Cardiac Electrophysiology and the Electrocardiogram


Different cardiac cells serve different and very specialized functions, but all are electrically active. The heart's electrical signal normally originates in a group of cells high in the right atrium that depolarize spontaneously; it then spreads throughout the heart from cell to cell ( Fig. 21-1 ). As this action potential propagates through the heart—sometimes carried by cells that form specialized conducting pathways and sometimes by the very cells that generate the force of contraction—it assumes different appearances within the different cardiac cells ( Fig. 21-2 ). Based on the speed of the upstroke, we can characterize action potentials as either slow (sinoatrial and atrioventricular nodes) or fast (atrial myocytes, Purkinje fibers, and ventricular myocytes).

Figure 21-1
Conduction pathways through the heart. A section through the long axis of the heart is shown.

Figure 21-2
Cardiac action potentials. The distinctive shapes of action potentials at five sites along the spread of excitation are shown.

Because the excitation of cardiac myocytes triggers contraction—a process called excitation-contraction coupling (see p. 229 )—the propagation of action potentials must be carefully timed to synchronize ventricular contraction and thereby optimize the ejection of blood. This chapter focuses on the membrane currents responsible for the generation and transmission of action potentials in heart tissue. We also examine how to record the heart's electrical flow by placing electrodes on the surface of the body to create one of the simplest and yet one of the most useful diagnostic tools available to the clinician—the electrocardiogram.

Electrophysiology of Cardiac Cells

The cardiac action potential starts in specialized muscle cells of the sinoatrial node and then propagates in an orderly fashion throughout the heart

The cardiac action potential originates in a group of cells called the sinoatrial (SA) node (see Fig. 21-1 ), located in the right atrium. These cells depolarize spontaneously and fire action potentials at a regular, intrinsic rate that is usually between 60 and 100 times per minute for an individual at rest. Both parasympathetic and sympathetic neural input can modulate this intrinsic pacemaker activity, or automaticity (see pp. 397–398 ).

Because cardiac cells are electrically coupled through gap junctions ( Fig. 21-3 A ), the action potential propagates from cell to cell in the same way that an action potential in nerve conducts along a single long axon. A spontaneous action potential originating in the SA node will conduct from cell to cell throughout the right atrial muscle and spread to the left atrium. The existence of discrete conducting pathways in the atria is still disputed. About one tenth of a second after its origination, the signal arrives at the atrioventricular (AV) node (see Fig. 21-1 ). The impulse does not spread directly from the atria to the ventricles because of the presence of a fibrous atrioventricular ring. Instead, the only available pathway is for the impulse to travel from the AV node to the His-Purkinje fiber system, a network of specialized conducting cells that carries the signal to the muscle of both ventricles.

Figure 21-3, Conduction in the heart. A, An action potential conducting from left to right causes intracellular current to flow from fully depolarized cells on the left, through gap junctions, and into cell A. Depolarization of cell A causes current to flow from cell A to cell B ( I AB ). Part of I AB discharges the capacitance of cell B (depolarizing cell B), and part flows downstream to cell C. B, Subthreshold depolarization of cell A decays with distance. C, The speed of conduction increases with greater depolarization of cell A (blue versus red curve) or with a more negative threshold.

The cardiac action potential conducts from cell to cell via gap junctions

The electrical influence of one cardiac cell on another depends on the voltage difference between the cells and on the resistance of the gap junction connecting them. A gap junction (see p. 205 ) is an electrical synapse (see Fig. 21-3 A ) that permits electrical current to flow between neighboring cells. According to Ohm's law, the current flowing between cell A and the adjacent cell B ( I AB ) is proportional to the voltage difference between the two cells (Δ V AB ) but inversely proportional to the electrical resistance between them ( R AB ):


I AB = V A V B R AB = Δ V AB R AB

When R AB is very small (i.e., when the cells are tightly coupled), the gap junctions are minimal barriers to the flow of depolarizing current.

Imagine that several interconnected cells are initially all at their normal resting potentials (see Fig. 21-3 B ). An action potential propagating from the left of cell A now injects depolarizing current into cell A. As a result, the cell depolarizes to V A , which is now somewhat positive compared with V B . Thus, a small depolarizing current (i.e., positive charges) will also move from cell A to cell B and depolarize cell B. In turn, current flowing from cell B will then depolarize cell C. By this process, the cells closest to the current source undergo the greatest depolarization.

Imagine that the injected current, coming from the active region of the heart to the left, depolarizes cell A just to its threshold (see Fig. 21-3 C , red curve) but that cell A has not yet fired an action potential. At this instant, the current passing from cell A to cell B cannot bring cell B to its threshold. Of course, cell A will eventually fire an action potential and, in the process, depolarize enough to inject enough current into cell B to raise cell B to its threshold. Thus, the action potential propagates down the chain of cells, but relatively slowly. On the other hand, if the active region to the left injects more current into cell A (see Fig. 21-3 C , blue curve)—producing a larger depolarization in cell A—the current passing from cell A to cell B will be greater and sufficient to depolarize cell B beyond its voltage threshold for a regenerative action potential. However, at this instant, the current passing from cell B to cell C is still not sufficient to trigger an action potential in cell C. That will have to wait until the active region moves closer to cell C, but the wait is not as long as in the first example (red curve in Fig. 21-3 C ). Thus, the action potential propagates more rapidly in this second example (blue curve in Fig. 21-3 C ).

In principle, we could make the action potential propagate more rapidly down the chain of cells in two ways. First, we could allow more ion channels to open in the active region of the heart, so that depolarizing current is larger (blue curve in Fig. 21-3 C ). Second, we could lower the threshold for the regenerative action potential (“more negative threshold” in Fig. 21-3 C ), so that even the small current represented by the red curve is now sufficient to trigger cell B.

Just as in a nerve axon conducting an action potential, the intracellular and extracellular currents in heart muscle must be equal and opposite. In the active region of the heart (to the left of cell A in Fig. 21-3 B ), cells have reached threshold and their action potentials provide the source of current that depolarizes cells that are approaching threshold (e.g., cells A and B). As cell A itself is depolarizing to and beyond threshold, its Na + and Ca 2+ channels are opening, enabling these cations (i.e., positive charge) to enter. The positive charge that enters cell A not only depolarizes cell A but also produces a flow of positive charge to cell B— intracellular current. This flow of positive charge discharges the membrane capacitance of cell B, thereby depolarizing cell B and releasing extracellular positive charges that had been associated with the membrane. The movement of this extracellular positive charge from around cell B toward the extracellular region around cell A constitutes the extracellular current. The flow of intracellular current from cell A to cell B and the flow of extracellular current from around cell B to around cell A are equal and opposite. It is the flow of this extracellular current in the heart that gives rise to an instantaneous electrical vector, which changes with time. Each point on an electrocardiogram (ECG) is the sum of the many such electrical vectors, generated by the many cells of the heart.

Cardiac action potentials have as many as five distinctive phases

The initiation time, shape, and duration of the action potential are distinctive for different parts of the heart, reflecting their different functions (see Fig. 21-2 ). These distinctions arise because the myocytes in each region of the heart have a characteristic set of channels and anatomy. Underlying cardiac action potentials are four major time-dependent and voltage-gated membrane currents ( Table 21-1 ): N21-1

TABLE 21-1
Major Cardiac Membrane Currents That Are Time Dependent and Voltage Gated
CURRENT NAME CHANNEL PROTEIN HUMAN GENE SYMBOL REVERSAL POTENTIAL OF CURRENT (mV) INHIBITORS
I Na Na + current Nav1.5 (voltage-gated Na + channel) SCN5A +60 TTX
Local anesthetics
I Ca Ca 2+ current Cav1.2 (L-type Ca 2+ channel) CACNA1C +120 Nifedipine
Verapamil
I K I to Kv4.3 + KChIP2 KCND3 + KCNIP2 −100 Tedisamil
Repolarizing Kv11.1 (HERG) + miRP1 * KCNH2 + KCNE 2 −100 Ba 2+
Cs +
TEA
Dolfetilide
E4031
Repolarizing Kv7.1 (KvLQT1) + minK * KCNQ1 + KCNE1 −100 HMR1556
L-768, 673
Benzopyran chromanol
Kir2.1
Kir2.2
KCNJ2
KCNJ12
−100 Ba 2+
ML133
G protein–activated I K,ACh Kir3.4 (GIRK4) * KCNJ5 −100
ATP-sensitive current, K ATP Kir6.1 + SUR1 or SUR2 *
Kir6.2 + SUR1 or SUR2 *
KCNJ8 + ABCC8 or ABCC9
KCNJ11 + ABCC8 or ABCC9
−100 Glibenclamide
I f (Na + + K + ) Pacemaker current HCN4 HCN4 −35 Cs +
GIRK, G protein–activated inwardly rectifying K + channel; HERG, human ether-à-go-go–related gene (related to Kv family of K + channel genes); KChIP2, Kv channel–interacting protein 2; TEA, tetraethylammonium; TTX, tetrodotoxin.

* These are heteromultimeric channels.

N21-1
Cardiac Ion Channels

The number of distinct ion channels found in heart cells has grown dramatically with the development of new tools. While the cellular and organ-level function follows the presentation in the text and this webnote, important subtleties in the detailed function can depend on the additional channel subtypes that may be expressed at varying levels and that can change under stress or during disease. For example, heart cells express not only the “cardiac” sodium channel (Nav1.5) but also other sodium channel types (e.g., Nav1.4, which is normally found in skeletal muscle; see Table 7-1 ). In addition to the L-type Ca 2+ channel, cardiac myocytes may also express the T-type Ca 2+ channel (see Table 7-2 ). In many diseases, the expression of the T-type Ca 2+ channel increases. Ventricular and atrial myocytes may express K + channels in a diversity much greater than described in the text. Moreover, the array of K + channels often changes in disease processes. eFigure 21-1 lists some of the prominent channels and how they contribute to the cardiac action potential.

eFigure 21-1, Membrane currents that underlie the cardiac action potential. The action potential time course is shown at top left with typical currents shown below on the left. The time course of inward (blue) and outward (green) currents is shown. The components of each channel type shown are presented on the right.

Reference

  • George AL: Molecular and genetic basis of sudden cardiac death. J Clin Invest 2013; 123: pp. 75-83.

  • 1

    The Na + current ( I Na ) is responsible for the rapid depolarizing phase of the action potential in atrial and ventricular muscle and in Purkinje fibers.

  • 2

    The Ca 2+ current ( I Ca ) is responsible for the rapid depolarizing phase of the action potential in the SA node and AV node; it also triggers contraction in all cardiomyocytes.

  • 3

    The K + current ( I K ) is responsible for the repolarizing phase of the action potential in all cardiomyocytes.

  • 4

    The pacemaker current ( I f ) is responsible, in part, for pacemaker activity in SA nodal cells, AV nodal cells, and Purkinje fibers.

Besides these four currents, channels carry numerous other currents in heart muscle. In addition, two electrogenic transporters N21-2 carry current across plasma membranes: the type 1 Na-Ca exchanger (NCX1; see pp. 123–124 ) and the Na-K pump (see pp. 115–117 ).

N21-2
Cardiac Currents Carried by Electrogenic Transporters

In addition to the channels listed in Table 21-1 , numerous other channels are present in heart muscle. The distribution of this large array of time- and voltage-dependent membrane currents (see Table 21-1 ) differs in each of the different cardiac cell types. In addition, there are yet other membrane channels (not shown in Table 21-1 ) that are responsible for “background” currents that we have not discussed, that are not gated by voltage, and that are not time dependent. These background currents can be modulated by diverse factors and help to shape the action potential.

In addition to all of the channels, cardiac cells have two electrogenic transporters that also carry current across the plasma membranes: the Na-Ca exchanger and the Na-K pump.

Na-Ca Exchanger

The Na-Ca exchanger (NCX; see pp. 123–124 and 126 ) is an electrogenic transporter that normally moves three Na + ions into the cell in order to extrude one Ca 2+ ion, using the electrochemical gradient for Na + as an energy source for transport. Under these conditions, the Na-Ca exchanger produces an inward or depolarizing current (i.e., a net inward movement of positive charge). However, if this electrochemical gradient reverses, as it transiently does early during the cardiac action potential (due to the positive V m ), the Na-Ca exchanger may be able to reverse and mediate entry of Ca 2+ and a net outward current. Later during the cardiac action potential, the Na-Ca exchanger returns to its original direction of operation (i.e., Ca 2+ extrusion and inward current). During the plateau phase of the action potential, the inward current mediated by the Na-Ca exchanger tends to prolong the action potential.

Na-K Pump

The Na-K pump is also an electrogenic transporter, normally moving two K + ions into the cell for every three Na + ions that it transports out of the cell, using ATP as an energy source (see pp. 115–117 ). Therefore, this pump produces an outward or hyperpolarizing current. Cardiotonic steroids (such as digoxin and ouabain) inhibit the Na-K pump and thereby cause an increase in [Na + ] i . This inhibition also reduces the outward current carried by the pump and therefore depolarizes the cell.

Traditionally, the changes in membrane potential ( V m ) during the cardiac action potential are divided into separate phases, as illustrated in Figure 21-4 A for cardiac action potentials from the SA node and in Figure 21-4 B for those from ventricular muscle.

Figure 21-4, Phases of cardiac action potentials. The records in this figure are idealized. I K , I Na , I Ca , and I f are currents through K + , Na + , Ca 2+ , and nonselective cation channels, respectively.

Phase 0 is the upstroke of the action potential. If the upstroke is due only to I Ca (see Fig. 21-4 A ), it will be slow. If the upstroke is due to both I Ca and I Na (see Fig. 21-4 B ), it will be fast.

Phase 1 is the rapid repolarization component of the action potential (when it exists). This phase is due to almost total inactivation of I Na or I Ca and may also depend on the activation of a minor K + current not listed previously, called I to (for t ransient o utward current).

Phase 2 is the plateau phase of the action potential, which is prominent in ventricular muscle. It depends on the continued entry of Ca 2+ or Na + ions through their major channels and on a minor membrane current due to the Na-Ca exchanger NCX1. N21-2

Phase 3 is the repolarization component of the action potential. It depends on I K (see Table 21-1 ).

Phase 4 constitutes the electrical diastolic phase of the action potential. V m during phase 4 is termed the diastolic potential; the most negative V m during phase 4 is the maximum diastolic potential. In SA and AV nodal cells, changes in I K , I Ca , and I f produce pacemaker activity during phase 4. Purkinje fibers also exhibit pacemaker activity but use only I f . Atrial and ventricular muscle have no time-dependent currents during phase 4.

The Na + current is the largest current in the heart

The Na + current (see Table 21-1 ) is the largest current in heart muscle, which may have as many as 200 Na + channels per square micrometer of membrane. These channels are abundant in ventricular and atrial muscle, in Purkinje fibers, and in specialized conduction pathways of the atria. This current is not present in SA or AV nodal cells.

The channel that underlies I Na is a classic voltage-gated Na + channel, with both α and β 1 subunits (see pp. 182–185 ). The unique cardiac α subunit (Nav1.5) has several phosphorylation sites that make it sensitive to stimulation by cAMP-dependent protein kinase (see p. 57 ). N21-3

N21-3
Cardiac Na + Channels

The channel that underlies I Na is a classic voltage-gated Na + channel, with both an α and β 1 subunit (see p. 187 and Fig. 7-12 A ). The cardiac α subunit differs from the brain α subunit in having a long cytoplasmic loop connecting the first and second repeats of its six membrane-spanning segments. This long loop has several phosphorylation sites, and it conveys a unique quality to the cardiac channel: phosphorylation by cAMP-dependent protein kinase (protein kinase A, or PKA; see p. 57 ) stimulates the cardiac channel, but inhibits the brain channel.

At the negative resting potentials of the ventricular muscle cells, the Na + channels are closed. However, these channels rapidly activate (in 0.1 to 0.2 ms) in response to local depolarization produced by conducted action potentials and produce a massive inward current that underlies most of the rapid upstroke of the cardiac action potential (phase 0 in Fig. 21-4 B ). If V m remains at a positive level, these channels close in a time-dependent process known as inactivation. This process, which is slower than activation but still fairly rapid (half-time, ~1 ms), is partly responsible for the rapid repolarization of the action potential (phase 1). At the potentials maintained during the plateau of the cardiac action potential—slightly positive to 0 mV during phase 2—a very small but important component of this current remains ( I Na,late ). The sustained level of I Na helps prolong phase 2. N21-4

N21-4
Late Na + Current

Although the primary purpose of I Na in ventricular and atrial myocytes is to support the rapid depolarization of the membrane potential during the upstroke of the cardiac action potential and to provide the inward current needed for rapid conduction, there are other aspects of its function. A small residual fraction of the I Na channels may incompletely inactivate or exist in a distinct kinetic mode following phase 1 of the action potential. This enables these channels to contribute current, now dubbed I Na,late , that lingers long into phases 2 and 3 of the ventricular and atrial action potentials. Both the inward current and the Na + influx attributed to I Na,late can contribute to changes in myocyte behavior that are proarrhythmic. Since many disease conditions enhance I Na,late there is an intense effort to identify and test therapeutic agents that block I Na,late with minimal impact on the early or normal I Na ( ). The specific post-translational modifications of the Na + channel protein subunits that underlie the late Na + channel state remain unknown but are under active investigation.

Reference

  • Maier LS, Sossalla S: The late Na current as a therapeutic target: Where are we?. J Mol Cell Cardiol 2013; 61: pp. 44-50.

In cardiac tissues other than the SA and AV nodes, the regenerative spread of the conducted action potential depends in large part on the magnitude of I Na (see Fig. 21-3 C ). The depolarization produced by the Na + current not only activates I Na in neighboring cells but also activates other membrane currents in the same cell, including I Ca and I K . For example, unlike in skeletal muscle, in which the action potential duration is relatively short, in cardiac myocytes the depolarization—initiated by Nav1.5—activates the L-type cardiac Ca 2+ channel (Cav1.2; see next section), which greatly prolongs the depolarizing phase of the cardiac action potential due to its long-duration opening events. Local anesthetic antiarrhythmic drugs, such as lidocaine, work by partially blocking I Na .

The Ca 2+ current in the heart passes primarily through L-type Ca 2+ channels

The Ca 2+ current ( I Ca ; see Table 21-1 ) is present in all cardiac myocytes. The L-type Ca 2+ channel (Cav1.2; see pp. 190–193 ) is the dominant one in the heart. T-type Ca 2+ channels, with different biophysical and pharmacological properties, are also present but in smaller amounts.

In the SA node, the role of I Ca , like that of the other time- and voltage-dependent membrane currents, is to contribute to pacemaker activity. In both the SA and AV nodes, I Ca is the inward current source that is responsible for the upstrokes (phase 0) of the SA and AV nodal action potentials. Because the nodal cells lack the larger I Na , their upstrokes are slower than those in atrial and ventricular muscle (compare A and B of Fig. 21-4 ). Therefore, the smaller I Ca discharges the membrane capacitance of neighboring cells in the SA and AV nodes less rapidly, so that the speed of the conducted action potential is much slower than that of any other cardiac tissue. This feature in the AV node leads to an electrical delay between atrial contraction and ventricular contraction that permits more time for the atria to empty blood into the ventricles.

Although it is smaller, I Ca sums with I Na during the upstroke of the action potentials of the ventricular and atrial muscle and the Purkinje fibers. In this way, it increases the velocity of the conducted action potential in these tissues. Like I Na , I Ca produces virtually no current at very negative potentials because the channels are closed. At more positive values of V m , the Ca 2+ channels rapidly activate (in ~1 ms) and, by a completely separate and time-dependent process, inactivate (half-time, 10 to 20 ms). N21-5 A small I Ca remains during phase 2 of the action potential, helping to prolong the plateau. In atrial and ventricular muscle cells, the Ca 2+ entering via L-type Ca 2+ channels activates the release of Ca 2+ from the sarcoplasmic reticulum (SR) by calcium-induced Ca 2+ release (see pp. 242–243 ). Blockers of L-type Ca 2+ channels —therapeutic agents such as verapamil, diltiazem, and nifedipine—act by inhibiting I Ca .

N21-5
Time Course of Ca 2+ Current in Ventricular Muscle

In Figure 21-4 B , the lower panel (red trace) illustrates the time course of the Ca 2+ current during an action potential in a ventricular myocyte.

During phase 4, at rest, where V m is maximally negative, the Ca 2+ channels are mostly closed and I Ca is a very small inward current. Following the depolarization produced by the very fast Na + channel during phase 0, the Ca 2+ channels activate (in ~1 ms), producing the rapid downstroke of the red I Ca record in Figure 21-4 B .

Next, by a completely separate and time-dependent process, the Ca 2+ channels inactivate at positive potentials (half-time, 10 to 20 ms), producing the slower decay of inward current toward the end of phase 1 in Figure 21-4 B . Along with the inactivation of the Na + channels and the opening of the Kv4.3 channels that underlie I to , the inactivation of Ca 2+ channels contributes to the small repolarization that defines phase 1 (see Fig. 21-4 B ). Note that, for both activation and inactivation, the cardiac Ca 2+ channels are about an order of magnitude slower than cardiac Na + channels.

During phase 2 of the action potential, a small I Ca remains, helping to prolong the plateau. This phase is represented by the flat portion of the red I Ca record displaced below the dashed zero-current line in Figure 21-4 B .

During phase 3, as V m returns to negative potentials, two things happen to Ca 2+ channels. First, the still-active Ca 2+ channels (which were activated by positive V m values) will go through a process of deactivation (caused by negative V m values). Second, the Ca 2+ channels that had been inactivated during phase 2 now begin to recover from inactivation. The net effect is that a minuscule Ca 2+ current remains during phase 4 … which takes us back to the beginning of this discussion.

The repolarizing K + current turns on slowly

Cardiac action potentials last two orders of magnitude longer than action potentials in skeletal muscle because the repolarizing K + current turns on very slowly and—in the case of atrial myocytes, Purkinje fibers, and ventricular myocytes—with a considerable delay. The repolarizing K + current ( I K ; see Table 21-1 ) is found in all cardiac myocytes and is responsible for repolarizing the membrane at the end of the action potential (phase 3 in Fig. 21-4 A, B ). Two currents underlie I K —a relatively rapid component ( ) carried by heteromeric HERG/miRP1 channels and a relatively slow component ( ) carried by heteromeric KvLQT1/minK channels (see Box 7-3 ). N21-6 The I K membrane current is very small at negative potentials. With depolarization, it slowly activates (20 to 100 ms) but does not inactivate. In SA and AV nodal cells, it contributes to pacemaker activity by slowly deactivating at the diastolic voltage.

N21-6
Cardiac K + Currents

Table 21-1 lists five K + currents:

  • I to —the transient outward current—occurs during phase 1 of the action potential. Along with the inactivation of the Na + channels and (a bit later) the inactivation of Ca 2+ channels, I to contributes to the small repolarization that defines phase 1 (see Fig. 21-4 B ). The Shaker-type K + channel (see pp. 193–196 ) Kv4.3 carries I to .

  • —the rapid repolarizing K + current—is the current arising from heteromultimeric channels composed of HERG and miRP subunits.

  • —the slow repolarizing K + current—arises from different heteromultimeric channels composed of KvLQT1 and minK subunits. In older terminology, the delayed-rectifier K + current is the sum of and .

  • —the inward-rectifying current that prevails at the resting potential. The channels are members of the Kir family ( KCNJ genes). The channels close during phase 0, and re-open at the end of phase 3.

  • GIRK—the G protein–activated, inwardly rectifying K + channels (also part of the Kir family; see pp. 197–198 )—open in response to ACh. Like many K + channels, the GIRK channels are comprised of two different GIRK subunits clustered as tetramers.

  • K ATP —the K + channels inhibited by intracellular ATP (like GIRKs, part of the IR family of K + channels; see pp. 197–198 )—contribute to the background K + current. The K ATP channel is a tetramer comprised of two different subunits, as is the case for the GIRK K + channels and the channels that give rise to the and currents.

In addition to I K , several other K + currents are present in cardiac tissue.

Early Outward K + Current (A-type Current)

Atrial and ventricular muscle cells have some early t ransient o utward current ( I to ). This current is activated by depolarization but rapidly inactivates. It contributes to phase 1 repolarization and is analogous to the A-type currents (see p. 193 ) seen in nerves. A Kv4.3 channel mediates the A-type current in heart and certain other cells.

G Protein–Activated K + Current

Acetylcholine activates muscarinic receptors and, through the βγ subunits of a G protein, activates an outward K + current mediated by GIRK K + channels (see pp. 197–198 ). This current is prominent in SA and AV nodal cells, where it decreases pacemaker rate by cell hyperpolarization. When activated, this current also slows the conduction of the action potential through the AV node.

K ATP Current

ATP-sensitive K + channels (K ATP ; see p. 198 ), activated by low intracellular [ATP], are present in abundance and may play a role in electrical regulation of contractile behavior. These channels are octamers, consisting of four subunits (Kir6.1 or Kir6.2) forming the pore of an inward-rectifier channel and four sulfonylurea receptors (SUR1 or SUR2).

The I f current is mediated by a nonselective cation channel

The pacemaker current ( I f ) is found in SA and AV nodal cells and in Purkinje fibers (see Fig. 21-4 A , blue curve). The channel underlying this current is a nonspecific cation channel called HCN (for h yperpolarization activated, c yclic n ucleotide gated; see pp. 162–165 ), with HCN4 being dominant in the adult heart. Because the HCN channels conduct both K + and Na + , the reversal potential of I f is around −20 mV, between the Nernst potentials for K + (about −90 mV) and Na + (about +50 mV). The HCN channels have the unusual property (hence the subscript f, for “funny” current) that they do not conduct at positive potentials but are activated by hyperpolarization at the end of phase 3. The activation is slow (100 ms), and the current does not inactivate. Thus, I f produces an inward, depolarizing current as it slowly activates at the end of phase 3. The I f current is not the only current that contributes to pacemaker activity; in SA and AV nodal cells, I Ca and I K also contribute significantly to the phase 4 depolarization.

Different cardiac tissues uniquely combine ionic currents to produce distinctive action potentials

The shape of the action potential differs among different cardiac cells because of the unique combination of various currents—both the voltage-gated/time-dependent currents discussed in the preceding four sections and the “background” currents—present in each cell type. N21-7 In Chapter 6 , we introduced Equation 6-12 , which describes V m in terms of the conductances for the different ions ( G Na , G K , G Ca , G Cl ) relative to the total membrane conductance ( G m ) and the equilibrium potentials ( E Na , E K , E Ca , E Cl ):


V m = G K G m E K + G Na G m E Na + G Ca G m E Ca + G Cl G m E Cl

N21-7
Contribution of Ionic Currents to the Action Potential

Equation 21-2 gives V m in terms of the weighted conductances of the various ions. Another, less general, way of expressing this concept is the Goldman-Hodgkin-Katz (GHK) equation, which we introduced in Chapter 6 . The GHK equation (given as Equation 6-9 and reproduced here) relates V m to the cellular permeability to different ions ( P Na , P K , P Cl ), as well as to the intracellular and extracellular concentrations of these ions:


V rev = R T F ln ( P K [ K + ] o + P Na [ Na + ] o + P Cl [ Cl ] i P K [ K + ] i + P Na [ Na + ] i + P Cl [ Cl ] o )

Several assumptions underlie the GHK equation, including that (1) the voltage varies linearly with distance through the membrane (constant-field assumption), (2) the ions move independently of one another, (3) the ions are driven only by their electrochemical gradients, (4) the permeabilities are constant, and (5) the total membrane current is zero (i.e., the individual ionic currents sum to zero and V m is constant). Although we derived this GHK equation with these assumptions—which are not strictly true during the action potential—the equation nevertheless embodies the notion that changes in permeabilities and concentrations of specific ions will affect the shape of the action potential.

Therefore, as the relative contribution of a particular membrane current becomes dominant, V m approaches the equilibrium potential for that membrane current ( Table 21-2 ). How fast V m changes during the action potential depends on the magnitude of each of the currents ( Equation 21-2 ). Not only does each current independently affect the shape of the action potential, but the voltage- and time-dependent currents interact with one another because they affect—and are affected by— V m . Other important influences on the shape of the cardiac action potential are the membrane capacitance of each cell and the geometry of the conduction pathway (e.g., AV node, bundle of His, ventricular muscle) as the action potential propagates from cell to cell in this functional syncytium via gap junctions. Therefore, it is easy to understand, at a conceptual level, how a particular cell's unique complement of ion channels, the properties of these channels at a particular instant in time, the intracellular ion concentrations, and the cell's geometry can all contribute to the shape of an action potential. N21-8

TABLE 21-2
Equilibrium Potentials
ION INTRACELLULAR CONCENTRATION (mM) EXTRACELLULAR CONCENTRATION (mM) EQUILIBRIUM POTENTIAL (mV)
Na + 10 145 +72
K + 120 4.5 −88
Cl 35 116 −32
H + pH = 7.1 pH = 7.4 −19
Ca 2+ 0.0001 1.0 +123

N21-8
Mathematical Modeling of the Heart

In this chapter and throughout the text, reference is often made to mathematical models and the way they are used to test interpretations of data and to integrate specific experimental findings into a larger physiological context. This approach is used increasingly in teaching, drug testing, and experimental investigations, and will be used in the future in personalized medicine. In heart and other organs, tissues, and cells, the primary weakness of mathematical models is model validation: How do we know that the choice of unknown or uncertain variables placed into the mathematical model is optimal and unprejudiced? This selection is now being done through optimization programs and approaches that, if successful, can be used to improve personalized medicine. Courses are available to begin the application of “systems biology” methods for all.

Powerful resources are available on the Web. The Virtual Cell is a modeling environment for physicians, scientists, and students who seek to investigate quantitative relationships in biology. This is a National Institutes of Health–funded resource and can be accessed and used without charge. Importantly, there is a growing community of users who share their models and modeling code.

References

  • Sarkar AX, Christini DJ, Sobie EA: Exploiting mathematical models to illuminate electrophysiological variability be­tween individuals. J Physiol 2012; 590: pp. 2555-2567.
  • Sobie EA, Lee YS, Jenkins SL, Iyengar R: Systems biology—biomedical modeling. Sci Signal 2011; 4: pp. tr2.
  • Sobie EA, Sarkar AX: Regression methods for parameter sensitivity analysis: Applications to cardiac arrhythmia mechanisms. Conf Proc IEEE Eng Med Biol Soc 2011; 2011: pp. 4657-4660.
  • VCell—The Virtual Cell. http://www.nrcam.uchc.edu/ Ac­cessed August 2015

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