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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
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
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
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