Cellular Automata Modeling of Stem‐Cell‐Driven Development of Tissue in the Nervous System

Mathematical and computational modeling enables biologists to integrate data from observations and experiments into a theoretical framework. In this review, we describe how developmental processes associated with stem‐cell‐driven growth of tissue in both the embryonic and adult nervous system can be modeled using cellular automata (CA). A cellular automaton is defined by its discrete nature in time, space, and state. The discrete space is represented by a uniform grid or lattice containing agents that interact with other agents within their local neighborhood. This possibility of local interactions of agents makes the cellular automata approach particularly well suited for studying through modeling how complex patterns at the tissue level emerge from fundamental developmental processes (such as proliferation, migration, differentiation, and death) at the single‐cell level. As part of this review, we provide a primer for how to define biologically inspired rules governing these processes so that they can be implemented into a CA model. We then demonstrate the power of the CA approach by presenting simulations (in the form of figures and movies) based on building models of three developmental systems: the formation of the enteric nervous system through invasion by neural crest cells; the growth of normal and tumorous neurospheres induced by proliferation of adult neural stem/progenitor cells; and the neural fate specification through lateral inhibition of embryonic stem cells in the neurogenic region of Drosophila.     

Gaia as a complex adaptive system

We define the Gaia system of life and its environment on Earth, review the status of the Gaia theory, introduce potentially relevant concepts from complexity theory, then try to apply them to Gaia. We consider whether Gaia is a complex adaptive system (CAS) in terms of its behaviour and suggest that the system is self-organizing but does not reside in a critical state. Gaia has supported abundant life for most of the last 3.8 Gyr. Large perturbations have occasionally suppressed life but the system has always recovered without losing the capacity for large-scale free energy capture and recycling of essential elements. To illustrate how complexity theory can help us understand the emergence of planetary-scale order, we present a simple cellular automata (CA) model of the imaginary planet Daisyworld. This exhibits emergent self-regulation as a consequence of feedback coupling between life and its environment. Local spatial interaction, which was absent from the original model, can destabilize the system by generating bifurcation regimes. Variation and natural selection tend to remove this instability. With mutation in the model system, it exhibits self-organizing adaptive behaviour in its response to forcing. We close by suggesting how artificial life ('Alife') techniques may enable more comprehensive feasibility tests of Gaia.     

Using cellular automata to generate image representation for biological sequences

Summary. A novel approach to visualize biological sequences is developed based on cellular automata (Wolfram, S. Nature 1984, 311, 419–424), a set of discrete dynamical systems in which space and time are discrete. By transforming the symbolic sequence codes into the digital codes, and using some optimal space-time evolvement rules of cellular automata, a biological sequence can be represented by a unique image, the so-called cellular automata image. Many important features, which are originally hidden in a long and complicated biological sequence, can be clearly revealed thru its cellular automata image. With biological sequences entering into databanks rapidly increasing in the post-genomic era, it is anticipated that the cellular automata image will become a very useful vehicle for investigation into their key features, identification of their function, as well as revelation of their fingerprint. It is anticipated that by using the concept of the pseudo amino acid composition (Chou, K.C. Proteins: Structure, Function, and Genetics, 2001, 43, 246–255), the cellular automata image approach can also be used to improve the quality of predicting protein attributes, such as structural class and subcellular location.     

Dynamic pattern processing with adaptive excitable media

We use an excitable medium for dynamic pattern processing. For this purpose the autowave structures arising from the light-sensitive Belouzov-Zhabotinsky reaction could serve as attractors. The dynamics is simulated as a non-linear network with local interaction in terms of cellular automata. With the help of a set of threshold electrodes the actual state is projected into a space of bytes. At the end of the adaptation procedure for the parameters we achieved the ability of this system for pattern recognition. Dynamic and statis pattern processing are compared with respect to information capacity and adaption time.     

Modeling the topological organization of cellular processes

The cell as a dynamical system presents the characteristics of having a dynamical structure. That is, the exact phase space of the system cannot be fixed before the evolution and integrative cell models must state the evolution of the structure jointly with the evolution of the cell state. This kind of dynamical systems is very challenging to model and simulate. New programming concepts must be developed to ease their modeling and simulation. In this context, the goal of the MGS project is to develop an experimental programming language dedicated to the simulation of this kind of systems. MGS proposes a unified view on several computational mechanisms (CHAM, Lindenmayer systems, Paun systems, cellular automata) enabling the specification of spatially localized computations on heterogeneous entities. The evolution of a dynamical structure is handled through the concept of transformation which relies on the topological organization of the system components. An example based on the modeling of spatially distributed biochemical networks is used to illustrate how these notions can be used to model the spatial and temporal organization of intracellular processes.     

Some reversible image operators from the point of view of cellular automata

In this paper image operators and cellular automata are treated from an unified point of view. A class of non-linear operators is described, which is characterized by a typical structure of its transition function and meets sufficient conditions for reversibility. These conditions are then extended to some other operators, featuring a more general structure, and numerous concrete examples, with particular reference to image processing, are given. Cascading reversible operators in opposite scan directions can provide a mean for obtaining processing windows, which surround symmetrically the respective central cells. The conditions to be met by the structure of the single operators and by their processing windows in order to yield a reversible cascade are examined and illustrated by means of examples. In spite of the severe limitations imposed by the reversibility requirement, a number of interesting and useful non-linear reversible operators remain available for image processing and cellular process simulation purposes.     

空间异质性对植物种群动态的影响:三种模拟方法的比较

为了讨论单一物种在异质性景观中的空间传播,将平均场近似模型和偶对近似模型的结果进行对比研究.本研究选择了有代表性的四邻域和八邻域时物种的传播情况,首先运用细胞自动机建立了理想模型,对偶对近似模型和平均场近似模型在全局密度和局域密度固定时随着出生率与死亡率比值变化的结果比较,以细胞自动机模型结果为依据,判断偶对近似与平均场近似哪个结果更加接近细胞自动机模型的结果.通过分析得到四邻域时在近似细胞自动机模型结果时偶对近似的结果优于平均场近似的结果,但是在八邻域时三个模型之间的差异性不再那么明显,偶对近似依然能够很好的预测细胞自动机模型的结果.     

Using Cellular Automata for Parking Recommendations in Smart Environments

In this work, we propose an innovative adaptive recommendation mechanism for smart parking. The cognitive RF module will transmit the vehicle location information and the parking space requirements to the parking congestion computing center (PCCC) when the driver must find a parking space. Moreover, for the parking spaces, we use a cellular automata (CA) model mechanism that can adjust to full and not full parking lot situations. Here, the PCCC can compute the nearest parking lot, the parking lot status and the current or opposite driving direction with the vehicle location information. By considering the driving direction, we can determine when the vehicles must turn around and thus reduce road congestion and speed up finding a parking space. The recommendation will be sent to the drivers through a wireless communication cognitive radio (CR) model after the computation and analysis by the PCCC. The current study evaluates the performance of this approach by conducting computer simulations. The simulation results show the strengths of the proposed smart parking mechanism in terms of avoiding increased congestion and decreasing the time to find a parking space.     

Mesophile versus thermophile: insights into the structural mechanisms of kinetic stability

Obtaining detailed knowledge of folding intermediate and transition state (TS) structures is critical for understanding protein folding mechanisms. Comparisons between proteins adapted to survive extreme temperatures with their mesophilic homologs are likely to provide valuable information on the interactions relevant to the unfolding transition. For kinetically stable proteins such as alpha-lytic protease (alphaLP) and its family members, their large free energy barrier to unfolding is central to their biological function. To gain new insights into the mechanisms that underlie kinetic stability, we have determined the structure and high temperature unfolding kinetics of a thermophilic homolog, Thermobifida fusca protease A (TFPA). These studies led to the identification of a specific structural element bridging the N and C-terminal domains of the protease (the "domain bridge") proposed to be associated with the enhanced high temperature kinetic stability in TFPA. Mutagenesis experiments exchanging the TFPA domain bridge into alphaLP validate this hypothesis and illustrate key structural details that contribute to TFPA's increased kinetic thermostability. These results lead to an updated model for the unfolding transition state structure for this important class of proteases in which domain bridge undocking and unfolding occurs at or before the TS. The domain bridge appears to be a structural element that can modulate the degree of kinetic stability of the different members of this class of proteases.     

RELATCH: relative optimality in metabolic networks explains robust metabolic and regulatory responses to perturbations

Predicting cellular responses to perturbations is an important task in systems biology. We report a new approach, RELATCH, which uses flux and gene expression data from a reference state to predict metabolic responses in a genetically or environmentally perturbed state. Using the concept of relative optimality, which considers relative flux changes from a reference state, we hypothesize a relative metabolic flux pattern is maintained from one state to another, and that cells adapt to perturbations using metabolic and regulatory reprogramming to preserve this relative flux pattern. This constraint-based approach will have broad utility where predictions of metabolic responses are needed.     

An evolving ontogenetic cellular system for better adaptiveness

In this paper, we present an original cellular system named Phuon. The main motivation behind this project is to go beyond classical cellular systems, such as cellular automata (CA). CA often lack adaptability and turn out to be very brittle in uncertain environment. The idea here is to add ontogeny to cellularity, growth and development being means of adaptation and thus robustness. However, we do not wish to develop yet another cellular system for the sake of it. What we are seeking in the long term is a developmental system for problem solving. This global aim enticed us into finding a way to map a desired global behavior of the system to the local behavior of a cell. Quite naturally a peculiar brand of genetic programming was used for that purpose. The results are still preliminary but in our view they already validate some of the hypotheses behind this work.     

Visualization of dynamic simulations of muscle thin filaments

Following a novel computational formalism, the thin filament of muscle can be modeled by a computational machine containing a large number of finite automata that have one-to-one correspondence with the constituent protein molecules.¹ Computer graphics can be used to visualize the correspondence between the states of finite automata and the configurations of protein molecules according to the structural data. The dynamic simulation of the muscle filament that corresponds to the concurrent state transitions of finite automata can be represented as a sequence of video images. The kinetic and structural knowledge of individual protein molecules is, therefore, integrated into a coherent and functional system. This type of computation and visualization can also be useful for the investigation of molecular structure, function, and interaction in various complex biological systems.     

A cellular automata model for simulating fed-batch penicillin fermentation process

A cellular automata model to simulate penicillin fed-batch fermentation process(CAPFM)was established in this study,based on a morphologically structured dynamic penicillin production model,that is in turn based on the growth mechanism of penicillin producing microorganisms and the characteristics of penicillin fed-batch fermentation.CAPFM uses the three-dimensional cellular automata as a growth space,and a Moore-type neighborhood as the cellular neighborhood.The transition roles of CAPFM are designed based on mechanical and structural kinetic models of penicillin batch-fed fermentation processes.Every cell of CAPFM represents a single or specific number of penicillin producing microorganisms,and has various state.The simulation experimental results show that CAPFM replicates the evolutionary behavior of penicillin batch-fed fermentation processes described by the structured penicillin production kinetic model accordingly.     

Harmonic analysis of Boolean networks: determinative power and perturbations

Consider a large Boolean network with a feed forward structure. Given a probability distribution on the inputs, can one find, possibly small, collections of input nodes that determine the states of most other nodes in the network? To answer this question, a notion that quantifies the determinative power of an input over the states of the nodes in the network is needed. We argue that the mutual information (MI) between a given subset of the inputs X={X₁,...,X_n} of some node i and its associated function f_i(X) quantifies the determinative power of this set of inputs over node i. We compare the determinative power of a set of inputs to the sensitivity to perturbations to these inputs, and find that, maybe surprisingly, an input that has large sensitivity to perturbations does not necessarily have large determinative power. However, for unate functions, which play an important role in genetic regulatory networks, we find a direct relation between MI and sensitivity to perturbations. As an application of our results, we analyze the large-scale regulatory network of Escherichia coli. We identify the most determinative nodes and show that a small subset of those reduces the overall uncertainty of the network state significantly. Furthermore, the network is found to be tolerant to perturbations of its inputs.     

Metabolic control theory: a structural approach

In the general framework of metabolic control theory, we describe a method of mathematical modelling that provides a way of analysing the sensitivity of a metabolic system to perturbations of the environment or of the internal state of this system. The method can be applied to any metabolic system, involving for instance conservation relationships, non-specific external parameters, etc., and leads in particular to a characterization of the control matrices and to a generalization of the summation and connectivity theorems. In this paper, we emphasize the structural characterizations and properties of the systems which depend only on the structure of the metabolic network, and not on the reaction kinetics. The advantage of this approach lies of course in the fact that the structure of the metabolic network is an invariant of the system which depends neither on the environment nor on the internal state of this system. The aim of this paper is to show the efficiency of such a structural approach.     

Structural principles for periodic orbits in glass networks

A piecewise-linear differential equation model framework for gene regulatory interactions (Glass networks) has allowed considerable analysis of qualitative dynamics in such systems, including periodicity, an important class of regulatory behaviors. Here, we present new results relating the structure of the network to its dynamics (structural principles). The structure we refer to is the state space of the network, which is a digraph on an n-cube in the case of a single threshold per gene. In particular, we show that for a wide class of cycles in the state space there exist parameter values, consistent with the graph structure, for which a periodic orbit exists in the network. For some classes, we show in addition that stable periodic orbits exist. These results extend greatly earlier work by Glass and Pasternack (J Math Biol 6:207–223, 1978).     

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.     

Astrobiological Complexity with Probabilistic Cellular Automata

The search for extraterrestrial life and intelligence constitutes one of the major endeavors in science, but has yet been quantitatively modeled only rarely and in a cursory and superficial fashion. We argue that probabilistic cellular automata (PCA) represent the best quantitative framework for modeling the astrobiological history of the Milky Way and its Galactic Habitable Zone. The relevant astrobiological parameters are to be modeled as the elements of the input probability matrix for the PCA kernel. With the underlying simplicity of the cellular automata constructs, this approach enables a quick analysis of large and ambiguous space of the input parameters. We perform a simple clustering analysis of typical astrobiological histories with "Copernican" choice of input parameters and discuss the relevant boundary conditions of practical importance for planning and guiding empirical astrobiological and SETI projects. In addition to showing how the present framework is adaptable to more complex situations and updated observational databases from current and near-future space missions, we demonstrate how numerical results could offer a cautious rationale for continuation of practical SETI searches.