Mathematical physiology 2 Systems physiology
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| 100 | 1 | |a Keener, James |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Mathematical physiology |n 2 |p Systems physiology |c James Keener ; James Sneyd |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York, NY |b Springer |c 2009 | |
| 300 | |a Getr. Zählung |b Ill., graph. Darst. | ||
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| 490 | 1 | |a Interdisciplinary applied mathematics |v 8,2 | |
| 490 | 0 | |a Mathematical biology | |
| 490 | 0 | |a Interdisciplinary applied mathematics |v ... | |
| 490 | 0 | |a Mathematical biology | |
| 700 | 1 | |a Sneyd, James |e Verfasser |4 aut | |
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| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-0-387-79388-7 |
| 830 | 0 | |a Interdisciplinary applied mathematics |v 8,2 |w (DE-604)BV004216726 |9 8,2 | |
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| adam_text | Table
of
Contents
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
xvi
Table of Contents
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
TheNa^Ca^ 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
Table of Contents
xvii
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
xviii
Table of Contents
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
Π
.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
Table of Contents
xix
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
xx
Table of Contents
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 II
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
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
Table of Contents
xxi
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
Na4 -
К 1
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
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
xxii
Table of Contents
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
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
Table of Contents
xxiii
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
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
xxjv Table of Contents
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 Cells
................................. 386
9.1.1
Bursting in the Pancreatic 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
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
Table of Contents
xxv
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
|
| adam_txt |
Table
of
Contents
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
xvi
Table of Contents
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
TheNa^Ca^ 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
Table of Contents
xvii
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
xviii
Table of Contents
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
Π
.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
Table of Contents
xix
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
xx
Table of Contents
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 II
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
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
Table of Contents
xxi
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
Na4"-
К"1"
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
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
xxii
Table of Contents
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
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
Table of Contents
xxiii
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
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
xxjv Table of Contents
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 Cells
. 386
9.1.1
Bursting in the Pancreatic 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
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
Table of Contents
xxv
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 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Keener, James Sneyd, James |
| author_facet | Keener, James Sneyd, James |
| author_role | aut aut |
| author_sort | Keener, James |
| author_variant | j k jk j s js |
| building | Verbundindex |
| bvnumber | BV035086047 |
| classification_rvk | SK 950 |
| ctrlnum | (OCoLC)315711407 (DE-599)BVBBV035086047 |
| dewey-full | 571 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 571 - Physiology & related subjects |
| dewey-raw | 571 |
| dewey-search | 571 |
| dewey-sort | 3571 |
| dewey-tens | 570 - Biology |
| discipline | Biologie Mathematik |
| discipline_str_mv | Biologie Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV035086047 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:08:57Z |
| indexdate | 2024-11-25T17:26:05Z |
| institution | BVB |
| isbn | 9780387793870 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016754230 |
| oclc_num | 315711407 |
| open_access_boolean | |
| owner | DE-703 DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-526 DE-83 DE-188 DE-19 DE-BY-UBM DE-11 |
| owner_facet | DE-703 DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-526 DE-83 DE-188 DE-19 DE-BY-UBM DE-11 |
| physical | Getr. Zählung Ill., graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| series | Interdisciplinary applied mathematics |
| series2 | Interdisciplinary applied mathematics Mathematical biology |
| spellingShingle | Keener, James Sneyd, James Mathematical physiology Interdisciplinary applied mathematics |
| title | Mathematical physiology |
| title_auth | Mathematical physiology |
| title_exact_search | Mathematical physiology |
| title_exact_search_txtP | Mathematical physiology |
| title_full | Mathematical physiology 2 Systems physiology James Keener ; James Sneyd |
| title_fullStr | Mathematical physiology 2 Systems physiology James Keener ; James Sneyd |
| title_full_unstemmed | Mathematical physiology 2 Systems physiology James Keener ; James Sneyd |
| title_short | Mathematical physiology |
| title_sort | mathematical physiology systems physiology |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016754230&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV035086036 (DE-604)BV004216726 |
| work_keys_str_mv | AT keenerjames mathematicalphysiology2 AT sneydjames mathematicalphysiology2 |