Gene regulatory networks: a coarse-grained, equation-free approach to multiscale computation

We present computer-assisted methods for analyzing stochastic models of gene regulatory networks. The main idea that underlies this equation-free analysis is the design and execution of appropriately-initialized short bursts of stochastic simulations; the results of these are processed to estimate coarse-grained quantities of interest, such as mesoscopic transport coefficients. In particular, using a simple model of a genetic toggle switch, we illustrate the computation of an effective free energy and of a state-dependent effective diffusion coefficient that characterize an unavailable effective Fokker-Planck equation. Additionally we illustrate the linking of equation-free techniques with continuation methods for performing a form of stochastic "bifurcation analysis"; estimation of mean switching times in the case of a bistable switch is also implemented in this equation-free context. The accuracy of our methods is tested by direct comparison with long-time stochastic simulations. This type of equation-free analysis appears to be a promising approach to computing features of the long-time, coarse-grained behavior of certain classes of complex stochastic models of gene regulatory networks, circumventing the need for long Monte Carlo simulations.Comment: 33 pages, submitted to The Journal of Chemical Physic

Could Fire and Rescue Services identify older people at risk of falls?

Protecting or improving the efficiency and effectiveness of services while reducing costs in response to public sector funding reductions is a significant challenge for all public service organisations. Preventing falls in older people is a major public health objective. We propose here an innovative model of community partnership with Fire and Rescue Services assisting falls prevention services to enhance the safety and well-being of older people in local communities through early identification of those who are at risk of injury from a fall or accidental domestic fire

Analysis of nucleation using mean first-passage time data from molecular dynamics simulation

We introduce a method for the analysis of nucleation using mean first-passage time (MFPT) statistics obtained by molecular dynamics simulation. The method is based on the Becker-Döring model for the dynamics of a nucleation-mediated phase change and rigorously accounts for the system size dependence of first-passage statistics. It is thus suitable for the analysis of systems in which the separation between time scales for nucleation and growth is small, due to either a small free energy barrier or a large system size. The method is made computationally practical by an approximation of the first-passage time distribution based on its cumulant expansion. Using this approximation, the MFPT of the model can be fit to data from molecular dynamics simulation in order to estimate valuable kinetic parameters, including the free energy barrier, critical nucleus size, and monomer attachment pre-factor, as well as the steady-state rates of nucleation and growth. The method is demonstrated using a case study on nucleation of n-eicosane crystals from the melt. For this system, we found that the observed distribution of first-passage times do not follow an exponential distribution at short times, rendering it incompatible with the assumptions made by some other methods. Using our method, the observed distribution of first-passage times was accurately described, and reasonable estimates for the kinetic parameters and steady-state rates of nucleation and growth were obtained