# Control Theory and Systems Biology (MIT Press)

Language: English

Pages: 358

ISBN: 0262013347

Format: PDF / Kindle (mobi) / ePub

Issues of regulation and control are central to the study of biological and biochemical systems. Thus it is not surprising that the tools of feedback control theory--engineering techniques developed to design and analyze self-regulating systems--have proven useful in the study of these biological mechanisms. Such interdisciplinary work requires knowledge of the results, tools and techniques of another discipline, as well as an understanding of the culture of an unfamiliar research community. This volume attempts to bridge the gap between disciplines by presenting applications of systems and control theory to cell biology that range from surveys of established material to descriptions of new developments in the field. The first chapter offers a primer on concepts from dynamical systems and control theory, which allows the life scientist with no background in control theory to understand the concepts presented in the rest of the book. Following the introduction of ordinary differential equation-based modeling in the first chapter, the second and third chapters discuss alternative modeling frameworks. The remaining chapters sample a variety of applications, considering such topics as quantitative measures of dynamic behavior, modularity, stoichiometry, robust control techniques, and network identification. ContributorsDavid Angeli, Declan G. Bates, Eric Bullinger, Peter S. Chang, Domitilla Del Vecchio, Francis J. Doyle III, Hana El-Samad, Dirk Fey, Rolf Findeisen, Simone Frey, Jorge Gonçalves, Pablo A. Iglesias, Brian P. Ingalls, Elling W. Jacobsen, Mustafa Khammash, Jongrae Kim, Eric Klavins, Eric C. Kwei, Thomas Millat, Jason E. Shoemaker, Eduardo D. Sontag, Stephanie R. Taylor, David Thorsley, Camilla Trané, Sean Warnick, Olaf Wolkenhauer

First Life: Discovering the Connections between Stars, Cells, and How Life Began

Stochastic Processes in Physics, Chemistry, and Biology (Lecture Notes in Physics)

Bacteria and Viruses (The Lucent Library of Science and Technology)

Junk DNA: A Journey Through the Dark Matter of the Genome

Backyard Biology: Investigate Habitats Outside Your Door with 25 Projects (Build It Yourself Series)

ðkÀ2 þ k3 Þs2 ðtÞ: dt 1 þ k4 s1q ðtÞ ð1:2bÞ We can represent this system with ! s1 s¼ ; s2 " and f ðsÞ ¼ f1 ðs1 ; s2 Þ f2 ðs1 ; s2 Þ # 2 6 ¼4 k1 þ k3 s2 À ðkÀ1 þ kÀ3 Þs1 3 7 5: k2 q þ kÀ3 s1 À ðkÀ2 þ k3 Þs2 1 þ k4 s 1 n In nearly all cases of interest, the function f does not depend linearly on the state s, in which case the vector equation (1.1) is known as a set of nonlinear di¤erential equations. Although, in general, it is not possible to obtain explicit solutions to such

are deﬁned for a special class of signals: they have to start at a ﬁnite value and eventually have to reach zero, which ensures that the integrals of equation (4.1) and equation (4.2) are ﬁnite. The challenge now is to develop quantitative measures capable of characterizing signals with an arbitrary ﬁnal state. 5 Control Strategies in Times of Adversity: How Organisms Survive Stressful Conditions Hana El-Samad Life in the microbial world is characterized by ﬁerce competition, nutritional

networks organized into hierarchies of interlocked feedback and feedforward loops. It also comes as no surprise that these stress-response systems, found embedded in the genomic blueprint of almost every bacterium studied to date, use a versatile battery of sophisticated control strategies to e‰ciently maintain the functionality and integrity of the bacterium under all challenging circumstances pertinent to its speciﬁc lifestyle. 5.1 Stress Responses: Universal Survival Strategies During the

which a stable point and a stable orbit coexist and values of n for which two stable orbits coexist. The interval of n values for which two stable orbits coexist is too small to be able to set n numerically in such an interval. Thus this interval is not practically relevant. The values of n for which a stable equilibrium and a stable periodic orbit coexist, known as hard excitation, is instead relevant. 112 Domitilla Del Vecchio and Eduardo D. Sontag The situation described in ﬁgure 6.6

Eduardo D. Sontag follows. Denoting concentrations with the same letters as the species themselves, we have the following vector of species, stoichiometry matrix G and vector of reaction rates RðxÞ: 3 2 3 3 2 2 k1 E Â S0 À1 1 0 0 0 1 S0 6 6 6 7 6 0 7 7 6 S1 7 6 kÀ1 ES0 7 0 1 À1 1 07 7 6 7 7 6 6 7 6 À1 7 6 E 7 6 1 1 0 0 07 7; G ¼ 6 6 k2 ES0 7: ; RðxÞ ¼ x ¼6 7 6 0 7 6 F 7 6 0 0 À1 1 17 6 7 6 6 k3 F Â S1 7 7 6 7 7 6 6 4 1 À1 À1 4 ES0 5 4 kÀ3 FS1 5 0 0 05 0 0 0 1 À1 À1 FS1 k4 FS1 From here, we can