PHYSIO - PH730 - Lecture 3
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)
