The Neuronal Membrane at Rest
BOX 3.1 BRAIN FOOD: A Review of Moles and Molarity
Relative Ion Permeabilities of the Membrane at Rest
BOX 3.4 PATH OF DISCOVERY: Feeling Around Inside Ion Channels in the Dark, by Chris Miller
The Importance of Regulating the External Potassium Concentration
BOX 3.5 OF SPECIAL INTEREST: Death by Lethal Injection
Consider the problem your nervous system confronts when you step on a thumbtack. Your reactions are automatic: You shriek with pain as you jerk up your foot. For this simple response to occur, breaking of the skin by the tack must be translated into neural signals that travel rapidly and reliably up the long sensory nerves of your leg. In the spinal cord, these signals are transferred to interneurons. Some of these neurons connect with the parts of your brain that interpret the signals as being painful. Others connect to the motor neurons that control the leg muscles that withdraw your foot. Thus, even this simple reflex, depicted in Figure 3.1, requires the nervous system to collect, distribute, and integrate information. A goal of cellular neurophysiology is to understand the biological mechanisms that underlie these functions.
FIGURE 3.1 A simple reflex. ➀ A person steps on a thumbtack. ➁ The breaking of the skin is translated into signals that travel up sensory nerve fibers (the direction of information flow, indicated by the arrows). ➂ In the spinal cord, the information is distributed to interneurons. Some of these neurons send axons to the brain where the painful sensation is registered. Others synapse on motor neurons, which send descending signals to the muscles. ➃ The motor commands lead to muscle contraction and withdrawal of the foot. Description
The neuron solves the problem of conducting information over a distance by using electrical signals that sweep along the axon. In this sense, axons act like telephone wires. The analogy stops there, however, because the type of signal used by the neuron is constrained by the special environment of the nervous system. In a copper telephone wire, information can be transferred over long distances at a high rate (about half the speed of light) because telephone wire is a superb conductor of electrons, is well insulated, and is suspended in air (air being a poor conductor of electricity). Electrons will, therefore, move within the wire instead of radiating away. In contrast, electrical charge in the cytosol of the axon is carried by electrically charged atoms (ions) instead of free electrons. This makes cytosol far less conductive than copper wire. Also, the axon is not especially well insulated and is bathed in salty extracellular fluid, which conducts electricity. Thus, like water flowing down a leaky garden hose, electrical current flowing down the axon would not go very far before it would leak out.
Fortunately, the axonal membrane has properties that enable it to conduct a special type of signal—the nerve impulse, or action potential—that overcomes these biological constraints. As we will see in a moment, the term “potential” refers to the separation of electrical charge across the membrane. In contrast to passively conducted electrical signals, action potentials do not diminish over distance; they are signals of fixed size and duration. Information is encoded in the frequency of action potentials of individual neurons as well as in the distribution and number of neurons firing action potentials in a given nerve. This type of code is somewhat like Morse code sent down an old fashioned telegraph wire; information is encoded in the pattern of electrical impulses. Cells capable of generating and conducting action potentials, which include both nerve and muscle cells, are said to have excitable membrane. The “action” in action potentials occurs at the cell membrane.
When a cell with excitable membrane is not generating impulses, it is said to be at rest. In the resting neuron, the cytosol along the inside surface of the membrane has a negative electrical charge compared to the outside. This difference in electrical charge across the membrane is called the resting membrane potential (or resting potential). The action potential is simply a brief reversal of this condition, and for an instant—about a thousandth of a second—the inside of the membrane becomes positively charged relative to the outside. Therefore, to understand how neurons signal one another, we must learn how the neuronal membrane at rest separates electrical charge, how electrical charge can be rapidly redistributed across the membrane during the action potential, and how the impulse can propagate reliably along the axon.
In this chapter, we begin our exploration of neuronal signaling by tackling the first question: How does the resting membrane potential arise? Understanding the resting potential is very important because it forms the foundation for understanding the rest of neuronal physiology. And knowledge of neuronal physiology is central to understanding the capabilities and limitations of brain function.
We begin our discussion of the resting membrane potential by introducing the three main players: the salty fluids on either side of the membrane, the membrane itself, and the proteins that span the membrane. Each of these has certain properties that contribute to establishing the resting potential.
Water is the main ingredient of both the fluid inside the neuron, the intracellular fluid or cytosol, and the outside fluid that bathes the neuron, the extracellular fluid. Electrically charged atoms—ions—that are dissolved in this water are responsible for the resting and action potentials.
Water. For our purpose here, the most important property of the water molecule (H2O) is its uneven distribution of electrical charge (Figure 3.2a). The two hydrogen atoms and the oxygen atom are bonded together covalently, which means they share electrons. The oxygen atom, however, has a greater affinity for electrons than does the hydrogen atom. As a result, the shared electrons spend more time associated with the oxygen atom than with the two hydrogen atoms. Therefore, the oxygen atom acquires a net negative charge (because it has extra electrons), and the hydrogen atoms acquire a net positive charge. Thus, H2O is said to be a polar molecule, held together by polar covalent bonds. This electrical polarity makes water an effective solvent of other charged or polar molecules; that is, other polar molecules tend to dissolve in water.
FIGURE 3.2 Water is a polar solvent. (a) Different representations of the atomic structure of the water molecule. The oxygen atom has a net negative electrical charge and the hydrogen atoms have a net positive electrical charge, making water a polar molecule. (b) A crystal of sodium chloride (NaCl) dissolves in water because the polar water molecules have a stronger attraction for the electrically charged sodium and chloride ions than the ions do for one another. Description
Ions. Atoms or molecules that have a net electrical charge are known as ions. Table salt is a crystal of sodium (Na+) and chloride (Cl–) ions held together by the electrical attraction of oppositely charged atoms. This attraction is called an ionic bond. Salt dissolves readily in water because the charged portions of the water molecule have a stronger attraction for the ions than the ions have for each other (Figure 3.2b). As each ion breaks away from the crystal, it is surrounded by a sphere of water molecules. Each positively charged ion (Na+, in this case) is covered by water molecules oriented so that the oxygen atoms (the negative pole) are facing the ion. Likewise, each negatively charged ion (Cl–) is surrounded by water molecules with the hydrogen atoms (with their net positive charge) facing the chloride ion. These clouds of water that surround each ion are called spheres of hydration, and they effectively insulate the ions from one another.
The electrical charge of an atom depends on the difference between its numbers of protons and electrons. When this difference is 1, the ion is said to be monovalent; when the difference is 2, the ion is divalent; and so on. Ions with a net positive charge are called cations; ions with a negative charge are called anions. Remember that ions are the major charge carriers in the conduction of electricity in biological systems, including the neuron. The ions of particular importance for cellular neurophysiology are the monovalent cations Na+ (sodium) and K+ (potassium), the divalent cation Ca2+ (calcium), and the monovalent anion Cl– (chloride).
As we have seen, substances with a net or uneven electrical charge will dissolve in water because of the polarity of the water molecule. These substances, including ions and polar molecules, are said to be “water-loving,” or hydrophilic. However, compounds whose atoms are bonded by nonpolar covalent bonds have no basis for chemical interactions with water. A nonpolar covalent bond occurs when the shared electrons are distributed evenly in the molecule so that no portion acquires a net electrical charge. Such compounds will not dissolve in water and are said to be “water-fearing,” or hydrophobic. A familiar example of a hydrophobic substance is olive oil, and, as you know, oil and water don’t mix. Another example is lipid, a class of water-insoluble biological molecules important to the structure of cell membranes. The lipids of the neuronal membrane contribute to the resting and action potentials by forming a barrier to water-soluble ions and, indeed, to water itself.
The main chemical building blocks of cell membranes are phospholipids. Like other lipids, phospholipids contain long nonpolar chains of carbon atoms bonded to hydrogen atoms. In addition, however, a phospholipid has a polar phosphate group (a phosphorus atom bonded to three oxygen atoms) attached to one end of the molecule. Thus, phospholipids are said to have a polar “head” (containing phosphate) that is hydrophilic, and a nonpolar “tail” (containing hydrocarbon) that is hydrophobic.
The neuronal membrane consists of a sheet of phospholipids, two molecules thick. A cross section through the membrane, shown in Figure 3.3, reveals that the hydrophilic heads face the outer and inner watery environments and the hydrophobic tails face each other. This stable arrangement is called a phospholipid bilayer, and it effectively isolates the cytosol of the neuron from the extracellular fluid.
FIGURE 3.3 The phospholipid bilayer. The phospholipid bilayer is the core of the neuronal membrane and forms a barrier to water-soluble ions.
The type and distribution of protein molecules distinguish neurons from other types of cells. The enzymes that catalyze chemical reactions in the neuron, the cytoskeleton that gives a neuron its special shape, and the receptors that are sensitive to neurotransmitters are all made up of protein molecules. The resting potential and action potential depend on special proteins that span the phospholipid bilayer. These proteins provide routes for ions to cross the neuronal membrane.
Protein Structure. In order to perform their many functions in the neuron, different proteins have widely different shapes, sizes, and chemical characteristics. To understand this diversity, let’s briefly review protein structure.
As mentioned in Chapter 2, proteins are molecules assembled from various combinations of 20 different amino acids. The basic structure of an amino acid is shown in Figure 3.4a. All amino acids have a central carbon atom (the alpha carbon), which is covalently bonded to four molecular groups: a hydrogen atom, an amino group (NH3+), a carboxyl group (COO–), and a variable group called the R group (R for residue). The differences among amino acids result from differences in the size and nature of these R groups (Figure 3.4b). The properties of the R group determine the chemical relationships in which each amino acid can participate.
FIGURE 3.4 Amino acids, the building blocks of protein. (a) Every amino acid has in common a central alpha carbon, an amino group (NH3+), and a carboxyl group (COO–). Amino acids differ from one another based on a variable R group. (b) The 20 different amino acids that are used by neurons to make proteins. Noted in parentheses are the common abbreviations used for the various amino acids. Description
Proteins are synthesized by the ribosomes of the neuronal cell body. In this process, amino acids assemble into a chain connected by peptide bonds, which join the amino group of one amino acid to the carboxyl group of the next (Figure 3.5a). Proteins made of a single chain of amino acids are also called polypeptides (Figure 3.5b).
FIGURE 3.5 The peptide bond and a polypeptide. (a) Peptide bonds attach amino acids together. The bond forms between the carboxyl group of one amino acid and the amino group of another. (b) A polypeptide is a single chain of amino acids. Description
The four levels of protein structure are shown in Figure 3.6. The primary structure is like a chain in which the amino acids are linked together by peptide bonds. As a protein molecule is being synthesized, however, the polypeptide chain can coil into a spiral-like configuration called an alpha helix. The alpha helix is an example of what is called the secondary structure of a protein molecule. Interactions among the R groups can cause the molecule to change its three-dimensional conformation even further. In this way, proteins can bend, fold, and assume a complex three-dimensional shape. This shape is called tertiary structure. Finally, different polypeptide chains can bond together to form a larger molecule; such a protein is said to have quaternary structure. Each of the different polypeptides contributing to a protein with quaternary structure is called a subunit.
FIGURE 3.6 Protein structure. (a) Primary structure: the sequence of amino acids in the polypeptide. (b) Secondary structure: coiling of a polypeptide into an alpha helix. (c) Tertiary structure: three-dimensional folding of a polypeptide. (d) Quaternary structure: different polypeptides bonded together to form a larger protein. Description
Channel Proteins. The exposed surface of a protein may be chemically heterogeneous. Regions where nonpolar R groups are exposed are hydrophobic and tend to associate readily with lipid. Regions with exposed polar R groups are hydrophilic and tend to avoid a lipid environment. Therefore, it is not difficult to imagine classes of rod-shaped proteins with polar groups exposed at either end but with only hydrophobic groups showing on their middle surfaces. This type of protein can be suspended in a phospholipid bilayer, with its hydrophobic portion inside the membrane and its hydrophilic ends exposed to the watery environments on either side.
Ion channels are made from just these sorts of membrane-spanning protein molecules. Typically, a functional channel across the membrane requires that four to six similar protein molecules assemble to form a pore between them (Figure 3.7). The subunit composition varies from one type of channel to the next, and this is what determines their different properties. One important property of most ion channels, specified by the diameter of the pore and the nature of the R groups lining it, is ion selectivity. Potassium channels are selectively permeable to K+. Likewise, sodium channels are permeable almost exclusively to Na+, calcium channels to Ca2+, and so on. Another important property of many channels is gating. Channels with this property can be opened and closed—gated—by changes in the local microenvironment of the membrane.
FIGURE 3.7 A membrane ion channel. Ion channels consist of membrane-spanning proteins that assemble to form a pore. In this example, the channel protein has five polypeptide subunits. Each subunit has a hydrophobic surface region (shaded) that readily associates with the phospholipid bilayer.
You will learn much more about channels as you work your way through this book. Understanding ion channels in the neuronal membrane is key to understanding cellular neurophysiology.
Ion Pumps. In addition to those that form channels, other membrane-spanning proteins come together to form ion pumps. Recall from Chapter 2 that adenosine triphosphate (ATP) is the energy currency of cells. Ion pumps are enzymes that use the energy released by the breakdown of ATP to transport certain ions across the membrane. We will see that these pumps play a critical role in neuronal signaling by transporting Na+ and Ca2+ from the inside of the neuron to the outside.
A channel across a membrane is like a bridge across a river (or, in the case of a gated channel, like a drawbridge): It provides a path to cross from one side to the other. The existence of a bridge does not necessarily compel us to cross it, however. The bridge we cross during our weekday commute may not be used on the weekend. The same can be said of membrane ion channels. The existence of an open channel in the membrane does not necessarily mean that there is a net movement of ions across the membrane. Such movement also requires that external forces be applied to drive them across. Because the functioning nervous system requires the movement of ions across the neuronal membrane, it is important that we understand these forces. Ionic movements through channels are influenced by two factors: diffusion and electricity.
Ions and molecules dissolved in water are in constant motion. This temperature-dependent, random movement tends to distribute the ions evenly throughout the solution. Therefore, there is a net movement of ions from regions of high concentration to regions of low concentration; this movement is called diffusion. For example, when a teaspoon of milk is added to a cup of hot tea, the milk tends to spread evenly through the tea solution. If the thermal energy of the solution is reduced, as with iced tea, the diffusion of milk molecules will take noticeably longer.
Although ions typically do not pass through a phospholipid bilayer directly, diffusion causes ions to be pushed through channels in the membrane. For example, if NaCl is dissolved in the fluid on one side of a permeable membrane (i.e., with channels that allow Na+ and Cl– passage), some Na+ and Cl– ions will cross until all are evenly distributed in the solutions on both sides (Figure 3.8). Like the milk molecules diffusing in the tea, the net movement is from the region of high concentration to the region of low concentration. (For a review of how concentrations are expressed, see Box 3.1.) Such a difference in concentration is called a concentration gradient. Thus, we say that ions will flow down a concentration gradient. The movement of ions across the membrane by diffusion, therefore, happens when (1) the membrane has channels permeable to the ions and (2) there is a concentration gradient across the membrane.
FIGURE 3.8 Diffusion. (a) NaCl has been dissolved on the left side of an impermeable membrane. The sizes of the letters Na+ and Cl– indicate the relative concentrations of these ions. (b) Channels are inserted in the membrane that allow the passage of Na+ and Cl–. Because there is a large concentration gradient across the membrane, there will be a net movement of Na+ and Cl– from the region of high concentration to the region of low concentration, from left to right. (c) In the absence of any other factors, the net movement of Na+ and Cl– across the membrane ceases when they are equally distributed on both sides of the permeable membrane. Description
Concentrations of substances are expressed as the number of molecules per liter of solution. The number of molecules is usually expressed in moles. One mole is 6.02 × 1023 molecules. A solution is said to be 1 Molar (M) if it has a concentration of 1 mole per liter. A 1 millimolar (mM) solution has 0.001 moles per liter. The abbreviation for concentration is a pair of brackets. Thus, we read [NaCl] = 1 mM as: “The concentration of the sodium chloride solution is 1 millimolar.”
In addition to diffusion down a concentration gradient, another way to induce a net movement of ions in a solution is to use an electrical field because ions are electrically charged particles. Consider the situation in Figure 3.9, where wires from the two terminals of a battery are placed in a solution containing dissolved NaCl. Remember, opposite charges attract and like charges repel. Consequently, there will be a net movement of Na+ toward the negative terminal (the cathode) and of Cl– toward the positive terminal (the anode). The movement of electrical charge is called electrical current, represented by the symbol I and measured in units called amperes (amps). According to the convention established by Benjamin Franklin, current is defined as being positive in the direction of positive-charge movement. In this example, therefore, positive current flows in the direction of Na+ movement, from the anode to the cathode.
FIGURE 3.9 The movement of ions influenced by an electrical field.
Two important factors determine how much current will flow: electrical potential and electrical conductance. Electrical potential, also called voltage, is the force exerted on a charged particle; it reflects the difference in charge between the anode and the cathode. More current will flow as this difference is increased. Voltage is represented by the symbol V and is measured in units called volts. As an example, the difference in electrical potential between the terminals of a car battery is 12 volts; that is, the electrical potential at one terminal is 12 volts more positive than that at the other.
Electrical conductance is the relative ability of an electrical charge to migrate from one point to another. It is represented by the symbol g and measured in units called siemens (S). Conductance depends on the number of ions or electrons available to carry electrical charge, and the ease with which these charged particles can travel through space. A term that expresses the same property in a different way is electrical resistance, the relative inability of an electrical charge to migrate. It is represented by the symbol R and measured in units called ohms (Ω). Resistance is simply the inverse of conductance (i.e., R = 1/g).
There is a simple relationship between potential (V), conductance (g), and the amount of current (I) that will flow. This relationship, known as Ohm’s law, may be written I = gV: Current is the product of the conductance and the potential difference. Notice that if the conductance is zero, no current will flow even when the potential difference is very large. Likewise, when the potential difference is zero, no current will flow even when the conductance is very large.
Consider the situation illustrated in Figure 3.10a, in which NaCl has been dissolved in equal concentrations on either side of a phospholipid bilayer. If we drop wires from the two terminals of a battery into the solution on either side, they generate a large potential difference across this membrane. No current will flow, however, because there are no channels to allow migration of Na+ and Cl– across the membrane; the conductance of the membrane is zero. Driving an ion across the membrane electrically, therefore, requires that (1) the membrane possesses channels permeable to that ion (to provide conductance) and (2) there is an electrical potential difference across the membrane (Figure 3.10b).
FIGURE 3.10 Electrical current flow across a membrane. (a) A voltage applied across a phospholipid bilayer causes no electrical current because there are no channels to allow the passage of electrically charged ions from one side to the other; the conductance of the membrane is zero. (b) Inserting channels in the membrane allows ions to cross. Electrical current flows in the direction of cation movement (from left to right, in this example). Description
The stage is now set. We have electrically charged ions in solution on both sides of the neuronal membrane. Ions can cross the membrane only by way of protein channels. The protein channels can be highly selective for specific ions. The movement of any ion through its channel depends on the concentration gradient and the difference in electrical potential across the membrane. Now let’s use this knowledge to explore the resting membrane potential.
The membrane potential is the voltage across the neuronal membrane at any moment, represented by the symbol Vm. Sometimes Vm is “at rest”; at other times it is not (such as during an action potential). Vm can be measured by inserting a microelectrode into the cytosol. A typical microelectrode is a thin glass tube with an extremely fine tip (diameter 0.5 μm) that can penetrate the membrane of a neuron with minimal damage. It is filled with an electrically conductive salt solution and is connected to a device called a voltmeter. The voltmeter measures the electrical potential difference between the tip of this microelectrode and a wire placed outside the cell (Figure 3.11). This method reveals that electrical charge is unevenly distributed across the neuronal membrane. The inside of the neuronal membrane is electrically negative relative to the outside. This steady difference, the resting potential, is maintained whenever a neuron is not generating impulses.
FIGURE 3.11 Measuring the resting membrane potential. A voltmeter measures the difference in electrical potential between the tip of a microelectrode inside the cell and a wire placed in the extracellular fluid, conventionally called “ground” because it is electrically continuous with the earth. Typically, the inside of the neuron is about –65 mV with respect to the outside. This potential is caused by the uneven distribution of electrical charge across the membrane (enlargement). Description
The resting potential of a typical neuron is about –65 millivolts (1 mV = 0.001 volts). Stated another way, for a neuron at rest, Vm = –65 mV. This negative resting membrane potential of the neuron is an absolute requirement for a functioning nervous system. To understand the negative membrane potential, we look to the ions that are present and how they are distributed inside and outside the neuron.
Consider a hypothetical cell in which the inside is separated from the outside by a pure phospholipid membrane with no proteins. Inside this cell, a concentrated potassium salt solution is dissolved, yielding K+ and A– anions (any molecules with a negative charge). Outside the cell is a solution with the same salt but diluted twentyfold with water. Although a large concentration gradient exists between the inside of the cell and the outside, there is no net movement of ions because the phospholipid bilayer, having no channel proteins, is impermeable to charged, hydrophilic atoms. Under these conditions, a microelectrode would record no potential difference between the inside and the outside of the cell. In other words, Vm would be equal to 0 mV because the ratio of K+ to A– on each side of the membrane equals 1; both solutions are electrically neutral (Figure 3.12a).
FIGURE 3.12 Establishing equilibrium in a selectively permeable membrane. (a) An impermeable membrane separates two regions: one of high salt concentration (inside) and the other of low salt concentration (outside). The relative concentrations of potassium (K+) and an impermeable anion (A–) are represented by the sizes of the letters. (b) Inserting a channel that is selectively permeable to K+ into the membrane initially results in a net movement of K+ down their concentration gradient, from left to right. (c) A net accumulation of positive charge on the outside and negative charge on the inside retards the movement of positively charged K+ from the inside to the outside. Equilibrium is established such that there is no net movement of ions across the membrane, leaving a charge difference between the two sides. Description
Consider how this situation would change if potassium channels were inserted into the phospholipid bilayer. Because of the selective permeability of these channels, K+ would be free to pass across the membrane, but A– would not. Initially, diffusion rules: K+ ions pass through the channels out of the cell, down the steep concentration gradient. Because A– is left behind, however, the inside of the cell membrane immediately begins to acquire a net negative charge, and an electrical potential difference is established across the membrane (Figure 3.12b). As the inside acquires more and more net negative charge, the electrical force starts to pull positively charged K+ ions back through the channels into the cell. When a certain potential difference is reached, the electrical force pulling K+ ions inside exactly counterbalances the force of diffusion pushing them out. Thus, an equilibrium state is reached in which the diffusional and electrical forces are equal and opposite, and the net movement of K+ across the membrane ceases (Figure 3.12c). The electrical potential difference that exactly balances an ionic concentration gradient is called an ionic equilibrium potential, or simply equilibrium potential, and it is represented by the symbol Eion. In this example, the equilibrium potential will be about –80 mV.
The example in Figure 3.12 demonstrates that generating a steady electrical potential difference across a membrane is a relatively simple matter. All that is required is an ionic concentration gradient and selective ionic permeability. Before moving on to the situation in real neurons, however, we can use this example to make four important points.
- Large changes in membrane potential are caused by minuscule changes in ionic concentrations. In Figure 3.12, channels were inserted, and K+ ions flowed out of the cell until the membrane potential went from 0 mV to the equilibrium potential of –80 mV. How much does this ionic redistribution affect the K+ concentration on either side of the membrane? Not very much. For a cell with a 50 μm diameter, containing 100 mM K+, it can be calculated that the concentration change required to take the membrane from 0 to –80 mV is about 0.00001 mM. That is, when the channels were inserted and the K+ flowed out until equilibrium was reached, the internal K+ concentration went from 100 to 99.99999 mM—a negligible drop in concentration.
- The net difference in electrical charge occurs at the inside and outside surfaces of the membrane. Because the phospholipid bilayer is so thin (less than 5 nm thick), it is possible for ions on one side to interact electrostatically with ions on the other side. Thus, the negative charges inside the neuron and the positive charges outside the neuron tend to be mutually attracted to the cell membrane. Consider how, on a warm summer evening, mosquitoes are attracted to the outside face of a window pane when the inside lights are on. Similarly, the net negative charge inside the cell is not distributed evenly in the cytosol but rather is localized at the inner face of the membrane (Figure 3.13). In this way, the membrane is said to store electrical charge, a property called capacitance.
FIGURE 3.13 The distribution of electrical charge across the membrane. The uneven charges inside and outside the neuron line up along the membrane because of electrostatic attraction across this very thin barrier. Notice that the bulk of the cytosol and extracellular fluid is electrically neutral.
- Ions are driven across the membrane at a rate proportional to the difference between the membrane potential and the equilibrium potential. Notice in our example in Figure 3.12 that when the channels were inserted, there was a net movement of K+ only as long as the electrical membrane potential differed from the equilibrium potential. The difference between the real membrane potential and the equilibrium potential (Vm – Eion) for a particular ion is called the ionic driving force. We’ll talk more about this in Chapters 4 and 5 when we discuss the movement of ions across the membrane during the action potential and synaptic transmission.
- If the concentration difference across the membrane is known for an ion, the equilibrium potential can be calculated for that ion. In our example in Figure 3.12, we assumed that K+ was more concentrated inside the cell. Based on this knowledge, we were able to deduce that the equilibrium potential would be negative if the membrane were selectively permeable to K+. Let’s consider another example, in which Na+ is more concentrated outside the cell (Figure 3.14). If the membrane contains sodium channels, Na+ would flow down the concentration gradient into the cell. The entry of positively charged ions would cause the cytosol on the inner surface of the membrane to acquire a net positive charge. The positively charged interior of the cell membrane would now repel Na+ ions, tending to push them back out through their channels. At a certain potential difference, the electrical force pushing Na+ ions out would exactly counterbalance the force of diffusion pushing them in. In this example, the membrane potential at equilibrium would be positive on the inside.
FIGURE 3.14 Another example of establishing equilibrium in a selectively permeable membrane. (a) An impermeable membrane separates two regions: one of high salt concentration (outside) and the other of low salt concentration (inside). (b) Inserting a channel that is selectively permeable to Na+ into the membrane initially results in a net movement of Na+ down its concentration gradient, from right to left. (c) A net accumulation of positive charge on the inside and negative charge on the outside retards the movement of positively charged Na+ from the outside to the inside. Equilibrium is established such that there is no net movement of ions across the membrane, leaving a charge difference between the two sides; in this case, the inside of the cell is positively charged with respect to the outside. Description
The examples in Figures 3.12 and 3.14 illustrate that if we know the ionic concentration difference across the membrane, we can figure out the equilibrium potential for any ion. Prove it to yourself. Assume that Ca2+ is more concentrated on the outside of the cell and that the membrane is selectively permeable to Ca2+. See if you can figure out whether the inside of the cell would be positive or negative at equilibrium. Try it again, assuming that the membrane is selectively permeable to Cl–, and that Cl– is more concentrated outside the cell. (Pay attention here; note the charge of the ion.)
The preceding examples show that each ion has its own equilibrium potential—the steady electrical potential that would occur if the membrane were permeable only to that ion. Thus, we can speak of the potassium equilibrium potential, EK; the sodium equilibrium potential, ENa; the calcium equilibrium potential, ECa; and so on. And knowing the electrical charge of the ion and the concentration difference across the membrane, we can easily deduce whether the inside of the cell would be positive or negative at equilibrium. In fact, the exact value of an equilibrium potential in mV can be calculated using an equation derived from the principles of physical chemistry, the Nernst equation, which takes into consideration the charge of the ion, the temperature, and the ratio of the external and internal ion concentrations. Using the Nernst equation, we can calculate the value of the equilibrium potential for any ion. For example, if K+ is concentrated twentyfold on the inside of a cell, the Nernst equation tells us that EK = –80 mV (Box 3.2).
The equilibrium potential for an ion can be calculated using the Nernst equation:
The Nernst equation can be derived from the basic principles of physical chemistry. Let’s see if we can make some sense of it.
Remember that equilibrium is the balance of two influences: diffusion, which pushes an ion down its concentration gradient, and electricity, which causes an ion to be attracted to opposite charges and repelled by like charges. Increasing the thermal energy of each particle increases diffusion and therefore increases the potential difference achieved at equilibrium. Thus, Eion is proportional to T. On the other hand, increasing the electrical charge of each particle decreases the potential difference needed to balance diffusion. Therefore, Eion is inversely proportional to the charge of the ion (z). We need not worry about R and F in the Nernst equation because they are constants.
At body temperature (37 °C), the Nernst equation for the important ions—K+, Na+, Cl–, and Ca2+ — simplifies to:
Therefore, to calculate the equilibrium potential for a certain type of ion at body temperature, all we need to know is the ionic concentrations on either side of the membrane. For instance, in the example we used in Figure 3.12, we stipulated that K+ was twentyfold more concentrated inside the cell:
Notice that there is no term in the Nernst equation for permeability or ionic conductance. Thus, calculating the value of Eion does not require knowledge of the selectivity or the permeability of the membrane for the ion. There is an equilibrium potential for each ion in the intracellular and extracellular fluid. Eion is the membrane potential that would just balance the ion’s concentration gradient, so that no net ionic current would flow if the membrane were permeable to that ion.
It should now be clear that the neuronal membrane potential depends on the ionic concentrations on both sides of the membrane. Approximate values for these concentrations appear in Figure 3.15. The important point is that K+ is more concentrated on the inside, and Na+ and Ca2+ are more concentrated on the outside.
FIGURE 3.15 Approximate ion concentrations on either side of a neuronal membrane. Eion is the membrane potential that would be achieved (at body temperature) if the membrane were selectively permeable to that ion. Description
How do these concentration gradients arise? Ionic concentration gradients are established by the actions of ion pumps in the neuronal membrane. Two ion pumps are especially important in cellular neurophysiology: the sodium-potassium pump and the calcium pump. The sodium-potassium pump is an enzyme that breaks down ATP in the presence of internal Na+. The chemical energy released by this reaction drives the pump, which exchanges internal Na+ for external K+. The actions of this pump ensure that K+ is concentrated inside the neuron and that Na+ is concentrated outside. Notice that the pump pushes these ions across the membrane against their concentration gradients (Figure 3.16). This work requires the expenditure of metabolic energy. Indeed, it has been estimated that the sodium-potassium pump expends as much as 70% of the total amount of ATP utilized by the brain.
FIGURE 3.16 The sodium-potassium pump. This ion pump is a membrane-associated protein that transports ions across the membrane against their concentration gradients at the expense of metabolic energy.
The calcium pump is also an enzyme that actively transports Ca2+ out of the cytosol across the cell membrane. Additional mechanisms decrease intracellular [Ca2+] to a very low level (0.0002 mM); these include intracellular calcium-binding proteins and organelles, such as mitochondria and types of endoplasmic reticulum, which sequester cytosolic calcium ions.
Ion pumps are the unsung heroes of cellular neurophysiology. They work in the background to ensure that the ionic concentration gradients are established and maintained. These proteins may lack the glamour of a gated ion channel, but without ion pumps, the resting membrane potential would not exist and the brain would not function.
Relative Ion Permeabilities of the Membrane at Rest
The pumps establish ionic concentration gradients across the neuronal membrane. With knowledge of these ionic concentrations, we can use the Nernst equation to calculate equilibrium potentials for the different ions (see Figure 3.15). Remember, though, that an equilibrium potential for an ion is the membrane potential that would result if a membrane were selectively permeable to that ion alone. In reality, however, neurons are not permeable to only a single type of ion. How does that affect our understanding?
Let’s consider a few scenarios involving K+ and Na+. If the membrane of a neuron were permeable only to K+, the membrane potential would equal EK, which, according to Figure 3.15, is –80 mV. On the other hand, if the membrane of a neuron were permeable only to Na+, the membrane potential would equal ENa, 62 mV. If the membrane were equally permeable to K+ and Na+, however, the resulting membrane potential would be some average of ENa and EK. What if the membrane were 40 times more permeable to K+ than it is to Na+? The membrane potential again would be between ENa and EK but much closer to EK than to ENa. This approximates the situation in real neurons. The actual resting membrane potential of –65 mV approaches, but does not reach, the potassium equilibrium potential of –80 mV. This difference arises because, although the membrane at rest is highly permeable to K+, there is also a steady leak of Na+ into the cell.
The resting membrane potential can be calculated using the Goldman equation, a mathematical formula that takes into consideration the relative permeability of the membrane to different ions. If we concern ourselves only with K+ and Na+, use the ionic concentrations in Figure 3.15, and assume that the resting membrane permeability to K+ is fortyfold greater than it is to Na+, then the Goldman equation predicts a resting membrane potential of –65 mV, the observed value (Box 3.3).
If the membrane of a real neuron were permeable only to K+, the resting membrane potential would equal EK, about –80 mV. But it does not; the measured resting membrane potential of a typical neuron is about –65 mV. This discrepancy is explained because real neurons at rest are not exclusively permeable to K+; there is also some Na+ permeability. Stated another way, the relative permeability of the resting neuronal membrane is quite high to K+ and low to Na+. If the relative permeabilities are known, it is possible to calculate the membrane potential at equilibrium by using the Goldman equation. Thus, for a membrane permeable only to Na+ and K+ at 37° C:
where Vm is the membrane potential, PK and PNa are the relative permeabilities to K+ and Na+, respectively, and the other terms are the same as for the Nernst equation.
If the resting membrane ion permeability to K+ is 40 times greater than it is to Na+, then solving the Goldman equation using the concentrations in Figure 3.15 yields:
The Wide World of Potassium Channels. As we have seen, the selective permeability of potassium channels is a key determinant of the resting membrane potential and therefore of neuronal function. What is the molecular basis for this ionic selectivity? Selectivity for K+ ions derives from the arrangement of amino acid residues that line the pore regions of the channels. It was a major breakthrough in 1987 when researchers succeeded in determining the amino acid sequences of a family of potassium channels in the fruit fly Drosophila melanogaster. While these insects may be annoying in the kitchen, they are extremely valuable in the lab because their genes can be studied and manipulated in ways that are not possible in mammals.
Normal flies, like humans, can be put to sleep with ether vapors. While conducting research on anesthetized insects, investigators discovered that flies of one mutant strain responded to the ether by shaking their legs, wings, and abdomen. This strain of fly was designated Shaker. Detailed studies soon explained the odd behavior by a defect in a particular type of potassium channel (Figure 3.17a). Using molecular biological techniques, it was possible to map the gene that was mutated in Shaker. Knowledge of the DNA sequence of what is now called the Shaker potassium channel enabled researchers to find the genes for other potassium channels based on sequence similarity. This analysis has revealed the existence of a very large number of different potassium channels, including those responsible for maintaining the resting membrane potential in neurons.
FIGURE 3.17 The structure of a potassium channel. (a) Shaker potassium channels in the cell membrane of the fruit fly Drosophila, viewed from above with an electron microscope. (Source: Li et al., 1994; Fig. 2.) (b) The Shaker potassium channel has four subunits arranged like staves of a barrel to form a pore. Enlargement: The tertiary structure of the protein subunit contains a pore loop, a part of the polypeptide chain that makes a hairpin turn within the plane of the membrane. The pore loop is a critical part of the filter that makes the channel selectively permeable to K+. Description
Most potassium channels have four subunits that are arranged like the staves of a barrel to form a pore (Figure 3.17b). Despite their diversity, the subunits of different potassium channels have common structural features that bestow selectivity for K+. Of particular interest is a region called the pore loop, which contributes to the selectivity filter that makes the channel permeable mostly to K+ (Figure 3.18).
FIGURE 3.18 A view of the potassium channel pore. The atomic structure of potassium-selective ion channels has recently been solved. Here we are looking into the pore from the outside in a three-dimensional model of the atomic structure. The red ball in the middle is a K+. (Source: Doyle et al., 1998.)
In addition to flies, the deadly scorpion also made an important contribution to the discovery of the pore loop as the selectivity filter. In 1988, Brandeis University biologist Chris Miller and his student Roderick MacKinnon observed that scorpion toxin blocks potassium channels (and poisons its victims) by binding tightly to a site within the channel pore. They used the toxin to identify the precise stretch of amino acids that forms the inside walls and selectivity filter of the channel (Box 3.4). MacKinnon went on to solve the three-dimensional atomic structure of a potassium channel. This accomplishment revealed, at long last, the physical basis of ion selectivity and earned MacKinnon the 2003 Nobel Prize in Chemistry. It is now understood that mutations involving only a single amino acid in this region can severely disrupt neuronal function.
For me, the practice of scientific discovery has always been tightly linked to play. The self-indulgent pleasure of just fiddling around with a problem is what motivated the early stages of every research project I’ve ever engaged in. Only later comes the intense itch scratching, scholarship, and sweat needed to attack—and sometimes solve—the puzzles presented by nature. The sandbox I’ve been playing in for the past 40 years contains what are to me the most fascinating of toys: ion channels, the membrane-spanning proteins that literally make the electrical signals of neurons, breathing life into the nervous system. To the extent that the brain is a computer—an inaccurate but evocative analogy—the ion channels are the transistors. In response to biological dictates, these tiny proteinaceous pores form diffusion pathways for ions such as Na+, K+, Ca2+, H+, and Cl–, which carry electrical charge across membranes, thereby generating, propagating, and regulating cell voltage signals. I fell in love with these proteins long ago when I accidentally stumbled upon an unexpected K+ channel in experiments initially aimed at capturing a completely different sort of beast, a Ca2+-activated enzyme, and over the years that love has only deepened as I’ve wandered around in a teeming electrophysiological zoo housing many species of ion channel proteins.
An undergraduate background in physics and subsequent experience as a high school math teacher delivered me in the 1970s to graduate school, post-doctoral training, and my own lab at Brandeis with no formal preparation in (and precious little knowledge of) neurobiology or electrophysiology. Picking up bits and pieces of these subjects from reading the literature and osmosing them from my surroundings, I became increasingly fascinated by how ion channels, at that time only just nailed down as proteins, could do their job of producing bioelectricity; in parallel, I grew increasingly horrified by what struck me as the overwhelming complexity of living cells and the ambiguity in molecular interpretation that would inevitably accompany experiments done exclusively on cellular membranes. This combination of fascination and horror provoked my attraction to simplified “artificial membranes” of defined composition, developed by Paul Mueller in the 1960s, with which to follow the electrical activities of ion channels isolated from their complex cellular homes. I worked out a method for inserting single channel molecules from excitable cells into these chemically controllable membranes and used it to record single K+ channels at a time when card-carrying neurobiologists were beginning to observe single channels in native excitable membranes with the then-new cellular patch-recording methods. I confess that my early technique-building experiments were just play. To watch and control individual protein molecules dancing electrically before my eyes in real time was—and still is—an indescribable thrill, regardless of the particular tasks the channels carry out for the cell.
Eventually, this play led me to compelling problems that could be advantageously attacked with this reductionist approach. By the mid-1980s, my lab was home to a collection of supremely talented post-docs—Gary Yellen, Rod MacKinnon, and Jacques Neyton among them—going after the remarkable ion selectivity of various K+ channels: How do they tell the difference between ions as similar as K+ and Na+, as they must do if neurons are to fire action potentials, and if we are to think, feel, and act? Having stumbled, while purposelessly fooling around with natural neurotoxins, on a scorpion venom peptide that blocks K+ channels, we used the power of single-channel analysis to show that this toxin works by plugging up the protein’s K+-selective pore, just like a cork in a bottle (Figure A). In 1988, Rod took our toxin peptide to a Cold Spring Harbor laboratory course he’d signed up for to learn how to express ion channels by recombinant DNA methods. There he made a key discovery: that the toxin also blocks Shaker, the first genetically manipulable K+ channel, cloned the previous year in the lab of Lily and Yuh-Nung Jan. This chance finding led us, by making specific mutations, to a localized region in the channel’s amino acid sequence that forms the outer entryway of the K+ selective pore, a result immediately applicable to the entire family of voltage-dependent K+, Na+, and Ca2+ channels. A few years later, Rod and Gary, as newly hatched independent investigators, collaboratively homed in on these pore sequences to find the ion-selectivity hot spots, a result that propelled Rod, 7 years later, to bag the first X-ray crystal structure of a K+ channel and to begin a whole new “structural era” in ion channel studies.
Figure A The extracellular opening of a K+ channel with bound scorpion toxin envisioned indirectly in the “pre-structural” days by probing the channel with the toxin of known structure. Points of interaction: site on channel that makes contact with toxin (dark blue circles), key lysine residue on toxin that intrudes into the narrow pore (pale blue circle with +), a K+ displaced downward into the pore by binding of toxin (yellow circle with +). The yellow scale bar represents 2 nm. (Source: Adapted from Goldstein et al. 1994. Neuron 12:1377–1388.)
Looking back at my wrestling matches with ion channels, it is clear that the greatest joy I’ve derived from this endeavor has arisen from seeing—and being surprised by—new and unexpected elements of beauty and coherence in the natural world. This feeling was described by the great theoretical physicist Richard Feynman who, in a riposte to a W.H. Auden poem that dismisses scientific motivation as merely utilitarian, asserted that research scientists, like poets, are driven mainly by aesthetic forces: “We want knowledge so we can love Nature more.”
An example of this is seen in a strain of mice called Weaver. These animals have difficulty maintaining posture and moving normally. The defect has been traced to the mutation of a single amino acid in the pore loop of a potassium channel found in specific neurons of the cerebellum, a region of the brain important for motor coordination. As a consequence of the mutation, Na+ as well as K+ can pass through the channel. Increased sodium permeability causes the membrane potential of the neurons to become less negative, thus disrupting neuronal function. (Indeed, the absence of the normal negative membrane potential in these cells is believed to be the cause of their untimely death.) In recent years, it has become increasingly clear that many inherited neurological disorders in humans, such as certain forms of epilepsy, are explained by mutations of specific potassium channels.
The Importance of Regulating the External Potassium Concentration. Because the neuronal membrane at rest is mostly permeable to K+, the membrane potential is close to EK. Another consequence of high K+ permeability is that the membrane potential is particularly sensitive to changes in the concentration of extracellular potassium. This relationship is shown in Figure 3.19. A tenfold change in the K+ concentration outside the cell, [K+]o, from 5 to 50 mM, would change the membrane potential from –65 to –17 mV. A change in membrane potential from the normal resting value (–65 mV) to a less negative value is called a depolarization of the membrane. Therefore, increasing extracellular potassium depolarizes neurons.
FIGURE 3.19 The dependence of membrane potential on external potassium concentration. Because the neuronal membrane at rest is mostly permeable to potassium, a tenfold change in [K+]o, from 5 to 50 mM, causes a 48 mV depolarization of the membrane. This function was calculated using the Goldman equation (see Box 3.3). Description
The sensitivity of the membrane potential to [K+]o has led to the evolution of mechanisms that tightly regulate extracellular potassium concentrations in the brain. One of these is the blood-brain barrier, a specialization of the walls of brain capillaries that limits the movement of potassium (and other bloodborne substances) into the extracellular fluid of the brain.
Glia, particularly astrocytes, also possess efficient mechanisms to take up extracellular K+ whenever concentrations rise, as they normally do during periods of neural activity. Remember, astrocytes fill most of the space between neurons in the brain. Astrocytes have membrane potassium pumps that concentrate K+ in their cytosol, and they also have potassium channels. When [K+]o increases, K+ enters the astrocyte through the potassium channels, causing the astrocyte membrane to depolarize. The entry of K+ increases the internal potassium concentration, [K+]i, which is believed to be dissipated over a large area by the extensive network of astrocytic processes. This mechanism for the regulation of [K+]o by astrocytes is called potassium spatial buffering (Figure 3.20).
FIGURE 3.20 Potassium spatial buffering by astrocytes. When brain [K+]o increases as a result of local neural activity, K+ enters astrocytes via membrane channels. The extensive network of astrocytic processes helps dissipate the K+ over a large area.
It is important to recognize that not all excitable cells are protected from increases in potassium. Muscle cells, for example, do not have equivalents to the blood-brain barrier or glial buffering mechanisms. Consequently, although the brain is relatively protected, elevations of [K+] in the blood can still have serious consequences on body physiology (Box 3.5).
On June 4, 1990, Dr. Jack Kevorkian shocked the medical profession by assisting in the suicide of Janet Adkins. Adkins, a 54-year-old, happily married mother of three, had been diagnosed with Alzheimer’s disease, a progressive brain disorder that always results in senile dementia and death. Mrs. Adkins had been a member of the Hemlock Society, which advocates euthanasia as an alternative to death by terminal illness. Dr. Kevorkian agreed to help Mrs. Adkins take her own life. In the back of a 1968 Volkswagen van at a campsite in Oakland County, Michigan, she was hooked to an intravenous line that infused a harmless saline solution. To choose death, Mrs. Adkins switched the solution to one that contained an anesthetic solution, followed automatically by potassium chloride. The anesthetic caused Mrs. Adkins to become unconscious by suppressing the activity of neurons in part of the brain called the reticular formation. Cardiac arrest and death were then caused by the KCl injection. The ionic basis of the resting membrane potential explains why the heart stopped beating.
Recall that the proper functioning of excitable cells (including those of cardiac muscle) requires that their membranes be maintained at the appropriate resting potential whenever they are not generating impulses. The negative resting potential is a result of selective ionic permeability to K+ and to the metabolic pumps that concentrate potassium inside the cell. However, as Figure 3.19 shows, membrane potential is very sensitive to changes in the extracellular concentration of potassium. A tenfold rise in extracellular K+ would severely diminish the resting potential. Although neurons in the brain are somewhat protected from large changes in [K+]o, other excitable cells in the body, such as muscle cells, are not. Without negative resting potentials, cardiac muscle cells can no longer generate the impulses that lead to contraction, and the heart immediately stops beating. Intravenous potassium chloride is, therefore, a lethal injection.
We have now explored the resting membrane potential. The activity of the sodium-potassium pump produces and maintains a large K+ concentration gradient across the membrane. The neuronal membrane at rest is highly permeable to K+, owing to the presence of membrane potassium channels. The movement of K+ ions across the membrane, down their concentration gradient, leaves the inside of the neuronal membrane negatively charged.
The electrical potential difference across the membrane can be thought of as a battery whose charge is maintained by the work of the ion pumps. In the next chapter, we see how this battery runs our brain.
ionic equilibrium potential (equilibrium potential) (p. 68)
1. What two functions do proteins in the neuronal membrane perform to establish and maintain the resting membrane potential?
2. On which side of the neuronal membrane are Na+ ions more abundant?
3. When the membrane is at the potassium equilibrium potential, in which direction (in or out) is there a net movement of potassium ions?
4. There is a much greater K+ concentration inside the cell than outside. Why, then, is the resting membrane potential negative?
5. When the brain is deprived of oxygen, the mitochondria within neurons cease producing ATP. What effect would this have on the membrane potential? Why?
Hille B. 2001. Ionic Channels of Excitable Membranes, 3rd ed. Sunderland, MA: Sinauer.
MacKinnon R. 2003. Potassium channels. Federation of European Biochemical Societies Letters 555:62–65.
Nicholls J, Martin AR, Fuchs PA, Brown DA, Diamond ME, Weisblat D. 2011. From Neuron to Brain, 5th ed. Sunderland, MA: Sinauer.
Somjen GG. 2004. Ions in the Brain: Normal Function, Seizures, and Stroke. New York: Oxford University Press.
Additional figures
