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Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology

Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology PDF Author: David Holcman
Publisher: Springer
ISBN: 3319626272
Category : Mathematics
Languages : en
Pages : 377

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Book Description
This book focuses on the modeling and mathematical analysis of stochastic dynamical systems along with their simulations. The collected chapters will review fundamental and current topics and approaches to dynamical systems in cellular biology. This text aims to develop improved mathematical and computational methods with which to study biological processes. At the scale of a single cell, stochasticity becomes important due to low copy numbers of biological molecules, such as mRNA and proteins that take part in biochemical reactions driving cellular processes. When trying to describe such biological processes, the traditional deterministic models are often inadequate, precisely because of these low copy numbers. This book presents stochastic models, which are necessary to account for small particle numbers and extrinsic noise sources. The complexity of these models depend upon whether the biochemical reactions are diffusion-limited or reaction-limited. In the former case, one needs to adopt the framework of stochastic reaction-diffusion models, while in the latter, one can describe the processes by adopting the framework of Markov jump processes and stochastic differential equations. Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology will appeal to graduate students and researchers in the fields of applied mathematics, biophysics, and cellular biology.

Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology

Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology PDF Author: David Holcman
Publisher: Springer
ISBN: 3319626272
Category : Mathematics
Languages : en
Pages : 377

View

Book Description
This book focuses on the modeling and mathematical analysis of stochastic dynamical systems along with their simulations. The collected chapters will review fundamental and current topics and approaches to dynamical systems in cellular biology. This text aims to develop improved mathematical and computational methods with which to study biological processes. At the scale of a single cell, stochasticity becomes important due to low copy numbers of biological molecules, such as mRNA and proteins that take part in biochemical reactions driving cellular processes. When trying to describe such biological processes, the traditional deterministic models are often inadequate, precisely because of these low copy numbers. This book presents stochastic models, which are necessary to account for small particle numbers and extrinsic noise sources. The complexity of these models depend upon whether the biochemical reactions are diffusion-limited or reaction-limited. In the former case, one needs to adopt the framework of stochastic reaction-diffusion models, while in the latter, one can describe the processes by adopting the framework of Markov jump processes and stochastic differential equations. Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology will appeal to graduate students and researchers in the fields of applied mathematics, biophysics, and cellular biology.

Stochastic Processes in Cell Biology

Stochastic Processes in Cell Biology PDF Author: Paul C. Bressloff
Publisher: Springer Nature
ISBN: 3030725154
Category : Biomathematics
Languages : en
Pages : 773

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Book Description
This book develops the theory of continuous and discrete stochastic processes within the context of cell biology. In the second edition the material has been significantly expanded, particularly within the context of nonequilibrium and self-organizing systems. Given the amount of additional material, the book has been divided into two volumes, with volume I mainly covering molecular processes and volume II focusing on cellular processes. A wide range of biological topics are covered in the new edition, including stochastic ion channels and excitable systems, molecular motors, stochastic gene networks, genetic switches and oscillators, epigenetics, normal and anomalous diffusion in complex cellular environments, stochastically-gated diffusion, active intracellular transport, signal transduction, cell sensing, bacterial chemotaxis, intracellular pattern formation, cell polarization, cell mechanics, biological polymers and membranes, nuclear structure and dynamics, biological condensates, molecular aggregation and nucleation, cellular length control, cell mitosis, cell motility, cell adhesion, cytoneme-based morphogenesis, bacterial growth, and quorum sensing. The book also provides a pedagogical introduction to the theory of stochastic and nonequilibrium processes Fokker Planck equations, stochastic differential equations, stochastic calculus, master equations and jump Markov processes, birth-death processes, Poisson processes, first passage time problems, stochastic hybrid systems, queuing and renewal theory, narrow capture and escape, extreme statistics, search processes and stochastic resetting, exclusion processes, WKB methods, large deviation theory, path integrals, martingales and branching processes, numerical methods, linear response theory, phase separation, fluctuation-dissipation theorems, age-structured models, and statistical field theory. This text is primarily aimed at graduate students and researchers working in mathematical biology, statistical and biological physicists, and applied mathematicians interested in stochastic modeling. Applied probabilists should also find it of interest. It provides significant background material in applied mathematics and statistical physics, and introduces concepts in stochastic and nonequilibrium processes via motivating biological applications. The book is highly illustrated and contains a large number of examples and exercises that further develop the models and ideas in the body of the text. It is based on a course that the author has taught at the University of Utah for many years.

Analytic Methods for Coagulation-Fragmentation Models, Volume II

Analytic Methods for Coagulation-Fragmentation Models, Volume II PDF Author: Jacek Banasiak
Publisher: CRC Press
ISBN: 1000001318
Category : Mathematics
Languages : en
Pages : 322

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Book Description
Analytic Methods for Coagulation-Fragmentation Models is a two-volume set that provides a comprehensive exposition of the mathematical analysis of coagulation-fragmentation models. Initially, an in-depth survey of coagulation-fragmentation processes is presented, together with an account of relevant early results obtained on the associated model equations. These provide motivation for the subsequent detailed treatment of more up-to-date investigations which have led to significant theoretical developments on topics such as solvability and the long-term behaviour of solutions. To make the account as self-contained as possible, the mathematical tools that feature prominently in these modern treatments are introduced at appropriate places. The main theme of Volume I is the analysis of linear fragmentation models, with Volume II devoted to processes that involve the nonlinear contribution of coagulation. Features of Volume II: A primer on weak compactness in L 1 and dynamical systems A comprehensive theory of solvability of the coagulation-fragmentation equation by both the semigroup and weak compactness methods, including a thorough analysis of the gelation and shattering phenomena A detailed analysis of the long-term dynamics of the coagulation-fragmentation equations with a state-of-the-art discussion on self-similar solutions

Network Bioscience, 2nd Edition

Network Bioscience, 2nd Edition PDF Author: Marco Pellegrini
Publisher: Frontiers Media SA
ISBN: 288963650X
Category :
Languages : en
Pages : 270

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Mitochondrial Genetics and Epigenetics

Mitochondrial Genetics and Epigenetics PDF Author: Caterina Garone
Publisher: Frontiers Media SA
ISBN: 2889662322
Category : Science
Languages : en
Pages :

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Asymptotics of Elliptic and Parabolic PDEs

Asymptotics of Elliptic and Parabolic PDEs PDF Author: David Holcman
Publisher: Springer
ISBN: 3319768956
Category : Mathematics
Languages : en
Pages : 444

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Book Description
This is a monograph on the emerging branch of mathematical biophysics combining asymptotic analysis with numerical and stochastic methods to analyze partial differential equations arising in biological and physical sciences. In more detail, the book presents the analytic methods and tools for approximating solutions of mixed boundary value problems, with particular emphasis on the narrow escape problem. Informed throughout by real-world applications, the book includes topics such as the Fokker-Planck equation, boundary layer analysis, WKB approximation, applications of spectral theory, as well as recent results in narrow escape theory. Numerical and stochastic aspects, including mean first passage time and extreme statistics, are discussed in detail and relevant applications are presented in parallel with the theory. Including background on the classical asymptotic theory of differential equations, this book is written for scientists of various backgrounds interested in deriving solutions to real-world problems from first principles.

Numerical Methods and Advanced Simulation in Biomechanics and Biological Processes

Numerical Methods and Advanced Simulation in Biomechanics and Biological Processes PDF Author: Miguel Cerrolaza
Publisher: Academic Press
ISBN: 0128117192
Category : Technology & Engineering
Languages : en
Pages : 454

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Book Description
Numerical Methods and Advanced Simulation in Biomechanics and Biological Processes covers new and exciting modeling methods to help bioengineers tackle problems for which the Finite Element Method is not appropriate. The book covers a wide range of important subjects in the field of numerical methods applied to biomechanics, including bone biomechanics, tissue and cell mechanics, 3D printing, computer assisted surgery and fluid dynamics. Modeling strategies, technology and approaches are continuously evolving as the knowledge of biological processes increases. Both theory and applications are covered, making this an ideal book for researchers, students and R&D professionals. Provides non-conventional analysis methods for modeling Covers the Discrete Element Method (DEM), Particle Methods (PM), MessLess and MeshFree Methods (MLMF), Agent-Based Methods (ABM), Lattice-Boltzmann Methods (LBM) and Boundary Integral Methods (BIM) Includes contributions from several world renowned experts in their fields Compares pros and cons of each method to help you decide which method is most applicable to solving specific problems

Encyclopedia of Cell Biology

Encyclopedia of Cell Biology PDF Author:
Publisher: Academic Press
ISBN: 0123947960
Category : Science
Languages : en
Pages : 3008

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Book Description
The Encyclopedia of Cell Biology offers a broad overview of cell biology, offering reputable, foundational content for researchers and students across the biological and medical sciences. This important work includes 285 articles from domain experts covering every aspect of cell biology, with fully annotated figures, abundant illustrations, videos, and references for further reading. Each entry is built with a layered approach to the content, providing basic information for those new to the area and more detailed material for the more experienced researcher. With authored contributions by experts in the field, the Encyclopedia of Cell Biology provides a fully cross-referenced, one-stop resource for students, researchers, and teaching faculty across the biological and medical sciences. Fully annotated color images and videos for full comprehension of concepts, with layered content for readers from different levels of experience Includes information on cytokinesis, cell biology, cell mechanics, cytoskeleton dynamics, stem cells, prokaryotic cell biology, RNA biology, aging, cell growth, cell Injury, and more In-depth linking to Academic Press/Elsevier content and additional links to outside websites and resources for further reading A one-stop resource for students, researchers, and teaching faculty across the biological and medical sciences

Advanced HPC-based Computational Modeling in Biomechanics and Systems Biology

Advanced HPC-based Computational Modeling in Biomechanics and Systems Biology PDF Author: Mariano Vázquez
Publisher: Frontiers Media SA
ISBN: 2889458172
Category :
Languages : en
Pages : 449

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Introduction to Quantitative Cell Biology

Introduction to Quantitative Cell Biology PDF Author: Wallace F. Marshall
Publisher: Biota Publishing
ISBN: 1615046690
Category : Science
Languages : en
Pages : 50

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Book Description
For the past decade or more, much of cell biology research has been focused on determining the key molecules involved in different cellular processes, an analytical problem that has been amenable to biochemical and genetic approaches. Now, we face an integrative problem of understanding how all of these molecules work together to produce living cells, a challenge that requires using quantitative approaches to model the complex interactions within a cell, and testing those models with careful quantitative measurements. This book is an introductory overview of the various approaches, methods, techniques, and models employed in quantitative cell biology, which are reviewed in greater detail in the other volumes in this e-book series. Particular emphasis is placed on the goals and purpose of quantitative analysis and modeling, and the special challenges that cell biology holds for understanding life at the physical level.