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Theoretical minimal RNA rings attempt to mimick life's primitive RNAs. At most 25 22-nucleotide-long RNA rings code once for each biotic amino acid, a start and a stop codon and form a stem-loop hairpin, resembling consensus tRNAs. We calculated, for each RNA ring's 22 potential splicing positions, similarities of predicted secondary structures with tRNA vs. rRNA secondary structures. Assuming rRNAs partly derived from tRNA accretions, we predict positive associations between relative secondary structure similarities with rRNAs over tRNAs and genetic code integration orders of RNA ring anticodon cognate amino acids. Analyses consider for each secondary structure all nucleotide triplets as potential anticodon. Anticodons for ancient, chemically inert cognate amino acids are most frequent in the 25 RNA rings. For RNA rings with primordial cognate amino acids according to tRNA-homology-derived anticodons, tRNA-homology and coding sequences coincide, these are separate for predicted cognate amino acids that presumably integrated late the genetic code. RNA ring secondary structure similarity with rRNA over tRNA secondary structures associates best with genetic code integration orders of anticodon cognate amino acids when assuming split anticodons (one and two nucleotides at the spliced RNA ring 5' and 3' extremities, respectively), and at predicted anticodon location in the spliced RNA ring's midst. Results confirm RNA ring homologies with tRNAs and CDs, ancestral status of tRNA half genes split at anticodons, the tRNA-rRNA axis of RNA evolution, and that single theoretical minimal RNA rings potentially produce near-complete proto-tRNA sets. Hence genetic code pre-existence determines 25 short circular gene- and tRNA-like RNAs. Accounting for each potential splicing position, each RNA ring potentially translates most amino acids, realistically mimicks evolution of the tRNA-rRNA translation machinery. These RNA rings 'of creation' remind the uroboros' (snake biting its tail) symbolism for creative regeneration.

Building a meaningful model of biological regulatory network is usually done by specifying the components (e.g. the genes) and their interactions, by guessing the values of parameters, by comparing the predicted behaviors to the observed ones, and by modifying in a trial-error process both architecture and parameters in order to reach an optimal fitness. We propose here a different approach to construct and analyze biological models avoiding the trial-error part, where structure and dynamics are represented as formal constraints. We apply the method to Hopfield-like networks, a formalism often used in both neural and regulatory networks modeling. The aim is to characterize automatically the set of all models consistent with all the available knowledge (about structure and behavior). The available knowledge is formalized into formal constraints. The latter are compiled into Boolean formula in conjunctive normal form and then submitted to a Boolean satisfiability solver. This approach allows to formulate a wide range of queries, expressed in a high level language, and possibly integrating formalized intuitions. In order to explore its potential, we use it to find cycles for 3-nodes networks and to determine the flower morphogenesis regulatory network of Arabidopsis thaliana. Applications of this technique are numerous and concern the building of models from data as well as the design of biological networks possessing specified behaviors.

Limit cycles, because they are constituted of a periodic succession of states (discrete or continuous) constitute a good manner to store information. From any points of the state space reached after a perturbation or stimulation of the cognitive system storing this information, one can aim to join through a more or less long return trajectory a precise neighbourhood of the asymptotic trajectory at a specific moment (or a specific place) on the limit cycle, i.e. where the information of interest stands. We propose that the isochronal fibration, initially imagined and described by A. T. Winfree may be an excellent way to connect directly those two locations. Each isochron is indeed the set of points in temporal phase with one single point of the attractor. The characterisation of the isochronal fibration of various dynamical systems is not easy and until now has principally only been done numerically but not analytically. By integrating the homogeneous solutions of the dynamical system we can solve this fibration in the case of the well known anharmonic pendulum. Other isochronal fibration on classical examples such as the van der Pol system and the non-symmetrical PFK limit cycle are obtained numerically and we also provide the first numerical study on 3-dimentional systems like the anharmonic pendulum with a linear relaxation on its third variable and the Lorenz attractor. The empirical approach seems us useful for dealing with the isochronal fibration which could constitute a powerful tool for understanding and controlling the dynamics of biological or biological-inspired systems.

The chronologic age classically used in demography is often unable to give useful information about which exact stage in development or aging processes has reached an organism. Hence, we propose here to explain in some applications for what reason the chronologic age fails in explaining totally the observed state of an organism, which leads to propose a new notion, the biological age. This biological age is essentially determined by the number of divisions before the Hayflick's limit the tissue or mitochondrion in a critical organ (in the sense where its loss causes the death of the whole organism) has already used for its development and adult phases. We give a precise definition of the biological age of an organ based on the Hayflick's limit of its cells and we introduce a desynchronization index (the cell entropy) for some critical tissues or membranes, which are mainly skin, intestinal endothelium, alveoli epithelium and mitochondrial inner membrane. In these actively metabolising interface tissues or membranes, there is a rapid turnover of cells, of their cytoplasmic constituents such as proteins, and of membrane lipids. The boundaries corresponding to these tissues, cells or membranes have vital functions of interface with the environment (protection, homeothermy, nutrition and respiration) and have a rapid turnover (the total cell renewal time is in mice equal to 3 weeks for the skin, 1.5 day for the intestine, 4 months for the alveolae and 11 days for mitochondrial inner membrane) conditioning their biological age. The biological age of a tissue is made of two major components: (1) first, its embryonic age based on the distance (in number of divisions) between the birth date of its first differentiated cell and the time until it reaches its final boundary at the end of its development and (2) second, its adult age whose complement until its death is just the lapse of time made of the sum of remaining cell cycle durations authorized by its Hayflick's limit. From this definition, we calculate the global biological lifespan of an organism and revisit notions like demographic survival curves, duration and synchrony of cell cycles, living boundaries from proto-cells to organs, and embryonic and adult phases duration.

We give in this paper indications about the dynamical impact (as phenotypic changes) coming from the main sources of perturbation in biological regulatory networks. First, we define the boundary of the interaction graph expressing the regulations between the main elements of the network (genes, proteins, metabolites, ...). Then, we search what changes in the state values on the boundary could cause some changes of states in the core of the system (robustness to boundary conditions). After, we analyse the role of the mode of updating (sequential, block sequential or parallel) on the asymptotics of the network, essentially on the occurrence of limit cycles (robustness to updating methods). Finally, we show the influence of some topological changes (e.g. suppression or addition of interactions) on the dynamical behaviour of the system (robustness to topology perturbations).

The genetic code has evolved from its initial non-degenerate wobble version until reaching its present state of degeneracy. By using the stereochemical hypothesis, we revisit the problem of codon assignations to the synonymy classes of amino-acids. We obtain these classes with a simple classifier based on physico-chemical properties of nucleic bases, like hydrophobicity and molecular weight. Then we propose simple RNA (or more generally XNA, with X for D, P or R) ring structures that present, overlap included, one and only one codon by synonymy class as solutions of a combinatory variational problem. We compare these solutions to sequences of present RNAs considered as relics, with a high interspecific invariance, like invariant parts of (t)RNAs and micro-RNAs. We conclude by emphasizing some optimal properties of the genetic code.

Morphogenesis is a key process in developmental biology. An important issue is the understanding of the generation of shape and cellular organisation in tissues. Despite of their great diversity, morphogenetic processes share common features. This work is an attempt to describe this diversity using the same formalism based on a cellular description. Tissue is seen as a multi-cellular system whose behaviour is the result of all constitutive cells dynamics. Morphogenesis is then considered as a spatiotemporal organization of cells activities. We show how this formalism relies on Reaction-Diffusion/Positional Information approach and how it permits to generalize its modelling possibilities. Three quite different applications for concrete morphogenetic processes are presented. The first one is a model for epithelial invagination, the second is a model of cellular differentiation by local cell-cell signalling. The last example is the secondary radial growth of conifer trees. From the mathematical point of view, different modelling tools are used according to the specificity of each process.

Both the physiological and the pathological morphogenetic processes that we can meet in embryogenesis, neogenesis and degenerative dysgenesis present common features: they are ruled by three different kinds of mechanisms, one related to cell migration, the second to cell differentiation and the third to cell proliferation. We deal here with an application to the cambial growth which essentially involves the third type of mechanism. Woody plants produce secondary tissue (secondary xylem and phloem) from a meristematic tissue called vascular cambium, responsible for the radial growth of a tree. This paper focuses on the formation of secondary xylem, considered in two dimensions in a cross-section framework. A new discrete modelling approach is used, based on the cellular scale, in order to attain a more accurate understanding of how the elementary microscopic behaviour of each cell takes part in the macroscopic morphogenesis. The mathematical model essentially uses an occurrence method simulating the main features of radial growth with simple geometric rules, such as Thom's division rule (Thom,1972)to account for the cell proliferation. The study applies to concrete instances in which the changes made in the geometrical cellular patterns of the vascular cambium clearly affect the shape of the tree, as in Pinus radiata (D. Don.).

This article addresses the physical chemical processes underlying biological self-organisation by which a homogenous solution of reacting chemicals spontaneously self-organises. Theoreticians have predicted that self-organisation can arise from a coupling of reactive processes with molecular diffusion. In addition, the presence of an external field, such as gravity, at a critical moment early in the process may determine the morphology that subsequently develops. The formation, in-vitro, of microtubules, a constituent of the cellular skeleton, shows this type of behaviour. The preparations spontaneously self-organise by reaction-diffusion and the morphology that develops depends upon the presence of gravity at a critical bifurcation time early in the process. Here, we present numerical simulations of a population of microtubules that reproduce this behaviour. Microtubules can grow from one end whilst shrinking from the other. The shrinking end leaves behind a chemical trail of high tubulin concentration. Neighbouring microtubules preferentially grow into these regions, whilst avoiding regions of low tubulin concentration. The chemical trails produced by individual microtubules thus activate and inhibit the formation of neighbouring microtubules and this progressively leads to self-organisation. Gravity acts by way of its directional interaction with the macroscopic density fluctuations present in the solution arising from microtubule disassembly.

Increasing interest has been paid to applications of fluorescence measurements to analyze physiological mechanisms in living cells. However, few studies have taken advantage of DNA quantification by fluorometry for dynamic assessment of chromatin organization as well as cell motion during the cell cycle. This approach involves both optimal conditions for DNA staining and cell tracking methods. In this context, this report describes a stoichiometric method for nuclear DNA specific staining, using the bisbenzimidazole dye Hoechst 33342 associated with verapamil, a calcium membrane channel blocker. This method makes it possible to correlate variations of nuclear DNA content with cell motion in cells that are maintained alive. Motion measurement is the second goal of this paper and it explains the snake-spline method, and the associated cell following method.