Membrane Potential

RC circuit parts

battery, resistor, capacitor

what circuit is used to model neurons?

a simple RC circuit

Rm

membrane resistance

both Rm and capacitor are associated with the

membrane properties of the neuron

Rex

extracellular resistance

Rc

cytoplasmic resistance

membrane resistance has two parts which are?

- resistance of the lipid bilayer

- resistance of the channels that are embedded in the lipid bilayer

lipid bilayer has a much ___ resistance than the resistance of a channel

higher

membrane resistance is a function of the

resistance of the channel

an ion is more likely to go through the ___ due to a?

channels; lower resistance

what charge is a cells resting membrane potential?

negative

resting membrane potential

the voltage difference between the inside and the outside of the cell when the cell is not active

voltage difference equation

Vin - Vout

if we impale a cell with a glass electrode we find that the inside of the cell is ____ compared to the outside of the cell

negative

for most cells, voltage difference is between

-20mV and -100mV

resting membrane potential of muscle cells

-90mV

resting membrane potential of small neurons

~ -65mV

common mechanism that neurons use to signal each other is?

synaptic transmission

synaptic transmission occurs between

a presynaptic neuron and a postsynaptic neuron

synaptic transmission occurs via? and involves?

transmitter release from the presynaptic neuron and involves changes in the membrane potential in the postsynaptic neuron

circuit component equivalent to cell component

battery = conc gradient

Resistor =

- Rm - lipids and channels

- Rc - cytoplasm

- Rex - extracellular fluid

Capacitor = membrane

concentration gradients provide the

source of electrochemical energy for the cell

resistance of the membrane

how difficult it is for charges to move through the membrane

resistance of the pure lipid bilayer is typically?

high, difficult for charges to move through, and normally constant

impact of open channels in the membrane

allows passage of ions, decreases the membrane resistance dramatically

typical capacitor

two parallel plates that sandwich a nonconducting material

the lipid membrane is relatively

non-conducting

resistance of the aqueous environment surrounding the membrane is typically?

low

capacitance depends on

surface area of the cell and the thickness of the membrane

the cell membrane acts both like a

capacitor and a resistor

the current in a circuit is carried by?

the current in a cell?

circuit = electrons

cell = ions: mostly K+,Na+,Ca2+, and Cl-

the cytoplasm and the extracellular space also have? important for?

resistance. This will be important in electrical signaling in nerves and in cardiac tissue

the resistance of a cell membrane is determined by two factors:

1. the resistance of the lipid bilayer.

2. the resistance of the channels in the lipid bilayer

the overall resistance of the cell membrane is primarily determined by

the number of open ion channels in the membrane

a battery is a source of

electrical potential energy

Potential energy of the following:

Bolt of lightning

Wall socket

Car Battery

Walkman battery

typical cell

Bolt of lightning 105

Wall socket 110

Car battery 12

Walkman battery 3

Typical cell 0.1

the material through which charges move has two basic properties:

resistance and capacitance

conductance is the reciprocal of the

resistance and can be used interchangeably with the resistance

resistance (of the resistor) depends on the

length of the resistor and the cross sectional area of the resistor

resistance is proportional to

Length,

Resistivity,

1/Cross-sectional area

resistance equation

R = pL/A

p - resitivity

l - length of resistor

a - cross sectional area of the resistor

units of resistance and conductance

r - ohms

c - siemens

capacitance represents the

ability of a material to separate charge and store charge

capacitance depends on the

surface area and the thickness of the capacitor

capacitance equation

C = eA/d

e - dielectric constant

A - surface area of capacitor

d - thickness of the capacitor

current

amount of charge moving per second

unit of current

coulombs/second = 6.24x10^18 charges/second

unit of capacitance

farad

ohms law

voltage across the resistor is proportional to the current flowing in the resistor. The proportionality constant is the resistor

ohms law equation

V=IR

R - proportionality constant

I - current

voltage across the capacitor is proportional to

the charge on the capacitor

capacitance/voltage equation

deltaV = (1/C)/Q

Q - charge

C - capacitor

current can be ___ into a circuit, causing?

injected, either positive or negative, changing the voltage across the circuit

voltage equation for current injection

v(t) = v0 + (vf - v0)(1-exp(-t/T)

V0

charges on capacitor due to V0, created from the battery and creates a voltage difference across the circuit

what happens to voltage when current is injected?

- as charges are injected into the circuit, they first accumulate on the capacitor.

- As more charge builds up on the capacitor the voltage across the capacitor increases(V = Q/C)

- after charges have been built up on the capacitor, continuous injection of charges into the circuit will cause them to move through the resistor (V=IR)

- After continuous injection of current, the voltage across the circuit will change exponentially as charges build up on the capacitor and then reach steady state as charges move through the resistor

what happens to voltage when current is injected? (simplified)

- most charge goes to capacitor bc of its lower resistance, building up on it, called "charging the capacitor"

- after capacitor has been charged (or as it's being charged), remaining charge goes through the resistor

- charge will keep flowing through the resistor as long as it continues being injected

what happens to V0 when current is injected?

it will rise exponentially, ending at Vfinal

what is the time constant of V0 to Vf with injected current?

t=RC

R - resistance

C - capacitance

how quickly the circuit responds to current injection is dependent on?

resistance and capacitance of the circuit

charge in biological systems is injected for a?

fixed amount of time

voltage before vs after injection is equal to

before - value determined by batter in circuit V0

after - rises to steady state value equal to V0 + Vf

Summary of the voltage equation:

if current (charge per time) is injected into a circuit the voltage across the circuit will change exponentially with time.

time constant for a cell is equal to the

membrane resistance x the membrane capacitance (RmCm)

nernst potential

The diffusion potential level across a membrane that exactly opposes the net diffusion of a particular ion through the membrane

nernst equation

E = (RT/ZF)ln([X] outside/[X]inside)

E - nernst potential

R - universal gas constant

T - temp

Z - charge on ion

F - faradays

X - conc based on which side

universal gas constant

8.315 joules/kelvin mole

faraday's constant

9.648 x 10^4 colomb/mole

Nernst potential is an ___ condition. At this...?

equilibrium; equilibrium the diffusion force is balanced by the electrical force

conditions for the nernst potential

1. the membrane must have some permeability to a charged particle.

2. there must be different concentrations of the charged particle on each side of the membrane.

3. the permeability of the other charged particles must be zero

Goldman-Hodgkin-Katz equation

used to calc the membrane potential for a cell for different ions, useful in predicting what the membrane potential will be under a variety of conditions

Goldman-Hodgkin-Katz equation says membrane potential depends on 3 things

1. the concentration of ions inside and outside of the cell

2. the permeability of the membrane for a particular ion

3. the temperature: for humans normally constant at around 37°C

when do you use the Goldman-Hodgkin-Katz equation

1. The cell membrane is only permeable to potassium.

2. The cell membrane is only permeable to sodium.

if the membrane is permeable only to potassium, the membrane potential will equal

the Nernst potential for potassium, thus -98mV

if the membrane is permeable only to sodium, the membrane potential will equal

the Nernst potential for sodium, thus +67mV

membrane potential is some combination of the Nernst potential for what? what is the range?

- for all of the different ions (including chloride and calcium) and depends on how permeable the membrane is to each of the ions

- membrane potential at any time can vary from the most negative Nernst potential (in this case potassium) to the most positive Nernst potential (in this case sodium)

Typical resting membrane potentials in cells are? why?

negative and close to the Nernst potential for potassium; most cells contain ungated or "leak" potassium channels that are always open

driving force

net electrochemical force that an ion feels, different for each ion in a cell

nernst potential for sodium

+67mV

nernst potential for potassium

-98mV

nernst potential for chlorine

-90mV

what is happening to a sodium ion and a potassium ion in a cell with a resting membrane potential of -70 mV?

will diffuse down its electrochemical gradient trying to reach its equilibrium which is the Nernst potential for that ion.

- sodium will be driven into the cell bc it is positive, which will depolarize the membrane

- potassium will be driven out of the cell, bc positive it will cause the cell to hyper polarize

at a resting membrane potential of -70 mV the driving force on sodium is?

-70 - 67 = -137 mV

at a resting membrane potential of -70 mV the driving force on potassium is

-70 - -98 = +28mV

driving force for potassium is ___ than for sodium because?

smaller; the resting membrane potential is closer to the Nernst potential for potassium

driving force equation

Driving Force x = Em - Ex

x - any ion

Ex - nernst potential of x

Em - membrane potential

For sodium Em-ENa is ___ since Em is

negative; always more negative than ENa

For potassium Em-EK is ___ since Em is?

positive; always more positive than EK

opposite sign for the driving force means that the ion is driven in the

opposite direction

(-) for sodium = inward, influx

(+) for potassium = outward, efflux

Na+ vs K+ current directions

inward vs outward

When the membrane potential is different than the Nernst potentials for any ion there will be a? this is prevented by?

- driving force on that ion, driving the ion into or out of the cell and eventually dissipating any ion gradients.

- prevented by the sodium potassium ATPase which pumps sodium out of the cell and potassium into the cell

At a membrane potential of -90 mV

• sodium flows into the cell (due to driving force) but is pumped out again

• potassium flows out of the cell (due to driving force) but is pumped back in

• the Nernst potential for chloride is often at the membrane potential and thus chloride is at electrochemical equilibrium.

when would the Na+-K+-ATPase be inhibited? (clinical examples)

- when the cell cannot make enough ATP, O2 is needed to make ATP so ATPase inhibition occurs when cells are deprived of oxygen.

- Clinically, seen in during a stroke (lack of oxygen to the brain) and during occlusion of the arteries as a result of atherosclerosis

If the Na+-K+-ATPase is inhibited:

1. Sodium will flow into the cell to try to make the cell membrane potential +67 mV

A. the concentration of sodium outside the cell will decrease

B. the concentration of sodium inside the cell will increase

2. Potassium will flow out of the cell to try to make the membrane potential -98 mV

A. the concentration of potassium outside the cell will increase

B. the concentration of potassium inside the cell will decrease

NA conc inside/outside and nernst

in - 12 mM

out - 145

nernst - +67mV

K conc inside/outside and nernst

in - 155

out - 4

-98mV

Cl conc inside/outside and nernst

in - 4

out - 123

-90 mV