In biological membranes that are permeable to water and ions but impermeable to other solutes, the diffusible ions cannot reach a concentration equilibrium. Instead, a state of electroneutrality is achieved on each side of the membrane, which requires that the diffusible ions be found in different concentrations on either side of the membrane. The Donnan equilibrium is a major contributing factor to the polarized state of cells, and appreciating it is vital to the understanding of neuronal physiology. This article presents a nonmathematical active-learning exercise that will help AP and college biology students understand how the Donnan equilibrium is achieved.
A course in human or animal physiology for biology majors typically includes a discussion of neuronal physiology, beginning with an introduction to the concept of membrane potential. In the textbooks I have adopted for my courses, cellular membrane potential is correctly attributed to two major factors – the Na+/K+-ATPase pump and the presence of impermeable intracellular anions (Randall et al., 2002; Widmaier et al., 2013). The continuous action of the Na+/K+-ATPase pump deposits sodium outside the cell and potassium inside the cell at a ratio of 3 Na+ : 2 K+, generating a separation of charge across the membrane. Deoxyribonucleic acid (DNA) carries a net negative charge due to the presence of negatively charged phosphate groups, and proteins can possess negative and positive moieties. Hence, these relatively large, nondiffusible anions immediately generate a separation of charge across the membrane. Moreover, these anions influence the movement of diffusible ions such as K+ and Cl−. Therefore, to facilitate a thorough understanding of neuronal physiology, it is helpful for students to understand in greater detail (than what is usually found in a textbook) the mechanism by which the presence of large anions contributes to membrane potential in excitable cells.
In cells, the presence of an impermeable anion on one side of a biological membrane influences the diffusion of permeable anions and cations across that membrane. The Gibbs-Donnan equilibrium describes the condition of subsequent reciprocal distribution of permeable ions that carry the same valence, expressed as [K+compartment 1] × [Cl−compartment 1] = [K+compartment 2] × [Cl−compartment 2] (Kurbel, 2008; Barrett et al., 2012). Under these circumstances, an electroneutral equilibrium is reached – the concentration ratios are equal, and within each compartment the number of anions equals the number of cations. Additionally, if compartment 1 represents the intracellular environment, then at equilibrium, [K+compartment 1] > [K+compartment 2] and [Cl−compartment 1] < [Cl−compartment 2] (Pitts, 1974).
This article is a suggestion on how these ideas might be discussed in the context of an active-learning exercise in a course that serves college or high school students (addressing Next Generation Science Standards HS LS1-1; NGSS Lead States, 2013). This activity is suitable for a class size of 22 but can be scaled up or down to accommodate various numbers of students as needed. Regarding background knowledge, it is expected that students understand major concepts in membrane physiology, including passive transport (simple diffusion, facilitated diffusion, osmosis) and active transport. Students should also understand that the two major forces that influence the movement of ions are concentration gradients (ions move from high to low concentration) and electrical gradients (ions are attracted to oppositely charged particles).
The items needed include a permanent marker, masking tape, and pieces of paper and poster board. Ten pieces of paper (no larger than a standard [8.5 × 11 inch] sheet of paper) should be labeled as “K+”. Ten pieces of paper (no larger than a standard sheet of paper) should be labeled “Cl−”. Two large pieces of poster board (with a width >18 inches) will be labeled “A”; one of these should be larger than the other, enough that the size difference can be visually appreciated.
In preparation for the activity, students should discuss the answers to the following questions (the answers are in brackets below).
List two forces that influence the movement of ions. [Concentration gradients and electrical gradients.]
- Figure 1 illustrates the initial distribution of permeable ions between two aqueous compartments separated by a membrane. Predict the distribution of those ions once diffusion equilibrium is reached.
[At equilibrium, three molecules of Na+ and three molecules of Cl− should be on each side of the membrane.]
In reference to the previous question, are there equal concentrations of water on either side of the membrane when diffusion equilibrium has been reached? Explain in terms of osmosis and osmotic gradients. [There are equal amounts of water on either side; there is no difference in the concentration of diffusible ions at equilibrium and therefore there is no osmotic gradient to drive the movement of water molecules.]
Molecules are never completely immobile. Predict the consequences of a molecule randomly crossing the membrane after diffusion equilibrium has been reached. [Once equilibrium has been reached, the movement of a molecule across the membrane will be counterbalanced by the movement of another ion of the same species across the membrane in the opposite direction.]
How would the presence of nondiffusible anions influence the movement of permeable ions? [Nondiffusible anions would attract cations and repel anions.]
How would the size of a nondiffusible anion influence the movement of permeable ions? [A larger nondiffusible anion would attract more cations and repel more anions than a smaller one.]
Generate two groups of 10 students; keep the groups separated by a “membrane” that is represented by tape on the floor. Gaps in the tape should be wide enough (about 12–18 inches) for students to pass though one abreast, while holding the piece of paper that represents their ion waist-high.
Students on one side of the membrane will be given paper labeled “K+”; students on the other side of the membrane will be given paper labeled “Cl−”.
The instructor should advise the students that the membrane is permeable to K+ and Cl− and ask them to predict the outcome of the demonstration. The instructor should then direct them to follow electrical and chemical gradients until equilibrium is reached. The students must move through the gaps of membrane holding their ion waist-high.
If the students have mastered the concept of diffusion, they will arrange themselves so that five “K+” and five “Cl−” are found on each side of the membrane (Figure 2).
With respect to K+ and Cl−, a concentration and electrical equilibrium will be reached.
The instructor should remind the students that biological membranes are freely permeable to water and question the students about the movement of water with respect to the osmotically active particles (K+ and Cl−). Equal distribution of particles on either side of the membrane and the permeability of the membrane to water allows equilibrium to be reached.
The students should demonstrate that after equilibrium is reached, net ion flux equals zero. This can be done by balancing the movement of any ion across the membrane with the movement of an ion of like species across the membrane in the opposite direction.
Generate two groups of nine students each; keep the groups separate by a permeable membrane, represented by pieces of tape on the floor. Gaps in the tape should be wide enough (about 12–18 inches) for the students to pass though one abreast, while holding their ion waist-high.
Nine students on one side of the membrane will be given paper labeled “K+”.
Nine students will be on the other side of the membrane; seven of these students will be given paper labeled “Cl−”, while the other two will have poster board of different sizes labeled “A−”. Use masking tape to label this side of the membrane “intracellular”.
The instructor should remind the students that “A−” represents proteins and DNA that would be present in the cell. The students should also be reminded that “A−” is impermeable to the membrane, as evidenced by the inability of the students holding “A−” to walk easily through the gap in the membrane.
The instructor should advise the students that the membrane is only permeable to K+ and Cl− and ask them to predict the outcome of the demonstration. The instructor should then direct the students to follow electrical and chemical gradients, until equilibrium is reached (Figure 3).
The instructor should encourage discussion among the students as they orient themselves and should carefully monitor their movements. As the students strategize and discuss, the instructor should advise the students that they may not assume that one “A−” attracts K+ in a 1:1 ratio and they may not assume that one “A−” repels “Cl−” in a 1:1 ratio.
The instructor should also ask the students to consider the movement of water molecules with respect to the osmotically active particles (K+ and Cl−).
The instructor should have the students consider why anion size may have different effects regarding osmosis.
Given the preceding information, the students will understand that diffusible ions will not be able to reach concentration equilibrium when nondiffusible anions are present. The students will also appreciate that larger anions (as compared to smaller ones) will influence the movement of a greater number of diffusible ions.
Generate two groups of students of nine students each; keep the groups separate by a “permeable membrane,” represented by tape on the floor. Gaps in the tape should be wide enough for the students to pass though one abreast, while holding their ion waist-high (~12–18 inches).
Nine students on one side of the membrane will be given paper labeled “K+”.
Nine students will be on the other side of the membrane – seven of these students will be given paper labeled “Cl−”; the other two will have poster board of different sizes labeled “A−”.
The instructor should advise the students that when concentration equilibriums cannot be reached, then ions will redistribute themselves such that the intracellular and extracellular compartments are electroneutral.
The instructor should advise the students that the net charge of the larger A− will be neutralized by three K+ and two Cl− and that the net charge of the smaller A− will be neutralized by two K+ and one Cl−. The instructor should ask the students to predict the outcome of the demonstration.
The instructor should direct the students to achieve electroneutrality on either side of the membrane and encourage discussion among them as they orient themselves (Figure 4).
The instructor should reiterate that the Gibbs-Donnan equilibrium is a state of electroneutrality that occurs when large nondiffusible anions are present on one side of a biological membrane.
Part 4 should be repeated with additional anions. If there are no additional students to bring into the activity, students who are present may be given multiple pieces of paper representing ions, but those pieces of paper must be of the same ion type (e.g., K+ or Cl−) or size (e.g., larger “A−” or smaller “A−”). When additional anions are incorporated into the activity, the subsequent separation of charge will be greater when the Gibbs-Donnan equilibrium is reached.
At the end of the exercise, the students may refer to the questions posed in part 1 to review and discuss their answers. Alternatively, the students could complete parts 2–4 of the activity with the background knowledge they have, and the questions in part 1 could be used as a post-activity review or a quiz. In more advanced courses, the instructor may have the students apply what they have learned in this demonstration to a basic mathematical scenario (e.g., “In a hypothetical cell, the concentration of major ions are as follows: Na+ = 20 mM; Cl− = 5 mM; A− = 165 mM. Ignoring any osmotic effects, what is the concentration of K+ in the cell?” [150 mM]) or have the students make predictions about the implications of the Gibbs-Donnan equilibrium on the regulation of cell volume.