Electrical Properties of Mammalian Cells

Matter is composed of atoms, which consist of positively charged nuclei and negatively charged electrons. Electrical phenomena occur whenever charges opposite in sign are separated or moved in a given direction; static electricity is the accumulation of electric charge. An electric current results when these charges flow across a permissive material, called a conductor. An ion current is a particular type of current carried by charges present on atoms or small molecules flowing in an aqueous solution. Separation of charges in an aqueous solution can be achieved by inserting an impermeable membrane in the solution itself. In mammalian cells, these membranes coincide with the plasma membrane, and its lipophilic composition ensures a remarkable level of electrical isolation for cells and tissues. Excitable as well as most nonexcitable cells are characterized by an asymmetric distribution of electric charges across the plasma membrane.

The biophysical bases for maintenance of this electric potential have been extensively investigated experimentally and modeled by mathematical simulations. Under normal resting conditions, mammalian cells allow transmembrane ion currents such that the internal portion of the cell is negatively charged; the presence of nonpermeant anions such as proteins also contributes to the maintenance of transmembrane potentials. This relatively stable state results in a net transmembrane potential of several millivolts and is commonly referred to as the resting membrane potential (RMP) (Fig. 49-1).

FIGURE 49-1 Relationship between resting potential and [K⁺]_out. The line represents the “ideal” case predicted by the Nernst equation (see Equation 3). Experimental measurements show a significant departure from a linear dependency at physiologic [K⁺]_out values. Resting potential values for excitable and nonexcitable central nervous system cells are shown. BBB, blood-brain barrier; RMP, resting membrane potential.

Most of what we know about the physiology of excitable cells was derived from electrical measurements (Fig. 49-2). Our knowledge of the complex properties of the CNS is based on the application to neuronal cells of simple physical rules governing the movement of charged particles. The physical principles of cell electrophysiology can be thus be compared with the biophysical rules governing flow of electric current through a so-called RC circuit (see Fig. 49-2), where electrons flow through a resistive component (in the case of living cells, represented by ion channels) set in parallel with a capacitive component (represented by the poorly conductive phospholipid bilayer). Ohm’s law describes the relationship between current flow (I) and the resulting voltage drop (E) across a resistor when no capacitive component is present. This is, of course, an abstract situation, in particular when dealing with ion fluxes across biologic membranes, but it allows one to understand the basic principles governing flow of electric current.

FIGURE 49-2 Methodologies commonly used for the investigation of mammalian central nervous system physiology. A, Neuronal and non-neuronal cells are investigated in vitro and in vivo by patch clamp recording. The electrophysiologic properties of the cell (“whole-cell configuration”) and of individual membrane channels (“cell-attached configuration”) can be investigated. B, The corresponding electric circuit for a cell is shown (see text). C, Voltage-activated channels are frequently studied by investigating the changes in channel and cellular properties that result from applied hyperpolarization and depolarization, whereas receptor-activated channels are usually studied by the application of appropriate receptor agonists and antagonists. D, The differences between voltage clamp and current clamp recordings are shown. Voltage clamp recordings allow the study of ion currents and their modulation by voltage, or transmitters/second messengers, whereas current clamp experimentation is commonly used to determine resting properties and the excitability of cells.

The following relationship constitutes Ohm’s law (or principle):

(1)

where I represents the current flowing through a resistance (R) when voltage is applied. In a hypothetical cell, this relationship can be written as follows:

(2)

where E_m represents the difference in voltage (in millivolts) between the inside and the outside of the cell, I_m represents the net current flowing at that particular time across the cell membrane, and R_m is the total membrane resistance. An important consequence of this relationship is that small changes in current will significantly affect cell RMP only when R_m is large. This is particularly important for inhibitory synaptic currents; for instance, in the case of γ-aminobutyric acid receptor A (GABA_A) activation, inhibition is achieved not only by hyperpolarizing cell RMP further away from the firing threshold but also by greatly increasing postsynaptic conductance,* thus reducing the synaptic efficacy of concomitant excitatory signals.

A mathematical derivation of Ohm’s law useful for studies of biologic membranes was first formulated by Nernst,¹ who described the relationship between intracellular and extracellular ion concentrations and changes in transmembrane potential attributable to permeation of an ion. In the case of potassium ions, the Nernst equation can be written as follows:

(3a)

where R and F are constants, T is the temperature at which the observation is performed, and Z is the charge of the permeant ion. Note that if the charge (sign, or “Z” in Equation 3) of the permeant ion is changed (e.g., if we look at the Nernst equation for chloride), the direction of the gradient is changed as well. The logarithm of the ratio between intracellular and extracellular K⁺ dominates the right side of the equation because RT/ZF is constant under most biologic conditions when temperature can be maintained within a few degrees. This equation predicts, as expected from Ohm’s law, that net potassium flux will approach zero when intracellular and extracellular potassium levels are isosmolar, that is, when E_K = 0 mV. Under physiologic conditions ([K⁺]_out = 3.5 mM; [K⁺]_in = 135 mM), the transmembrane potential at which potassium flux will be nil is around −90 mV.* This value constitutes the potassium equilibrium potential at these concentrations. Note that small changes in the extracellular potassium concentration will cause relatively large changes in the fraction of total membrane currents attributable to potassium ions. Because permeability to potassium is essential for maintenance of RMP, a net increase in extracellular potassium will cause a significant departure from RMP (see Fig. 49-1).

In practical form, the Nernst equation for potassium can be rewritten by converting to log₁₀ and calculating RT/ZF at 20°C. This rearrangement leads to

(4)

It can be seen that a 10-fold change in the concentration gradient for potassium can produce a 58-mV change in membrane potential. Because under normal conditions there is an almost 40-fold outward gradient for potassium ions and a 12-fold inward gradient for sodium ions, the resulting equilibrium potentials are −92 mV and +65 mV, respectively. Since the membrane at rest is much more permeable to potassium than to sodium (see later), RMP is closer to E_K than to E_Na.

Two additional considerations can help us understand the genesis of cell RMP: (1) if the membrane is exclusively permeant to K⁺ and no active, electrogenic transport of ions occurs, the cell potential will tend toward E_K and only small movements of K⁺ will be sufficient to maintain RMP at −92 mV, and (2) if the membrane potential is clamped at E_K, net potassium flux will be zero (as predicted by the fact that E_K is the equilibrium potential for potassium). If the membrane potential is held positive with respect to E_K, outward potassium currents will develop; conversely, if RMP is held at potentials negative with respect to E_K, inward potassium fluxes will develop. Interestingly, the notion that cell RMP is controlled by potassium ions was first derived independently from direct observations: Julius Bernstein in 1902 correctly predicted that in most mammalian cells, potassium ions govern the transmembrane voltage difference.² Direct experimental evidence was achieved only half a century later when a microelectrode could be placed into cells to directly measure RMP and the effects of changing [K⁺]_out. Bernstein also proposed that selective potassium permeability was lost during the process of excitation, during which numerous “pores” opened to allow entry of other small ions (Cl⁻ and Na⁺).² This theory explained several features of the regulation of RMP and generation of action potentials, including the depolarizing effects of [K⁺]_out.

In fact, a prediction of the formalism just presented is that RMP changes linearly with [K⁺]_out. As shown in Figure 49-1, experimental evidence contradicts this notion, at least in the case of mammalian neurons.† Most neurons depolarize significantly after large changes in extracellular potassium, whereas changes around physiologic potassium concentrations do not significantly affect neuronal RMP. This can only be due to concomitant participation of other conductances. Although the exact nature of the ionic conductances contributing to the regulation of neuronal RMP varies between different neurons, a generic set of equations predict how these “parallel” conductances may affect E_m. The most illustrious of these equations was provided by Goldman, who described the expected RMP in a cell endowed with more than one ion current mechanism as

(5)

where G_K, G_Na, and G_Cl represent the conductances for potassium, sodium, and chloride.³ Note that these conductance values are multiplied by the relative chemical concentration gradient for each ion, thus combining the “passive” electro-osmotic tendency for ion permeation with the average conductance of the membrane for a particular ion. Note also that if G_Cl and G_Na are close to zero, the transmembrane potential is governed almost exclusively by potassium ions and their conductance. This condition is common at resting potential in most neurons and glial cells, where I_K (and to some extent I_pump) determines RMP (Fig. 49-3).

FIGURE 49-3 Maintenance of neuronal resting membrane potential. At rest, passive movement of potassium out of the cell is balanced by movement of sodium into the cell. The ion fluxes are the product of the electrochemical gradient and the membrane conductance for each ion. The high gradient but low conductance of sodium influx is balanced by the lower gradient (at resting membrane potential) but higher conductance of potassium efflux. To prevent the dissipation of ionic gradients over time, the electrogenic sodium-potassium adenosine triphosphate (Na⁺,K⁺-ATPase) pump extrudes three sodium ions in exchange for two potassium ions per molecule of adenosine triphosphate expended, thereby further hyperpolarizing the membrane.

In 1949, Alan Hodgkin and Bernard Katz first applied the Goldman equation systematically to changes in membrane potentials evoked by altering external ion concentrations in the squid giant axon.⁴ They measured changes in RMP induced by changes in [K⁺]_out, [Na⁺]_out, and [Cl⁻]_out. They discovered that although changes in extracellular potassium dramatically changed RMP, comparable changes in [Na⁺]_out had little effect. Changing [Cl⁻]_out had an intermediate effect. The following permeability ratios were obtained at rest:

(6a)

When the measurements were performed at the peak of the action potential, however, these values changed dramatically to yield

(6b)

Therefore, when the predominant membrane conductance is P_K, the Goldman equation can be reduced to the Nernst equation for potassium:

(3b)

whereas when P_Na predominates, the following applies:

(3c)

which is approximately the peak value of action potential overshoot. Direct measurement of changes in the relative permeability for Na⁺ and K⁺ contradicted one of the hypotheses formulated by Bernstein, who incorrectly predicted that neuronal excitation was due to loss of potassium permeability rather than activation of an inward sodium current (Table 49-1). Had this hypothesis been correct, the maximum depolarizing value reached during the action potential would have been around 0 mV and not at +30 mV as experimentally determined by Hodgkin and Katz.

TABLE 49-1 Glossary of Commonly Used Electrophysiologic Terms

EPSP, excitatory postsynaptic potential; IPSP, inhibitory postsynaptic potential; RMP, resting membrane potential.

It has become apparent more recently that I_Na is not the only ionic current that can generate action potentials; calcium ions also play an important role in neuronal excitability. Similarly, I_K is not the exclusive component of the electrical regulation of cell resting properties inasmuch as several other conductances are involved in the control of neuronal resting potential.

Ion Channels in Neurons and Glia

Ion channels are protein channels in cell membranes that allow ions to pass from the extracellular solution to the intracellular solution and vice versa. Similarly, transporters are specialized enzymes that carry specific ions or molecules across otherwise impermeant membranes or against electro-osmotic gradients. Not surprisingly, from a purely thermodynamic (or energetic) point of view, ion channels are less “expensive” to operate, whereas pumps or exchangers require considerable consumption of energy. Most ion channels and pumps are selective in that they allow only certain ions to pass, and an individual cell has ion channels with various ion selectivity. In the context of studies of biologic cell membranes, the term ion selectivity refers to the ability of all cell membranes to distinguish between various ions such as Na⁺, K⁺, Ca²⁺, and Cl⁻. We will focus on Na⁺, K⁺, and Ca²⁺ channels. All of these voltage-gated channels are made up of one or more pore-forming α subunits and variable numbers of accessory subunits, denoted β, γ, and so on. The α subunits determine ion selectivity and mediate the voltage-sensing functions of the channel. This ion selectivity involves specific pores or channels in the cell membrane, with certain channels being specific for certain ions and the opening or closing (gating) of channels depending on conditions and various interactions with ligands binding to receptors. These receptors are in some cases part of the channel itself and in other cases neighboring entities that control channel dynamics. The selectivity of an ion channel can be “gated,” with the channel effectively opened or closed, and ion channels are said to be voltage gated or ligand gated, depending on how the change in selectivity is provoked. A summary of the most studied CNS ion channels is presented in Table 49-2.

Genesis of Fast Sodium Action Potentials and Properties of Sodium Channels

Neuronal cells use a single type of signaling based on all-or-nothing action potentials. Sodium action potentials such as those recorded in axons or cell bodies are relatively invariant in normal tissue, and thus the shape and duration of these electrical signals do not change significantly within neuronal subtypes in the nervous system. Calcium action potentials are similarly predictable, but the underlying ionic mechanism can be rather complex, depending on the cell type and its topographic location within the cell (see later). The terms sodium action potential and calcium action potential refer to the initial (depolarizing) phase of these rapid changes in membrane polarity. Although genetic or molecular alteration of I_Na and I_Ca can significantly affect neuronal firing and, ultimately, central and peripheral nervous system neurophysiology, it must be remembered that gross changes in neuronal excitability may also result by altering the repolarization phase of individual action potentials.

Action potentials have a characteristic shape once a certain threshold is reached. In normal tissue, stereotyped electrical events follow the initial depolarization (Fig. 49-4). The sequence can be described as follows: (1) RMP moves from an initial negative value (−65 to −80 mV for most neurons) toward the so-called threshold for activation of sodium channels (around −40 mV). This change can be slow and may occur spontaneously as a result of fluctuations in RMP; the threshold is reached rapidly when the initial depolarization is triggered by a synaptic potential (or a summation of synaptic potentials). (2) After reaching the threshold value, an extremely rapid (1 to 2 msec) depolarization occurs because of opening of sodium channels and massive influx of sodium ions into the cell. (3) Termination of the “upstroke” phase depends on a combination of factors: voltage– and time-dependent inactivation of I_Na and a concomitant decrease in the driving force for sodium occurring in parallel with voltage-dependent activation of I_K. (4) Further increases in the permeability to potassium ions restore the pre–action potential RMP values and force the membrane toward E_K. (5) Under most circumstances, an undershoot of cell resting voltage occurs (a few millivolts from RMP) as a result of residual activation of I_K and the contribution of the electrogenic sodium-potassium adenosine triphosphatase (Na⁺,K⁺-ATPase) extruding 3 Na⁺ ions in exchange for 2 K⁺. The return to pre–action potential voltage favors the so-called removal of inactivation, a necessary step that allows a subsequent cycle of depolarization-induced action potential firing. This stereotyped and relatively simple sequence of events is typically recorded in axons; other more complex interactions of various I_Na and I_K values may lead to slightly different voltage profiles.

FIGURE 49-4 Changes in conductance during generation of an action potential.

From a functional standpoint, it is important to remember that the genesis of fast sodium action potentials is a hallmark of neuronal function, to the degree that during neurophysiologic recordings, the presence or absence of Na⁺ spikes is frequently used to determine the neuronal or glial cell type. Recently, this notion has been challenged, and glial “action potentials” have been reported with increasing frequency. These responses, however, appear to usually be associated with pathologic conditions (brain tumors, epilepsy), and the old perception that neuronal cells are the exclusive tenants of sufficient I_Na density to promote active responses is still generally accepted. Within the same neuronal cell, Na⁺ channels involved in the generation of action potentials can be located heterogeneously, and it is common for clusters of channels to be located at specific and crucial membrane segments. The most commonly encountered clustering of Na⁺ channels occurs at the node of Ranvier of myelinated axons, but clustering also occurs at synaptic contacts, dendrites, and cell bodies, in proximity to the initial segment of axons.

Early pharmacologic studies attempting to elucidate the ionic correlates of the action potential greatly benefited from the availability of naturally occurring toxins that specifically and powerfully block I_Na. The magic bullet for sodium channels was tetrodotoxin (TTX),⁵ a lethal poison produced by a selected species of puffer fish (Fugu). TTX is present in large quantities in the liver and female genital organs, but the real culinary treat is the testes of this hermaphroditic animal. Separation of the toxic portions is paramount to survival of the consumer. The sea anemone toxin (ATX) and α-scorpion toxin are also powerful blockers of I_Na. TTX and other natural toxins block the external portion of the ion channel. Interestingly, although most sodium channels are blocked by micromolar concentrations of TTX, genetic ablation of one amino acid (Tyr or Phe) in the sequence of the ion channel protein confers relative resistance to TTX because binding of the toxin is restricted to this region.⁶ The amazing specificity of TTX binding suggested that normally occurring variation in the amino acid sequence of ion channels may prove to be an extremely important determinant of not only the pharmacologic properties of the channels but also their inactivation/activation/voltage dependency. In fact, although the poisonous actions of TTX are primarily due to direct blockade of Na⁺ fluxes through the channel’s pore, ATX and α-scorpion toxin bind to a portion responsible for channel inactivation. Mutations in these regions cause faulty inactivation, a condition linked to neuropathogenesis.

The biophysical correlates of Na⁺ channel function are well understood today. The general scheme of

explains the properties of whole-cell I_Na recorded from neurons. The voltage dependency of each process justifies the initial depolarization required to promote the opening of channels; the consequent depolarization induced by sodium current promotes further opening of channels, the process being terminated by time- and voltage-dependent closure of the channels. The passage from closed to open (and visa versa) is referred to as activation (deactivation), whereas the passage from open to inactivated is called inactivation. Removal of inactivation occurs when the channel returns to its closed state.

From a structural point of view, Na⁺ channels are constituted by αβ1β2 heterotrimers, often with four repeated domains each with six-membrane–spanning subunits. The voltage sensor is located on the fourth transmembrane domain. Different subunits are represented differently in the central and peripheral nervous systems. According to the recent literature, the following tissue-specific localization and pharmacology can be derived: for α subunits, SCN1A is primarily expressed in brain tissue and is blocked by TTX and saxitoxin (SXT). The most abundant brain α subunit is encoded by SCN2A1; this subunit is also found in peripheral nerves, in the initial axonal segment, and in the nodes of Ranvier (TTX and SXT sensitive). SCN2A2 and SC2NA3 are predominantly expressed in the brain, whereas SCN4A encodes channels found in muscle. In addition to TTX, these channels are sensitive to ω-conotoxins (GIIIA, GIIIB, GIIIC). Mutations of these channels are responsible for hyperkalemic periodic paralysis, paramyotonia, and myotonia. The SCN5A subunit is expressed in the heart and in denervated skeletal muscle; in the heart, these channels are responsible for upstroke of the action potential. These subunits are resistant to blockade by TTX and SXT; mutations of these genes are involved in subtypes of long QT syndrome, a cardiac condition that is sometimes associated with epileptic seizures. SCN6A (uterus), SCN10A, SCN11A, and SCN9A (dorsal root ganglion) are all sensitive to TTX. The molecular nature of glial sodium channels and the contribution of a specific α subunit are not fully understood at present. β Subunits are bound covalently to α subunits and provide inactivation kinetics to Na⁺ channels. Mutations of these SCN1B and SCN1A subunits have been linked to generalized epilepsy with febrile seizures (see Catterall and colleagues⁷ and Gambardella and Marini⁸ for review of voltage-gated ion channel–related hereditary diseases).

The fact that even slight mutations cause profound deficits in sodium channel function and that these mutations result in neurological diseases leads to the hypothesis that replacement of defective channels by gene therapy may repristinate the loss of function caused by the initial genetic deficit. If a single gene mutation is responsible (as in cystic fibrosis and in a number of neurological disorders) and if the tissue to be transfected with the repair mechanism is accessible (such as skeletal muscle), it is possible that viral delivery of genetic products may alleviate the consequences of faulty ion channels. A positive outcome with this approach is somehow dependent on the pathogenesis of the disease itself. If the observed deficit is the consequence solely of the inherited mutation, replacement by a normal genotype is likely to be successful. If, however, the initial deficit has led to extensive rearrangement of neuronal connections or if the deficit causes extensive neuronal cell death (such as in epilepsy), it is unclear whether restoring normal function by simple gene replacement may be beneficial. It is also worth remembering that although a small fraction of neurological disorders are clearly imputable to a single gene mutation affecting a particular ion channel, the most common forms of disease result from a complex interaction of initial genotypic changes followed by adaptive responses, including apoptosis or necrosis. Finally, given that mutations of crucial ionic mechanisms such as I_Na affect cardiac, neuronal, and muscular function, it is possible that a large number of mutations are nonvital and that the vital mutations are possible because of redundancy of gene expression or compensatory overexpression of similar ion channel proteins.

Phenotypic changes caused by relatively minor alterations in ion channel gating sometimes become clinically relevant when concomitant deficits not necessarily associated with action potentials are present. This is the case, for example, in mutations of the SCN4A subunit leading to hyperkalemic periodic paralysis. For the paralytic symptoms to occur, patients must concomitantly experience variations in plasma potassium (by either K⁺ intake or exercise followed by rest). This leads to opening of Na⁺ channels that switch to a non-inactivating mode, thereby leading to the development of a persistent inward Na⁺ current. The ensuing depolarization of muscle membrane will further increase [K⁺]_out via loss through voltage-dependent K⁺ channels and thus aggravate the initial trigger. Furthermore, the persistent depolarization causes inactivation of normal Na⁺ channels, which leads to rapid loss of tissue excitability and paralysis. This example demonstrates the complex interactions between normal and abnormal ion channels expressed in a certain cell type, the importance of the extracellular milieu in biophysical signaling via ion channels, and the difficulties associated with the diagnosis of altered ion channel phenotypes.