Dynamical Systems in Neuroscience:

Electrophysiology of Neurons 27InsideOutsideInsideOutsideInsideOutsideK + Na + Cl -A - Na +Cl -DiffusionK +Cl - Na +K + A -A -K +K +Cl -A -Na + Na +A - Cl -K +Na +A -K + Na + Na +A -Cl -A -K +Cl -A - Na +A -K +Na +Cl - A - K + Cl -DiffusionDiffusionK + A -K + Cl - K + A - Na + Cl -K +A - K +A -K +Na +A - A -K +K +K +A - K +A - K +Cl -A - K +A - ClA - Electric-ElectricNaPotential+ K + A -KPotential+Na +A - Na +A - K +A -K +Cl -K +A - A - K+Na +Na +K +Cl -A - A -K +Na +A -Cl -Cl -K +Cl -a b cFigure 2.2: Diffusion of K + ions down the concentration gradient though the membrane(a) creates an electric potential force pointing in the opposite direction (b) until thediffusion and electrical forces counter each other (c). The resulting transmembranepotential (2.1) is referred to as the Nernst equilibrium potential for K + .where [Ion] in and [Ion] out are concentrations of the ions inside and outside the cell,respectively, R is the universal gas constant (8, 315 mJ/(K ◦·Mol)), T is temperature indegrees Kelvin (K ◦ = 273.16+C ◦ ), F is Faraday’s constant (96, 480 Coulombs/Mol),z is the valence of the ion (z = 1 for Na + and K + , z = −1 for Cl − , and z = 2 forCa 2+ ). Substituting the numbers, taking log 10 instead of natural ln and using bodytemperature T = 310 ◦ K (37 ◦ C) results inE ion ≈ 62 log [Ion] out[Ion] in(mV)for monovalent (z = 1) ions. Nernst equilibrium potentials in a typical mammalianneuron are summarized in Fig. 2.1.2.1.2 Ionic currents and conductancesIn the rest of the book V denotes the membrane potential and E Na , E Ca , E K , and E Cldenote the Nernst equilibrium potentials. When the membrane potential equals theequilibrium potential, say E K , the net K + current, denoted as I K (µA/cm 2 ), is zero(this is the definition of the Nernst equilibrium potential for K + ). Otherwise, the netK + current is proportional to the difference of potentials, i.e.I K = g K (V − E K ) ,