This monograph sketches out a broad spectrum of problems (from evolution and metabolism to morphogenesis and biogeographical dynamics) whose solution has been impacted by mathematical models. Each of the selected examples has led to the recognition—and set direction to further study—of certain fundamental but unintuitive properties of biological systems, such as the making and breaking of specific symmetries that underlie morphogenesis. Whether they are long-established or only recently accepted, these models are selected for being thought-provoking and illuminating both the achievements and the gaps in our current understanding of the given area of biology. The selection of models is also meant to bring to the fore the existing degree of unity in the quantitative approach to diverse general-biological questions and in the systems-level properties that are discovered across the levels of biological organization. It is the thesis of this book that further cultivation of such unity is a way forward as we progress toward a general theory of living matter. This is an ideal book for students (in the broadest sense) of biology who wish to learn from this attempt to present the exemplary models, their methodological lessons, and the outline of a unified theory of living matter that is now beginning to emerge. In addition to a doctoral student preparing for quantitative biology research, this reader could also be an interdisciplinary scientist transitioning to biology. The latter—for example, a physicist or an engineer—may be comfortable with the mathematical apparatus and prepared to quickly enter the intended area of work, but desires a broader foundation in biology from the quantitative perspective.

"Math and bio 2010 grew out of 'Meeting the Challenges: Education across the Biological, Mathematical and Computer Sciences,' a joint project of the Mathematical Association of America (MAA), the National Science Foundation Division of Undergraduate Education (NSF DUE), the National Institute of General Medical Sciences (NIGMS), the American Association for the Advancement of Science (AAAS), and the American Society for Microbiology (ASM)."--Foreword, p. vi

Application of recent advances, such as non-equilibrium thermodynamics, the maintenance concept and the material balancing method, to the description, of microbial growth has suggested new experimental approaches which have yielded a wealth of data. These data have been used to develop mathematical models of microbial growth and metabolism, and the models have made it possible to direct the metabolism of a microorganism in such a way that more of a certain desired product is made. While a full quantitative description of all aspects of microbial growth and metabolism is till remote, the new approaches are opening up large areas of new potential -- it is now possible, for instance, to deal with individual cells in a population and with quantitative aspects of product formation and optimisation. Microbiologists, biochemists and physiologists will find this an invaluable update on a field of great promise.

The development of the life sciences may be said to have effected a gradual transition from a more or less intuitive prescientific approach based on crude observation, via a more refined type of observation to experimentation and hence to the level of formal theories. Quantitative methods are introduced at the second level; they comprise: (a) quantitative design of experiments; (b) regrouping of experimental results; (c) evalua tion of results by means of mathematical or special statistical techniques. The last step implies the introduction of theoretical concepts, but we are not justified in speaking of theoretical science unless true theoretical con siderations-models or hypotheses-precede experiment, and this is then followed by an attempt to link results with theory so as to verify the theory. Biology at present seems to lie somewhere between the second and third level mentioned above, not yet having achieved the status of a theoretical science in all its branches. Thus, though the need for quantification and mathematical formulation is widely recognized, many biologists still believe that e.g. general systems theory is too abstract to be of use in handling concrete problems. Those, however, who look critically at the present state of affairs cannot adopt this attitude.

The aim of this monograph is to summarize the essential features which characterize the behavior of regulatory systems. Firstly we discuss the laws which govern ligand binding in thermodynamic terms. The basic cooperative and allosteric phenomena are des cribed in thermodynamic terms without assuming any particular mo del. Then the molecular models developed by Monod, Wyman and Changeux and by Koshland, Nemethy and Filmer are presented in detail. Special emphasis has been given to the analysis of the Hill coefficient and its meaning both in thermodynamic terms and in terms of the two allosteric models: the concerted model of Monod, Wyman and Changeux and the sequential model of Koshland, Nemethy and Filmer. Special types of cooperativities are dis cussed in some detail namely, cooperativity stemming from ligand coupled protein association or dissociation, negative cooperati vity and half-of-the-sites reactivity. A slightly extended space was devoted to the discussion of negative cooperativity and half of-the-sites reactivity, since the existence of these phenomena and their possible biological importance is less of a common knowledge than positive cooperativity. This monograph does not attempt to be a review of specific examples analyzed according to one model or another. Rather, an attempt is made to provide the reader with the quantitative tools to analyze any specific regulatory system. Last but not least, I would like to thank Prof. F. W. Dahlquist from the Institute of Molecular Biology, the University of Oregon (Eugene) and Prof. D. E. Koshland, Jr.

An introduction to the quantitative modeling of biological processes, presenting modeling approaches, methodology, practical algorithms, software tools, and examples of current research. The quantitative modeling of biological processes promises to expand biological research from a science of observation and discovery to one of rigorous prediction and quantitative analysis. The rapidly growing field of quantitative biology seeks to use biology's emerging technological and computational capabilities to model biological processes. This textbook offers an introduction to the theory, methods, and tools of quantitative biology. The book first introduces the foundations of biological modeling, focusing on some of the most widely used formalisms. It then presents essential methodology for model-guided analyses of biological data, covering such methods as network reconstruction, uncertainty quantification, and experimental design; practical algorithms and software packages for modeling biological systems; and specific examples of current quantitative biology research and related specialized methods. Most chapters offer problems, progressing from simple to complex, that test the reader's mastery of such key techniques as deterministic and stochastic simulations and data analysis. Many chapters include snippets of code that can be used to recreate analyses and generate figures related to the text. Examples are presented in the three popular computing languages: Matlab, R, and Python. A variety of online resources supplement the the text. The editors are long-time organizers of the Annual q-bio Summer School, which was founded in 2007. Through the school, the editors have helped to train more than 400 visiting students in Los Alamos, NM, Santa Fe, NM, San Diego, CA, Albuquerque, NM, and Fort Collins, CO. This book is inspired by the school's curricula, and most of the contributors have participated in the school as students, lecturers, or both. Contributors John H. Abel, Roberto Bertolusso, Daniela Besozzi, Michael L. Blinov, Clive G. Bowsher, Fiona A. Chandra, Paolo Cazzaniga, Bryan C. Daniels, Bernie J. Daigle, Jr., Maciej Dobrzynski, Jonathan P. Doye, Brian Drawert, Sean Fancer, Gareth W. Fearnley, Dirk Fey, Zachary Fox, Ramon Grima, Andreas Hellander, Stefan Hellander, David Hofmann, Damian Hernandez, William S. Hlavacek, Jianjun Huang, Tomasz Jetka, Dongya Jia, Mohit Kumar Jolly, Boris N. Kholodenko, Markek Kimmel, Michał Komorowski, Ganhui Lan, Heeseob Lee, Herbert Levine, Leslie M Loew, Jason G. Lomnitz, Ard A. Louis, Grant Lythe, Carmen Molina-París, Ion I. Moraru, Andrew Mugler, Brian Munsky, Joe Natale, Ilya Nemenman, Karol Nienałtowski, Marco S. Nobile, Maria Nowicka, Sarah Olson, Alan S. Perelson, Linda R. Petzold, Sreenivasan Ponnambalam, Arya Pourzanjani, Ruy M. Ribeiro, William Raymond, William Raymond, Herbert M. Sauro, Michael A. Savageau, Abhyudai Singh, James C. Schaff, Boris M. Slepchenko, Thomas R. Sokolowski, Petr Šulc, Andrea Tangherloni, Pieter Rein ten Wolde, Philipp Thomas, Karen Tkach Tuzman, Lev S. Tsimring, Dan Vasilescu, Margaritis Voliotis, Lisa Weber

Quantitative methods are revolutionizing modern molecular and cellular biology. Groundbreaking technical advances are fueling the rapid expansion in our ability to observe, as seen in multidisciplinary studies that integrate theory, computation, experimental assays, and the control of microenvironments. Integrating new experimental and theoretical methods, Quantitative Biology: From Molecular to Cellular Systems gives both new and established researchers a solid foundation for starting work in this field. The book is organized into three sections: Fundamental Concepts covers bold ideas that inspire novel approaches in modern quantitative biology. It offers perspectives on evolutionary dynamics, system design principles, chance and memory, and information processing in biology. Methods describes recently developed or improved techniques that are transforming biological research. It covers experimental methods for studying single-molecule biochemistry, small-angle scattering from biomolecules, subcellular localization of proteins, and single-cell behavior. It also describes theoretical methods for synthetic biology and modeling random variations among cells. Molecular and Cellular Systems focuses on specific biological systems where modern quantitative biology methods are making an impact. It incorporates case studies of biological systems for which new concepts or methods are increasing our understanding. Examples include protein kinase at the molecular level, the genetic switch of phage lambda at the regulatory system level, and Escherichia coli chemotaxis at the cellular level. In short, Quantitative Biology presents practical tools for the observation, modeling, design, and manipulation of biological systems from the molecular to the cellular levels.