Morphogenesis software based on epigenetic code concept.

The process of morphogenesis is an evolution of shape of an organism together with the differentiation of its parts. This process encompasses numerous biological processes ranging from embryogenesis to regeneration following crisis such as amputation or transplantation. A fundamental theoretical question is where exactly do these instructions for (re-)construction reside and how are they implemented? We have recently proposed a set of concepts, aiming to respond to these questions and to provide an appropriate mathematical formalization of the geometry of morphogenesis [1]. First, we consider a possibility that the evolution of shape is determined by epigenetic information, responsible for realization of different types of cell events. Second, we suggest a set of rules for converting this epigenetic information into instructive signals for cell event for each cell, as well as for transforming it after each cell event. Next we give notions of cell state, determined by its epigenetic array, and cell event, which is a change of cell state, and formalize development as a graph (tree) of cell states connected by 5 types of cell events, corresponding to the processes of cell division, cell growth, cell death, cell movement and cell differentiation. Here we present a Morphogenesis software capable to simulate an evolution of a 3D embryo starting from zygote, following a set of rules, based on our theoretical assumptions, and thus to provide a proof-of-concept of the hypothesis of epigenetic code regulation. The software creates a developing embryo and a corresponding graph of cell events according to the zygotic epigenetic spectrum and chosen parameters of the developmental rules. Variation of rules influencing the resulting shape of an embryo may help elucidating the principal laws underlying pattern formation.

Computational models for the dynamics of early mouse embryogenesis.

Early embryonic development, from the zygote to the blastocyst, is a paradigm of a dynamic, self-organised process. It involves gene expression, mechanical interactions between cells, cell division and inter- and intracellular signalling. Imaging and transcriptomic data have significantly improved our understanding of early embryogenesis in mammals. However, they also reveal a great level of complexity. How the genetic, mechanical, and regulatory processes interact to ensure reproducible development is thus much investigated by computational modelling, which allows a dissection of the mechanisms controlling cell fate decisions. In this review, we discuss the main types of modelling approaches that have been used to investigate the dynamics of preimplantation mammalian development. We also discuss the insights provided by modelling into our understanding of the specification processes leading to the three types of cells in the embryo 4.5 days after fertilization: the trophectoderm, the epiblast and the primitive endoderm.

Signalling-modulated gene regulatory networks in early mammalian development.

Early mammalian embryo is a paradigm of dynamic, self-organised process. It involves gene expression, cell division and intercellular signalling. How these processes interact to ensure reproducible development is being often investigated by modelling, which allows to dissect the mechanisms controlling cell fate decisions. In this work, we present two models based on ordinary differential equations describing the first and second specification processes in the mouse embryo. Together, they describe the cell fate decisions leading to the first three cell lineages which form the blastocyst 4.5 days after fertilisation: the trophectoderm, the epiblast and the primitive endoderm. Both specifications rely on multistability, and signalling allows the selection of the appropriate steady-state. In addition to the gene regulatory network, the first specification process is indeed controlled by the Hippo pathway, which is itself controlled by cell polarity and cell-to-cell contacts. This leads to a spatially organised arrangement of cells. The second specification process is controlled by Fgf signalling and leads to a salt and pepper distribution of the two cell types. We discuss the respective mechanisms and their physiological implications.

Modeling-Based Investigation of the Effect of Noise in Cellular Systems.

Noise is pervasive in cellular biology and inevitably affects the dynamics of cellular processes. Biological systems have developed regulatory mechanisms to ensure robustness with respect to noise or to take advantage of stochasticity. We review here, through a couple of selected examples, some insights on possible robustness factors and constructive roles of noise provided by computational modeling. In particular, we focus on (1) factors that likely contribute to the robustness of oscillatory processes such as the circadian clocks and the cell cycle, (2) how reliable coding/decoding of calcium-mediated signaling could be achieved in presence of noise and, in some cases, enhanced through stochastic resonance, and (3) how embryonic cell differentiation processes can exploit stochasticity to create heterogeneity in a population of identical cells.

Modeling of the effects of IL-17 and TNF-α on endothelial cells and thrombus growth.

Rheumatoid and psoriatic arthritis are chronic inflammatory diseases, with massive increase of cardiovascular events (CVE), and contribution of the cytokines TNF-α and IL-17. Chronic inflammation inside the joint membrane or synovium results from the activation of fibroblasts/synoviocytes, and leads to the release of cytokines from monocytes (Tumor Necrosis Factor or TNF) and from T lymphocytes (Interleukin-17 or IL-17). At the systemic level, the very same cytokines affect endothelial cells and vessel wall. We have previously shown [1,2] that IL-17 and TNF-α, specifically when combined, increase procoagulation, decrease anticoagulation and increase platelet aggregation, leading to thrombosis. These results are the basis for the models of interactions between IL-17 and TNF, and genes expressed by activated endothelial cells. This work is devoted to mathematical modeling and numerical simulations of blood coagulation and clot growth under the influence of IL-17 and TNF-α. We show that they can provoke thrombosis, leading to the complete or partial occlusion of blood vessels. The regimes of blood coagulation and conditions of occlusion are investigated in numerical simulations and in approximate analytical models. The results of mathematical modeling allow us to predict thrombosis development for an individual patient.

A multiscale model of early cell lineage specification including cell division.

Embryonic development is a self-organised process during which cells divide, interact, change fate according to a complex gene regulatory network and organise themselves in a three-dimensional space. Here, we model this complex dynamic phenomenon in the context of the acquisition of epiblast and primitive endoderm identities within the inner cell mass of the preimplantation embryo in the mouse. The multiscale model describes cell division and interactions between cells, as well as biochemical reactions inside each individual cell and in the extracellular matrix. The computational results first confirm that the previously proposed mechanism by which extra-cellular signalling allows cells to select the appropriate fate in a tristable regulatory network is robust when considering a realistic framework involving cell division and three-dimensional interactions. The simulations recapitulate a variety of in vivo observations on wild-type and mutant embryos and suggest that the gene regulatory network confers differential plasticity to the different cell fates. A detailed analysis of the specification process emphasizes that developmental transitions and the salt-and-pepper patterning of epiblast and primitive endoderm cells from a homogenous population of inner cell mass cells arise from the interplay between the internal gene regulatory network and extracellular signalling by Fgf4. Importantly, noise is necessary to create some initial heterogeneity in the specification process. The simulations suggest that initial cell-to-cell differences originating from slight inhomogeneities in extracellular Fgf4 signalling, in possible combination with slightly different concentrations of the key transcription factors between daughter cells, are able to break the original symmetry and are amplified in a flexible and self-regulated manner until the blastocyst stage.

Modeling the photoperiodic entrainment of the plant circadian clock.

The circadian clock is an endogenous 24 hour rhythm that helps organisms anticipate and adapt to daily and seasonal variations in environment, such as the day/night cycle or changing temperatures. The plant clock is a complex network of transcription factors that regulate each other, forming interlocked feedback loops. Most of its components are light-regulated in some way, making the system highly sensitive to changes in light conditions. Here, we explore the mechanisms by which the plant clock adapts to changing day length. We first present some experimental data illustrating the variety of behaviors found in seedlings exposed to external day/night cycles different from 24h. We then use a mathematical model to characterize the response of the clock to a wide range of external cycle lengths and photoperiods. We show the existence of several domains of periodic entrainment with different ratios between the external cycle length and the period of the clock, and the presence of quasiperiodic and chaotic behaviors outside of the entrainment range. We simulate knockout mutants with impaired clock function and theoretical variants with diminished light sensitivity to highlight the role of a complex network and multiple light inputs in keeping the clock entrained over a wide range of conditions.

On a model of pattern regeneration based on cell memory.

We present here a new model of the cellular dynamics that enable regeneration of complex biological morphologies. Biological cell structures are considered as an ensemble of mathematical points on the plane. Each cell produces a signal which propagates in space and is received by other cells. The total signal received by each cell forms a signal distribution defined on the cell structure. This distribution characterizes the geometry of the cell structure. If a part of this structure is removed, the remaining cells have two signals. They keep the value of the signal which they had before the amputation (memory), and they receive a new signal produced after the amputation. Regeneration of the cell structure is stimulated by the difference between the old and the new signals. It is stopped when the two signals coincide. The algorithm of regeneration contains certain rules which are essential for its functioning, being the first quantitative model of cellular memory that implements regeneration of complex patterns to a specific target morphology. Correct regeneration depends on the form and the size of the cell structure, as well as on some parameters of regeneration.

Target morphology and cell memory: a model of regenerative pattern formation.

Despite the growing body of work on molecular components required for regenerative repair, we still lack a deep understanding of the ability of some animal species to regenerate their appropriate complex anatomical structure following damage. A key question is how regenerating systems know when to stop growth and remodeling - what mechanisms implement recognition of correct morphology that signals a stop condition? In this work, we review two conceptual models of pattern regeneration that implement a kind of pattern memory. In the first one, all cells communicate with each other and keep the value of the total signal received from the other cells. If a part of the pattern is amputated, the signal distribution changes. The difference fromthe original signal distribution stimulates cell proliferation and leads to pattern regeneration, in effect implementing an error minimization process that uses signaling memory to achieve pattern correction. In the second model, we consider a more complex pattern organization with different cell types. Each tissue contains a central (coordinator) cell that controls the tissue and communicates with the other central cells. Each of them keeps memory about the signals received from other central cells. The values of these signals depend on the mutual cell location, and the memory allows regeneration of the structure when it is modified. The purpose of these models is to suggest possible mechanisms of pattern regeneration operating on the basis of cell memory which are compatible with diverse molecular implementation mechanisms within specific organisms.