a fundamental property of cells is that through the use of ion transporters they maintain intracellular ion concentrations that differ from those of the extracellular environment (15). Although it is not known precisely how this difference in ion concentrations came about in evolution, numerous studies indicate that the intracellular ion concentrations of cells likely reflect the extracellular conditions at the time when the first cells arose. It is hypothesized that the earliest cells (or protocells) had leaky membranes and evolved in habitats with high K+/Na+ ratios and relatively high concentrations of the Zn2+, Mn2+, and phosphates. These early environments may have been ocean hydrothermal vents or inland geothermal systems. In either case, migration of the early cells to the high Na+ and low K+ conditions of the ocean required ion-impermeable membranes, ion-selective channels, and ion pumps capable of maintaining the gradients. Evolution took advantage of the large disparity between internal and external K+ and utilized it as a source for a resting membrane potential (4, 10, 13, 14).
The existence of K+-specific ion channels in the membranes of virtually all cells results in a membrane potential (Vm) across the cell membrane, making the inside of the cell electrically negative relative to the extracellular solution. In addition, certain classes of cells, notably neurons and muscle cells, also have voltage-sensitive Na+ channels in their membranes, rendering these cells excitable. Opening of the Na+ channels results in an influx of positive Na+ ions (known as the action potential), resulting in a transient change of Vm from its negative resting state to positive potential. This mechanism is at the heart of neuronal signaling and muscle contraction (9).
One of the most difficult concepts for students to master is a logical and intuitive understanding of how an ionic gradient can be utilized to establish an electrical potential difference across a biological membrane. In my experience, dealing with students at all levels, from high school through medical school, the vast majority never master this concept. The electrical potential of membranes remains something of a mystery cloaked in an uncomfortable equation and carries with it a sense of uneasiness. This problem appears to be widespread. Silverthorn (19) conducted a study of upper division undergraduates who had completed a semester of neurophysiology that covered the Nernst and Goldman equations. She concluded that most students had only a superficial understanding of the ionic basis for the membrane potential (Vm). For instance, the vast majority either couldn’t predict or couldn’t explain the effect on Vm of changing extracellular K+.
In teaching Vm to second-year medical students, I have found an approach that I believe takes the mystery out of this concept. Additionally, it has proven successful in communicating this idea to college undergraduates and even high school students. The essence of the approach is to regard establishing Vm as an engineering problem by imagining a cell building its membrane potential stepwise, using only simple principles familiar to all high school graduates. The first step toward understanding Vm is to discuss the foundational principles (Table 1). Students are typically very comfortable with these ideas and find them intuitive.
The first two assumptions state that, through random motion, ions move independently and diffuse down their concentration gradients. Students intuitively understand that random collision will lead to this form of diffusion. From these ideas, we can demonstrate that diffusion is an energy source and that the amount of work that can be done is proportional to the log of the concentration gradient (Fig. 1A). To establish a concentration gradient across the membrane, the cell utilizes the Na+/K+ ATPase, which pumps K+ into the cell and Na+ out, thereby establishing concentration gradients for the two ions. This ATP-dependent pump is involved in active transport of the two ions against their concentration gradients. It moves 3 Na+ out and 2 K+ in with each pump cycle. The maintenance of the gradients is energetically very expensive, and it is estimated that approximately one-third of the brain’s metabolism is dedicated to supplying ATP in support of this process. K+ is high inside and low outside, and the situation for Na+ is just the reverse. Although concentration gradients are established for different ion species before establishment of Vm, there are equal concentrations of total ions inside and outside of the cell and every positive ion is accompanied by a negative partner, resulting in charge neutrality.
We focus on K+, which has an approximately 140:4 inside/outside ratio (see Fig. 5) and has channels that are open in the resting state. The magnitude of this concentration gradient is illustrated in Fig. 1B. We note that through random motion there will be many more collisions on the inside of the membrane than on the outside. When a channel permeable to K+ is placed in the membrane, the more frequent random collisions on the inside membrane surface (Fig. 2A) will result in a net exit of K+ ions through the channel (Fig. 2B). This is an energy source. Imagine a paddle wheel placed inside the channel. The greater number of collisions from the exiting ions will cause the wheel to turn in one direction (Fig. 2C). If one imagines the paddle wheel connected to a coil spring, then with each turn of the wheel the spring will be compressed and energy will be stored. The amount of work that can be done as a result of diffusional energy is Wd/mole = RT ln (Cin/Cout). As mentioned above, the equation states that the amount of energy is a function of the steepness of the concentration gradient. This is an idea that students find intuitive. Slightly more sophisticated students can appreciate that it takes the form of a differential equation representing a case in which the rate of change is a function of the size of the concentration gradient.
A second energy source, which is electrical energy, is established as a consequence of diffusion across the membrane. In the ground state, positive and negative ions on both sides of the membrane balance one another exactly. This balance is disrupted by placing an ion channel in the membrane that is selective for K+ ions and impermeable to other ions, including Na+ and negatively charged ions. Every time a K+ ion exits through the channel, a negative partner has been left behind (Fig. 3, A and B). This results in an accumulation of negatively charged ions on the inside of the membrane and positively charged ions on the outside of the membrane (Fig. 3C). The oppositely charged ions attract each other across the membrane. Individual ions still move randomly, but now a bias or drift is imposed upon the random motion due to electrical attraction. The alignment of positive and negative charge across the membrane establishes an electric potential across the cell membrane. The work done is described by the equation We/mole = VmFZ. This simply states that amount of work that can be done equals the strength of the membrane potential (Vm) times a constant known as Faraday’s number (F) times the number of elementary charges per ion (Z). The positive and negative ions are closely apposed across the membrane, and consequently overall charge neutrality is preserved.
As more K+ ions leave the cell, the potential increases, which results in an ever greater bias on the motion of the positive ions outside the cell, resulting in a greater number of K+ ions colliding with the membrane’s outer surface. This will increase the number of K+ ions entering the channel from the outside. Equilibrium is achieved when Vm grows sufficiently strong such that the number of K+ ions entering the channel from the outside due to electrical drift is equal to the number entering from the inside due to diffusional collisions. At this point, the diffusional and electrical forces balance and we have which when rearranged, gives us the Nernst equation:
This is how Vm is established. Its source is the alignment of positive and negative ions on either side of the membrane. This creates an electric field across the membrane, which biases the movement of ions in relationship to the membrane and orients transmembrane proteins by acting upon their charged residues. Changes in Vm result in changing the orientation (conformation) of membrane proteins, thereby effecting a rapid signal (Fig. 3D). It is important to note that with the exception of those charges lined up along the membrane surface, all charged ions inside and outside the membrane still have a partner of the opposite sign, preserving net neutrality. The unaccompanied charges aligned along the membrane interact with their opposites on the other side, preserving charge neutrality. It requires only a miniscule number of K+ exiting to establish Vm, and consequently this ion movement has no meaningful effect on ion concentrations inside or outside the cell.
It is clear that the key to establishing Vm is having an ion channel that is selective for K+ ions. A channel that permitted both positive and negative charges to pass through it would never lead to a membrane potential, because each time a K+ ion exited the cell, it would attract a negative partner, thereby maintaining charge neutrality. Similarly, if the channel was equally permeable to Na+ ions, then they would be able to flow down their concentration gradient, bringing positive charge into the cell. To understand K+ channel selectivity, we need to consider the manner in which charged ions interact with water molecules. Each positively charged ion coordinates the H2O molecules such that it orients the negatively charged oxygen atom toward it (Fig. 4A). Each species of ion has a certain number of H2O surrounding it (e.g., 8 for K+), and very importantly, each ion has a characteristic distance at which it interacts with the oxygen. For a K+ ion, this distance is 2.7 Å, whereas it is 2.3 Å for a Na+ ion. Energetically, it is highly unfavorable for a K+ ion to interact with the oxygen at the characteristic distance of a Na+ ion and vice versa. This is the key to selectivity for ion channels. A channel selective for K+ ions mimics the aqueous environment for these ions by presenting oxygen atoms in its amino acid residues in such a manner that a K+ ion can interact with them at precisely 2.7 Å, a distance highly favorable for K+ ions and highly unfavorable for other ion species (Fig. 4A). In 2003, Jiang et al. (8) demonstrated that the K+ channel possesses precisely this property. It spans the membrane and has a pore that will allow only for K+ ions to pass through due to the arrangement of its residues (Fig. 4C). The manner in which the channel pore mimics the aqueous environment is demonstrated in Fig. 4D.
To recapitulate, the key to creating Vm is the establishment of a concentration gradient for a charged ionic species across the cell membrane together with the presence of an ion channel that is selective for that particular ion. This results in the ion exiting the cell through its channel, thereby creating a charge imbalance. As the charge imbalance increases, the resulting electric field imposes a drift upon the ions that is opposite to the direction of diffusion. Equilibrium is established when the electrical potential grows sufficiently strong such that it just balances the diffusional force. At that point, there are equal numbers of ions entering the channel from the outside due to electrical drift as there are exiting due to diffusional force.
Once this concept is mastered, it is easy for the student to understand the behavior of Na+ and other ions, given their concentration gradients. Figure 5 lists the extracellular and intracellular concentrations for the membrane-permeable ions, their ratios, equilibrium potentials, and their typical effect on Vm. In company with the ionic ratios, the triangles represent the direction and steepness of the ionic gradients (albeit not to scale). In addition to the actions of K+ and Na+ that have already been discussed, Cl− ions flowing down their concentration gradient bring negative charge into the cell, resulting in membrane hyperpolarization. The action of Ca2+ ions is more subtle. The main effect of Ca2+ ions entering the cell is to activate Ca2+-dependent K+ channels. This results in a large egress of K+ that hyperpolarizes the membrane. So despite the fact that positive Ca2+ ions enter the cell, their effect is swamped by the exit of a much greater number of K+ ions. The manner in which multiple conductances result in Vm is discussed in an earlier paper (2).
A further point that may be of interest to more advanced students concerns the direct contribution of the Na+/K+ ATPase to Vm. As discussed above, the Na+/K+ membrane pump maintains ionic concentrations by exchanging 3 Na+ (out) for 2 K+ (in) with each cycle. The net egress of one positive charge with each cycle represents a negative current entering the cell. Recalling that V = IR (Table 1), we see that a negative current flowing across the membrane will contribute to Vm by causing it to be more negative. This has been demonstrated to be true in many cells, and the portion of Vm that is provided by the pump varies with cell type, depending upon things such as size, membrane resistance, current size, etc. For instance, in a molluscan neuron, the activity of the Na+/K+ ATPase contributes −10 mV to Vm (5, 6).
The approach described in this paper provides an intuitive understanding of how Vm is established by the concentration gradient for K+ ions. This approach is complimentary to other approaches, including a variety of demonstrations, laboratory exercises, and computer simulations. For example, Wright’s (21) refresher on the generation of the resting potential provides a careful and thorough analysis of the Nernst equation, provides an excellent explanation of how the equation is developed, and leads to a deep understanding of the process at the level of the actual number of ions involved. One can find a variety of either computer- or web-based simulations and exercises that teach Vm, including those reported by Barry (1) and by Dwyer et al. (3). There are also multiple simulations and laboratory demonstrations of Vm. Milanick (11) has developed a simple and elegant visualization of ionic gradients contributing to membrane potential through color changes in a solution. This approach uses different colored solutes to represent each ionic species, color intensity as an indicator of concentration, and valves to represent ionic conductances. Procopio (15a) uses hydraulic analogs to teach the Vm concept. Using valves to connect ionic gradient reservoirs to the Vm reservoir, this author represents different equilibrium potentials by the height of the various water columns in each reservoir and models cell capacitance by the size of the Vm reservoir. The height of the water column in the Vm reservoir represents the membrane potential and can be directly related to the heights of the columns in the ionic gradient reservoirs and the relative degree of opening of their valves (11). Moran et al. (12) developed a simple and inexpensive laboratory demonstration of the establishment of Vm by placing differing concentrations of K+H2PO4− on opposite sides of a dialysis membrane and using a pH meter as the detector. A similar approach was taken by Shlyonsky (18) in which polycarbonate filters were used to establish bioelectric potentials that could be recorded using a pH meter.
There have been several living preparations used to demonstrate bioelectrical potentials. Thurman (20) developed a preparation using frog Sartorius muscle for demonstrating the role of K+ in setting Vm and also used the exercise to teach students hypothesis testing. Ribiero-Filho et al. (16) used the contractions in a ring-like preparation from rat mesenteric artery as an indicator of changes in membrane potential in response to changes in ionic gradients. Schwab et al. (17) developed a demonstration of Vm by measuring the membrane potential of Xeonopus laevis oocytes in response to stepwise changes in external K+. All of these approaches are synergistic with the intuitive program described in this paper, and I believe that if students first work through an intuitive understanding, these complimentary experiences will be enhanced. A series of PowerPoint slides that presents this approach is available from the author on request.
No conflicts of interest, financial or otherwise, are declared by the author.
D.L.C. conception and design of research; D.L.C. prepared figures; D.L.C. drafted manuscript; D.L.C. edited and revised manuscript; D.L.C. approved final version of manuscript.
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