Neuromembrane

Neuromembrane#

About Neuromembrane

Neuromembrane was made by a team of University of Alberta researchers and a company known as Atmist. Many thanks to Christelle Sabatier, Michael Wright, and Declan Ali for sharing similar lesson plans. Their ideas are integrated here.

Part I: Resting membrane potential#

First, we’ll explore the properties of the membrane that lead to a resting membrane potential. By the end of this part, you will be able to:

  • Explain how a negative resting membrane potential is maintained

  • Identify the factors that determine and maintain resting membrane potential

  • Use the Goldman-Hodgkin-Katz to calculate the membrane potential given the concentrations and permeabilities of K+ and Na+

  • Generate simulation data to illustrate the dependence of the resting membrane potential on K+

Protocol#

  1. Go to https://neuromembrane.biology.ualberta.ca/ and click “Continue to App.”

  2. To open the resting membrane potential simulation, click on the top left to open a menu of stimulations. Choose “Resting Potential Simulation.”

    On the right hand side, you’ll see a membrane. The area below the membrane is the inside of the cell. The area above the membrane is the outside of the cell.

  3. This simulation will open by default without any leak channels or pumps. Let’s first add a couple of leak channels to the membrane and observe what happens. Click the plus sign next to “LEAK CHANNELS” to add a Na+ and K+ channel to the membrane.

Reflection

These single channels represent many, many channels in the membrane that are allowing either Na+ or K+ to cross. By default, these will open with a relative permeability of 0.05:1 (Na:K). Note that at these default settings, there is also equal [Na+] and [K+] inside and outside of the membrane.

  1. First, we’ll observe what happens over time when we have more K+ permeability, but equal ion concentrations. Before running the simulation, write a 1-2 sentence prediction for what will happen in Table 1.

  2. Once you have your prediction, click on the play button to run the simulation. You can also change the speed so that it will run faster. What happens to the voltage over time? Why is the voltage across the membrane this value? Write your observations in Table 1.

  3. In order to modify the concentration across the membrane, we’ll need a Na+/K+ pump. Click the plus button next to Na+/K+ pump to add one to the membrane.

  4. Notice that the CONCENTRATION SETTINGS have now changed as well. Change these concentrations back to the previous settings — where all of the concentrations are 50 mM. Before running Simulation #2, write your 1-2 sentence prediction in Table 1.

  5. Run Simulation #2 and observe what happens to the membrane potential. Has adding a Na+/K+ pump changed anything about the resting membrane potential? Why or why not? Add your observations to the table. For this simulation, note that we’re just using the Na/K pump to be able to change the concentration across the membrane. The Na/K is not operational (yet).

  6. Go back to the settings page. In real neurons, ion concentrations are not equivalent. Change the concentrations of K+ and Na+ back to their default values (Na: 10 mM inside, 140 mM outside; K+: 140 mM inside, 4 mM outside) to reflect more biological values across the membrane. Write your prediction for Simulation #3 in the table.

  7. Run the simulation again and observe what happens to the membrane potential.

Log your predictions

What happens to the voltage over time? Why is the voltage across the membrane this value? Write your observations in a table formatted to one like Table 1, below. Here is a Google Spreadsheet Template.

Table 1. Simulation predictions & observations

Sim #

Types of Channels

[Ion]

PNa/K

Prediction

Observation

1

Leak channels only

All 50 mM

5 Na+; 100 K+

2

Leak channels & Na+/K+ pump

All 50 mM

5 Na+; 100 K+

3

Leak channels & Na+/K+ pump

Na+ high outside; K+ high inside

5 Na+; 100 K+

4

Leak channels & Na+/K+ pump

Na+ high outside; K+ high inside

100 Na+; 5 K+

5

Leak channels & Na+/K+ pump

Na+ high outside; K+ high inside

100 Na+; 100 K+

  1. Using the Goldman-Hodgkin-Katz (GHK) equation for Na+ and K+ only, calculate what the voltage across the membrane should be for simulation #3 and show your work. Does this match the voltage in the simulation? Answer Q1 on the quiz. Report your answer in mV.

Here are a few hints to help you:

  • P is relative permeability; other constants can be found on the lecture slides.

  • To simplify, you may determine a constant for the first portion of the equation (RT/F) and use that for future calculations.

  • You can use “Insert > Equation” in Google Docs or Microsoft Word to show your work, or simply jot it on paper, take a picture, and paste it here.

  • Google search has a built-in scientific calculator! You can bring it up by typing any formula into the search bar. For example, type =5*150 into Google Search.

Q1. Calculation of GHK

Using the GHK equation for Na⁺ and K⁺ only, calculate the voltage across the membrane for simulation #3 and show your work. Does this match the voltage in the simulation? Report your answer in mV.

  1. Finally, let’s check to see how much ion permeability matters. Go back to the settings page and reverse the Na+ and K+ permeabilities.

  2. Write your prediction for Simulation #4 in Table 1.

  3. Run Simulation #4 and observe what happens. Record your observations in Table 1 and respond to the question below. Answer Q2 on the quiz. Report your answer in mV.

Q2.

With the high permeability to Na⁺ and low permeability to K⁺, what is the resting membrane potential? Report your value in mV out to one decimal point.

  1. On the settings page, set both the Na+ and K+ permeabilities to 100. Write your prediction in Table 1.

  2. Run the simulation to see what happens, record your observations, and respond to the question below. Answer Q3 on the quiz.

Q3.

Which of these simulations best models a typical neural membrane?

  1. Next, we’ll check to see whether or not the membrane potential depends on [K+]out. Reset the permeabilities and ion concentrations to the default values.

  2. Systematically change [K+]out to fill in the table below. Hint: if you hover over the chart on the left, you’ll be able to see the precise voltage.

Q4

Complete Table 2 and then answer Q4 on the quiz. You can use the Table 2 tab on the Google Spreadsheet template.

Table 2. Dependence of Vrest on [K+]out

[K+]out (mM)

Vrest (mV)

4

10

20

50

200

  1. Click the “Toggle Circuit Diagram” button on the top right hand corner to overlay circuit components.

Q5.

In a few words, describe what each of the following are modeling in the neuron. The first one has been done for you. Once you’re done, answer Q5 on the quiz.

Component

What it models

I_Na

sodium current across the membrane

g_Na

E_Na

I_K

g_K

E_K

Part II: Passive membrane simulation#

In this part, you’ll set up a simulation that models one portion of an axon or dendrite. By the end of this part, you will be able to:

  • Describe how voltage passively spreads through an axon or dendrite

  • Understand length and time constants

  • Determine how the passive spread of voltage is affected by diameter and membrane capacitance

Protocol#

  1. Go to https://neuromembrane.biology.ualberta.ca/ (if you’re not already there) and open up the “Passive Membrane Simulation” (or Cable Theory Simulation) in the menu in the top left corner.

  2. Add an external recording electrode that is two length constants (λ) away from your stimulating electrode by clicking the + button and changing the value after the second recording site. Answer Q6 on the quiz.

  3. Inspect the parameters on the left hand side of the screen. To see how these electrical components are being modeled, click on 3D on the bottom to toggle to a 2D diagram, and then choose “Show Circuit Diagram.” Answer Q7 on the quiz.

  4. Re-set the cable settings and click on “CREATE SIMULATION” to run our first iteration of this passive current injection. Observe the top plot to fill out row one in Table 3. For your “observations,” take a close look at the Voltage vs. Time plot.

Reflection

Why is our current injection this shape when recorded across the membrane?

Table 3. Current injection results

Sim #

Diameter

Cm

Peak voltage at 2λ

Distance to 2λ electrode

Voltage at 0λ electrode @ 28 ms

Voltage at 2λ electrode @ 28 ms

Observations

1

5 µm

1

2

2 µm

1

3

2 µm

2

  1. The dorsal root ganglion axon of a giant blue whale has a diameter of ~2 µm. In the CABLE SETTINGS on the left, change the diameter of the simulated axon to model this axon.

Reflection

With this smaller diameter of 2 µm, do other parameters of the membrane (bottom of the CABLE SETTINGS window) change? If so, why?

  1. Run the simulation with the smaller diameter and observe the Voltage vs Time plot again. Hint: you can use the Autoscale button (![][image2]) if the trace goes off the plot. Fill out Table 3 for this 2 µm cable simulation.

  2. Double the specific capacitance of the membrane, from 1 to 2 μF/cm2. Describe what happens to the time constant and the resulting voltage over time plot with more capacitance in Table 3.

Optional: Later in the course, you may want to use the Neuromembrane simulator to model the action potential. There is a protocol here.

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