resting membrane potential excitable membranes resting membrane potential Basic Neuroscience NBL 120 (2007)

overview electrical signaling dendritic synaptic inputs transfer to the soma generate APs axonal propagation ionic basis of RMP passive membrane properties AP initiation & propagation

resting membrane potential electrochemical gradients equilibrium potentials - Nernst equation driving forces – Ohm’s Law GHK equation

what does the membrane do? separate and maintain (pumps) gradients of solutions with different concentrations of charged ions selectively allow certain ionic species to cross the membrane hence…..

measurement + - 0 mV DS Weiss

measurement + - 0 mV -70 mV DS Weiss

resting membrane potential what is it? electrical potential difference between the inside and outside of the cell why does it exist? differences in the concentrations of charged ions inside and outside the cell selective permeability of the membrane to certain ions active pumping of ions across the membrane

diffusion

Einstein Brownian motion (diffusion) random-walk ions appear to move down their concentration gradients very fast over short distances for small molecules / ions ≈ 1 m in 1 ms

how to create a RMP electrochemical Na-K exchanger (& others) pumps ions against their concentration gradients 2K ions in and 3Na ions out net negativity to the RMP requires energy (ATP) not generally required for maintaining the RMP in the absence of activity, but necessary for setting up initial conditions by creating concentration gradients

initial conditions: at equilibrium: different distribution of a K-salt membrane is only permeable to K there is no potential difference across the membrane at equilibrium: K ions diffuse down concentration gradient anions are left behind: net negativity develops inside the cell further movement of ions is opposed by the potential difference

r.m.p. review Try here?

can we calculate the potential? RT [x]outside Ex = ln zF [x]inside this equation determines the voltage at which the electrical and chemical forces are balanced; there is NO net movement of ions.

the Nernst potential for K if K is 10-fold higher on the inside in excitable cells the RMP is primarily determined by K ions.………………….but Ex = ln [x]outside [x]inside RT zF = log [K]o [K]i 60 z = -60 mV

there are other ions….. ion [X]in [X]out Eq. (mV) K 155 4 -98 Na 12 145 +67 Cl 4.2 123 -90

general rule ENa +67 membrane potential (mV) relationship between: membrane potential ion equilibrium potentials if the membrane becomes more permeable to one ion over other ions then the membrane potential will move towards the equilibrium potential for that ion (basis of AP). DRIVING FORCE artificial manipulation of MP - reverse direction of current flow (hence reversal potential) RMP ECl -90 EK -98

other ions affect RMP different ions have different distributions e.g. Na high outside / K high inside cell membrane is not uniformly permeable (“leaky”) to all ions relative permeability of an ion determines its contribution to the RMP Goldman-Hodgkin-Katz (GHK) equation a small permeability to Na and Cl offsets some of the potential set up by K in reality the cell membrane is a < negative than EK

calculating the true RMP driving force on an ion X will vary with MP = (Em - Ex) Ohm’s law V = IR = Ig, or transformed I = gV Ix = gx (Em - Ex) there will be no current if: no channels for ion X are open (no conductance) no driving force (MP is at Ex)

chord conductance equation IK=gK (Em-EK) INa=gNa (Em-ENa) ICl=gCl (Em-ECl) at steady state: IK + INa + ICl = 0 therefore: gK (Em-EK) + gNa (Em-ENa) + gCl (Em-ECl) = 0 gK gK+gNa+gCl gNa gK+gNa+gCl gCl gK+gNa+gCl Em = EK+ ENa + ECl

GHK equation relative permeabilities ionic concentrations PK[K]o + PNa[Na]o + PCl[Cl]i PK[K]i + PNa[Na]i + PCl[Cl]o RT F Em = ln