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Contents tagged “mathematical models”

There are 5 contents with the tag “mathematical models”:

  1. Historicity at the heart of biology

    Historicity at the heart of biology

    Theory in Biosciences


    Most mathematical modeling in biology rely on the epistemology of physics. By contrast, we argue that historicity comes first in biology.

    Abstract

    Most mathematical modeling in biology relies either implicitly or explicitly on the epistemology of physics. The underlying conception is that the historicity of biological objects would not matter to understand a situation here and now, or, at least, historicity would not impact the method of modeling. We analyze that it is not the case with concrete examples. Historicity forces a conceptual reconfiguration where equations no longer play a central role. We argue that all observations depend on objects defined by their historical origin instead of their relations as in physics. Therefore, we propose that biological variations and historicity come first, and regularities are constraints with limited validity in biology. Their proper theoretical and empirical use requires specific rationales.

    Keywords: Historicity, Organization, Epistemology, Mathematical modeling, Constraints

  2. Analyses d’ouvrages : Franck Varenne, From models to simulations

    Analyses d’ouvrages : Franck Varenne, From models to simulations

    Revue d’histoire des sciences


    L’invention et le développement des ordinateurs a ouvert de nouvelles possibilités pour la modélisation. En physique, l’existence de théories mathématisées

    Abstract

    L’invention et le développement des ordinateurs a ouvert de nouvelles possibilités pour la modélisation. En physique, l’existence de théories mathématisées permet d’utiliser l’ordinateur pour calculer des solutions approchées à des problèmes déjà bien circonscrits théoriquement et épistémologiquement. En biologie, par contre, il n’existe pas de théorie jouant ce rôle épistémologique, et l’informatique a permis l’émergence de pratiques de modélisation combinant plusieurs cadres mathématiques. L’ouvrage de Franck Varenne porte sur ces pratiques novatrices, leur histoire et leur épistémologie, à travers le cas des simulations de morphogenèse d’arbres et plus généralement de plantes.

  3. A Primer on Mathematical Modeling in the Study of Organisms and Their Parts

    A Primer on Mathematical Modeling in the Study of Organisms and Their Parts

    Systems Biology


    How do mathematical models convey meaning? What is required to build a model? An introduction for biologists and philosophers.

    Abstract

    Mathematical modeling is a very powerful tool for understanding natural phenomena. Such a tool carries its own assumptions and should always be used critically. In this chapter, we highlight the key ingredients and steps of modeling and focus on their biological interpretation. In particular, we discuss the role of theoretical principles in writing models. We also highlight the meaning and interpretation of equations. The main aim of this chapter is to facilitate the interaction between biologists and mathematical modelers. We focus on the case of cell proliferation and motility in the context of multicellular organisms.

    Keywords: Equations, Mathematical modeling, Parameters, Proliferation, Theory

    Citation
    Montévil, Maël. 2018. “A Primer on Mathematical Modeling in the Study of Organisms and Their Parts.” In Systems Biology, edited by Mariano Bizzarri, 41–55. Methods in Molecular Biology. New York, NY: Springer. https://doi.org/10.1007/978-1-4939-7456-6_4
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  4. Modeling mammary organogenesis from biological first principles: Cells and their physical constraints

    Modeling mammary organogenesis from biological first principles: Cells and their physical constraints

    Progress in Biophysics and Molecular Biology


    We developed a mathematical model of mammary gland based on proper biological principles: the default state of cells and the principle of organization.

    Abstract

    Abstract In multicellular organisms, relations among parts and between parts and the whole are contextual and interdependent. These organisms and their cells are ontogenetically linked: an organism starts as a cell that divides producing non-identical cells, which organize in tri-dimensional patterns. These association patterns and cells types change as tissues and organs are formed. This contextuality and circularity makes it difficult to establish detailed cause and effect relationships. Here we propose an approach to overcome these intrinsic difficulties by combining the use of two models; 1) an experimental one that employs 3D culture technology to obtain the structures of the mammary gland, namely, ducts and acini, and 2) a mathematical model based on biological principles. The typical approach for mathematical modeling in biology is to apply mathematical tools and concepts developed originally in physics or computer sciences. Instead, we propose to construct a mathematical model based on proper biological principles. Specifically, we use principles identified as fundamental for the elaboration of a theory of organisms, namely i) the default state of cell proliferation with variation and motility and ii) the principle of organization by closure of constraints. This model has a biological component, the cells, and a physical component, a matrix which contains collagen fibers. Cells display agency and move and proliferate unless constrained; they exert mechanical forces that i) act on collagen fibers and ii) on other cells. As fibers organize, they constrain the cells on their ability to move and to proliferate. The model exhibits a circularity that can be interpreted in terms of closure of constraints. Implementing the mathematical model shows that constraints to the default state are sufficient to explain ductal and acinar formation, and points to a target of future research, namely, to inhibitors of cell proliferation and motility generated by the epithelial cells. The success of this model suggests a step-wise approach whereby additional constraints imposed by the tissue and the organism could be examined in silico and rigorously tested by in vitro and in vivo experiments, in accordance with the organicist perspective we embrace.

    Keywords: Ductal morphogenesis, Mathematical models, Organicism, Organizational closure, Acinar morphogenesis, Mammary gland morphogenesis

    Citation
    Montévil, Maël, L. Speroni, Carlos Sonnenschein, and Ana M. Soto. 2016. “Modeling Mammary Organogenesis from Biological First Principles: Cells and Their Physical Constraints.” Progress in Biophysics and Molecular Biology 122 (1): 58–69. https://doi.org/10.1016/j.pbiomolbio.2016.08.004
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  5. In search of principles for a Theory of Organisms

    In search of principles for a Theory of Organisms

    Journal of biosciences


    Lacking an operational theory to understand life cycles hinders progress in biology. We discuss elements towards such a theory, such as inertia and thermodynamics.

    Abstract

    Lacking an operational theory to explain the organization and behaviour of matter in unicellular and multicellular organisms hinders progress in biology. Such a theory should address life cycles from ontogenesis to death. This theory would complement the theory of evolution that addresses phylogenesis, and would posit theoretical extensions to accepted physical principles and default states in order to grasp the living state of matter and define proper biological observables. Thus, we favour adopting the default state implicit in Darwin’s theory, namely, cell proliferation with variation plus motility, and a framing principle, namely, life phenomena manifest themselves as non-identical iterations of morphogenetic processes. From this perspective, organisms become a consequence of the inherent variability generated by proliferation, motility and self-organization. Morphogenesis would then be the result of the default state plus physical constraints, like gravity, and those present in living organisms, like muscular tension.

    Keywords: Animals, Biological Evolution, Biophysics/methods, Cell Division, Mice, Models, Morphogenesis, Thermodynamics

    Citation
    Longo, Giuseppe, Mael Montevil, Carlos Sonnenschein, and Ana M. Soto. 2015. “In Search of Principles for a Theory of Organisms.” Journal of Biosciences 40 (5): 955–68. https://doi.org/10.1007/s12038-015-9574-9
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