Simple Mathematical Models of Gene Regulatory Dynamics
This is a short and self-contained introduction to the field of mathematical modeling of gene-networks in bacteria. As an entry point to the field, we focus on the analysis of simple gene-network dynamics. The notes commence with an introduction to the de
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Michael C. Mackey Moisés Santillán Marta Tyran-Kamińska Eduardo S. Zeron
Simple Mathematical Models of Gene Regulatory Dynamics
Lecture Notes on Mathematical Modelling in the Life Sciences
Editors-in-Chief: Michael C. Mackey Angela Stevens Series editors Martin Burger Maurice Chacron Odo Diekmann Anita Layton Jinzhi Lei Mark Lewis Lakshminarayanan Mahadevan Philip Maini Masayasu Mimura Claudia Neuhauser Hans G. Othmer Mark Peletier Alan S Perelson Charles S. Peskin Luigi Preziosi Jonathan Rubin Moisés Santillán Christoph Schütte
The rapid pace and development of the research in mathematics, biology and medicine has opened a niche for a new type of publication - short, up-to-date, readable lecture notes covering the breadth of mathematical modelling, analysis and computation in the life-sciences, at a high level, in both printed and electronic versions. The volumes in this series are written in a style accessible to researchers, professionals and graduate students in the mathematical and biological sciences. They can serve as an introduction to recent and emerging subject areas and/or as an advanced teaching aid at colleges, institutes and universities. Besides monographs, we envision that this series will also provide an outlet for material less formally presented and more anticipatory of future needs, yet of immediate interest because of the novelty of its treatment of an application, or of the mathematics being developed in the context of exciting applications. It is important to note that the LMML focuses on books by one or more authors, not on edited volumes. The topics in LMML range from the molecular through the organismal to the population level, e.g. genes and proteins, evolution, cell biology, developmental biology, neuroscience, organ, tissue and whole body science, immunology and disease, bioengineering and biofluids, population biology and systems biology. Mathematical methods include dynamical systems, ergodic theory, partial differential equations, calculus of variations, numerical analysis and scientific computing, differential geometry, topology, optimal control, probability, stochastics, statistical mechanics, combinatorics, algebra, number theory, etc., which contribute to a deeper understanding of biomedical problems.
More information about this series at http://www.springer.com/series/10049
Michael C. Mackey • Moisés Santillán • Marta Tyran-Kami´nska • Eduardo S. Zeron
Simple Mathematical Models of Gene Regulatory Dynamics
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Michael C. Mackey Department of Physiology McGill University Montreal, QC Canada
Moisés Santillán Unidad Monterrey Cinvestav del IPN Apodaca, NL Mexico
Marta Tyran-Kami´nska Institute of Mathematics University of Silesia Katowice Poland
Eduardo S. Zeron Departamento de Matemáticas Cinvestav del IPN Ciudad de México Mexico
ISSN 2193-4789 ISSN 2193-4797 (electronic) Lecture Notes on Mathematical Modelling in the Life Sciences ISBN 978-3-319-45317-0 ISBN 978-3-319-45318-7 (eBook) DOI 10.1007/978-3-319-45318-7 Library of Congress Control Number: 2016956565 © S
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