Predictability in Cellular Automata

Modelled as finite homogeneous Markov chains, probabilistic cellular automata with local transition probabilities in (0, 1) always posses a stationary distribution. This result alone is not very helpful when it comes to predicting the final configuration; one needs also a formula connecting the probabilities in the stationary distribution to some intrinsic feature of the lattice configuration. Previous results on the asynchronous cellular automata have showed that such feature really exists. It is the number of zero-one borders within the automaton''s binary configuration. An exponential formula in the number of zero-one borders has been proved for the 1-D, 2-D and 3-D asynchronous automata with neighborhood three, five and seven, respectively. We perform computer experiments on a synchronous cellular automaton to check whether the empirical distribution obeys also that theoretical formula. The numerical results indicate a perfect fit for neighbourhood three and five, which opens the way for a rigorous proof of the formula in this new, synchronous case.     

Combinatorial Properties of Some Cellular Automata Related to the Mosaic Cycle Concept

A cellular automaton that is related to the "mosaic cycle concept" is considered. We explain why such automata sustain very often, but not always, n-periodic trajectories (n being the number of states of the automaton). Our work is a first step in the direction of a theory of these type of automata which might be useful in modeling mosaic successions.     

Adaptive properties of living beings: proposal for a generic mechanism. (Self-programming machines III)

Living systems are capable to have appropriate responses to unpredictable environment. This kind of self-organization seems to operate as a self-programming machine, i.e. an organization able to modify itself. Until now the models of self-organization of living beings proposed are functions solutions of differential systems or transition functions of automata. These functions are fixed and these models are therefore unable to modify their organization. On the other hand, computer science propose a lot of models having the properties of adaptive systems of living beings, but all these models depend on the comparison between a goal and the results and ingenious choices of parameters by programmers, whereas there are no programmer's intention nor choice in the living systems. From two best known examples of adaptive systems of living beings, nervous system and immune system that have in common that the external signals modify the rewriting of their organization and therefore work as self-organizing machines, we devised machines with a finite set of inputs, based upon a recurrence, are able to rewrite their organization (Self-programming machines or m(sp)) whenever external conditions vary and have striking properties of adaptation. M(sp) have similar properties whatever the operation defining the recurrence maybe. These results bring us to make the following statement: adaptive properties of living systems can be explained by their ability to rewrite their organization whenever external conditions vary under the only assumption that the rewriting mechanism be a deterministic constant recurrence in a finite state set.     

Automata network theories in immunology: Their utility and their underdetermination

Small networks of threshold automata are used to model complex interactions between populations of regulatory cells (helpers and suppressors, antigen specific and anti-idiotypic) which participate in the immune response. The models, being discrete and semiquantitative, are well adapted to the situation of incomplete information often encounteredin vivo. However, the dynamics of many different network structures usually end up in the same attractor set. Thus, many different theories are equivalent in their explicative power for the same facts. This property, known as underdetermination of the theories by the facts, is given a quantitative estimate. It appears that such an underdetermination, as a kind of irreductible complexity, can be expected in manyin vivo biological processes, even when the number of interacting and functionally coupled elements is relatively small.     

Automata simulation of the selection process

A complete simulation of the selection process can be constructed using a population of self-replicating finite-state automata. The entire population is challenged with a repeating sequence of inputs, and those individuals that are best able to recognize the input sequence are allowed to replicate most rapidly. Replication proceeds with imperfect fidelity, so that under the constraint of constant total population size, a quasispecies distribution of error copies is obtained. The operation of this simulation provides an essential representation of an evolving system. When the input sequence is altered, the structure of the existing population is destabilized, and a new quasispecies distribution emerges. The ability of the system to respond to changes in the input and the structure of the quasispecies distribution are shown to be critically dependent on the fidelity of replication.     

Energy minimization method using automata network for sequence and side-chain conformation prediction from given backbone geometry

Globular proteins have high packing densities as a result of residue side chains in the core achieving a tight, complementary packing. The internal packing is considered the main determinant of native protein structure. From that point of view, we present here a method of energy minimization using an automata network to predict a set of amino acid sequences and their side-chain conformations from a desired backbone geometry for de novo design of proteins. Using discrete side-chain conformations, that is, rotamers, the sequence generation problem from a given backbone geometry becomes one of combinatorial problems. We focused on the residues composing the interior core region and predicted a set of amino acid Sequences and their side-chain conformations only from a given backbone geometry. The kinds of residues were restricted to six hydrophobic amino acids (Ala, Ile, Met, Leu, Phe, and Val) because the core regions are almost always composed of hydrophobic residues. The obtained sequences were well packed as was the native sequence. The method can be used for automated sequence generation in the de novo design of proteins. © 1994 Wiley-Liss, Inc.     

Categories of (ℓ, ℛ)-systems

We show that when we represent (ℓ, ℛ)-systems with fixed genome as automata (sequential machines), we get automata with output-dependent states. This yields a short proof that ((ℓ, ℛ)-systems from a subcategory of automata—and with more homomorphisms than previously exhibited. We show how ((ℓ, ℛ)-systems with variable genetic structure may be represented as automata and use this embedding to set up a larger subcategory of the category of automata. An analogy with dynamical systems is briefly discussed. This paper presents a formal exploration and extension of some of the ideas presented by Rosen (Bull. Math. Biophyss,26, 103–111, 1964;28, 141–148;28 149–151). We refer the reader to these papers, and references cited therein, for a discussion of the relevance of this material to relational biology.     

Neurosemantics,neurons and system theory

Following the concept of internal representations, signal processing in a neuronal system has to be evaluated exclusively based on internal system characteristics. Thus, this approach omits the external observer as a control function for sensory integration. Instead, the configuration of the system and its computational performance are the effects of endogenous factors. Such self-referential operation is due to a strictly local computation in a network and, thereby, computations follow a set of rules that constitute the emergent behaviour of the system. These rules can be shown to correspond to a “logic” that is intrinsic to the system, an idea which provides the basis for neurosemantics.     

A structural perspective on the dynamics of kinesin motors

Despite significant fluctuation under thermal noise, biological machines in cells perform their tasks with exquisite precision. Using molecular simulation of a coarse-grained model and theoretical arguments, we envisaged how kinesin, a prototype of biological machines, generates force and regulates its dynamics to sustain persistent motor action. A structure-based model, which can be versatile in adapting its structure to external stresses while maintaining its native fold, was employed to account for several features of kinesin dynamics along the biochemical cycle. This analysis complements our current understandings of kinesin dynamics and connections to experiments. We propose a thermodynamic cycle for kinesin that emphasizes the mechanical and regulatory role of the neck linker and clarify issues related to the motor directionality, and the difference between the external stalling force and the internal tension responsible for the head-head coordination. The comparison between the thermodynamic cycle of kinesin and macroscopic heat engines highlights the importance of structural change as the source of work production in biomolecular machines.     

Computational Modeling of Proteins based on Cellular Automata: A Method of HP Folding Approximation

The design of a protein folding approximation algorithm is not straightforward even when a simplified model is used. The folding problem is a combinatorial problem, where approximation and heuristic algorithms are usually used to find near optimal folds of proteins primary structures. Approximation algorithms provide guarantees on the distance to the optimal solution. The folding approximation approach proposed here depends on two-dimensional cellular automata to fold proteins presented in a well-studied simplified model called the hydrophobic–hydrophilic model. Cellular automata are discrete computational models that rely on local rules to produce some overall global behavior. One-third and one-fourth approximation algorithms choose a subset of the hydrophobic amino acids to form H–H contacts. Those algorithms start with finding a point to fold the protein sequence into two sides where one side ignores H’s at even positions and the other side ignores H’s at odd positions. In addition, blocks or groups of amino acids fold the same way according to a predefined normal form. We intend to improve approximation algorithms by considering all hydrophobic amino acids and folding based on the local neighborhood instead of using normal forms. The CA does not assume a fixed folding point. The proposed approach guarantees one half approximation minus the H–H endpoints. This lower bound guaranteed applies to short sequences only. This is proved as the core and the folds of the protein will have two identical sides for all short sequences.     

Principles of biological pattern formation: swarming and aggregation viewed as selforganization phenomena

Migration automaton models are introduced which offer the possibility to directly analyse essential selforganization properties of biological pattern formation at the cellular level. We present examples of migration automata as models of collective motion and cellular aggregation—patterns that are typical for example in the life cycle of Myxobacteria. Linear stability analysis of the corresponding automaton Boltzmann equation allows to distinguish orientation-dependent (collective motion) and density-dependent (aggregation) instabilities. Presented at the National Symposium on Evolution of Life.     

Computer simulation of the effects of shoe cushioning on internal and external loading during running impacts

Biomechanical aspects of running injuries are often inferred from external loading measurements. However, previous research has suggested that relationships between external loading and potential injury-inducing internal loads can be complex and nonintuitive. Further, the loading response to training interventions can vary widely between subjects. In this study, we use a subject-specific computer simulation approach to estimate internal and external loading of the distal tibia during the impact phase for two runners when running in shoes with different midsole cushioning parameters. The results suggest that: (1) changes in tibial loading induced by footwear are not reflected by changes in ground reaction force (GRF) magnitudes; (2) the GRF loading rate is a better surrogate measure of tibial loading and stress fracture risk than the GRF magnitude; and (3) averaging results across groups may potentially mask differential responses to training interventions between individuals.     

Hydrodynamics optimization in butterfly swimming: position, drag coefficient and performance.

A kinematic study allowed to define the three most propulsive positions during a butterfly swimming cycle, which were: the end of the external sweep, the end of the internal sweep and the end of thrust. These instantaneous positions were different for the ex-world champion Pankratov when compared to another swimmer. Using manikins and a drag-measuring device, we showed that the end of the internal sweep induced the highest drag values and that Pankratov may reduce energy expenditure by taking up a particular position during the end of the swimming cycle. These results point out the relations between swimming movements, passive drag and swimmers' performance.     

Genital variation in a dimorphic moth Selenia tetralunaria (Lepidoptera, Geometridae)

Insect genitals vary greatly among species and provide a key tool for species-level taxonomy. Insects differing in the genitalia are often treated as discrete, reproductively isolated species. This principle dates back to the lock-and-key hypothesis, which states that genitalia vary between species in order to provide a mechanical reproductive isolation system. Thus, the hypothesis assumes low within-species variability in genital traits. However, recent studies suggest that sexual selection may be responsible for the evolution of insect genitalia. We studied allometry and genital size and shape variation in a dimorphic moth Selenia tetralunaria . We found that the genitalia showed negative allometry in relation to body size as reported in many insect and spider species. This allometry was stronger in internal genital structures than it was in external genitalia. We also found that there was more variation in internal compared with external genitalia. Finally, we found that the shape of genital structures differed between morphs in all three examined areas. S. tetralunaria is among the first reported cases of genitally dimorphic insect species. Considerable variation in internal genitalia and especially the presence of genital shape differences between morphs were not consistent with the predictions of the lock-and-key hypothesis.  © 2006 The Linnean Society of London, Biological Journal of the Linnean Society , 2006, 87 , 297–307.     

Optical measurement of mechanical forces inside short DNA loops

Knowledge of the mechanical properties of double-stranded DNA (dsDNA) is essential to understand the role of dsDNA looping in gene regulation and the mechanochemistry of molecular machines that operate on dsDNA. Here, we use a newly developed tool, force sensors with optical readout, to measure the forces inside short, strained loops composed of both dsDNA and single-stranded DNA. By varying the length of the loops and their proportion of dsDNA, it was possible to vary their internal forces from 1 pN to >20 pN. Surprisingly, internal loop forces changed erratically as the amount of dsDNA was increased for a given loop length, with the effect most notable in the smallest loop (57 nucleotides). Monte Carlo simulations based on the helical wormlike chain model accurately predict internal forces when more than half of the loop is dsDNA but fail otherwise. Mismatches engineered into the double-stranded regions increased flexibility, suggesting that Watson-Crick basepaired dsDNA can withstand high compressive forces without recourse to multibase melts. Fluorescence correlation spectroscopy further excluded transient melting (microsecond to millisecond duration) as a mechanism for relief of compressive forces in the tested dsDNAs. DNA loops with integrated force sensors may allow the comprehensive mapping of the elasticity of short dsDNAs as a function of both sequence and salt.     

Plant uptake of radiocaesium: a review of mechanisms, regulation and application

Soil contamination with radiocaesium (Cs) has a long-term radiological impact because it is readily transferred through food chains to human beings. Plant uptake is the major pathway for the migration of radiocaesium from soil to human diet. The plant-related factors that control the uptake of radiocaesium are reviewed. Of these, K supply exerts the greatest influence on Cs uptake from solution. It appears that the uptake of radiocaesium is operated mainly by two transport pathways on plant root cell membranes, namely the K(+) transporter and the K(+) channel pathway. Cationic interactions between K and Cs on isolated K-channels or K transporters are in agreement with studies using intact plants. The K(+) transporter functioning at low external potassium concentration (often <0.3 mM) shows little discrimination against Cs(+), while the K(+) channel is dominant at high external potassium concentration with high discrimination against Cs(+). Caesium has a high mobility within plants. Although radiocaesium is most likely taken up by the K transport systems within the plant, the Cs:K ratio is not uniform within the plant. Difference in internal Cs concentration (when expressed on a dry mass basis) may vary by a factor of 20 between different plant species grown under similar conditions. Phytoremediation may be a possible option to decontaminate radiocaesium-contaminated soils, but its major limitation is that it takes an excessively long time (tens of years) and produces large volumes of waste.     

Diversity and survival of artificial lifeforms under sedimentation and random motion

Cellular automata are often used to explore the numerous possible scenarios of what could have occurred at the origins of life and before, during the prebiotic ages, when very simple molecules started to assemble and organise into larger catalytic or informative structures, or to simulate ecosystems. Artificial self-maintained spatial structures emerge in cellular automata and are often used to represent molecules or living organisms. They converge generally towards homogeneous stationary soups of still-life creatures. It is hard for an observer to believe they are similar to living systems, in particular because nothing is moving anymore within such simulated environments after few computation steps, because they present isotropic spatial organisation, because the diversity of self-maintained morphologies is poor, and because when stationary states are reached the creatures are immortal. Natural living systems, on the contrary, are composed of a high diversity of creatures in interaction having limited lifetimes and generally present a certain anisotropy of their spatial organisation, in particular frontiers and interfaces. In the present work, we propose that the presence of directional weak fields such as gravity may counter-balance the excess of mixing and disorder caused by Brownian motion and favour the appearance of specific regions, i.e. different strata or environmental layers, in which physical–chemical conditions favour the emergence and the survival of self-maintained spatial structures including living systems. We test this hypothesis by way of numerical simulations of a very simplified ecosystem model. We use the well-known Game of Life to which we add rules simulating both sedimentation forces and thermal agitation. We show that this leads to more active (vitality and biodiversity) and robust (survival) dynamics. This effectively suggests that coupling such physical processes to reactive systems allows the separation of environments into different milieux and could constitute a simple mechanism to form ecosystem frontiers or elementary interfaces that would protect and favour the development of fragile auto-poietic systems.     

Unraveling proteins: a molecular mechanics study

An internal coordinate molecular mechanics study of unfolding peptide chains by external stretching has been carried out to predict the type of force spectra that may be expected from single-molecule manipulation experiments currently being prepared. Rather than modeling the stretching of a given protein, we have looked at the behavior of simple secondary structure elements (alpha-helix, beta-ribbon, and interacting alpha-helices) to estimate the magnitude of the forces involved in their unfolding or separation and the dependence of these forces on the way pulling is carried out as well as on the length of the structural elements. The results point to a hierarchy of forces covering a surprisingly large range and to important orientational effects in the response to external stress.