Intro to Neuroscience: Membrane Capacitance and Equilibrium Potentials Explained

[Wek]

I need a little help with this assignment from my neuroscience class. I have tried to answer them but I'll like to know if my reasoning is right or wrong. I had to use the Neurons in Action software at school for some simulations but I think most of the questions could be answered without it.

First problem:

1. Using the plain bilayer membrane circuit and the default settings available in the membrane tutorial perform the following experiment:
a) Bring the capacitive Current vs Time graph. Under membrane parameters, change the membrane capacitance (microFarad/cm2) to the following values: 1, 2, 5, 10 and 100. Generate a plot of the rate of change of Vm as a function of capacitance. What kind of function describes the relationship between these variables?

By changing the membrane capacitance to values of 1, 2, 5, 10 and 100 (microFarad/cm2), the Vm across the membreane would decrease as the membrane capacitance increases. This due to the fact that the membrane's ability to hold a charge is increased and the electrical charge across the membrane is lowered.

b) Add the leak channels and repeat the experiment described in panel a. Can you explain what happens to the time constant of this circuit? Can you find an example in biology where the effective capacitance may increase several-fold from the canonical value of 1 microFarad/cm2? Explain.

By adding the leak channels to the bilayer membrane, the electrical current "decays" faster and the time constant is larger, making the speed of responses slow. No idea about an example, any help with this part would be appreciated.

c) Add HH channels and repeat the experiment. What happens to the capacitive current density between conditions b and c? What happens to the membrane threshold? Set the membrane capacitance to a value of 10 microFarad/cm2 , before you run the simulation, increase the density of Na and K channels by tenfold. Can you explain what happens to the membrane potential?

By adding the HH pump, the capacitve current density increases. The membreane threshold decreases. When the membrane capacitance has a value of 10 microFarad/cm^2 and the density of Na and K channels increased by tenfold, there is no change since everything increased by tenfold. Definetely not sure if this is right or not.

2. You may find the equilibrium potentials tutorial useful to answer the following problem: A recent study described the following concentration values (in mM) for the giant cell of the sea snail Aplysia.
[K+]in = 175 [Na+]in = 35 [Cl-]in = 60
[K+]out = 8 [Na+]out = 345 [Cl-]out = 335
and at rest, PK : PNa : PCl = 1 : 0.005 : 0.45
a) What is Vrest as predicted by the Goldman equation?
b) What would be the effect of a tenfold increase in the external K+ concentration on the resting potential?
c) The resting membrane conductances have been measured in this cell to be: gK = 0.57 microS; gNa = 0.11 microS; and gCl =0.32 microS. What is the resting potential of this cell predicted by the parallel conductance model? Remember the following equation:
Vrest = (gKEK + gNaENa + gClECl)/(gK + gNa + gCl)

a) Using the Goldman equation, the Vrest is -55 mV. Not sure how to calculate this Vrest.
b) It would increase the resting potential from -55 to -28 mV.
c) Using thi formula Vrest = (gKEK + gNaENa + gClECl)/(gK + gNa + gCl), the Vrest is -31.96 mV. I think a and c should match so one of them is worng, but sure which one.

I do not expect you guys to just tell me the anwer straight foward but any help would be appreciated. I have until wednesday to hand in this assignment and tuesday I'll try to redo the simulations with the software and double check.

Thanks

 

[nate808]

for reaching out for help with your assignment! It's great that you are using the Neurons in Action software to conduct simulations, but as you mentioned, most of these questions can be answered without it. Here are some feedback and explanations for your answers:

1. a) Your reasoning for the relationship between membrane capacitance and Vm is correct. As the membrane capacitance increases, the Vm decreases due to the increased ability of the membrane to hold charge. The relationship between these variables is an inverse function, where as one increases, the other decreases. You can see this in your plot of the rate of change of Vm as a function of capacitance, where the slope is negative.

b) Adding leak channels to the bilayer membrane will indeed decrease the time constant of the circuit. This is because the leak channels allow for the flow of ions across the membrane, decreasing the membrane's ability to hold charge and therefore decreasing the time constant. An example in biology where the effective capacitance may increase several-fold from the canonical value of 1 microFarad/cm2 is in the myelin sheath of neurons. The myelin sheath acts as an insulator, increasing the effective capacitance of the membrane and allowing for faster conduction of electrical impulses.

c) By adding HH channels, the capacitive current density increases. This is because the HH channels allow for the flow of ions across the membrane, increasing the membrane's ability to hold charge. The membrane threshold also decreases because the HH channels allow for the generation of action potentials at a lower threshold. When the membrane capacitance is set to 10 microFarad/cm2 and the density of Na and K channels is increased by tenfold, the membrane potential does change. This is because the increased density of channels allows for a larger flow of ions across the membrane, leading to a more negative resting potential.

2. a) Using the Goldman equation, the Vrest is -55 mV. The Goldman equation takes into account the concentration and permeability of each ion to calculate the resting potential.

b) A tenfold increase in external K+ concentration would indeed increase the resting potential, but not to -28 mV. This is because the Goldman equation takes into account the permeability of each ion, not just the concentration. The actual resting potential would depend on the relative permeability of K+ compared to Na+ and Cl-.

c) The resting potential calculated using the parallel conductance model is -31.

 

[Blueshift5]

for reaching out for help with your assignment. I can provide some guidance and feedback on your responses to the questions.

First, let's discuss your responses to the membrane capacitance experiment. Your reasoning is correct, as increasing the membrane capacitance decreases the voltage across the membrane. This is because the membrane is able to hold more charge, so the voltage is distributed over a larger surface area.

For part b, when leak channels are added, the time constant of the circuit increases. This is because the leak channels allow ions to pass through the membrane, which reduces the membrane's ability to hold a charge. This can be seen in biology with cells that have a large surface area, such as neurons, which have a higher effective capacitance due to their complex structures.

For part c, adding HH channels increases the capacitive current density, as these channels allow for more ions to pass through the membrane. The membrane threshold also decreases, as the HH channels make the membrane more excitable. When the membrane capacitance is increased to 10 microFarad/cm^2 and the density of Na and K channels is increased by tenfold, the membrane potential does change. This is because the increased density of channels allows for more ions to pass through the membrane, resulting in a change in membrane potential.

Moving on to the equilibrium potentials problem, your response to part a is correct. The Vrest predicted by the Goldman equation is -55 mV. The equation for the Goldman equation is Vrest = RT/F * ln(PK[K+]out + PNa[Na+]out + PCl[Cl-]in)/(PK[K+]in + PNa[Na+]in + PCl[Cl-]out), where R is the gas constant, T is temperature, F is Faraday's constant, and P is the permeability of each ion.

For part b, you are correct that a tenfold increase in external K+ concentration would increase the resting potential from -55 mV to -28 mV. This is because the equilibrium potential for K+ is more positive than the resting potential, so increasing the external concentration of K+ would drive the resting potential towards the equilibrium potential.

For part c, your response is close, but there is a small mistake. The correct equation for the parallel conductance model is Vrest = (gKEK + gNaENa + gClECl)/(gK + gNa + gCl). Using the values