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Architects of Structural Biology: Bragg, Perutz, Kendrew, Hodgkin

John Meurig Thomas

Designed for the non-specialist, the explanations and illustrations used here describe the work, personalities, collaborations, and idiosyncrasies of four of the most distinguished Nobel Laureates of ... More

Designed for the non-specialist, the explanations and illustrations used here describe the work, personalities, collaborations, and idiosyncrasies of four of the most distinguished Nobel Laureates of the twentieth century. They exploited a discovery made over a century ago about the nature of X-rays, and thereby created a new branch of science. This enabled them to elucidate, in atomic detail, the structure and mode of action of molecules of the living world: enzymes, vitamins, and viruses, as well as antibiotics. Perutz and Kendrew, from their pioneering work using X-ray diffraction on haemoglobin and myoglobin, the proteins that transport and store oxygen in all animals, led them to establish in 1962 one of the most successful research centres ever—the Laboratory of Molecular Biology (LMB) in Cambridge. Medicines discovered there are used worldwide to treat leukaemia, arthritis, and other diseases. Their work also led to the creation in the United States of the Protein Data Bank that guides scientists in understanding the misfolding of proteins, which cause Alzheimer’s disease, Parkinson’s disease, and other neurodegenerative diseases. This book is first a memoir of these scientists and their contemporaries, many of them friends of the author. Second, it is an insight into the great excitement associated with structural molecular biology, which directly informs our understanding of ourselves. Third, it describes how two renowned research centres in the United Kingdom—the LMB and the Davy-Faraday Research Laboratory—achieved iconic status. It also highlights the importance of the popularization of science, of which Bragg, Perutz, and Kendrew, as well as Dorothy Hodgkin (who solved the structures of penicillin and vitamin B12) were experts.Less

Basic X-Ray Scattering for Soft Matter

Wim H. de Jeu

X-ray scattering is a well-established technique in materials science. Several excellent textbooks exist in the field, typically written by physicists who use mathematics to make things clear. Often ... More

X-ray scattering is a well-established technique in materials science. Several excellent textbooks exist in the field, typically written by physicists who use mathematics to make things clear. Often these books do not reach students and scientists in the field of soft matter (polymers, liquid crystals, colloids, and self-assembled organic systems), who usually have a chemical-oriented background with limited mathematics. Moreover, often these people like to know more about x-ray scattering as a technique to be used, but do not necessarily intend to become an expert. This volume is unique in trying to accommodate both points. The aim of the book is to explain basic principles and applications of x-ray scattering in a simple way. The intention is a paperback of limited size that people will like to have on hand rather than on a shelf. Second, it includes a large variety of examples of x-ray scattering of soft matter with, at the end of each chapter, a more elaborate case study. Third, the book contains a separate chapter on the different types of order/disorder in soft matter that play such an important role in modern self-assembling systems. Finally, the last chapter treats soft matter surfaces and thin film that are increasingly used in coatings and in many technological applications (liquid crystal displays, nanostructured block copolymer films). There is a niche for a book of this type that potentially addresses a large group of (soft matter) students and scientists.Less

Biological Small Angle Scattering: Theory and Practice

Eaton E. Lattman, Thomas D. Grant, and Edward H. Snell

The technique of small angle solution scattering has been revolutionized in the last two decades. Exponential increases in computing power, parallel algorithm development, and the development of ... More

The technique of small angle solution scattering has been revolutionized in the last two decades. Exponential increases in computing power, parallel algorithm development, and the development of synchrotron, free-electron X-ray sources, and neutron sources, have combined to allow new classes of studies for biological specimens. These include time-resolved experiments in which functional motions of proteins are monitored on a picosecond timescale, and the first steps towards determining actual electron density fluctuations within particles. In addition, more traditional experiments involving the determination of size and shape, and contrast matching that isolate substructures such as nucleic acid, have become much more straightforward to carry out, and simultaneously require much less material. These new capabilities have sparked an upsurge of interest in solution scattering on the part of investigators in related disciplines. Thus, this book seeks to guide structural biologists to understand the basics of small angle solution scattering in both the X-ray and neutron case, to appreciate its strengths, and to be cognizant of its limitations. It is also directed at those who have a general interest in its potential. The book focuses on three areas: theory, practical aspects and applications, and the potential of developing areas. It is an introduction and guide to the field but not a comprehensive treatment of all the potential applications.Less

Biomedical Fluid Dynamics: Flow and Form

Troy Shinbrot

This book provides an overview of fundamental methods and advanced topics associated with complex, especially biological, fluids. The contents are taken from a graduate level course taught to ... More

This book provides an overview of fundamental methods and advanced topics associated with complex, especially biological, fluids. The contents are taken from a graduate level course taught to biomedical engineers, many of whom are math averse. Consequently the book is organized around gentle historical foundations and illustrative tabletop experiments to make for accessible reading. The book begins with derivations of fundamental equations, defined in the simplest terms possible, and adds embellishments one at a time to build toward the analysis of complex fluid dynamics an and introduction to spontaneous pattern formation. Topics covered include elastic surfaces, flow through elastic tubes, pulsatile flows, effects of entrances, branches, and bends, shearing flows, effects of increased Reynolds number, inviscid flows, rheology in complex fluids, statistical mechanics, diffusion, and self-assembly.Less

Cognitive Biology: Dealing with Information from Bacteria to Minds

Gennaro Auletta

The book provides a new conceptual scaffold for further research in biology and cognition by introducing the new field of Cognitive Biology. It is a systems biology approach showing that further ... More

The book provides a new conceptual scaffold for further research in biology and cognition by introducing the new field of Cognitive Biology. It is a systems biology approach showing that further progress in this field will depend on a deep recognition of developmental processes, as well as on the consideration of the developed organism as an agent able to modify and control its surrounding environment. The role of cognition, the means through which the organism is able to cope with its environment, cannot be underestimated. In particular, it is shown that this activity is grounded on a theory of information based on Bayesian probabilities. The organism is considered as a cybernetic system able to integrate a processor as a source of variety (the genetic system), a regulator of its own homeostasis (the metabolic system), and a selecting system separating the self from the non-self (the membrane in unicellular organisms).Less

Computer Simulation of Liquids: Second Edition

Michael P. Allen and Dominic J. Tildesley

This book provides a practical guide to molecular dynamics and Monte Carlo simulation techniques used in the modelling of simple and complex liquids. Computer simulation is an essential tool in ... More

This book provides a practical guide to molecular dynamics and Monte Carlo simulation techniques used in the modelling of simple and complex liquids. Computer simulation is an essential tool in studying the chemistry and physics of condensed matter, complementing and reinforcing both experiment and theory. Simulations provide detailed information about structure and dynamics, essential to understand the many fluid systems that play a key role in our daily lives: polymers, gels, colloidal suspensions, liquid crystals, biological membranes, and glasses. The second edition of this pioneering book aims to explain how simulation programs work, how to use them, and how to interpret the results, with examples of the latest research in this rapidly evolving field. Accompanying programs in Fortran and Python provide practical, hands-on, illustrations of the ideas in the text.Less

Dielectric Relaxation in Biological Systems: Physical Principles, Methods, and Applications

Valerica Raicu and Yuri Feldman (eds)

This book covers the theoretical basis, experimental methods, and practical applications of the dielectric properties of biological systems, such as water, electrolytes and polyelectrolytes, ... More

This book covers the theoretical basis, experimental methods, and practical applications of the dielectric properties of biological systems, such as water, electrolytes and polyelectrolytes, solutions of biological macromolecules, cell suspensions, and cellular systems. The first six chapters cover theoretical, methodological, and experimental aspects of relaxation and dispersion in biological dielectrics at molecular, cellular, and cellular aggregate levels. Applications are presented in the following eight chapters, which are organized in the order of increased complexity, beginning with pure water, amino acids, and proteins, continuing with vesicles and simple cells such as erythrocytes, and then with more complex, organelle-containing cells and cellular aggregates. The first three chapters assume some knowledge of calculus and advanced mathematical methods in electricity and magnetism.Less

Evolution of Networks: From Biological Nets to the Internet and WWW

S.N. Dorogovtsev and J.F.F. Mendes

The aim of this book is to understand networks and the basic principles of their structural organization and evolution. The ideas are presented in a clear and a pedagogical way. Special attention is ... More

The aim of this book is to understand networks and the basic principles of their structural organization and evolution. The ideas are presented in a clear and a pedagogical way. Special attention is given to real networks, both natural and artificial, including the Internet and the World Wide Web. Collected empirical data and numerous real applications of existing theories are discussed in detail, as well as the topical problems of communication and other networks.Less

First Steps in Random Walks: From Tools to Applications

J. Klafter and I. M. Sokolov

The name “random walk” for a problem of a displacement of a point in a sequence of independent random steps was coined by Karl Pearson in 1905 in a question posed to readers of “Nature”. The same ... More

The name “random walk” for a problem of a displacement of a point in a sequence of independent random steps was coined by Karl Pearson in 1905 in a question posed to readers of “Nature”. The same year, a similar problem was formulated by Albert Einstein in one of his Annus Mirabilis works. Even earlier problem was posed by Louis Bachelier in his thesis devoted to the theory of financial speculations in 1900. Nowadays theory of random walks was proved useful in physics and chemistry (diffusion, reactions, mixing in flows), economics, biology (from animal spread to motion of subcellular structures) and in many other disciplines. The random walk approach serves not only as a model of simple diffusion but of many complex sub‐ and superdiffusive transport processes as well. This book discusses main variants of the random walks and gives the most important mathematical tools for their theoretical description.Less

Fluid Dynamics: Part 1: Classical Fluid Dynamics

Anatoly I. Ruban and Jitesh S. B. Gajjar

This book, the first of a four-part series on fluid dynamics, consists of four chapters on classical theory suitable for an introductory undergraduate course. Chapter 1 discusses the continuum ... More

This book, the first of a four-part series on fluid dynamics, consists of four chapters on classical theory suitable for an introductory undergraduate course. Chapter 1 discusses the continuum hypothesis and introduces macroscopic functions. The forces acting inside a fluid are analysed, and the Navier–Stokes equations are derived for incompressible and compressible fluids. Chapter 2 studies the properties of flows represented by exact solutions of the Navier–Stokes equations, including Couette flow between two parallel plates, Hagen–Poiseuille flow through a pipe, and Kármán flow above an infinite rotating disk. Chapter 3 deals with inviscid incompressible flows, starting with a discussion of integrals of the Euler equations, the Bernoulli integral, and the Cauchy–Lagrange integral. Kelvin’s Circulation Theorem is proved, and used to identify physical situations where a flow can be treated as potential. Attention is principally directed at two-dimensional potential flows. These can be described in terms of a complex potential, allowing the full power of the theory of functions of a complex variable to be used. The method of conformal mapping is introduced and used to study various flows, including flow past Joukovskii aerofoils. Chapter 4 introduces the elements of gasdynamics, describing compressible flows of a perfect gas, including supersonic flows. Particular attention is paid to the theory of characteristics, which is used, for example, to analyse Prandtl–Meyer flow over a body surface bend and a corner. Shock waves are discussed and the chapter concludes with analysis of unsteady flows, including the theory of blast waves.Less

Fluid Dynamics: Part 2: Asymptotic Problems of Fluid Dynamics

Anatoly I. Ruban

The book is the second part in a series which describes fluid dynamics. The book introduces asymptotic methods, and their applications to fluid dynamics. It first discusses the mathematical aspects ... More

The book is the second part in a series which describes fluid dynamics. The book introduces asymptotic methods, and their applications to fluid dynamics. It first discusses the mathematical aspects of the asymptotic theory. This is followed by an exposition of the results of inviscid flow theory, starting with subsonic flows past thin aerofoils. This includes unsteady flow theory and the analysis of separated flows. The book then considers supersonic flow past a thin aerofoil, where the linear approximation leads to the Ackeret formula for the pressure. It also discusses the second-order Buzemann approximation, and the flow behaviour at large distances from the aerofoil. Then the properties of transonic and hypersonic flows are discussed in detail. The book concludes with a discussion of viscous low-Reynolds-number flows. Two classical problems of the low-Reynolds-number flow theory are considered: the flow past a sphere and the flow past a circular cylinder. In both cases the flow analysis leads to a difficulty, known as Stoke’s paradox. The book shows that this paradox can be resolved using the formalism of matched asymptotic expansions.Less

Fluid Dynamics: Part 3 Boundary Layers

Anatoly I. Ruban

This is Part 3 of a book series on fluid dynamics. This is designed to give a comprehensive and coherent description of fluid dynamics, starting with chapters on classical theory suitable for an ... More

This is Part 3 of a book series on fluid dynamics. This is designed to give a comprehensive and coherent description of fluid dynamics, starting with chapters on classical theory suitable for an introductory undergraduate lecture courses, and then progressing through more advanced material up to the level of modern research in the field. This book is devoted to high-Reynolds number flows. It begins by analysing the flows that can be described in the framework of Prandtl’s 1904 classical boundary-layer theory. These analyses include the Blasius boundary layer on a flat plate, the Falkner-Skan solutions for the boundary layer on a wedge surface, and other applications of Prandtl’s theory. It then discusses separated flows, and considers first the so-called ‘self-induced separation’ in supersonic flow that was studied in 1969 by Stewartson and Williams, as well as by Neiland, and led to the ‘triple-deck model’. It also presents Sychev’s 1972 theory of the boundary-layer separation in an incompressible fluid flow past a circular cylinder. It discusses the triple-deck flow near the trailing edge of a flat plate first investigated in 1969 by Stewartson and in 1970 by Messiter. It then considers the incipience of the separation at corner points of the body surface in subsonic and supersonic flows. It concludes by covering the Marginal Separation theory, which represents a special version of the triple-deck theory, and describes the formation and bursting of short separation bubbles at the leading edge of a thin aerofoil.Less

Fluid Mechanics: A Geometrical Point of View

S. G. Rajeev

Starting with a review of vector fields and their integral curves, the book presents the basic equations of the subject: Euler and Navier–Stokes. Some solutions are studied next: ideal flows using ... More

Starting with a review of vector fields and their integral curves, the book presents the basic equations of the subject: Euler and Navier–Stokes. Some solutions are studied next: ideal flows using conformal transformations, viscous flows such as Couette and Stokes flow around a sphere, shocks in the Burgers equation. Prandtl’s boundary layer theory and the Blasius solution are presented. Rayleigh–Taylor instability is studied in analogy with the inverted pendulum, with a digression on Kapitza’s stabilization. The possibility of transients in a linearly stable system with a non-normal operator is studied using an example by Trefethen et al. The integrable models (KdV, Hasimoto’s vortex soliton) and their hamiltonian formalism are studied. Delving into deeper mathematics, geodesics on Lie groups are studied: first using the Lie algebra and then using Milnor’s approach to the curvature of the Lie group. Arnold’s deep idea that Euler’s equations are the geodesic equations on the diffeomorphism group is then explained and its curvature calculated. The next three chapters are an introduction to numerical methods: spectral methods based on Chebychev functions for ODEs, their application by Orszag to solve the Orr–Sommerfeld equation, finite difference methods for elementary PDEs, the Magnus formula and its application to geometric integrators for ODEs. Two appendices give an introduction to dynamical systems: Arnold’s cat map, homoclinic points, Smale’s horse shoe, Hausdorff dimension of the invariant set, Aref ’s example of chaotic advection. The last appendix introduces renormalization: Ising model on a Cayley tree and Feigenbaum’s theory of period doubling.Less

Foams: Structure and Dynamics

Isabelle Cantat, Sylvie Cohen-Addad, Florence Elias, François Graner, Reinhard Höhler, Olivier Pitois, Florence Rouyer, and Arnaud Saint-Jalmes

Simon Cox (ed.)

Aqueous foams are studied both as materials with many applications, and as model systems for fields ranging from metallurgy to mathematics to biology. They are complex fluids with unique and unusual ... More

Aqueous foams are studied both as materials with many applications, and as model systems for fields ranging from metallurgy to mathematics to biology. They are complex fluids with unique and unusual properties, exemplified as much by their multiscale structure as by the dynamical processes through which they evolve and even their dual liquid-like and solid-like behaviour. In this book, readers can easily find clear, up-to-date answers to their questions regarding the physical and physico-chemical properties of aqueous foams, explained using current knowledge of their structure, their stability, and their rheology. Newcomers to the field will find descriptions of numerous applications of foams in daily life and in industrial processes, the definition of basic concepts, hundreds of figures, and simple experiments to perform at home. Those who want to proceed further will find updated references, exercises with solutions, appendices with experimental and numerical techniques, and boxed text with the further mathematical detail.Less

From Molecules to Living Organisms: An Interplay Between Biology and Physics: Lecture Notes of the Les Houches School of Physics: Volume 102, July 2014

Eva Pebay-Peyroula, Hugues Nury, François Parcy, Rob W. H. Ruigrok, Christine Ziegler, and Leticia F. Cugliandolo (eds)

The aim of this book is to provide new ideas for studying living matter by a simultaneous understanding of behavior from molecules to the cell, to the whole organism in the light of physical ... More

The aim of this book is to provide new ideas for studying living matter by a simultaneous understanding of behavior from molecules to the cell, to the whole organism in the light of physical concepts. Indeed, forces guide most biological phenomena. In some cases these forces can be well-described and thus used to model a particular biological phenomenon. This is exemplified here by the study of membranes, where their shapes and curvatures can be modeled using a limited number of parameters that are measured experimentally. The growth of plants is another example where the combination of physics, biology and mathematics leads to a predictive model. The laws of thermodynamics are essential, as they dictate the behavior of proteins, or more generally biological molecules, in an aqueous environment. Integrated studies from the molecule to a larger scale need a combination of cutting-edge approaches, such as the use of new X-ray sources, in-cell NMR, cryo-electron microscopy or single-molecule microscopy. Some are described in dedicated chapters while others are mentioned in discussion of particular topics, such as the interactions between HIV and host cells which are being progressively deciphered thanks to recent developments in various types of microscopy. All the concepts and methods developed in this book are illustrated alongside three main biological questions: host–pathogen interactions, plant development and flowering and membrane processes. Through these examples, the book intends to highlight how integrated biology including physics and mathematics is a very powerful approach.Less

Introduction to Engineering Fluid Mechanics

Marcel Escudier

Turbojet and turbofan engines, rocket motors, road vehicles, aircraft, pumps, compressors, and turbines are examples of machines which require a knowledge of fluid mechanics for their design. The aim ... More

Turbojet and turbofan engines, rocket motors, road vehicles, aircraft, pumps, compressors, and turbines are examples of machines which require a knowledge of fluid mechanics for their design. The aim of this undergraduate-level textbook is to introduce the physical concepts and conservation laws which underlie the subject of fluid mechanics and show how they can be applied to practical engineering problems. The first ten chapters are concerned with fluid properties, dimensional analysis, the pressure variation in a fluid at rest (hydrostatics) and the associated forces on submerged surfaces, the relationship between pressure and velocity in the absence of viscosity, and fluid flow through straight pipes and bends. The examples used to illustrate the application of this introductory material include the calculation of rocket-motor thrust, jet-engine thrust, the reaction force required to restrain a pipe bend or junction, and the power generated by a hydraulic turbine. Compressible-gas flow is then dealt with, including flow through nozzles, normal and oblique shock waves, centred expansion fans, pipe flow with friction or wall heating, and flow through axial-flow turbomachinery blading. The fundamental Navier-Stokes equations are then derived from first principles, and examples given of their application to pipe and channel flows and to boundary layers. The final chapter is concerned with turbulent flow. Throughout the book the importance of dimensions and dimensional analysis is stressed. A historical perspective is provided by an appendix which gives brief biographical information about those engineers and scientists whose names are associated with key developments in fluid mechanics.Less

The Long Road to Stockholm: The Story of Magnetic Resonance Imaging - An Autobiography

Peter Mansfield

This book describes the author's life from the age of 5 in 1939 through to 2010. The first chapter describes his evacuation to Devon during the blitz and following the V1 and V2 attacks on London. At ... More

This book describes the author's life from the age of 5 in 1939 through to 2010. The first chapter describes his evacuation to Devon during the blitz and following the V1 and V2 attacks on London. At the end of hostilities he worked briefly in the printing industry but decided to pursue his real interests in science by joining the Rocket Propulsion Department at Westcott near Aylesbury. Following National Service and University he married and went to the USA for 2 years returning in 1964 as a Lecturer in Physics at the University of Nottingham. In 1972 he spent a sabbatical period in Heidleberg. During this period he interacted with his student, Peter Grannell, in Nottingham on the then novel idea of magnetic resonance imaging which led to his first paper on MRI presented at the first Specialised Colloque Ampère held in Krakow in 1973. Later in 1975 he met Godfrey Hounsfield, inventor of the CT scanner, at the EMI Central Research Laboratories in Hayes, Middlesex. This meeting sparked of an interest leading to EMI producing their own MRI scanner. In 1980-82 other MRI groups at Nottingham, led by Professor Andrew and Dr Moore, left Nottingham to set up in the U.S.A. This exodus left him free to steam on with his group's developments of high speed imaging. These were the Golden Years in MRI at Nottingham. In 1987 a new Vice Chancellor, Colin Campbell took over the running of the University of Nottingham. He was extremely helpful to him in their acquiring a new building dedicated to their work with MRI. In the early 90's there was considerable speculation about whether there should be a Nobel Prize in MRI. This speculation was initiated in the U.S.A by the Journal “Diagnostic Imaging”. But interest soon faded. Further developments in MRI led finally to a Nobel Prize in Physiology or Medicine in 2003 awarded jointly with Paul Lauterbur. There were some antagonisims to MRI especially from Raymond Damadian, but these were settled or ignored. New ideas for reducing acoustic noise were explored and a 50 dB reduction achieved on a rectangular plate construction. However, on a circular gradient coil system, the best noise reduction achieved was around 30 dB. His two brothers, Conrad and Sidney together with a number of friends and colleagues central to his progress in MRI, are included in the Epilogue.Less

Materials for the 21st Century

David Segal

The book is a general text that shows how materials can contribute to solving problems facing nations in the 21st century. It is illustrated with diverse applications and highlights the potential of ... More

The book is a general text that shows how materials can contribute to solving problems facing nations in the 21st century. It is illustrated with diverse applications and highlights the potential of existing materials for everyday life, healthcare and the economies of nations. There are 13 chapters and a glossary of 500 materials with their descriptions, historical development, their use or potential use and a range of references. Specific areas include synthetic polymers (e.g. nylon), natural polymers (e.g. proteins, cellulose) and the role of materials in the development of digital computers and in healthcare. Solid-state lighting, energy supplies in the 21st century, disruptive technologies and intellectual property, in particular patents, are discussed. The book concludes by asking how the 21st century will be characterised. Will it be the Silicon Age, Genomic Age or New Polymer Age, as examples?Less

Microrheology

Eric M. Furst and Todd M. Squires

We present a comprehensive overview of microrheology, emphasizing the underlying theory, practical aspects of its implementation, and current applications to rheological studies in academic and ... More

We present a comprehensive overview of microrheology, emphasizing the underlying theory, practical aspects of its implementation, and current applications to rheological studies in academic and industrial laboratories. Key methods and techniques are examined, including important considerations to be made with respect to the materials most amenable to microrheological characterization and pitfalls to avoid in measurements and analysis. The fundamental principles of all microrheology experiments are presented, including the nature of colloidal probes and their movement in fluids, soft solids, and viscoelastic materials. Microrheology is divided into two general areas, depending on whether the probe is driven into motion by thermal forces (passive), or by an external force (active). We present the theory and practice of passive microrheology, including an in-depth examination of the Generalized Stokes-Einstein Relation (GSER). We carefully treat the assumptions that must be made for these techniques to work, and what happens when the underlying assumptions are violated. Experimental methods covered in detail include particle tracking microrheology, tracer particle microrheology using dynamic light scattering and diffusing wave spectroscopy, and laser tracking microrheology. Second, we discuss the theory and practice of active microrheology, focusing specifically on the potential and limitations of extending microrheology to measurements of non-linear rheological properties, like yielding and shear-thinning. Practical aspects of magnetic and optical tweezer measurements are preseted. Finally, we highlight important applications of microrheology, including measurements of gelation, degradation, high-throughput rheology, protein solution viscosities, and polymer dynamics.Less

Models of Cellular Regulation

Baltazar Aguda, Avner Friedman, and Visiting Associate Professor, The Ohio State University

The human genome of three billion letters has been sequenced. So have the genomes of thousands of other organisms. With unprecedented resolution, modern technologies are allowing us to peek into the ... More

The human genome of three billion letters has been sequenced. So have the genomes of thousands of other organisms. With unprecedented resolution, modern technologies are allowing us to peek into the world of genes, biomolecules, and cells, and flooding us with data of immense complexity that we are just barely beginning to understand. A huge gap separates our knowledge of the components of a cell and what is known from our observations of its physiology. This book explores what has been done to close this gap of understanding between the realms of molecules and biological processes. It contains illustrative mechanisms and models of gene regulatory networks, DNA replication, the cell cycle, cell death, differentiation, cell senescence, and the abnormal state of cancer cells. The mechanisms are biomolecular in detail, and the models are mathematical in nature.Less