Rosalind J. Allen

Sampling rare switching events in biochemical networks.

Bistable biochemical switches are widely found in gene regulatory networks and signal transduction pathways. Their switching dynamics are difficult to study, however, because switching events are rare, and the systems are out of equilibrium. We present a simulation method for predicting the rate and mechanism of the flipping of these switches. We apply it to a genetic switch and find that it is highly efficient. The path ensembles for the forward and reverse processes do not coincide. The method is widely applicable to rare events and nonequilibrium processes.

Simulating rare events in equilibrium or nonequilibrium stochastic systems

We present three algorithms for calculating rate constants and sampling transition paths for rare events in simulations with stochastic dynamics. The methods do not require a priori knowledge of the phase-space density and are suitable for equilibrium or nonequilibrium systems in stationary state. All the methods use a series of interfaces in phase space, between the initial and final states, to generate transition paths as chains of connected partial paths, in a ratchetlike manner. No assumptions are made about the distribution of paths at the interfaces. The three methods differ in the way that the transition path ensemble is generated. We apply the algorithms to kinetic Monte Carlo simulations of a genetic switch and to Langevin dynamics simulations of intermittently driven polymer translocation through a pore. We find that the three methods are all of comparable efficiency, and that all the methods are much more efficient than brute-force simulation.

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 conventional simulation run. Over the past several decades, specialized 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.

Challenges in microbial ecology: building predictive understanding of community function and dynamics

The importance of microbial communities (MCs) cannot be overstated. MCs underpin the biogeochemical cycles of the earth’s soil, oceans and the atmosphere, and perform ecosystem functions that impact plants, animals and humans. Yet our ability to predict and manage the function of these highly complex, dynamically changing communities is limited. Building predictive models that link MC composition to function is a key emerging challenge in microbial ecology. Here, we argue that addressing this challenge requires close coordination of experimental data collection and method development with mathematical model building. We discuss specific examples where model–experiment integration has already resulted in important insights into MC function and structure. We also highlight key research questions that still demand better integration of experiments and models. We argue that such integration is needed to achieve significant progress in our understanding of MC dynamics and function, and we make specific practical suggestions as to how this could be achieved.

Forward flux sampling-type schemes for simulating rare events: Efficiency analysis

We analyze 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 nonequilibrium rare event problem proposed by Maier and Stein [Phys. Rev. E 48, 931 (1993)]. For this problem, our analysis gives accurate quantitative predictions for the computational efficiency of the three methods.

Continuum Theory of Phase Separation Kinetics for Active Brownian Particles

Active Brownian particles (ABPs), when subject to purely repulsive interactions, are known to undergo activity-induced phase separation broadly resembling an equilibrium (attraction-induced) gas-liquid coexistence. Here we present an accurate continuum theory for the dynamics of phase-separating ABPs, derived by direct coarse graining, capturing leading-order density gradient terms alongside an effective bulk free energy. Such gradient terms do not obey detailed balance; yet we find coarsening dynamics closely resembling that of equilibrium phase separation. Our continuum theory is numerically compared to large-scale direct simulations of ABPs and accurately accounts for domain growth kinetics, domain topologies, and coexistence densities.

Computing stationary distributions in equilibrium and nonequilibrium systems with forward flux sampling

We present a method for computing stationary distributions for activated processes in equilibrium and nonequilibrium systems using forward flux sampling. 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 nonequilibrium rare event problem proposed by Maier and Stein, to nucleation in a 2-dimensional Ising system, and to the flipping of a genetic switch.

Effects of Macromolecular Crowding on Genetic Networks

The intracellular environment is crowded with proteins, DNA, and other macromolecules. Under physiological conditions, macromolecular crowding can alter both molecular diffusion and the equilibria of bimolecular reactions and therefore is likely to have a significant effect on the function of biochemical networks. We propose a simple way to model the effects of macromolecular crowding on biochemical networks via an appropriate scaling of bimolecular association and dissociation rates. We use this approach, in combination with kinetic Monte Carlo simulations, to analyze the effects of crowding on a constitutively expressed gene, a repressed gene, and a model for the bacteriophage λ genetic switch, in the presence and absence of nonspecific binding of transcription factors to genomic DNA. Our results show that the effects of crowding are mainly caused by the shift of association-dissociation equilibria rather than the slowing down of protein diffusion, and that macromolecular crowding can have relevant and counterintuitive effects on biochemical network performance.

Role of Multicellular Aggregates in Biofilm Formation

ABSTRACT In traditional models of in vitro biofilm development, individual bacterial cells seed a surface, multiply, and mature into multicellular, three-dimensional structures. Much research has been devoted to elucidating the mechanisms governing the initial attachment of single cells to surfaces. However, in natural environments and during infection, bacterial cells tend to clump as multicellular aggregates, and biofilms can also slough off aggregates as a part of the dispersal process. This makes it likely that biofilms are often seeded by aggregates and single cells, yet how these aggregates impact biofilm initiation and development is not known. Here we use a combination of experimental and computational approaches to determine the relative fitness of single cells and preformed aggregates during early development of Pseudomonas aeruginosa biofilms. We find that the relative fitness of aggregates depends markedly on the density of surrounding single cells, i.e., the level of competition for growth resources. When competition between aggregates and single cells is low, an aggregate has a growth disadvantage because the aggregate interior has poor access to growth resources. However, if competition is high, aggregates exhibit higher fitness, because extending vertically above the surface gives cells at the top of aggregates better access to growth resources. Other advantages of seeding by aggregates, such as earlier switching to a biofilm-like phenotype and enhanced resilience toward antibiotics and immune response, may add to this ecological benefit. Our findings suggest that current models of biofilm formation should be reconsidered to incorporate the role of aggregates in biofilm initiation. IMPORTANCE During the past decades, there has been a consensus around the model of development of a biofilm, involving attachment of single planktonic bacterial cells to a surface and the subsequent development of a mature biofilm. This study presents results that call for a modification of this rigorous model. We show how free floating biofilm aggregates can have a profound local effect on biofilm development when attaching to a surface. Our findings show that an aggregate landing on a surface will eventually outcompete the biofilm population arising from single cells attached around the aggregate and dominate the local biofilm development. These results point to a regime where preformed biofilm aggregates may have a fitness advantage over planktonic cells when it comes to accessing nutrients. Our findings add to the increasingly prominent comprehension that biofilm lifestyle is the default for bacteria and that planktonic single cells may be only a transition state at the most. During the past decades, there has been a consensus around the model of development of a biofilm, involving attachment of single planktonic bacterial cells to a surface and the subsequent development of a mature biofilm. This study presents results that call for a modification of this rigorous model. We show how free floating biofilm aggregates can have a profound local effect on biofilm development when attaching to a surface. Our findings show that an aggregate landing on a surface will eventually outcompete the biofilm population arising from single cells attached around the aggregate and dominate the local biofilm development. These results point to a regime where preformed biofilm aggregates may have a fitness advantage over planktonic cells when it comes to accessing nutrients. Our findings add to the increasingly prominent comprehension that biofilm lifestyle is the default for bacteria and that planktonic single cells may be only a transition state at the most.

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 anticancer 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 nonuniform 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 combating the emergence of resistance.