Modelling fungus dispersal scenarios using cellular automata

This study focused on representing spatio-temporal patterns of fungal dispersal using cellular automata. Square lattices were used, with each site representing a host for a hypothetical fungus population. Four possible host states were allowed: resistant, permissive, latent or infectious. In this model, the probability of infection for each of the healthy states (permissive or resistant) in a time step was determined as a function of the host's susceptibility, seasonality, and the number of infectious sites and the distance between them. It was also assumed that infected sites become infectious after a pre-specified latency period, and that recovery is not possible. Several scenarios were simulated to understand the contribution of the model's parameters and the spatial structure on the dynamic behaviour of the modelling system. The model showed good capability for representing the spatio-temporal pattern of fungus dispersal over planar surfaces. With a specific problem in mind, the model can be easily modified and used to describe field behaviour, which can contribute to the conservation and development of management strategies for both natural and agricultural systems.     

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.     

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.     

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.     

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/.     

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.     

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.

     

Simulation of wastewater treatment by aerobic granules in a sequencing batch reactor based on cellular automata

In the present paper, aerobic granules were developed in a sequencing batch reactor (SBR) using synthetic wastewater, and 81 % of granular rate was obtained after 15-day cultivation. Aerobic granules have a 96 % BOD removal to the wastewater, and the reactor harbors a mount of biomass including bacteria, fungi and protozoa. In view of the complexity of kinetic behaviors of sludge and biological mechanisms of the granular SBR, a cellular automata model was established to simulate the process of wastewater treatment. The results indicate that the model not only visualized the complex adsorption and degradation process of aerobic granules, but also well described the BOD removal of wastewater and microbial growth in the reactor. Thus, CA model is suitable for simulation of synthetic wastewater treatment. This is the first report about dynamical and visual simulation of treatment process of synthetic wastewater in a granular SBR.     

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.     

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.     

“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。     

Non-collagenous ECM proteins in blood vessel morphogenesis and cancer

Background

The extracellular matrix (ECM) is constituted by diverse composite structures, which determine the specific to each organ, histological architecture and provides cells with biological information, mechanical support and a scaffold for adhesion and migration. The pleiotropic effects of the ECM stem from the dynamic changes in its molecular composition and the ability to remodel in order to effectively regulate biological outcomes. Besides collagens, fibronectin and laminin are two major fiber-forming constituents of various ECM structures.

Scope of review

This review will focus on the properties and the biological functions of non-collagenous extracellular matrix especially on laminin and fibronectin that are currently emerging as important regulators of blood vessel formation and function in health and disease.

Major conclusions

The ECM is a fundamental component of the microenvironment of blood vessels, with activities extending beyond providing a vascular scaffold; extremely versatile it directly or indirectly modulates all essential cellular functions crucial for angiogenesis, including cell adhesion, migration, proliferation, differentiation and lumen formation. Specifically, fibronectin and laminins play decisive roles in blood vessel morphogenesis both during embryonic development and in pathological conditions, such as cancer.

General significance

Emerging evidence demonstrates the importance of ECM function during embryonic development, organ formation and tissue homeostasis. A wealth of data also illustrates the crucial role of the ECM in several human pathophysiological processes, including fibrosis, skeletal diseases, vascular pathologies and cancer. Notably, several ECM components have been identified as potential therapeutic targets for various diseases, including cancer. This article is part of a Special Issue entitled Matrix-mediated cell behaviour and properties.