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This book highlights the theory and practical applications of the chemical master equation (CME) approach for very large biochemical networks, which provides a powerful general framework for model building in a variety of biological networks. The aim of the book is to not only highlight advanced numerical solution methods for the CME, but also reveal their potential by means of practical examples. The case studies presented are mainly from biology; however, the applications from novel methods are discussed comprehensively, underlining the interdisciplinary approach in simulation and the potential of the chemical master equation approach for modelling bionetworks. The book is a valuable guide for researchers, graduate students, and professionals alike.
This monograph presents the development of novel model-based methodologies for engineering self-organized and self-assembled systems. The work bridges the gap between statistical mechanics and control theory by tackling a number of challenges for a class of distributed systems involving a specific type of constitutive components, namely referred to as Smart Minimal Particles. The results described in the volume are expected to lead to more robust, dependable, and inexpensive distributed systems such as those endowed with complex and advanced sensing, actuation, computation, and communication capabilities.
It is well known that many realistic mathematical models of biological and chemical systems, such as enzyme cascades and gene regulatory networks, need to include stochasticity. These systems can be described as Markov processes and are modelled using the Chemical Master Equation (CME). The CME is a differential difference equation (continuous in time and discrete in the state space) for the probability of a certain state at a given time. The state space is the population count of species in the system. A successful method for computing the CME is the Finite State Projection Method (FSP). The purpose of this literature is to provide methods to help enhance the computation speed of the CME. We introduce an extension to the FSP method called the Optimal Finite State Projection method (OFSP). The OFSP method keeps the support of the approximation close to the smallest theoretical size, which in turn reduces the computation complexity and increases speed-up. We then introduce the Parallel Finite State Projection method (PFSP), a method to distribute the computation of the CME over multiple cores, to allow the computation of systems with a large CME support. Finally, a method for estimating the support a priori is introduced, called the Gated One Reaction Domain Expansion (GORDE). GORDE is the first domain selection method in the CME literature which can guarantee that the support proposed by the method will give the desired FSP approximation error.
Thisvolumecontainstheproceedingsofthe?rstinternationalmeetingonFormal Methods in Systems Biology, held at Microsoft Research, Cambridge, UK, June 4–5, 2008. While there are several venues that cover computational methods in systems biology,there is to date no single conference that brings together the application of the range of formal methods in biology. Therefore, convening such a meeting could prove extremely productive. The purpose of this meeting was to identify techniques for the speci?cation, development and veri?cation of biological m- els.Italsofocusedonthedesignoftoolstoexecuteandanalyzebiologicalmodels in ways that can signi?cantly advance our understanding of biological systems. As a forum for this discussion we invited key scientists in the area of formal methods to this unique meeting. Although this was a one-o? meeting, we are exploring the possibility of this forming the ?rst of what might become an annual conference. Presentations at the meeting were by invitation only; future meetings are expected to operate on a submission and review basis. The Steering Committee and additional referees reviewed the invited papers. Each submission was evaluated by at least two referees. The volume includes nine invited contributions. Formal Methods in Systems Biology 2008 was made possible by the cont- bution and dedication ofmany people. First of all,we wouldlike to thank allthe authors who submitted papers. Secondly, we would like to thank our additional invited speakers and participants. We would also like to thank the members of the Steering Committee for their valuable comments. Finally, we ackno- edge the help of the administrative and technical sta? at the MicrosoftResearch Cambridge lab.
This textbook focuses on stochastic analysis in systems biology containing both the theory and application. While the authors provide a review of probability and random variables, subsequent notions of biochemical reaction systems and the relevant concepts of probability theory are introduced side by side. This leads to an intuitive and easy-to-follow presentation of stochastic framework for modeling subcellular biochemical systems. In particular, the authors make an effort to show how the notion of propensity, the chemical master equation and the stochastic simulation algorithm arise as consequences of the Markov property. The text contains many illustrations, examples and exercises to illustrate the ideas and methods that are introduced. Matlab code is also provided where appropriate. Additionally, the cell cycle is introduced as a more complex case study. Senior undergraduate and graduate students in mathematics and physics as well as researchers working in the area of systems biology, bioinformatics and related areas will find this text useful.
Quantum physics provides the concepts and their mathematical formalization that lend themselves to describe important properties of biological networks topology, such as vulnerability to external stress and their dynamic response to changing physiological conditions. A theory of networks enhanced with mathematical concepts and tools of quantum physics opens a new area of biological physics, the one of systems biological physics.
Genome sequences are now available that enable us to determine the biological components that make up a cell or an organism. The discipline of systems biology examines how these components interact and form networks, and how the networks generate whole cell functions corresponding to observable phenotypes. This textbook, devoted to systems biology, describes how to model networks, how to determine their properties, and how to relate these to phenotypic functions. The prerequisites are some knowledge of linear algebra and biochemistry. Though the links between the mathematical ideas and biological processes are made clear, the book reflects the irreversible trend of increasing mathematical content in biology education. Therefore to assist both teacher and student, in an associated website Palsson provides problem sets, projects and Powerpoint slides, and keeps the presentation in the book concrete with illustrative material and experimental results.
Complex reaction networks arise in molecular biology and many other different fields of science such as ecology and social study. A familiar approach to modeling such problems is to find their master equation. In systems biology, the equation is called the chemical master equation (CME), and solving the CME is a difficult task, because of the curse of dimensionality. The goal of this dissertation is to alleviate this curse via the use of the finite state projection (FSP), in both cases where the CME matrix is constant (if the reaction rates are time-independent) or time-varying (if the reaction rates change over time). The work includes a theoretical characterization of the FSP truncation technique by showing that it can be put in the framework of inexact Krylov methods that relax matrix-vector products and compute them expediently by trading accuracy for speed. We also examine practical applications of our work in delay CME and parameter inference through local and global optimization schemes.
While technological advancements have been critical in allowing researchers to obtain more and better quality data about cellular processes and signals, the design and practical application of computational models of genomic regulation continues to be a challenge. Emerging Research in the Analysis and Modeling of Gene Regulatory Networks presents a compilation of recent and emerging research topics addressing the design and use of technology in the study and simulation of genomic regulation. Exploring both theoretical and practical topics, this publication is an essential reference source for students, professionals, and researchers working in the fields of genomics, molecular biology, bioinformatics, and drug development.