Resting Membrane Potential

• Membrane potential at which neuron membrane is at rest, ie does not fire action potential

• Written as Vr

Ionic Equilibrium Potential

• Membrane Potential (potential difference across the plasma membrane) at which the net flow of an ion type = zero

• The number of ions moving into the cell = the number of ions moving out of the cell for a particular species of ion

Nernst Equation Variables

• Assumes that membrane is permeable to that ion

• As temperature increases the diffusion increases

• As charge on the molecule increases, it decreases the potential differences needed to balance diffusion forces.

Simplified Eion (at 37°C)

• Ena = 61.54mV log [Na]o/[Na]I = 62 mV

• EK = 61.54mV log [K]o/[K]I = -80 mV

• ECa = 30.77mV log [Ca]o/[Ca]I = 123 mV

• CCl = -61.54mV log [Cl]o/[Cl]I = - 65 mV

•Eion = 2.303 RT/zF log [ion]o/[ion]in

Goldman Equation

• Vr= RT/F ln Pk[K]o+Pna[Na]o+PCl[Cl]i Pk[K]I+Pna[Na]I+PCl[Cl]o

Also known as the constant field equation because it assumes that electrical field of the membrane potential is equal across the span of the membrane

Membrane Permeability

• Membrane is 50 more permeable to K than to Na

• Pk/Pna = 50

• PCl/Pk = 0

• The membrane is so impermeable to Chloride that you drop it from the equation

Goldman Equation

• Eion = 2.303 RT/zF log Pk[K]o+Pna[Na]o Pk[K]I+Pna[Na]I

• Vr= 61.54 mV log 50[5]o +1[150]o 50[100]i+1[15]I

• = - 65mV

•Vr= RT/F ln Pk[K]o+ Pna[Na]o+ PCl[Cl]i

Pk[K]I+ Pna[Na]I+ PCl[Cl]o

Not to study

• Donnans equilibrium

• Osmolarity considerations

Action Potential

Changes in Ion Permeability allows inward Na flux and triggers an increased outward K flux through voltage gated ion channels

Causes transient change in Membrane Potential

The change in ion permeability is triggered by transient depolarization of the membrane

Conductance = g• How many charges (ions) enters or leaves

cell (inverse of resistance)

• due to:– number of channels/membrane area

• Highest density at axon hillock

– number of open channels – ion concentration on either side of

membrane – Measured in Siemens (S), in cells pS (pico; -12)

Historical Figures• Hodgkin and Huxley

won Nobel Prize for Voltage clamp in 1961

• used to identify the ion species that flowed during action potential

• Clamped Vm at 0mv to remove electric driving force than varied external ion concentration and observed ion efflux during a voltage step

• Sakman and Nehr won Nobel Prize for Patch Clamp in 1991

• measured ion flow through individual channels

• shows that each channel is either in open or closed configuration with no intermediate. The sum of many recordings gives you the shape of sodium conductance.

Information Coding

• Is NOT in shape of action potential

• Is in the action potential frequency of firing —how many are triggered

• In the action potentials pattern or timing of propagation

Conductance = g• How many charges (ions) enters or

leaves cell (inverse of resistance)• due to:

– number of channels/membrane area• Highest density at axon hillock

– number of open channels – ion concentration on either side of

membrane – Measured in Siemens (S), in cells pS (pico; -12)

Generation of Resting Membrane Potential (-70mV)

• Plasma membrane

• Selective permeability, permeable to K, not Na

• Unequal distribution of ions across membrane– Due to open potassium channels and closed

sodium and chloride channels

• Action of ion pumps 3Na/2K ATPase

Ion Inside Outside Cross PM

K+ 125 5 yes

NA+ 12 120 no

Cl- 5 125 yes

H2O 55,000 55,000 yes

Anion- 108 0 no

Ionic Equilibrium Potential

• The membrane potential that balances the ions concentration gradient so that there is no net current for that ion.

• No permeability factor.

Equilibrium Potential of An Ion

• The membrane potential at which the net driving force propelling the ion in = the net driving force propelling the ion out.

• Written Eion; ENa, ECl, EK

Nernst Equation

• Eion = 2.303 RT/zF log [ion]o/[ion]in

• Eion = ionic equilibrium potential

• Z= charge of ion

• F= Faraday’s constant

• T= absolute temperature (0Kelvin/-273°C)

• R= gas constant

Action PotentialsCan travel up to100 meters/second

Usually 10-20 m/s0.1sec delay between muscle and sensory neuron action potential

Action Potential: a transient and rapid sequence of changes in the membrane potential

Membrane Permeability

• Membrane is 50 more permeable to K than to Na

• Pk/Pna = 50

• PCl/Pk = 0

• The membrane is so impermeable to Chloride that you drop it from the equation

Goldman Equation

• Eion = 2.303 RT/zF log Pk[K]o+Pna[Na]o Pk[K]I+Pna[Na]I

• Vr= 61.54 mV log 50[5]o +1[150]o 50[100]i+1[15]I

• = - 65mV

•Vr= RT/F ln Pk[K]o+ Pna[Na]o+ PCl[Cl]i

Pk[K]I+ Pna[Na]I+ PCl[Cl]o

Ion Permeability• Changes during action potential

• The plasma membrane becomes permeable to sodium ions– Permeability increases from 0.02 to 20=1000

fold increase

• Causes Em aka Vr to approach Ena at positive voltages = +20mV

rising

overshoot

Falling

undershoot

6 Characteristics of an Action Potential

• #1 Triggered by depolarization

• a less negative membrane potential that occurs transiently

• Understand depolarization, repolarization and hyperpolarization

#2 Threshold

• Threshold depolarization needed to trigger the action potential

• 10-20 mV depolarization must occur to trigger action potential

#3 All or None

• Are all-or- none event

• Amplitude of AP is the same regardless of whether the depolarizing event was weak (+20mV) or strong (+40mV).

#4 No Change in Size

• Propagates without decrement along axon

The shape (amplitude & time) of the action potential does not change as it travels along the axon

#5 Reverses Polarity

• At peak of action potential the membrane potential reverses polarity

• Becomes positive inside as predicted by the Ena Called OVERSHOOT

• Return to membrane potential to a more negative potential than at rest

• Called UNDERSHOOT

#6 Refractory Period

• Absolute refractory period follows an action potential. Lasts 1 msec

• During this time another action potential CANNOT be fired even if there is a transient depolarization.

• Limits firing rate to 1000AP/sec

Stimulating electrode:Introduces current that candepolarize or hyper-polarize

Recording electrode:Records change in Potential of the membraneAt a distance away

Time (msec)

Voltage (mVolts) along Y axis

At Threshold Na influx equals K efflux

Voltage Sensitive Ion Channels

• Sodium

• Potassium

Ionic Equilibrium Potential

• Membrane Potential (potential difference across the plasma membrane) at which the net flow of an ion type = zero

• The number of ions moving into the cell = the number of ions moving out of the cell for a particular species of ion

Regenerative Process:

Once one Na channelOpens, Na enters,Depolarizes membrane, More and more NaChannels open leading toMore sodium influx & causes upward & depolarizing (more +) phase of the AP

What does a sodium Channel look like?

It is one large proteinWith 4 domains thatEach loop through the Plasma membrane 7Times.

Property of Voltage Dependent Sodium Channel

• Sodium channel opens for 1-2 millisecond following threshold depolarization

• then inactivates and does not open even if Vm is depolarized.

• This is called sodium channel inactivation and contributes to the repolarization of Vm

•M gate= activation gate on Na channel; opens quickly when membrane is depolarized

•H gate- inactivation gate on Na channel; Closes slowly after membrane is depolarized

•causes the absolute refractory period for AP propagation

Na Channel Gates

Potassium Channel Property

• K channels open with a delay and stay open for length of depolarization

• Repolarize the Vm to Ek= -75mV which is why you have hyperpolarization.

• Also called a delayed rectifier channel

•K channels have a single gate (n) that stays open as long as Vm is depolarized.

• n gate on K channels opens very slowly this allows the Vm to depolarize due to Na influx; Na and K currents do not offset each other right away

Gate on the Delayed Rectifier Potassium Channel

Refractory Period

• Refractory period due to Na channel inactivation and the high gk

• Subsequent Action potential cannot be generated

2 ways to increase AP propagation speed

• Increase internal diameter of axon which decreases the internal resistance to ion flow

• Increase the resistance of the plasma membrane to charge flow by insulating it with myelin.

See and understandwhat happens to the formOf the action potentialWhen you add a voltageSensitive calcium channelAnd a calcium gatedPotassium channel

Test question : think aboutThis and the next 2 slides

Channel Density

• Density is how many channels are in a unit area of plasma membrane, ie how closely they are packed together.

• Determines the length of the membrane that will be depolarized at a given time

Understand

• Regenerative nature of action potential• Orthodromic and antidromic • Voltage gates in sodium channel• Threshold potential sodium and potassium fluxes

are balanced• Initial segment of axon = axon hillock• Two mechanisms for increasing speed of action

potential propagation• Saltatory conduction

Understand

• Action potential occurs because sodium and potassium fluxes change the charge on the cell membrane not because the fluxes change ion concentrations.

Definition

V=IR V=voltage, I=current, R=resistance

 • g=1/R g=conductance

• Vm=membrane voltage

 • Vr=voltage of membrane at rest

Permeability and Conductance

• gna is low at Vr because sodium channels are closed

• gk is higher than gna at Vr because some potassium channels are open.

• V=I/R Ohms Law

• G=conductance=1/R

Definitions

• Current=net flow of ions per unit time

• 1 ampere of current represents movement of 1 coulomb of charge per second

• Resistance- frictional forces that resists movement of ions or charges

• Measured in ohm

• Current (A)= V/R

Definitions

• Conductance is the reciprocal of resistance and measures the ease with which current flows in an object.

• Measured in siemens (S)

• Capacitance refers to the ability of plasma membrane to store or separate charges of opposite signs.

• Myelin has high capacitance so stores charges and ions do not move across the membrane

• Measured in Farads