Geometry and Non-linear Dynamics Underlying Excitability Phenotypes in Biophysical Models of Membrane Potential
نویسندگان
چکیده
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Chapter 1 Preliminary concepts and literature review . . . . . . . . . . . . . . . 11 1.1 Cellular excitability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.1.1 Membranes, ionic gradients, and transport . . . . . . . . . . . . . 12 1.1.2 Electrical signaling and action potentials . . . . . . . . . . . . . . 12 1.2 Dynamical systems describing excitability . . . . . . . . . . . . . . . . . . 14 1.3 Historical overview of modeling membrane potential . . . . . . . . . . . . 17 1.3.1 The Hodgkin and Huxley model. . . . . . . . . . . . . . . . . . . . 19 1.3.2 The Fitz-Hugh model. . . . . . . . . . . . . . . . . . . . . . . . . 25 1.3.3 After FitzHugh... Noble, DiFrancesco, Rinzel, Morris & Lecar, AvRon, Ermentrout, Terman, Endresen, and many more . . . . . . 31 Chapter 2 Transmembrane transport . . . . . . . . . . . . . . . . . . . . . . . . 32 2.1 Diffusion, generalized drift and the Einstein relation . . . . . . . . . . . . 33 2.2 Electrodiffusion, electrical drift, and the Nernst-Planck Equation . . . . . . 34 2.2.1 The Nernst-Plank equation . . . . . . . . . . . . . . . . . . . . . 35 2.2.2 The Nernst equilibrium . . . . . . . . . . . . . . . . . . . . . . . . 35 2.3 Transport and membrane proteins . . . . . . . . . . . . . . . . . . . . . . 36 2.3.1 General formalism to describe changes in membrane protein conformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.3.2 Flux mediated by transporters . . . . . . . . . . . . . . . . . . . . 39 2.4 Membrane Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 2.4.1 Transport mediated by channels from a kinetic perspective . . . . . 52 2.4.2 Whole membrane currents and channel gating . . . . . . . . . . . 53 2.4.3 Fitting gating parameters . . . . . . . . . . . . . . . . . . . . . . . 58 2.4.4 Tables with representative parameters . . . . . . . . . . . . . . . 59 2.5 Summary and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Chapter 3 Reduced biophysical pacemaking model . . . . . . . . . . . . . . . . 64
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