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Type 2 Diabetes Defeated

How I Healed my Diabetes

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Preface v

Acknowledgments ix

I Cellular Physiology 1

1 Biochemical Reactions 3

1.1 The Law of Mass Action 3

1.2 Enzyme Kinetics 5

1.2.1 The Equilibrium Approximation 6

1.2.2 The Quasi-Steady-State Approximation 7

1.2.3 Enzyme Inhibition 9

1.2.4 Cooperativity 12

1.3 Glycolysis and Glycolytic Oscillations 16

1.4 Appendix: Math Background 24

1.4.1 Basic Techniques 26

1.4.2 Asymptotic Analysis 27

1.4.3 Enzyme Kinetics and Singular Perturbation Theory 28

1.5 Exercises 30

2 Cellular Homeostasis 33

2.1 The Cell Membrane 33

2.2 Diffusion 36

2.2.2 Diffusion Coefficients 37

2.2.3 Diffusion Through a Membrane: Ohm's Law 38

2.3 Facilitated Diffusion 38

2.3.1 Facilitated Diffusion in Muscle Respiration 42

2.4 Carrier-Mediated Transport 44

2.4.1 Glucose Transport 45

2.5 Active Transport 48

2.6 The Membrane Potential 51

2.6.1 The Nernst Equilibrium Potential 51

2.6.2 Electrodiffusion: The Goldman-Hodgkin-Katz Equations ... 53

2.6.3 Electrical Circuit Model of the Cell Membrane 56

2.7 Osmosis 58

2.8 Control of Cell Volume 59

2.8.1 A Pump-Leak Model 60

2.8.2 Volume Regulation and Ionic Transport 67

2.9 Exercises 72

3 Membrane Ion Channels 74

3.1 Current-Voltage Relations 74

3.1.1 Steady-State and Instantaneous Current-Voltage Relations . . 76

3.2 Independence, Saturation, and the Ussing Flux Ratio 78

3.3 Electrodiffusion Models 82

3.3.1 Multi-ion Flux: The Poisson-Nernst-Planck Equations 83

3.4 Barrier Models 87

3.4.1 Nonsaturating Barrier Models 89

3.4.2 Saturating Barrier Models: One-Ion Pores 93

3.4.3 Saturating Barrier Models: Multi-Ion Pores 99

3.4.4 Protein Ion Exchangers 102

3.5 Channel Gating 103

3.5.2 Multiple Subunits 105

3.5.3 The Sodium Channel 106

3.5.4 Drugs and Toxins 111

3.6 Exercises 112

4 Excitability 116

4.1 The Hodgkin-Huxley Model 117

4.1.1 History of the Hodgkin-Huxley Equations 119

4.1.2 Voltage and Time Dependence of Conductances 121

4.1.3 Qualitative Analysis 130

4.2 Two-Variable Models 136

4.2.1 Phase-Plane Behavior 139

4.3 Appendix: Cardiac Cells 142

4.3.1 Purkinje Fibers 143

4.3.2 Sinoatrial Node 148

4.3.3 Ventricular Cells 149

4.3.4 Summary 151

4.3.5 Further Developments 152

4.4 Exercises 153

5 Calcium Dynamics 160

5.1 Calcium Oscillations 163

5.2 The Two-Pool Model 163

5.2.1 Excitability and Oscillations 166

5.3 The Mechanisms of Calcium Release 168

5.3.1 IP3 Receptors 168

5.3.2 Ryanodine Receptors 178

5.4 Exercises 185

6 Bursting Electrical Activity 188

6.1 Bursting in the Pancreatic ^-Cell 190

6.1.1 Phase-Plane Analysis 191

6.2 Parabolic Bursting 196

6.3 A Classification Scheme for Bursting Oscillations 198

6.3.1 Type III Bursting 199

6.3.2 Type Ib Bursting 200

6.3.3 Summary of Types I, II, and III 202

6.4 Bursting in Clusters 202

6.4.1 Channel-Sharing 202

6.5 Qualitative Bursting Models 209

6.5.1 A Polynomial Model 210

6.6 Exercises 213

7 Intercellular Communication 216

7.1 Chemical Synapses 217

7.1.1 Quantal Nature of Synaptic Transmission 218

7.1.2 Presynaptic Voltage-Gated Calcium Channels 220

7.1.3 Calcium Diffusion, Binding, and Facilitation 226

7.1.4 Neurotransmitter Kinetics 229

7.1.5 The Postsynaptic Membrane Potential 233

7.1.6 Drugs and Toxins 235

7.2 Gap Junctions 236

7.2.1 Effective Diffusion Coefficients 236

7.2.2 Homogenization 238

7.2.3 Measurement of Permeabilities 241

7.2.4 The Role of Gap-Junction Distribution 241

7.3 Exercises 247

8 Passive Electrical Flow in Neurons 249

8.1 The Cable Equation 251

8.2 Dendritic Conduction 254

8.2.1 Boundary Conditions 255

8.2.2 Input Resistance 256

8.2.3 Branching Structures 256

8.3 The Rail Model of a Neuron 259

8.3.1 A Semi-Infinite Neuron with a Soma 261

8.3.2 A Finite Neuron and Soma 261

8.3.3 Other Compartmental Models 264

8.4 Appendix: Transform Methods 265

8.5 Exercises 265

9 Nonlinear Wave Propagation 268

9.1 Brief Overview of Wave Propagation 268

9.2 Traveling Fronts 270

9.2.1 The Bistable Equation 270

9.3 Myelination 276

9.3.1 The Discrete Bistable Equation 277

9.4 Traveling Pulses 281

9.4.1 The FitzHugh-Nagumo Equations 281

9.4.2 The Hodgkin-Huxley Equations 289

9.5 Periodic Wave Trains 291

9.5.1 Piecewise Linear FitzHugh-Nagumo Equations 292

9.5.2 Singular Perturbation Theory 293

9.5.3 Kinematics 295

9.6 Exercises 296

10 Wave Propagation in Higher Dimensions 299

10.1 Propagating Fronts 300

10.1.1 Plane Waves 300

10.1.2 Waves with Curvature 301

10.2 Spatial Patterns and Spiral Waves 305

10.2.1 More About Spirals 308

10.3 Exercises 310

11 Cardiac Propagation 312

11.1 Cardiac Fibers 313

11.1.1 Cellular Coupling 313

11.1.2 Propagation Failure 317

11.2 Myocardial Tissue 320

11.2.1 The Bidomain Model 320

11.3 Appendix: The Homogenization of a Periodic Conductive Domain . . 327

11.4 Exercises 332

12 Calcium Waves 333

12.1 Waves in the Two-Pool Model 334

12.1.1 A Piecewise Linear Model 334

12.1.2 Numerical Study of the Nonlinear Model 336

12.1.3 The Speed-Curvature Equation 337

12.2 Spiral Waves in Xenopus 338

12.3 Calcium Buffering 341

12.3.1 Buffers with Fast Kinetics 342

12.3.2 The Existence of Buffered Waves 343

12.3.3 The Shape and Speed of Buffered Waves 344

12.4 Discrete Calcium Sources 346

12.5 Intercellular Calcium Waves 348

12.6 Exercises 352

13 Regulation of Cell Function 355

13.1 The lac Operon 357

13.1.1 Glucose Oscillations 360

13.2 Cell Cycle Control 361

13.2.1 The G1 Checkpoint 363

13.2.2 The G2 Checkpoint 366

13.2.3 Control of M-Phase 368

13.2.4 Conclusion 374

13.3 Exercises 375

II Systems Physiology 377

14 Cardiac Rhythmicity 379

14.1 The Electrocardiogram 379

14.1.1 The Scalar ECG 379

14.1.2 The Vector ECG 380

14.2 Pacemakers 389

14.2.1 Pacemaker Synchrony 389

14.2.2 Critical Size of a Pacemaker 394

14.3 Cardiac Arrhythmias 401

14.3.1 Atrioventricular Node 401

14.3.2 Reentrant Arrhythmias 409

14.4 Defibrillation 414

14.4.1 The Direct Stimulus Threshold 420

14.4.2 The Defibrillation Threshold 422

14.5 Appendix: The Phase Equations 424

14.6 Exercises 429

15 The Circulatory System 434

15.1 Blood Flow 435

15.2 Compliance 439

15.3 The Microcirculation and Filtration 441

15.4 Cardiac Output 443

15.5 Circulation 446

15.5.1 A Simple Circulatory System 446

15.5.2 A Simple Linear Circulatory System 448

15.5.3 A Multicompartment Circulatory System 450

15.6 Cardiac Regulation 457

15.6.1 Autoregulation 457

15.6.2 The Baroreceptor Loop 461

15.7 Fetal Circulation 464

15.7.1 Pathophysiology of the Circulatory System 468

15.8 The Arterial Pulse 469

15.8.1 The Conservation Laws 470

15.8.2 The Windkessel Model 471

15.8.3 A Small-Amplitude Pressure Wave 473

15.8.4 Shock Waves in the Aorta 473

15.9 Exercises 478

16 Blood 480

16.1 Blood Plasma 480

16.2 Erythrocytes 482

16.2.1 Myoglobin and Hemoglobin 482

16.2.2 Hemoglobin Saturation Shifts 485

16.2.3 Carbon Dioxide Transport 488

16.2.4 Red Blood Cell Production 490

16.3 Leukocytes 495

16.3.1 Leukocyte Chemotaxis 496

16.3.2 The Inflammatory Response 498

16.4 Clotting 508

16.4.1 The Clotting Cascade 508

16.4.2 Platelets 510

16.5 Exercises 512

17 Respiration 516

17.1 Capillary-Alveoli Gas Exchange 517

17.1.1 Diffusion Across an Interface 517

17.1.2 Capillary-Alveolar Transport 518

17.1.3 Carbon Dioxide Removal 522

17.1.4 Oxygen Uptake 523

17.1.5 Carbon Monoxide Poisoning 524

17.2 Ventilation and Perfusion 527

17.3 Regulation of Ventilation 531

17.4 The Respiratory Center 535

17.5 Exercises 539

18 Muscle 542

18.1 Crossbridge Theory 543

18.2 The Force-Velocity Relationship: The Hill Model 547

18.2.1 Fitting Data 550

18.2.2 Some Solutions of the Hill Model 552

18.3 A Simple Crossbridge Model: The Huxley Model 554

18.3.1 Isotonic Responses 559

18.3.2 Other Choices for Rate Functions 561

18.4 Determination of the Rate Functions 562

18.4.1 A Continuous Binding Site Model 562

18.4.2 A General Binding Site Model 563

18.4.3 The Inverse Problem 565

18.5 The Discrete Distribution of Binding Sites 569

18.6 High Time-Resolution Data 570

18.6.1 High Time-Resolution Experiments 570

18.6.2 The Model Equations 571

18.7 Exercises 577

19 Hormone Physiology 579

19.1 Ovulation in Mammals 581

19.1.1 The Control of Ovulation 582

19.1.2 Other Models of Ovulation 592

19.2 Pulsatile Secretion of Luteinizing Hormone 593

19.3 Pulsatile Insulin Secretion 594

19.3.1 Ultradian Oscillations 596

19.3.2 Insulin Oscillations with Intermediate Frequency 603

19.4 Adaptation of Hormone Receptors 607

19.5 Exercises 609

20 Renal Physiology 612

20.1 The Glomerulus 612

20.1.1 The Juxtaglomerular Apparatus 615

20.2 Urinary Concentration: The Loop of Henle 619

20.2.1 The Countercurrent Mechanism 623

20.2.2 The Countercurrent Mechanism in Nephrons 625

20.3 Exercises 635

21 The Gastrointestinal System 637

21.1 Fluid Absorption 637

21.2 Gastric Protection 642

21.2.1 A Steady-State Model 643

21.2.2 Gastric Acid Secretion and Neutralization 649

21.3 Coupled Oscillators in the Small Intestine 650

21.3.1 Temporal Control of Contractions 650

21.3.2 Waves of Electrical Activity 651

21.3.3 Models of Coupled Oscillators 652

21.4 Exercises 663

22 The Retina and Vision 665

22.1 Retinal Light Adaptation 666

22.1.1 Weber's Law and Contrast Detection 668

22.1.2 Intensity-Response Curves and the Naka-Rushton Equation . 669

22.1.3 A Linear Input-Output Model 671

22.1.4 A Nonlinear Feedback Model 673

22.2 Photoreceptor Physiology 675

22.2.1 The Initial Cascade 678

22.2.2 Light Adaptation in Cones 680

22.3 Photoreceptor and Horizontal Cell Interactions 685

22.3.1 Lateral Inhibition: A Qualitative Model 685

22.3.2 Lateral Inhibition: A Quantitative Model 687

22.4 Receptive Fields 692

22.5 The Pupil Light Reflex 695

22.5.1 Linear Stability Analysis 697

22.6 Appendix: Linear Systems Theory 698

22.7 Exercises 699

23 The Inner Ear 701

23.1 Frequency Tuning 704

23.1.1 Cochlear Mechanics and the Place Theory of Hearing 705

23.2 Models of the Cochlea 707

23.2.1 Equations of Motion for an Incompressible Fluid 707

23.2.2 The Basilar Membrane as a Harmonic Oscillator 708

23.2.3 A Numerical Solution 710

23.2.4 Long-Wave and Short-Wave Models 711

23.2.5 More Complex Models 719

23.3 Electrical Resonance in Hair Cells 720

23.3.1 An Electrical Circuit Analogue 721

23.3.2 A Mechanistic Model of Frequency Tuning 724

23.4 Exercises 727

Appendix: Units and Physical Constants 729

References 731

Index 751

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PART I

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