arXiv subjects

Rosalind J. Allen

Publications and source records attributed to Rosalind J. Allen.

At least 37 records · Page 2Linked to original sources

arXiv2012

Mutational pathway determines whether drug gradients accelerate evolution of drug-resistant cells

Drug gradients are believed to play an important role in the evolution of bacteria resistant to antibiotics and tumors resistant to anti-cancer drugs. We use a statistical physics model to study the evolution of a population of malignant cells exposed to drug gradients, where drug resistance emerges via a mutational pathway involving multiple mutations. We show that a non-uniform drug distribution has the potential to accelerate the emergence of resistance when the mutational pathway involves a long sequence of mutants with increasing resistance, but if the pathway is short or crosses a fitness valley, the evolution of resistance may actually be slowed down by drug gradients. These predictions can be verified experimentally, and may help to improve strategies for combatting the emergence of resistance.

q-bio.PE↗

arXiv2012

Computing the local pressure in molecular dynamics simulations

Computer simulations of inhomogeneous soft matter systems often require accurate methods for computing the local pressure. We present a simple derivation, based on the virial relation, of two equivalent expressions for the local (atomistic) pressure in a molecular dynamics simulation. One of these expressions, previously derived by other authors via a different route, involves summation over interactions between particles within the region of interest; the other involves summation over interactions across the boundary of the region of interest. We illustrate our derivation using simulations of a simple osmotic system; both expressions produce accurate results even when the region of interest over which the pressure is measured is very small.

cond-mat.soft↗

arXiv2012

Computing sensitivity coefficients in Brownian dynamics simulations by Malliavin weight sampling

We present a method for computing parameter sensitivities and response coefficients in Brownian dynamics simulations. The method involves tracking auxiliary variables (Malliavin weights) in addition to the usual particle positions, in an unperturbed simulation. The Malliavin weights sample the derivatives of the probability density with respect to the parameters of interest and are also interesting dynamical objects in themselves. Malliavin weight sampling is simple to implement, applies to equilibrium or nonequilibrium, steady state or time-dependent systems, and scales more efficiently than standard finite difference methods

cond-mat.stat-mech↗

arXiv2012

Mixed population of competing TASEPs with a shared reservoir of particles

We introduce a mean-field theoretical framework to describe multiple totally asymmetric simple exclusion processes (TASEPs) with different lattice lengths, entry and exit rates, competing for a finite reservoir of particles. We present relations for the partitioning of particles between the reservoir and the lattices: these relations allow us to show that competition for particles can have non-trivial effects on the phase behavior of individual lattices. For a system with non-identical lattices, we find that when a subset of lattices undergoes a phase transition from low to high density, the entire set of lattice currents becomes independent of total particle number. We generalize our approach to systems with a continuous distribution of lattice parameters, for which we demonstrate that measurements of the current carried by a single lattice type can be used to extract the entire distribution of lattice parameters. Our approach applies to populations of TASEPs with any distribution of lattice parameters, and could easily be extended beyond the mean-field case.

cond-mat.stat-mech↗

arXiv2012

Steady-state parameter sensitivity in stochastic modeling via trajectory reweighting

Parameter sensitivity analysis is a powerful tool in the building and analysis of biochemical network models. For stochastic simulations, parameter sensitivity analysis can be computationally expensive, requiring multiple simulations for perturbed values of the parameters. Here, we use trajectory reweighting to derive a method for computing sensitivity coefficients in stochastic simulations without explicitly perturbing the parameter values, avoiding the need for repeated simulations. The method allows the simultaneous computation of multiple sensitivity coefficients. Our approach recovers results originally obtained by application of the Girsanov measure transform in the general theory of stochastic processes [A. Plyasunov and A. P. Arkin, J. Comp. Phys. 221, 724 (2007)]. We build on these results to show how the method can be used to compute steady-state sensitivity coefficients from a single simulation run, and we present various efficiency improvements. For models of biochemical signaling networks the method has a particularly simple implementation. We demonstrate its application to a signaling network showing stochastic focussing and to a bistable genetic switch, and present exact results for models with linear propensity functions.

physics.comp-ph↗

arXiv2012

Non-Stationary Forward Flux Sampling

We present a new method, Non-Stationary Forward Flux Sampling, that allows efficient simulation of rare events in both stationary and non-stationary stochastic systems. The method uses stochastic branching and pruning to achieve uniform sampling of trajectories in phase space and time, leading to accurate estimates for time-dependent switching propensities and time-dependent phase space probability densities. The method is suitable for equilibrium or non-equilibrium systems, in or out of stationary state, including non-Markovian or externally driven systems. We demonstrate the validity of the technique by applying it to a one-dimensional barrier crossing problem that can be solved exactly, and show its usefulness by applying it to the time-dependent switching of a genetic toggle switch.

q-bio.MN↗

arXiv2011

Noise-driven oscillations in microbial population dynamics

Microbial populations in the natural environment are likely to experience growth conditions very different from those of a typical laboratory xperiment. In particular, removal rates of biomass and substrate are unlikely to be balanced under realistic environmental conditions. Here, we consider a single population growing on a substrate under conditions where the removal rates of substrate and biomass are not necessarily equal. For a large population, with deterministic growth dynamics, our model predicts that this system can show transient (damped) oscillations. For a small population, demographic noise causes these oscillations to be sustained indefinitely. These oscillations arise when the dynamics of changes in biomass are faster than the dynamics of the substrate, for example, due to a high microbial death rate and/or low substrate flow rates. We show that the same mechanism can produce sustained stochastic oscillations in a two-species, nutrient-cycling microbial ecosystem. Our results suggest that oscillatory population dynamics may be a common feature of small microbial populations in the natural environment, even in the absence of complex interspecies interactions.

q-bio.PE↗

arXiv2011

Nucleation in a sheared Ising model: effects of external field

Simulations using the Forward Flux Sampling method have shown a nonmonotonic de- pendence of the homogeneous nucleation rate on the shear rate for a sheared two dimensional Ising model [R. J. Allen et al, arXiv cond-mat/0805.3029]. For quasi-equilibrium systems (i.e. in the absence of shear), Classical Nucleation Theory (CNT) predicts the dependence of the critical cluster size and the nucleation rate on the external magnetic field. We investigate the behaviour of the sheared Ising model as a function of the external field. At low exter- nal field strength, the same nonmonotonic behaviour holds and the peak in the nucleation rate is remarkably insensitive to the field strength. This suggests that the same external field-dependence holds for the enhancement of nucleation by shear at low shear rates and the suppression of shear at high shear rates. At high field strength, the nucleation behaviour is qualitatively different. We also analyse the size and shape of the largest cluster in the transition state configurations, as a function of the external field. In the sheared system, the transition state cluster becomes larger and more elongated as the field strength decreases. We compare our results for the sheared system to the predictions of the CNT for the quasi- equilibrium case, and find that the CNT cannot easily be used to describe nucleation in the system under shear.

cond-mat.soft↗

arXiv2010

A dynamical phase transition in a model for evolution with migration

Migration between different habitats is ubiquitous among biological populations. In this Letter, we study a simple quasispecies model for evolution in two different habitats, with different fitness landscapes, coupled through one-way migration. Our model applies to asexual, rapidly evolving organisms such as microbes. Our key finding is a dynamical phase transition at a critical value of the migration rate. The time to reach steady state diverges at this critical migration rate. Above the transition, the population is dominated by immigrants from the primary habitat. Below the transition, the genetic composition of the population is highly non-trivial, with multiple coexisting quasispecies which are not native to either habitat. Using results from localization theory, we show that the critical migration rate may be very small --- demonstrating that evolutionary outcomes can be very sensitive to even a small amount of migration.

q-bio.PE↗

arXiv2010

Switching and growth for microbial populations in catastrophic responsive environments

Phase variation, or stochastic switching between alternative states of gene expression, is common among microbes, and may be important in coping with changing environments. We use a theoretical model to assess whether such switching is a good strategy for growth in environments with occasional catastrophic events. We find that switching can be advantageous, but only when the environment is responsive to the microbial population. In our model, microbes switch randomly between two phenotypic states, with different growth rates. The environment undergoes sudden "catastrophes", the probability of which depends on the composition of the population. We derive a simple analytical result for the population growth rate. For a responsive environment, two alternative strategies emerge. In the "no switching" strategy, the population maximises its instantaneous growth rate, regardless of catastrophes. In the "switching" strategy, the microbial switching rate is tuned to minimise the environmental response. Which of these strategies is most favourable depends on the parameters of the model. Previous studies have shown that microbial switching can be favourable when the environment changes in an unresponsive fashion between several states. Here, we demonstrate an alternative role for phase variation in allowing microbes to maximise their growth in catastrophic responsive environments.

q-bio.PE↗

arXiv2009

A multi-purpose modular system for high-resolution microscopy at high hydrostatic pressure

We have developed a modular system for high-resolution microscopy at high hydrostatic pressure. The system consists of a pressurised cell of volume ~100 microlitres, a temperature controlled holder, a ram and a piston. We have made each of these components in several versions which can be interchanged to allow a wide range of applications. Here, we report two pressure cells with pressure ranges 0.1-700MPa and 0.1-100MPa, which can be combined with hollow or solid rams and pistons. Our system is designed to work with fluorescent samples (using a confocal or epifluorescence microscope), but also allows for transmitted light microscopy via the hollow ram and piston. The system allows precise control of pressure and temperature [-20-70C], as well as rapid pressure quenching. We demonstrate its performance and versatility with two applications: time-resolved imaging of colloidal phase transitions caused by pressure changes between 0.1MPa and 101MPa, and imaging the growth of Escherichia coli bacteria at 50MPa. We also show that the isotropic-nematic phase transition of pentyl-cyanobiphenyl (5CB) liquid crystal provides a simple, convenient and accurate method for calibrating pressure in the range 0.1-200MPa.

physics.optics↗

arXiv2009

Forward Flux Sampling for rare event simulations

Rare events are ubiquitous in many different fields, yet they are notoriously difficult to simulate because few, if any, events are observed in a conventiona l simulation run. Over the past several decades, specialised simulation methods have been developed to overcome this problem. We review one recently-developed class of such methods, known as Forward Flux Sampling. Forward Flux Sampling uses a series of interfaces between the initial and final states to calculate rate constants and generate transition paths, for rare events in equilibrium or nonequilibrium systems with stochastic dynamics. This review draws together a number of recent advances, summarizes several applications of the method and highlights challenges that remain to be overcome.

cond-mat.stat-mech↗

arXiv2009

Computing stationary distributions in equilibrium and non-equilibrium systems with Forward Flux Sampling

We present a method for computing stationary distributions for activated processes in equilibrium and non-equilibrium systems using Forward Flux Sampling (FFS). In this method, the stationary distributions are obtained directly from the rate constant calculations for the forward and backward reactions; there is no need to perform separate calculations for the stationary distribution and the rate constant. We apply the method to the non-equilibrium rare event problem proposed by Maier and Stein, to nucleation in a 2-dimensional Ising system, and to the flipping of a genetic switch.

cond-mat.soft↗

arXiv2009

DNA looping provides stability and robustness to the bacteriophage lambda switch

The bistable gene regulatory switch controlling the transition from lysogeny to lysis in bacteriophage lambda presents a unique challenge to quantitative modeling. Despite extensive characterization of this regulatory network, the origin of the extreme stability of the lysogenic state remains unclear. We have constructed a stochastic model for this switch. Using Forward Flux Sampling simulations, we show that this model predicts an extremely low rate of spontaneous prophage induction in a recA mutant, in agreement with experimental observations. In our model, the DNA loop formed by octamerization of CI bound to the O_L and O_R operator regions is crucial for stability, allowing the lysogenic state to remain stable even when a large fraction of the total CI is depleted by nonspecific binding to genomic DNA. DNA looping also ensures that the switch is robust to mutations in the order of the O_R binding sites. Our results suggest that DNA looping can provide a mechanism to maintain a stable lysogenic state in the face of a range of challenges including noisy gene expression, nonspecific DNA binding and operator site mutations.

q-bio.MN↗

arXiv2009

Statistical physics of a model binary genetic switch with linear feedback

We study the statistical properties of a simple genetic regulatory network that provides heterogeneity within a population of cells. This network consists of a binary genetic switch in which stochastic flipping between the two switch states is mediated by a "flipping" enzyme. Feedback between the switch state and the flipping rate is provided by a linear feedback mechanism: the flipping enzyme is only produced in the on switch state and the switching rate depends linearly on the copy number of the enzyme. This work generalises the model of [Phys. Rev. Lett., 101, 118104] to a broader class of linear feedback systems. We present a complete analytical solution for the steady-state statistics of the number of enzyme molecules in the on and off states, for the general case where the enzyme can mediate flipping in either direction. For this general case we also solve for the flip time distribution, making a connection to first passage and persistence problems in statistical physics. We show that the statistics of the model are non-Poissonian, leading to a peak in the flip time distribution. The occurrence of such a peak is analysed as a function of the parameter space. We present a new relation between the flip time distributions measured for two relevant choices of initial condition. We also introduce a new correlation measure to show that this model can exhibit long-lived temporal correlations, thus providing a primitive form of cellular memory. Motivated by DNA replication as well as by evolutionary mechanisms involving gene duplication, we study the case of two switches in the same cell. This results in correlations between the two switches; these can either positive or negative depending on the parameter regime.

cond-mat.soft↗

arXiv2008

Exact solution of a model DNA-inversion genetic switch with orientational control

DNA inversion is an important mechanism by which bacteria and bacteriophage switch reversibly between phenotypic states. In such switches, the orientation of a short DNA element is flipped by a site-specific recombinase enzyme. We propose a simple model for a DNA inversion switch in which recombinase production is dependent on the switch state (orientational control). Our model is inspired by the fim switch in Escherichia coli. We present an exact analytical solution of the chemical master equation for the model switch, as well as stochastic simulations. Orientational control causes the switch to deviate from Poissonian behaviour: the distribution of times in the on state shows a peak and successive flip times are correlated.

q-bio.MN↗

arXiv2008

Homogeneous nucleation under shear in a two-dimensional Ising model: cluster growth, coalescence and breakup

We compute rates and pathways for nucleation in a sheared two dimensional Ising model with Metropolis spin flip dynamics, using Forward Flux Sampling (FFS). We find a peak in the nucleation rate at intermediate shear rate. We analyse the origin of this peak using modified shear algorithms and committor analysis. We find that the peak arises from an interplay between three shear-mediated effects: shear-enhanced cluster growth, cluster coalescence and cluster breakup. Our results show that complex nucleation behaviour can be found even in a simple driven model system. This work also demonstrates the use of FFS for simulating rare events, including nucleation, in nonequilibrium systems.

cond-mat.soft↗

arXiv2006

Forward Flux Sampling-type schemes for simulating rare events: Efficiency analysis

We analyse the efficiency of several simulation methods which we have recently proposed for calculating rate constants for rare events in stochastic dynamical systems, in or out of equilibrium. We derive analytical expressions for the computational cost of using these methods, and for the statistical error in the final estimate of the rate constant, for a given computational cost. These expressions can be used to determine which method to use for a given problem, to optimize the choice of parameters, and to evaluate the significance of the results obtained. We apply the expressions to the two-dimensional non-equilibrium rare event problem proposed by Maier and Stein. For this problem, our analysis gives accurate quantitative predictions for the computational efficiency of the three methods.

cond-mat.other↗