylene) sheets that mimic the geometry of a wine-rack-like structure have been predicted to exhibit negative Poisson's ratios off-axis. However, their potential to exhibit negative linear compressibility (NLC) has remained largely unexplored. In this work, the compressibility and other mechanical properties of wine-rack-like poly(phenylacetylene) networks with 1,2,4,5 tetra-substituted phenyls as well as their equivalent with allene or cyclobutadiene centres are simulated to assess their ability to exhibit negative linear compressibility on-axis and off-axis. It is shown that some of these systems can indeed exhibit negative linear compressibility whilst others exhibit a near-zero compressibility. The results are compared to the compressibility properties of other poly(phenylacetylene) networks reported in literature as well as with those predicted from the analytical model for an idealised wine-rack structure deforming through hinging. Results suggest that these mechanical properties are arising from a wine-rack-like mechanism, and there is a good agreement with the theoretical model, especially for systems with longer acetylene chains whose geometry is closer to that of the idealised wine-rack.University of MaltaENDEAVOUR Scholarship Scheme (Malta

Model Reduction for the Chemical Master Equation: an Information-Theoretic Approach

The complexity of mathematical models in biology has rendered model reduction an essential tool in the quantitative biologist's toolkit. For stochastic reaction networks described using the Chemical Master Equation, commonly used methods include time-scale separation, the Linear Mapping Approximation and state-space lumping. Despite the success of these techniques, they appear to be rather disparate and at present no general-purpose approach to model reduction for stochastic reaction networks is known. In this paper we show that most common model reduction approaches for the Chemical Master Equation can be seen as minimising a well-known information-theoretic quantity between the full model and its reduction, the Kullback-Leibler divergence defined on the space of trajectories. This allows us to recast the task of model reduction as a variational problem that can be tackled using standard numerical optimisation approaches. In addition we derive general expressions for the propensities of a reduced system that generalise those found using classical methods. We show that the Kullback-Leibler divergence is a useful metric to assess model discrepancy and to compare different model reduction techniques using three examples from the literature: an autoregulatory feedback loop, the Michaelis-Menten enzyme system and a genetic oscillator

Approximation and inference methods for stochastic biochemical kinetics-a tutorial review

Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose dynamics are governed by the chemical master equation. Despite its simple structure, no analytic solutions to the chemical master equation are known for most systems. Moreover, stochastic simulations are computationally expensive, making systematic analysis and statistical inference a challenging task. Consequently, significant effort has been spent in recent decades on the development of efficient approximation and inference methods. This article gives an introduction to basic modelling concepts as well as an overview of state of the art methods. First, we motivate and introduce deterministic and stochastic methods for modelling chemical networks, and give an overview of simulation and exact solution methods. Next, we discuss several approximation methods, including the chemical Langevin equation, the system size expansion, moment closure approximations, time-scale separation approximations and hybrid methods. We discuss their various properties and review recent advances and remaining challenges for these methods. We present a comparison of several of these methods by means of a numerical case study and highlight some of their respective advantages and disadvantages. Finally, we discuss the problem of inference from experimental data in the Bayesian framework and review recent methods developed the literature. In summary, this review gives a self-contained introduction to modelling, approximations and inference methods for stochastic chemical kinetics