Stochastic Analysis of Biochemical Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Stochastic Analysis of Biochemical Systems write by David F. Anderson. This book was released on 2015-04-23. Stochastic Analysis of Biochemical Systems available in PDF, EPUB and Kindle. This book focuses on counting processes and continuous-time Markov chains motivated by examples and applications drawn from chemical networks in systems biology. The book should serve well as a supplement for courses in probability and stochastic processes. While the material is presented in a manner most suitable for students who have studied stochastic processes up to and including martingales in continuous time, much of the necessary background material is summarized in the Appendix. Students and Researchers with a solid understanding of calculus, differential equations and elementary probability and who are well-motivated by the applications will find this book of interest. David F. Anderson is Associate Professor in the Department of Mathematics at the University of Wisconsin and Thomas G. Kurtz is Emeritus Professor in the Departments of Mathematics and Statistics at that university. Their research is focused on probability and stochastic processes with applications in biology and other areas of science and technology. These notes are based in part on lectures given by Professor Anderson at the University of Wisconsin – Madison and by Professor Kurtz at Goethe University Frankfurt.
Stochastic Approaches for Systems Biology
Stochastic Approaches for Systems Biology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Stochastic Approaches for Systems Biology write by Mukhtar Ullah. This book was released on 2011-07-12. Stochastic Approaches for Systems Biology available in PDF, EPUB and Kindle. 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.
On Moments and Timing
On Moments and Timing - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook On Moments and Timing write by Khem Raj Ghusinga. This book was released on 2018. On Moments and Timing available in PDF, EPUB and Kindle. At the level of individual living cells, key species such as genes, mRNAs, and proteins are typically present in small numbers. Consequently, the biochemical reactions involving these species are inherently noisy and result in considerable cell-to-cell variability. This thesis outlines two mathematical tools to quantify stochasticity in these biochemical reaction systems: (i) a novel computational method that provides exact lower and upper bounds on statistical moments of population counts of important species, and (ii) a first-passage time framework to study noise in the timing of a cellular event that occurs when population count of an underlying regulatory protein attains a critical threshold. ☐ The method to compute bounds on moments builds upon the well-known linear dynamical system that describes the time evolution of statistical moments. However, except for some ideal cases, this dynamical system is not closed in the sense that lower-order moments depend upon some higher-order moments. To overcome this issue, our method exploits the fact that statistical moments of a random variable must satisfy constraints that are compactly represented through the positive semidefiniteness of moment matrices. We find lower and upper bounds on a moment of interest via a semidefinite program that includes linear constraints obtained from moment dynamics, along with semidefinite constraints on moment matrices. We further show that these bounds improve as the size of the semidefinite program is increased by including dynamics of more moments as well as constraints involving them. We also extend the scope of this method for stochastic hybrid systems, which are a more general class of stochastic systems that integrate discrete and continuous dynamics. ☐ The second tool proposed in this thesis - a first-passage time framework to study event timing - is based on the premise that several cellular events in living cells occur upon attainment of critical levels by corresponding regulatory proteins. Two particular examples that we study here are the lysis of a bacterial cell infected by the virus bacteriophage lambda and the cell-division in exponentially growing bacterial cells. We provide analytical calculations for the first-passage time distribution and its moments for both these examples. We show that the first-passage time statistics can be used to explain several experimentally observed behaviors in both these systems. Finally, the thesis discusses potential directions for future research.
Stochastic Modelling for Systems Biology
Stochastic Modelling for Systems Biology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Stochastic Modelling for Systems Biology write by Darren J. Wilkinson. This book was released on 2006-04-18. Stochastic Modelling for Systems Biology available in PDF, EPUB and Kindle. Although stochastic kinetic models are increasingly accepted as the best way to represent and simulate genetic and biochemical networks, most researchers in the field have limited knowledge of stochastic process theory. The stochastic processes formalism provides a beautiful, elegant, and coherent foundation for chemical kinetics and there is a wealth of associated theory every bit as powerful and elegant as that for conventional continuous deterministic models. The time is right for an introductory text written from this perspective. Stochastic Modelling for Systems Biology presents an accessible introduction to stochastic modelling using examples that are familiar to systems biology researchers. Focusing on computer simulation, the author examines the use of stochastic processes for modelling biological systems. He provides a comprehensive understanding of stochastic kinetic modelling of biological networks in the systems biology context. The text covers the latest simulation techniques and research material, such as parameter inference, and includes many examples and figures as well as software code in R for various applications. While emphasizing the necessary probabilistic and stochastic methods, the author takes a practical approach, rooting his theoretical development in discussions of the intended application. Written with self-study in mind, the book includes technical chapters that deal with the difficult problems of inference for stochastic kinetic models from experimental data. Providing enough background information to make the subject accessible to the non-specialist, the book integrates a fairly diverse literature into a single convenient and notationally consistent source.
Stochastic Chemical Reaction Systems in Biology
Stochastic Chemical Reaction Systems in Biology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Stochastic Chemical Reaction Systems in Biology write by Hong Qian. This book was released on 2021-10-18. Stochastic Chemical Reaction Systems in Biology available in PDF, EPUB and Kindle. This book provides an introduction to the analysis of stochastic dynamic models in biology and medicine. The main aim is to offer a coherent set of probabilistic techniques and mathematical tools which can be used for the simulation and analysis of various biological phenomena. These tools are illustrated on a number of examples. For each example, the biological background is described, and mathematical models are developed following a unified set of principles. These models are then analyzed and, finally, the biological implications of the mathematical results are interpreted. The biological topics covered include gene expression, biochemistry, cellular regulation, and cancer biology. The book will be accessible to graduate students who have a strong background in differential equations, the theory of nonlinear dynamical systems, Markovian stochastic processes, and both discrete and continuous state spaces, and who are familiar with the basic concepts of probability theory.
