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定量生理学（Quantitative Physiology）

作者: 陈尚宾（Shangbin Chen） , [俄罗斯] Alexey Zaikin(阿列克谢。扎伊金

出版社: 华中科技大学出版社

出版时间: 2021-04

版次: 1

ISBN: 9787568066785

定价: 138.00

装帧: 平装

开本: 16开

纸张: 胶版纸

页数: 260页

字数: 678千字

分类: 教材教辅考试>教材>大学教材>工程技术

4人买过

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. 陈尚宾博士，武汉光电国家研究中心副教授，博士生导师。2001年于湖北师范学院获物理学学士学位，2006年于华中科技大学获生物医学工程博士学位。2006年8月至今在华中科技大学工作；其间2008年2-5月在英国Bradford大学做访问学者，2010-2012在加拿大英属哥伦比亚大学（UBC）做博士后研究两年。其研究工作涉及神经光学成像、神经系统建模、定量生理学，已主持完成国家自然科学基金两项。已在Journal of Neuroscience，Biophysical Journal，Frontiers in Neuroscience等期刊发表第一作者（含通讯）论文十余篇。2007年荣获湖北省自然科学奖一等奖（排名5）。合作者Alexey Zaikin教授是世界顶尖高校伦敦大学学院（UCL）系统医学和应用数学讲席教授，研究兴趣包括系统生物学、理论生物物理学、生物非线性动力学和随机性建模等。Zaikin教授已发表学术论文逾百篇，包含Physical Review Letters多篇，谷歌学术统计h指数29。Zaikin教授自2016年以来短期受聘于华中科技大学工程科学学院，参与《定量生理学》课程教学。 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

11.1 Influence of Stochasticity . . . . . .  87

11.2 Review of Noise-Induced Effects . . . . . . . . . . 89

11.3 NewMechanisms of Noise-Induced Effects . 91

11.4 Noise-Induced Effects . . . . . . 93

11.4.1 Stochastic Resonance in Bone Remodelling as a Tool to Prevent

Bone Loss in Osteopenic Conditions 93

11.4.2 Transitions in the Presence of Additive Noise and On-Off

Intermittency . . . . . .  98

11.4.3 Phase Transitions Induced by Additive Noise. . . . . . . . 103

11.4.4 Noise-Induced Excitability . . . . . . . . 109

11.5 Doubly Stochastic Effects . . . . . . . . 113

11.5.1 Doubly Stochastic Resonance . . . . . . 113

11.5.2 A Simple Electronic Circuit Model for Doubly Stochastic

Resonance . . . . . . . . . .  117

11.5.3 Doubly Stochastic Coherence: Periodicity via Noise-Induced

Symmetry in Bistable NeuralModels . . . . . . . . . . . 120

11.6 New Effects in Noise-Induced Propagation . . 125

11.6.1 Noise-Induced Propagation in Monostable Media . . . . . . . . .125

11.6.2 Noise-Induced Propagation and Frequency Selection of

Bichromatic Signals in BistableMedia . . . . . . . . 128

11.7 Noise-Induced Resonant Effects and Resonant Effects in the Presence of

Noise . . . . . . . . 129

11.7.1 Vibrational Resonance in a Noise-Induced Structure . . . . . . . . . . . . 129

11.7.2 System Size Resonance in Coupled Noisy Systems . . . . . . . . . . . . . 133

11.7.3 Coherence Resonance and Polymodality in Inhibitory Coupled

Excitable Oscillators . . . . . . . . . . . . . 136

11.8 Applications and Open Questions . . . . . . . . . . 140

11.9 Questions . . . . . 141

References . . . . . . . . . . 141

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

12.1 Nonlinear Dynamics in Synthetic Biology. . . 147

12.2 Clustering and Oscillation Death in Genetic Networks . . . . . . .  148

12.2.1 The Repressilator with QuorumSensing Coupling . . . . . . . . . . . . . 148

12.2.2 The Dynamical Regimes for a Minimal System of Repressilators

Coupled via Phase-Repulsive Quorum Sensing . . . . . . . .  150

12.3 Systems Size Effects in Coupled Genetic Networks . . . . . . .  152

12.3.1 Clustering and Enhanced Complexity of the Inhomogeneous

Regimes . . . . . . . .  153

12.3.2 Clustering Due to Regular Oscillations in Cell Colonies . . . . . . . . . 154

12.3.3 Parameter Heterogeneity on the Regular-Attractor Regime . . . . . . 155

12.3.4 Irregular and Chaotic Self-Oscillations in Colonies of Identical

Cells . 155

xviii Contents

12.4 The Constructive Role of Noise in Genetic Networks. . . . . . . . .  157

12.4.1 Noise-Induced Oscillations in Circadian Gene Networks . . . . . . . . 157

12.4.2 Noise-Induced Synchronisation and Rhythms. . . . . . . . .  158

12.5 Speed Dependent Cellular Decision Making (SdCDM) in Noisy Genetic

Networks . . . . . 160

12.5.1 Speed Dependent Cellular Decision Making in a Small Genetic

Switch 161

12.5.2 Speed Dependent Cellular Decision Making in Large Genetic

Networks . . . . . . . . .  162

12.6 What is a Genetic Intelligence? . . . . . . . . . . . . 164

12.6.1 Supervised Learning . . . . . . . . . . . . . 164

12.6.2 Associative Learning . . . . . . . . . . . . . 166

12.6.3 Classification of Complex Inputs . . . 166

12.6.4 Applications and Implications of Bio-Artificial Intelligence . . . . . . 169

12.7 Effect of Noise in Intelligent Cellular Decision Making . . . . . . . . . . . . . . . . . 169

12.7.1 Stochastic Resonance in an Intracellular Associative Genetic

Perceptron . . . . . . .  169

12.7.2 Stochastic Resonance in Classifying Genetic Perceptron . . . . . . . . 174

12.8 Questions . . . . . 183

References . . . . . . . . . . 183

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

Acronyms

3M The modelling, model, and modeller are introduced in this book of Quantitative Physiology

AcCoA Acetyl-CoA: It is an intermediary molecule that participates in many biochemical reactions in carbohydrates,

fatty acids, and amino acids metabolism

ADP Adenosine diphosphate: It is an important organic compound in metabolism and is essential to the flow of

energy in living cells

AI Artificial intelligence: It is sometimes called machine intelligence, in contrast to the human intelligence

AIDS Acquired immunodeficiency syndrome: It is a transmissible disease caused by the human immunodeficiency

virus (HIV)

AP Action potential: An action potential is a rapid rise and subsequent fall in membrane potential of a neuron

ATP Adenosine triphosphate: The ubiquitous molecule necessary for intracellular energy storage and transfer

BMI Body mass index: It is a measure of body fat based on height and weight that applies to adult men and women

BRAIN Brain Research through Advancing Innovative Neurotechnologies: The BRAIN Initiative launched in April

2013 is focused on revolutionising our understanding of the human brain

CA Cellular automaton: It is a specifically shaped group of model cells known for evolving through multiple and

discrete time steps according to a rule set depending on neighbouring cell states

CICR Calcium-induced calcium release: The autocatalytic release of Ca2  from the endoplasmic or sarcoplasmic

reticulum through IP3 receptors or ryanodine receptors. CICR causes the fast release of large amounts of

Ca2  from internal stores and is the basis for Ca2  oscillations and waves in a wide variety of cell types

CNS Central nervous system: It is the part of the nervous system consisting of the brain and spinal cord

CR Coherence resonance: It refers to a phenomenon in which addition of certain amount of external noise in

excitable system makes its oscillatory responses most coherent

CSD Cortical spreading depression: It is characterised by the propagation of depolarisation waves across the grey

matter at a velocity of 2–5 mm/min

CVD Cardiovascular disease: It is a class of diseases that involve the heart or blood vessels

DFBA Dynamic flux balance analysis: It is the dynamic extension of flux balance analysis (FBA)

DNA Deoxyribonucleic acid: It is a molecule comprised of two chains that coil around each other to form a double

helix carrying the genetic information

DSC Doubly stochastic coherence

DSE Doubly stochastic effects

EC coupling Excitation–contraction coupling: It describes a series of events, from the production of an electrical impulse

(action potential) to the contraction of muscles

ECF Extracellular fluid: The portion of the body fluid comprises the interstitial fluid and blood plasma

ECG Electrocardiogram (or EKG): The record is produced by electrocardiography to represent the heart’s electrical

action

ECS Extracellular space: It is usually taken to be outside the plasma membranes and occupied by fluid

EEG Electroencephalography: It is an electrophysiological monitoring method to record electrical activity of the

brain

ER Endoplasmic reticulum: An internal cellular compartment in non-muscle cells acting as an important Ca2

store. The analogous compartment in muscle cells is termed the sarcoplasmic reticulum (SR)

ETC Electron transport chain

FA Fatty acid: It is the building block of the fat in our bodies and in the food we eat

FBA Flux balance analysis: It is a widely used approach for studying biochemical networks

xix

xx Acronyms

FHC Familial hypertrophic cardiomyopathy: It is a heart condition characterised by thickening (hypertrophy) of

the heart (cardiac) muscle

FHN FitzHugh–Nagumo model: It is named after Richard FitzHugh and Jin-Ichi Nagumo for describing a

prototype of an excitable system (e.g., a neuron)

GFP Green fluorescent protein: A protein, originally derived from a jellyfish, that exhibits bright green fluorescence

when exposed to blue or ultraviolet light

GRN Gene regulatory network or genetic regulatory network: It is a collection of regulators that interact with each

other and with other substances in the cell to govern the gene expression levels of mRNA and proteins

Glu Glucose: Glucose is a simple sugar with the molecular formula C6H12O6

Gly Glycogen: It is amultibranched polysaccharide of glucose that serves as a form of energy storage in organisms

HBP Human Brain Project: It is a European Commission Future and Emerging Technologies Flagship started on

1 October 2013

HGP Human Genome Project: It is an international project with the goal of determining the sequence of nucleotide

base pairs that make up human DNA and of identifying and mapping all genes of the human genome from

both a physical and a functional standpoint

HH model The Hodgkin–Huxley model: It is a mathematical model that describes how action potentials in neurons are

initiated and propagated

II Integrated information: It is ameasure of the degree to which the components of a system areworking together

to produce outputs

IP3 Inositol 1,4,5-trisphosphate: A second messenger responsible for the release of intracellular Ca2  from

internal stores, through IP3 receptors

ICS Intracellular space: It is taken to be inside the cell

iPS Induced pluripotent stem cells: They are a type of pluripotent stem cell that can be generated directly from

adult cells

ISIH Interspike interval histogram

IUPS The International Union of Physiological Societies

Lac Lactate (or Lactic acid): It has the molecular formula CH3CH(OH)CO2H

LC Limit cycle

MFT Mean field theory: It studies the behaviour of large and complex stochastic models by using a simpler model

MOMA Minimisation of metabolic adjustment: It is used as an objective function for FBA

NADH Nicotinamide adenine dinucleotide hydride

NADPH Nicotinamide adenine dinucleotide phosphate

NIE Noise-induced excitability

NIT Noise-induced transition

NSR National Simulation Resource

ODE Ordinary differential equation: It is a differential equation containing one or more functions of one

independent variable and its derivatives

PC Phosphocreatine: It is a phosphorylated creatine molecule that serves as a rapidly mobilisable reserve of

high-energy phosphates in skeletal muscle and the brain

PDE Partial differential equation: It is a differential equation that contains beforehand unknown multivariable

functions and their partial derivatives

PDF Probability distribution function

PE Potential energy

PNS Peripheral nervous system

Pyr Pyruvate: It is a key intermediate in several metabolic pathways throughout the cell

RD Reaction–diffusion: A reaction–diffusion system consists of the diffusion of material and the production of

that material by reaction

RFP Red fluorescent protein

SCN The suprachiasmatic nuclei

SdCDM Speed dependent cellular decision making

SERCA Sarcoplasmic/endoplasmic reticulum Ca2  ATPase: A Ca2  ATPase pump that transports Ca2  up its

concentration gradient from the cytoplasm to the ER/SR

SGN Synthetic gene network

Acronyms xxi

SNR Signal to noise ratio

SR Sarcoplasmic reticulum:An internal cellular compartment in muscle cells that functions as an important Ca2

store. The analogous compartment in non-muscle cells is called the endoplasmic reticulum (ER)

SR Stochastic resonance: It is a phenomenon where a signal can be boosted by adding white noise to the signal

TCA cycle Tricarboxylic acid cycle or the Krebs cycle: It is a series of chemical reactions used by all aerobic organisms

to generate energy through the oxidation of acetyl-CoA into carbon dioxide and chemical energy in the form

of guanosine triphosphate (GTP)

TF Transcription factor: It is a protein that binds to specific DNA sequences, thereby controlling the rate of

transcription of genetic information from DNA to messenger RNA

TGF Tubuloglomerular feedback

UCS Ultimate compressive stress

VGCC Voltage-gated Ca2  channels: Membrane Ca2  channels that open in response to depolarisation of the cell

membrane

VR Vibrational resonance

WHO World Health Organization: It is a specialised agency of the United Nations to direct international health
内容简介:
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.
作者简介:
陈尚宾博士，武汉光电国家研究中心副教授，博士生导师。2001年于湖北师范学院获物理学学士学位，2006年于华中科技大学获生物医学工程博士学位。2006年8月至今在华中科技大学工作；其间2008年2-5月在英国Bradford大学做访问学者，2010-2012在加拿大英属哥伦比亚大学（UBC）做博士后研究两年。其研究工作涉及神经光学成像、神经系统建模、定量生理学，已主持完成国家自然科学基金两项。已在Journal of Neuroscience，Biophysical Journal，Frontiers in Neuroscience等期刊发表第一作者（含通讯）论文十余篇。2007年荣获湖北省自然科学奖一等奖（排名5）。合作者Alexey Zaikin教授是世界顶尖高校伦敦大学学院（UCL）系统医学和应用数学讲席教授，研究兴趣包括系统生物学、理论生物物理学、生物非线性动力学和随机性建模等。Zaikin教授已发表学术论文逾百篇，包含Physical Review Letters多篇，谷歌学术统计h指数29。Zaikin教授自2016年以来短期受聘于华中科技大学工程科学学院，参与《定量生理学》课程教学。
目录:
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

11.1 Influence of Stochasticity . . . . . .  87

11.2 Review of Noise-Induced Effects . . . . . . . . . . 89

11.3 NewMechanisms of Noise-Induced Effects . 91

11.4 Noise-Induced Effects . . . . . . 93

11.4.1 Stochastic Resonance in Bone Remodelling as a Tool to Prevent

Bone Loss in Osteopenic Conditions 93

11.4.2 Transitions in the Presence of Additive Noise and On-Off

Intermittency . . . . . .  98

11.4.3 Phase Transitions Induced by Additive Noise. . . . . . . . 103

11.4.4 Noise-Induced Excitability . . . . . . . . 109

11.5 Doubly Stochastic Effects . . . . . . . . 113

11.5.1 Doubly Stochastic Resonance . . . . . . 113

11.5.2 A Simple Electronic Circuit Model for Doubly Stochastic

Resonance . . . . . . . . . .  117

11.5.3 Doubly Stochastic Coherence: Periodicity via Noise-Induced

Symmetry in Bistable NeuralModels . . . . . . . . . . . 120

11.6 New Effects in Noise-Induced Propagation . . 125

11.6.1 Noise-Induced Propagation in Monostable Media . . . . . . . . .125

11.6.2 Noise-Induced Propagation and Frequency Selection of

Bichromatic Signals in BistableMedia . . . . . . . . 128

11.7 Noise-Induced Resonant Effects and Resonant Effects in the Presence of

Noise . . . . . . . . 129

11.7.1 Vibrational Resonance in a Noise-Induced Structure . . . . . . . . . . . . 129

11.7.2 System Size Resonance in Coupled Noisy Systems . . . . . . . . . . . . . 133

11.7.3 Coherence Resonance and Polymodality in Inhibitory Coupled

Excitable Oscillators . . . . . . . . . . . . . 136

11.8 Applications and Open Questions . . . . . . . . . . 140

11.9 Questions . . . . . 141

References . . . . . . . . . . 141

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

12.1 Nonlinear Dynamics in Synthetic Biology. . . 147

12.2 Clustering and Oscillation Death in Genetic Networks . . . . . . .  148

12.2.1 The Repressilator with QuorumSensing Coupling . . . . . . . . . . . . . 148

12.2.2 The Dynamical Regimes for a Minimal System of Repressilators

Coupled via Phase-Repulsive Quorum Sensing . . . . . . . .  150

12.3 Systems Size Effects in Coupled Genetic Networks . . . . . . .  152

12.3.1 Clustering and Enhanced Complexity of the Inhomogeneous

Regimes . . . . . . . .  153

12.3.2 Clustering Due to Regular Oscillations in Cell Colonies . . . . . . . . . 154

12.3.3 Parameter Heterogeneity on the Regular-Attractor Regime . . . . . . 155

12.3.4 Irregular and Chaotic Self-Oscillations in Colonies of Identical

Cells . 155

xviii Contents

12.4 The Constructive Role of Noise in Genetic Networks. . . . . . . . .  157

12.4.1 Noise-Induced Oscillations in Circadian Gene Networks . . . . . . . . 157

12.4.2 Noise-Induced Synchronisation and Rhythms. . . . . . . . .  158

12.5 Speed Dependent Cellular Decision Making (SdCDM) in Noisy Genetic

Networks . . . . . 160

12.5.1 Speed Dependent Cellular Decision Making in a Small Genetic

Switch 161

12.5.2 Speed Dependent Cellular Decision Making in Large Genetic

Networks . . . . . . . . .  162

12.6 What is a Genetic Intelligence? . . . . . . . . . . . . 164

12.6.1 Supervised Learning . . . . . . . . . . . . . 164

12.6.2 Associative Learning . . . . . . . . . . . . . 166

12.6.3 Classification of Complex Inputs . . . 166

12.6.4 Applications and Implications of Bio-Artificial Intelligence . . . . . . 169

12.7 Effect of Noise in Intelligent Cellular Decision Making . . . . . . . . . . . . . . . . . 169

12.7.1 Stochastic Resonance in an Intracellular Associative Genetic

Perceptron . . . . . . .  169

12.7.2 Stochastic Resonance in Classifying Genetic Perceptron . . . . . . . . 174

12.8 Questions . . . . . 183

References . . . . . . . . . . 183

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

Acronyms

3M The modelling, model, and modeller are introduced in this book of Quantitative Physiology

AcCoA Acetyl-CoA: It is an intermediary molecule that participates in many biochemical reactions in carbohydrates,

fatty acids, and amino acids metabolism

ADP Adenosine diphosphate: It is an important organic compound in metabolism and is essential to the flow of

energy in living cells

AI Artificial intelligence: It is sometimes called machine intelligence, in contrast to the human intelligence

AIDS Acquired immunodeficiency syndrome: It is a transmissible disease caused by the human immunodeficiency

virus (HIV)

AP Action potential: An action potential is a rapid rise and subsequent fall in membrane potential of a neuron

ATP Adenosine triphosphate: The ubiquitous molecule necessary for intracellular energy storage and transfer

BMI Body mass index: It is a measure of body fat based on height and weight that applies to adult men and women

BRAIN Brain Research through Advancing Innovative Neurotechnologies: The BRAIN Initiative launched in April

2013 is focused on revolutionising our understanding of the human brain

CA Cellular automaton: It is a specifically shaped group of model cells known for evolving through multiple and

discrete time steps according to a rule set depending on neighbouring cell states

CICR Calcium-induced calcium release: The autocatalytic release of Ca2  from the endoplasmic or sarcoplasmic

reticulum through IP3 receptors or ryanodine receptors. CICR causes the fast release of large amounts of

Ca2  from internal stores and is the basis for Ca2  oscillations and waves in a wide variety of cell types

CNS Central nervous system: It is the part of the nervous system consisting of the brain and spinal cord

CR Coherence resonance: It refers to a phenomenon in which addition of certain amount of external noise in

excitable system makes its oscillatory responses most coherent

CSD Cortical spreading depression: It is characterised by the propagation of depolarisation waves across the grey

matter at a velocity of 2–5 mm/min

CVD Cardiovascular disease: It is a class of diseases that involve the heart or blood vessels

DFBA Dynamic flux balance analysis: It is the dynamic extension of flux balance analysis (FBA)

DNA Deoxyribonucleic acid: It is a molecule comprised of two chains that coil around each other to form a double

helix carrying the genetic information

DSC Doubly stochastic coherence

DSE Doubly stochastic effects

EC coupling Excitation–contraction coupling: It describes a series of events, from the production of an electrical impulse

(action potential) to the contraction of muscles

ECF Extracellular fluid: The portion of the body fluid comprises the interstitial fluid and blood plasma

ECG Electrocardiogram (or EKG): The record is produced by electrocardiography to represent the heart’s electrical

action

ECS Extracellular space: It is usually taken to be outside the plasma membranes and occupied by fluid

EEG Electroencephalography: It is an electrophysiological monitoring method to record electrical activity of the

brain

ER Endoplasmic reticulum: An internal cellular compartment in non-muscle cells acting as an important Ca2

store. The analogous compartment in muscle cells is termed the sarcoplasmic reticulum (SR)

ETC Electron transport chain

FA Fatty acid: It is the building block of the fat in our bodies and in the food we eat

FBA Flux balance analysis: It is a widely used approach for studying biochemical networks

xix

xx Acronyms

FHC Familial hypertrophic cardiomyopathy: It is a heart condition characterised by thickening (hypertrophy) of

the heart (cardiac) muscle

FHN FitzHugh–Nagumo model: It is named after Richard FitzHugh and Jin-Ichi Nagumo for describing a

prototype of an excitable system (e.g., a neuron)

GFP Green fluorescent protein: A protein, originally derived from a jellyfish, that exhibits bright green fluorescence

when exposed to blue or ultraviolet light

GRN Gene regulatory network or genetic regulatory network: It is a collection of regulators that interact with each

other and with other substances in the cell to govern the gene expression levels of mRNA and proteins

Glu Glucose: Glucose is a simple sugar with the molecular formula C6H12O6

Gly Glycogen: It is amultibranched polysaccharide of glucose that serves as a form of energy storage in organisms

HBP Human Brain Project: It is a European Commission Future and Emerging Technologies Flagship started on

1 October 2013

HGP Human Genome Project: It is an international project with the goal of determining the sequence of nucleotide

base pairs that make up human DNA and of identifying and mapping all genes of the human genome from

both a physical and a functional standpoint

HH model The Hodgkin–Huxley model: It is a mathematical model that describes how action potentials in neurons are

initiated and propagated

II Integrated information: It is ameasure of the degree to which the components of a system areworking together

to produce outputs

IP3 Inositol 1,4,5-trisphosphate: A second messenger responsible for the release of intracellular Ca2  from

internal stores, through IP3 receptors

ICS Intracellular space: It is taken to be inside the cell

iPS Induced pluripotent stem cells: They are a type of pluripotent stem cell that can be generated directly from

adult cells

ISIH Interspike interval histogram

IUPS The International Union of Physiological Societies

Lac Lactate (or Lactic acid): It has the molecular formula CH3CH(OH)CO2H

LC Limit cycle

MFT Mean field theory: It studies the behaviour of large and complex stochastic models by using a simpler model

MOMA Minimisation of metabolic adjustment: It is used as an objective function for FBA

NADH Nicotinamide adenine dinucleotide hydride

NADPH Nicotinamide adenine dinucleotide phosphate

NIE Noise-induced excitability

NIT Noise-induced transition

NSR National Simulation Resource

ODE Ordinary differential equation: It is a differential equation containing one or more functions of one

independent variable and its derivatives

PC Phosphocreatine: It is a phosphorylated creatine molecule that serves as a rapidly mobilisable reserve of

high-energy phosphates in skeletal muscle and the brain

PDE Partial differential equation: It is a differential equation that contains beforehand unknown multivariable

functions and their partial derivatives

PDF Probability distribution function

PE Potential energy

PNS Peripheral nervous system

Pyr Pyruvate: It is a key intermediate in several metabolic pathways throughout the cell

RD Reaction–diffusion: A reaction–diffusion system consists of the diffusion of material and the production of

that material by reaction

RFP Red fluorescent protein

SCN The suprachiasmatic nuclei

SdCDM Speed dependent cellular decision making

SERCA Sarcoplasmic/endoplasmic reticulum Ca2  ATPase: A Ca2  ATPase pump that transports Ca2  up its

concentration gradient from the cytoplasm to the ER/SR

SGN Synthetic gene network

Acronyms xxi

SNR Signal to noise ratio

SR Sarcoplasmic reticulum:An internal cellular compartment in muscle cells that functions as an important Ca2

store. The analogous compartment in non-muscle cells is called the endoplasmic reticulum (ER)

SR Stochastic resonance: It is a phenomenon where a signal can be boosted by adding white noise to the signal

TCA cycle Tricarboxylic acid cycle or the Krebs cycle: It is a series of chemical reactions used by all aerobic organisms

to generate energy through the oxidation of acetyl-CoA into carbon dioxide and chemical energy in the form

of guanosine triphosphate (GTP)

TF Transcription factor: It is a protein that binds to specific DNA sequences, thereby controlling the rate of

transcription of genetic information from DNA to messenger RNA

TGF Tubuloglomerular feedback

UCS Ultimate compressive stress

VGCC Voltage-gated Ca2  channels: Membrane Ca2  channels that open in response to depolarisation of the cell

membrane

VR Vibrational resonance

WHO World Health Organization: It is a specialised agency of the United Nations to direct international health

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