This book gives a concise overview of the mathematical foundations of kinetics used in chemistry and systems biology. The analytical and numerical methods used to solve complex rate equations with the widely used deterministic approach will be described, with primary focus on practical aspects important in designing experimental studies and the evaluation of data. The introduction of personal computers transformed scientific attitudes in the last two decades considerably as computational power ceased to be a limiting factor. Despite this improvement, certain time-honored approximations in solving rate equations such as the pre-equilibrium or the steady-state approach are still valid and necessary as they concern the information content of measured kinetic traces. The book shows the role of these approximations in modern kinetics and will also describe some common misconceptions in this field.

This book gives a concise overview of the mathematical foundations of kinetics used in chemistry and systems biology. The analytical and numerical methods used to solve complex rate equations with the widely used deterministic approach will be described, with primary focus on practical aspects important in designing experimental studies and the evaluation of data. The introduction of personal computers transformed scientific attitudes in the last two decades considerably as computational power ceased to be a limiting factor. Despite this improvement, certain time-honored approximations in solving rate equations such as the pre-equilibrium or the steady-state approach are still valid and necessary as they concern the information content of measured kinetic traces. The book shows the role of these approximations in modern kinetics and will also describe some common misconceptions in this field.

This volume reviews the theory and simulation methods of stochastic kinetics by integrating historical and recent perspectives, presents applications, mostly in the context of systems biology and also in combustion theory. In recent years, due to the development in experimental techniques, such as optical imaging, single cell analysis, and fluorescence spectroscopy, biochemical kinetic data inside single living cells have increasingly been available. The emergence of systems biology brought renaissance in the application of stochastic kinetic methods.

Fifty years ago, a new approach to reaction kinetics began to emerge: one based on mathematical models of reaction kinetics, or formal reaction kinetics. Since then, there has been a rapid and accelerated development in both deterministic and stochastic kinetics, primarily because mathematicians studying differential equations and algebraic geometry have taken an interest in the nonlinear differential equations of kinetics, which are relatively simple, yet capable of depicting complex behavior such as oscillation, chaos, and pattern formation. The development of stochastic models was triggered by the fact that novel methods made it possible to measure molecules individually. Now it is high time to make the results of the last half-century available to a larger audience: students of chemistry, chemical engineering and biochemistry, not to mention applied mathematics. Based on recent papers, this book presents the most important concepts and results, together with a wealth of solved exercises. The book is accompanied by the authors’ Mathematica package, ReactionKinetics, which helps both students and scholars in their everyday work, and which can be downloaded from http://extras.springer.com/ and also from the authors’ websites. Further, the large set of unsolved problems provided may serve as a springboard for individual research.

Chemical kinetics may be considered as a prototype of nonlinear science, since the velocities of a reaction are generally nonlinear functions of the quantities of reactants. Although an actual chemical process is spatially extensive and involves very large numbers of constituent particles and a considerable number of intermediate transition compounds, the behavior--equilibria, periodicity, or chaos--may be described by the stoichiometric equations for a relatively small number of reactants. The macroscopic description of the kinetics can be deterministic, by a low-order system of nonlinear ordinary differential equations with polynomial right-hand sides, or stochastic, in terms of Markov jump processes. This volume surveys the mathematical models of chemical kinetics--their algebraic structure, mass action deterministic models, continuous time, discrete state stochastic models, and spatial effects mediated by diffusion. Further, the metalanguage of chemical kinetics is used to describe behavior in systems of interacting components, in neurochemistry, population biology, and ecology.

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.

A guide to the theoretical and computational toolkits for the modern study of molecular kinetics in condensed phases Molecular Kinetics in Condensed Phases: Theory, Simulation and Analysis puts the focus on the theory, algorithms, simulations methods and analysis of molecular kinetics in condensed phases. The authors – noted experts on the topic – offer a detailed and thorough description of modern theories and simulation methods to model molecular events. They highlight the rigorous stochastic modelling of molecular processes and the use of mathematical models to reproduce experimental observations, such as rate coefficients, mean first passage times and transition path times. The book’s exploration of simulations examines atomically detailed modelling of molecules in action and the connections of these simulations to theory and experiment. The authors also explore the applications that range from simple intuitive examples of one- and two-dimensional systems to complex solvated macromolecules. This important book: Offers an introduction to the topic that combines theory, simulation and analysis Presents a guide written by authors that are well-known and highly regarded leaders in their fields Contains detailed examples and explanation of how to conduct computer simulations of kinetics. A detailed study of a two-dimensional system and of a solvated peptide are discussed. Discusses modern developments in the field and explains their connection to the more traditional concepts in chemical dynamics Written for students and academic researchers in the fields of chemical kinetics, chemistry, computational statistical mechanics, biophysics and computational biology, Molecular Kinetics in Condensed Phases is the authoritative guide to the theoretical and computational toolkits for the study of molecular kinetics in condensed phases.