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• W2111659160 abstract "HomeCirculation ResearchVol. 91, No. 11An Electric Field Mechanism for Transmission of Excitation Between Myocardial Cells Free AccessEditorialPDF/EPUBAboutView PDFView EPUBSections ToolsAdd to favoritesDownload citationsTrack citationsPermissions ShareShare onFacebookTwitterLinked InMendeleyReddit Jump toFree AccessEditorialPDF/EPUBAn Electric Field Mechanism for Transmission of Excitation Between Myocardial Cells Nicholas Sperelakis Nicholas SperelakisNicholas Sperelakis From the Department of Molecular and Cellular Physiology, University of Cincinnati College of Medicine, Cincinnati, Ohio. Search for more papers by this author Originally published29 Nov 2002https://doi.org/10.1161/01.RES.0000045656.34731.6DCirculation Research. 2002;91:985–987A long-standing dogma in basic electrophysiology of the heart has been that the atrial and ventricular myocardial cells are interconnected by low-resistance pathways mediated by gap-junction connexon channels.1 This dogma became established based on the publications of a number of investigators, including Weidmann,2 Woodbury and Crill,3 and DeMello.4 It was concluded that the input resistance of myocardial cells in a bundle was very low (eg, 30 KΩ), the length constant (λ) of the bundle was very long (eg, 1.5 mm), and that local-circuit action current spreads readily from cell to cell. The ultrastructure of mammalian myocardium showed presence of numerous gap junctions.5 This dogma has become ingrained in most textbooks and advanced reference books dealing with the heart.This dogma still lives on despite the facts that it is now accepted that the input resistance is high (eg, 5 to 40 MΩ) and the length constant is very short (eg, 150 to 350 μm) (see references in Sperelakis and McConnell6,7). For example, an input resistance for myocardial cells, measured in isolated cell pairs, was ≈27 to 37 MΩ,8 and the λ value for myocardial bundles was reported to be 357 μm.9 Propagation in cardiac muscle is now accepted as being discontinuous (or saltatory) in nature.10 In addition, gap junctions are scarce or absent in the hearts of nonmammalian vertebrates, such as birds, lizards, frogs, and fish (for references, see Reference 6). Despite this, the hearts in those lower vertebrates function normally.The low-resistance dogma was first challenged in 1959 by Sperelakis and colleagues,11 in experiments on frog heart. Subsequently, they published a series of studies on mammalian hearts based on biophysical measurements and demonstrated that, in many cases, there were not low-resistance connections between myocardial cells. Most of this evidence is summarized in two recent review articles.6,7 This evidence included data showing that parallel strands of myocardial cells within a bundle cause the bundle to act as a cable with a relatively long length constant (eg, 1.0 to 1.5 mm), and that the length constant of the bundle dominates and thus can explain the long λ obtained by Weidmann2 and others.In parallel with the biophysical experiments, we carried out a series of theoretical studies, beginning in 1969 and continuing up to the present time. One seminal study, published in 1977 by Sperelakis and Mann,12 gave a physical circuit analysis and a mathematical computer analysis that demonstrated that an electrical transmission of excitation can occur between heart cells not interconnected by low-resistance pathways. The mechanism for this propagation over a chain of cells was by the electric field (EF) that develops in the narrow junctional clefts between cells (intercalated disks) when the prejunctional membrane fires an action potential (AP) giving rise to a negative cleft potential (Vjc). The mathematical model was subsequently refined and expanded in a series of studies.13,14 One of these studies showed that K+ accumulation at the cell junction would facilitate propagation by the EF mechanism.15 Another one of these studies16 showed that propagation had a staircase shape or discontinuous conduction, and that propagation velocity was close to the physiological value. All excitable units in the surface membrane of each cell fired simultaneously, and the delay at each junction was ≈0.4 ms. Thus, almost all propagation time was consumed at the cell junctions, resulting in the staircase shape.This staircase shape is similar to what was found in theoretical studies of propagation in cardiac muscle.17,18 Excitation jumped from cell junction to cell junction. The staircase propagation can account for the discontinuous conduction observed in cardiac muscle by Spach et al.19 Subsequent theoretical simulations conducted by Spach et al20 also showed discontinuous conduction. Pertsov and Medvinskii21 also concluded that propagation can occur between excitable cells without the necessity of gap-junction low-resistance connections.Sperelakis and colleagues22,23 constructed electric circuits that mimicked excitable membranes of heart cells, and then placed a number of these excitable units in series to simulate a chain of myocardial cells not connected by low-resistance pathways. Stimulation of the first excitable unit/cell resulted in propagation of excitation over the entire chain, with junctional delays of ≈0.5 ms. When the last cell of the chain was connected back to the first cell, reentry of excitation occurred repetitively. Transmission of excitation from cell to cell apparently occurred by a combination of the electric field mechanism and some local-circuit current. Capacitative coupling also was demonstrated to occur when the cells were connected by capacitors.Sperelakis and colleagues24,25 (Sperelakis N, Ramasamy L, Murali KPV, unpublished data, 2002) then embarked on a study of propagation in cardiac muscle and smooth muscle with simulated APs using the PSpice program (Cadence Co) for electronic circuit analysis and design. One advantage of this computer program is that the actual complex circuit can be drawn, and the values for the circuit components readily changed. The parameter values (for standard conditions) were selected to give a resting potential (RP) of −80 mV for myocardial cells and −55 mV for smooth muscle cells, AP overshoot to +30 mV and +10 mV, and maximal rate of rise of the AP (+dV/dt max) of ≈150 V/sec and 10 V/sec, respectively. The parameter values were selected to reflect an input resistance of 20 MΩ for myocardial cells and 30 MΩ for smooth muscle cells and an input capacitance of 100 pF and 50 pF, respectively. Cell length was assumed to be 150 μm and 200 μm, respectively. Each simulated cell had 3 or 5 excitable units to represent the surface membrane (SM) and one excitable unit to represent each junctional membrane (JM) (intercalated disk). There were no low-resistance connections between cells. Most experiments were done on a linear chain of 6 cells (cardiac muscle) or 10 cells (smooth muscle). Electrical stimulation (rectangular current pulse of 0.5 nA and 0.5 ms) was applied to the inside of the first cell (cell No. 1) of each chain.Stimulation of cell No. 1 caused excitation of that cell, followed by sequential activation of the other cells in the chain.24 There was a junctional delay of ≈0.4 ms (cardiac muscle) or 4 ms (smooth muscle). The surface membrane units in each cell fired simultaneously, thus causing propagation to have a staircase shape (discontinuous conduction). Therefore, almost all of the propagation time is consumed at the cell junctions. A relatively large EF potential (negative) developed in each junctional cleft (Vjc) when the prejunctional membrane (pre-JM) fired an AP. This negative cleft potential depolarizes the postjunctional membrane (post-JM) by an equal amount due to a patch-clamp action. Thus, the post-JM is brought to its threshold for firing, which then brings the surface membrane to its threshold. The post-JM and pre-JM fire slightly before the surface membrane. Vjc causes a pronounced step on the rising phase of the AP in the post-JM. The magnitude of Vjc is a function of several factors, including the value of Rjc, the radial resistance (shunting) of the junctional cleft (which reflects the closeness of apposition of the two junctional membranes). The higher the Rjc, the greater the Vjc, and hence the faster the propagation velocity.The extracellular longitudinal resistance had a dual effect on propagation velocity (θ).25 The cell chain was assumed to be bathed in a large volume of Ringer solution connected to ground and having longitudinal (Rol) and radial (Ror) components. Increase of Rol and Ror above the standard values of 1.0 KΩ each, first produced some slowing of θ (eg, at 10 KΩ and 100 KΩ), followed by marked speeding of θ (eg, at 1.0 MΩ and 10 MΩ). The latter result indicates that local-circuit current flow between cells cannot be the mechanism for transmission of excitation across the junctions. This conclusion is also consistent with the observation that large increases in Rjcl, the longitudinal resistance of the junctional cleft, higher than the standard value of 7Ω (eg, to values as high as 7.0 MΩ) had no effect whatsoever on θ.Experiments were done to ascertain the effect of adding gap-junction (g-j) channels in parallel with the EF mechanism (Sperelakis N, Murali KPV, unpublished data, 2002). To do this, a variable resistance was placed across each junction in the chain, from the inside of one cell to the inside of the contiguous cell. It was found that adding only one g-j channel increased θ slightly, and adding 10 or 100 channels produced further increase in θ. However, adding 1000 or 10 000 channels caused θ to greatly increase way above the physiological value and the excited length to encompass all cells in the chain. Therefore, in those tissues in which gap junctions are present, only a small fraction of the channels must be open at any instant of time. Vaidya et al26 reported that, in connexin43 (Cx43)–deficient knockout mice, propagation velocity is slowed in late embryonic ventricular muscle. In Cx40 knockout adult mice, conduction velocity in the His-Purkinje system was slowed to ≈59% of the wild-type control.27 It is very important to note that propagation did occur in the absence of connexons. The slowing of propagation observed is consistent with the present results.Experiments were also performed to examine transverse propagation between parallel chains of myocardial cells, with no low-resistance connections between cells in each chain or between chains (Sperelakis N, unpublished data, 2002). The longitudinal resistance of the interstitial fluid (ISF) space between chains (Rol2) and the radial (or transverse) resistance of the interstitial space (Ror2) was increased above their standard values of 100 KΩ and 100 Ω, respectively. The closer the packing of the parallel chains within a muscle bundle, the higher the Rol2 and the lower the Ror2. With the standard values, stimulation of cell No. 1 of the top chain (A-chain) produced propagation down the A-chain, followed by transverse propagation into the B-chain, then followed by propagation into the C-chain. The velocity of activation of cells in the B-chain and C-chain was faster than that in the stimulated A-chain, probably indicating multiple crossover points. Stimulation of cell No. 1 of the B-chain produced propagation down the B-chain, followed by transverse propagation simultaneously into the A-chain and C-chain. Raising Rol2 to 1.0 MΩ and 10 MΩ (to reflect tighter packing of the chains) caused faster transverse propagation. Raising or lowering Ror2 had only little effect on transverse propagation, thus indicating that local-circuit current flow into the neighboring chains was not involved. Therefore, it is likely that the EF potential, developed in the interstitial space when the surface membrane units fire an AP, is the mechanism for the transverse spread of excitation. That is, Rol2 is equivalent to Rjc for longitudinal propagation. Barr and Plonsey28 reported a similar electrical interaction through the interstitial space between parallel fibers of excitable cells. It was shown that when two isolated bundles of cardiac muscle are closely appositioned over a short distance, when one bundle was stimulated, the impulse jumped to the second bundle after a short delay.29In summary, the PSpice simulation shows that transmission of excitation across cell junctions in cardiac muscle and smooth muscle can occur by an electrical mechanism that does not involve low-resistance gap-junction connections and local-circuit current flow. The mechanism that is involved is the EF negative potential (Vjc) that develops in the narrow junctional clefts during excitation of the prejunctional membrane, which causes depolarization of the postjunctional membrane to its threshold. The magnitude of Vjc depends on the magnitude of Rjc, the radial (shunt) resistance of the junctional cleft. Rjc reflects the closeness of apposition of the pre-JM and post-JM. Propagation along a chain of cells not only can occur when the external longitudinal resistance (Rol) is very high but also is actually speeded. This fact, along with the fact that raising the longitudinal resistance of the junctional cleft (Rjcl) to very high values had no effect on propagation velocity θ, argues that local-circuit current flow is not involved in transmission from cell to cell. Transverse propagation also occurs between parallel chains of cells not interconnected by low-resistance pathways. Given that the external radial (transverse) resistance of the interstitial space (Ror2) had little or no effect on transverse propagation, this indicates that local-circuit flow is not the mechanism for the transverse spread of excitation. It is likely that the EF that develops in the narrow interstitial space during firing of the surface membrane of a cell acts to excite the cell in the neighboring chain. Consistent with this view, the longitudinal resistance of the interstitial space (Rol2) had a pronounced effect on transverse propagation. Therefore, propagation can occur both longitudinally and transversely by an electrical means that does not involve gap-junction connections and local-circuit current. When gap-junction channels are added, they work in parallel with the EF mechanism to speed velocity. But, when 1000 or 10 000 channels are added, propagation velocity becomes very fast and nonphysiological.The opinions expressed in this editorial are not necessarily those of the editors or of the American Heart Association.FootnotesCorrespondence to Prof Nicholas Sperelakis, PhD, Department of Molecular and Cellular Physiology, University of Cincinnati College of Medicine, Cincinnati, OH 45267-0576. E-mail [email protected] References 1 Arnsdorf M, Makielski JC. Excitability and impulse propagation. In: Sperelakis N, Kurachi Y, Terzic A, Cohen MV, eds. Heart Physiology and Pathophysiology. 4th ed. San Diego, Calif: Academic Press; 2001:99–132.Google Scholar2 Weidmann S. The diffusion of radiopotassium across intercalated disks of mammalian cardiac muscle. J Physiol. 1966; 187: 323–342.CrossrefMedlineGoogle Scholar3 Woodbury JW, Crill WE. The potential in the gap between two abutting cardiac muscle cells. Biophys J. 1970; 10: 1076–1083.CrossrefMedlineGoogle Scholar4 DeMello WC. Effect of intracellular injection of calcium and strontium in cell communication in heart. J Physiol. 1975; 250: 231–245.CrossrefMedlineGoogle Scholar5 Larsen WJ, Veenstra RD. Biology of gap junctions. In: Sperelakis N, ed. Cell Physiology Sourcebook: A Molecular Approach. 3rd ed. San Diego, Calif: Academic Press; 2001:523–537.Google Scholar6 Sperelakis N, McConnell K. An electric field mechanism for in transmission of excitation from cell to cell in cardiac muscles and smooth muscles. In: Mohan RM, ed. Research Advances in Biomedical Engineering. Bombay, India: Global Research Network. 2001: 2: 39–66.Google Scholar7 Sperelakis N, McConnell K. Electric field interactions between closely abutting excitable cells. In: IEEE Eng Med Biol Mag. 2002: 21: 77–89.CrossrefMedlineGoogle Scholar8 Metzer P, Weingart R. Electrotonic current flow in cell pairs isolated from adult rat hearts. J Physiol. 1985; 366: 177–195.CrossrefMedlineGoogle Scholar9 Kleber AG, Riegger CB, Janse MJ. Extracellular K+ and H+ shifts in early ischemia: mechanisms and relation to changes in impulse propagation. J Mol Cell Cardiol. 1987; 19: 35–44.CrossrefMedlineGoogle Scholar10 Spooner PM, Joyner RW, Jalife J, eds. Discontinuous Conduction in the Heart. Armonk, NY: Futura Publishing; 1997.Google Scholar11 Sperelakis N, Hoshiko T, Berne RM. Evidence for non-syncytial nature of cardiac muscle from impedance measurements. Proc Soc Exp Med Biol. 1959; 101: 602–604.CrossrefMedlineGoogle Scholar12 Sperelakis N, Mann JE. Evaluation of electric field changes in the cleft between excitable cells. J Theor Biol. 1977; 64: 71–96.CrossrefMedlineGoogle Scholar13 Mann JE, Sperelakis N, Ruffner JA. Alterations in sodium channel gate propagation with the Hodgkin-Huxley equations applied to an electric field model for interaction between excitable cells. IEEE Trans Biomed Eng. 1981; 28: 655–661.MedlineGoogle Scholar14 Sperelakis N. Electrical field model for electric interactions between myocardial cells. In: Sideman S, Beyar R, eds. Electromechanical Activation, Metabolism, and Perfusion of the Heart Simulation and Experimental Models. Boston, Mass: Martinus Nijhoff; 1987:77–113.Google Scholar15 Sperelakis N, LoBrocco B, Mann JE, Marshall R. Potassium accumulation in intercellular junctions combined with electric field interaction for propagation in cardiac muscle. Innov Technol Biol Med. 1985; 6: 24–43.Google Scholar16 Picone JB, Sperelakis N, Mann JE. Expanded model of the electric field hypothesis for propagation in cardiac muscle. Math Comput Model. 1991; 15: 17–35.Google Scholar17 Diaz PJ, Rudy Y, Plonsey R. Intercalated discs as a cause for discontinuous propagation in cardiac muscle: a theoretical simulation. Ann Biomed Eng. 1983; 11: 177–189.CrossrefMedlineGoogle Scholar18 Rudy Y, Quan W. Effects of the discrete cellular structure on electrical propagation in cardiac tissue. In: Sideman S, Beyar R, eds. Electromechanical Activation, Metabolism, and Perfusion of the Heart: Simulation and Experimental Models. Boston, Mass: Martinus Nijhoff; 1987:61–76.Google Scholar19 Spach MS, Miller WT, Geselowitz DB, Barr RC, Kootsey JM, Johnson EA. The discontinuous nature of propagation in normal canine cardiac muscle: evidence for recurrent discontinuities of intracellular resistance that affect the membrane currents. Circ Res. 1981; 48: 39–54.LinkGoogle Scholar20 Spach M, Dolber S, Heidiage JF. Use of computer simulations for combined experimental-theoretical study of anisotropic discontinuous propagation at a microscopic level in the cardiac muscle. In: Sideman S, Beyar R, eds. Electromechanical Activation, Metabolism, and Perfusion of the Heart: Simulation and Experimental Models. Boston, Mass: Martinus Nijhoff; 1987:3–25.Google Scholar21 Pertsov AM, Medvinskii AB. Electric coupling in cells without highly permeable cell contacts. Biofizika. 1976; 21: 698–700.MedlineGoogle Scholar22 Sperelakis N, Rollins C, Bryant SH. An electronic analog simulation for cardiac arrhythmias and reentry. J Cardiovasc Electrophysiol. 1990; 1: 294–302.CrossrefGoogle Scholar23 Ge J, Sperelakis N, Ortiz-Zuazaga H. Simulation of action potential propagation with electronic circuits. Innov Technol Biol Med. 1993; 14: 404–420.Google Scholar24 Sperelakis N, Ramasamy L. Propagation in cardiac muscle and smooth muscle based on electric field transmission at cell junctions: an analysis by PSpice. IEEE Eng Med Biol Mag. 2002; 21: 177–190.Google Scholar25 Sperelakis N, Murali KPV. Effect of external resistance on propagation of action potentials in cardiac muscle and visceral smooth muscle in PSpice simulation. Math Comput Model. In press.Google Scholar26 Vaidya D, Tamaddon HS, Lo CW, Taffet SM, Delmar M, Morley GE, Jalife J. Null mutation of connexin43 causes slow propagation of ventricular activation in the late stages of mouse embryonic development. Circ Res. 2001; 88: 1196–1202.CrossrefMedlineGoogle Scholar27 Tamaddon HS, Vaidya D, Simon AM, Paul DL, Jalife J, Morley GE. High-resolution optical mapping of the right bundle branch in connexin40 knockout mice reveals slow conduction in the specialized conduction system. Circ Res. 2000; 87: 929–936.CrossrefMedlineGoogle Scholar28 Barr RC, Plonsey R. Electrophysiological interaction through the interstitial space between adjacent unmyelinated parallel fibers. Biophys J. 1992; 61: 1164–1175.CrossrefMedlineGoogle Scholar29 Suenson M. Ephaptic impulse transmission between ventricular myocardial cells in vitro. 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