Geometry of Morphogenesis

We introduce a formalism for the geometry of eukaryotic cells and organisms.Cells are taken to be star-convex with good biological reason. This allows for a convenient description of their extent in space as well as all manner of cell surface gradients. We assume that a spectrum of such cell surface markers determines an epigenetic code for organism shape. The union of cells in space at a moment in time is by definition the organism taken as a metric subspace of Euclidean space, which can be further equipped with an arbitrary measure. Each cell determines a point in space thus assigning a finite configuration of distinct points in space to an organism, and a bundle over this configuration space is introduced with fiber a Hilbert space recording specific epigenetic data. On this bundle, a Lagrangian formulation of morphogenetic dynamics is proposed based on Gromov-Hausdorff distance which at once describes both embryo development and regenerative growth

Inference on tissue transplantation experiments

We review studies on tissue transplantation experiments for various species: one piece of the donor tissue is excised and transplanted into a slit in the host tissue, then observe the behavior of this grafted tissue. Although we have known the results of some transplantation experiments, there are many more possible experiments with unknown results. We develop a penalty function-based method that uses the known experimental results to infer the unknown experimental results. Similar experiments without similar results get penalized and correspond to smaller probability. This method can provide the most probable results of a group of experiments or the probability of a specific result for each experiment. This method is also generalized to other situations. Besides, we solve a problem: how to design experiments so that such a method can be applied most efficiently

Basic, simple and extendable kinetic model of protein synthesis

Protein synthesis is one of the most fundamental biological processes, which consumes a significant amount of cellular resources. Despite existence of multiple mathematical models of translation, varying in the level of mechanistical details, surprisingly, there is no basic and simple chemical kinetic model of this process, derived directly from the detailed kinetic model. One of the reasons for this is that the translation process is characterized by indefinite number of states, thanks to existence of polysomes. We bypass this difficulty by applying a trick consisting in lumping multiple states of translated mRNA into few dynamical variables and by introducing a variable describing the pool of translating ribosomes. The simplest model can be solved analytically under some assumptions. The basic and simple model can be extended, if necessary, to take into account various phenomena such as the interaction between translating ribosomes, limited amount of ribosomal units or regulation of translation by microRNA. The model can be used as a building block (translation module) for more complex models of cellular processes. We demonstrate the utility of the model in two examples. First, we determine the critical parameters of the single protein synthesis for the case when the ribosomal units are abundant. Second, we demonstrate intrinsic bi-stability in the dynamics of the ribosomal protein turnover and predict that a minimal number of ribosomes should pre-exists in a living cell to sustain its protein synthesis machinery, even in the absence of proliferation.Comment: 22 pages, 9 figure

Target morphology and cell memory: a model of regenerative pattern formation Cell Memory Can Regulate Morphogenesis and Regeneration

International audienceDespite the growing body of work on molecular components required for regenerative repair, westill lack a deep understanding of the ability of some animal species to regenerate their appropriatecomplex anatomical structure following damage. A key question is how regenerating systemsknow when to stop growth and remodeling – what mechanisms implement recognition of correctmorphology that signals a stop condition? In this work, we review two conceptual modelsof pattern regeneration that implement a kind of pattern memory. In the first one, all cells communicatewith each other and keep the value of the total signal received from the other cells. If apart of the pattern is amputated, the signal distribution changes. The difference from the originalsignal distribution stimulates cell proliferation and leads to pattern regeneration, in effect implementingan 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 withthe other central cells. Each of them keeps memory about the signals received from other centralcells. The values of these signals depend on the mutual cell location, and the memory allowsregeneration of the structure when it is modified. The purpose of these models is to suggestpossible mechanisms of pattern regeneration operating on the basis of cell memory which arecompatible with diverse molecular implementation mechanisms within specific organisms

Dynamical modeling of microRNA action on the protein translation process.

International audienceBACKGROUND: Protein translation is a multistep process which can be represented as a cascade of biochemical reactions (initiation, ribosome assembly, elongation, etc.), the rate of which can be regulated by small non-coding microRNAs through multiple mechanisms. It remains unclear what mechanisms of microRNA action are the most dominant: moreover, many experimental reports deliver controversial messages on what is the concrete mechanism actually observed in the experiment. Nissan and Parker have recently demonstrated that it might be impossible to distinguish alternative biological hypotheses using the steady state data on the rate of protein synthesis. For their analysis they used two simple kinetic models of protein translation. RESULTS: In contrary to the study by Nissan and Parker, we show that dynamical data allow discriminating some of the mechanisms of microRNA action. We demonstrate this using the same models as developed by Nissan and Parker for the sake of comparison but the methods developed (asymptotology of biochemical networks) can be used for other models. We formulate a hypothesis that the effect of microRNA action is measurable and observable only if it affects the dominant system (generalization of the limiting step notion for complex networks) of the protein translation machinery. The dominant system can vary in different experimental conditions that can partially explain the existing controversy of some of the experimental data. CONCLUSIONS: Our analysis of the transient protein translation dynamics shows that it gives enough information to verify or reject a hypothesis about a particular molecular mechanism of microRNA action on protein translation. For multiscale systems only that action of microRNA is distinguishable which affects the parameters of dominant system (critical parameters), or changes the dominant system itself. Dominant systems generalize and further develop the old and very popular idea of limiting step. Algorithms for identifying dominant systems in multiscale kinetic models are straightforward but not trivial and depend only on the ordering of the model parameters but not on their concrete values. Asymptotic approach to kinetic models allows putting in order diverse experimental observations in complex situations when many alternative hypotheses co-exist

On a Model of Pattern Regeneration Based on Cell Memory

International audienceWe 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

Prognostic impact of vitamin B6 metabolism in lung cancer

Patients with non-small cell lung cancer (NSCLC) are routinely treated with cytotoxic agents such as cisplatin. Through a genome-wide siRNA-based screen, we identified vitamin B6 metabolism as a central regulator of cisplatin responses in vitro and in vivo. By aggravating a bioenergetic catastrophe that involves the depletion of intracellular glutathione, vitamin B6 exacerbates cisplatin-mediated DNA damage, thus sensitizing a large panel of cancer cell lines to apoptosis. Moreover, vitamin B6 sensitizes cancer cells to apoptosis induction by distinct types of physical and chemical stress, including multiple chemotherapeutics. This effect requires pyridoxal kinase (PDXK), the enzyme that generates the bioactive form of vitamin B6. In line with a general role of vitamin B6 in stress responses, low PDXK expression levels were found to be associated with poor disease outcome in two independent cohorts of patients with NSCLC. These results indicate that PDXK expression levels constitute a biomarker for risk stratification among patients with NSCLC.publishedVersio

Centrality and the shortest path approach in the human interactome

Many notions and concepts for network analysis, including the shortest path approach, came to systems biology from the theory of graphs - the field of mathematics that studies graphs. We studied the relationship between the shortest paths and a biologically meaningful molecular path between vertices in human molecular interaction networks. We analyzed the sets of the shortest paths in the human interactome derived from HPRD and HIPPIE databases between all possible combinations of start and end proteins in eight signaling pathways in the KEGG database - NF-kappa B, MAPK, Jak-STAT, mTOR, ErbB, Wnt, TGF-beta, and the signaling part of the apoptotic process. We investigated whether the shortest paths match the canonical paths. We studied whether centrality of vertices and paths in the subnetworks induced by the shortest paths can highlight vertices and paths that are part of meaningful molecular paths. We found that the shortest paths match canonical counterparts only for canonical paths of length 2 or 3 interactions. The shortest paths match longer canonical counterparts with shortcuts or substitutions by protein complex members. We found that high centrality vertices are part of the canonical paths for up to 80% of the canonical paths depending on the database and the length

Acta Biotheoretica Mathematical and philosophical foundations of biological and biomedical science A Conceptual Model of Morphogenesis and Regeneration

International audienceThis paper is devoted to computer modelling of the development andregeneration of multicellular biological structures. Some species (e.g. planaria andsalamanders) are able to regenerate parts of their body after amputation damage, butthe global rules governing cooperative cell behaviour during morphogenesis are notknown. Here, we consider a simplified model organism, which consists of tissuesformed around special cells that can be interpreted as stemcells. We assume that stemcells communicate with each other by a set of signals, and that the values of thesesignals depend on the distance between cells. Thus the signal distribution characterizeslocation of stem cells. If the signal distribution is changed, then the difference betweenthe initial and the current signal distribution affects the behaviour of stem cells—e.g.as a result of an amputation of a part of tissue the signal distribution changes whichstimulates stem cells to migrate to new locations, appropriate for regeneration of theproper pattern. Moreover, as stem cells divide and form tissues around them, theycontrol the form and the size of regenerating tissues. This two-level organization of themodel organism, with global regulation of stem cells and local regulation of tissues,allows its reproducible development and regeneration