Modeling and Simulation of Biological Networks
About this Title
Reinhard C. Laubenbacher, Virginia Bioinformatics Institute at Virginia Tech, Blacksburg, VA, Editor
Publication: Proceedings of Symposia in Applied Mathematics
Publication Year: 2007; Volume 64
ISBNs: 978-0-8218-3964-5 (print); 978-0-8218-9279-4 (online)
It is the task of computational biology to help elucidate the unique characteristics of biological systems. This process has barely begun, and many researchers are testing computational tools that have been used successfully in other fields. Mathematical and statistical network modeling is an important step toward uncovering the organizational principles and dynamic behavior of biological networks. Undoubtedly, new mathematical tools will be needed, however, to meet this challenge. The workhorse of this effort at present comprises the standard tools from applied mathematics, which have proven to be successful for many problems. But new areas of mathematics not traditionally considered applicable are contributing other powerful tools.
This volume is intended to introduce this topic to a broad mathematical audience. The aim is to explain some of the biology and the computational and mathematical challenges we are facing. The different chapters provide examples of how these challenges are met, with particular emphasis on nontraditional mathematical approaches. The volume features a broad spectrum of networks across scales, ranging from biochemical networks within a single cell to epidemiological networks encompassing whole cities.
Chapter topics include phylogenetics and gene finding using tools from statistics and algebraic geometry, biochemical network inference using tools from computational algebra, control-theoretic approaches to drug delivery using differential equations, and interaction-based modeling and discrete mathematics applied to problems in population dynamics and epidemiology.
Graduate students and research mathematicians interested in mathematical biology.
Table of Contents
- Lior Pachter – An introduction to reconstructing ancestral genomes [MR 2359647]
- Elizabeth S. Allman and John A. Rhodes – Phylogenetics [MR 2359648]
- Brandilyn Stigler – Polynomial dynamical systems in systems biology [MR 2359649]
- Suzanne Lenhart and John T. Workman – An introduction to optimal control applied to immunology problems [MR 2359650]
- Christopher L. Barrett, Keith Bisset, Stephen Eubank, Madhav V. Marathe, V. S. Anil Kumar and Henning S. Mortveit – Modeling and simulation of large biological, information and socio-technical systems: an interaction-based approach [MR 2359651]