Quantitative physiology¶¨Á¿ÉúÀíѧ

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 ¦Ä-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¨CHuxley Model of Neuron Firing . . . . . . . . . 62

8.3 The FitzHugh¨CNagumo 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