Download or read book Stochastic Narrow Escape in Molecular and Cellular Biology written by David Holcman and published by Springer. This book was released on 2015-09-08 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers recent developments in the non-standard asymptotics of the mathematical narrow escape problem in stochastic theory, as well as applications of the narrow escape problem in cell biology. The first part of the book concentrates on mathematical methods, including advanced asymptotic methods in partial equations, and is aimed primarily at applied mathematicians and theoretical physicists who are interested in biological applications. The second part of the book is intended for computational biologists, theoretical chemists, biochemists, biophysicists, and physiologists. It includes a summary of output formulas from the mathematical portion of the book and concentrates on their applications in modeling specific problems in theoretical molecular and cellular biology. Critical biological processes, such as synaptic plasticity and transmission, activation of genes by transcription factors, or double-strained DNA break repair, are controlled by diffusion in structures that have both large and small spatial scales. These may be small binding sites inside or on the surface of the cell, or narrow passages between subcellular compartments. The great disparity in spatial scales is the key to controlling cell function by structure. This volume reports recent progress on resolving analytical and numerical difficulties in extracting properties from experimental data, biophysical models, and from Brownian dynamics simulations of diffusion in multi-scale structures.

Download or read book Stochastic Processes Multiscale Modeling and Numerical Methods for Computational Cellular Biology written by David Holcman and published by Springer. This book was released on 2017-10-04 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Asymptotics of Elliptic and Parabolic PDEs written by David Holcman and published by Springer. This book was released on 2018-05-25 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Chemical Kinetics Beyond The Textbook written by Katja Lindenberg and published by World Scientific. This book was released on 2019-08-27 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: Processes involving randomly moving particles, which react either upon encounter or via distance-dependent reaction rates, are ubiquitous in nature. A few stray examples are recombination of ions or holes and electrons, excitation energy migration and quenching, trapping of particles by other species, coagulation, binding of ligands and proteins to specific sites, chemotaxis, catalytically-induced self-propulsion, polymerization, growth of dendrites or aggregates, or nuclei of a new phase.Several decades ago, it was recognized that the kinetic behavior in some systems with reactions and random transport is strongly affected by many factors, which were not taken into account in previous studies. These are, to name but a few, fluctuations in the spatial distributions of the reactants and fluctuations of the reactivity, some essentially many-particle phenomena, effects of anomalous diffusion, molecular crowding, as well as the internal geometry of the reaction bath. Within recent years, along with a growing interest in chemical processes ocurring in biological systems or cellular environments, numerous advances have been made and considerable knowledge has been acquired. These seminal contributions are, however, scattered among many journals and no attempt has been made so far to present a unified picture.This book presents a general overview of different contemporary facets of chemical kinetics in a variety of different environments. It includes 23 seminal works and reviews on different aspects of reaction processes in chemical, physical and biophysical systems, both theoretical and experimental.

Download or read book Stochastic Processes in Cell Biology written by Paul C. Bressloff and published by Springer Nature. This book was released on 2022-01-04 with total page 773 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Influence of Inter and Intra Synaptic Factors on Information Processing in the Brain written by Vito Di Maio and published by Frontiers Media SA. This book was released on 2019-10-14 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Any brain activity relies on the interaction of thousands of neurons, each of which integrating signals from thousands of synapses. While neurons are undoubtedly the building blocks of the brain, synapses constitute the main loci of information transfer that lead to the emergence of neuronal code. Investigating synaptic transmission constitutes a multi-faceted challenge that brings together a large number of techniques and expertise ranging from experimental to computational approaches, bringing together paradigms spanning from molecular to neural network level. In this book, we have collected a series of articles that present foundational work aimed at shedding much-needed light on brain information processing, synaptic transmission and neural code formation. Some articles present analyses of regulatory mechanisms underlying neural code formation and its elaboration at the molecular level, while others use computational and modelling approaches to investigate, at synaptic, neuronal and inter-neuronal level, how the different mechanisms involved in information processing interact to generate effects like long-term potentiation (LTP), which constitutes the cellular basis of learning and memory. This collection, although not exhaustive, aims to present a framework of the most used investigational paradigms and showcase results that may, in turn, generate novel hypotheses and ideas for further studies and investigations.

Download or read book Frontiers in Physics 2017 2018 Editor s Choice written by Thomas Beyer and published by Frontiers Media SA. This book was released on 2019-02-22 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: Launched in 2013, Frontiers in Physics consists of 18 specialties covering all areas of research in physics. With over 500 published manuscripts, the journal is now indexed in SCIE with the first impact factor coming in 2019. Frontiers in Physics aims to become the largest and most cited open access multidisciplinary physics journal. This eBook collects what the Specialty Chief Editors of the journal believed were the most interesting manuscripts published over the past two years. It is a nice collection, which will offer the reader the chance to have a quick overview of the specialties of the journal and offer a glimpse into the state of the art of physics. We must confess that it has been quite challenging to select only one article per specialty section given the many important manuscripts published by the journal in 2017 and 2018. We invite our reader to have a look at the journal homepage and browse what we have published so far. It includes articles on topics very different from each other, written by both early career scientists and well-known researchers, ranging from the indisputable advance of the field to the more bold. We hope you enjoy reading our first edition of the Frontiers in Physics Editor's Choice eBook! Professor Alex Hansen (Field Chief Editor) and Dr Claudio Bogazzi (Journal Manager)

Download or read book Stochastic Processes in Cell Biology written by Paul C. Bressloff and published by Springer. This book was released on 2021-09-28 with total page 699 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Theory and Applications of Stochastic Differential Equations written by Zeev Schuss and published by . This book was released on 1980 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents theory, sources, and applications of stochastic differential equations of Ito's type; those containing white noise. Closely studies first passage problems by modern singular perturbation methods and their role in various fields of science. Introduces analytical methods to obtain information on probabilistic quantities. Demonstrates the role of partial differential equations in this context. Clarifies the relationship between the complex mathematical theories involved and sources of the problem for physicists, chemists, engineers, and other non-mathematical specialists.

Download or read book Brownian Dynamics at Boundaries and Interfaces written by Zeev Schuss and published by Springer Science & Business Media. This book was released on 2013-08-15 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Brownian dynamics serve as mathematical models for the diffusive motion of microscopic particles of various shapes in gaseous, liquid, or solid environments. The renewed interest in Brownian dynamics is due primarily to their key role in molecular and cellular biophysics: diffusion of ions and molecules is the driver of all life. Brownian dynamics simulations are the numerical realizations of stochastic differential equations that model the functions of biological micro devices such as protein ionic channels of biological membranes, cardiac myocytes, neuronal synapses, and many more. Stochastic differential equations are ubiquitous models in computational physics, chemistry, biophysics, computer science, communications theory, mathematical finance theory, and many other disciplines. Brownian dynamics simulations of the random motion of particles, be it molecules or stock prices, give rise to mathematical problems that neither the kinetic theory of Maxwell and Boltzmann, nor Einstein’s and Langevin’s theories of Brownian motion could predict. This book takes the readers on a journey that starts with the rigorous definition of mathematical Brownian motion, and ends with the explicit solution of a series of complex problems that have immediate applications. It is aimed at applied mathematicians, physicists, theoretical chemists, and physiologists who are interested in modeling, analysis, and simulation of micro devices of microbiology. The book contains exercises and worked out examples throughout.

Download or read book Elementary Fluid Dynamics written by D. J. Acheson and published by Oxford University Press. This book was released on 1990-03-15 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a clear and concise introduction to both theory and application of fluid dynamics. It has a wide scope, frequent references to experiments, and numerous exercises (with hints and answers).

Download or read book Modeling the 3D Conformation of Genomes written by Guido Tiana and published by CRC Press. This book was released on 2019-01-15 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a timely summary of physical modeling approaches applied to biological datasets that describe conformational properties of chromosomes in the cell nucleus. Chapters explain how to convert raw experimental data into 3D conformations, and how to use models to better understand biophysical mechanisms that control chromosome conformation. The coverage ranges from introductory chapters to modeling aspects related to polymer physics, and data-driven models for genomic domains, the entire human genome, epigenome folding, chromosome structure and dynamics, and predicting 3D genome structure.

Download or read book The Mathematics of Diffusion written by John Crank and published by Oxford University Press. This book was released on 1979 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Though it incorporates much new material, this new edition preserves the general character of the book in providing a collection of solutions of the equations of diffusion and describing how these solutions may be obtained.

Download or read book Molecular Dynamics written by Ben Leimkuhler and published by Springer. This book was released on 2015-05-18 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the mathematical underpinnings of algorithms used for molecular dynamics simulation, including both deterministic and stochastic numerical methods. Molecular dynamics is one of the most versatile and powerful methods of modern computational science and engineering and is used widely in chemistry, physics, materials science and biology. Understanding the foundations of numerical methods means knowing how to select the best one for a given problem (from the wide range of techniques on offer) and how to create new, efficient methods to address particular challenges as they arise in complex applications. Aimed at a broad audience, this book presents the basic theory of Hamiltonian mechanics and stochastic differential equations, as well as topics including symplectic numerical methods, the handling of constraints and rigid bodies, the efficient treatment of Langevin dynamics, thermostats to control the molecular ensemble, multiple time-stepping, and the dissipative particle dynamics method.

Download or read book Physics in Molecular Biology written by Kim Sneppen and published by Cambridge University Press. This book was released on 2005-08-25 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, first published in 2005, is a discussion for advanced physics students of how to use physics to model biological systems.

Download or read book Molecular and Cellular Biophysics written by Meyer B. Jackson and published by Cambridge University Press. This book was released on 2006-01-12 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: Molecular and Cellular Biophysics provides advanced undergraduate and graduate students with a foundation in the basic concepts of biophysics. Students who have taken physical chemistry and calculus courses will find this book an accessible and valuable aid in learning how these concepts can be used in biological research. The text provides a rigorous treatment of the fundamental theories in biophysics and illustrates their application with examples. Conformational transitions of proteins are studied first using thermodynamics, and subsequently with kinetics. Allosteric theory is developed as the synthesis of conformational transitions and association reactions. Basic ideas of thermodynamics and kinetics are applied to topics such as protein folding, enzyme catalysis and ion channel permeation. These concepts are then used as the building blocks in a treatment of membrane excitability. Through these examples, students will gain an understanding of the general importance and broad applicability of biophysical principles to biological problems.

Download or read book Quantum Adaptivity in Biology From Genetics to Cognition written by Masanari Asano and published by Springer. This book was released on 2015-04-14 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines information processing performed by bio-systems at all scales: from genomes, cells and proteins to cognitive and even social systems. It introduces a theoretical/conceptual principle based on quantum information and non-Kolmogorov probability theory to explain information processing phenomena in biology as a whole. The book begins with an introduction followed by two chapters devoted to fundamentals, one covering classical and quantum probability, which also contains a brief introduction to quantum formalism, and another on an information approach to molecular biology, genetics and epigenetics. It then goes on to examine adaptive dynamics, including applications to biology, and non-Kolmogorov probability theory. Next, the book discusses the possibility to apply the quantum formalism to model biological evolution, especially at the cellular level: genetic and epigenetic evolutions. It also presents a model of the epigenetic cellular evolution based on the mathematical formalism of open quantum systems. The last two chapters of the book explore foundational problems of quantum mechanics and demonstrate the power of usage of positive operator valued measures (POVMs) in biological science. This book will appeal to a diverse group of readers including experts in biology, cognitive science, decision making, sociology, psychology, and physics; mathematicians working on problems of quantum probability and information and researchers in quantum foundations.