Mathematical Physiology

J Keener, J Sneyd

Table of contents :
Preface……Page 6
Acknowledgments……Page 10
Contents……Page 12
1.1 The Law of Mass Action……Page 24
1.2 Enzyme Kinetics……Page 26
1.3 Glycolysis and Glycolytic Oscillations……Page 37
1.4 Appendix: Math Background……Page 45
1.5 Exercises……Page 51
2.1 The Cell Membrane……Page 54
2.2 Diffusion……Page 57
2.3 Facilitated Diffusion……Page 59
2.4 Carrier-Mediated Transport……Page 65
2.5 Active Transport……Page 69
2.6 The Membrane Potential……Page 72
2.7 Osmosis……Page 79
2.8 Control of Cell Volume……Page 80
2.9 Exercises……Page 93
3.1 Current–Voltage Relations……Page 95
3.2 Independence, Saturation, and the Ussing Flux Ratio……Page 99
3.3 Electrodiffusion Models……Page 103
3.4 Barrier Models……Page 108
3.5 Channel Gating……Page 124
3.6 Exercises……Page 133
4 Excitability……Page 137
4.1 The Hodgkin–Huxley Model……Page 138
4.2 Two-Variable Models……Page 157
4.3 Appendix: Cardiac Cells……Page 163
4.4 Exercises……Page 174
5 Calcium Dynamics……Page 181
5.2 The Two-Pool Model……Page 184
5.3 The Mechanisms of Calcium Release……Page 189
5.4 Exercises……Page 206
6 Bursting Electrical Activity……Page 209
6.1 Bursting in the Pancreatic β-Cell……Page 211
6.2 Parabolic Bursting……Page 217
6.3 A Classification Scheme for Bursting Oscillations……Page 219
6.4 Bursting in Clusters……Page 223
6.5 Qualitative Bursting Models……Page 230
6.6 Exercises……Page 234
7 Intercellular Communication……Page 237
7.1 Chemical Synapses……Page 238
7.2 Gap Junctions……Page 257
7.3 Exercises……Page 268
8 Passive Electrical Flow in Neurons……Page 270
8.1 The Cable Equation……Page 272
8.2 Dendritic Conduction……Page 275
8.3 The Rall Model of a Neuron……Page 280
8.5 Exercises……Page 286
9.1 Brief Overview of Wave Propagation……Page 289
9.2 Traveling Fronts……Page 291
9.3 Myelination……Page 297
9.4 Traveling Pulses……Page 302
9.5 Periodic Wave Trains……Page 312
9.6 Exercises……Page 317
10 Wave Propagation in Higher Dimensions……Page 320
10.1 Propagating Fronts……Page 321
10.2 Spatial Patterns and Spiral Waves……Page 326
10.3 Exercises……Page 331
11 Cardiac Propagation……Page 333
11.1 Cardiac Fibers……Page 334
11.2 Myocardial Tissue……Page 341
11.3 Appendix: The Homogenization of a Periodic Conductive Domain……Page 348
11.4 Exercises……Page 353
12 Calcium Waves……Page 354
12.1 Waves in the Two-Pool Model……Page 355
12.2 Spiral Waves in Xenopus……Page 359
12.3 Calcium Buffering……Page 362
12.4 Discrete Calcium Sources……Page 367
12.5 Intercellular Calcium Waves……Page 369
12.6 Exercises……Page 373
13 Regulation of Cell Function……Page 376
13.1 The lac Operon……Page 378
13.2 Cell Cycle Control……Page 382
13.3 Exercises……Page 396
14.1 The Electrocardiogram……Page 400
14.2 Pacemakers……Page 410
14.3 Cardiac Arrhythmias……Page 422
14.4 Defibrillation……Page 435
14.5 Appendix: The Phase Equations……Page 445
14.6 Exercises……Page 450
15 The Circulatory System……Page 455
15.1 Blood Flow……Page 456
15.2 Compliance……Page 460
15.3 The Microcirculation and Filtration……Page 462
15.4 Cardiac Output……Page 464
15.5 Circulation……Page 467
15.6 Cardiac Regulation……Page 478
15.7 Fetal Circulation……Page 485
15.8 The Arterial Pulse……Page 490
15.9 Exercises……Page 499
16.1 Blood Plasma……Page 501
16.2 Erythrocytes……Page 503
16.3 Leukocytes……Page 516
16.4 Clotting……Page 529
16.5 Exercises……Page 533
17 Respiration……Page 537
17.1 Capillary–Alveoli Gas Exchange……Page 538
17.2 Ventilation and Perfusion……Page 548
17.3 Regulation of Ventilation……Page 552
17.4 The Respiratory Center……Page 556
17.5 Exercises……Page 560
18 Muscle……Page 563
18.1 Crossbridge Theory……Page 564
18.2 The Force–Velocity Relationship: The Hill Model……Page 568
18.3 A Simple Crossbridge Model: The Huxley Model……Page 575
18.4 Determination of the Rate Functions……Page 583
18.5 The Discrete Distribution of Binding Sites……Page 590
18.6 High Time-Resolution Data……Page 591
18.7 Exercises……Page 598
19 Hormone Physiology……Page 600
19.1 Ovulation in Mammals……Page 602
19.2 Pulsatile Secretion of Luteinizing Hormone……Page 614
19.3 Pulsatile Insulin Secretion……Page 615
19.4 Adaptation of Hormone Receptors……Page 628
19.5 Exercises……Page 630
20.1 The Glomerulus……Page 633
20.2 Urinary Concentration: The Loop of Henle……Page 640
20.3 Exercises……Page 656
21.1 Fluid Absorption……Page 658
21.2 Gastric Protection……Page 663
21.3 Coupled Oscillators in the Small Intestine……Page 671
21.4 Exercises……Page 684
22 The Retina and Vision……Page 686
22.1 Retinal Light Adaptation……Page 687
22.2 Photoreceptor Physiology……Page 696
22.3 Photoreceptor and Horizontal Cell Interactions……Page 706
22.4 Receptive Fields……Page 713
22.5 The Pupil Light Reflex……Page 716
22.6 Appendix: Linear Systems Theory……Page 719
22.7 Exercises……Page 720
23 The Inner Ear……Page 722
23.1 Frequency Tuning……Page 725
23.2 Models of the Cochlea……Page 728
23.3 Electrical Resonance in Hair Cells……Page 741
23.4 Exercises……Page 748
Appendix: Units and Physical Constants……Page 750
References……Page 752
Index……Page 772