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.     

PRODUCTIVITY AND DIVERSITY IN A CROSS‐FEEDING POPULATION OF ARTIFICIAL ORGANISMS

Cross‐feeding interactions are a common feature of many microbial systems, such as colonies of Escherichia coli grown on a single limiting resource, and microbial consortia cooperatively degrading complex compounds. We have studied this phenomenon from an abstract point of view by considering artificial organisms that metabolize binary strings from a shared environment. The organisms are represented as simple cellular automaton rules and the analog of energy in the system is an approximation of the Shannon entropy of the binary strings. Only organisms that increase the entropy of the transformed strings are allowed to replicate. This system exhibits a large degree of species diversity, which increases when the flow of binary strings into the system is reduced. Investigating the relation between ecosystem productivity and diversity we find that diversity is negatively correlated with biomass production and energy uptake, while it correlates positively with energy‐uptake efficiency. By performing invasion experiments, we show that the source of diversity is negative frequency‐dependent selection acting among the different species, and that some of these interactions are intransitive, another mechanism known to promote diversity.     

Predicting protein structural classes with pseudo amino acid composition: an approach using geometric moments of cellular automaton image

A novel approach was developed for predicting the structural classes of proteins based on their sequences. It was assumed that proteins belonging to the same structural class must bear some sort of similar texture on the images generated by the cellular automaton evolving rule [Wolfram, S., 1984. Cellular automation as models of complexity. Nature 311, 419-424]. Based on this, two geometric invariant moment factors derived from the image functions were used as the pseudo amino acid components [Chou, K.C., 2001. Prediction of protein cellular attributes using pseudo amino acid composition. Proteins: Struct., Funct., Genet. (Erratum: ibid., 2001, vol. 44, 60) 43, 246-255] to formulate the protein samples for statistical prediction. The success rates thus obtained on a previously constructed benchmark dataset are quite promising, implying that the cellular automaton image can help to reveal some inherent and subtle features deeply hidden in a pile of long and complicated amino acid sequences.     

A simple mechanism for complex social behavior

The evolution of cooperation is a paradox because natural selection should favor exploitative individuals that avoid paying their fair share of any costs. Such conflict between the self-interests of cooperating individuals often results in the evolution of complex, opponent-specific, social strategies and counterstrategies. However, the genetic and biological mechanisms underlying complex social strategies, and therefore the evolution of cooperative behavior, are largely unknown. To address this dearth of empirical data, we combine mathematical modeling, molecular genetic, and developmental approaches to test whether variation in the production of and response to social signals is sufficient to generate the complex partner-specific social success seen in the social amoeba Dictyostelium discoideum. Firstly, we find that the simple model of production of and response to social signals can generate the sort of apparent complex changes in social behavior seen in this system, without the need for partner recognition. Secondly, measurements of signal production and response in a mutant with a change in a single gene that leads to a shift in social behavior provide support for this model. Finally, these simple measurements of social signaling can also explain complex patterns of variation in social behavior generated by the natural genetic diversity found in isolates collected from the wild. Our studies therefore demonstrate a novel and elegantly simple underlying mechanistic basis for natural variation in complex social strategies in D. discoideum. More generally, they suggest that simple rules governing interactions between individuals can be sufficient to generate a diverse array of outcomes that appear complex and unpredictable when those rules are unknown.     

Extrapolation methods for climate time series revisited – Spatial correlations in climatic fluctuations influence simulated tree species abundance and migration

Simulations of tree population dynamics under past and future climatic changes with time- and space-discrete models often suffer from a lack of detailed long-term climate time series that are required to drive these models. Inter- and extrapolation methods which are applied to generate long-term series differ in terms of whether they do or do not account for spatial correlation of climatic fluctuations. In this study we compared tree species abundance and migration outcomes from simulations using extrapolation methods generating spatially correlated (SC) and spatially independent (SI) climatic fluctuations. We used the spatially explicit and linked forest-landscape model TreeMig and a simple cellular automaton to demonstrate that spatial correlation of climatic fluctuations affects simulation outcomes. We conclude that methods to generate long-term climate time series should account for the spatial correlation of climatic fluctuations found in available climate records when simulating tree species abundance and migration.     

CompuCell, a multi-model framework for simulation of morphogenesis

MOTIVATION: CompuCell is a multi-model software framework for simulation of the development of multicellular organisms known as morphogenesis. It models the interaction of the gene regulatory network with generic cellular mechanisms, such as cell adhesion, division, haptotaxis and chemotaxis. A combination of a state automaton with stochastic local rules and a set of differential equations, including subcellular ordinary differential equations and extracellular reaction-diffusion partial differential equations, model gene regulation. This automaton in turn controls the differentiation of the cells, and cell-cell and cell-extracellular matrix interactions that give rise to cell rearrangements and pattern formation, e.g. mesenchymal condensation. The cellular Potts model, a stochastic model that accurately reproduces cell movement and rearrangement, models cell dynamics. All these models couple in a controllable way, resulting in a powerful and flexible computational environment for morphogenesis, which allows for simultaneous incorporation of growth and spatial patterning. RESULTS: We use CompuCell to simulate the formation of the skeletal architecture in the avian limb bud. AVAILABILITY: Binaries and source code for Microsoft Windows, Linux and Solaris are available for download from http://sourceforge.net/projects/compucell/     

Cellular automaton simulation examining progenitor hierarchy structure effects on mammary ductal carcinoma in situ

A computer simulation is used to model ductal carcinoma in situ, a form of non-invasive breast cancer. The simulation uses known histological morphology, cell types, and stochastic cell proliferation to evolve tumorous growth within a duct. The ductal simulation is based on a hybrid cellular automaton design using genetic rules to determine each cell's behavior. The genetic rules are a mutable abstraction that demonstrate genetic heterogeneity in a population. Our goal was to examine the role (if any) that recently discovered mammary stem cell hierarchies play in genetic heterogeneity, DCIS initiation and aggressiveness. Results show that simpler progenitor hierarchies result in greater genetic heterogeneity and evolve DCIS significantly faster. However, the more complex progenitor hierarchy structure was able to sustain the rapid reproduction of a cancer cell population for longer periods of time.     

Genetic and molecular mechanisms of pattern formation inArabidopsis flower development

One of the great unanswered questions in the biology of both plants and animals is “How do simple groups of embryonic cells develop into complex and highly structured organisms, or parts of organisms?” The answers are only beginning to be known; the processes involved include establishment of positional information, and its interpretation into patterns of cell division and cellular differentiation. One remarkable and attractive example of the formation of a complex structure from a simple group of cells is the development of a flower, with its characteristic types, numbers and patterns of floral organs. Because of the ease with which plants (especially the plantArabidopsis thaliana) can be manipulated in the laboratory, flowers provide a unique opportunity to learn some of the fundamental rules of development.     

Plant Vascular Biology and Agriculture

<正>The evolution of animal and plant vascular systems played a pivotal role in the advancement from simple to complex organisms, through the provision of a delivery system for the distribution     

Worms by number

This paper investigates alternation patterns in length, shape and orientation of dorsal cirri (fleshy segmental appendages) of phyllodocidans, a large group of polychaete worms (Annelida). We document the alternation patterns in several families of Phyllodocida (Syllidae, Hesionidae, Sigalionidae, Polynoidae, Aphroditidae and Acoetidae) and identify the simple mathematical rule bases that describe the progression of these sequences. Two fundamentally different binary alternation patterns were found on the first four segments: 1011 for nereidiform families and 1010 for aphroditiform families. The alternation pattern in all aphroditiform families matches a simple one-dimensional cellular automaton and that for Syllidae (nereidiform) matches the Fibonacci string sequence. Hesionidae (nereidiform) showed the greatest variation in alternation patterns, but all corresponded to various known substitution rules. Comparison of binary patterns of the first 22 segments using a distance measure supports the current ideas on phylogeny within Phyllodocida. These results suggest that gene(s) involved in post-larval segmental growth employ a switching sequence that corresponds to simple mathematical substitution rules.     

Linking Myometrial Physiology to Intrauterine Pressure; How Tissue-Level Contractions Create Uterine Contractions of Labor

The mechanisms used to coordinate uterine contractions are not known. We develop a new model based on the proposal that there is a maximum distance to which action potentials can propagate in the uterine wall. This establishes “regions”, where one action potential burst can rapidly recruit all the tissue. Regions are recruited into an organ-level contraction via a stretch-initiated contraction mechanism (myometrial myogenic response). Each uterine contraction begins with a regional contraction, which slightly increases intrauterine pressure. Higher pressure raises tension throughout the uterine wall, which initiates contractions of more regions and further increases pressure. The positive feedback synchronizes regional contractions into an organ-level contraction. Cellular automaton (CA) simulations are performed with Mathematica. Each “cell” is a region that is assigned an action potential threshold. An anatomy sensitivity factor converts intrauterine pressure to regional tension through the Law of Laplace. A regional contraction occurs when regional tension exceeds regional threshold. Other input variables are: starting and minimum pressure, burst and refractory period durations, enhanced contractile activity during an electrical burst, and reduced activity during the refractory period. Complex patterns of pressure development are seen that mimic the contraction patterns observed in laboring women. Emergent behavior is observed, including global synchronization, multiple pace making regions, and system memory of prior conditions. The complex effects of nifedipine and oxytocin exposure are simulated. The force produced can vary as a nonlinear function of the number of regions. The simulation directly links tissue-level physiology to human labor. The concept of a uterine pacemaker is re-evaluated because pace making activity may occur well before expression of a contraction. We propose a new classification system for biological CAs that parallels the 4-class system of Wolfram. However, instead of classifying the rules, biological CAs should classify the set of input values for the rules that describe the relevant biology.     

BIO-LGCA: A cellular automaton modelling class for analysing collective cell migration

Collective dynamics in multicellular systems such as biological organs and tissues plays a key role in biological development, regeneration, and pathological conditions. Collective tissue dynamics—understood as population behaviour arising from the interplay of the constituting discrete cells—can be studied with on- and off-lattice agent-based models. However, classical on-lattice agent-based models, also known as cellular automata, fail to replicate key aspects of collective migration, which is a central instance of collective behaviour in multicellular systems. To overcome drawbacks of classical on-lattice models, we introduce an on-lattice, agent-based modelling class for collective cell migration, which we call biological lattice-gas cellular automaton (BIO-LGCA). The BIO-LGCA is characterised by synchronous time updates, and the explicit consideration of individual cell velocities. While rules in classical cellular automata are typically chosen ad hoc, rules for cell-cell and cell-environment interactions in the BIO-LGCA can also be derived from experimental cell migration data or biophysical laws for individual cell migration. We introduce elementary BIO-LGCA models of fundamental cell interactions, which may be combined in a modular fashion to model complex multicellular phenomena. We exemplify the mathematical mean-field analysis of specific BIO-LGCA models, which allows to explain collective behaviour. The first example predicts the formation of clusters in adhesively interacting cells. The second example is based on a novel BIO-LGCA combining adhesive interactions and alignment. For this model, our analysis clarifies the nature of the recently discovered invasion plasticity of breast cancer cells in heterogeneous environments.     

Emergence of complex social networks from spatial structure and rules of thumb: a modelling approach

Individual-based computer models show that simple heuristic governing individuals’ behavior may suffice to generate complex patterns of social behavior at the group level such as those observed in animal societies. ‘GrooFiWorld’ is an example of such kind of computer models. In this model, self-organization and simple behavioral rules generate complex patterns of social behavior like those described in tolerant and intolerant societies of macaques. Social complexity results from the socio-spatial structure of the group, the nature of which is, in turn, a side-effect of intensity of aggression. The model suggests that a similar mechanism may give rise to complex social structures in macaques. It is, however, unknown if the spatial structure of the model and that of macaques are indeed similar. Here we used social networks analysis as a proxy for spatial structure of the group. Our findings show that the social networks of the model share similar qualitative features with those of macaques. As group size increases, the density and the average individual eigenvector centrality decrease and the modularity and centralization of the network increase. In social networks emerging from simulations resembling intolerant societies the density is lower, the modularity and centralization are higher, and the individuals ranking higher in the dominance hierarchy are more central than in the social networks emerging from simulations resembling egalitarian societies. Given the qualitative similarity between the social networks of the model and that of empirical data, our results suggest that the spatial structure of macaques is similar to that of the model. It seems thus plausible that, as in the model, the spatial structure combined with simple behavioral rules plays a role in the emergence of complex social networks and complex social behavior in macaques.     

Using priced timed automaton to analyse the energy consumption in cloud computing environment

According to the fact that cloud servers have different energy consumption on different running states, as well as the energy waste problem caused by the mismatching between cloud servers and cloud tasks, we carry out researches on the energy optimal method achieved by a priced timed automaton for the cloud computing center in this paper. The priced timed automaton is used to model the running behaviors of the cloud computing system. After introducing the matching matrix of cloud tasks and cloud resources as well as the power matrix of the running states of cloud servers, we design a generation algorithm for the cloud system automaton based on the generation rules and reduction rules given ahead. Then, we propose another algorithm to settle the minimum path energy consumption problem in the cloud system automaton, therefore obtaining an energy optimal solution and an energy optimal value for the cloud system. A case study and repeated experimental analyses manifest that our method is effective and feasible.     

Approximating Optimal Behavioural Strategies Down to Rules-of-Thumb: Energy Reserve Changes in Pairs of Social Foragers

Functional explanations of behaviour often propose optimal strategies for organisms to follow. These ‘best’ strategies could be difficult to perform given biological constraints such as neural architecture and physiological constraints. Instead, simple heuristics or ‘rules-of-thumb’ that approximate these optimal strategies may instead be performed. From a modelling perspective, rules-of-thumb are also useful tools for considering how group behaviour is shaped by the behaviours of individuals. Using simple rules-of-thumb reduces the complexity of these models, but care needs to be taken to use rules that are biologically relevant. Here, we investigate the similarity between the outputs of a two-player dynamic foraging game (which generated optimal but complex solutions) and a computational simulation of the behaviours of the two members of a foraging pair, who instead followed a rule-of-thumb approximation of the game''s output. The original game generated complex results, and we demonstrate here that the simulations following the much-simplified rules-of-thumb also generate complex results, suggesting that the rule-of-thumb was sufficient to make some of the model outcomes unpredictable. There was some agreement between both modelling techniques, but some differences arose – particularly when pair members were not identical in how they gained and lost energy. We argue that exploring how rules-of-thumb perform in comparison to their optimal counterparts is an important exercise for biologically validating the output of agent-based models of group behaviour.     

From intracellular signaling to population oscillations: bridging size- and time-scales in collective behavior

Collective behavior in cellular populations is coordinated by biochemical signaling networks within individual cells. Connecting the dynamics of these intracellular networks to the population phenomena they control poses a considerable challenge because of network complexity and our limited knowledge of kinetic parameters. However, from physical systems, we know that behavioral changes in the individual constituents of a collectively behaving system occur in a limited number of well-defined classes, and these can be described using simple models. Here, we apply such an approach to the emergence of collective oscillations in cellular populations of the social amoeba Dictyostelium discoideum. Through direct tests of our model with quantitative in vivo measurements of single-cell and population signaling dynamics, we show how a simple model can effectively describe a complex molecular signaling network at multiple size and temporal scales. The model predicts novel noise-driven single-cell and population-level signaling phenomena that we then experimentally observe. Our results suggest that like physical systems, collective behavior in biology may be universal and described using simple mathematical models.     

Bioinspirations: cell-inspired small-scale systems for enabling studies in experimental biomechanics

Biomechanical forces govern the behaviors of organisms and their environment and examining these behaviors to understand the underlying phenomena is an important challenge. One experimental approach for probing these interactions between organisms and their biomechanical environment uses biologically-inspired, artificial surrogates that reproduce organic mechanical systems. For the case of complex, multicellular organisms, robot surrogates have been particularly effective, such as in the analysis of the fins of fish and insects' wings. This biologically-inspired approach is also exciting when examining cell-scale responses as multicellular organisms' behavior is directly influenced by the integrated interactions of smaller-scale components (i.e., cells). In this review, we introduce the burgeoning field of engineering of artificial cells, which focuses on developing cell-scale entities replicating cellular behaviors. We describe both a bottom-up approach to constructing artificial cells, using molecular components to directly assemble artificial cells, as well as a top-down approach, in which living cells are encapsulated in a single entity whose behavior is determined by its constituent members. In particular, we discuss the potential role of these artificial cells as implantable controllers, designed to alter the mechanical behavior of a host organism. Eventually, artificial cells designed to function as small-scale controllers may help alter organisms' phenotypes.     

A canonical model of multistability and scale-invariance in biological systems

Multistability and scale-invariant fluctuations occur in a wide variety of biological organisms from bacteria to humans as well as financial, chemical and complex physical systems. Multistability refers to noise driven switches between multiple weakly stable states. Scale-invariant fluctuations arise when there is an approximately constant ratio between the mean and standard deviation of a system's fluctuations. Both are an important property of human perception, movement, decision making and computation and they occur together in the human alpha rhythm, imparting it with complex dynamical behavior. Here, we elucidate their fundamental dynamical mechanisms in a canonical model of nonlinear bifurcations under stochastic fluctuations. We find that the co-occurrence of multistability and scale-invariant fluctuations mandates two important dynamical properties: Multistability arises in the presence of a subcritical Hopf bifurcation, which generates co-existing attractors, whilst the introduction of multiplicative (state-dependent) noise ensures that as the system jumps between these attractors, fluctuations remain in constant proportion to their mean and their temporal statistics become long-tailed. The simple algebraic construction of this model affords a systematic analysis of the contribution of stochastic and nonlinear processes to cortical rhythms, complementing a recently proposed biophysical model. Similar dynamics also occur in a kinetic model of gene regulation, suggesting universality across a broad class of biological phenomena.