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Announcements:. Last lecture Organization of the nervous system Introduction to the neuron Today – electrical potential Generating membrane potential Nernst equation Goldman equation Maintaining ionic distributions. Neural Signaling. A Simple Circuit. Between neurons. Within
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Last lecture • Organization of the nervous system • Introduction to the neuron • Today – electrical potential • Generating membrane potential • Nernst equation • Goldman equation • Maintaining ionic distributions
Neural Signaling A Simple Circuit Between neurons Within neurons chemical & electrical electrical
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
Resting potential Measuring Membrane Potential amplifier microelectrode Reference electrode 0 mV cell -80 mV time Bathing solution
Electrophysiology techniques Silver / Silver chloride wire electrode Amplifier output Reference electrode 3M KCl solution Very tiny hole (<<0.1m) Glass micropipette
Resting Membrane Potential • How is it generated? • differential distribution of ions inside and outside the cell • Selective Permeability of the membrane to some ions
How does unequal concentration of ions give rise to membrane potential ?
Cl- Cl- Cl- Cl- Equal concentrations of ions 0 volts Artificial ion selective membrane (only K+, not Cl-) voltmeter K+ I II K+ 0.01 M KCL 0.01 M KCL K+ K+ No net movement
Cl- Cl- Cl- Cl- Cl- Cl- Unequal concentrations of ions volts - + Ion selective membrane (only K+, not Cl-) K+ I II K+ K+ K+ 0.1 M KCL 0.01 M KCL K+ K+ K+ K+ concentration gradient
K+ K+ K+ K+ K+ K+ K+ K+ K+ K+ K+ K+ K+ K+ Cl- Cl- Cl- Cl- Cl- Cl- Cl- Cl- Cl- Cl- Cl- Cl- Cl- Cl- Cl- Cl- Cl- Cl- Initial New Equilibrium + + + + + + CHEMICAL CHEMICAL ELECTRICAL
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 IIbecomes +, movement of K+ is repelled • Every K+ near the membrane has two opposing forces acting on it: • Chemical gradient • 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: • only a very small number of ions actually contribute to the electrical potential • 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 Ion Concentration I Temp (K) Gas Constant Equilibrium Potential of X ion (eg. K+) in Volts Ion Concentration II Valence of ion (-1, +1, +2) Faraday constant
Nernst Equation • At 18C, for a monovalent ion, and converting to log10 ,the equation simplifies to:
By convention electrical potential inside of cells is expressed relative to the outside of the cell
in out 0.1 M KCL 0.02 M KCL Example: K+ = -0.040 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
in out Na+ Na+ Na+ Na+ Na+ Na+ 0.1 M KCl 0.02 M NaCl 0.01 M KCl 0.2 M NaCl K+ K+ K+ K+ K+ K+ What if there is more than one permeable ion? Permeable to K+ and Na+, but not Cl-
To calculate the overall potential of multiple ions • use the Goldman Equation • Considers the permeability of ions and their concentrations
Goldman equation Voltage Ion concentration Permeability Because Cl is negative
Goldman equation • Example, typical mammalian cell: • Assume permeability for Na is 1/100 of permeability for K, and permeability of Cl is 0 • 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 • Unequal distributions of an ion across a selective membrane • causes an electrochemical potential called the equilibrium potential • Two opposing forces act on ions at the membrane • A chemical force down the concentration gradient • An opposing electrical force
Summary & Key Concepts • The equilibrium potential for an ion is described by the Nernst equation • Cell membranes are permeable to more than one ion • the membrane electrical potential is described by the Goldman equation
So What??? • Everythingthe 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 • -120 mV • 0 • +60 mV • -30 mV