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Stephen Hawking says that the next 21st century will be the century of complexity and indeed now Systems Biology or Medicine means dealing with complexity. Both genome and physiome have been emerged in studying complex physiological systems. Computational and mathematical modelling has been regarded as an efficient tool to boost understanding about the living systems in normal or pathophysiological states.
This textbook introduces the students and researchers to the modelling and computational study of physiology (i.e. quantitative physiology), which is an increasingly important branch of systems biology. The topics cover basic methodology, case practices and advanced applications. This book aims to build multiscale model for investigating the function in living systems, or, how organisms, organ systems, organs, cells, and biomolecules carry out the chemical or physical functions that exist in a living system. Some of the models related on gene expression, calcium signalling, neural activity, blood dynamics and bone mechanics have been addressed. This book is devoted to set a paradigm for quantitative physiology by integrating biology, mathematics, physics and informatics etc.

Part I Applied Methodology
1 Introduction to Quantitative Physiology . . . . . . . . 3
1.1 Understanding Physiology . . . . . . . . . . . . . . . . 3
1.2 Towards Quantitative Science . . . . . . . . . . . . . 4
1.3 FromGenome to Physiome . . . . . . . . . . . . . . . 5
1.4 Dealing with Complexity . . . . . . . . . . . . . . . . . 6
1.5 Why It Is Timely to Study Quantitative Physiology . . . . . . . . . . 6
1.5.1 Multi-Omic Revolution in Biology . 6
1.5.2 Big Data and PersonalisedMedicine 7
1.5.3 Genetic Editing and Synthetic Biology . . . . . . . . . . 8
1.6 Questions . . . . . 8
References . . . . . . . . . . 8
2 Systems and Modelling . . . . . . . . . 11
2.1 Modelling Process . . . . . . . . 11
2.2 Physiological Organ Systems . . . . . . . . 13
2.3 EquationModels . . . . . . . . . . 14
2.4 Using ODEs in Modelling Physiology . . . . . . 16
2.4.1 Modelling Oscillations . . . . . . . . . . . 16
2.4.2 Linear Stability Analysis . . . . . . . . . . 16
2.4.3 Solving ODEs with the δ-Function . 17
2.5 Conservation Laws in Physiology . . . . . . . . . . 18
2.5.1 Conservation ofMomentumand Energy . . . . . . . . .18
2.5.2 Boxing With and Without Gloves . . 19
2.5.3 RotationalMovement . . . . . . . . . . . . 20
2.6 Questions . . . . . 20
References . . . . 21
3 Introduction to Basic Modelling . . . . . . . 23
3.1 Building a SimpleMathematicalModel . . . . . 23
3.1.1 Model of Falling Flea . . . . . . . . . . . . 23
3.1.2 Scaling Arguments. . . . . . 25
3.1.3 Example: How High Can an Animal Jump? . . . . . . . 25
3.1.4 Example: How Fast Can we Walk before Breaking into a Run? . . . 25
3.2 Models that InvolveMetabolic Rate . . . . . . . . 26
3.2.1 Modelling Metabolic Rate . . . . . . . . 26
3.2.2 Example:Why do Large Birds find it Harder to Fly? . . . . . . . . . . . 27
3.2.3 Ludwig von Bertalanffy’s GrowthModel . . . . . . . 28
3.3 Questions . . . . . 29
Reference . . . . . . . . . . 29
xv
xvi Contents
4 Modelling Resources 31
4.1 Open Courses. . 31
4.2 Modelling Software . . . . . . . 31
4.3 Model Repositories . . . . . . . 34
4.4 Questions . . . . . 35
References . . . . . . . . . . 35
Part II Basic Case Studies
5 Modelling Gene Expression . . . . . . . 39
5.1 Modelling Transcriptional Regulation and Simple Networks . . . . . . . . . . . . . 39
5.1.1 Basic Notions and Equations. . . . . . . 39
5.1.2 Equations for Transcriptional Regulation . . . . . . . 39
5.1.3 Examples of Some Common Genetic Networks . . . . . . 41
5.2 Simultaneous Regulation by Inhibition and Activation . . . . . . . .. 42
5.3 Autorepressor with Delay. . . . . . . . 43
5.4 Bistable Genetic Switch . . . . . . . . . 44
5.5 Questions . . . . . 44
References . . . . . . . . . . 45
6 Metabolic Network . . 47
6.1 Metabolismand Network . . . . . . . 47
6.2 ConstructingMetabolic Network . . . . . . . . . . 49
6.3 Flux Balance Analysis . . . . . . . . 50
6.4 MyocardialMetabolic Network. . . . . . . . . . . . 51
6.5 Questions . . . . . 51
References . . . . . . . . . . 52
7 Calcium Signalling . . 53
7.1 Functions of Calcium . . . . . . 53
7.2 Calcium Oscillations . . . . . . . . 54
7.3 CalciumWaves 59
7.4 Questions . . . . . 59
References . . . . . . . . . . 60
8 Modelling Neural Activity . . . . . . . 61
8.1 Introduction to Brain Research . . . . . . . . . . . . 61
8.2 The Hodgkin–Huxley Model of Neuron Firing . . . . . . . . . 62
8.3 The FitzHugh–Nagumo Model: A Model of the HH Model . . . . . . . . . . . . . 63
8.3.1 Analysis of Phase Plane with Case Ia = 0 . . . . . . . . 63
8.3.2 Case Ia > 0 and Conditions to Observe a Limit Cycle . . . . . . . . . . 64
8.4 Questions . . . . . 65
References . . . . . . . . . . 66
9 Blood Dynamics . . . . 67
9.1 Blood Hydrodynamics . . . . . . . 67
9.1.1 Basic Equations . . . . . . . . . . . . . . . . . 67
9.1.2 Poiseuille’s Law . . . . . . . . 67
9.2 Properties of Blood and ESR . . . . . . . 68
9.3 Elasticity of Blood Vessels . . . . . . 69
9.4 The PulseWave 69
9.5 Bernoulli’s Equation and What Happened to Arturo Toscanini in 1954 . . . . 70
9.6 The Korotkoff Sounds . . . . . . . . 71
9.7 Questions . . . . . 71
Reference . . . . . . . . . . . 72
Contents xvii
10 Bone and Body Mechanics . . . . . 73
10.1 Elastic Deformations and the Hooke’s Law. . 73
10.2 Why Long Bones are Hollow or Bending of Bones . . . . . . . . 74
10.3 Viscoelasticity of Bones . . . . . . . 77
10.4 Questions . . . . . 83
Reference . . . . . . . . . . 83
Part III Complex Applications
11 Constructive Effects of Noise . . . . . . . 87
. . . . . . . . . .

12 Complex and Surprising Dynamics in Gene Regulatory Networks . . . . . . . . . . 147
. . . . . . . . . .

13 Modelling Complex Phenomena in Physiology . . . 189
13.1 Cortical Spreading Depression (CSD) . . . . . . 189
13.1.1 What is CSD . . . . . . . . 189
13.1.2 Models of CSD . . . . . . . 189
13.1.3 Applications of CSDModels . . . . . . 192
13.1.4 Questions. . . . . . . . 196
13.2 Heart Physiome 197
13.2.1 Cardiovascular System. . . . . . . . . . . . 197
13.2.2 Heart Physiome . . . . . . . . . . . . . . . . . 198
13.2.3 Multi-Level Modelling . . . . . . . . . . . . 199
13.2.4 Questions. . . . . . . 201
13.3 Modelling of Kidney Autoregulation . . . . . . . 202
13.3.1 Renal Physiology . . . . . . . 202
13.3.2 Experimental Observations . . . . . . . . 204
13.3.3 Model of Nephron Autoregulation . . 205
13.3.4 Questions. . . . . . . . . .209
13.4 Brain Project . . 209
13.4.1 Mystery of Brain . . . . . . . . . . . . . . . . 209
13.4.2 Brain Projects . . . . . . . . . . . . . . . . . . . 210
13.4.3 Brain Simulation . . . . . . . 212
13.4.4 Mammalian Brain as a Network of Networks . . . . . . .215
13.4.5 Calculation of Integrated Information . . . . . . . . . . . . . . 223
13.4.6 Astrocytes and Integrated Information Theory of Consciousness . . 224
13.4.7 Questions. . . . . . . . . . . . 233
References . . . . . . . . . . 233

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