Lab 2 - Membrane Resting Potential

Pre-Lab Information

In these exercises, you will model the generation of membrane potentials in living cells by creating an artificial “cell” with a semi-permeable membrane.  This model cell will allow you to control the concentration of several ions “inside” and “outside” the cell and measure the resulting membrane potentials.  The results of these experiments can then be used to determine the relative permeability of the membrane to different ions as well as the membrane capacitance.

Background

Many of the necessary background concepts for this lab were presented in the Bio 449 lecture on resting membrane potentials.  Below is a summary of that information.

A membrane potential (V_m) is generated whenever electrochemical gradients result in an unequal distribution of charges on either side of a membrane.  This will occur when the following conditions are met:

• Ion concentrations differ on either side of the membrane – If all ions are at the same concentration on both sides of the membrane, there is no gradient (chemical or electrical) to drive net diffusion, so no net movement of ions (=electrical charge) will occur.
• The membrane is not impermeable – If no ions can penetrate the membrane, then no diffusion will occur, and again no charge can develop.
• The membrane is not equally permeable to all ions – If all ions can flow equally well through the membrane, then there will be no difference in the diffusion of differently charged ions, and so no net charge can develop.

If a membrane is permeable to just one ion, the potential that develops can be calculated using the Nernst equation.  The simplified form is:

where

E_X is the membrane potential for ion X in millivolts

z is the valance of the ion

[C_e] is the concentration of X in the extracellular fluid

[C_i] is the concentration of X in the intracellular (cytosolic) fluid

If the membrane is permeable to more than one ion, we normally need to use the Goldman equation to calculate V_m. For cases where we have one cation and one anion in equal amounts, we can use a modified form of this equation:

where

V_m is the membrane potential in millivolts

P_C and P_A are the membrane permeabilities for the cation C and anion A

[C_e] is the concentration of the compound CA (the combined cation and anion) in the extracellular fluid

[Ci] is the concentration of X in the intracellular (cytosolic) fluid

An additional set of equations we did not cover in lecture allows you to calculate the number of ions that actually diffuse across the membrane to create the membrane potential.  These equations require knowledge of the membrane’s capacitance (C_m), which is its ability to store a charge.

The total charge stored by the membrane is

where

Q is the total charge stored in C/cm² (coulombs/cm²)

C_m is membrane capacitance F/cm² (farads/cm²)

V_m is membrane potential

To get the number of ions, we divide Q by the charge per ion and multiply by the surface area of the membrane, so

where

N is the total number of ions required to develop the membrane potential

A is surface area of the membrane in cm² (approximately 0.7)

e is the charge per ion in coulombs (= 1.6 × 10^-19)

Substituting values gives:

Exercises

We will model the generation of membrane potentials in a cell using an apparatus similar to the one shown below:

An artificial membrane is sandwiched between two chambers that hold solutions representing cytosol (left chamber) and extracellular fluid (right chamber).  Solutions of different concentrations and compositions can be placed on either side of the membrane and allowed to reach their electrochemical equilibrium, which happens quite rapidly.  We can then look at the net movement of ions across this membrane and the resulting membrane potentials.  We will do this for different concentrations of KH₂PO₄, which dissociates to form a potassium cation and a phosphate anion. The membrane potential (in mV) resulting from each combination of solutions is first amplified using the differential amp and then passed into the PowerLab.

Once we have gathered data on the voltages in our setup, we will compare these observed values of membrane potential to the expected potentials for single ion systems, using the Nernst equation.  Based on these comparisons, we will estimate the permeability of the membrane to different ions and calculate the number of ions that move across the membrane to generate the observed potential.

Initial Setup

PowerLab

• Connect the two electrode cables to the positive and negative inputs of channel 1 of the differential amplifier. Make sure both these channels are turned on, and that the DC/AC knob is set to DC. The output of the amp will now be the difference in potential (voltage) between the two electrodes. Set the gain to 100×. Finally, connect the output from the amplifier to the channel 1 input of the PowerLab.
• Open Chart, and set the display to a single channel.  Using the Channel Function drop-down menu (probably labeled “Channel 1”), select “Input Amplifier…”.  Make sure the “AC” box is not checked.  The membrane voltage you’ll be monitoring will not be changing very rapidly, so set the sampling speed fairly low – probably 4 or 10/s.  You will be measuring voltages in the range of about -100 to +100mV, but remember that these will be multiplied by 100, so set the voltage range accordingly.

Solutions

• You will need ion solutions of various concentrations handy.  For the first set of experiments, the salt we will use is KH₂PO₄.  Use the stock 10mM solution to create 5, 1, 0.5 and 0.1mM solutions.  Note that you will not be able to make all of these at once unless you share solutions with another lab group, but you will need the 0.1mM solution to begin with.

Membrane apparatus

• Locate the membrane chamber and the hose clamp that holds the two halves together.  Practice getting the two halves clamped together before getting your membrane sample.
• Apply a light layer of silicon grease (available from your TA) around the opening on each half of the membrane chamber.  This is to help keep the solutions from leaking out, but you do not want the grease spreading all over the membrane.
• Obtain a piece of membrane from your TA, place it over the hole in one of the chamber halves, then clamp both chamber halves together.  One chamber half will represent the cytosol in our model cell, the other the extracellular fluid
• Fill both sides of the chamber with about 5ml of 0.1mM KH₂PO₄.  (The membrane will dry out if left in air for more than a few minutes.)  Check for leaks.
• Obtain two lengths of tubing with agar-KCl mixture. Insert one end of one tube into one of the chamber halves, and one end of the other tube into the other chamber half. Using a piece of sandpaper, clean the silver wire on the end of each electrode, and then insert one electrode into the free end of each tube so that about half the silver wire is in the KCl agar. Note which side of your apparatus gets the minus electrode (the top connection on the differential amplifier) – this will be the “outside” of the model cell.

Experiments

Effects on increasing cytosolic K⁺ concentration on V_m

• In your initial setup, V_m should be zero, but probably does not register as such in Chart.  You can deal with this by either adding or subtracting a constant value to all your results (the value you get when both chambers have the same solutions), or by trying to adjust the DC offset until the input is zero.
• Change the concentration of KH₂PO₄ in the “cytosol” from 0.1mM through all the available concentrations up to 10mM, and obtain V_m for each.
  [The chamber can be emptied using a pipette.  For each new solution, add once and remove immediately to rinse the chamber, add the solution again, then wait for the voltage to come to (or near) equilibrium.  Then replace the solutions on both sides with the same solution again in case ion flow has changed the concentrations.]
• Follow the instructions on the worksheet as data become available.

Credits

This laboratory was adapted from one presented by William M. Moran, Jerod Denton, Kelly Wilson, Matt Williams, and Steven W. Runge as "A simple, inexpensive method for teaching how membrane potentials are generated" in Advances in Physiological Educucation, Dec 1999; 277: 51 - 59.