431,510 research outputs found

    Mathematical models in Developmental Biology

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    We will introduce some of the mathematical modeling tools that have been introduced in the field of Developmental Biology, focusing in specific problems in embryogenesis. The use of multiscale models based on a combination of ordinary and partial differential equations is a well established research paradigm in this area by now. After reviewing some of the past and present contributions, we will discuss both their merits and shortcomings in the light of recent experimental results.Universidad de Málaga. Campus de Excelencia Andalucía Tech

    The dawn of mathematical biology

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    In this paper I describe the early development of the so-called mathematical biophysics, as conceived by Nicolas Rashevsky back in the 1920's, as well as his latter idealization of a "relational biology". I also underline that the creation of the journal "The Bulletin of Mathematical Biophysics" was instrumental in legitimating the efforts of Rashevsky and his students, and I finally argue that his pioneering efforts, while still largely unacknowledged, were vital for the development of important scientific contributions, most notably the McCulloch-Pitts model of neural networks.Comment: 9 pages, without figure

    A Molecular Biology Database Digest

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    Computational Biology or Bioinformatics has been defined as the application of mathematical and Computer Science methods to solving problems in Molecular Biology that require large scale data, computation, and analysis [18]. As expected, Molecular Biology databases play an essential role in Computational Biology research and development. This paper introduces into current Molecular Biology databases, stressing data modeling, data acquisition, data retrieval, and the integration of Molecular Biology data from different sources. This paper is primarily intended for an audience of computer scientists with a limited background in Biology

    For principled model fitting in mathematical biology

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    The mathematical models used to capture features of complex, biological systems are typically non-linear, meaning that there are no generally valid simple relationships between their outputs and the data that might be used to validate them. This invalidates the assumptions behind standard statistical methods such as linear regression, and often the methods used to parameterise biological models from data are ad hoc. In this perspective, I will argue for an approach to model fitting in mathematical biology that incorporates modern statistical methodology without losing the insights gained through non-linear dynamic models, and will call such an approach principled model fitting. Principled model fitting therefore involves defining likelihoods of observing real data on the basis of models that capture key biological mechanisms.Comment: 7 pages, 3 figures. To appear in Journal of Mathematical Biology. The final publication is available at Springer via http://dx.doi.org/10.1007/s00285-014-0787-

    Periodic pattern formation in reaction-diffusion systems -an introduction for numerical simulation

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    The aim of the present review is to provide a comprehensive explanation of Turing reaction–diffusion systems in sufficient detail to allow readers to perform numerical calculations themselves. The reaction–diffusion model is widely studied in the field of mathematical biology, serves as a powerful paradigm model for self-organization and is beginning to be applied to actual experimental systems in developmental biology. Despite the increase in current interest, the model is not well understood among experimental biologists, partly because appropriate introductory texts are lacking. In the present review, we provide a detailed description of the definition of the Turing reaction–diffusion model that is comprehensible without a special mathematical background, then illustrate a method for reproducing numerical calculations with Microsoft Excel. We then show some examples of the patterns generated by the model. Finally, we discuss future prospects for the interdisciplinary field of research involving mathematical approaches in developmental biology
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