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.     

Phase transition in spatial epidemics using cellular automata with noise

One of the central issues in studying the complex population patterns observed in nature is the role of stochasticity. In this paper, the effects of additive spatiotemporal random variations—noise—are introduced to an epidemic model. The no-noise model exhibits a phase transition from a disease-free state to an endemic state. However, this phase transition can revert in a resonance-like manner depending on noise intensity when introducing nonzero random variations to the model. On the other hand, given a regime where disease can persist, noise can induce disappearance of the phase transition. The results obtained show that noise plays a tremendous role in the spread of the disease state, which has implications for how we try to prevent, and eventually eradicate, disease.     

Designing convergent cellular automata

Cellular automata (CA) have been used by biologists to study dynamic non-linear systems where the interaction between cell behaviour and end-pattern is investigated. It is difficult to achieve convergence of a CA towards a specific static pattern and a common solution is to use genetic algorithms and evolve a ruleset that describes cell behaviour. This paper presents an alternative means of designing CA to converge to specific static patterns. A matrix model is introduced and analysed then a design algorithm is demonstrated. The algorithm is significantly less computationally intensive than equivalent evolutionary algorithms, and not limited in scale, complexity or number of dimensions.     

Dynamic cellular automata: an alternative approach to cellular simulation

A wide variety of approaches, ranging from Petri nets to systems of partial differential equations, have been used to model very specific aspects of cellular or biochemical functions. Here we describe how an agent-based or dynamic cellular automata (DCA) approach can be used as a very simple, yet very general method to model many different kinds of cellular or biochemical processes. Specifically, using simple pairwise interaction rules coupled with random object moves to simulate Brownian motion, we show how the DCA approach can be used to easily and accurately model diffusion, viscous drag, enzyme rate processes, metabolism (the Kreb's cycle), and complex genetic circuits (the repressilator). We also demonstrate how DCA approaches are able to accurately capture the stochasticity of many biological processes. The success and simplicity of this technique suggests that many other physical properties and significantly more complicated aspects of cellular behavior could be modeled using DCA methods. An easy-to-use, graphically-based computer program, called SimCell, was developed to perform the DCA simulations described here. It is available at http://wishart.biology.ualberta.ca/SimCell/.     

Projected changes in distributions of Australian tropical savanna birds under climate change using three dispersal scenarios

Identifying the species most vulnerable to extinction as a result of climate change is a necessary first step in mitigating biodiversity decline. Species distribution modeling (SDM) is a commonly used tool to assess potential climate change impacts on distributions of species. We use SDMs to predict geographic ranges for 243 birds of Australian tropical savannas, and to project changes in species richness and ranges under a future climate scenario between 1990 and 2080. Realistic predictions require recognition of the variability in species capacity to track climatically suitable environments. Here we assess the effect of dispersal on model results by using three approaches: full dispersal, no dispersal and a partial-dispersal scenario permitting species to track climate change at a rate of 30 km per decade. As expected, the projected distributions and richness patterns are highly sensitive to the dispersal scenario. Projected future range sizes decreased for 66% of species if full dispersal was assumed, but for 89% of species when no dispersal was assumed. However, realistic future predictions should not assume a single dispersal scenario for all species and as such, we assigned each species to the most appropriate dispersal category based on individual mobility and habitat specificity; this permitted the best estimates of where species will be in the future. Under this "realistic" dispersal scenario, projected ranges sizes decreased for 67% of species but showed that migratory and tropical-endemic birds are predicted to benefit from climate change with increasing distributional area. Richness hotspots of tropical savanna birds are expected to move, increasing in southern savannas and southward along the east coast of Australia, but decreasing in the arid zone. Understanding the complexity of effects of climate change on species' range sizes by incorporating dispersal capacities is a crucial step toward developing adaptation policies for the conservation of vulnerable species.     

Modelling the larval dispersal of Acanthaster planci

The desire to understand the observed patterns of Acanthaster population spread throughout the Great Barrier Reef (GBR) has necessitated the development of numerical models which are capable of simulating the hydrodynamics associated with large assemblages of reefs over the time scale of larval dispersal. Models are presented which provide an overview of the physical processes controlling the advection of larvae within the Cairns Section of the GBR Marine Park, on the scale of tens to hundreds of kilometres. The relevant scales and relative importance of the distinct processes are discussed. The models are based on a previously tested numerical hydrodynamic model and are validated by comparison with observations documented in the physical oceanographic literature. Overall, model outputs correspond well to our understanding of the large-scale features and dynamics of water circulation over the continental shelf. Regional variation in circulation predicted by the models may result in significant differences in the movement of larvae.     

Predictive landscapes hidden beneath biological cellular automata

To celebrate Hans Frauenfelder’s achievements, we examine energy(-like) “landscapes” for complex living systems. Energy landscapes summarize all possible dynamics of some physical systems. Energy(-like) landscapes can explain some biomolecular processes, including gene expression and, as Frauenfelder showed, protein folding. But energy-like landscapes and existing frameworks like statistical mechanics seem impractical for describing many living systems. Difficulties stem from living systems being high dimensional, nonlinear, and governed by many, tightly coupled constituents that are noisy. The predominant modeling approach is devising differential equations that are tailored to each living system. This ad hoc approach faces the notorious “parameter problem”: models have numerous nonlinear, mathematical functions with unknown parameter values, even for describing just a few intracellular processes. One cannot measure many intracellular parameters or can only measure them as snapshots in time. Another modeling approach uses cellular automata to represent living systems as discrete dynamical systems with binary variables. Quantitative (Hamiltonian-based) rules can dictate cellular automata (e.g., Cellular Potts Model). But numerous biological features, in current practice, are qualitatively described rather than quantitatively (e.g., gene is (highly) expressed or not (highly) expressed). Cellular automata governed by verbal rules are useful representations for living systems and can mitigate the parameter problem. However, they can yield complex dynamics that are difficult to understand because the automata-governing rules are not quantitative and much of the existing mathematical tools and theorems apply to continuous but not discrete dynamical systems. Recent studies found ways to overcome this challenge. These studies either discovered or suggest an existence of predictive “landscapes” whose shapes are described by Lyapunov functions and yield “equations of motion” for a “pseudo-particle.” The pseudo-particle represents the entire cellular lattice and moves on the landscape, thereby giving a low-dimensional representation of the cellular automata dynamics. We outline this promising modeling strategy.

     

A cellular automata model of enzyme kinetics

We have developed a cellular automata model of an enzyme reaction with a substrate in water. The model produces Michaelis-Menten kinetics with good Lineweaver-Burk plots. The variation in affinity parameters predicts that, in general, hydrophobic substrates are more reactive with enzymes, this attribute being more important than the relationship between enzyme and substrate. The ease of generation and the illustrative value of the model lead us to believe that cellular automata models have a useful role in the study of dynamic phenomena such as enzyme kinetics.     

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.     

Modelling of different circular end-of-use scenarios for smartphones

The International Journal of Life Cycle Assessment - Repairing, refurbishing and remanufacturing are three strategies of the Circular Economy (CE), aiming at closing product cycles and maintaining...     

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.     

A cellular automata model of tumor-immune system interactions

We present a hybrid cellular automata-partial differential equation model of moderate complexity to describe the interactions between a growing tumor next to a nutrient source and the immune system of the host organism. The model allows both temporal and two-dimensional spatial evolution of the system under investigation and is comprised of biological cell metabolism rules derived from both the experimental and mathematical modeling literature. We present numerical simulations that display behaviors which are qualitatively similar to those exhibited in tumor-immune system interaction experiments. These include spherical tumor growth, stable and unstable oscillatory tumor growth, satellitosis and tumor infiltration by immune cells. Finally, the relationship between these different growth regimes and key system parameters is discussed.     

“生态位”元胞自动机在土地可持续规划模型中的应用

快速城市化带来了一系列的环境生态问题。有必要把生态学的概念引进城市规划中,以减少城市发展带来的弊端。提出了基于“生态位”的元胞自动机（CA）的新模型,并将其应用在土地利用规划中。探讨了如何通过“生态位”元胞自动机和GIS的结合进行城市土地可持续利用的规划。该模型可方便地探索不同土地利用政策下城市土地利用发展情景,能够为城市规划提供有用的决策支持。旨在探索通过模拟的手段对城市土地利用进行合理的规划。将该模型应用于快速发展的广州市,并取得了较有意义的结果。     

Modelling cellular systems with PySCeS

SUMMARY: The Python Simulator for Cellular Systems (PySCeS) is an extendable research tool for the numerical analysis and investigation of cellular systems. AVAILABILITY: PySCeS is distributed as Open Source Software under the GNU General Public Licence and is available for download from http://pysces.sourceforge.net CONTACT: bgoli@sun.ac.za.     

Inferring dispersal patterns of the generalist root fungus Armillaria mellea

Investigating the dispersal of the root-pathogenic fungus Armillaria mellea is necessary to understand its population biology. Such an investigation is complicated by both its subterranean habit and the persistence of genotypes over successive host generations. As such, host colonization by resident mycelia is thought to outcompete spore infections. We evaluated the contributions of mycelium and spores to host colonization by examining a site in which hosts pre-date A. mellea. Golden Gate Park (San Francisco, CA, USA) was established in 1872 primarily on sand dunes that supported no resident mycelia. Genotypes were identified by microsatellite markers and somatic incompatibility pairings. Spatial autocorrelation analyses of kinship coefficients were used to infer spore dispersal distance. The largest genotypes measured 322 and 343 m in length, and 61 of the 90 total genotypes were recovered from only one tree. The absence of multilocus linkage disequilibrium and the high proportion of unique genotypes suggest that spore dispersal is an important part of the ecology and establishment of A. mellea in this ornamental landscape. Spatial autocorrelations indicated a significant spatial population structure consistent with limited spore dispersal. This isolation-by-distance pattern suggests that most spores disperse over a few meters, which is consistent with recent, direct estimates based on spore trapping data.     

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.