The rational design of theoretical minimal RNA rings predetermines AUG as the universal start codon. This design maximizes coded amino acid diversity over minimal sequence length, defining in silico theoretical minimal RNA rings, candidate ancestral genes. RNA rings code for 21 amino acids and a stop codon after three consecutive translation rounds, and form a degradation‐delaying stem‐loop hairpin. Twenty‐five RNA rings match these constraints, ten start with the universal initiation codon AUG. No first codon bias exists among remaining RNA rings. (...) RNA ring design predetermines AUG as initiation codon. This is the only explanation yet for AUG as start codon. RNA ring design determines additional RNA ring gene‐ and tRNA‐like properties described previously, because it presumably mimics constraints on life's primordial RNAs. (shrink)

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. (shrink)

We give in this paper indications about the dynamical impact 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 . Then, we search what changes in the state values on the boundary could cause some changes of states in the core of the system . After, we analyse the role of the mode of updating on the asymptotics of the (...) network, essentially on the occurrence of limit cycles . Finally, we show the influence of some topological changes on the dynamical behaviour of the system. (shrink)

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. (shrink)

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.). (shrink)

This paper deals with the problem of reconstruction of the intergenic interaction graph from the raw data of genetic co-expression coming with new technologies of bio-arrays (DMA-arrays, protein-arrays, etc.). These new imaging devices in general only give information about the asymptotical part (fixed configurations of co-expression or limit cycles of such configurations) of the dynamical evolution of the regulatory networks (genetic and/or proteic) underlying the functioning of living systems. Extracting the casual structure and interaction coefficients of a gene interaction network (...) from the observed configurations is a complex problem. But if all the fixed configurations are supposedly observed and if they are factorizable into two or more subsets of values, then the interaction graph possesses as many connected components as the number of factors and the solution is obtained in polynomial time. This new result allows us for example to partly solve the topology of the genetic regulatory network ruling the flowering in Arabidopsis thaliana. (shrink)

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 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 tRNAs and micro-RNAs. We conclude by emphasizing some optimal properties of the genetic code. (shrink)

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. (shrink)

The problem of stability in population dynamics concerns many domains of application in demography, biology, mechanics and mathematics. The problem is highly generic and independent of the population considered (human, animals, molecules,…). We give in this paper some examples of population dynamics concerning nucleic acids interacting through direct nucleic binding with small or cyclic RNAs acting on mRNAs or tRNAs as translation factors or through protein complexes expressed by genes and linked to DNA as transcription factors. The networks made of (...) these interactions between nucleic acids (considered respectively as edges and nodes of their interaction graph) are complex, but exhibit simple emergent asymptotic behaviours, when time tends to infinity, called attractors. We show that the quantity called attractor entropy plays a crucial role in the study of the stability and robustness of such genetic networks. (shrink)

Building a meaningful model of biological regulatory network is usually done by specifying the components 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. 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. (shrink)

MicroRNAs are non-coding parts of nuclear and mitochondrial genomes, preventing the weakest part of the genetic regulatory networks from being expressed and preventing the appearance of a too many attractors in these networks. They have also a great influence on the chromatin clock, which ensures the updating of the genetic regulatory networks. The post-transcriptional inhibitory activity by the microRNAs, which is partly unspecific, is due firstly to their possibly direct negative action during translation by hybridizing tRNAs, especially those inside the (...) mitochondrion, hence slowing mitochondrial respiration, and secondly to their action on a large number of putative m-RNA targets like those involved in immunetworks; We show that the circuits in the core of the interaction graphs are responsible for the small number of dedicated attractors that correspond to genetically controlled functions, partly due to a general filtering by the microRNAs. We analyze this influence as well as their impact on important functions like the control by the p53 network over the apoptosis/proliferation system and the homeostasis of the energy metabolism. In this last case, we show the role of two kinds of microRNAs, both involved in the control of the mitochondrial genome: (1) nuclear microRNAs, called mitoMirs, inhibiting mitochondrial genes and (2) putative mitochondrial microRNAs inhibiting the tRNAs functioning. (shrink)

Many apparently complex mechanisms in biology, especially in embryology and molecular biology, can be explained easily by reasoning at the level of the “efficient cause” of the observed phenomenology: the mechanism can then be explained by a simple geometrical argument or a variational principle, leading to the solution of an optimization problem, for example, via the co-existence of a minimization and a maximization problem . Passing from a microscopic level to the macroscopic level often involves an averaging effect that gives (...) birth to a global functional feature . We will illustrate these general principles by building in four different domains of application “a minima” models and showing the main properties of their solutions: extraction of a minimal RNA structure functioning as the first “peptidic machine,” a kind of ancestral ribosome; study of a genetic regulatory network of Drosophila centred on Engrailed gene and expressing successively two genes inside a limit cycle; study of a genetic network regulating neural activity and proliferation in mammals; and study of a simple geometric model of epiboly in zebrafish. (shrink)

Compact set valued iterations generalize classical point iterations quite naturally by replacing the function f with a tube f in the discrete iterations equation. In Section 3, some bifurcation results about logistic tube iterations are given. In Section 4, an analogous dynamical behaviour for the phase response tube involved in the entrainment of the respiratory rhythm is studied.

Theoretical minimal RNA rings are candidate primordial genes evolved for non‐redundant coding of the genetic code's 22 coding signals (one codon per biogenic amino acid, a start and a stop codon) over the shortest possible length: 29520 22‐nucleotide‐long RNA rings solve this min‐max constraint. Numerous RNA ring properties are reminiscent of natural genes. Here we present analyses showing that all RNA rings lack dinucleotide CG (a mutable, chemically instable dinucleotide coding for Arginine), bearing a resemblance to known CG‐depleted genomes. CG (...) in “incomplete” RNA rings (not coding for all coding signals, with only 3–12 nucleotides) gradually decreases towards CG absence in complete, 22‐nucleotide‐long RNA rings. Presumably, feedback loops during RNA ring growth during evolution (when amino acid assignment fixed the genetic code) assigned Arg to codons lacking CG (AGR) to avoid CG. Hence, as a chemical property of base pairs, CG mutability restructured the genetic code, thereby establishing itself as genetically encoded biological information. (shrink)

Modelling contagious diseases needs to include a mechanistic knowledge about contacts between hosts and pathogens as specific as possible, e.g., by incorporating in the model information about social networks through which the disease spreads. The unknown part concerning the contact mechanism can be modelled using a stochastic approach. For that purpose, we revisit SIR models by introducing first a microscopic stochastic version of the contacts between individuals of different populations (namely Susceptible, Infective and Recovering), then by adding a random perturbation (...) in the vicinity of the endemic fixed point of the SIR model and eventually by introducing the definition of various types of random social networks. We propose as example of application to contagious diseases the HIV, and we show that a micro-simulation of individual based modelling (IBM) type can reproduce the current stable incidence of the HIV epidemic in a population of HIV-positive men having sex with men (MSM). (shrink)

Random simulation of complex dynamical systems is generally used in order to obtain information about their asymptotic behaviour (i.e., when time or size of the system tends towards infinity). A fortunate and welcome circumstance in most of the systems studied by physicists, biologists, and economists is the existence of an invariant measure in the state space allowing determination of the frequency with which observation of asymptotic states is possible. Regions found between contour lines of the surface density of this invariant (...) measure are called confiners. An example of such confiners is given for a formal neural network capable of learning. Finally, an application of this methodology is proposed in studying dependency of the network's invariant measure with regard to: 1) the mode of neurone updating (parallel or sequential), and 2) boundary conditions of the network (searching for phase transitions). (shrink)

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. (shrink)

The French school of theoretical biology has been mainly initiated in Poitiers during the sixties by scientists like J. Besson, G. Bouligand, P. Gavaudan, M. P. Schützenberger and R. Thom, launching many new research domains on the fractal dimension, the combinatorial properties of the genetic code and related amino-acids as well as on the genetic regulation of the biological processes. Presently, the biological science knows that RNA molecules are often involved in the regulation of complex genetic networks as effectors, e.g., (...) activators, inhibitors or hybrids. Examples of such networks will be given showing that there exist RNA “relics” that have played an important role during evolution and have survived in many genomes, whose probability distribution of their sub-sequences is quantified by the Shannon entropy, and the robustness of the dynamics of the networks they regulate can be characterized by the Kolmogorov–Sinaï dynamic entropy and attractor entropy. (shrink)

The classical models of epidemics dynamics by Ross and McKendrick have to be revisited in order to incorporate elements coming from the demography (fecundity, mortality and migration) both of host and vector populations and from the diffusion and mutation of infectious agents. The classical approach is indeed dealing with populations supposed to be constant during the epidemic wave, but the presently observed pandemics show duration of their spread during years imposing to take into account the host and vector population changes (...) as well as the transient or permanent migration and diffusion of hosts (susceptible or infected), as well as vectors and infectious agents. Two examples are presented, one concerning the malaria in Mali and the other the plague at the middle-age. (shrink)

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. (shrink)

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. (shrink)

Morphogenesis is a general concept in biology including all the processes which generate tissue shapes and cellular organizations in a living organism. Many hybrid formalizations have been proposed for modelling morphogenesis in embryonic or adult animals, like gastrulation. We propose first to study the ventral furrow invagination as the initial step of gastrulation, early stage of embryogenesis. We focus on the study of the connection between the apical constriction of the ventral cells and the initiation of the invagination. For that, (...) we have created a 3D biomechanical model of the embryo of the Drosophila melanogaster based on the finite element method. Each cell is modelled by an elastic hexahedron contour and is firmly attached to its neighbouring cells. A uniform initial distribution of elastic and contractile forces is applied to cells along the model. Numerical simulations show that invagination starts at ventral curved extremities of the embryo and then propagates to the ventral medial layer. Then, this observation already made in some experiments can be attributed uniquely to the specific shape of the embryo and we provide mechanical evidence to support it. Results of the simulations of the “pill-shaped” geometry of the Drosophila melanogaster embryo are compared with those of a spherical geometry corresponding to the Xenopus lævis embryo. Eventually, we propose to study the influence of cell proliferation on the end of the process of invagination represented by the closure of the ventral furrow. (shrink)

We propose to study the wound healing in Zebrafish by using firstly a differential approach for modelling morphogens diffusion and cell chemotactic motion, and secondly a hybrid model of tissue regeneration, where cells are considered as individual objects and molecular concentrations are described by partial differential equations.