Simulation of vessel morphogenesis using cellular automata

We present a cellular automaton model, including lateral inhibition of an autocatalytic morphogen, as well as a genetic switch that differentiates tissue into substrate-depleting vessels. This model yields isotropic morphogenesis, including: dichotomous and lateral branching, blind vessel ends, and closed loops due to anastosmosis. The algorithm consists of a list of simple rules describing the essential biophysical features, permitting comfortable programming and fast computations. Depending on the choice of the substrate s, the model is applicable to leaf veins (s is auxin), insect trachea (s is CO2) or neovascularization (s is an angiogenesis factor). Sequential addition of rules can be correlated to evolutionary steps in leaf morphogenesis.     

Local variations in spatial synchrony of influenza epidemics

Background

Understanding the mechanism of influenza spread across multiple geographic scales is not complete. While the mechanism of dissemination across regions and states of the United States has been described, understanding the determinants of dissemination between counties has not been elucidated. The paucity of high resolution spatial-temporal influenza incidence data to evaluate disease structure is often not available.

Methodology and Findings

We report on the underlying relationship between the spread of influenza and human movement between counties of one state. Significant synchrony in the timing of epidemics exists across the entire state and decay with distance (regional correlation = 62%). Synchrony as a function of population size display evidence of hierarchical spread with more synchronized epidemics occurring among the most populated counties. A gravity model describing movement between two populations is a stronger predictor of influenza spread than adult movement to and from workplaces suggesting that non-routine and leisure travel drive local epidemics.

Conclusions

These findings highlight the complex nature of influenza spread across multiple geographic scales.     

Evaluation of dynamic behavior forecasting parameters in the process of transition rule induction of unidimensional cellular automata

The simulation of the dynamics of a cellular systems based on cellular automata (CA) can be computationally expensive. This is particularly true when such simulation is part of a procedure of rule induction to find suitable transition rules for the CA. Several efforts have been described in the literature to make this problem more treatable. This work presents a study about the efficiency of dynamic behavior forecasting parameters (DBFPs) used for the induction of transition rules of CA for a specific problem: the classification by the majority rule. A total of 8 DBFPs were analyzed for the 31 best-performing rules found in the literature. Some of these DBFPs were highly correlated each other, meaning they yield the same information. Also, most rules presented values of the DBFPs very close each other. An evolutionary algorithm, based on gene expression programming, was developed for finding transition rules according a given preestablished behavior. The simulation of the dynamic behavior of the CA is not used to evaluate candidate transition rules. Instead, the average values for the DBFPs were used as reference. Experiments were done using the DBFPs separately and together. In both cases, the best induced transition rules were not acceptable solutions for the desired behavior of the CA. We conclude that, although the DBFPs represent interesting aspects of the dynamic behavior of CAs, the transition rule induction process still requires the simulation of the dynamics and cannot rely only on the DBFPs.     

Synchronous and asynchronous updating in cellular automata.

We analyze the properties of a synchronous and of various asynchronous methods to iterate cellular automata. Asynchronous methods in which the time variable is not explicitly defined, operate by specifying an updating order of the cells. The statistical properties of this order have significant consequences for the dynamics and the patterns generated by the cellular automata. Stronger correlations between consecutive steps in the updating order result in more, artificial structure in the patterns. Among these step-driven methods, using random choice with replacement to pick the next cell for updating, yields results that are least influenced by the updating method. We also analyse a time-driven method in which the state transitions of single cells are governed by a probability per unit time that determines an exponential distribution of the waiting time until the next transition. The statistical properties of this method are completely independent of the size of the grid. Consecutive updating steps therefore show no correlation at all. The stationary states of a cellular automaton do not depend on whether a synchronous or asynchronous updating method is used. Their basins of attraction might, however, be vastly different under synchronous and asynchronous iteration. Cyclic dynamics occur only with synchronous updating.     

Spatial pattern switching enables cyclic evolution in spatial epidemics

Infectious diseases often spread as spatial epidemic outbreak waves. A number of model studies have shown that such spatial pattern formation can have important consequences for the evolution of pathogens. Here, we show that such spatial patterns can cause cyclic evolutionary dynamics in selection for the length of the infectious period. The necessary reversal in the direction of selection is enabled by a qualitative change in the spatial pattern from epidemic waves to irregular local outbreaks. The spatial patterns are an emergent property of the epidemic system, and they are robust against changes in specific model assumptions. Our results indicate that emergent spatial patterns can act as a rich source for complexity in pathogen evolution.     

Dynamics of HIV infection studied with cellular automata and conformon-P systems

Recently a cellular automaton (CA) has been used to model the dynamics of HIV infection, with interesting results. We replicate and further test this model, and we introduce an alternative model based on conformon-P (cP) systems. We find (in common with other recently published comments) that the CA model is very sensitive to initial conditions and produces appropriate qualitative dynamics only for a narrow range of rule probabilities. In contrast, the cP system model is robust to a wide range of conditions and parameters, with more reproducible qualitative agreement to the overall dynamics and to the densities of healthy and infected cells observed in vivo.     

Ocean acidification affects competition for space: projections of community structure using cellular automata

Historical ecological datasets from a coastal marine community of crustose coralline algae (CCA) enabled the documentation of ecological changes in this community over 30 years in the Northeast Pacific. Data on competitive interactions obtained from field surveys showed concordance between the 1980s and 2013, yet also revealed a reduction in how strongly species interact. Here, we extend these empirical findings with a cellular automaton model to forecast ecological dynamics. Our model suggests the emergence of a new dominant competitor in a global change scenario, with a reduced role of herbivory pressure, or trophic control, in regulating competition among CCA. Ocean acidification, due to its energetic demands, may now instead play this role in mediating competitive interactions and thereby promote species diversity within this guild.     

Asynchronous adaptive time step in quantitative cellular automata modeling

Background  

The behaviors of cells in metazoans are context dependent, thus large-scale multi-cellular modeling is often necessary, for which cellular automata are natural candidates. Two related issues are involved in cellular automata based multi-cellular modeling: how to introduce differential equation based quantitative computing to precisely describe cellular activity, and upon it, how to solve the heavy time consumption issue in simulation.     

Evaluating spatial constraints in cellular assembly processes using a Monte Carlo approach

Biomolecular behavior commonly involves complex sets of interacting components that are challenging to understand through solution-based chemical theories. Molecular assembly is especially intriguing in the cellular environment because of its links to cell structure in processes such as chemotaxis. We use a coarse-grained Monte Carlo simulation to elucidate the importance of spatial constraints in molecular assembly. We have performed a study of actin filament polymerization through this space-aware probabilistic lattice-based model. Quantitative results are compared with nonspatial models and show convergence over a wide parameter space, but marked divergence over realistic levels corresponding to macromolecular crowding inside cells and localized actin concentrations found at the leading edge during cell motility. These conclusions have direct implications for cell shape and structure, as well as tumor cell migration.     

Phase transition in dimorphic fungi

The morphogenetic process, the transition from the micelial to fungal growth phase in imperfect microscopic dimorphic fungi Phaeococcomyces de Hoog (strain Ch49), induced by high concentrations of transition metal ions, was considered in terms of the phase transition theory. It was shown that, although microscopic dimorphic fungi developing in the culture represent a system far from equilibrial, the transitions from the micelial to fungal phase under determined external influences have features characteristic for a common phase transition.     

Phase transition in tensionless surfaces

We study the critical behavior of the Laplacian roughening model, which describes the growth of tensionless surfaces. This type of growth phenomena is very important, for instance, in biological membranes and in molecular beam epitaxy. We summarize previous analytical and numerical results and point out their contradictions and differences, thus making clear the context of our work. Our contribution, achieved through large-scale numerical simulations, is the confirmation that the model exhibits a single continuous phase transition: the transition takes place between a continuum massless (i.e., with infinite correlation length) bilaplacian behavior and a massive propagator (finite correlation length).     

Chlamydial infection and spatial ascension of the female genital tract: a novel hybrid cellular automata and continuum mathematical model

Sexually transmitted chlamydial infection initially establishes in the endocervix in females, but if the infection ascends the genital tract, significant disease, including infertility, can result. Many of the mechanisms associated with chlamydial infection kinetics and disease ascension are unknown. We attempt to elucidate some of these processes by developing a novel mathematical model, using a cellular automata–partial differential equation model. We matched our model outputs to experimental data of chlamydial infection of the guinea-pig cervix and carried out sensitivity analyses to determine the relative influence of model parameters. We found that the rate of recruitment and action of innate immune cells to clear extracellular chlamydial particles and the rate of passive movement of chlamydial particles are the dominant factors in determining the early course of infection, magnitude of the peak chlamydial time course and the time of the peak. The rate of passive movement was found to be the most important factor in determining whether infection would ascend to the upper genital tract. This study highlights the importance of early innate immunity in the control of chlamydial infection and the significance of motility-diffusive properties and the adaptive immune response in the magnitude of infection and in its ascension.     

Phase transition in natural collagen]

The state of water protons and peptide chains in natural collagen was investigated by the method of nuclear magnetic resonance. The study of orientation and temperature dependence of collagen PMR spectra allows us to mage a conclusion about the considerable disorder of mutual orientation in the polypeptide chains at the temperature above -4 degrees C. Under these conditions it was observed that natural collagen was near to the liquid-crystal. The phasic transition at -4 degrees C was discovered, the latter was followed by an abrupt change of the character of water proton mobility and by the change of orientation of collagen fibres order. The thermal effect of transition was measured, the latter presents 18k/gr of the whole specimen.     

Phase transition in vector spin glasses

We first give an experimental and theoretical introduction to spin glasses, and then discuss the nature of the phase transition in spin glasses with vector spins. Results of Monte Carlo simulations of the Heisenberg spin glass model in three dimensions are presented. A finite size scaling analysis of the correlation length of the spins and chiralities shows that there is a single, finite-temperature transition at which both spins and chiralities order.     

Phase transition in charged lipid membranes

Experimental results on the effect of electrostatics on bilayer phase transitions are compared with corresponding data for monolayers and the predictions of electrical double layer theory. The two substantial conclusions which emerge are that: (i) double layer theory based on a continuous surface charge distribution cannot explain all the relevant data, a situation which may be improved by taking into account the discrete nature of the surface charge distribution; (ii) the crystal - liquid crystal phase transition of charged bilayer membranes is always a continuous one which takes place through an intermediate state consisting of both fluid and frozen domains.     

不同样本方案下遗传元胞自动机的土地利用模拟及景观评价

利用元胞自动机(cellular automata,CA)模拟土地利用情景,有助于理解其变化机理,并为土地资源持续利用提供空间决策支持.本文基于生物进化过程的遗传算法(genetic algo-rithm,GA)将CA参数编码成为染色体,在模拟结果与真实结果差异值的引导下,通过选择、杂交和变异算子使最优的染色体得以遗传和保留,从而建立智能优化的元胞自动机模型.以浙江省嘉兴市1992-2008年土地利用变化为例,分别利用6%(66个·km-2)和3%(33个·km-2)两种样本方案构建遗传CA模型进行土地利用变化模拟,并通过混淆矩阵、Kappa系数和景观指数对模拟结果进行评估.结果表明:遗传CA模拟结果能在数量、位置和景观格局上以超过80%的水平接近真实分类,且大样本量构建的遗传CA的模拟精度更高;2008年的模拟精度和景观综合指数低于2001年,表明遗传CA的模拟精度和景观综合指数随模拟时间而衰减.     

Influence of infection rate and migration on extinction of disease in spatial epidemics

Extinction of disease can be explained by the patterns of epidemic spreading, yet the underlying causes of extinction are far from being well understood. To reveal a mechanism of disease extinction, a cellular automata model with both birth, death rate and migration is presented. We find that, in single patch, when the infection rate is small or large enough, the disease will disappear for a long time. When the invasion form is in the coexistence of stable spiral and turbulent wave state, the disease will persist. Also, we find that the migration has dual effects on the epidemic spreading. On one hand, in the extinction region of single patch, if the migration rate is large enough, there is a phase transition from the disease free to endemic state in two patches. On the other hand, migration will induce extinction in the regime, which can ensure the persistence of the disease in single patch, due to emergence of anti-phase synchrony. The results obtained well reveal the effect of infection rate and migration on the extinction of the disease, which enriches the finding in the filed of epidemiology and may provide some new ideas to control the disease in the real world.     

Contribution of cellular contractility to spatial and temporal variations in cellular stiffness

Scanning probe microscopy and immunofluorescence observations indicated that cellular stiffness was attributed to a contractile network structure consisting of stress fibers. We measured temporal variations in cellular stiffness when cellular contractility was regulated by dosing with lysophosphatidic acid or Y-27632. This experiment revealed a clear relation between cellular stiffness and contractility: Increases in contractility caused cells to stiffen. On the other hand, decreases in contractility reduced cellular stiffness. In both cases, not only the stiffness of the stress fibers but also that of the whole of the cell varied. Immunofluorescence observations of myosin II and vinculin indicated that the stiffness variations induced by the regulation of cellular contractility were mainly due to rearrangements of the contractile actin network on the dorsal surface. Taken together, our findings provide evidence that the actin cytoskeletal network and its contractility features provide and modulate the mechanical stability of adherent cells.     

Phase transition in charged lipid membranes.

Experimental results on the effect of electrostatics on bilayer phase transitions are compared with corresponding data for monolayers and the predictions of electrical double layer theory. The two substantial conclusions which emerge are that: (i) double layer theory based on a continuous surface charge distribution cannot explain all the relevant data, a situation which may be improved by taking into account the discrete nature of the surface charge distribution; (ii) the crystal - liquid crystal phase transition of charged bilayer membranes is always a continuous one which takes place through an intermediate state consisting of both fluid and frozen domains.