## Computational Cell BiologyChristopher P. Fall, Eric S. Marland, John M. Wagner, John J. Tyson 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, we 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 c- putational 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. The ideal class would comprise both biology and applied math students, who might be encouraged to collaborate on exercises or class projects. We assume as little mathematical and biological background as we feel we can get away with, and we proceed fairly slowly. The techniques and approaches covered in the ?rst half of the book will form a basis for some elementary modeling or as a lead in to more advanced topics covered in the second half of the book. |

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### Contents

Christopher P Fall | 3 |

Theory | 12 |

Phase Plane Analysis | 18 |

7 | 49 |

Transporters and Pumps | 53 |

3 | 54 |

Fast and Slow Time Scales | 77 |

Exercises | 98 |

9 | 236 |

4 | 243 |

6 | 250 |

Bela Novak | 261 |

4 | 267 |

B 5 | 269 |

9 | 274 |

11 | 277 |

WholeCell Models | 101 |

53 | 125 |

Intercellular Communication | 140 |

Spatial Modeling 171 | 170 |

57 | 178 |

59 | 187 |

91 | 193 |

Modeling Intracellular Calcium Waves and Sparks | 198 |

B Solving and Analyzing Dynamical Systems Using XPPAUT | 210 |

B 3 | 221 |

Biochemical Oscillations | 230 |

98 | 232 |

Modeling | 285 |

15 | 294 |

29 | 300 |

Modeling Fluctuations in Macroscopic Currents with Stochastic | 302 |

TwoState Channels Stochasticity and Discreteness in an Excitable Membrane Model 11 6 1 Phenomena Induced by Stochasticity and Discreteness | 313 |

A Qualitative Analysis of Differential Equations | 323 |

Numerical Algorithms | 439 |

463 | |

464 | |

466 | |

### Other editions - View all

Computational Cell Biology Christopher P. Fall,Eric S. Marland,John M. Wagner,John J. Tyson Limited preview - 2007 |

Computational Cell Biology Christopher P. Fall,Eric S. Marland,John M. Wagner No preview available - 2014 |

Computational Cell Biology Christopher P. Fall,Eric S. Marland,John M. Wagner,John J. Tyson No preview available - 2010 |

### Common terms and phrases

action potential activity approximation assume axon behavior bifurcation diagram binding bistable buffer Ca2+ concentration Ca2+ release Ca2+]ER calcium Cdh1 cell cycle cellular Chapter chemical computational cyclin cytoplasm cytosol depolarized differential equations diffusion coefficient dimensionless directional diagrams dynamics eigenvalues electrical enzyme equilibrium example excitatory Exercise expression fast feedback fertilization Ca2+ wave flux function G1 phase gating given glucose GLUT transporter gonadotroph Hopf bifurcation Iapp inactivation inhibition initial conditions input insulin intracellular ion channels IP3R Keizer kinetic ligand limit cycle linear mathematical mechanism membrane potential molecular molecules Morris–Lecar model negative neurons nondimensional nullclines oscillations parameter values phase plane phosphorylation plasma membrane plot postsynaptic propagating protein rate constants reaction receptors scale shown in Figure shows simulation slow solution spatial spike stable steady steady–state stochastic synaptic trajectory transition variables velocity voltage Wee1 XPPAUT