Oscillating epidemics in a dynamic network model: stochastic and mean-field analysis

An adaptive network model using SIS epidemic propagation with link-type-dependent link activation and deletion is considered. Bifurcation analysis of the pairwise ODE approximation and the network-based stochastic simulation is carried out, showing that three typical behaviours may occur; namely, oscillations can be observed besides disease-free or endemic steady states. The oscillatory behaviour in the stochastic simulations is studied using Fourier analysis, as well as through analysing the exact master equations of the stochastic model. By going beyond simply comparing simulation results to mean-field models, our approach yields deeper insights into the observed phenomena and help better understand and map out the limitations of mean-field models

Probing Evolutionary Repeatability: Neutral and Double Changes and the Predictability of Evolutionary Adaptation

The question of how organisms adapt is among the most fundamental in evolutionary biology. Two recent studies investigated the evolution of Escherichia coli in response to challenge with the antibiotic cefotaxime. Studying five mutations in the beta-lactamase gene that together confer significant antibiotic resistance, the authors showed a complex fitness landscape that greatly constrained the identity and order of intermediates leading from the initial wildtype genotype to the final resistant genotype. Out of 18 billion possible orders of single mutations leading from non-resistant to fully-resistant form, they found that only 27 (1.5x10(-7)%) pathways were characterized by consistently increasing resistance, thus only a tiny fraction of possible paths are accessible by positive selection. I further explore these data in several ways.Allowing neutral changes (those that do not affect resistance) increases the number of accessible pathways considerably, from 27 to 629. Allowing multiple simultaneous mutations also greatly increases the number of accessible pathways. Allowing a single case of double mutation to occur along a pathway increases the number of pathways from 27 to 259, and allowing arbitrarily many pairs of simultaneous changes increases the number of possible pathways by more than 100 fold, to 4800. I introduce the metric 'repeatability,' the probability that two random trials will proceed via the exact same pathway. In general, I find that while the total number of accessible pathways is dramatically affected by allowing neutral or double mutations, the overall evolutionary repeatability is generally much less affected.These results probe the conceivable pathways available to evolution. Even when many of the assumptions of the analysis of Weinreich et al. (2006) are relaxed, I find that evolution to more highly cefotaxime resistant beta-lactamase proteins is still highly repeatable

Live to cheat another day: bacterial dormancy facilitates the social exploitation of beta-lactamases

The breakdown of antibiotics by β-lactamases may be cooperative, since resistant cells can detoxify their environment and facilitate the growth of susceptible neighbours. However, previous studies of this phenomenon have used artificial bacterial vectors or engineered bacteria to increase the secretion of β-lactamases from cells. Here, we investigated whether a broad-spectrum β-lactamase gene carried by a naturally occurring plasmid (pCT) is cooperative under a range of conditions. In ordinary batch culture on solid media, there was little or no evidence that resistant bacteria could protect susceptible cells from ampicillin, although resistant colonies could locally detoxify this growth medium. However, when susceptible cells were inoculated at high densities, late-appearing phenotypically susceptible bacteria grew in the vicinity of resistant colonies. We infer that persisters, cells that have survived antibiotics by undergoing a period of dormancy, founded these satellite colonies. The number of persister colonies was positively correlated with the density of resistant colonies and increased as antibiotic concentrations decreased. We argue that detoxification can be cooperative under a limited range of conditions: if the toxins are bacteriostatic rather than bacteridical; or if susceptible cells invade communities after resistant bacteria; or if dormancy allows susceptible cells to avoid bactericides. Resistance and tolerance were previously thought to be independent solutions for surviving antibiotics. Here, we show that these are interacting strategies: the presence of bacteria adopting one solution can have substantial effects on the fitness of their neighbours

The impact of contact tracing in clustered populations

The tracing of potentially infectious contacts has become an important part of the control strategy for many infectious diseases, from early cases of novel infections to endemic sexually transmitted infections. Here, we make use of mathematical models to consider the case of partner notification for sexually transmitted infection, however these models are sufficiently simple to allow more general conclusions to be drawn. We show that, when contact network structure is considered in addition to contact tracing, standard “mass action” models are generally inadequate. To consider the impact of mutual contacts (specifically clustering) we develop an improvement to existing pairwise network models, which we use to demonstrate that ceteris paribus, clustering improves the efficacy of contact tracing for a large region of parameter space. This result is sometimes reversed, however, for the case of highly effective contact tracing. We also develop stochastic simulations for comparison, using simple re-wiring methods that allow the generation of appropriate comparator networks. In this way we contribute to the general theory of network-based interventions against infectious disease

Cooperative secretions facilitate host range expansion in bacteria

The majority of emergent human pathogens are zoonotic in origin, that is, they can transmit to humans from other animals. Understanding the factors underlying the evolution of pathogen host range is therefore of critical importance in protecting human health. There are two main evolutionary routes to generalism: organisms can tolerate multiple environments or they can modify their environments to forms to which they are adapted. Here we use a combination of theory and a phylogenetic comparative analysis of 191 pathogenic bacterial species to show that bacteria use cooperative secretions that modify their environment to extend their host range and infect multiple host species. Our results suggest that cooperative secretions are key determinants of host range in bacteria, and that monitoring for the acquisition of secreted proteins by horizontal gene transfer can help predict emerging zoonoses

Predictability of evolutionary trajectories in fitness landscapes

Experimental studies on enzyme evolution show that only a small fraction of all possible mutation trajectories are accessible to evolution. However, these experiments deal with individual enzymes and explore a tiny part of the fitness landscape. We report an exhaustive analysis of fitness landscapes constructed with an off-lattice model of protein folding where fitness is equated with robustness to misfolding. This model mimics the essential features of the interactions between amino acids, is consistent with the key paradigms of protein folding and reproduces the universal distribution of evolutionary rates among orthologous proteins. We introduce mean path divergence as a quantitative measure of the degree to which the starting and ending points determine the path of evolution in fitness landscapes. Global measures of landscape roughness are good predictors of path divergence in all studied landscapes: the mean path divergence is greater in smooth landscapes than in rough ones. The model-derived and experimental landscapes are significantly smoother than random landscapes and resemble additive landscapes perturbed with moderate amounts of noise; thus, these landscapes are substantially robust to mutation. The model landscapes show a deficit of suboptimal peaks even compared with noisy additive landscapes with similar overall roughness. We suggest that smoothness and the substantial deficit of peaks in the fitness landscapes of protein evolution are fundamental consequences of the physics of protein folding.Comment: 14 pages, 7 figure

A new multicompartmental reaction-diffusion modeling method links transient membrane attachment of E. coli MinE to E-ring formation

Many important cellular processes are regulated by reaction-diffusion (RD) of molecules that takes place both in the cytoplasm and on the membrane. To model and analyze such multicompartmental processes, we developed a lattice-based Monte Carlo method, Spatiocyte that supports RD in volume and surface compartments at single molecule resolution. Stochasticity in RD and the excluded volume effect brought by intracellular molecular crowding, both of which can significantly affect RD and thus, cellular processes, are also supported. We verified the method by comparing simulation results of diffusion, irreversible and reversible reactions with the predicted analytical and best available numerical solutions. Moreover, to directly compare the localization patterns of molecules in fluorescence microscopy images with simulation, we devised a visualization method that mimics the microphotography process by showing the trajectory of simulated molecules averaged according to the camera exposure time. In the rod-shaped bacterium _Escherichia coli_, the division site is suppressed at the cell poles by periodic pole-to-pole oscillations of the Min proteins (MinC, MinD and MinE) arising from carefully orchestrated RD in both cytoplasm and membrane compartments. Using Spatiocyte we could model and reproduce the _in vivo_ MinDE localization dynamics by accounting for the established properties of MinE. Our results suggest that the MinE ring, which is essential in preventing polar septation, is largely composed of MinE that is transiently attached to the membrane independently after recruited by MinD. Overall, Spatiocyte allows simulation and visualization of complex spatial and reaction-diffusion mediated cellular processes in volumes and surfaces. As we showed, it can potentially provide mechanistic insights otherwise difficult to obtain experimentally

Exploring pig trade patterns to inform the design of risk-based disease surveillance and control strategies

An understanding of the patterns of animal contact networks provides essential information for the design of risk-based animal disease surveillance and control strategies. This study characterises pig movements throughout England and Wales between 2009 and 2013 with a view to characterising spatial and temporal patterns, network topology and trade communities. Data were extracted from the Animal and Plant Health Agency (APHA)’s RADAR (Rapid Analysis and Detection of Animal-related Risks) database, and analysed using descriptive and network approaches. A total of 61,937,855 pigs were moved through 872,493 movements of batches in England and Wales during the 5-year study period. Results show that the network exhibited scale-free and small-world topologies, indicating the potential for diseases to quickly spread within the pig industry. The findings also provide suggestions for how risk-based surveillance strategies could be optimised in the country by taking account of highly connected holdings, geographical regions and time periods with the greatest number of movements and pigs moved, as these are likely to be at higher risk for disease introduction. This study is also the first attempt to identify trade communities in the country, information which could be used to facilitate the pig trade and maintain disease-free status across the country in the event of an outbreak

The Role of Regulated mRNA Stability in Establishing Bicoid Morphogen Gradient in Drosophila Embryonic Development

The Bicoid morphogen is amongst the earliest triggers of differential spatial pattern of gene expression and subsequent cell fate determination in the embryonic development of Drosophila. This maternally deposited morphogen is thought to diffuse in the embryo, establishing a concentration gradient which is sensed by downstream genes. In most model based analyses of this process, the translation of the bicoid mRNA is thought to take place at a fixed rate from the anterior pole of the embryo and a supply of the resulting protein at a constant rate is assumed. Is this process of morphogen generation a passive one as assumed in the modelling literature so far, or would available data support an alternate hypothesis that the stability of the mRNA is regulated by active processes? We introduce a model in which the stability of the maternal mRNA is regulated by being held constant for a length of time, followed by rapid degradation. With this more realistic model of the source, we have analysed three computational models of spatial morphogen propagation along the anterior-posterior axis: (a) passive diffusion modelled as a deterministic differential equation, (b) diffusion enhanced by a cytoplasmic flow term; and (c) diffusion modelled by stochastic simulation of the corresponding chemical reactions. Parameter estimation on these models by matching to publicly available data on spatio-temporal Bicoid profiles suggests strong support for regulated stability over either a constant supply rate or one where the maternal mRNA is permitted to degrade in a passive manner