Passive Membrane Properties Flashcards
What are the units and important equations for the following:
* Resistance (R)
* Conductance (g)
Resistance = ohms
Conductance = Siemans or Mhos
g= 1/R
What are the units and important equations for the following:
* Charge (Q)
* Current (I)
* Electrical Potential (V or E)
* Capacitance (C)
Charge (Q) = Coulombs (c)
Current (I) = Amperes (A)
Electrical potential (V or E) = Volts (V)
Capacitance (C) = Farads (F)
- V = IR
- R = V/I
- g = I/V
- C= Q/E
The ionic equivalent of conductance is…
The ionic equivalent of voltage is…
The ionic equivalent of capacitance is…
1) …ion channels
2) …driving force
3) …hydrophobic plasma membrane
Current
Net flow of charge. By conventionn, direction of current flow = direction of flow of positive charges. Note that following anions results in charge moving in the opposite direction.
Conditions for getting current flow across membrane?
- Something has to carry the charge (has to have ions).
- Have to have a pasageway (typically, open ion channels)
- Must have a driving force (concentration gradient, voltage)
Passive membrane properties
Passive elctrical properties are membrane properties that allow neurons to conduct electrical impulses without using voltage-gated ion channels
1) Membrane resistance (rm)
2) Membrane capacitance (cm)
3) Intracellular (axonal) resistance (ra)
What is affected by passive properties?
- The magnitude of change in membrane potential after current entry.
- The time course of change in membrane potentials after current entry (Tau)
- The distance over which the change in voltage travels.
- Speed of action potential propagation.
Membrane Resistance (rm)
- Membrane resistance determines how much the membrane potential will change in response to current (V=IR)
- Membrane resistance is reflective of the # of leak channels present in membrane at any given time.
0 leak channels = high resistance
lots of leak channels = low resistance - RM: specific resistance (resistance per unit area) that changes depending on how leaky the membrane is; so if more leak channels then lower membrane resistance (little r)
Active rm vs Passive rm
Passive conductance:
* Channels open at rest
* not voltage-gated channels (are leak channels)
* Set the resting potential in the GHK equation (Pk:PNa:PCl = 1:0.04:0.45)
Active conductance:
* Channels closed at rest
* Voltage-ated channels (Na and K channels that make up AP)
* Channels that are open during AP.
Describe:
Specific Resistance (rM)
Membrane Resistance (rm)
Input Resistance (r in)
Specific Resistance (rM): the resistance of a unit area (how leaky the membrane is).
Unit: ohm cm2
Membrane Resistance (rm): Resistance of an entire cell (with channels).
Unit: ohms
Input resistance (r in): Talking about an active resistance, not a passive membrane resistance. rm measured for an entire cell plus the access resistance of your recording pipette.
Plumber’s version of a membrane: R
Membrane Capacitance (Cm)
- Capacitance, in this case, is the property of the cell’s lipid bilayer being able to store charge and how that affects the “charging of the rest of the cell” you would record.
- When you inject current, you reach steady state, but gradual change in voltage as you inject current because of membrane has inherent capacitance.
- Capacitor: pair of conductors, seperated by an insulating layer, on which equal but opposite electrical charges have been placed. As these charges accumulate, it gets harder and harder to deliver more of the same type of charge to that side of the capacitor.
- Charges accumulate on both inside and outside of lipid membrane when you are injecting current, not 100% of that current goes into affecting the membrane potential, some of it has to get stored on the capacitor (aka the membrane).
- Different memrane has different capacitance
Smaller capacitance = holds less charge.
Circuit model of a membrane
Rin + Cin
* A passive cell membrane can be modeled as a resistor (ion channels) and capacior (lipid membrane) in parallel.
* If you have a resistor and capacitor in parallel, then current injected into a cell will first try to charge up capacitor, as resistor offers more resistance. As capacitor charges up, less current goes there until it becomes fully charged and then will go to resistor instead. These two currents, Ir and Ic, must always equal to the total charge you inject into the cell.
* Since Im= Ir + Ic as the capacitor gets charged, the amount of current flowing through the resistor gradually increases Vm as the voltage reaches a steady state.
How does size influence rm and Cm?
Purkinje Neuron vs Tecale neuron
Large Small
rm/rinput < rm/rinput
cm/cinput > cm/cinput
- Capacitance depends on membrane. More membrane = more capacitance.
- Larger cells have lower resistance (inversely proportianal to surface area, more surface area = more channels) but higher capacitance (proportional to surface area).
Current clamp experiment
recording the voltage, injecting current and seing what happens to the voltage.
Membrane time Constant (Tau)
- Membrane time constant is the amount of time between begining of depolarization and the time for the depolarization to reach 63% of its maximum.
- Membrane time constant (tau) determines the rate of change in Vm and is equal to CinRin.
- One Tau = the time the membrane takes to rise to 63% or decay to 37% of Vmax (maximum depolarization).
- If you have a membrane that is really good at holding charge (high capacitance) then Tau will get stretched out and would look more slopy/ gradual.
- Reflective of the amount of time it takes for capacitor/membrane to charge before resistor/channels during current injection. Afterwards current removed, residual charge dissipates from capacitor and allows for some residual current to pass through resistors.
- The bigger the time constant = the more summation. If the membrane holds charge for a longer period of time then there will be depolarization present at that spot for a longer time which allows the cell to summate stuff more easily. Membrane time constant slows it down and allows the cell to summate stuff more easily.
Internal (axial) resistance: ra
- Axial resistance is dictated by how big the inside of the axon is.
- Determines how far and how fast an impulse will travel. This is dependent upon the specific resistance of the cytoplasm and the diameter of the central core.
- Note that extracellular resistance also exists but it is negligeable.
- Think of it as a highway: let’s say you have the same number of cars travelling down a highway that has 7 lanes as a highway with one lane. The one lane highway cars are going to habe bottleneck effect, trouble travelling. Same # of cars on the 7 lane highway will have a much easier time.
- Narrow axon creates an internal resistance for charges travelling down the axon. If you have big axon = lower resistance (less blockage for ions to flow through)
Membrane length constant (lambda)
The length constant is how far does the signal travel before decaying.
* Lambda = sqr root (rm/ra)
* The membrane voltage change drops to 37% of max for each length constant away from site of current injection.
* What is important is how far we are from the original current injection when the depolarization drops to 37% of its max.
* Attenuation is a direct function of lambda/length constant. Voltage at position 0 is the max voltgate (Vo) (where current introduced).
* With lambda, can calculate voltage at any given length x away from the site of injection.
Important: lambda is proportional to sqrt(radius)
Relationship between area, circumference and length constant
Thick axons have thick length constants.
* Larger area/ cross-section = more ions can pass through
* larger circumference = more channels
Greater lambda means ions can travel more quiclky down longer lenghts of membrane.
As area increases, lambda gets bigger because the axial resistance (ra) decreases more than the membrane resistance (rm). The axial resistance decreases more because if you change the SA of the cross-section, the radius has more impact. If you make radius bigger then it is increasing the SA more than the membrane.
Saltatory conduction, reviseted. Focus on myelin’s effect on lambda
When you wrap the membrane in myelin:
* Membrane capacitance becomes extremely great. So great that even if there were channels in the myelinated areas, it would not be possible for ions to flow since there is so much capacitance to charge. Making it significantly harder for resistors to charge.
1/Ct = 1/C1+1/C2 + 1/C3 …
**Lambda = sqrt (rm/ra) -> rm increases with myelination, ra stays constant (internal diameter of axon stays the same) = larger lambda. **
- Bigger lambda means the depolarization can travel way bigger distances before it decays 37% of its maximum (very good summation).
Tau = Cmrm Cm decreases, rm increases = tau stays the same (myelin = resistors and capacitors in series = Tau remains constant).
- Travel larger distances, have the AP decayl less over that distance BUT it takes the same amount od time. Increasing speed -> allows for rapid propagation of AP from one node of ranvier on to the next.
Temporal and Spatial Summation
Temporal summation is just a phenomenon that happens when you have 2 stimuli at the same point but two differents times (ex: seperated by 30ms). Two stimuli that happen at same dendritic spine seperated by certain amount of time.
* Cell with short time constant will be unable to summate becausse initial response would have already faded, but with longer time constant, that means the depolarization will still be happening in that segment of the cell when the 2nd depolarization hits and will make it more likely for thosse two signals to summate.
Spatial summation is two different points at the same time. If these two stimulations at two different points are travelling along axons that have really long lenght constants then it maximizes the chances of them coinciding and sumating.
Longer Tau or Lambda constants = better summation
Summation allows for better learning
Less summation allows for high fidelity information transfer.
