PHYSIO - PH730 - Lecture 3

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Resting membrane potential

-70mV (steady voltage difference across the cell membrane)

E(k) at 37 C is?

-96 mV

Cable properties of neurons

-membrane resistance/conductance -membrane capacitance -intracellular resistance of cytoplasm

Cell membrane can be represented by what?

A circuit containing a resistor and a capacitor in parallel -When current is passed across it, the behavior of this circuit is similar to the passive electrical behavior of a cell (the electrical response of cells when the changes in voltage are not of sufficient magnitude or direction to open ion channels, and thus the ion conductances are constant) Resistance (inverse of cell conductance) represents the contribution of all the ion channels that allow the movement of charges Capacitor represents the dielectric properties of the lipid bilayer that separates the two conducting electrolyte solutions (for cells, 1 uF/cm2)

Microelectrode

A piece of glass tubing drawn out to a tip about 1 micron in diameter and filled with a salt solution that measures the membrane potential

How do we increase the concentration of K+?

Add a neutral salt to the external solution (increase the concentration of the accompanying anion without a change in the net electrical charge). By increasing the external concentration, the K+ concentration gradient is reduced, the efflux of K+ is less and the membrane potential is less negative (membrane depolarizes)

all-or-nothing

principle that either a neuron is sufficiently stimulated and an action potential occurs or a neuron isn't sufficiently stimulated and an action potential doesn't occur

Impact of each ion in determining the membrane potential is_____ to the membrane permeability for that ion

proportional (ie a membrane with a high permeability for K+ and a lower Na+ permeability will have a membrane potential that is closer to the equilibrium potential for K+)

Equation for charge q?

q = capacitance * voltage capacitance of cell membrane usually 1uF/cm2

How is membrane conductance determined?

By the intrinsic conductances of the ion channels permeable to that ion, their density of distribution in the membrane and their fractional open time (the fraction of time the channels remain in the open state)

electrogenic

Capable of generating an electrical current; usually applied to membrane transporters that create electrical currents while translocating ions.

The higher the internal or external resistances (Ri or Ro) the ______ the distance over which the current spreads

shorter

Graded local potentials increase or decrease in amplitude with distance as they spread on the membrane from the point of origin?

Decrease in amplitude

Decrement of local potential as a function of the distance along a nerve cell process equation

DeltaVx = DeltaV0 * e^-(x/lambda) -DeltaVx = local potential at a distance x -Delta V0 = amplitude of local potential at point of stimulation -lambda = length or space constant given by this equation Lambda = sqrt [(Rm/(Ri + Ro)]

Ion concentration and equilibrium potential for Cl-

ECF = 110 ICF = 10 Eion = -64

Ion concentration and equilibrium potential for Na+

ECF = 140 ICF = 12 Eion = +66

Ion concentration and equilibrium potential for Ca2+

ECF = 2 ICF = 10^-4 Eion = +130

Ion concentration and equilibrium potential for K_

ECF = 4 ICF = 150 Eion = -96

If we allow K+ channels to open, K+ will move out of a cell (because of concentration gradient). Because no other ion can move across the membrane, the outward movement of positive charges creates a difference in electrical potential, with the cell interior negative respect to the extracellular fluid. What is this difference called?

Electrical potential difference (in this case, being negative inside generates an electrical force which opposites the migration of K+ out of the cell) The electrical potential difference reaches a value that balances the driving force due to the K+ concentration gradient. Net movement will be zero and K+ will be at equilibrium

The shorter the time constant the ______ the membrane can be depolarized to reach threshold and the ____ will the conduction be

sooner; faster

Na+/K+ ATPase has what direct contribution to the membrane potential?

For every ATP hydrolyzed this enzyme typically moves 3 Na+ ions out and 2 K+ ions in, so every cycle has a net transfer of one positive charge out of the cell (pump is electrogenic), so this makes the membrane potential more negative than predicted from concentration gradients and membrane conductances alone

Length/space constant

How far the current will spread along the inside of an ion (and in so doing influences the voltage along that distance)

Equation of current carried by a given ion based on driving force and ion conductance?

I(ion) = g(ion)*(Vm-E(ion)) g(ion) = ion conductance (conductance = inverse of resistance, g = 1/R)

Current carried by an ion is related to its net flux (J ion) in what equation?

I(ion) = z(ion)*F*J(ion) F = Faraday's constant (96,500 coulombs/equivalent) J(ion) - net flux of ion (moles/cm2s)

Equation for surface charge?

surface charge = capacitance* (eq/F) (?) 1 pEq/cm2

Total membrane conductance is the sum of what?

Individual ion conductances

Total membrane current is the sum of what?

Individual ionic currents

ouabain

Inhibits sodium pump (Na+/K+) by binding the K+ site. (blocker of the Na+/K+ ATPase/removes external K+)

Why do action potentials propagate more rapidly in larger diameter axons?

Larger diameters allow for smaller resistance to current, so current travels farther

Cl- concentration gradient moves where?

Move Cl= from the ECF to the cytosol

K+ concentration gradient moves where?

Move K+ from the cytosol to the ECF

Na+ concentration gradient moves where?

Move Na+ from the ECF to the cytosol

Excitable cells

Nerve and muscle cells can rapidly and transiently alter their membrane permeabilities. This brings about fluctuations in membrane potential. The rapid fluctuations are responsible for producing electrical impulses in nerve and muscle cells.

What is the relation between potentials originating at synapses on certain size dendrites and the distance the potentials travel?

Potentials originating at synapses on thin dendrites (small lambda) will dissipate over shorter distances than those from synapses at thicker dendrites (larger lambda) and will have less effect on the neuronal activity

Cell membrane resting potential is due to what?

Primarily the passive diffusional efflux of K+ ions, with less contribution from the other ions because of their lower permeability, and a small component due to the electrogenic Na+ pump

Total membrane current can be represented as what in a circuit?

Set of parallel branches, each with its own 'battery' E(ion)

Charge separation

the imbalance of charges between two locations (also known as 'static electricity')

Receptor or generator potentials

Small depolarization similar to the depolarization produced by injection of current; originated by specialized structures in response to specific stimuli (e.g. pressure, heat, etc.) Permeability of Na+ of a local area of the membrane increases, shifting the membrane potential closer to E(Na)

threshold

the level of stimulation required to trigger a neural impulse (critical voltage to depolarize a cell membrane)

If the membrane were permeable to several ions, then the zero current condition at rest will be:

Sum of the currents is 0 Vm = Sum of [ion conductance* ion equilibrium]/membrane condutance

Goldman-Hodgkin-Katz equation

the membrane potential that results from the contribution of all ions that can cross the membrane Vm = RT/F * ln[P(ion)[ion] out/P(ion)[ion]in]

Electrical potential difference

The change in potential energy per unit charge in an electric field

Axon hillock

The conical region of a neuron's axon where it joins the cell body; typically the region where nerve signals is generated (due to the large density of voltage-gated channels that it contains)

Net flux of an ion across a membrane is determined by what?

The ion net driving force and its membrane permeability

Electrical events recorded from cells represent what?

The movement, or flux, of ions through the membranes

Depolarization

The process during the action potential when sodium is rushing into the cell causing the interior to become more positive. Loss of a state of polarity; loss or reduction of negative membrane potential Can be jump started by injecting positive charges into the cell

What is another effect of the spread of current in axons and dendrites?

The rise of the electrotonic potential becomes longer and more sigmoidal as the distance from the injection point increases, and results in an increase in the apparent time constant tau. This is a consequence of the uneven distribution of current at the axonal membrane, with more current leaking out in proximal than in distal areas

What does the space constant depend on?

The thickness of the axon or dendrite

Equilibrium potential of an ion

Value of the electrical potential required to balance the driving force due to the concentration gradient of the ion

Based on driving force and ion conductance, what is the equation for voltage?

Vm = E(ion) + [I(ion)/g(ion)]

Voltage decreasing with time during discharge of the capacitor

Vt = Vmax*e^-(t/Rm*Cm) -Vt = membrane voltage at time t -Vmax = steady-state voltage attaind during passage of the current -Rm = membrane resistance -Cm = membrane capacitance

Voltage increasing with time during charging of a capacitor (similar to passing a current pulse across a cell membrane)

Vt = Vmax[1-e^-(t/Rm*Cm)]

When is steady state reached?

When the net current flow across the cell membrane is zero (so when I(ion1) + I(ion2) = 0) or g(ion1)*(Vm-E(ion1)) + g(ion1)*(Vm-E(ion2)) = - In this case, Vm = [g(ion1)*E(ion1) + g(ion2)*E(ion2)]/[g(ion1+g(ion2)]

If there are two ions moving across the membrane, when is steady state achieved?

When the net electrical current across the membrane becomes zero (so when the ions move at the same rate). The final electrical potential difference will be a function of the difference in the ions' permeabilities (if permeabilities were the same, electrical potential difference would be zero)

Action potential

a neural impulse; a brief electrical charge that travels down an axon (spike)

Local potential

an electrical potential that is initiated by stimulation at a specific site, which is a graded response that spreads passively across the cell membrane, decreasing in strength with time and distance (graded electrical signal that depends on the electrical properties of the cell membrane)

The larger the lambda the _____ the current will go

farther

The higher the membrane resistance r*m, the _____ the current spreads

further

The longitudinal (internal resistance) Ri is __________ to the cross sectional area of the axon

inversely proportional

If there is no restricted volume for the axon, R0 can be compared to Ri, and the expression for lambda can be approximated as...?

lambda = sqrt (Rm/Ri)

Current preferentially flowers through ____ resistance pathways

low

Electromotive force

the rate at which energy is drawn from a source that produces a flow of electricity in a circuit (equilibrium potential, generated by the ion concentration gradient)

Time constant

time taken for a quantity that decreases exponentially to decrease to 0.37% of its initial value (in this case, time it takes for voltage to drop to 37% of initial value during discharge, or to reach 63% of its final value during charge of the capacitor) Tau = Rm*Cm

Synapses

tiny gaps between dendrites and axons of different neurons (about 20 nm between neurons) neurotransmitters (chemical transmitter substance) can diffuse across this short extracellular space to the receiving neuron (binds to the receptors on the membrane of the target cell, causing a small depolarization similar to the depolarization produced by the injection of current)

Charge deficit in terms of ion concentrations

unit = mEq/L *apply macroscopic (or bulk) electroneutrality condition to solutions of electrolytes because of enormous strength of the electrical force)


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