2 - Membrane Electrical Properties Flashcards
What is Ohm’s law (for voltage change across a resistor)?
V=ir
V=i/g
V= voltage
i = current (amperes)
g = conductance
r = resistance
A drop in pressure is analogous to drop in _______
Voltage
How does a capacitor (thin insulator) store charge?
The electric field of each neg charge accumulated at capacitor will attract a positive charge to accumulate on the other side of the capacitor
- larger insulated area stores more charge
- capacitor will only charge up to the voltage supplied by the battery
How might we increase the surface area of an insulator?
Connect more capacitors in parallel
What are two ways to increase the storage capacity of a thin insulator (capacitor)?
-increase the surface area of the insulator
-Decrease the thickness
The ability to store charge is defined as ________
The ability to store charge is defined as capacitance (c)
-How much charge (q) can be stored at a capacitor per voltage applied across the capacitor
How is the charge accumulation across a capacitor related to voltage?
Unless the insulating material of the capacitor is destroyed, the charge (q) accumulation across a capacitor increases proportionally with the applied voltage (v)
How to calculate capacitance?
c = q/v
or
cv=q
c = capacitance
q = charge
v = voltage
What is the unit of capacitance?
Farad (F)
What is the unit of charge (q)?
coulomb (C)
How is an ion channel in the plasma membrane analogous to an electrical circuit?
Closed channel?
Open channel with no voltage dependence?
Open channel with voltage (or ligand) dependence
- Lipid membrane
- thin insulator (Capacitor)
- with saline on both sides of conductor
- thin insulator (Capacitor)
2.Closed channel = open circuit (infinite resistance)
3.Open channel no voltage dependence = Resistor (no variability)
4.Open channel with voltage dependence = variable resistor (eg faucet whose flow can be changed)
What determines the specific capacitance of biological membranes?
The properties and thickness of the lipid bilayer
-hydrophobic tails of major membrane phospholipids (acting as the insulator) all have similar insulating properties and lengths
-When all else is equal, a thinner
layer of the same insulator can
store more charge (ie will have a
larger capacitance)
How do you convert coulomb (charge) to number of mol?
By using faraday’s constant
How to convert #mol to # of ions?
Use avogadro’s number (6x10^23 molecules/mol)
rm is the resistance of the cells membrane and is also known as the _______
How can it be calculated?
rm is the resestance of the cells membrane and is also know as the input resistance
How can it be calculated?
r = v/i
What are two examples of a cells with negligible cytoplasm resistance relative to the channels at the plasma membrane?
- Small cell that is essentially round and has no thin processes
- A long axon cannulated with an axial electrode (as in classical experiments of Hodgkin and Huxley)
Cells with negligible cytoplasmic resistance have the SAME membrane potential throughout the cell = isopotential
- doesn’t happen naturally
What is isopotential?
Cell whose membrane has the same potential throughout and thus have negligible cytoplasmic resistance
= doesn’t happen naturally
Cell surface membrane area is proportional to which feature of a circuit?
Cell capacitance
Cell surface area is proportional to which feature of a circuit?
Cell conductance
What is the relationship between cell resistance and cell surface area?
Cell resistance is proportional to 1/ (cell surface area) – “holes”
Resistance decreases as the number of ion channels increases
Stored charge =
Stored charge = q = cV
c - capacitance - is determined by the area and physical properties of the membrane
The rate of change in the voltage (dV/dt) across a capacitor is directly proportional to ______
The rate of change in the voltage (dV/dt) across a capacitor is directly proportional to a steady current applied
The concept of tau (time constant) when the rise and decay with time are both exponential:
In one time constant, the voltage charges up to _____ or discharges own to _____ of the steady-state maximum value
The concept of tau (time constant) when the rise and decay with time are both exponential:
In one time constant, the voltage charges up to 63% or discharges own to 37% of the steady-state maximum value
For a piece of membrane or an isopotential cell how can tau (time constant) be calculated?
tau = rm x cm
rm measured experimentally
cm=tau/rm = tau/rinput
If a cell increases its membrane surface area while the number of opened channels remains unchanged, how will tau be effected?
Tau should increase proportionally with cm
If a cell increases the number of opened channels while its membrane surface area remains unchanged, how will tau be effected?
tau should decrease proportionally with the decrease in rm
if a cell increases its surface membrane area while the density of opened channels remains unchanged, how will tau be effected?
tau is not expected to change
- because the increase in cm is accompanied by a proportional decrease in rm
Because the axon is usually orders of magnitude longer than its axonal diameter, the axopolasm of every short segment of axon is conencted to any adjacent segment via ________
Because the axon is usually orders of magnitude longer than its axonal diameter, the axopolasm of every short segment of axon is conencted to any adjacent segment via cytoplasmic resistance* (cannot be ignored)
*Also called internal or axial resistance
Why does an infinitely long axon have exactly exponential decay in voltage with distance
If the axon is infinitely long, the the combined resistance for all of the rm’s and ris connected to the rest of one side of the axon is a constant term regardless of the distance from the site of injection
After each segment the current is always split between rm and a constant term therefore in both directions a fixed fraction of the current flowing along the axoplasm of the axon will be lost after each segment
Fixed fractional loss of current at each segment dictates that the ________ membrane potential will decay _____ with distance (in either direction from the site of constant current injection)
Fixed fractional loss of current at each segment dictates that the *steady-state membrane *potential will decay exponentially with distance (in either direction from the site of constant current injection)
How is the length constant (λ) defined
In neurobiology, the length constant (λ) is a mathematical constant used to quantify the distance that a graded electric potential will travel along a neurite via passive electrical conduction. The greater the value of the length constant, the farther the potential will travel
For exponential voltage (V) decay with distance (x)
Vx=V0(e-x/λ)
At x = λ
Vλ=V0e-1 = V0/e = V0/2.7 = 37% of V0
At a longitudinal distance of one length constant away from the site of constant current injection, the steady-state voltage drops to ________ of V0
At a longitudinal distance of one length constant away from the site of constant current injection, the steady-state voltage drops to 37% of V0
How can you calculate the length constant (λ) for a long axon?
The value of λ (in cm) is the square root of (rm/ri)
rm = membrane resistance
ri = axial resistance
The shape of the voltage response (in time) during the injection of a square pulse of current varies with the ________ between the site of injection and the site of recording
The shape of the voltage response (in time) during the injection of a square pulse of current varies with the distance between the site of injection and the site of recording
Which two parameters varied with the distance from the site of injection in a long axon?
- Steady-state change in voltage (concept of length constant λ)
- The shape of the rise and fall in voltage
When is the Vm rise and fall exponential? Is this true for other distances?
within ~1 length constant
Not true either further away or closer than 1λ
How does the shape of the rise or fall in voltage with time change?
- at distances <1λ
- at 1λ
- at distanced > 1λ
How does the shape of the rise or fall in voltage with time change?
- at distances <1λ
-faster than an exponential function - at 1λ
-exponential - at distanced > 1λ
-slower than an exponential function
Consequences of the change in rise or fall of voltage with time?
A brief (~1ms) injection into 1 point of the axon is very inefficient at charging up distal sites of that axon
The inward Na+ current that depolarizes the axon during AP lasts ~1ms
