Decompression sickness can occur in divers even when recommended decompression procedures are followed. Furthermore, the physiological state of individuals can significantly affect bubbling variability. These informations highlight the need for personalized input to improve decompression in SCUBA diving. The main objective of this study is to propose a fundamental framework for a new approach to inert gas exchanges. A physiological model of oxygen delivery to organs and tissues has been built and adapted to nitrogen. The validation of the model was made by transferring the N2 to CO2. Under normobaric conditions (air breathing, oxygen breathing, and static apnea) and hyperbaric conditions, the O2 model replicates the reference physiological Po2 (Spearman correlation tests P < 0.001). The inert gas models can simulate inert gas partial pressures under normobaric and hyperbaric conditions. However, the lack of reference values prevents direct validation of this new model. Therefore, the N2 model has been transferred to CO2. The resulting CO2 model has been validated by comparing it with physiological reference values (Spearman correlation tests P < 0.01). The validity of the CO2 model constructed from the N2 model demonstrates the plausibility of this physiological model of inert gas exchanges. In the context of personalized decompression procedures, the proposed model is of significant interest as it enables the integration of physiological and morphological parameters (blood and respiratory flows, alveolo-capillary diffusion, respiratory and blood volumes, oxygen consumption rate, fat mass, etc.) into a model of nitrogen saturation/desaturation, in which oxygen and CO2 partial pressures can also be incorporated.NEW & NOTEWORTHY This is the first model of inert gas transport based on the physiology of respiratory gas. It was built for O2 delivery and validated against literature data; it was then transposed to N2 exchanges. The transposition procedure was checked by transposing the N2 model to CO2 (and validated against literature data). This model opens the possibility to integrate physiological and morphological inputs in a personalized decompression procedure in SCUBA diving.

Precambrian metasediments provide a unique archive for understanding Earth’s earliest biosphere, however traces of microbial life preserved in ancient rocks are often controversial. In this study we leveraged several micro- to nano-scale techniques to study filamentous structures previously reported in clastic sediments of the 3.22 Ga Moodies Group, Barberton Greenstone Belt, S. Africa. We performed petrographic, mineralogical, electron microprobe, confocal fluorescence and electron microscopy analyses of these structures in order to evaluate their biogenicity and syngenecity. We also examined drill core samples of deep-water iron formations from the 2.46 Ga Joffre member of the Brockman Iron Formation (Hamersley Basin, W. Australia) to better understand their potential biogenicity. In both cases, we aimed to resolve primary vs. secondary mineral assemblages and their relation to filamentous or sedimentary structures. In the Moodies Group samples, filamentous structures were resolved by confocal imaging and revealed to be crosscut by later metamorphic phases, highlighting their syngenetic nature. Three-dimensional imaging reveals that while the filamentous structures are not necessarily associated with grain boundaries (e.g., as organic coatings), they form both sheets and filaments, complicating their interpretation but not ruling out a biological origin. No organic microstructures appeared to be preserved in our Dales Gorge samples. We also examined the possible application of electron paramagnetic resonance spectroscopy (EPR) to carbonaceous matter in ancient silica-rich matrices, similar to [Bourbin et al. (2013)][1], using samples from the Brockman iron formation. While resonance associated with organic matter was largely unresolvable in the Brockman iron formation samples due to their low organic matter contents, large effects on the EPR spectra were apparent stemming from the presence of magnetic iron minerals, highlighting the need to carefully consider sample composition in EPR analyses targeting ancient organic matter. Collectively, this study highlights the added value of micro- to nano-scale techniques as applied to Precambrian metasediments containing traces of ancient life, for example in revealing the pre-metamorphic emplacement and three-dimensional structure of filaments in the Moodies Group, but also the potential drawbacks and pitfalls, such as the case of strong magnetic mineral interference in EPR analysis of organic matter in trace abundance in the Dales Gorge.### Competing Interest StatementThe authors have declared no competing interest. [1]: #ref-2

In this opinion paper we make the statement that hybrid models in oncology are required as a mean for enhanced data integration. In the context of systems oncology, experimental and clinical data need to be at the heart of the models developments from conception to validation to ensure a relevant use of the models in the clinical context. The main applications pursued are to improve diagnosis and to optimize therapies.We first present the Successes achieved thanks to hybrid modelling approaches to advance knowledge, treatments or drug discovery. Then we present the Challenges that need to be addressed to allow for a better integration of the model parts and of the data into the models. And finally, the Hopes with a focus towards making personalised medicine a reality.

Simulation of complex biological systems with agent-based models is becoming more relevant with the increase in Graphics Processing Unit (GPU) power. In those simulations, up to millions of virtual cells are individually computed, involving daunting processing times. An important part of computational models is the algorithm that manages how agents perceive their surroundings. This can be particularly problematic in three-dimensional environments where agents have deformable virtual membranes. This article presents a GPU algorithm that gives the possibility for agents to integrate the signals scattered on their virtual membrane. It is detailed to be coded in languages like OpenCL or Cuda. Its performances are tested to show its speed with current GPU devices. Finally, it was implemented inside an existing software to test and illustrate the possibilities it offers.

New biomedical advances at cellular level give the possibility to develop more and more accurate computational models of cells. Moreover, the increasing power of graphical processor units allows the simulation of millions of interacting virtual cells. This paper summarizes efforts made to create multicellular simulators, their attended benefits and their inevitable drawbacks. In particular, it presents the new software SimCells that simulate the dynamics of multicellular systems using a graphically programmable multiagent system. A fully functional example of the tumoral and blood vessel codevelopment is also detailed.

Biological growth can be defined as a set of processes that cause tissues or organs to develop and maintain. When simulating this growth in DynCell, a C++ virtual reality simulator, questions arise about how the shape is controlled and maintained in a stable state whilst cells renew. In order to understand tissue growth, we elaborated a mathematical model based on viability theory and morphological analysis. In our model, each cell is defined as a control system. Moreover, each cell includes the same genetic information, which can lead to differentiated cell types. Cells interact with each other during the growth process and take decisions on their fate (cell division, differentiation, migration or apoptosis) according to the genetic information, the position of the other cells and the micro‐environmental cues provided by the extra cellular matrix. From a mathematical point of view, cellular division implies a multi‐valued dynamic. To formalize this dynamic, we have used mutational equations instead of differential equations usually utilized for classic dynamical systems. Cells successively divide according to a controlled topology, and ultimately generate the shape of the organism. This shape reaches a morphological equilibrium, up to a time horizon. To attain a defined topology, it is essential to control cell polarization and cell division. In biological organisms, this control is performed by fractones, extra‐cellular matrix structures anchored near the surface of the cells. Fractones contains heparan sulfate proteoglycans (HSPG) that bind, concentrate and dispatch growth factors to the target cells to ultimatly control cell proliferation and differentiation. Fractones constantly change their HSPG motives to bind different growth factors that either promote or inhibit stem cell proliferation and differentiation. The role of fractones as captors or activators of growth factors ultimately permits biological construction in a much finer mode than with simple reaction‐diffusion models. Using our fractone model, it is possible to generate and renew shapes throughout the tissue except at the interface of tissue layers. Indeed, we have found that our model is not sufficient for cells bordering tissue layers. Therefore, we hypothesize that basement membranes, i.e. specialized coats of extracellular matrix, chemically similar to fractones, become the leading components that control cell proliferation and the layout interface between organized tissues. In conclusion, our model strongly suggests that basement membranes and fractones are essential for the proper control of development and maintenance of biological organisms.This abstract is from the Experimental Biology 2018 Meeting. There is no full text article associated with this abstract published in The FASEB Journal.

Modelling and teaching complex biological systems is a difficult process. Multi-Agent Based Simulations (MABS) have proved to be an appropriate approach both in research and education when dealing with such systems including emergent, self-organizing phenomena. This chapter presents NetBioDyn, an original software aimed at biologists (students, teachers, researchers) to easily build and simulate complex biological mechanisms observed in multicellular and molecular systems. Thanks to its specific graphical user interface guided by the multi-agent paradigm, this software does not need any prerequisite in computer programming. It thus allows users to create in a simple way bottom-up models where unexpected behaviours can emerge from many interacting entities. This multi-platform software has been used in middle schools, high schools and universities since 2010. A qualitative survey is also presented, showing its ability to adapt to a wide and heterogeneous audience. The Java executable and the source code are available online at http://virtulab.univ-brest.fr.

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.

Research done in the last century on Porifera has provided insights into the molecular mechanism of the biological processes of cell adhesion, innate immunity, and self-recognition. Evidence that this mechanism is based on glyconectin selfassembly is shown by the structure to function relationships deduced from studies of carbohydrates isolated from three different sponge species. The structural studies were performed on purified glyconectin carbohydrates from Microciona prolifera, Halichondria panicea and Cliona celata using nuclear magnetic resonance and mass spectrometry. Seventeen novel, speciesspecific carbohydrate sequences were revealed that belong to the Porifera glyconectin family. The functional, cell recognition analyses of carbohydrate self-association were performed by measuring binding forces between individual glycan molecules under physiological conditions; the results show that the association strength between homotypic pairs of glycans (400 pN) are higher than those between heterotypic pairs (20 pN). This difference is sufficient to explain the species-specific separation of glycan-coated beads in vitro and the sorting of cells in nature. We propose that the glyconectin carbohydrates, which are the constituents on the cell surface that are the most exposed to the environment, were responsible for the molecular recognition processes that underpinned the emergence of multi-cellularity.

Modeling and teaching complex biological systems is a difficult process. The Multi-Agent paradigm has proved to be an appropriate approach, both in research and education, to grasp the complexity of these systems and investigating the underlying concepts of emergence and self-organization. As such, Agent-Based software are more and more used in life sciences to implement these models in virtual environments and simulate them. However, most of these software require knowledge and skills in programming languages, such as Java or the NetLogo environment. The gap between most of Agent-Based software prerequisites and the actual programming skills of (future) biologists has to be reduced and the processes of implementing a model and simulate it made more intuitive. To answer this issue, we propose a smart, intuitive and open-source software aimed at biologists (students, teachers, researchers) to easily build and simulate complex biological mechanisms observed in multicellular and molecular systems. Thanks to its specific graphical user interface guided by the Multi-Agent paradigm (entities, behaviors and interactions) NetBioDyn does not need any prerequisite or knowledge in computer programming. It thus allows users to create in a simple way bottom-up models where unexpected behaviors can emerge from simple reactive interacting entities, and test hypothesis by creating various simulations, while providing at any time a simplified and complete view of the system's state. NetBioDyn has been successfully used to investigate systems such as two marine bacteria involved in a predator-prey relationship or the blood coagulation mechanisms in a small section of a vein. Moreover, NetBioDyn tackles the well-known problem of calibrating a model with interdependent, interconnected parameters by including a self-adjusting Multi-Agent System. This tools aims to automatically find the proper values for all the parameters involved in a simulation (interactions’ probabilities, entities’ lifespan etc.) according to real results obtained for example in vitro.

The complexity of biological tissue morphogenesis makes in silico simulations of such system very interesting in order to gain a better understanding of the underlying mechanisms ruling the development of multicellular tissues. This complexity is mainly due to two elements: firstly, biological tissues comprise a large amount of cells; secondly, these cells exhibit complex interactions and behaviors. To address these two issues, we propose two tools: the first one is a virtual cell model that comprise two main elements: firstly, a mechanical structure (membrane, cytoskeleton, and cortex) and secondly, the main behaviors exhibited by biological cells, i.e., mitosis, growth, differentiation, molecule consumption, and production as well as the consideration of the physical constraints issued from the environment. An artificial chemistry is also included in the model. This virtual cell model is coupled to an agent-based formalism. The second tool is a simulator that relies on the OpenCL framework. It allows efficient parallel simulations on heterogenous devices such as micro-processors or graphics processors. We present two case studies validating the implementation of our model in our simulator: cellular proliferation controlled by cell signalling and limb growth in a virtual organism.

By interacting with pathogens, lactic acid bacteria (LAB) are able to contribute to food safety. By means of their lactic acid production which induces pH decrease, LAB influence the growth of pathogens. The aim of this study is to model and simulate lactic acid production, pH evolution, according to carbohydrate concentration in media, temperature, water activity and ratio of both population.

Nous presentons ici une nouvelle approche permettant d'apprehender l'emergence de formes lors du developpement cellulaire. Nous nous sommes fixes comme hypothese qu'au-dela de l'influence des forces mecaniques et de l'expression genetique, les contraintes s'appliquant a la cellule au cours du developpement cellulaire jouaient un role important dans l'acquisition de formes particulieres. Cependant, pour comprendre l'evolution d'un systeme vivant du point de vue informatique, les modeles existants representent individuellement les elements du systeme global puis les mettent en interaction entre eux mais aussi avec un environnement. Ces simulations revelent des effets collectifs inattendus dont la theorie mathematique est parfois tres difficiles a etablir. Pour etudier ce passage de l'individuel au collectif, qui est au cœur des theories recentes de la complexite, on utilise une formalisation issue de la theorie de la viabilite. Les algorithmes s'inspirant de cette theorie decrivent la co-evolution des formes et des contraintes morphologiques au cours des divisions cellulaires. Mais aussi la dynamique de chaque element de l'ensemble, dynamique dependant tout de meme de celle de l'ensemble. La morphogenese que nous etudions ici est donc un processus de generation de formes par un systeme cellulaire evoluant dans le temps a l'aide d'une fonction de controle et soumis a des contraintes. Chaque entite du systeme est une cellule appliquant un controle a chaque pas de temps, regulier. L'ensemble cellule+controle amene le systeme d'un etat a un autre tel qu'il respecte un certain nombre de contraintes. Cette evolution du systeme reste discrete car son etat, son ensemble de controles et son evaluation sont consideres a des intervalles de temps reguliers. L'etude est faite sur l'ensemble des evolutions possibles d'une forme initiale par deux mecanismes cellulaires que sont la mitose et l'apoptose. Les regles d'evolution d'une forme etudiees et comprises avec ces deux mecanismes, permettent de concevoir des controles de feedback en cas de perturbations de la forme. Ce qui nous garantirait par la suite une certaine robustesse de la forme par autopoiese. Cette etude des evolutions d'une forme pose des problemes importants sur le plan algorithmique et informatique. Tout d'abord la representation des ensembles en construction qui necessite beaucoup de memoire. Ensuite, le parcours de ces ensembles qui est souvent tres couteux en temps. Nous avons donc propose un modele pour la representation des ensembles de formes. Ensuite, nous avons developpe des algorithmes pour gouverner la creation et l'evolution de ces ensembles ainsi que la dynamique de chacun de leurs elements. Les algorithmes implementent des concepts de la theorie des ensembles et de la theorie de la viabilite. La theorie de la viabilite [1] propose un ensemble de concepts et de methodes pour controler un systeme dynamique afin de le maintenir dans un ensemble de contraintes de viabilite. Nous caracterisons ici ce qui definit notre modele d'evolution d'ensemble de formes : Etat: l'etat du systeme au temps n est En, l'ensemble des formes atteintes au temps n. Contraintes : pour quitter un etat du systeme vers un autre, c'est a dire pour atteindre un ensemble de formes a partir d'un autre, les cellules dans chaque forme sont soumises a un certain nombre de contraintes. Sur le plan comportemental, elles doivent obeir a des regles biologiques et sur le plan physique, elles doivent respecter les contraintes du voisinage et de l'environnement. Controle : chaque cellule dans chaque forme au temps n est autorisee a appliquer tout controle qui lui permet une action respectant les contraintes a ce temps. Implemente avec le mecanisme de mitose, le programme permet: de connaitre l'ensemble des evolutions futures jusqu'a un temps donne d'une forme initiale placee dans une grille 2D, de disposer de l'ensemble des chemins qui permettent d'arriver a une forme donnee en un temps fini a partir d'une forme initiale, de pouvoir archiver pour chaque forme et chaque etape de sa construction, la dynamique en jeu. Ce modele nous permet de connaitre l'ensemble des formes possibles a n nombre de cellules. Ainsi, il nous est possible de connaitre dans cet ensemble, le chemin qui mene vers des formes qui sont proches des patterns (organisme ou tumeur) que nous voulons etudier. Et par la, quels sont les chemins a eviter, c'est a dire menant vers des patterns indesirables. Cette evaluation peut etre faite a chaque pas de temps ou une forme est atteinte. Nous avons procede a sa validation grâce a l'outil de simulation de morphogenese Dyncell [2]. Il permet a partir d'une cellule avec un programme de generer un pattern en suivant les instructions contenues dans ce programme. Le calcul et le parcours d'ensembles s'apparentent a un probleme combinatoire. Les complexites aussi bien en temps qu'en memoire sont des verrous pour appliquer les algorithmes a des cas d'etude plus interessants. C'est pour cela que nous avons travaille sur l'optimisation. En effet, nous avons veille a ce qu'il n'y ait pas de redondance dans chaque ensemble de formes atteint aussi bien pour la forme que pour ses differentes transformations geometriques. Nous avons aussi limite les reifications de certains concepts du modele tels que Cellule, Grille, Environnement etc. Cela nous a permis d'avoir un gain considerable en memoire. Il est aussi possible dans l'ensemble des evolutions de la forme initiale de n'extraire en un temps donne qu'un sous-ensemble defini dans un catalogue au debut du programme. En plus de ces techniques d'optimisation, nous avons procede a la parallelisation de notre modele sur processeur multicœurs. Nous savons que la lecture et l'evolution de chaque forme dans un ensemble est independante de celles d'une autre. Par contre, lorsqu'elle est creee et ajoutee a un ensemble, la forme doit garantir la condition d'unicite au sein des autres formes deja existantes. Donc, des systemes d'exclusion mutuelle ont ete envisages tout en ayant une synchronisation apres calcul de l'ensemble pour s'assurer de la non redondance. Cependant, ces mecanismes sont elabores de sorte que les avantages de la parallelisation ne soient pas sacrifies. Implemente avec le mecanisme d'apoptose, le programme permet : de connaitre l'ensemble des evolutions futures d'une forme donnee par apoptose jusqu'a un temps defini et les chemins pour revenir a la forme initiale pour chacune des evolutions, de trouver, s'ils existent, les suites de couple cellule+controle qui permettent d'aller d'une forme a une autre par apoptose. Ce modele nous permet, en cas de mort prematuree de cellules suite a un degât cellulaire (necrose) de disposer des differentes facons de regenerer la forme initiale avec les cellules restantes. Il n'est pas pris en compte l'ordre des actions. Pour chacun des deux modeles (mitose et apoptose), les ensembles crees a chaque pas de temps ainsi que l'historique de leur creation sont stockes dans un graphe. Et des scripts sont generes pour l'affichage des formes.

Below the influence of the mechanical cues and genetic expression, constraints underlying the developmental process play a key role in forms' emergence. Theses constraints lead to cells' differentiation and sometimes determine the directions of cells growth. To better understand these phenomena, we present in this paper our work focused primarily on a development of a mathematical model. A one which takes into account the co-evolution of cellular dynamics with it's environment. To study the influence of the developmental constraints, we have developed algorithms to make and explore a base of genomes. The purpose of this exploration is first to check conditions under which specific genes are activated. Then, this exploration allows us to follow the conditions of emergence of some patterns that lead to a specific shape. From our model, we found a genome that can generate the French flag. With this French flag pattern and its genome starting, we addressed the following question: is there another genome in the simulated base that achieves the same shape, i.e. the French flag pattern?

In the context of tissue morphogenesis study, in silico simulations can be seen as experiments in a virtual lab bench. Such simulations can facilitate the comprehension of a system, the test of hypotheses or the incremental refining of a model and its parameters. In silico simulations must be efficient and provide the possibility to simulate large tissues, containing thousands of cells. We propose to study tissue morphogenesis at the cellular level using our virtual biomechanical cell model. This model is based on a mass/spring system and coupled to a multi-agent system. We validated the relevance of our model through a case study: a cell sorting. Moreover, we took advantage of the large parallelism offered by graphics processing units (GPU), which contain up to thousands of cores: we implemented our model with the OpenCL framework. We ran large scale simulations, with up to 10(6) of our virtual cells. We studied the performance of our system on a CPU Intel Core i7 860, and two GPUs: a NVidia GeForce GT440 and a Nvidia GeForce GTX 690. The absence of synchronization in our implementation allowed the full benefits of the parallelism of these hardwares.

Mechanical contraints play a key role in tissue morphogenesis. We propose to study these mechanisms at the cellular level, thanks to our virtual biomechanical cell model. This model defines biological cell behaviors, such as cell motility, mitosis and adhesion as well as methods to evaluate cell compression/stretching and shearing. The evaluation of these constraints allows the virtual cells to respond by changing their color during simulation and lead to the observation of emerging patterns in cell differentiation during tissue growth: the main purpose of this evaluation is to give the cells the ability to respond to mechanical constraints by differentiating. This approach allows to study the influence of mechanotransduction during tissue morphogenesis.

The first aim of simulation in virtual environment is to help biologists to have a better understanding of the simulated system. The cost of such simulation is significantly reduced compared to that of in vivo simulation. However, the inherent complexity of biological system makes it hard to simulate these systems on non-parallel architectures: models might be made of sub-models and take several scales into account; the number of simulated entities may be quite large. Today, graphics cards are used for general purpose computing which has been made easier thanks to frameworks like CUDA or OpenCL. Parallelization of models may however not be easy: parallel computer programing skills are often required; several hardware architectures may be used to execute models. In this paper, we present the software architecture we built in order to implement various models able to simulate multi-cellular system. This architecture is modular and it implements data structures adapted for graphics processing units architectures. It allows efficient simulation of biological mechanisms.

The number N of detectable (i.e. communicating) extraterrestrial civilizations in the Milky Way galaxy is usually done by using the Drake equation. This equation was established in 1961 by Frank Drake and was the first step to quantifying the SETI field. Practically, this equation is rather a simple algebraic expression and its simplistic nature leaves it open to frequent re-expression An additional problem of the Drake equation is the time-independence of its terms, which for example excludes the effects of the physico-chemical history of the galaxy. Recently, it has been demonstrated that the main shortcoming of the Drake equation is its lack of temporal structure, i.e., it fails to take into account various evolutionary processes. In particular, the Drake equation doesn't provides any error estimation about the measured quantity. Here, we propose a first treatment of these evolutionary aspects by constructing a simple stochastic process which will be able to provide both a temporal structure to the Drake equation (i.e. introduce time in the Drake formula in order to obtain something like N(t)) and a first standard error measure.

In biology, recent techniques in confocal microscopy have produced experimental data which highlights the importance of cellular dynamics in the evolution of biological shapes. Thus, to understand the mechanisms underlying the morphogenesis of multi-cellular organisms, we study this cellular dynamic system in terms of its properties: cell multiplication, cell migration, and apoptosis. Besides, understanding the convergence of the system toward a stable form, involves local interactions between cells. Indeed, the way that cells self-organize through these interactions determines the resulting form. Along with the mechanisms of convergence highlighted above, the dynamic system also undergoes controls established by the nature on the organisms growth. Hence, to let the system viable, the global behavior of cells has to be assessed at every state of their developement and must satisfy the constraints. Otherwise, the whole system self-adapts in regard to its global behavior. Thus, we must be able to formalize in a proper metric space a metaphor of cell dynamics in order to find conditions (decisions, states) that would make cells to self-organize and in which cells self-adapt so as to always satisfy operational constraints (such as those induced by the tissue or the use of resources). Therefore, the main point remains to find conditions in which the system is viable and maintains its shape while renewing. The aim of this paper is to explain the mathematical foundations of this work and describe a simulation tool to study the morphogenesis of a virtual organism.