431,510 research outputs found
Mathematical models in Developmental Biology
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
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
Recommended from our members
Mathematical Biology
Mathematical biology is a fast growing field of research, which on one hand side faces challenges resulting from the enormous amount of data provided by experimentalists in the recent years, on the other hand new mathematical methods may have to be developed to meet the demand for explanation and prediction on how specific biological systems function
Recommended from our members
Mathematical Biology
This years meeting on Mathematical Biology focussed on the mathematical modeling and analysis of some specific bio-medical questions, where quite detailed experimental findings are available. A main aim for this decision was to further deepen the exchange between the fields, on the long run in a similar manner as known e.g. from mathematics and physics. Talks by mathematicians and talks by experimentalists on related scientific questions were put back to back, wherever possible
A Molecular Biology Database Digest
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
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
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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