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Concept: Stochastic


Increasing the durability of crop resistance to plant pathogens is one of the key goals of virulence management. Despite the recognition of the importance of demographic and environmental stochasticity on the dynamics of an epidemic, their effects on the evolution of the pathogen and durability of resistance has not received attention. We formulated a stochastic epidemiological model, based on the Kramer-Moyal expansion of the Master Equation, to investigate how random fluctuations affect the dynamics of an epidemic and how these effects feed through to the evolution of the pathogen and durability of resistance. We focused on two hypotheses: firstly, a previous deterministic model has suggested that the effect of cropping ratio (the proportion of land area occupied by the resistant crop) on the durability of crop resistance is negligible. Increasing the cropping ratio increases the area of uninfected host, but the resistance is more rapidly broken; these two effects counteract each other. We tested the hypothesis that similar counteracting effects would occur when we take account of demographic stochasticity, but found that the durability does depend on the cropping ratio. Secondly, we tested whether a superimposed external source of stochasticity (for example due to environmental variation or to intermittent fungicide application) interacts with the intrinsic demographic fluctuations and how such interaction affects the durability of resistance. We show that in the pathosystem considered here, in general large stochastic fluctuations in epidemics enhance extinction of the pathogen. This is more likely to occur at large cropping ratios and for particular frequencies of the periodic external perturbation (stochastic resonance). The results suggest possible disease control practises by exploiting the natural sources of stochasticity.

Concepts: Scientific method, Epidemiology, Infectious disease, Effect, Affect, Ratio, Epidemic, Stochastic


Many multicellular systems problems can only be understood by studying how cells move, grow, divide, interact, and die. Tissue-scale dynamics emerge from systems of many interacting cells as they respond to and influence their microenvironment. The ideal “virtual laboratory” for such multicellular systems simulates both the biochemical microenvironment (the “stage”) and many mechanically and biochemically interacting cells (the “players” upon the stage). PhysiCell-physics-based multicellular simulator-is an open source agent-based simulator that provides both the stage and the players for studying many interacting cells in dynamic tissue microenvironments. It builds upon a multi-substrate biotransport solver to link cell phenotype to multiple diffusing substrates and signaling factors. It includes biologically-driven sub-models for cell cycling, apoptosis, necrosis, solid and fluid volume changes, mechanics, and motility “out of the box.” The C++ code has minimal dependencies, making it simple to maintain and deploy across platforms. PhysiCell has been parallelized with OpenMP, and its performance scales linearly with the number of cells. Simulations up to 105-106 cells are feasible on quad-core desktop workstations; larger simulations are attainable on single HPC compute nodes. We demonstrate PhysiCell by simulating the impact of necrotic core biomechanics, 3-D geometry, and stochasticity on the dynamics of hanging drop tumor spheroids and ductal carcinoma in situ (DCIS) of the breast. We demonstrate stochastic motility, chemical and contact-based interaction of multiple cell types, and the extensibility of PhysiCell with examples in synthetic multicellular systems (a “cellular cargo delivery” system, with application to anti-cancer treatments), cancer heterogeneity, and cancer immunology. PhysiCell is a powerful multicellular systems simulator that will be continually improved with new capabilities and performance improvements. It also represents a significant independent code base for replicating results from other simulation platforms. The PhysiCell source code, examples, documentation, and support are available under the BSD license at and

Concepts: DNA, Cell, Cancer, Carcinoma in situ, Simulation, Computer simulation, Source code, Stochastic


We outline our perspective on stochastic chemical kinetics, paying particular attention to numerical simulation algorithms. We first focus on dilute, well-mixed systems, whose description using ordinary differential equations has served as the basis for traditional chemical kinetics for the past 150 years. For such systems, we review the physical and mathematical rationale for a discrete-stochastic approach, and for the approximations that need to be made in order to regain the traditional continuous-deterministic description. We next take note of some of the more promising strategies for dealing stochastically with stiff systems, rare events, and sensitivity analysis. Finally, we review some recent efforts to adapt and extend the discrete-stochastic approach to systems that are not well-mixed. In that currently developing area, we focus mainly on the strategy of subdividing the system into well-mixed subvolumes, and then simulating diffusional transfers of reactant molecules between adjacent subvolumes together with chemical reactions inside the subvolumes.

Concepts: Mathematics, Chemical reaction, Simulation, Differential equation, Computer simulation, Mathematical model, Ordinary differential equation, Stochastic


We show that regenerating planarians' normal anterior-posterior pattern can be permanently rewritten by a brief perturbation of endogenous bioelectrical networks. Temporary modulation of regenerative bioelectric dynamics in amputated trunk fragments of planaria stochastically results in a constant ratio of regenerates with two heads to regenerates with normal morphology. Remarkably, this is shown to be due not to partial penetrance of treatment, but a profound yet hidden alteration to the animals' patterning circuitry. Subsequent amputations of the morphologically normal regenerates in water result in the same ratio of double-headed to normal morphology, revealing a cryptic phenotype that is not apparent unless the animals are cut. These animals do not differ from wild-type worms in histology, expression of key polarity genes, or neoblast distribution. Instead, the altered regenerative bodyplan is stored in seemingly normal planaria via global patterns of cellular resting potential. This gradient is functionally instructive, and represents a multistable, epigenetic anatomical switch: experimental reversals of bioelectric state reset subsequent regenerative morphology back to wild-type. Hence, bioelectric properties can stably override genome-default target morphology, and provide a tractable control point for investigating cryptic phenotypes and the stochasticity of large-scale epigenetic controls.

Concepts: Gene, Gene expression, Evolution, Regeneration, Phenotype, Anatomy, Pattern, Stochastic


The present study focused on beating synchronization, and tried to elucidate the interlayer regulatory mechanisms between the cells and clump in beating synchronization with using the stochastic simulations which realize the beating synchronizations in beating cells with low cell-cell conductance. Firstly, the fluctuation in interbeat intervals (IBIs) of beating cells encouraged the process of beating synchronization, which was identified as the stochastic resonance. Secondly, fluctuation in the synchronized IBIs of a clump decreased as the number of beating cells increased. The decrease in IBI fluctuation due to clump formation implied both a decline of the electrophysiological plasticity of each beating cell and an enhancement of the electrophysiological stability of the clump. These findings were identified as the community effects. Because IBI fluctuation and the community effect facilitated the beating stability of the cell and clump, these factors contributed to the spontaneous ordering in beating synchronization. Thirdly, the cellular layouts in clump affected the synchronized beating rhythms. The synchronized beating rhythm in clump was implicitly regulated by a complicated synergistic effect among IBI fluctuation of each beating cell, the community effect and the cellular layout. This finding was indispensable for leading an elucidation of mechanism of emergence. The stochastic simulations showed the necessity of considering the synergistic effect, to elucidate the interlayer regulatory mechanisms in biological system.

Concepts: DNA, Gene, Organism, Effect, Affect, Theodor Schwann, Stochastic


PURPOSE: Nearly half of cancer metastases become clinically evident five or more years after primary tumor treatment; thus metastatic cells survived without emerging for extended periods. This dormancy has been explained by at least two countervailing scenarios: cellular quiescence and balanced proliferation; these entail dichotomous mechanistic etiologies. To examine the boundary parameters for balanced proliferation, we performed in silico modeling. EXPERIMENTAL DESIGN: To illuminate the balanced proliferation hypothesis, we explored the specific boundary probabilities under which proliferating micrometastases would remain dormant. A two-state Markov chain Monte Carlo model simulated micrometastatic proliferation and death according to stochastic survival probabilities. We varied these probabilities across 100 simulated patients each with 1,000 metastatic deposits and documented whether the micrometastases exceeded one million cells, died out, or remained dormant (survived 1,218 generations). RESULTS: The simulations revealed a narrow survival probability window (49.7 - 50.8 percent) that allowed for dormancy across a range of starting cell numbers, and even then for only a small fraction of micrometastases. The majority of micrometastases died out quickly even at survival probabilities that led to rapid emergence of a subset of micrometastases. Within dormant metastases, cell populations depended sensitively on small survival probability increments. CONCLUSIONS: Metastatic dormancy as explained solely by balanced proliferation is bounded by very tight survival probabilities. Considering the far larger survival variability thought to attend fluxing microenvironments, it is more probable that these micrometastatic nodules undergo at least periods of quiescence rather than exclusively being controlled by balanced proliferation.

Concepts: Cancer, Simulation, Monte Carlo, Probability, Theory, Markov chain Monte Carlo, Stochastic process, Stochastic


It has been assumed that DNA synthesis by the leading- and lagging-strand polymerases in the replisome must be coordinated to avoid the formation of significant gaps in the nascent strands. Using real-time single-molecule analysis, we establish that leading- and lagging-strand DNA polymerases function independently within a single replisome. Although average rates of DNA synthesis on leading and lagging strands are similar, individual trajectories of both DNA polymerases display stochastically switchable rates of synthesis interspersed with distinct pauses. DNA unwinding by the replicative helicase may continue during such pauses, but a self-governing mechanism, where helicase speed is reduced by ∼80%, permits recoupling of polymerase to helicase. These features imply a more dynamic, kinetically discontinuous replication process, wherein contacts within the replisome are continually broken and reformed. We conclude that the stochastic behavior of replisome components ensures complete DNA duplication without requiring coordination of leading- and lagging-strand synthesis. PAPERCLIP.

Concepts: DNA, DNA replication, DNA polymerase, Polymerase, Stochastic


Natural arches, pillars and other exotic sandstone formations have always been attracting attention for their unusual shapes and amazing mechanical balance that leave a strong impression of intelligent design rather than the result of a stochastic process. It has been recently demonstrated that these shapes could have been the result of the negative feedback between stress and erosion that originates in fundamental laws of friction between the rock’s constituent particles. Here we present a deeper analysis of this idea and bridge it with the approaches utilized in shape and topology optimisation. It appears that the processes of natural erosion, driven by stochastic surface forces and Mohr-Coulomb law of dry friction, can be viewed within the framework of local optimisation for minimum elastic strain energy. Our hypothesis is confirmed by numerical simulations of the erosion using the topological-shape optimisation model. Our work contributes to a better understanding of stochastic erosion and feasible landscape formations that could be found on Earth and beyond.

Concepts: Mathematics, Mass, Force, Sandstone, Classical mechanics, Mathematical optimization, Stochastic, Intelligent design


Stochastic simulations are one of the cornerstones of the analysis of dynamical processes on complex networks, and are often the only accessible way to explore their behavior. The development of fast algorithms is paramount to allow large-scale simulations. The Gillespie algorithm can be used for fast simulation of stochastic processes, and variants of it have been applied to simulate dynamical processes on static networks. However, its adaptation to temporal networks remains non-trivial. We here present a temporal Gillespie algorithm that solves this problem. Our method is applicable to general Poisson (constant-rate) processes on temporal networks, stochastically exact, and up to multiple orders of magnitude faster than traditional simulation schemes based on rejection sampling. We also show how it can be extended to simulate non-Markovian processes. The algorithm is easily applicable in practice, and as an illustration we detail how to simulate both Poissonian and non-Markovian models of epidemic spreading. Namely, we provide pseudocode and its implementation in C++ for simulating the paradigmatic Susceptible-Infected-Susceptible and Susceptible-Infected-Recovered models and a Susceptible-Infected-Recovered model with non-constant recovery rates. For empirical networks, the temporal Gillespie algorithm is here typically from 10 to 100 times faster than rejection sampling.

Concepts: Simulation, Operations research, Simulation123, Mathematical model, Stochastic


The aim of this study was to define a method for evaluating a player’s decisions during a game based on the success probability of his actions and for analyzing the player strategy inferred from game actions. There were developed formal definitions of i) the stochastic process of player decisions in game situations and ii) the inference process of player strategy based on his game decisions. The method was applied to the context of soccer goalkeepers. A model of goalkeeper positioning, with geometric parameters and solutions to optimize his position based on the ball position and trajectory, was developed. The model was tested with a sample of 65 professional goalkeepers (28.8 ± 4.1 years old) playing for their national teams in 2010 and 2014 World Cups. The goalkeeper’s decisions were compared to decisions from a large dataset of other goalkeepers, defining the probability of success in each game circumstance. There were assessed i) performance in a defined set of classes of game plays; ii) entropy of goalkeepers' decisions; and iii) the effect of goalkeepers' positioning updates on the outcome (save or goal). Goalkeepers' decisions were similar to the ones with the lowest probability of goal on the dataset. Goalkeepers' entropy varied between 24% and 71% of the maximum possible entropy. Positioning dynamics in the instants that preceded the shot indicated that, in goals and saves, goalkeepers optimized their position before the shot in 21.87% and 83.33% of the situations, respectively. These results validate a method to discriminate successful performance. In conclusion, this method enables a more precise assessment of a player’s decision-making ability by consulting a representative dataset of equivalent actions to define the probability of his success. Therefore, it supports the evaluation of the player’s decision separately from his technical skill execution, which overcomes the scientific challenge of discriminating the evaluation of a player’s decision performance from the action result.

Concepts: Game theory, Decision making, Definition, Decision theory, Probability, Logic, Inference, Stochastic