Atnaujinkite slapukų nuostatas

El. knyga: Cellular Biophysics and Modeling: A Primer on the Computational Biology of Excitable Cells

5.00/5 (2 ratings by Goodreads)
(College of William and Mary, Virginia)
  • Formatas: PDF+DRM
  • Išleidimo metai: 14-Mar-2019
  • Leidėjas: Cambridge University Press
  • Kalba: eng
  • ISBN-13: 9781108683265
Kitos knygos pagal šią temą:
Cellular Biophysics and Modeling: A Primer on the Computational Biology of Excitable CellsDidesnis paveikslėlis
  • Formatas: PDF+DRM
  • Išleidimo metai: 14-Mar-2019
  • Leidėjas: Cambridge University Press
  • Kalba: eng
  • ISBN-13: 9781108683265
Kitos knygos pagal šią temą:

DRM apribojimai

  • Kopijuoti:

    neleidžiama

  • Spausdinti:

    neleidžiama

  • El. knygos naudojimas:

    Skaitmeninių teisių valdymas (DRM)
    Leidykla pateikė šią knygą šifruota forma, o tai reiškia, kad norint ją atrakinti ir perskaityti reikia įdiegti nemokamą programinę įrangą. Norint skaityti šią el. knygą, turite susikurti Adobe ID . Daugiau informacijos  čia. El. knygą galima atsisiųsti į 6 įrenginius (vienas vartotojas su tuo pačiu Adobe ID).

    Reikalinga programinė įranga
    Norint skaityti šią el. knygą mobiliajame įrenginyje (telefone ar planšetiniame kompiuteryje), turite įdiegti šią nemokamą programėlę: PocketBook Reader (iOS / Android)

    Norint skaityti šią el. knygą asmeniniame arba „Mac“ kompiuteryje, Jums reikalinga  Adobe Digital Editions “ (tai nemokama programa, specialiai sukurta el. knygoms. Tai nėra tas pats, kas „Adobe Reader“, kurią tikriausiai jau turite savo kompiuteryje.)

    Negalite skaityti šios el. knygos naudodami „Amazon Kindle“.

An integrated guide to cellular biophysics and nonlinear dynamics, introducing students to the mathematical modeling of excitable cells. It combines empirical physiology and mathematical theory to present key interdisciplinary tools, highlighting how quantitative approaches can complement and advance bench research.

What every neuroscientist should know about the mathematical modeling of excitable cells. Combining empirical physiology and nonlinear dynamics, this text provides an introduction to the simulation and modeling of dynamic phenomena in cell biology and neuroscience. It introduces mathematical modeling techniques alongside cellular electrophysiology. Topics include membrane transport and diffusion, the biophysics of excitable membranes, the gating of voltage and ligand-gated ion channels, intracellular calcium signalling, and electrical bursting in neurons and other excitable cell types. It introduces mathematical modeling techniques such as ordinary differential equations, phase plane, and bifurcation analysis of single-compartment neuron models. With analytical and computational problem sets, this book is suitable for life sciences majors, in biology to neuroscience, with one year of calculus, as well as graduate students looking for a primer on membrane excitability and calcium signalling.

Recenzijos

'In this text, Conradi Smith does an excellent job of teaching students with no mathematical training beyond calculus how to use differential equations to understand the basic principles of cell physiology and excitability. He skilfully walks students through the steps of modeling and analysis, all the while working to develop intuition and insight into how things work. His emphasis on computational methods for solution as well as graphical and geometrical means for interpretation enables him to communicate complex ideas in understandable ways. Furthermore, his patience and attention to detail will be appreciated by those students who have not had extensive exposure to the art of mathematical modeling. This text is a wonderful addition to the mathematical biology textbook literature.' James P. Keener, University of Utah

Daugiau informacijos

What every neuroscientist should know about the mathematical modeling of excitable cells, presented at an introductory level.
Preface xi
1 Introduction
1(12)
1.1 Why Study Biophysics?
1(1)
1.2 Neurons are Brain Cells
2(1)
1.3 Cellular Biophysics
3(2)
1.4 Dynamical Systems Modeling
5(1)
1.5 Benefits and Limitations of Mathematical Models
6(1)
1.6 Minimal Models and Graphical Methods
7(1)
1.7 Biophysics and Dynamics Together
8(1)
1.8 Discussion
9(4)
Solutions
11(1)
Notes
11(2)
Part I Models and Ordinary Differential Equations
13(100)
2 Compartmental Modeling
15(27)
2.1 Physical Dimensions and Material Balance
15(1)
2.2 A Model of Intracellular Calcium Concentration
16(1)
2.3 The Initial Value Problem and its Solution
17(2)
2.4 Checking the Solution
19(1)
2.5 Interpreting the Solution
19(3)
2.6 Calcium Dynamics and Disease
22(2)
2.7 Appendix: Solving dc/dt = j -- kc with c(0) = C0
24(1)
2.8 Discussion
25(17)
Supplemental Problems
27(6)
Solutions
33(6)
Notes
39(3)
3 Phase Diagrams
42(17)
3.1 Phase Diagram for a Single Compartment Model
42(2)
3.2 Stable and Unstable Steady States
44(1)
3.3 Phase Diagram of a Nonlinear ODE
45(2)
3.4 Classifying Steady States
47(2)
3.5 Stability Analysis Requiring Higher Derivatives
49(1)
3.6 Scalar ODEs with Multiple Stable Steady States
50(1)
3.7 Discussion
51(8)
Supplemental Problems
55(2)
Solutions
57(1)
Notes
58(1)
4 Ligands, Receptors and Rate Laws
59(22)
4.1 Mass Action Kinetics
59(1)
4.2 Reaction Order and Physical Dimensions of Rate Constants
60(1)
4.3 Isomerization -- ODEs and a Conserved Quantity
61(2)
4.4 Isomerization -- Phase Diagram and Solutions
63(2)
4.5 Bimolecular Association of Ligand and Receptor
65(4)
4.6 Sequential Binding
69(1)
4.7 Sigmoidal Binding Curves
70(2)
4.8 Binding Curves and Hill Functions
72(2)
4.9 Discussion
74(7)
Supplemental Problems
75(2)
Solutions
77(2)
Notes
79(2)
5 Function Families and Characteristic Times
81(17)
5.1 Functions and Relations
81(1)
5.2 Scaling and Shifting of Functions
82(2)
5.3 Qualitative Analysis of Functions
84(4)
5.4 Characteristic Times
88(2)
5.5 Discussion
90(8)
Supplemental Problems
93(1)
Solutions
94(2)
Notes
96(2)
6 Bifurcation Diagrams of Scalar ODEs
98(15)
6.1 A Single-Parameter Family of ODEs
98(1)
6.2 Fold Bifurcation
99(2)
6.3 Transcritical Bifurcation
101(1)
6.4 Pitchfork Bifurcations
102(3)
6.5 Bifurcation Types and Symmetry
105(1)
6.6 Structural Stability
106(2)
6.7 Further Reading
108(5)
Supplemental Problems
109(1)
Solutions
110(1)
Notes
111(2)
Part II Passive Membranes
113(56)
7 The Nernst Equilibrium Potential
115(17)
7.1 Cellular Compartments and Electrical Potentials
115(1)
7.2 Nernst Equilibrium Potential
116(3)
7.3 Derivation of the Nernst Equation
119(2)
7.4 Calculating Nernst Equilibrium Potentials
121(1)
7.5 Chemical Potential
122(2)
7.6 Discussion
124(8)
Supplemental Problems
129(1)
Solutions
130(1)
Notes
130(2)
8 The Current Balance Equation
132(22)
8.1 Membrane Voltage
132(1)
8.2 Ionic Fluxes and Currents
132(1)
8.3 Ionic Currents and Voltage
133(1)
8.4 Applied Currents and Voltage
134(1)
8.5 The Current Balance Equation
135(2)
8.6 Constitutive Relation for Ionic Membrane Current
137(2)
8.7 The Phase Diagram for Voltage of Passive Membranes
139(1)
8.8 Exponential Time Constant for Membrane Voltage
140(3)
8.9 Discussion
143(11)
Supplemental Problems
147(2)
Solutions
149(4)
Notes
153(1)
9 GHK Theory of Membrane Permeation
154(15)
9.1 Goldman-Hodgkin-Katz Theory -- Assumptions
154(1)
9.2 Physical Dimensions of the GHK Current Equation
155(1)
9.3 The Goldman-Hodgkin-Katz Current Equation
156(1)
9.4 Limiting Conductances Implied by GHK Theory
157(2)
9.5 Derivation of the GHK Current Equation
159(2)
9.6 Further Reading and Discussion
161(8)
Supplemental Problems
164(1)
Solutions
165(3)
Notes
168(1)
Part III Voltage-Gated Currents
169(64)
10 Voltage-Gated Ionic Currents
171(14)
10.1 Voltage-Dependent Gating and Permeation Block
171(2)
10.2 The L-Type Calcium Current ICav
173(3)
10.3 The Inward Rectifying Potassium Current IKir
176(1)
10.4 The Hyperpolarization-Activated Cation Current Jsag
177(1)
10.5 The Depolarization-Activated Potassium Current IKv
177(2)
10.6 Qualitative Features of Current-Voltage Relations
179(1)
10.7 Further Reading and Discussion
180(5)
Supplemental Problems
181(1)
Solutions
182(1)
Notes
183(2)
11 Regenerative Ionic Currents and Bistability
185(14)
11.1 Regenerative Currents and Membrane Bistability
185(3)
11.2 Response of a Bistable Membrane to Applied Current Pulses
188(1)
11.3 Membrane Currents and Fold Bifurcations
188(2)
11.4 Bifurcation Diagram for the Bistable ICav + IL Membrane
190(1)
11.5 Overlaying Trajectories on the Bifurcation Diagram
191(1)
11.6 Bistable Membrane Voltage Mediated by IKir
191(2)
11.7 Further Reading and Discussion
193(6)
Supplemental Problems
197(1)
Solutions
197(1)
Notes
198(1)
12 Voltage-Clamp Recording
199(17)
12.1 Current-Clamp and Voltage-Clamp Recording
199(4)
12.2 Modeling Delayed Activation of Ionic Currents
203(3)
12.3 Voltage Clamp and Transient Ionic Currents
206(3)
12.4 Modeling Transient Ionic Currents
209(2)
12.5 Further Reading and Discussion
211(5)
Supplemental Problems
213(1)
Solutions
213(2)
Notes
215(1)
13 Hodgkin-Huxley Model of the Action Potential
216(17)
13.1 The Squid Giant Axon
216(3)
13.2 The Hodgkin-Huxley Model
219(2)
13.3 Excitability in the Hodgkin-Huxley Model
221(3)
13.4 Repetitive Spiking (Oscillations)
224(1)
13.5 Further Reading and Discussion
225(8)
Supplemental Problems
229(1)
Solutions
230(1)
Notes
230(3)
Part IV Excitability and Phase Planes
233(62)
14 The Morris-Lecar Model
235(17)
14.1 The Morris-Lecar Model
235(2)
14.2 The Reduced Morris-Lecar Model
237(2)
14.3 The Morris-Lecar Phase Plane
239(2)
14.4 Phase Plane Analysis of Membrane Excitability
241(3)
14.5 Phase Plane Analysis of Membrane Oscillations
244(4)
14.6 Further Reading and Discussion
248(4)
Supplemental Problems
249(2)
Solutions
251(1)
Notes
251(1)
15 Phase Plane Analysis
252(23)
15.1 The Phase Plane for Two-Dimensional Autonomous ODEs
252(3)
15.2 Direction Fields of Two-Dimensional Autonomous ODEs
255(1)
15.3 Nullclines for Two-Dimensional Autonomous ODEs
256(2)
15.4 How to Sketch a Phase Plane
258(5)
15.5 Phase Planes and Steady States
263(2)
15.6 Discussion
265(10)
Supplemental Problems
268(1)
Solutions
269(4)
Notes
273(2)
16 Linear Stability Analysis
275(20)
16.1 Solutions for Two-Dimensional Linear Systems
275(3)
16.2 Real and Distinct Eigenvalues -- Saddles and Nodes
278(3)
16.3 Complex Conjugate Eigenvalues -- Spirals
281(3)
16.4 Criterion for Stability
284(1)
16.5 Further Reading and Discussion
285(10)
Supplemental Problems
290(1)
Solutions
291(2)
Notes
293(2)
Part V Oscillations and Bursting
295(73)
17 Type II Excitability and Oscillations (Hopf Bifurcation)
297(22)
17.1 Fitzhugh-Nagumo Model
297(3)
17.2 Phase Plane Analysis of Resting Steady State
300(3)
17.3 Loss of Stability with Increasing J (Depolarization)
303(1)
17.4 Analysis of Hopf Bifurcations
304(6)
17.5 Limit Cycle Fold Bifurcation
310(3)
17.6 Further Reading and Discussion
313(6)
Supplemental Problems
315(1)
Solutions
316(1)
Notes
317(2)
18 Type I Excitability and Oscillations (SNIC and SHO Bifurcations)
319(19)
18.1 Saddle-Node on an Invariant Circle
319(4)
18.2 Saddle Homoclinic Bifurcation
323(1)
18.3 Square-Wave Bursting
324(4)
18.4 Calcium-Activated Potassium Currents as Slow Variable
328(3)
18.5 Further Reading and Discussion
331(7)
Supplemental Problems
335(1)
Solutions
336(1)
Note
337(1)
19 The Low-Threshold Calcium Spike
338(15)
19.1 Post-Inhibitory Rebound Bursting
338(4)
19.2 Fast/Slow Analysis of Post-Inhibitory Rebound Bursting
342(1)
19.3 Rhythmic Bursting in Response to Hyperpolarization
343(1)
19.4 Fast/Slow Analysis of Rhythmic Bursting
344(2)
19.5 Minimal Model of the Low-Threshold Calcium Spike
346(3)
19.6 Further Reading and Discussion
349(4)
Solutions
351(1)
Notes
351(2)
20 Synaptic Currents
353(15)
20.1 Electrical Synapses
353(2)
20.2 Electrical Synapses and Synchrony
355(1)
20.3 Chemical Synapses
356(1)
20.4 Phase Plane Analysis of Instantaneously Coupled Cells
357(5)
20.5 Reciprocally Coupled Excitatory Neurons
362(1)
20.6 Further Reading and Discussion
363(5)
Supplemental Problems
365(2)
Solutions
367(1)
Note
367(1)
Afterword 368(3)
References 371(9)
Index 380
Greg Conradi Smith is a Professor in the Department of Applied Science and Neuroscience Program Faculty Affiliate at the College of William and Mary, Virginia. He was organizer of the Cold Spring Harbor Laboratory Summer School on Computational Cell Biology (200814). His research focuses on mathematical aspects of cell physiology and neuroscience.
Daugiau apie elektronines knygas Daugiau apie elektronines knygas
Pastovi nuoroda: https://www.kriso.lt/db/97811086832652e.html
Raktažodžiai: