By Christopher P. Fall, Eric S. Marland, John M. Wagner, John J. Tyson

This textbook offers an advent to dynamic modeling in molecular phone biology, taking a computational and intuitive process. particular illustrations, examples, and workouts are incorporated in the course of the textual content. Appendices containing mathematical and computational concepts are supplied as a reference tool.

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1: Basis of the Ionic Battery balanced by the force generated by the chemical potential, δg, contained in the residual concentration difference. The equilibrium potential, where the electrical and chemical forces are balanced, is given by the Nernst equation. The Nernst equation is derived from the expression for the change in Gibbs free energy when one mole of an ion of valence z is moved across a membrane: ∆G = RT ln [ion]in + ∆V F z. 1) At equilibrium, ∆G is zero. 1, T is temperature (in kelvin), and z is the valence of the ion as previously deÞned.

Because [K+ ] is greater on one side of the membrane, K+ ions diffuse through the K+ pore down the concentration gradient. Because the membrane is not permeable to the anion A− , each K+ ion that passes down the concentration gradient carries a positive charge that is not balanced by an accompanying A− . 3 (A) Concentration and charge are balanced on each side of the membrane, so there is no ∆V across the membrane. (B) Due to the nonselective pore, charge and concentration are balanced everywhere, and so there is no ∆V across the membrane.

For example, the membrane potential for a cell containing Na+ , K+ , and Cl− ions would be Vm = (VNa · gNa ) + (VK · gK ) + (VCl · gCl ) . 5) Because the resting membrane potential is the weighted average of Nernst potentials for the various ions, the ion with the greatest permeability contributes the most (see Exercise 1c). 2 The Membrane Model membrane model–( We know from Ohm’s law that current ßows down a voltage gradient in proportion to the resistance in the circuit. Current is therefore expressed as I= V = gV.

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