Computational Cell Biology

Автор(ы):Christofer P. Fall
06.10.2007
Год изд.:2002
Описание: This text is an introduction to dynamical modeling in cell biology. It is not meant as a complete overview of modeling or of particular models in cell biology. Rather, author use selected biological examples to motivate the concepts and techniques used in computational cell biology. This is done through a progression of increasingly more complex cellular functions modeled with increasingly complex mathematical and computational techniques. There are other excellent sources for material on mathematical cell biology and so the focus here truly is computer modeling. This does not mean that there are no mathematical techniques introduced, because some of them are absolutely vital, but it does mean that much of the mathematics is explained in a more intuitive fashion, while we allow the computer to do most of the work. The target audience for this text is mathematically sophisticated cell biology or neuroscience students or mathematics students who wish to learn about modeling in cell biology.
Оглавление:
Computational Cell Biology — обложка книги. Обложка книги.
I Introductory Course [1]
  1 Dynamic Phenomena in Cells [3]
    1.1 Scope of Cellular Dynamics [3]
    1.2 Computational Modeling in Biology [8]
      1.2.1 Cartoons, Mechanisms, and Models [8]
      1.2.2 The Role of Computation [9]
      1.2.3 The Role of Mathematics [10]
    1.3 A Simple Molecular Switch [11]
    1.4 Solving and Analyzing Differential Equations [13]
      1.4.1 Numerical Integration of Differential Equations [15]
      1.4.2 Introduction to Numerical Packages [18]
    1.5 Exercises [20]
  2 Voltage Gated Ionic Currents [21]
    2.1 Basis of the Ionic Battery [23]
      2.1.1 The Nernst Potential: Charge Balances Concentration [24]
      2.1.2 The Resting Membrane Potential [26]
    2.2 The Membrane Model [27]
      2.2.1 Equations for Membrane Electrical Behavior [28]
    2.3 Activation and Inactivation Gates [29]
      2.3.1 Models of Voltage-Dependent Gating [29]
      2.3.2 The Voltage Clamp [31]
    2.4 Interacting Ion Channels: The Morris-Lecar Model [34]
      2.4.1 Phase Plane Analysis [36]
      2.4.2 Stability Analysis [38]
      2.4.3 Why Do Oscillations Occur? [40]
      2.4.4 Excitability and Action Potentials [43]
      2.4.5 Type I and Type II Spiking [44]
    2.5 The Hodgkin-fluxley Model [45]
    2.6 FitzHugh-Nagumo Class Models [47]
    2.7 Summary [49]
    2.8 Exercises [50]
  3 Transporters and Pumps [53]
    3.1 Passive Transport [54]
    3.2 Transporter Rates [57]
      3.2.1 Algebraic Method [59]
      3.2.2 Diagrammatic Method [60]
      3.2.3 Rate of the GLUT Transporter [62]
    3.3 The Na+/Glucose Cotransporter [65]
    3.4 SERCA Pumps [70]
    3.5 Transport Cycles [73]
    3.6 Exercises [76]
  4 Fast and Slow Time Scales [77]
    4.1 The Rapid Equilibrium Approximation [78]
    4.2 Asymptotic Analysis of Time Scales [82]
    4.3 Glucose-Dependent Insulin Secretion [83]
    4.4 Ligand Gated Channels [88]
    4.5 The Neuromuscular Junction [90]
    4.6 The Inositol Trisphosphate (IP(?)) receptor [91]
    4.7 Michaelis-Menten Kinetics [94]
    4.8 Exercises [98]
  5 Whole-Cell Models [101]
    5.1 Models of ER and PM Calcium Handling [102]
      5.1.1 Flux Balance Equations with Rapid Buffering [103]
      5.1.2 Expressions for the Fluxes [106]
    5.2 Calcium Oscillations in the Bullfrog Sympathetic Ganglion Neuron [107]
      5.2.1 Ryanodine Receptor Kinetics: The Keizer-Levine Model [108]
      5.2.2 Bullfrog Sympathetic Ganglion Neuron Closed-Cell Model [111]
      5.2.3 Bullfrog Sympathetic Ganglion Neuron Open-Cell Model [113]
    5.3 The Pituitary Gonadotroph [115]
      5.3.1 The ER Oscillator in a Closed Cell [116]
      5.3.2 Open-Cell Model with Constant Calcium Influx [122]
      5.3.3 The Plasma Membrane Oscillator [124]
      5.3.4 Bursting Driven by the ER in the Full Model [126]
    5.4 The Pancreatic Beta Cell [128]
      5.4.1 Chay-Keizer Model [129]
      5.4.2 Chay-Keizer with an ER [133]
    5.5 Exercises [136]
  6 Intercellular Communication [140]
    6.1 Electrical Coupling and Gap Junctions [141]
      6.1.1 Synchronization of Two Oscillators [142]
      6.1.2 Asynchrony Between Oscillators [143]
      6.1.3 Cell Ensembles, Electrical Coupling Length Scale [144]
    6.2 Synaptic Transmission Between Neurons [146]
      6.2.1 Kinetics of Postsynaptic Current [147]
      6.2.2 Synapses: Excitatory and Inhibitory; Fast and Slow [148]
    6.3 When Synapses Might (or Might Not) Synchronize Active Cells [150]
    6.4 Neural Circuits as Computational Devices [153]
    6.5 Large-Scale Networks [159]
    6.6 Exercises [165]
II Advanced Material [169]
  7 Spatial Modeling [171]
    7.1 One-Dimensional Formulation [173]
      7.1.1 Conservation in One Dimension [173]
      7.1.2 Fick's Law of Diffusion [175]
      7.1.3 Advection [176]
      7.1.4 Flux of Ions in a Field [177]
      7.1.5 The Cable Equation [177]
      7.1.6 Boundary and Initial Conditions [178]
    7.2 Important Examples with Analytic Solutions [179]
      7.2.1 Diffusion Through a Membrane [179]
      7.2.2 Ion Flux Through a Channel [180]
      7.2.3 Voltage Clamping [181]
      7.2.4 Diffusion in a Long Dendrite [181]
      7.2.5 Diffusion into a Capillary [183]
    7.3 Numerical Solution of the Diffusion Equation [184]
    7.4 Multidimensional Problems [186]
      7.4.1 Conservation Law in Multiple Dimensions [186]
      7.4.2 Fick's Law in Multiple Dimensions [187]
      7.4.3 Advection in Multiple Dimensions [188]
      7.4.4 Boundary and Initial Conditions for Multiple Dimensions [188]
      7.4.5 Diffusion in Multiple Dimensions: Symmetry [188]
    7.5 Traveling Waves in Nonlinear Reaction-Diffusion Equations [189]
      7.5.1 Traveling Wave Solutions [190]
      7.5.2 Traveling Wave in the Fitzhugh-Nagumo Equations [192]
    7.6 Exercises [195]
  8 Modeling Intracellular Calcium Waves and Sparks [198]
    8.1 Microfluorometric Measurements [198]
    8.2 A Model of the Fertilization Calcium Wave [200]
    8.3 Including Calcium Buffers in Spatial Models [202]
    8.4 The Effective Diffusion Coefficient [203]
    8.5 Simulation of a Fertilization Calcium Wave [204]
    8.6 Simulation of a Traveling Front [204]
    8.7 Calcium Waves in the Immature Xenopus Oocycte [208]
    8.8 Simulation of a Traveling Pulse [208]
    8.9 Simulation of a Kinematic Wave [210]
    8.10 Spark-Mediated Calcium Waves [213]
    8.11 The FireJDiffuse^ire Model [214]
    8.12 Modeling Localized Calcium Elevations [220]
    8.13 Steady-State Localized Calcium Elevations [222]
      8.13.1 The Steady-State Excess Buffer Approximation (EBA) [224]
      8.13.2 The Steady-State Rapid Buffer Approximation (RBA) [225]
      8.13.3 Complementarity of the Steady-State EBA and RBA [226]
    8.14 Exercises [227]
  9 Biochemical Oscillations [230]
    9.1 Biochemical Kinetics and Feedback [232]
    9.2 Regulatory Enzymes [236]
    9.3 Two-Component Oscillators Based on Autocatalysis [239]
      9.3.1 SubstrateJDepletion Oscillator [240]
      9.3.2 Activator-Inhibitor Oscillator [242]
    9.4 Three-Component Networks Without Autocatalysis [243]
      9.4.1 Positive Feedback Loop and the Routh-Hurwitz Theorem [244]
      9.4.2 Negative Feedback Oscillations [244]
      9.4.3 The Goodwin Oscillator [244]
    9.5 Time-Delayed Negative Feedback [247]
      9.5.1 Distributed Time Lag and the Linear Chain Trick [248]
      9.5.2 Discrete Time Lag [249]
    9.6 Circadian Rhythms [250]
    9.7 Exercises [255]
  10 Cell Cycle Controls [261]
    10.1 Physiology of the Cell Cycle in Eukaryotes [261]
    10.2 Molecular Mechanisms of Cell Cycle Control [263]
    10.3 A Toy Model of Start and Finish [265]
      10.3.1 Hysteresis in the Interactions Between Cdk and APC [266]
      10.3.2 Activation of the APC at Anaphase [267]
    10.4 A Serious Model of the Budding Yeast Cell Cycle [269]
    10.5 Cell Cycle Controls in Fission Yeast [273]
    10.6 Checkpoints and Surveillance Mechanisms [276]
    10.7 Division Controls in Egg Cells [276]
    10.8 Growth and Division Controls in Metazoans [278]
    10.9 Spontaneous Limit Cycle or Hysteresis Loop? [279]
    10.10 Exercises [281]
  11 Modeling the Stochastic Gating of Ion Channels [285]
    11.1 Single-Channel Gating and a Two-State Model [285]
      11.1.1 Modeling Channel Gating as a Markov Process [286]
      11.1.2 The Transition Probability Matrix [288]
      11.1.3 Dwell Times [289]
      11.1.4 Monte Carlo Simulation [290]
      11.1.5 Simulating Multiple Independent Channels [291]
      11.1.6 Gillespie's Method [292]
    11.2 An Ensemble of Two-State Ion Channels [293]
      11.2.1 Probability of Finding N Channels in the Open State [293]
      11.2.2 The Average Number of Open Channels [296]
      11.2.3 The Variance of the Number of Open Channels [297]
    11.3 Fluctuations in Macroscopic Currents [298]
    11.4 Modeling Fluctuations in Macroscopic Currents with Stochastic ODEs [302]
      11.4.1 Langevin Equation for an Ensemble of Two-State Channels [304]
      11.4.2 Fokker-Planck Equation for an Ensemble of Two-State Channels [306]
    11.5 Membrane Voltage Fluctuations [307]
      11.5.1 Membrane Voltage Fluctuations with an Ensemble of Two-State Channels [309]
    11.6 Stochasticity and Discreteness in an Excitable Membrane Model [311]
      11.6.1 Phenomena Induced by Stochasticity and Discreteness [312]
      11.6.2 The Ensemble Density Approach Applied to the Stochastic Morris-Lecar Model [313]
      11.6.3 Langevin Formulation for the Stochastic Morris-Lecar Model [314]
    11.7 Exercises [317]
  12 Molecular Motors: Theory [320]
    12.1 Molecular Motions as Stochastic Processes [323]
      12.1.1 Protein Motion as a Simple Random Walk [323]
      12.1.2 Polymer Growth [325]
      12.1.3 Sample Paths of Polymer Growth [327]
      12.1.4 The Statistical Behavior of Polymer Growth [329]
    12.2 Modeling Molecular Motions [330]
      12.2.1 The Langevin Equation [330]
      12.2.2 Numerical Simulation of the Langevin Equation [332]
      12.2.3 The Smoluchowski Model [333]
      12.2.4 First Passage Time [334]
    12.3 Modeling Chemical Reactions [335]
    12.4 A Mechanochemical Model [338]
    12.5 Numerical Simulation of Protein Motion [339]
      12.5.1 Numerical Algorithm that Preserves Detailed Balance [340]
      12.5.2 Boundary Conditions [341]
      12.5.3 Numerical Stability [342]
      12.5.4 Implicit Discretization [344]
    12.6 Derivations and Comments [345]
      12.6.1 The Drag Coefficient [345]
      12.6.2 The Equipartition Theorem [345]
      12.6.3 A Numerical Method for the Langevin Equation [346]
      12.6.4 Some Connections with Thermodynamics [347]
      12.6.5 Jumping Beans and Entropy [349]
      12.6.6 Jump Rates [350]
      12.6.7 Jump Rates at an Absorbing Boundary [351]
    12.7 Exercises [353]
  13 Molecular Motors: Examples [354]
    13.1 Switching in the Bacterial Flagellar Motor [354]
    13.2 A Motor Driven by a'Hashing Potential [359]
    13.3 The Polymerization Ratchet [362]
    13.4 Simplified Model of the F0 Motor [364]
      13.4.1 The Average Velocity of the Motor in the Limit of Fast Diffusion [366]
      13.4.2 Brownian Ratchet vs. Power Stroke [369]
      13.4.3 The Average Velocity of the Motor When Chemical Reactions Are as Fast as Diffusion [369]
    13.5 Other Motor Proteins [374]
    13.6 Exercises [376]
  A Qualitative Analysis of Differential Equations [378]
    A.1 Matrix and Vector Manipulation [379]
    А.2 A Brief Review of Power Series [380]
    A.3 Linear ODEs [382]
      A.3.1 Solution of Systems of Linear ODEs [383]
      A.3.2 Numerical Solutions of ODEs [385]
      A.3.3 Eigenvalues and Eigenvectors [386]
    A.4 Phase Plane Analysis [388]
      A.4.1 Stability of Linear Steady States [390]
      A.4.2 Stability of a Nonlinear Steady States [392]
    A.5 Bifurcation Theory [395]
      A.5.1 Bifurcation at a Zero Eigenvalue [396]
      A.5.2 Bifurcation at a Pair of Imaginary Eigenvalues [398]
    A.6 Perturbation Theory [401]
      A.6.1 Regular Perturbation [401]
      A.6.2 Resonances [403]
      A.6.3 Singular Perturbation Theory [405]
    A.7 Exercises [408]
  В Solving and Analyzing Dynamical Systems Using XPPAUT [410]
    B.1 Basics of Solving Ordinary Differential Equations [411]
      B.1.1 Creating the ODE File [411]
      B.1.2 Running the Program [412]
      B.1.3 The Main Window [413]
      B.1.4 Solving the Equations, Graphing, and Plotting [414]
      B.1.5 Saving and Printing Plots [416]
      B.1.6 Changing Parameters and Initial Data [418]
      B.1.7 Looking at the Numbers: The Data Viewer [419]
      B.1.8 Saving and Restoring the State of Simulations [420]
      B.1.9 Important Numerical Parameters [421]
      B.1.10 Command Summary: The Basics [422]
    B.2 Phase Planes and Nonlinear Equations [422]
      B.2.1 Direction Fields [423]
      B.2.2 Nullclines and Fixed Points [423]
      B.2.3 Command Summary: Phase Planes and Fixed Points [426]
    B.3 Bifurcation and Continuation [427]
      B.3.1 General Steps for Bifurcation Analysis [427]
      B.3.2 Hopf Bifurcation in the FitzHugh-Nagumo Equations [428]
      B.3.3 Hints for Computing Complete Bifurcation Diagrams [430]
    B.4 Partial Differential Equations: The Method of Lines [432]
    B.5 Stochastic Equations [434]
      B.5.1 A Simple Brownian Ratchet [434]
      B.5.2 A Sodium Channel Model [434]
      B.5.3 A Flashing Ratchet [436]
  С Numerical Algorithms [439]
References [451]
Index [463]
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