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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 E ion (at 37°C) E na = 61.54mV log [Na]o/[Na]I = 62 mV E K = 61.54mV log [K]o/[K]I = -80 mV E Ca = 30.77mV log [Ca]o/[Ca]I = 123 mV C Cl = -61.54mV log [Cl]o/[Cl]I = - 65 mV E ion = 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 P k /P na = 50 P Cl /P k = 0 The membrane is so impermeable to Chloride that you drop it from the equation

Goldman Equation E ion = 2.303 RT/zF log P k [K]o+P na [Na]o P k [K]I+P na [Na]I Vr= 61.54 mV log50o +1o 50i+1I = - 65mV Vr= RT/F ln P k [K]o+ P na [Na]o+ P Cl [Cl]i Pk[K]I+ P na [Na]I+ P Cl [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+1255yes NA+12120no Cl-5125yes H2O55,000 yes Anion-1080no

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 E ion ; E Na, E Cl, E K

Nernst Equation E ion = 2.303 RT/zF log [ion] o /[ion] in E ion = ionic equilibrium potential Z= charge of ion F= Faraday’s constant T= absolute temperature ( 0Kelvin/-273 ° C) R= gas constant

Action Potentials Can travel up to 100 meters/second Usually 10-20 m/s 0.1sec 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 P k /P na = 50 P Cl /P k = 0 The membrane is so impermeable to Chloride that you drop it from the equation

Goldman Equation E ion = 2.303 RT/zF log P k [K]o+P na [Na]o P k [K]I+P na [Na]I Vr= 61.54 mV log50o +1o 50i+1I = - 65mV Vr= RT/F ln P k [K]o+ P na [Na]o+ P Cl [Cl]i Pk[K]I+ P na [Na]I+ P Cl [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 E m aka V r to approach E na 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 E na 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 can depolarize or hyper-polarize Recording electrode: Records change in Potential of the membrane At 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 channel Opens, Na enters, Depolarizes membrane, More and more Na Channels open leading to More sodium influx & causes upward & depolarizing (more +) phase of the AP

What does a sodium Channel look like? It is one large protein With 4 domains that Each loop through the Plasma membrane 7 Times.

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 understand what happens to the form Of the action potential When you add a voltage Sensitive calcium channel And a calcium gated Potassium channel Test question : think about This 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=IRV=voltage, I=current, R=resistance g=1/Rg=conductance Vm=membrane voltage Vr=voltage of membrane at rest

Permeability and Conductance g na is low at V r because sodium channels are closed g k is higher than g na at V r 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

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