Announcements:

Last lecture 1.Organization of the nervous system 2.Introduction to the neuron Today – electrical potential 1.Generating membrane potential 2.Nernst equation 3.Goldman equation 4.Maintaining ionic distributions

Neural Signaling Within neurons Between neurons electrical chemical & electrical A Simple Circuit

Bioelectric Potentials Neurons have an electrical potential (voltage) across the cell membrane The inside of the cell is more negative than the outside –called the Resting Membrane Potential

Measuring Membrane Potential cell microelectrode amplifier 0 mV -80 mV time Resting potential Reference electrode Bathing solution

Electrophysiology techniques Amplifier output Glass micropipette Silver / Silver chloride wire electrode 3M KCl solution Very tiny hole (<<0.1  m) Reference electrode

Resting Membrane Potential How is it generated? 1.differential distribution of ions inside and outside the cell 2.Selective Permeability of the membrane to some ions

How does unequal concentration of ions give rise to membrane potential ?

Equal concentrations of ions 0.01 M KCL 0.01 M KCL Artificial ion selective membrane (only K+, not Cl - ) I II voltmeter No net movement 0 volts Cl - K+K+ K+K+ K+K+ K+K+

Unequal concentrations of ions 0.1 M KCL 0.01 M KCL Ion selective membrane (only K+, not Cl - ) I K+ concentration gradient Cl - K+K+ K+K+ K+K+ K+K+ +- volts K+K+ K+K+ Cl - K+K+ II

CHEMICAL K+K+ K+K+ K+K+ K+K+ K+K+ K+K+ Initial ELECTRICAL K+K+ K+K+ K+K+ K+K New Equilibrium CHEMICAL K+K+ K+K+ Cl - K+K+ K+K+

Unequal concentrations of ions Initial diffusion of K+ down concentration gradient from I to II This causes + charge to accumulate in II because + and - charges are separated –Remember that Cl - can’t cross the membrane ! Therefore II becomes positive relative to I

Equilibrium Potential As II becomes +, movement of K+ is repelled Every K + near the membrane has two opposing forces acting on it: 1.Chemical gradient 2.Electrical gradient These two forces exactly balance each other Called the electrochemical equilibrium

The electrical potential that develops is called the equilibrium potential for the ion. Electrical potential at which there is no net movement of the ion Note: 1.only a very small number of ions actually contribute to the electrical potential 2.the overall concentrations of K and Cl in solution do not change.

To calculate the equilibrium potential of any ion (eg. K, Na, Ca,) at any concentration – we use the Nernst Equation:

Nernst Equation Equilibrium Potential of X ion (eg. K+) in Volts Valence of ion (-1, +1, +2) Faraday constant Gas Constant Temp (  K) Ion Concentration I Ion Concentration II

Nernst Equation At 18  C, for a monovalent ion, and converting to log 10,the equation simplifies to:

By convention electrical potential inside of cells is expressed relative to the outside of the cell

Example: K M KCL 0.02 M KCL out in = Volts = - 40 mV

Therefore, –initial movement of K+ down concentration gradient –When electrical potential of -40 mV develops, there will be no net movement of K+ –Thus K+ is in electrochemical equilibrium

What if there is more than one permeable ion? 0.1 M KCl 0.02 M NaCl 0.01 M KCl 0.2 M NaCl out in Na + K+K+ Permeable to K + and Na +, but not Cl - K+K+ K+K+ K+K+ K+K+ K+K+

To calculate the overall potential of multiple ions use the Goldman Equation Considers the permeability of ions and their concentrations

Goldman equation Permeability Ion concentration Because Cl is negative Voltage

Goldman equation Example, typical mammalian cell: 1.Assume permeability for Na is 1/100 of permeability for K, and permeability of Cl is 0 2.Assume [K] in = 140, [K] out =5 [Na] in =10, [Na] out =120

Goldman equation The resting membrane potential of most cells is predicted by the Goldman equation

Summary & Key Concepts 1.Unequal distributions of an ion across a selective membrane causes an electrochemical potential called the equilibrium potential 2.Two opposing forces act on ions at the membrane 1.A chemical force down the concentration gradient 2.An opposing electrical force

Summary & Key Concepts 3.The equilibrium potential for an ion is described by the Nernst equation 4.Cell membranes are permeable to more than one ion 5.the membrane electrical potential is described by the Goldman equation

So What??? Everything the nervous system and muscles do depends on the resting membrane potential

Sample question If two concentrations of KCl solution across a membrane give an equilibrium potential for K + of -60 mV, what will the equilibrium potential be if the concentrations on each side are reversed A.-120 mV B.0 C.+60 mV D.-30 mV