Verfügbarkeit: Mathematical physiology

Mathematical physiology: 1 Cellular physiology

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Hauptverfasser:	Keener, James (VerfasserIn), Sneyd, James (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	New York, NY Springer 2009
Ausgabe:	2. ed.
Schriftenreihe:	Interdisciplinary applied mathematics 8,1
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	Getr. Zählung Ill., graph. Darst.
ISBN:	9780387758466

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Datensatz im Suchindex

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adam_text	Table of Contents CONTENTS, I: Cellular Physiology Preface to the Second Edition vii Preface to the First Edition ix Acknowledgments xiii 1 Biochemical Reactions 1 1.1 The Law of Mass Action ............................ 1 1.2 Thermodynamics and Rate Constants .................... 3 1.3 Detailed Balance ................................ 6 1.4 Enzyme Kinetics ................................ 7 1.4.1 The Equilibrium Approximation .................. 8 1.4.2 The Quasi-Steady-State Approximation ............. 9 1.4.3 Enzyme Inhibition .......................... 12 1.4.4 Cooperativity ............................. 15 1.4.5 Reversible Enzyme Reactions ................... 20 1.4.6 The Goldbeter-Koshland Function ................ 21 1.5 Glycolysis and Glycolytic Oscillations .................... 23 xvi Table of Contents 1.6 Appendix: Math Background ......................... 33 1.6.1 Basic Techniques ........................... 35 1.6.2 Asymptotic Analysis ......................... 37 1.6.3 Enzyme Kinetics and Singular Perturbation Theory ...... 39 1.7 Exercises ..................................... 42 2 Cellular Homeostasis 49 2.1 The Cell Membrane ............................... 49 2.2 Diffusion ..................................... 51 2.2.1 Fick s Law ............................... 52 2.2.2 Diffusion Coefficients ........................ 53 2.2.3 Diffusion Through a Membrane: Ohm s Law .......... 54 2.2.4 Diffusion into a Capillary ...................... 55 2.2.5 Buffered Diffusion .......................... 55 2.3 Facilitated Diffusion .............................. 58 2.3.1 Facilitated Diffusion in Muscle Respiration ........... 61 2.4 Carrier-Mediated Transport .......................... 63 2.4.1 Glucose Transport .......................... 64 2.4.2 Symports and Antiports ....................... 67 2.4.3 Sodium-Calcium Exchange ..................... 69 2.5 Active Transport ................................. 73 2.5.1 A Simple ATPase ........................... 74 2.5.2 Active Transport of Charged Ions ................. 76 2.5.3 A Model of the Na^K4 ATPase .................. 77 2.5.4 Nuclear Transport .......................... 79 2.6 The Membrane Potential ........................... 80 2.6.1 The Nernst Equilibrium Potential ................. 80 2.6.2 Gibbs-Donnan Equilibrium .................... 82 2.6.3 Electrodiffusion: The Goldman-Hodgkin-Katz Equations . . 83 2.6.4 Electrical Circuit Model of the Cell Membrane ......... 86 2.7 Osmosis ....................................... 88 2.8 Control of Cell Volume ............................. 90 2.8.1 A Pump-Leak Model ......................... 91 2.8.2 Volume Regulation and Ionic Transport ............. 98 2.9 Appendix: Stochastic Processes ....................... 103 2.9.1 Markov Processes ........................... 103 2.9.2 Discrete-State Markov Processes .................. 105 2.9.3 Numerical Simulation of Discrete Markov Processes ..... 107 2.9.4 Diffusion ................................ 109 2.9.5 Sample Paths; the Langevin Equation .............. 110 2.9.6 The Fokker-Planck Equation and the Mean First Exit Time . Ill 2.9.7 Diffusion and Fick s Law ...................... 114 2.10 Exercises ..................................... 115 Table of Contents xvii 3 Membrane Ion Channels 121 3.1 Current-Voltage Relations ........................... 121 3.1.1 Steady-State and Instantaneous Current-Voltage Relations . 123 3.2 Independence, Saturation, and the Ussing Flux Ratio .......... 125 3.3 Electrodiffusion Models ............................ 128 3.3.1 Multi-Ion Flux: The Poisson-Nernst-Planck Equations ... . 129 3.4 Barrier Models ................................. 134 3.4.1 Nonsaturating Barrier Models ................... 136 3.4.2 Saturating Barrier Models: One-Ion Pores ............ 139 3.4.3 Saturating Barrier Models: Multi-Ion Pores ........... 143 3.4.4 Electrogenic Pumps and Exchangers ............... 145 3.5 Channel Gating ................................. 147 3.5.1 A Two-State K+ Channel ....................... 148 3.5.2 Multiple Subunits ........................... 149 3.5.3 The Sodium Channel ......................... 150 3.5.4 Agonist-Controlled Ion Channels ................. 152 3.5.5 Drugs and Toxins ........................... 153 3.6 Single-Channel Analysis ............................ 155 3.6.1 Single-Channel Analysis of a Sodium Channel ......... 155 3.6.2 Single-Channel Analysis of an Agonist-Controlled Ion Channel ................................. 158 3.6.3 Comparing to Experimental Data ................. 160 3.7 Appendix: Reaction Rates ........................... 162 3.7.1 The Boltzmann Distribution .................... 163 3.7.2 A Fokker-Planck Equation Approach ............... 165 3.7.3 Reaction Rates and Kramers Result ............... 166 3.8 Exercises ..................................... 170 4 Passive Electrical Flow in Neurons 175 4.1 The Cable Equation .............................. 177 4.2 Dendritic Conduction ............................. 180 4.2.1 Boundary Conditions ........................ 181 4.2.2 Input Resistance ........................... 182 4.2.3 Branching Structures ........................ 182 4.2.4 A Dendrite with Synaptic Input .................. 185 4.3 The Rail Model of a Neuron .......................... 187 4.3.1 A Semi-Infinite Neuron with a Soma ............... 187 4.3.2 A Finite Neuron and Soma ..................... 189 4.3.3 Other Compartmental Models ................... 192 4.4 Appendix: Transform Methods ........................ 192 4.5 Exercises ..................................... 193 xviii Table of Contents 5 Excitability 195 5.1 The Hodgkin-Huxley Model ......................... 196 5.1.1 History of the Hodgkin-Huxley Equations ........... 198 5.1.2 Voltage and Time Dependence of Conductances ........ 200 5.1.3 Qualitative Analysis ......................... 210 5.2 The FitzHugh-Nagumo Equations ...................... 216 5.2.1 The Generalized FitzHugh-Nagumo Equations ......... 219 5.2.2 Phase-Plane Behavior ........................ 220 5.3 Exercises ..................................... 223 6 Wave Propagation in Excitable Systems 229 6.1 Brief Overview of Wave Propagation .................... 229 6.2 Traveling Fronts ................................. 231 6.2.1 The Bistable Equation ........................ 231 6.2.2 Myelination .............................. 236 6.2.3 The Discrete Bistable Equation .................. 238 6.3 Traveling Pulses ................................. 242 6.3.1 The FitzHugh-Nagumo Equations ................ 242 6.3.2 The Hodgkin-Huxley Equations .................. 250 6.4 Periodic Wave Trains .............................. 252 6.4.1 Piecewise-Linear FitzHugh-Nagumo Equations ........ 253 6.4.2 Singular Perturbation Theory ................... 254 6.4.3 Kinematics ............................... 256 6.5 Wave Propagation in Higher Dimensions .................. 257 6.5.1 Propagating Fronts .......................... 258 6.5.2 Spatial Patterns and Spiral Waves ................. 262 6.6 Exercises ..................................... 268 7 Calcium Dynamics 273 7.1 Calcium Oscillations and Waves ....................... 276 7.2 Well-Mixed Cell Models: Calcium Oscillations ............... 281 7.2.1 Influx .................................. 282 7.2.2 Mitochondria ............................. 282 7.2.3 Calcium Buffers ............................ 282 7.2.4 Calcium Pumps and Exchangers .................. 283 7.2.5 IP3 Receptors ............................. 285 7.2.6 Simple Models of Calcium Dynamics ............... 293 7.2.7 Open- and Closed-Cell Models ................... 296 7.2.8 IP3 Dynamics ............................. 298 7.2.9 Ryanodine Receptors ......................... 301 7.3 Calcium Waves ................................. 303 7.3.1 Simulation of Spiral Waves in Xenopus .............. 306 7.3.2 Traveling Wave Equations and Bifurcation Analysis ...... 307 Table of Contents xix 7.4 Calcium Buffering ............................... 309 7.4.1 Fast Buffers or Excess Buffers ................... 310 7.4.2 The Existence of Buffered Waves ................. 313 7.5 Discrete Calcium Sources ........................... 315 7.5.1 The Fire-Diffuse-Fire Model .................... 318 7.6 Calcium Puffs and Stochastic Modeling .................. 321 7.6.1 Stochastic IPR Models ........................ 323 7.6.2 Stochastic Models of Calcium Waves ............... 324 7.7 Intercellular Calcium Waves ......................... 326 7.7.1 Mechanically Stimulated Intercellular Ca2+ Waves ....... 327 7.7.2 Partial Regeneration ......................... 330 7.7.3 Coordinated Oscillations in Hepatocytes ............. 331 7.8 Appendix: Mean Field Equations ....................... 332 7.8.1 Microdomains............................. 332 7.8.2 Homogenization; Effective Diffusion Coefficients ....... 336 7.8.3 Bidomain Equations ......................... 341 7.9 Exercises ..................................... 341 8 Intercellular Communication 347 8.1 Chemical Synapses ............................... 348 8.1.1 Quantal Nature of Synaptic Transmission ............ 349 8.1.2 Presynaptic Voltage-Gated Calcium Channels .......... 352 8.1.3 Presynaptic Calcium Dynamics and Facilitation ........ 358 8.1.4 Neurotransmitter Kinetics ..................... 364 8.1.5 The Postsynaptic Membrane Potential .............. 370 8.1.6 Agonist-Controlled Ion Channels ................. 371 8.1.7 Drugs and Toxins ........................... 373 8.2 Gap Junctions .................................. 373 8.2.1 Effective Diffusion Coefficients ................... 374 8.2.2 Homogenization ........................... 376 8.2.3 Measurement of Permeabilities .................. 377 8.2.4 The Role of Gap-Junction Distribution .............. 377 8.3 Exercises ..................................... 383 9 Neuroendocrine Cells 385 9.1 Pancreatic β Cells ................................ 386 9.1.1 Bursting in the Pancreatic β Cell .................. 386 9.1.2 ER Calcium as a Slow Controlling Variable ........... 392 9.1.3 Slow Bursting and Glycolysis .................... 399 9.1.4 Bursting in Clusters ......................... 403 9.1.5 A Qualitative Bursting Model .................... 410 9.1.6 Bursting Oscillations in Other Cell Types ............. 412 xx Table of Contents 9.2 Hypothalamic and Pituitary Cells ...................... 419 9.2.1 The Gonadotroph ........................... 419 9.3 Exercises ..................................... 424 10 Regulation of Cell Function 427 10.1 Regulation of Gene Expression ........................ 428 10.1.1 The trp Repressor........................... 429 10.1.2 The lac Operon ............................ 432 10.2 Circadian Clocks ................................ 438 10.3 The Cell Cycle .................................. 442 10.3.1 A Simple Generic Model ....................... 445 10.3.2 Fission Yeast .............................. 452 10.3.3 A Limit Cycle Oscillator in the Xenopus Oocyte ......... 461 10.3.4 Conclusion ............................... 468 10.4 Exercises ..................................... 468 Appendix: Units and Physical Constants A-l References R-l Index 1-1 CONTENTS, II: Systems Physiology Preface to the Second Edition vii Preface to the First Edition ix Acknowledgments xiii 11 The Circulatory System 471 11.1 Blood Flow .................................... 473 11.2 Compliance ................................... 476 11.3 The Microcirculation and Filtration ..................... 479 11.4 Cardiac Output ................................. 482 11.5 Circulation .................................... 484 11.5.1 A Simple Circulatory System .................... 484 11.5.2 A Linear Circulatory System .................... 486 11.5.3 A Multicompartment Circulatory System ............ 488 11.6 Cardiovascular Regulation .......................... 495 11.6.1 Autoregulation ............................ 497 11.6.2 The Baroreceptor Loop ....................... 500 11.7 Fetal Circulation ................................ 507 11.7.1 Pathophysiology of the Circulatory System ........... 511 Table of Contents xxi 11.8 The Arterial Pulse ................................ 513 11.8.1 The Conservation Laws ....................... 513 11.8.2 The Windkessel Model ........................ 514 11.8.3 A Small-Amplitude Pressure Wave ................. 516 11.8.4 Shock Waves in the Aorta ...................... 516 11.9 Exercises ..................................... 521 12 The Heart 523 12.1 The Electrocardiogram ............................ 525 12.1.1 The Scalar ECG ............................ 525 12.1.2 The Vector ECG ............................ 526 12.2 Cardiac Cells ................................... 534 12.2.1 Purkinje Fibers ............................ 535 12.2.2 Sinoatrial Node ............................ 541 12.2.3 Ventricular Cells ........................... 543 12.2.4 Cardiac Excitation-Contraction Coupling ............ 546 12.2.5 Common-Pool and Local-Control Models ............ 548 12.2.6 The L-type Ca2+ Channel ...................... 550 12.2.7 The Ryanodine Receptor ...................... 551 12.2.8 The Na+-Ca2+ Exchanger ...................... 552 12.3 Cellular Coupling ................................ 553 12.3.1 One-Dimensional Fibers ....................... 554 12.3.2 Propagation Failure ......................... 561 12.3.3 Myocardial Tissue: The Bidomain Model ............. 566 12.3.4 Pacemakers .............................. 572 12.4 Cardiac Arrhythmias .............................. 583 12.4.1 Cellular Arrhythmias ......................... 584 12.4.2 Atrioventricular Node — Wenckebach Rhythms ......... 586 12.4.3 Reentrant Arrhythmias ....................... 593 12.5 Defibrillation ................................... 604 12.5.1 The Direct Stimulus Threshold ................... 608 12.5.2 The Defibrillation Threshold .................... 610 12.6 Appendix: The Sawtooth Potential ...................... 613 12.7 Appendix: The Phase Equations ....................... 614 12.8 Appendix: The Cardiac Bidomain Equations ............... 618 12.9 Exercises ..................................... 622 13 Blood 627 13.1 Blood Plasma .................................. 628 13.2 Blood Cell Production ............................. 630 13.2.1 Periodic Hematological Diseases .................. 632 13.2.2 A Simple Model of Blood Cell Growth .............. 633 13.2.3 Peripheral or Local Control? .................... 639 xxii Table of Contents 13.3 Erythrocytes ................................... 643 13.3.1 Myoglobin and Hemoglobin .................... 643 13.3.2 Hemoglobin Saturation Shifts ................... 648 13.3.3 Carbon Dioxide Transport ...................... 649 13.4 Leukocytes .................................... 652 13.4.1 Leukocyte Chemotaxis ........................ 653 13.4.2 The Inflammatory Response .................... 655 13.5 Control of Lymphocyte Differentiation ................... 665 13.6 Clotting ...................................... 669 13.6.1 The Clotting Cascade ......................... 669 13.6.2 Clotting Models ............................ 671 13.6.3 In Vitro Clotting and the Spread of Inhibition .......... 671 13.6.4 Platelets ................................ 675 13.7 Exercises ..................................... 678 14 Respiration 683 14.1 Capillary-Alveoli Gas Exchange ....................... 684 14.1.1 Diffusion Across an Interface .................... 684 14.1.2 Capillary-Alveolar Transport .................... 685 14.1.3 Carbon Dioxide Removal ...................... 688 14.1.4 Oxygen Uptake ............................ 689 14.1.5 Carbon Monoxide Poisoning .................... 692 14.2 Ventilation and Perfusion ........................... 694 14.2.1 The Oxygen-Carbon Dioxide Diagram .............. 698 14.2.2 Respiratory Exchange Ratio .................... 698 14.3 Regulation of Ventilation ........................... 701 14.3.1 A More Detailed Model of Respiratory Regulation ....... 706 14.4 The Respiratory Center ............................ 708 14.4.1 A Simple Mutual Inhibition Model ................ 710 14.5 Exercises ..................................... 714 15 Muscle 717 15.1 Crossbridge Theory ............................... 719 15.2 The Force-Velocity Relationship: The Hill Model ............. 724 15.2.1 Fitting Data .............................. 726 15.2.2 Some Solutions of the Hill Model ................. 727 15.3 A Simple Crossbridge Model: The Huxley Model ............. 730 15.3.1 Isotonic Responses .......................... 737 15.3.2 Other Choices for Rate Functions ................. 738 15.4 Determination of the Rate Functions .................... 739 15.4.1 A Continuous Binding Site Model ................. 739 15.4.2 A General Binding Site Model ................... 741 15.4.3 The Inverse Problem ......................... 742 Table of Contents xxiii 15.5 The Discrete Distribution of Binding Sites ................. 747 15.6 High Time-Resolution Data .......................... 748 15.6.1 High Time-Resolution Experiments ................ 748 15.6.2 The Model Equations ........................ 749 15.7 In Vitro Assays .................................. 755 15.8 Smooth Muscle ................................. 756 15.8.1 The Hai-Murphy Model ....................... 756 15.9 Large-Scale Muscle Models .......................... 759 15.10 Molecular Motors ................................ 759 15.10.1 Brownian Ratchets .......................... 760 15.10.2 The Tilted Potential .......................... 765 15.10.3 Flashing Ratchets ........................... 767 15.11 Exercises ..................................... 770 16 The Endocrine System 773 16.1 The Hypothalamus and Pituitary Gland .................. 775 16.1.1 Pulsatile Secretion of Luteinizing Hormone ........... 777 16.1.2 Neural Pulse Generator Models .................. 779 16.2 Ovulation in Mammals ............................. 784 16.2.1 A Model of the Menstrual Cycle .................. 784 16.2.2 The Control of Ovulation Number ................. 788 16.2.3 Other Models of Ovulation ..................... 802 16.3 Insulin and Glucose .............................. 803 16.3.1 Insulin Sensitivity .......................... 804 16.3.2 Pulsatile Insulin Secretion ..................... 806 16.4 Adaptation of Hormone Receptors ..................... 813 16.5 Exercises ..................................... 816 17 Renal Physiology 821 17.1 The Glomerulus ................................. 821 17.1.1 Autoregulation and Tubuloglomerular Oscillations ....... 825 17.2 Urinary Concentration: The Loop of Henle ................ 831 17.2.1 The Countercurrent Mechanism .................. 836 17.2.2 The Countercurrent Mechanism in Nephrons .......... 837 17.3 Models of Tubular Transport ......................... 848 17.4 Exercises ..................................... 849 18 The Gastrointestinal System 851 18.1 Fluid Absorption ................................ 851 18.1.1 A Simple Model of Fluid Absorption ............... 853 18.1.2 Standing-Gradient Osmotic Flow ................. 857 18.1.3 Uphill Water Transport ....................... 864 xxiv Table of Contents 18.2 Gastric Protection ............................... 866 18.2.1 A Steady-State Model ........................ 867 18.2.2 Gastric Acid Secretion and Neutralization ............ 873 18.3 Coupled Oscillators in the Small Intestine ................. 874 18.3.1 Temporal Control of Contractions ................. 874 18.3.2 Waves of Electrical Activity ..................... 875 18.3.3 Models of Coupled Oscillators ................... 878 18.3.4 Interstitial Cells of Cajal ....................... 887 18.3.5 Biophysical and Anatomical Models ............... 888 18.4 Exercises ..................................... 890 19 The Retina and Vision 893 19.1 Retinal Light Adaptation ........................... 895 19.1.1 Weber s Law and Contrast Detection ............... 897 19.1.2 Intensity-Response Curves and the Naka-Rushton Equation . 898 19.2 Photoreceptor Physiology ........................... 902 19.2.1 The Initial Cascade .......................... 905 19.2.2 Light Adaptation in Cones ..................... 907 19.3 A Model of Adaptation in Amphibian Rods ................ 912 19.3.1 Single-Photon Responses ...................... 915 19.4 Lateral Inhibition ................................ 917 19.4.1 A Simple Model of Lateral Inhibition ............... 919 19.4.2 Photoreceptor and Horizontal Cell Interactions ......... 921 19.5 Detection of Motion and Directional Selectivity .............. 926 19.6 Receptive Fields ................................. 929 19.7 The Pupil Light Reflex ............................. 933 19.7.1 Linear Stability Analysis ....................... 935 19.8 Appendix: Linear Systems Theory ...................... 936 19.9 Exercises ..................................... 939 20 The Inner Ear 943 20.1 Frequency Tuning ................................ 946 20.1.1 Cochlear Macromechanics ..................... 947 20.2 Models of the Cochlea ............................. 949 20.2.1 Equations of Motion for an Incompressible Fluid ....... 949 20.2.2 The Basilar Membrane as a Harmonic Oscillator ........ 950 20.2.3 An Analytical Solution ........................ 952 20.2.4 Long-Wave and Short-Wave Models ................ 953 20.2.5 More Complex Models ........................ 962 20.3 Electrical Resonance in Hair Cells ...................... 962 20.3.1 An Electrical Circuit Analogue ................... 964 20.3.2 A Mechanistic Model of Frequency Tuning ........... 966 Table of Contents xxv 20.4 The Nonlinear Cochlear Amplifier ...................... 969 20.4.1 Negative Stiffness, Adaptation, and Oscillations ........ 969 20.4.2 Nonlinear Compression and Hopf Bifurcations ......... 971 20.5 Exercises ..................................... 973 Appendix: Units and Physical Constants A-l References R-l Index M
adam_txt	Table of Contents CONTENTS, I: Cellular Physiology Preface to the Second Edition vii Preface to the First Edition ix Acknowledgments xiii 1 Biochemical Reactions 1 1.1 The Law of Mass Action . 1 1.2 Thermodynamics and Rate Constants . 3 1.3 Detailed Balance . 6 1.4 Enzyme Kinetics . 7 1.4.1 The Equilibrium Approximation . 8 1.4.2 The Quasi-Steady-State Approximation . 9 1.4.3 Enzyme Inhibition . 12 1.4.4 Cooperativity . 15 1.4.5 Reversible Enzyme Reactions . 20 1.4.6 The Goldbeter-Koshland Function . 21 1.5 Glycolysis and Glycolytic Oscillations . 23 xvi Table of Contents 1.6 Appendix: Math Background . 33 1.6.1 Basic Techniques . 35 1.6.2 Asymptotic Analysis . 37 1.6.3 Enzyme Kinetics and Singular Perturbation Theory . 39 1.7 Exercises . 42 2 Cellular Homeostasis 49 2.1 The Cell Membrane . 49 2.2 Diffusion . 51 2.2.1 Fick's Law . 52 2.2.2 Diffusion Coefficients . 53 2.2.3 Diffusion Through a Membrane: Ohm's Law . 54 2.2.4 Diffusion into a Capillary . 55 2.2.5 Buffered Diffusion . 55 2.3 Facilitated Diffusion . 58 2.3.1 Facilitated Diffusion in Muscle Respiration . 61 2.4 Carrier-Mediated Transport . 63 2.4.1 Glucose Transport . 64 2.4.2 Symports and Antiports . 67 2.4.3 Sodium-Calcium Exchange . 69 2.5 Active Transport . 73 2.5.1 A Simple ATPase . 74 2.5.2 Active Transport of Charged Ions . 76 2.5.3 A Model of the Na^K4" ATPase . 77 2.5.4 Nuclear Transport . 79 2.6 The Membrane Potential . 80 2.6.1 The Nernst Equilibrium Potential . 80 2.6.2 Gibbs-Donnan Equilibrium . 82 2.6.3 Electrodiffusion: The Goldman-Hodgkin-Katz Equations . . 83 2.6.4 Electrical Circuit Model of the Cell Membrane . 86 2.7 Osmosis . 88 2.8 Control of Cell Volume . 90 2.8.1 A Pump-Leak Model . 91 2.8.2 Volume Regulation and Ionic Transport . 98 2.9 Appendix: Stochastic Processes . 103 2.9.1 Markov Processes . 103 2.9.2 Discrete-State Markov Processes . 105 2.9.3 Numerical Simulation of Discrete Markov Processes . 107 2.9.4 Diffusion . 109 2.9.5 Sample Paths; the Langevin Equation . 110 2.9.6 The Fokker-Planck Equation and the Mean First Exit Time . Ill 2.9.7 Diffusion and Fick's Law . 114 2.10 Exercises . 115 Table of Contents xvii 3 Membrane Ion Channels 121 3.1 Current-Voltage Relations . 121 3.1.1 Steady-State and Instantaneous Current-Voltage Relations . 123 3.2 Independence, Saturation, and the Ussing Flux Ratio . 125 3.3 Electrodiffusion Models . 128 3.3.1 Multi-Ion Flux: The Poisson-Nernst-Planck Equations . . 129 3.4 Barrier Models . 134 3.4.1 Nonsaturating Barrier Models . 136 3.4.2 Saturating Barrier Models: One-Ion Pores . 139 3.4.3 Saturating Barrier Models: Multi-Ion Pores . 143 3.4.4 Electrogenic Pumps and Exchangers . 145 3.5 Channel Gating . 147 3.5.1 A Two-State K+ Channel . 148 3.5.2 Multiple Subunits . 149 3.5.3 The Sodium Channel . 150 3.5.4 Agonist-Controlled Ion Channels . 152 3.5.5 Drugs and Toxins . 153 3.6 Single-Channel Analysis . 155 3.6.1 Single-Channel Analysis of a Sodium Channel . 155 3.6.2 Single-Channel Analysis of an Agonist-Controlled Ion Channel . 158 3.6.3 Comparing to Experimental Data . 160 3.7 Appendix: Reaction Rates . 162 3.7.1 The Boltzmann Distribution . 163 3.7.2 A Fokker-Planck Equation Approach . 165 3.7.3 Reaction Rates and Kramers'Result . 166 3.8 Exercises . 170 4 Passive Electrical Flow in Neurons 175 4.1 The Cable Equation . 177 4.2 Dendritic Conduction . 180 4.2.1 Boundary Conditions . 181 4.2.2 Input Resistance . 182 4.2.3 Branching Structures . 182 4.2.4 A Dendrite with Synaptic Input . 185 4.3 The Rail Model of a Neuron . 187 4.3.1 A Semi-Infinite Neuron with a Soma . 187 4.3.2 A Finite Neuron and Soma . 189 4.3.3 Other Compartmental Models . 192 4.4 Appendix: Transform Methods . 192 4.5 Exercises . 193 xviii Table of Contents 5 Excitability 195 5.1 The Hodgkin-Huxley Model . 196 5.1.1 History of the Hodgkin-Huxley Equations . 198 5.1.2 Voltage and Time Dependence of Conductances . 200 5.1.3 Qualitative Analysis . 210 5.2 The FitzHugh-Nagumo Equations . 216 5.2.1 The Generalized FitzHugh-Nagumo Equations . 219 5.2.2 Phase-Plane Behavior . 220 5.3 Exercises . 223 6 Wave Propagation in Excitable Systems 229 6.1 Brief Overview of Wave Propagation . 229 6.2 Traveling Fronts . 231 6.2.1 The Bistable Equation . 231 6.2.2 Myelination . 236 6.2.3 The Discrete Bistable Equation . 238 6.3 Traveling Pulses . 242 6.3.1 The FitzHugh-Nagumo Equations . 242 6.3.2 The Hodgkin-Huxley Equations . 250 6.4 Periodic Wave Trains . 252 6.4.1 Piecewise-Linear FitzHugh-Nagumo Equations . 253 6.4.2 Singular Perturbation Theory . 254 6.4.3 Kinematics . 256 6.5 Wave Propagation in Higher Dimensions . 257 6.5.1 Propagating Fronts . 258 6.5.2 Spatial Patterns and Spiral Waves . 262 6.6 Exercises . 268 7 Calcium Dynamics 273 7.1 Calcium Oscillations and Waves . 276 7.2 Well-Mixed Cell Models: Calcium Oscillations . 281 7.2.1 Influx . 282 7.2.2 Mitochondria . 282 7.2.3 Calcium Buffers . 282 7.2.4 Calcium Pumps and Exchangers . 283 7.2.5 IP3 Receptors . 285 7.2.6 Simple Models of Calcium Dynamics . 293 7.2.7 Open- and Closed-Cell Models . 296 7.2.8 IP3 Dynamics . 298 7.2.9 Ryanodine Receptors . 301 7.3 Calcium Waves . 303 7.3.1 Simulation of Spiral Waves in Xenopus . 306 7.3.2 Traveling Wave Equations and Bifurcation Analysis . 307 Table of Contents xix 7.4 Calcium Buffering . 309 7.4.1 Fast Buffers or Excess Buffers . 310 7.4.2 The Existence of Buffered Waves . 313 7.5 Discrete Calcium Sources . 315 7.5.1 The Fire-Diffuse-Fire Model . 318 7.6 Calcium Puffs and Stochastic Modeling . 321 7.6.1 Stochastic IPR Models . 323 7.6.2 Stochastic Models of Calcium Waves . 324 7.7 Intercellular Calcium Waves . 326 7.7.1 Mechanically Stimulated Intercellular Ca2+ Waves . 327 7.7.2 Partial Regeneration . 330 7.7.3 Coordinated Oscillations in Hepatocytes . 331 7.8 Appendix: Mean Field Equations . 332 7.8.1 Microdomains. 332 7.8.2 Homogenization; Effective Diffusion Coefficients . 336 7.8.3 Bidomain Equations . 341 7.9 Exercises . 341 8 Intercellular Communication 347 8.1 Chemical Synapses . 348 8.1.1 Quantal Nature of Synaptic Transmission . 349 8.1.2 Presynaptic Voltage-Gated Calcium Channels . 352 8.1.3 Presynaptic Calcium Dynamics and Facilitation . 358 8.1.4 Neurotransmitter Kinetics . 364 8.1.5 The Postsynaptic Membrane Potential . 370 8.1.6 Agonist-Controlled Ion Channels . 371 8.1.7 Drugs and Toxins . 373 8.2 Gap Junctions . 373 8.2.1 Effective Diffusion Coefficients . 374 8.2.2 Homogenization . 376 8.2.3 Measurement of Permeabilities . 377 8.2.4 The Role of Gap-Junction Distribution . 377 8.3 Exercises . 383 9 Neuroendocrine Cells 385 9.1 Pancreatic β Cells . 386 9.1.1 Bursting in the Pancreatic β Cell . 386 9.1.2 ER Calcium as a Slow Controlling Variable . 392 9.1.3 Slow Bursting and Glycolysis . 399 9.1.4 Bursting in Clusters . 403 9.1.5 A Qualitative Bursting Model . 410 9.1.6 Bursting Oscillations in Other Cell Types . 412 xx Table of Contents 9.2 Hypothalamic and Pituitary Cells . 419 9.2.1 The Gonadotroph . 419 9.3 Exercises . 424 10 Regulation of Cell Function 427 10.1 Regulation of Gene Expression . 428 10.1.1 The trp Repressor. 429 10.1.2 The lac Operon . 432 10.2 Circadian Clocks . 438 10.3 The Cell Cycle . 442 10.3.1 A Simple Generic Model . 445 10.3.2 Fission Yeast . 452 10.3.3 A Limit Cycle Oscillator in the Xenopus Oocyte . 461 10.3.4 Conclusion . 468 10.4 Exercises . 468 Appendix: Units and Physical Constants A-l References R-l Index 1-1 CONTENTS, II: Systems Physiology Preface to the Second Edition vii Preface to the First Edition ix Acknowledgments xiii 11 The Circulatory System 471 11.1 Blood Flow . 473 11.2 Compliance . 476 11.3 The Microcirculation and Filtration . 479 11.4 Cardiac Output . 482 11.5 Circulation . 484 11.5.1 A Simple Circulatory System . 484 11.5.2 A Linear Circulatory System . 486 11.5.3 A Multicompartment Circulatory System . 488 11.6 Cardiovascular Regulation . 495 11.6.1 Autoregulation . 497 11.6.2 The Baroreceptor Loop . 500 11.7 Fetal Circulation . 507 11.7.1 Pathophysiology of the Circulatory System . 511 Table of Contents xxi 11.8 The Arterial Pulse . 513 11.8.1 The Conservation Laws . 513 11.8.2 The Windkessel Model . 514 11.8.3 A Small-Amplitude Pressure Wave . 516 11.8.4 Shock Waves in the Aorta . 516 11.9 Exercises . 521 12 The Heart 523 12.1 The Electrocardiogram . 525 12.1.1 The Scalar ECG . 525 12.1.2 The Vector ECG . 526 12.2 Cardiac Cells . 534 12.2.1 Purkinje Fibers . 535 12.2.2 Sinoatrial Node . 541 12.2.3 Ventricular Cells . 543 12.2.4 Cardiac Excitation-Contraction Coupling . 546 12.2.5 Common-Pool and Local-Control Models . 548 12.2.6 The L-type Ca2+ Channel . 550 12.2.7 The Ryanodine Receptor . 551 12.2.8 The Na+-Ca2+ Exchanger . 552 12.3 Cellular Coupling . 553 12.3.1 One-Dimensional Fibers . 554 12.3.2 Propagation Failure . 561 12.3.3 Myocardial Tissue: The Bidomain Model . 566 12.3.4 Pacemakers . 572 12.4 Cardiac Arrhythmias . 583 12.4.1 Cellular Arrhythmias . 584 12.4.2 Atrioventricular Node — Wenckebach Rhythms . 586 12.4.3 Reentrant Arrhythmias . 593 12.5 Defibrillation . 604 12.5.1 The Direct Stimulus Threshold . 608 12.5.2 The Defibrillation Threshold . 610 12.6 Appendix: The Sawtooth Potential . 613 12.7 Appendix: The Phase Equations . 614 12.8 Appendix: The Cardiac Bidomain Equations . 618 12.9 Exercises . 622 13 Blood 627 13.1 Blood Plasma . 628 13.2 Blood Cell Production . 630 13.2.1 Periodic Hematological Diseases . 632 13.2.2 A Simple Model of Blood Cell Growth . 633 13.2.3 Peripheral or Local Control? . 639 xxii Table of Contents 13.3 Erythrocytes . 643 13.3.1 Myoglobin and Hemoglobin . 643 13.3.2 Hemoglobin Saturation Shifts . 648 13.3.3 Carbon Dioxide Transport . 649 13.4 Leukocytes . 652 13.4.1 Leukocyte Chemotaxis . 653 13.4.2 The Inflammatory Response . 655 13.5 Control of Lymphocyte Differentiation . 665 13.6 Clotting . 669 13.6.1 The Clotting Cascade . 669 13.6.2 Clotting Models . 671 13.6.3 In Vitro Clotting and the Spread of Inhibition . 671 13.6.4 Platelets . 675 13.7 Exercises . 678 14 Respiration 683 14.1 Capillary-Alveoli Gas Exchange . 684 14.1.1 Diffusion Across an Interface . 684 14.1.2 Capillary-Alveolar Transport . 685 14.1.3 Carbon Dioxide Removal . 688 14.1.4 Oxygen Uptake . 689 14.1.5 Carbon Monoxide Poisoning . 692 14.2 Ventilation and Perfusion . 694 14.2.1 The Oxygen-Carbon Dioxide Diagram . 698 14.2.2 Respiratory Exchange Ratio . 698 14.3 Regulation of Ventilation . 701 14.3.1 A More Detailed Model of Respiratory Regulation . 706 14.4 The Respiratory Center . 708 14.4.1 A Simple Mutual Inhibition Model . 710 14.5 Exercises . 714 15 Muscle 717 15.1 Crossbridge Theory . 719 15.2 The Force-Velocity Relationship: The Hill Model . 724 15.2.1 Fitting Data . 726 15.2.2 Some Solutions of the Hill Model . 727 15.3 A Simple Crossbridge Model: The Huxley Model . 730 15.3.1 Isotonic Responses . 737 15.3.2 Other Choices for Rate Functions . 738 15.4 Determination of the Rate Functions . 739 15.4.1 A Continuous Binding Site Model . 739 15.4.2 A General Binding Site Model . 741 15.4.3 The Inverse Problem . 742 Table of Contents xxiii 15.5 The Discrete Distribution of Binding Sites . 747 15.6 High Time-Resolution Data . 748 15.6.1 High Time-Resolution Experiments . 748 15.6.2 The Model Equations . 749 15.7 In Vitro Assays . 755 15.8 Smooth Muscle . 756 15.8.1 The Hai-Murphy Model . 756 15.9 Large-Scale Muscle Models . 759 15.10 Molecular Motors . 759 15.10.1 Brownian Ratchets . 760 15.10.2 The Tilted Potential . 765 15.10.3 Flashing Ratchets . 767 15.11 Exercises . 770 16 The Endocrine System 773 16.1 The Hypothalamus and Pituitary Gland . 775 16.1.1 Pulsatile Secretion of Luteinizing Hormone . 777 16.1.2 Neural Pulse Generator Models . 779 16.2 Ovulation in Mammals . 784 16.2.1 A Model of the Menstrual Cycle . 784 16.2.2 The Control of Ovulation Number . 788 16.2.3 Other Models of Ovulation . 802 16.3 Insulin and Glucose . 803 16.3.1 Insulin Sensitivity . 804 16.3.2 Pulsatile Insulin Secretion . 806 16.4 Adaptation of Hormone Receptors . 813 16.5 Exercises . 816 17 Renal Physiology 821 17.1 The Glomerulus . 821 17.1.1 Autoregulation and Tubuloglomerular Oscillations . 825 17.2 Urinary Concentration: The Loop of Henle . 831 17.2.1 The Countercurrent Mechanism . 836 17.2.2 The Countercurrent Mechanism in Nephrons . 837 17.3 Models of Tubular Transport . 848 17.4 Exercises . 849 18 The Gastrointestinal System 851 18.1 Fluid Absorption . 851 18.1.1 A Simple Model of Fluid Absorption . 853 18.1.2 Standing-Gradient Osmotic Flow . 857 18.1.3 Uphill Water Transport . 864 xxiv Table of Contents 18.2 Gastric Protection . 866 18.2.1 A Steady-State Model . 867 18.2.2 Gastric Acid Secretion and Neutralization . 873 18.3 Coupled Oscillators in the Small Intestine . 874 18.3.1 Temporal Control of Contractions . 874 18.3.2 Waves of Electrical Activity . 875 18.3.3 Models of Coupled Oscillators . 878 18.3.4 Interstitial Cells of Cajal . 887 18.3.5 Biophysical and Anatomical Models . 888 18.4 Exercises . 890 19 The Retina and Vision 893 19.1 Retinal Light Adaptation . 895 19.1.1 Weber's Law and Contrast Detection . 897 19.1.2 Intensity-Response Curves and the Naka-Rushton Equation . 898 19.2 Photoreceptor Physiology . 902 19.2.1 The Initial Cascade . 905 19.2.2 Light Adaptation in Cones . 907 19.3 A Model of Adaptation in Amphibian Rods . 912 19.3.1 Single-Photon Responses . 915 19.4 Lateral Inhibition . 917 19.4.1 A Simple Model of Lateral Inhibition . 919 19.4.2 Photoreceptor and Horizontal Cell Interactions . 921 19.5 Detection of Motion and Directional Selectivity . 926 19.6 Receptive Fields . 929 19.7 The Pupil Light Reflex . 933 19.7.1 Linear Stability Analysis . 935 19.8 Appendix: Linear Systems Theory . 936 19.9 Exercises . 939 20 The Inner Ear 943 20.1 Frequency Tuning . 946 20.1.1 Cochlear Macromechanics . 947 20.2 Models of the Cochlea . 949 20.2.1 Equations of Motion for an Incompressible Fluid . 949 20.2.2 The Basilar Membrane as a Harmonic Oscillator . 950 20.2.3 An Analytical Solution . 952 20.2.4 Long-Wave and Short-Wave Models . 953 20.2.5 More Complex Models . 962 20.3 Electrical Resonance in Hair Cells . 962 20.3.1 An Electrical Circuit Analogue . 964 20.3.2 A Mechanistic Model of Frequency Tuning . 966 Table of Contents xxv 20.4 The Nonlinear Cochlear Amplifier . 969 20.4.1 Negative Stiffness, Adaptation, and Oscillations . 969 20.4.2 Nonlinear Compression and Hopf Bifurcations . 971 20.5 Exercises . 973 Appendix: Units and Physical Constants A-l References R-l Index M
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spelling	Keener, James Verfasser aut Mathematical physiology 1 Cellular physiology James Keener ; James Sneyd 2. ed. New York, NY Springer 2009 Getr. Zählung Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Interdisciplinary applied mathematics 8,1 Mathematical biology Interdisciplinary applied mathematics ... Sneyd, James Verfasser aut (DE-604)BV035086036 1 Erscheint auch als Online-Ausgabe 978-0-387-75847-3 Interdisciplinary applied mathematics 8,1 (DE-604)BV004216726 8,1 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016754224&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Keener, James Sneyd, James Mathematical physiology Interdisciplinary applied mathematics
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title_full	Mathematical physiology 1 Cellular physiology James Keener ; James Sneyd
title_fullStr	Mathematical physiology 1 Cellular physiology James Keener ; James Sneyd
title_full_unstemmed	Mathematical physiology 1 Cellular physiology James Keener ; James Sneyd
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