2 - membrane electrical properties

Question 1

What is Ohm’s law (for voltage change across a resistor)?

Answer 1

V=ir

V=i/g

V= voltage

i = current (amperes)

g = conductance

r = resistance

Question 2

A drop in pressure is analogous to drop in _______

Answer 2

voltage

Question 3

How does a capacitor (thin insulator) store charge?

Answer 3

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

Question 4

how might we increase the surface area of an insulator?

Answer 4

Connect more capacitors in parallel

Question 5

What are two ways to increase the storage capacity of a thin insulator (capacitor)?

Answer 5

• increase the surface area of the insulator
• Decrease the thickness

Question 6

The ability to store charge is defined as ________

Answer 6

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

Question 7

How is the charge accumulation across a capacitor related to voltage?

Answer 7

Unless the insulating material of the capacitor is destroyed, the charge (q) accumulation across a capacitor increases proportionally with the applied voltage (v)

Question 8

How to calculate capacitance?

Answer 8

c = q/v

or

cv=q

c = capacitance

q = charge

v = voltage

Question 9

What is the unit of capacitance?

Answer 9

Farad (F)

Question 10

What is the unit of charge (q)?

Answer 10

coulomb (C)

Question 11

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

Answer 11

• Lipid membrane
  
  • thin insulator (Capacitor)
    
    • with saline on both sides of conductor
• Closed channel = open circuit (infinite resistance)
• Open channel no voltage dependence = Resistor (no variability)
• Open channel with voltage dependence = variable resistor (eg faucet whose flow can be changed)

Question 12

What determines the specific capacitance of biological membranes?

Answer 12

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)

Question 13

How do you convert coulomb (charge) to number of mol?

Answer 13

By using faraday’s constant

Question 14

How to convert #mol to # of ions?

Answer 14

Use avogadro’s number (6x10^23 molecules/mol)

Question 15

r_m is the resistance of the cells membrane and is also known as the _______

How can it be calculated?

Answer 15

r_m is the resestance of the cells membrane and is also know as the input resistance

How can it be calculated?

r = v/i

Question 16

What are two examples of a cells with negligible cytoplasm resistance relative to the channels at the plasma membrane?

Answer 16

• 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

Question 17

What is isopotential?

Answer 17

Cell whose membrane has the same potential throughout and thus have negligible cytoplasmic resistance

= doesn’t happen naturally

Question 18

Cell surface membrane area is proportional to which feature of a circuit?

Answer 18

Cell capacitance

Question 19

Cell surface area is proportional to which feature of a circuit?

Answer 19

Cell conductance

Question 20

What is the relationship between cell resistance and cell surface area?

Answer 20

Cell resistance is proportional to 1/ (cell surface area) – “holes”

Resistance decreases as the number of ion channels increases

Question 21

Stored charge =

Answer 21

Stored charge = q = cV

c - capacitanc - is determined by the area and physical properties of the membrane

Question 22

The rate of change in the voltage (dV/dt) across a capacitor is directly proportional to ______

Answer 22

The rate of change in the voltage (dV/dt) across a capacitor is directly proportional to a steady current applied

Question 23

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

Answer 23

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

Question 24

For a piece of membrane or an isopotential cell how can tau (time constant) be calculated?

Answer 24

tau = r_m x c_m

r_m measured experimentally

c_m=tau/rm = tau/r_input

Question 25

If a cell increases its membrane surface area while the number of opened channels remains unchanged, how will tau be effected?

Answer 25

Tau should increase proportionally with c_m

Question 26

If a cell increases the number of opened channels while its membrane surface area remains unchanged, how will tau be effected?

Answer 26

tau should decrease proportionally with the decrease in r_m

Question 27

if a cell increases its surface membrane area while the density of opened channels remains unchanged, how will tau be effected?

Answer 27

tau is not expected to change

• because the increase in c_m is accompanied by a proportional decrease in r_m

Question 28

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 ________

Answer 28

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

Question 29

Why does an infinitely long axon have exactly exponential decay in voltage with distance

Answer 29

If the axon is infinitely long, the the combined resistance for all of the r_m’s and r_is 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 r_m 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

Question 30

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)

Answer 30

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)

Question 31

How is the length constant (λ) defined

Answer 31

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)

V_x=V₀(e^-x/λ)

At x = λ

V_λ=V₀e^-1 = V₀/e = V₀/2.7 = 37% of V₀

Question 32

At a longitudinal distance of one length constant away from the site of constant current injection, the steady-state voltage drops to ______ of V₀

Answer 32

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

Question 33

How can you calculate the length constant (λ) for a long axon?

Answer 33

The value of λ (in cm) is the square root of (r_m/r_i)

r_m = membrane resistance

r_i = axial resistance

Question 34

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

Answer 34

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

Question 35

Which two parameters varied with the distance from the site of injection in a long axon?

Answer 35

1. Steady-state change in voltage (concept of length constant λ)
2. The shape of the rise and fall in voltage

Question 36

When is the Vm rise and fall exponential? Is this true for other distances?

Answer 36

within ~1 length constant

Not true either further away or closer than 1λ

Question 36

When is the Vm rise and fall exponential? Is this true for other distances?

Answer 36

within ~1 length constant

Not true either further away or closer than 1λ

Question 37

How does the shape of the rise or fall in voltage with time change?

• at distances <1λ
• at 1λ
• at distanced > 1λ

Answer 37

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

Question 38

Consequences of the change in rise or fall of voltage with time?

Answer 38

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