Adv Physiol Educ 37: 392–400, 2013; doi:10.1152/advan.00068.2013.

Sourcebook of Laboratory Activities in Physiology

Ion permeability of artificial membranes evaluated by diffusion potential and electrical resistance measurements Vadim Shlyonsky Department of Physiopathology, Université Libre de Bruxelles, Bruxelles, Belgium Submitted 21 June 2013; accepted in final form 19 August 2013

Shlyonsky V. Ion permeability of artificial membranes evaluated by diffusion potential and electrical resistance measurements. Adv Physiol Educ 37: 392– 400, 2013; doi:10.1152/advan.00068.2013.—In the present article, a novel model of artificial membranes that provides efficient assistance in teaching the origins of diffusion potentials is proposed. These membranes are made of polycarbonate filters fixed to 12-mm plastic rings and then saturated with a mixture of creosol and n-decane. The electrical resistance and potential difference across these membranes can be easily measured using a low-cost volt-ohm meter and home-made Ag/AgCl electrodes. The advantage of the model is the lack of ionic selectivity of the membrane, which can be modified by the introduction of different ionophores to the organic liquid mixture. A membrane treated with the mixture containing valinomycin generates voltages from ⫺53 to ⫺25 mV in the presence of a 10-fold KCl gradient (in to out) and from ⫺79 to ⫺53 mV in the presence of a bi-ionic KCl/NaCl gradient (in to out). This latter bi-ionic gradient potential reverses to a value from ⫹9 to ⫹20 mV when monensin is present in the organic liquid mixture. Thus, the model can be build stepwise, i.e., all factors leading to the development of diffusion potentials can be introduced sequentially, helping students to understand the quantitative relationships of ionic gradients and differential membrane permeability in the generation of cell electrical signals. liquid junction potential; Nernst potential; Goldman-Hodgkin-Katz equation; ion selectivity; ionophore

of electrical signals recorded from different organs during several medical tests, such as electrocardiography, electroencephalography, electromyography, or electroretinography, is not immediately easy to understand for students. They learn that the electrical activity of a living tissue implies the existence of a potential difference between two points in space and that, in every living being, such a potential difference has a cellular origin. Yet, it is often tough for students to realize that this potential difference across the plasma membrane results from a charge separation due to simultaneous fulfillment of two fundamental conditions: the existence of ionic gradients across the membrane and a differential discrimination of ionic species by the membrane. Additional difficulty consists in distinguishing equilibrium Nernst potentials from steady-state potentials predicted by the Goldman-HodgkinKatz (GHK) equation. The available didactic resources assisting students in the study of cellular electrical phenomena include a number of computer simulations using either simple GHK equation spreadsheets or some more sophisticated computer models (1, 3). Although computer simulations have a lot of advantages, they present with important limitations: they lack actual human interaction and

THE ORIGIN

Address for reprint requests and other correspondence: V. Shlyonsky, Route de Lennik 808, CP604, Bruxelles 1070, Belgium (e-mail: vshlyons@ulb. ac.be). 392

hands-on experience. Demonstrations of analog models of membrane potentials based either on principles of hydrostatic and air pressures (21) or based on principles of color mixing (16) overcome these limitations and represent good alternatives to computer models. An ideal teaching setup would be that of an experiment that generates directly values of membrane electrical activity, such as, for example, laboratory practices using muscle preparations (15, 22, 23). However, this kind of experiment involves some non-negligible ethical considerations. Efficient replacement of live tissue has been suggested in the form of artificial membranes made of either polysulphonic ion exchange resin (1) or ion-selective filter membranes (4, 14) or even dialysis membranes (18). All of these membranes have intrinsic ion selectivity. Here, I propose a novel model of artificial membranes that provides efficient assistance in teaching the origins of diffusion potentials. These membranes are made of polycarbonate filters saturated with a mixture of organic liquids. The electrical resistance and potential difference across these membranes can be easily measured using a household volt-ohm meter and home-made Ag/AgCl electrodes. The advantage of the model is the lack of clear ionic selectivity of the membrane, which can be further modified by the introduction of different ionophores to the mixture. In other words, all factors leading to the development of diffusion potentials can be introduced sequentially to the model, thus helping students to understand the quantitative relationships of ionic gradients and differential membrane permeability in the generation of cell electrical signals. In the present article, I describe laboratory experiments that were integrated in 2007 in the general physiology curriculum of the second year of undergraduate medical, biomedical, and dentistry studies at the Faculty of Medicine of the Université Libre de Bruxelles as well as in the elements of general physiology curriculum of the third year of undergraduate studies in civil engineering (with biomedical option) at the Faculty of the Applied Sciences of the Université Libre de Bruxelles. This laboratory activity takes ⬃3 h. After completing this activity, the student will be able to: 1. Explain that membrane potential results from charge separation due to the diffusion of charged particles in the presence of a concentration gradient across that membrane. 2. Explain the physiological meaning of Nernst potential and the reason why experimental diffusion potentials are always different from this potential. 3. Manipulate the GHK equation to extract values of ion permeability ratios. 4. Predict the values of membrane potential for any given ionic condition and membrane permeability property. Before doing this activity, students should have a basic understanding of biological membrane structure and properties and be familiar with the Nernst equilibrium and Goldman

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Sourcebook of Laboratory Activities in Physiology MEMBRANE ION PERMEABILITY AND DIFFUSION POTENTIALS

steady-state phenomena. For some inquiry applications, student should have a notion about charge accumulation by electrical capacitors. Students should be also familiar with the use of a volt-ohm meter, but no other prerequisite skills are required. METHODS

Equipment and Supplies In the search for model membranes that could be easily used in the student laboratory, I turned my attention to polycarbonate filter membranes saturated with organic solvents, which were first described in the early 1960s (7). The biophysical properties of these membranes in the presence of various solvents have been studied in details (8 –11, 19, 20). A potential difference across these membranes developed within minutes after exposure to aqueous solutions, and stirring was not required to get stable values (7). Unfortunately, most solvents described in these studies confer to the membrane either clear ion selectivity or extremely high electrical resistances (9); some of them are very toxic or flammable to be used in the classroom. I screened different organic liquids with dielectric constants in the range of 3–11 and opted for a mixture of 15% (vol/vol) creosol (2-methoxy-4-methylphenol) in n-decane. Ionophores can be directly dissolved in this mixture. As reported by Ilani (7), virtually all types of polycarbonate membranes yielded the same results. List of Materials The following materials are needed: 1. Millipore HATF cellulose acetate/nitrate membranes with 0.45-␮m pore diameter (catalog no. HATF29325, Millipore). Other types of polycarbonate membranes give similar results. 2. Plastic rings of 12 mm in diameter. These can be purchased as inserts (catalog no. 3401, Corning Transwell) or cut into pieces of 15 mm in depth from a plastic tube of 12 mm in diameter (such as a 25-ml serological pipette, catalog no. 86.1685.001, Sarstedt). 3. Technical grade chloroform and ethanol. 4. Solutions of 1 M KCl, 0.1 M KCl, and 1 M NaCl. 5. Six-well tissue culture plastic plates (catalog no. 92406, TPP). These are equivalent to any other cups of minimum 3 cm in diameter; however, a multiwell format is preferred. 6. Silver wire of 0.5 mm (catalog no. 327026, Sigma-Aldrich), insulated copper wire, and banana plugs. 7. Bleach liquid (Clorox, eau de Javel, or equivalent). 8. Agarose (catalog no. A9539, Sigma-Aldrich) and 1-ml plastic syringes. 9. A low-cost volt-ohm meter capable of measuring resistances up to 40 M⍀ and voltages down to 0.1 mV (DMM-8020, Tecpel). 10. A Metex4650A/MetexM-3890D multimeter or equivalent with RS232 or USB connectivity. 11. A low-cost PC (PIII running on Windows XP) and data-logging software. 12. A solvent mixture (prepared daily) of 150 ␮l creosol (catalog no. W267104, Sigma-Aldrich) and 850 ␮l n-decane (catalog no. D901, Sigma-Aldrich). 13. Ionophores [0.1 mg valinomycin (catalog no. 60403, SigmaAldrich) dissolved in 300 ␮l of the solvent mixture and 0.1 mg monensin (catalog no. M5273, Sigma-Aldrich) dissolved in 300 ␮l of the solvent mixture]. 14. Plastic tweezers and paper towels. 15. A 1-ml automatic pipette (or graduated Pasteur pipette) and 0.2-ml automatic pipette. Assembly Instructions The Millipore HATF cellulose acetate/nitrate membranes were affixed to the plastic rings using chloroform to make cup-like struc-

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tures, referred to as inserts. In detail, the bottom surface of the plastic ring is brought into contact with chloroform for 10 –15 s to slightly melt the plastic and then immediately pressed against the polycarbonate membrane. The parts are glued instantly. After several minutes of drying, the filter is cut out using scissors. An application of 20 ␮l of the solvent mixture is sufficient to completely saturate the membrane. When the membrane becomes uniformly dark after solvent application, to prevent further evaporation the insert is filled with 0.5 ml of 1 M KCl solution and placed in a six-well tissue culture plastic plate prefilled with 3 ml of 1 M KCl solution. Two other wells are filled with 3 ml of 0.1 M KCl and 1 M NaCl, respectively. Electrical measurements were done using Ag/AgCl electrodes connected to the chamber via 3%/1 M KCl agar bridges made from 1-ml plastic syringes. Briefly, agarose is melted in 1 M KCl on a hotplate. While the agarose is still hot, plastic syringes are fully filled with agarose by pulling out the piston and then immediately placed into ice-cold 1 M KCl for storage. A copper wire is soldered at one end to a banana plug and at another end to a 5-cm-long Ag wire. Four centimeters of silver wire are folded into a helix (on a match, for example), cleaned in alcohol, and then covered with AgCl by putting the electrodes into liquid bleach for 1 h. To minimize potential offsets, electrodes should be chloridized in pairs, with the banana plugs interconnected. The electrodes are then inserted into agar in the syringes. Figure 1 shows a photo of the experimental setup. The measuring electrode was connected to the inside of the insert, whereas the reference electrode was placed in the well of the plate (see Figs. 1 and 2). According to this connection setup, the well of the plastic plate is the virtual ground. The potential difference and electrical resistance were monitored using a low-cost volt-ohm meter. In the case when continuous

Fig. 1. Experimental setup. 1, 6-well plastic plate; 2, Transwell inserts with a polycarbonate membrane; 3, 3% agar/1 M KCl bridges; 4, syringe caps to prevent the agar bridge from drying during storage; 5, Ag/AgCl electrodes; 6, paper towel; 7, plastic tweezers; 8, electrode support stand; 9, volt-ohm meter.

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Fig. 2. Schematics of the experimental setups showing different liquid interfaces and the corresponding liquid junction potentials (ELJ).

recordings of membrane electrical resistance and membrane voltage were needed, we used a multimeter connected to a low-cost PC using a RS232 cable. Data acquisition was accomplished using Metex data-logging software. A paper towel was provided to wipe the liquid from beneath the insert and from the electrodes during the transfer of the insert from one experimental condition to another, i.e., between wells filled with different solutions. All reagents used in this laboratory exercise were purchased from Sigma-Aldrich. HATF 293-mm membrane disk filters were obtained from Millipore, and this pack quantity is sufficient for the preparation of hundreds of diffusion chambers, as described above. In our hands, a one-time investment of no more than 1,000 euros was sufficient to create 10 working posts and to run these laboratories for at least 5 yr (20 student groups/semester). The filter inserts are reusable; in this case, they should be soaked after use in a 1:1 mixture of ethanol and water. In the case of filter reutilization, it is necessary to keep filters that were in contact with ionophores separate from others, because even traces of valinomycin or monensin significantly modify the selectivity of filters that receive the solvent mixture without ionophores. In the eventuality of a broken filter membrane, inserts can be replaced without delay. A detailed description of the protocol is described below in APPENDIX: MEMBRANE PERMEABILITY.

the electrical resistance of the two Ag/AgCl electrodes. These values are the offsets and should be subtracted from all further results. In addition, this measurement serves to check whether all electrical connections are in order. The first run of experiments is performed with a nontreated membrane, which represents a model of a large-pore membrane. It should be noted that the polycarbonate material is slightly hydrophobic, so it takes time to saturate the membrane with aqueous solution. Thus, it is advisable to soak the filter inserts intended for experimentation with nontreated membranes in 1 M KCl solution overnight. Before experimentation, students are informed that in macroscopically large pores the liquids from the external and internal compartments meet to form an interface between two liquid phases. The only potential difference that can be generated at such a liquid interface is due to the difference in ion mobility in the solution in the presence of an ion gradient between the two solutions. This is the so-called liquid junction (LJ) potential (ELJ), which can be reasonably estimated using the following generalized Henderson equation (2):

Safety Considerations

where R is the gas constant, T is the absolute temperature, F is the Faraday constant,

Although the quantity of organic liquids used to treat the membranes is very small, it is necessary to run this laboratory in a well-ventilated room, and the person actually manipulating the solvent should wear protective gloves. Ideally, only the teacher should have access to the solvent. After treating the filter, the teacher immediately adds 0.5 ml of 1 M KCl to the filter insert to prevent further evaporation. Students should use tweezers to transfer filter inserts from one well to another. At the end of the manipulation, solutions that have been in contact with the organic mixture should be collected and disposed of in the center of chemical waste collection. Instructions Low-cost volt-ohmmeters do not have an offset adjustment. Accordingly, the first measurement of the potential difference is done with both electrodes put in the vial containing 1 M KCl. This estimates electrodes asymmetry (potential offset) as well as measures

ELJ ⫽

RT F

Sf ⫽

⫻ Sf ⫻ ln

n zi2 ⫻ ui ⫻ ain,i兲 共 兺i⫽1 n 共 兺i⫽1 zi2 ⫻ ui ⫻ aext,i兲

n zi ⫻ ui ⫻ (aext,i ⫺ ain,i) 兺i⫽1 n 兺i⫽1 zi2 ⫻ ui ⫻ (aext,i ⫺ ain,i)

and u, a, and z represent the mobility, activity, and charge of each ion species (i), respectively, and in and ext are the internal and external compartments, respectively. Ion activity (a) is the product of the ion concentration (C) and ion activity coefficient (␥), as follows: a⫽ ␥C. Ion activity coefficients for different concentrations of NaCl and KCl can be found in Ref. 13. In brief, the activity coefficient for 0.1 M KCl is 0.96, for 1 M KCl is 0.915, and for 1 M NaCl is 0.63. To gain time, student may use a spreadsheet to calculate LJ potentials. This spreadsheet is available for download on the following website of Prof. J. Kenyon (University of Nevada): http://www.medicine.nevada.edu/ physio/docs/jp.xls. Students need to realize that there are actually three liquid interfaces in this initial set of experiments: the first

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Table 1. ELJ values in experiments with nontreated polycarbonate membranes

ELJ, liquid junction potential; ELJ,total, total liquid junction potential.

between the measuring electrode and the solution in the internal compartment, the second between the internal and external compartments, and the third between the solution in the external compartment and the reference electrode (Table 1 and Fig. 2). In further experiments with membranes saturated with solvent, the second interface will disappear (Table 2 and Fig. 2). The total LJ potential is calculated as follows: ELJ,total ⫽ ELJ,meas.el ⫹ ELJ,memb.interface ⫹ ELJ,ref.el where ELJ,meas.el is the LJ potential between 1 M KCl in the measuring electrode and the solution in the internal compartment, ELJ, memb.interface is the LJ potential between the solutions in the internal and external compartments, which equals zero for treated membranes, and ELJ,ref.el is the LJ potential between the solution in the external compartment and 1 M KCl in the reference electrode. After performing the calculation, students realize that LJ potentials for nontreated membranes (in the absence of solvent) compensate each other, so the total LJ potential equals zero in all experimental conditions (Table 1 and Fig. 2). For treated membranes, ELJ, total ⫽ 0 mV in the symmetrical condition, ELJ, total ⫽ ⫹1.1 mV in asymmetric KCl solutions, and ELJ, total ⫽ ⫺3.3 mV in the bi-ionic condition (1 M KCl in/1 M NaCl out; Table 2 and Fig. 2). After this introduction to LJ potentials, students are advised that the actual diffusion potential across the membrane (Ememb) is calculated as follows: Ememb ⫽ Emeasured ⫺ Eoffset ⫺ ELJ,total where Emeasured is the actually measured membrane potential, ELJ is the total liquid junction potential and Eoffset is the offset potential.

After this, students proceed to the next run of measurements, first with a membrane treated with the mixture of organic liquids and then with a membrane treated with the mixture of organic liquids, in which valinomycin or monensin is added. Troubleshooting It is advisable to measure electrical resistance for each ionic condition before measuring voltage. If the observed value of resistance does not fall within the expected range (too low or too high) or if it demonstrates abrupt changes, the filter should be replaced. During the course of this laboratory, one can observe two to three failing filters (out of 40 filters used). The acceptable range of resistances is shown in Table 3, which should serve as a comparative tool. As shown in Fig. 3, the resistance value of treated filters takes a minimum of 5 min to stabilize, especially before the first measurement. It should be also noted that wiping the solution beneath the insert during its transfer from one well to another well has a significant impact on the value of electrical resistance (Fig. 3A, traces 3 and 4). We consider this as normal behavior since we take out a portion of organic liquid from the membrane when we remove aqueous liquid adjacent to it. Figure 3 also shows that the stabilization of the membrane voltage value takes ⬃2 min. RESULTS

Results of a typical experiment and the range of values actually observed by students are shown in Table 3. A common student error consists in nonrespect of the

Table 2. ELJ values in experiments with polycarbonate membranes treated with the creosol and n-decane mixture

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Table 3. Results of a typical experiment and the range of observed values Number

Measured Resistance, k⍀

Condition

Measured Potential, mV

Membrane Resistance, k⍀

Calculated ELJ,total

Experimental Membrane Potential, mV

Offset 1

Both electrodes in 1 M KCl

2.2 (2 to 5)

⫹1.2 (⫺2 to ⫹2) Nontreated membrane

2 3 4

1 M KCl in/1 M KCl out 1 M KCl in/0.1 M KCl out 1 M KCl in/1 M NaCl out

3.0 3.2 2.9

⫹1.2 ⫹1.4 ⫹1.3

0 0 0

0.8 (0.5–1.0) 1.0 (0.5–1.0) 0.7 (0.5–1.0)

0 (⫺0.5 to ⫹0.5) ⫹0.2 (⫺0.5 to ⫹0.5) ⫹0.1 (⫺0.5 to ⫹0.5)

Membrane without ionophore 5 6 7

1 M KCl in/1 M KCl out 1 M KCl in/0.1 M KCl out 1 M KCl in/1 M NaCl out

21,000 14,000 10,000

⫹1.5 ⫺1.8 ⫺1.4

0 ⫹1.1 ⫺3.3

21,000 (10,000–35,000) 14,000 (5,000–15,000) 10,000 (1,000–10,000)

⫹0.3 (⫺1 to ⫹1) ⫺4.1 (⫺6 to ⫺1) ⫹0.7 (⫺1 to ⫹1)

10,000 (3,000–15,000) 4,000 (1,000–6,000) 2,000 (1,000–4,000)

⫹0.2 (⫺1 to ⫹1) ⫺49.4 (⫺53 to ⫺25) ⫺66.3 (⫺79 to ⫺52)

9,000 (5,000–20,000)

⫹11.8 (⫹9 to ⫹20)

Membrane with valinomycin 8 9 10

1 M KCl in/1 M KCl out 1 M KCl in/0.1 M KCl out 1 M KCl in/1 M NaCl out

10,000 4,000 2,000

⫹1.4 ⫺48.2 ⫺69.0

0 ⫹1.1 ⫺3.3

Membrane with monensin 11

1 M KCl in/1 M NaCl out

9,000

⫹9.7

electrodes’ polarity, and this should be rectified by the teacher. Laboratory Report Students then proceed to the completion of the laboratory report, which permits them to evaluate their work. In this report, students are required to perform several calculations and to answer the following questions: Question 1. Explain why the electrical resistance of polycarbonate filters increases after treatment of the membrane with organic (hydrophobic) liquid. Why does this electrical resistance decrease after the addition of ionophores?

⫺3.3

Question 2. Explain why there is no potential difference across the membrane in symmetrical ionic conditions. Justify this by calculations. Question 3. Calculate the Nernst potential for K⫹ and Cl⫺ for the condition of 1 M [KCl]in/0.1 M [KCl]out (T ⫽ 25°C), where [KCl]in and [KCl]out are the internal and external KCl concentrations, respectively. Compare these two values with experimental membrane potential values under this condition (filter without ionophore and filter with valinomycin). To do this, put the values of the Nernst potential on the axis and then place the experimental potentials within the range formed by these two theoretical values. Comment on the selectivity of the membrane. Are the membranes ideally selective to one ion species? As an alternative approach, students may use Montal’s equation to calculate K⫹ and Cl⫺ transference numbers (tK and tCl, respectively), which show the fraction of the current carried by each ion (17), as follows: ti ⫽ (Vm ⁄ 2Ei) ⫹ 0.5

Fig. 3. Continuous recordings of membrane resistance (A) and membrane voltage (B). A: 1, electrode resistance offset recording (both electrodes are placed in 1 M KCl); 2, the membrane insert treated with a mixture of creosol and n-decane without ionophore is filled with 0.5 ml of 1 M KCl, placed in a well containing 3 ml of 1 M KCl, and connected to the circuit; and 3 and 4, before the second and third connections, the insert is taken from the well, the liquid beneath is wiped away, and the insert is put again into the same well. B: 1, electrode potential offset recording (both electrodes are placed in 1 M KCl); and 2, recording from the membrane treated with a mixture of creosol and n-decane containing valinomycin, filled with 0.5 ml of 1 M KCl, placed in a well containing 3 ml of 1 M NaCl, and connected to the circuit.

where ti is the transference number of ion i, Vm is the experimental membrane voltage, and Ei is the Nernst potential of ion i under the ionic conditions used. Question 4. Develop the GHK equation to extract a selectivity coefficient (PK/PCl) for the condition of 1 M [KCl]in/0.1 M [KCl]out (T ⫽ 25°C). Calculate this for the two membranes (filter without ionophore and filter with valinomycin). Comment on the membrane selectivity for K⫹ versus Cl⫺. Teachers are advised to verify that the final equation should be as follows: PK PCl

⫽

[Cl]in ⫺ [Cl]ext ⫻ 10Vm ⁄ 58.5 [K]in ⫻ 10Vm ⁄ 58.5 ⫺ [K]ext

Question 5. Develop the Goldman equation to extract a selectivity coefficient (PK/PNa) for the condition of 1 M [KCl]in/1 M [NaCl]out, where [NaCl]out is the external NaCl

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Sourcebook of Laboratory Activities in Physiology MEMBRANE ION PERMEABILITY AND DIFFUSION POTENTIALS

concentration. Calculate this for the three types of membranes (filter without ionophore, filter with valinomycin, and filter with monensin). Comment on the membrane selectivity for K⫹ versus Na⫹. Explain how a membrane can generate diffusion potentials of opposite signs for the same ionic gradient. Teachers are advised to verify that the final equation should be as follows: PK PNa

⫽ 10⫺Vm ⁄ 58.5

Inquiry Application Students may be asked to design and perform an experiment that could provide additional evidence showing that a membrane modified by valinomycin is selective to K⫹. Here, I expect that they could suggest using variable KCl gradients across the membrane to show that under all experimental conditions measured membrane potential follows the predicted value of the K⫹ Nernst potential and not that of Cl⫺. Another anticipated suggestion is to use a defined bi-ionic gradient (for example, 10:1). This would permit the calculation of exact Nernst potentials for K⫹ and Na⫹ and the consequent calculation of ion transference numbers (tK and tNa, respectively), similar to that described above for the KCl gradient. In this case, students should also realize that the LJ potential correction is different. Another inquiry application of this manipulation is to ask students to prove that the bulk electroneutrality of the two compartments is not modified when they observe large diffusion potentials in the presence of valinomycin. In fact, this manipulation can be modified to include membrane capacitance (Cm) measurements using the same voltmeter. For these membranes, the actually observed electrical capacitance amounts to ⬃25–50 nF. This measurement permits the calculation of the number of ions necessary to generate Vm, as previously described by Moran and colleagues (18). Briefly, values of Cm and Vm allow the following calculation of stored charge (Q): Q ⫽ Cm ⫻ Vm If we then divide Q by the value of elementary charge (1.6 ⫻ 10⫺19 C), we can obtain the number of ions that crossed the membrane to generate Vm. Based on the experimental voltage data (Table 3), we obtain 1.3–3.95 ⫻ 10⫺9 C of the stored charge, which corresponds to 0.8 –2.5 ⫻ 1010 translocated K⫹ ions. Since initially we had 0.5 ml of 1 M KCl in the insert (3.1 ⫻ 1020 K⫹ ions), we can state that the translocated ions did not modify the bulk electroneutrality. At the end of the practical part, to check whether students understood the matter well, they are given the following exercise: A membrane separates two compartments of the same volume. We consider that the ratio of the volume to the surface of the membrane is similar to that of living cells. The internal compartment contains 90 mM KCl and 10 mM NaCl; the external compartment contains 90 mM NaCl, 10 mM KCl, and 200 mM sucrose. Calculate the Vm at 37°C under the following conditions.

Condition 1. The membrane is 10 times more permeable to K⫹ than to Na⫹ and impermeable to other molecules and ions.

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ANSWER. This exercise is a simple application of the GHK equation, in which PK ⫽ 10, PNa ⫽ 1, and PCl ⫽ 0. This calculation gives a Vm of ⫺41 mV. Condition 2. The membrane is 10 times more permeable to Cl⫺ than to K⫹ and Na⫹ and impermeable to other molecules and ions. ANSWER. There are two ways to solve this exercise. Students may note that the two compartments are bulk electroneutral and that the concentrations of the most permeable ion are equal across the membrane, so there is no reason for the development of a diffusion potential. Alternatively, students get a value of Vm equal to 0 mV by simple application of the GHK equation, in which PCl ⫽ 10, PK ⫽ 1, and PNa ⫽ 1. Condition 3. The membrane is permeable only to sucrose. ANSWER. Again, students note that the two compartments are bulk electroneutral and that sucrose is not charged, so there is no reason for the development of diffusion potential (Vm ⫽ 0 mV). Condition 4. The membrane is equally permeable to all molecules and ions. ANSWER. There are two ways to solve this exercise. Students note that the two compartments are bulk electroneutral and that the membrane does not discriminate ions, so there is no reason for the development of diffusion potential. Alternatively, students get a value of Vm equal to 0 mV by simple application of the GHK equation, in which PCl ⫽ 1, PK ⫽ 1, and PNa ⫽ 1. Condition 5. The membrane is 1,000 times more permeable to water than to K⫹, whereas K⫹ permeates 10 times faster than Na⫹. The membrane is impermeable to sucrose and Cl⫺. ANSWER. To solve this exercise, students should have assisted in the preceding laboratory practicum on osmosis. They should realize that the system is not at osmotic equilibrium and since water diffuses faster than ions, first an osmotic flow of water will occur. It will stop when the osmolarities of the two compartments become identical. The osmolarity of the internal compartment is 200 mosm/l and the osmolarity of the external compartment is 400 mosm/l. This means that the osmolarity of the internal compartment will increase from 200 to 300 mosm/l and that the concentrations of all ions will increase 1.5-fold, whereas the osmolarity of the external compartment will decrease from 400 to 300 mosm/l and that the concentrations of all ions will decrease to a value of 0.75-fold of the initial value. After the calculation of the new ion concentration values at the osmotic equilibrium, student should obtain a value of ⫺60 mV by the application of the GHK equation, in which PK ⫽ 10, PNa ⫽ 1, and PCl ⫽ 0. In summary, in the present article, a novel model of artificial membranes that provides efficient assistance in teaching the origins of diffusion potentials is proposed. This model has several advantages compared with those previously published (1, 4, 14, 18). First, it does not require the use of an Ussing chamber. Second, the membrane lacks ionic selectivity, which can be consequently modified by the introduction of different ionophores. Finally, because of such membrane property flexibility, the model can be easily adapted to an inquiry format. Taken together, this model helps students to understand the quantitative relationships of ionic gradients and differential membrane permeability in the generation of cell electrical signals. In my experience, the introduction of this laboratory to the curriculum permitted me to significantly increase the

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MEMBRANE ION PERMEABILITY AND DIFFUSION POTENTIALS

level of difficulty of common exam questions on this matter and did not compromise mean exam notes. Additional Resources For additional information on this topic, please see Refs. 5, 6, and 12. APPENDIX: MEMBRANE PERMEABILITY

Materials Materials needed by student groups. The following are materials for a group of two students: 1. Four polycarbonate filter inserts 2. A six-well plastic plate 3. One pair of Ag/AgCl electrodes with agar bridges 4. A volt-ohm meter 5. Fifty milliliters of 1 M KCl solution 6. Fifty milliliters of 0.1 M KCl solution 7. Fifty milliliters of 1 M NaCl solution 8. Three graduated Pasteur pipettes 9. Paper towels 10. Plastic tweezers Materials needed by the teacher. The following are materials are needed by the teacher for the laboratory: 1. Four hundred microliters of 15% creosol in n-decane 2. Valinomycin solution (0.1 mg in 300 ␮l of 15% creosol in n-decane) 3. Monensin solution (0.1 mg in 300 ␮l of 15% creosol in n-decane) 4. A 20-␮l automatic pipette 5. Gloves Protocol Fill three wells of a six-well plate with 3 ml each of 1 M KCl, 0.1 M KCl, and 1 M NaCl, respectively. Connect the reference electrode, marked as , to “COM” of the voltmeter and connect second electrode to “V” of the voltmeter. Measurement 1. Place both electrodes in a well containing 1 M KCl. Measure the resistance first and then the voltage. Wait for stable values in each case. Fill one insert with 0.5 ml of 1 M KCl and place it in a well containing 1 M KCl. This particular insert should be saturated with 1 M KCl overnight. Measurement 2. Place the reference electrode in the well and the measuring electrode into the insert. Measure the resistance first and then the voltage. Wait for stable values in each case.

Measurement 3. Take the insert from the well, carefully wipe the excess liquid beneath it using a paper towel, and transfer the insert to the well containing 0.1 M KCl. Place the reference electrode in the well and the measuring electrode into the insert. Measure the resistance first and then the voltage. Wait for stable values in each case. Measurement 4. Take the insert from the well, carefully wipe the excess liquid beneath it using a paper towel, and transfer the insert to the well containing 1 M NaCl. Place the reference electrode in the well and the measuring electrode into the insert. Measure the resistance first and then the voltage. Wait for stable values in each case. Make the teacher treat the membrane in the second insert using the creosol and n-decane mixture. As soon as the membrane becomes dark, fill the insert with 0.5 ml of 1 M KCl and place it in a well containing 1 M KCl. Measurement 5. Place the reference electrode in the well and the measuring electrode into the insert. Measure the resistance first and then the voltage. Wait for stable values in each case (up to 5 min). Note that the resistance of the membrane increases, but the voltage is still close to zero. Measurement 6. Take the insert from the well, carefully wipe the excess liquid beneath it using a paper towel, and transfer the insert to the well containing 0.1 M KCl. Place the reference electrode in the well and the measuring electrode into the insert. Measure the resistance first and then the voltage. Wait for stable values in each case. Note that the resistance of the membrane may slightly decrease, but the voltage is still close to zero. Measurement 7. Take the insert from the well, carefully wipe the excess liquid beneath it using a paper towel, and transfer the insert to the well containing 1 M NaCl. Place the reference electrode in the well and the measuring electrode into the insert. Measure the resistance first and then the voltage. Wait for stable values in each case. Note that the resistance of the membrane may further slightly decrease, but the voltage is still close to zero. Make the teacher treat the membrane in the third insert using a solution of valinomycin in the creosol and n-decane mixture. As soon as the membrane becomes dark, fill the insert with 0.5 ml of 1 M KCl and place it in a well containing 1 M KCl. Measurement 8. Place the reference electrode in the well and the measuring electrode into the insert. Measure the resistance first and then the voltage. Wait for stable values in each case (up to 5 min). Measurement 9. Take the insert from the well, carefully wipe the excess liquid beneath it using a paper towel, and transfer the insert to the well containing 0.1 M KCl. Place the reference electrode in the well and the measuring electrode into the insert. Measure the resis-

Table A1. ELJ values in experiments with nontreated polycarbonate membranes

Advances in Physiology Education • doi:10.1152/advan.00068.2013 • http://advan.physiology.org

Sourcebook of Laboratory Activities in Physiology MEMBRANE ION PERMEABILITY AND DIFFUSION POTENTIALS

399

Table A2. ELJ values in experiments with polycarbonate membranes treated with the creosol and n-decane mixture

Report

tance first and then the voltage. Wait for stable values in each case. Note that the resistance of the membrane may slightly decrease. Measurement 10. Take the insert from the well, carefully wipe the excess liquid beneath it using a paper towel, and transfer the insert to the well containing 1 M NaCl. Place the reference electrode in the well and the measuring electrode into the insert. Measure the resistance first and then the voltage. Wait for stable values in each case. Note that the résistance of the membrane may further slightly decrease. Make teacher treat the membrane in the fourth insert using a solution of monensin in the creosol and n-decane mixture. As soon as the membrane becomes dark, fill the insert with 0.5 ml of 1 M KCl and place it in a well containing 1 M NaCl. Measurement 11. Place the reference electrode in the well and the measuring electrode into the insert. Measure the resistance first and then the voltage. Wait for stable values in each case (up to 5 min). Calculate LJ potentials using the spreadsheet. The total LJ potential is calculated as follows:

1. Explain why the electrical resistance of polycarbonate filters increases after treatment of the membrane with organic (hydrophobic) liquid. Why does this electrical resistance decrease after the addition of ionophores? 2. Explain why there is no potential difference across the membrane in symmetrical ionic conditions. Justify this by calculations. 3. Calculate the Nernst potential for K⫹ and Cl⫺ for the condition of 1 M [KCl]in/0.1 M [KCl]out (T ⫽ 25°C). Compare these two values with the experimental Vm values under this condition (filter without ionophore and filter with valinomycin). To do this, put the values of Nernst potential on the axis and then place experimental potentials within the range formed by these two theoretical values. Comment on the selectivity of the membrane. Are the membranes ideally selective to one ion species? 4. Alternatively, calculate tK and tCl, which show the fraction of the current carried by each ion, as follows:

ELJ,total ⫽ ELJ,meas.el ⫹ ELJ,memb.interface ⫹ ELJ,ref.el

ti ⫽ (Vm ⁄ 2Ei) ⫹ 0.5

Fill Tables A1 and A2 with data. Take into account that the activity coefficient for 0.1 M KCl is 0.96, for 1 M KCl is 0.915, and for 1 M NaCl is 0.63. Fill Table A3 with data. Calculate the membrane resistance by subtracting the offset resistance from the measured membrane resistance. Calculate Vm by subtracting the offset voltage and corresponding ELJ,total from the measured potential: Ememb ⫽ Emeasured ⫺ Eoffset ⫺ ELJ,total

5. Develop the GHK equation to extract PK/PCl for the condition of 1 M [KCl]in/0.1 M [KCl]out (T ⫽ 25°C). Calculate this for the two membranes (filter without ionophore and filter with valinomycin). Comment on the membrane selectivity for K⫹ versus Cl⫺. 6. Develop the Goldman equation to extract PK/PNa for the condition of 1 M [KCl]in/1 M [NaCl]out. Calculate this for the three types of membranes (filter without ionophore, filter with valinomycin, and filter with monensin). Comment on the membrane selectivity for K⫹

Table A3. Results Number

Condition

Measured Resistance, k⍀

1

Both electrodes in 1 M KCl

2 3 4

1 M KCl in/1 M KCl out 1 M KCl in/0.1 M KCl out 1 M KCl in/1 M NaCl out

5 6 7

1 M KCl in/1 M KCl out 1 M KCl in/0.1 M KCl out 1 M KCl in/1 M NaCl out

8 9 10

1 M KCl in/1 M KCl out 1 M KCl in/0.1 M KCl out 1 M KCl in/1 M NaCl out

11

1 M KCl in/1 M NaCl out

Measured Potential, mV

Calculated ELJ,total

Membrane Resistance, k⍀

Offset Nontreated membrane

Membrane without ionophore

Membrane with valinomycin

Membrane with monensin

Advances in Physiology Education • doi:10.1152/advan.00068.2013 • http://advan.physiology.org

Experimental Membrane Potential, mV

Sourcebook of Laboratory Activities in Physiology 400

MEMBRANE ION PERMEABILITY AND DIFFUSION POTENTIALS

versus Na⫹. Explain how a membrane can generate diffusion potentials of opposite signs for the same ionic gradient.

Exercise A membrane separates two compartments of the same volume. We consider that the ratio of the volume to the surface of the membrane is similar to that of living cells. The internal compartment contains 90 mM KCl and 10 mM NaCl; the external compartment contains 90 mM NaCl, 10 mM KCl, and 200 mM sucrose. Calculate the Vm at 37°C under the following conditions: Condition 1. The membrane is 10 times more permeable to K⫹ than to Na⫹ and impermeable to other molecules and ions. Condition 2. The membrane is 10 times more permeable to Cl⫺ than to K⫹ and Na⫹ and impermeable to other molecules and ions. Condition 3. The membrane is permeable only to sucrose. Condition 4. The membrane is equally permeable to all molecules and ions. Condition 5. The membrane is 1,000 times more permeable to water than to K⫹, whereas K⫹ permeates 10 times faster than Na⫹. The membrane is impermeable to sucrose and Cl⫺. ACKNOWLEDGMENTS The author expresses gratitude to Sarah Sariban-Sohraby and David Gall for invaluable comments on the manuscript that increased its clarity. The author thanks Robert Naeije for support and Renaud Beauwens, David Gall, Philippe Golstein, and Hassan Jijackly for the opportunity to perform this manipulation in the frame of their courses, since the student feedback permitted an opportunity to fine tune this laboratory. The author also thanks Raphael Crutzen for years of tireless technical assistance and current participation as a laboratory teaching assistant. GRANTS This work was supported by the Fonds d’Encouragement a` la Recherche of Université Libre de Bruxelles. DISCLOSURES No conflicts of interest, financial or otherwise, are declared by the author(s). AUTHOR CONTRIBUTIONS Author contributions: V.S. conception and design of research; V.S. performed experiments; V.S. analyzed data; V.S. interpreted results of experiments; V.S. prepared figures; V.S. drafted manuscript; V.S. edited and revised manuscript; V.S. approved final version of manuscript. REFERENCES 1. Barry PH. ARTMEM–an interactive graphical program simulating membrane potential measurements across artificial membranes. Ann Biomed Eng 22: 218 –225, 1994.

2. Barry PH, Lynch JW. Liquid junction potentials and small cell effects in patch-clamp analysis. J Membr Biol 121: 101–171, 1991. 3. Carnevale NT, Hines ML. The NEURON Book. Cambridge, UK: Cambridge Univ. Press, 2006. 4. Christopher K. Diffusion Potentials Across an Artificial Membrane (online). http://www.ableweb.org/volumes/vol-20/mini2.christopher.pdf [29 August 2013]. 5. Guyton AC, Hall JE. Textbook of Medical Physiology (10th ed.). Philadelphia, PA: Saunders, 2000. 6. Hille B. Ionic Channel of Excitable Membranes (1st ed.). Sunderland, MA: Sinauer Associates, 1984. 7. Ilani A. K-Na discrimination by porous filters saturated with organic solvents as expressed by diffusion potentials. J Gen Physiol 46: 839 – 850, 1963. 8. Ilani A. Ion discrimination by “Millipore” filters saturated with organic solvents. I. Cation selectivity, mobility and relative permeability of membranes saturated with bromobenzene. Biochim Biophys Acta 94: 405– 414, 1965. 9. Ilani A. Ion discrimination by “Millipore” filters saturated with organic solvents. II. The significance of the hydrophobic medium. Biochim Biophys Acta 94: 415– 422, 1965. 10. Ilani A. Interaction between cations in hydrophobic solvent-saturated filters containing fixed negative charges. Biophys J 6: 329 –352, 1966. 11. Ilani A, Tzivoni D. Hydrogen ions in hydrophobic membranes. Biochim Biophys Acta 163: 429 – 438, 1968. 12. Knudsen OS. Biological Membranes: Theory of Transport, Potentials and Electric Impulses. Cambridge: Cambridge Univ. Press, 2002. 13. Lide DR. CRC Handbook of Chemistry and Physics (84 ed.). Sarasota, FL: CRC, 2004. 14. Manalis RS, Hastings L. Electrical gradients across an ion-exchange membrane in student’s artificial cell. J Appl Physiol 36: 769 –770, 1974. 15. Marzullo TC, Gage GJ. The SpikerBox: a low cost, open-source bioamplifier for increasing public participation in neuroscience inquiry. PLos One 7: e30837, 2012. 16. Milanick M. Changes of membrane potential demonstrated by changes in solution color. Adv Physiol Educ 33: 230, 2009. 17. Montal M. Lipid-polypeptide interactions in bilayer lipid membranes. J Membr Biol 7: 245–266, 1972. 18. Moran WM, Denton J, Wilson K, Williams M, Runge SW. A simple, inexpensive method for teaching how membrane potentials are generated. Adv Physiol Educ 22: 51–59, 1999. 19. Shohami E, Ilani A. Relation between the dielectric constant of hydrophobic cation exchange membrane and membrane permeability to counterions. Biophys J 13: 1232–1241, 1973. 20. Shohami E, Ilani A. Model hydrophobic ion exchange membrane. Biophys J 13: 1242–1260, 1973. 21. Sircar SS. A hydrostatic model of membrane potential. Adv Physiol Educ 12: 77– 80, 1994. 22. Thurman CL. Resting membrane potentials: a student test of alternate hypotheses. Adv Physiol Educ 14: 37– 41, 1995. 23. Yoshida S. Simple techniques suitable for student use to record action potentials from the frog heart. Adv Physiol Educ 25: 176 –186, 2001.

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