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.     

Self-organized perturbations enhance class IV behavior and 1/f power spectrum in elementary cellular automata

In this paper, we propose a new class of cellular automata based on the modification of its state space. It is introduced to model a computation which is exposed to an environment. We formalized the computation as extension and projection processes of its state space and resulting misidentifications of the state. This is motivated to embed the role of an environment into the system itself, which naturally induces self-organized internal perturbations rather than the usual external perturbations. Implementing this structure into the elementary cellular automata, we characterized its effect by means of input entropy and power spectral analysis. As a result, the cellular automata with this structure showed robust class IV behavior and a 1/f power spectrum in a wide range of rule space comparative to the notion of the edge of chaos.     

Evolutionary contingency and SETI revisited

The well-known argument against the Search for ExtraTerrestrial Intelligence (SETI) due to George Gaylord Simpson is re-analyzed almost half a century later, in the light of our improved understanding of preconditions for the emergence of life and intelligence brought about by the ongoing “astrobiological revolution”. Simpson’s argument has been enormously influential, in particular in biological circles, and it arguably fueled the most serious opposition to SETI programmes and their funding. I argue that both proponents and opponents of Simpson’s argument have occasionally mispresented its core content. Proponents often oversimplify it as just another consequence of biological contingency, thus leaving their position open to general arguments limiting the scope of contingency in evolution (such as the recent argument of Geerat Vermeij based on selection effects in the fossil record). They also tend to neglect that the argument has been presented as essentially atemporal, while referring to entities and processes that are likely to change over time; this has become even less justifiable as our astrobiological knowledge increased in recent years. Opponents have failed to see that the weaknesses in Simpson’s position could be removed by restructuring of the argument; I suggest one way of such restructuring, envisioned long ago in the fictional context by Stanislaw Lem. While no firm consensus has emerged on the validity of Simpson’s argument so far, I suggest that, contrary to the original motivation, today it is less an anti-SETI argument, and more an astrobiological research programme. In this research programme, SETI could be generalized into a platform for testing some of the deepest assumptions about evolutionary continuity and the relative role of contingency versus convergence on unprecedented spatial and temporal scales.     

Cytokine-induced signaling networks prioritize dynamic range over signal strength

Signaling networks respond to diverse stimuli, but how the state of the signaling network is relayed to downstream cellular responses is unclear. We modeled how incremental activation of signaling molecules is transmitted to control apoptosis as a function of signal strength and dynamic range. A linear relationship between signal input and response output, with the dynamic range of signaling molecules uniformly distributed across activation states, most accurately predicted cellular responses. When nonlinearized signals with compressed dynamic range relay network activation to apoptosis, we observe catastrophic, stimulus-specific prediction failures. We develop a general computational technique, "model-breakpoint analysis," to analyze the mechanism of these failures, identifying new time- and stimulus-specific roles for Akt, ERK, and MK2 kinase activity in apoptosis, which were experimentally verified. Dynamic range is rarely measured in signal-transduction studies, but our experiments using model-breakpoint analysis suggest it may be a greater determinant of cell fate than measured signal strength.     

Modeling symmetric macromolecular structures in Rosetta3

Symmetric protein assemblies play important roles in many biochemical processes. However, the large size of such systems is challenging for traditional structure modeling methods. This paper describes the implementation of a general framework for modeling arbitrary symmetric systems in Rosetta3. We describe the various types of symmetries relevant to the study of protein structure that may be modeled using Rosetta's symmetric framework. We then describe how this symmetric framework is efficiently implemented within Rosetta, which restricts the conformational search space by sampling only symmetric degrees of freedom, and explicitly simulates only a subset of the interacting monomers. Finally, we describe structure prediction and design applications that utilize the Rosetta3 symmetric modeling capabilities, and provide a guide to running simulations on symmetric systems.     

Identifying conformational states of macromolecules by eigen-analysis of resampled cryo-EM images

We present the codimensional principal component analysis (PCA), a novel and straightforward method for resolving sample heterogeneity within a set of cryo-EM 2D projection images of macromolecular assemblies. The method employs PCA of resampled 3D structures computed using subsets of 2D data obtained with a novel hypergeometric sampling scheme. PCA provides us with a small subset of dominating "eigenvolumes" of the system, whose reprojections are compared with experimental projection data to yield their factorial coordinates constructed in a common framework of the 3D space of the macromolecule. Codimensional PCA is unique in the dramatic reduction of dimensionality of the problem, which facilitates rapid determination of both the plausible number of conformers in the sample and their 3D structures. We applied the codimensional PCA to a complex data set of Thermus thermophilus 70S ribosome, and we identified four major conformational states and visualized high mobility of the stalk base region.     

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.     

How trophic interaction strength depends on traits

A key problem in community ecology is to understand how individual-level traits give rise to population-level trophic interactions. Here, we propose a synthetic framework based on ecological considerations to address this question systematically. We derive a general functional form for the dependence of trophic interaction coefficients on trophically relevant quantitative traits of consumers and resources. The derived expression encompasses—and thus allows a unified comparison of—several functional forms previously proposed in the literature. Furthermore, we show how a community’s, potentially low-dimens ional, effective trophic niche space is related to its higher-dimensional phenotypic trait space. In this manner, we give ecological meaning to the notion of the “dimensionality of trophic niche space.” Our framework implies a method for directly measuring this dimensionality. We suggest a procedure for estimating the relevant parameters from empirical data and for verifying that such data matches the assumptions underlying our derivation.     

Landscape Diversity Influences Dispersal and Establishment of Pest with Complex Nutritional Ecology

We studied the effects of landscape structure on species with resource nutritional partition between the immature and adult stages by investigating how food quality and spatial structure of a landscape may affect the invasion and colonization of the insect pest, Diabrotica speciosa. To this end, we formulated two bidimensional stochastic cellular automata, one for the insect immature stage and the other for the adult stage. The automata are coupled by adult oviposition and emergence. Further, each automata site has a specific culture type, which can affect differently the fitness attributes of immatures and adults, such as mortality, development and oviposition rates. We derived the mean-field approximation for these automata model, from which we obtained conditions for insect invasion. We ran numerical simulations using entomological parameters obtained from laboratory experiments (using bean, soybean, potato, and corn crops), and we compared the results of the automata with the ones given by the mean-field approximation. Finally, using artificially generated landscapes, we discussed how the structured heterogeneous landscape can affect dispersal and establishment of insect populations.     

模拟青霉素发酵过程中菌体生长动态的细胞自动机模型

在青霉素发酵生产机理及其动力学微分方程模型的基础上,建立了模拟青霉素分批发酵过程中菌体生长动态的细胞自动机模型(CABGM)。CABGM采用三维细胞自动机作为菌体生长空间,采用Moore型邻域作为细胞邻域,其演化规则根据青霉素分批发酵过程中菌体生长机理和动力学微分方程模型设计。CABGM中的每一个细胞既可代表单个的青霉素产生菌,又可代表特定数量的青霉素产生菌,它具有不同的状态。对CABGM进行了统计特性的理论分析和仿真实验,理论分析和仿真实验结果均证明了CABGM能一致地复现动力学微分方程模型所描述的青霉素分批发酵菌体生长过程。最后,对所建模型在实际生产过程中的应用问题进行了分析,指出了需要进一步研究的问题。     

How do high-level specifications of the brain relate to variational approaches?

High-level specification of how the brain represents and categorizes the causes of its sensory input allows to link "what is to be done" (perceptual task) with "how to do it" (neural network calculation). In this article, we describe how the variational framework, which encountered a large success in modeling computer vision tasks, has some interesting relationships, at a mesoscopic scale, with computational neuroscience. We focus on cortical map computations such that "what is to be done" can be represented as a variational approach, i.e., an optimization problem defined over a continuous functional space. In particular, generalizing some existing results, we show how a general variational approach can be solved by an analog neural network with a given architecture and conversely. Numerical experiments are provided as an illustration of this general framework, which is a promising framework for modeling macro-behaviors in computational neuroscience.     

基于细胞自动机的实体肿瘤生长动态建模

基于细胞自动机方法,建立了一种简单的实体肿瘤免疫性系统模型,用来模拟实体肿瘤生长过程中的情况．我们基于二维随机、离散细胞自动机计算方法,在生物细胞水平上,建立了一种肿瘤免疫性系统生长模型．该模型考虑了免疫反应的宏观性质,描绘了癌细胞和机体免疫系统之间的细胞相互作用,表现了围绕在肿瘤机体周围,免疫系统细胞的免疫作用发展情况．我们研究了常规细胞自动机模型,设计出实体肿瘤模型随机演化生长规则．最终,构建离散细胞自动机肿瘤免疫性系统模型,并做了相应的数值仿真试验．通过对仿真模型不同参数的调整,最终的仿真结果表明,该模型能反映肿瘤免疫性系统基本的相关性质．     

Use of computational fluid dynamics as a tool for establishing process design space for mixing in a bioreactor

The concept of "design space" plays an integral part in implementation of quality by design for pharmaceutical products. ICH Q8 defines design space as "the multidimensional combination and interaction of input variables (e.g., material attributes) and process parameters that have been demonstrated to provide assurance of quality. Working within the design space is not considered as a change. Movement out of the design space is considered to be a change and would normally initiate a regulatory post-approval change process. Design space is proposed by the applicant and is subject to regulatory assessment and approval." Computational fluid dynamics (CFD) is increasingly being used as a tool for modeling of hydrodynamics and mass transfer. In this study, a laboratory-scale aerated bioreactor is modeled using CFD. Eulerian-Eulerian multiphase model is used along with dispersed k-ε turbulent model. Population balance model is incorporated to account for bubble breakage and coalescence. Multiple reference frame model is used for the rotating region. We demonstrate the usefulness of CFD modeling for evaluating the effects of typical process parameters like impeller speed, gas flow rate, and liquid height on the mass transfer coefficient (k(L)a). Design of experiments is utilized to establish a design space for the above mentioned parameters for a given permissible range of k(L)a.     

Evolved cellular automata for protein secondary structure prediction imitate the determinants for folding observed in nature

We demonstrate the first application of cellular automata to the secondary structure predictions of proteins. Cellular automata use localized interactions to simulate global phenomena, which resembles the protein folding problem where individual residues interact locally to define the global protein conformation. The protein's amino acid sequence was input into the cellular automaton and rules for updating states were evolved using a genetic algorithm. An optimized accuracy (Q3) for the RS126 and CB513 dataset of 58.21% and 56.51%, respectively, could be obtained. Thus, the current work demonstrates the applicability of a rather simple algorithm on a problem as complex as protein secondary structure prediction.     

Modeling the process of rate selection in neuronal activity

We present the elements of a mathematical computational model that reflects the experimental finding that the time-scale of a neuron is not fixed; but rather varies with the history of its stimulus. Unlike most physiological models, there are no pre-determined rates associated with transitions between states of the system nor are there pre-determined constants associated with adaptation rates; instead, the model is a kind of "modulating automata" where the rates emerge from the history of the system itself. We focus in this paper on the temporal dynamics of a neuron and show how a simple internal structure will give rise to complex temporal behavior. The internal structure modeled here is an abstraction of a reasonably well-understood physiological structure. We also suggest that this behavior can be used to transform a "rate" code into a "temporal one".     

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.     

A general modeling framework for describing spatially structured population dynamics

Variation in movement across time and space fundamentally shapes the abundance and distribution of populations. Although a variety of approaches model structured population dynamics, they are limited to specific types of spatially structured populations and lack a unifying framework. Here, we propose a unified network‐based framework sufficiently novel in its flexibility to capture a wide variety of spatiotemporal processes including metapopulations and a range of migratory patterns. It can accommodate different kinds of age structures, forms of population growth, dispersal, nomadism and migration, and alternative life‐history strategies. Our objective was to link three general elements common to all spatially structured populations (space, time and movement) under a single mathematical framework. To do this, we adopt a network modeling approach. The spatial structure of a population is represented by a weighted and directed network. Each node and each edge has a set of attributes which vary through time. The dynamics of our network‐based population is modeled with discrete time steps. Using both theoretical and real‐world examples, we show how common elements recur across species with disparate movement strategies and how they can be combined under a unified mathematical framework. We illustrate how metapopulations, various migratory patterns, and nomadism can be represented with this modeling approach. We also apply our network‐based framework to four organisms spanning a wide range of life histories, movement patterns, and carrying capacities. General computer code to implement our framework is provided, which can be applied to almost any spatially structured population. This framework contributes to our theoretical understanding of population dynamics and has practical management applications, including understanding the impact of perturbations on population size, distribution, and movement patterns. By working within a common framework, there is less chance that comparative analyses are colored by model details rather than general principles.