What every neuroscientist should know about the mathematical modeling of excitable cells, presented at an introductory level.

This edited volume contains a selection of chapters that are an outgrowth of the - ropean Conference on Mathematical and Theoretical Biology (ECMTB05, Dresden, Germany, July 2005). The peer-reviewed contributions show that mathematical and computational approaches are absolutely essential for solving central problems in the life sciences, ranging from the organizational level of individual cells to the dynamics of whole populations. The contributions indicate that theoretical and mathematical biology is a diverse and interdisciplinary ?eld, ranging from experimental research linked to mathema- cal modeling to the development of more abstract mathematical frameworks in which observations about the real world can be interpreted, and with which new hypotheses for testing can be generated. Today, much attention is also paid to the development of ef?cient algorithms for complex computation and visualisation, notably in molecular biology and genetics. The ?eld of theoretical and mathematical biology and medicine has profound connections to many current problems of great relevance to society. The medical, industrial, and social interests in its development are in fact indisputable.

This book provides an introduction to two important aspects of modern bioch- istry, molecular biology, and biophysics: computer simulation and data analysis. My aim is to introduce the tools that will enable students to learn and use some f- damental methods to construct quantitative models of biological mechanisms, both deterministicandwithsomeelementsofrandomness;tolearnhowconceptsofpr- ability can help to understand important features of DNA sequences; and to apply a useful set of statistical methods to analysis of experimental data. The availability of very capable but inexpensive personal computers and software makes it possible to do such work at a much higher level, but in a much easier way, than ever before. TheExecutiveSummaryofthein?uential2003reportfromtheNationalAcademy of Sciences, “BIO 2010: Transforming Undergraduate Education for Future - search Biologists” [12], begins The interplay of the recombinant DNA, instrumentation, and digital revolutions has p- foundly transformed biological research. The con?uence of these three innovations has led to important discoveries, such as the mapping of the human genome. How biologists design, perform, and analyze experiments is changing swiftly. Biological concepts and models are becoming more quantitative, and biological research has become critically dependent on concepts and methods drawn from other scienti?c disciplines. The connections between the biological sciences and the physical sciences, mathematics, and computer science are rapidly becoming deeper and more extensive.

Computational modeling is emerging as a powerful new approach to study and manipulate biological systems. Multiple methods have been developed to model, visualize, and rationally alter systems at various length scales, starting from molecular modeling and design at atomic resolution to cellular pathways modeling and analysis. Higher time and length scale processes, such as molecular evolution, have also greatly benefited from new breeds of computational approaches. This book provides an overview of the established computational methods used for modeling biologically and medically relevant systems.

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.

This book covers a wide scope of biological approaches to such biological phenomena as cell division, motility, collective cell behavior, multicellular structures, morphogenesis, and tumor development. Over the past two decades, biologists have generated large sets of experimental data and discovered a lot of facts that need explanation. This biological boom attracts physicists who believe they can help to develop a theoretical framework in biology and explain complete biological phenomena using basic principles. This is the first book to present recent advances in biophysical studies of the different aspects of cell life. This book presents recent advances in biophysical studies of living cells and gives the impression that a combination of quantitative live cell observations, detailed biochemical and biophysical data, and mathematical modeling are capable to answer many important biological questions and to achieve a more complete understanding of such complex phenomena.

This work shows how the cellular Potts model can be used as a framework for model building and how extended models can achieve even better biological practicality, accuracy, and predictive power. It focuses on ways to integrate and interface the basic cellular Potts model at the mesoscopic scale with approaches that accurately model microscopic dynamics. These extensions are designed to create a nested and hybrid environment, where the evolution of a biological system is realistically driven by the constant interplay and flux of information between the different levels of description.