Bio 3411 Problem Set #7 Name:__________________________ TA Name:____________________ This Problem Set will be DUE: Nov. 15th at the beginning of class 1.(1 point) List3 differences between active and passive propagation, Why do passively
propagated signals only travel a short distance in neurons (please mention the length
constant, internal resistance, and membrane resistance in your answer) ?
active propagation: slow, doesn't decrement, energy distributed along length;
passive propagation:fast, decrements, energy enters at a single point
Passive propagated signal travel a short distance in neurons because voltage is lost to resistance
as the signal is propagated. The length constant, which is the distance it takes for the voltage to
drop down to 1/e of its original value, is defined as (Rm/Ri)1/2, where Rm is membrane resistance
and Ri is internal resistance. The Ri/Rm ratio is large in neurons, so the length constant is small
relative to that of an extension cord.
2.(0.5 point)
i)__ Potassium channels are open at rest while Sodium___ channels are mostlyclosed at
rest.
ii)_concentration gradient__and __electrical gradient_are the two forces that are equal
and opposite at the equilibrium potential of an ion.
3. (0.5 point) Why does the resting membrane potential of some neurons deviate slightly
from the equilibrium potential of K+, while the resting potential of glial cells is almost
always EK?
This occurs because of the presence of sodium (or chloride) channels in some neurons that
contribute to resting conductance. However, these are not open in glial cells, so the resting
potential is principally due to potassium conductance, and thus very close to EK.
4. (4 points)The ion concentrations of a typical neuron in the squid axon are something
like:
K+
Na+
ClCa++
Inside (mM)
200
40
25
0.001
Outside (mM)
2
400
250
1
a. (0.5 point) What’s the definition of equilibrium potential for an ion? What’s the
definition of resting potential for a cell?
For a specific ion, the electrical potential that exactly counterbalances diffusion due to the
concentration gradient is called the equilibrium potential
Resting Membrane Potential is the voltage (charge) difference across the cell membrane
when the cell is at rest. It is the product of the distribution of charged ions
b. (1 point) Calculate the equilibrium potential for each ion in the squid axon.
E_K+= 58log(2/200)= -116 mv
E_Na+=58log(400/40)= +58 mv
E_Cl- = 58log(25/250) = -58 mv
E_Ca++=29log(1/0.001)= +87 mv
Using a microelectrode, you measure this cell’s resting membrane potential at –90 mV.
c.(0.5 point) Is this cell permeable to only K+? If not, what else might it be permeable to?
The resting membrane potential is not equal to EK, so it is not only permeable to K+ at rest, it
might also be permeable to Na+ or Ca++
d.(0.5 point)At this resting potential, is there a net flow of K+ and if so, which direction?
yes. outside cell
f. (1.5 points) If this same cell were to become permeable principally to Ca++, which
direction would the net flow of Ca++ ions be? What would the new resting membrane
potential be if the cell were to maintain a permeability only to Ca++? What would the new
intra- and extracellular concentrations of Ca++ be when this new equilibrium potential is
reached?
inside cell. E(Ca) = 29log(1/0.001) = +87mV. It's same/unchanged.
5.(1 point) The equilibrium potential for K+ and Cl- are both within the range of the
observed resting potential. How can you distinguish which one is responsible for the
generation of resting potential (hint: Salkoff handout)?
Change the extracellular concentration of K or Cl. Then measure the resting potential. If
an ion contributes to the RP, the RP will change when its extracellular concentration is
changed. If one of the ions has no conductance at rest, then changing its extracellular
concentration will have no effect on the RP. REMEMBER THAT ONLY AN ION
WITH CONDUCTANCE CONTRIBUTES TO THE MEMBRANE POTENTIAL.
6. (3 points) For the sake of clarity, for calculation questions, please circle your final
answer.
Ion
K+
Na+
Cl-
Inside neuron
250
40
16
Outside neuron
25
400
160
Use the Nerst Equation and GHK Equation to solve the following problems.
At rest, a neuron is primarily permeable to K+, however there is some Na+ permeability
as well.
a. (0.5 point) What effect does additional Na+ permeability at rest have on the membrane
potential (as opposed to K+ permeability only)?
Na+ permeability at rest can make the membrane potential less negative than Ek only.
b.(1 point) If the relative permeability of K+ to Na+ at rest is 100 to 1, what is the actual
resting potential of this neuron? (At no chloride permeability)
c. (0.5 point) How does this compare to the resting potential for a neuron permeable to
K+ alone?
Less hyperpolarized.
Ek= 58log[[K+]out/[K+]in] = 58log[2.5/250] = -116mV
d.(1 points) Now let's add GABA to this neuron, which will open Cl- ion channels.
i. If the Cl- relative permeability to Na+ is 10 to 1, what is the new resting potential?
(taking into account K+ and Na+ permeability at in part 1b.)
V = 58log[(Pk[K]out + PNa[Na]out + Pcl[Cl]in) / (Pk[K]in + PNa[Na] +in Pcl[Cl])out]
= 58log[(100*2.5 + 1*400 + 10*16) / (100*250 + 1*40 + 10*160)
= -87.99 mV
ii. At this resting potential, which direction will each permeable ion be flowing?
K flows out of the cell (Ek = -116mv)
Na flows into the cell (ENa = 58mV)
Cl flows out of the cell (ECl = -58mv)