The effect of adding many gap-junctions (g-j) channels between contiguous cells in a linear chain on transverse propagation between parallel chains was examined in a 5 × 5 model (5 parallel chains of 5 cells each) for cardiac muscle. The action potential upstrokes were simulated using the PSpice program for circuit analysis. Either a single cell was stimulated (cell A1) or the entire chain was stimulated simultaneously (A-chain). Transverse velocity was calculated from the total propagation time (TPT) from when the first AP crossed a V m  of -20 mV and the last AP crossed -20 mV. The number of g-j channels per junction was varied from zero to 100, 1,000 and 10,000 (R gj  of ∞, 100 MΩ, 10 MΩ, 1.0 MΩ, respectively). The longitudinal resistance of the interstitial fluid (ISF) space between the parallel chains (R ol2 ) was varied between 200 KΩ (standard value) and 1.0, 5.0, and 10 MΩ. The higher the R ol2  value, the tighter the packing of the chains. It was found that adding many g-j channels inhibited transverse propagation by blocking activation of all 5 chains, unless R ol2  was greatly increased above the standard value of 200 KΩ. This was true for either method of stimulation. This was explained by, when there is strong longitudinal coupling between all 5 cells of a chain awaiting excitation, there must be more transfer energy (i.e., more current) to simultaneously excite all 5 cells of a chain.

Introduction We have developed an electric field hypothesis for the mechanism of transmission of excitation from one cell to the next that does not require gap-junction channels [ 1 - 4 ]. In the electric field hypothesis, the electrical voltage that develops in the narrow junctional cleft (V jc ) when the prejunctional membrane generates an action potential, serves to depolarize the postjunctional membrane its threshold, by a patch-clamp-like effect. The parameters that affect the magnitude of Vjc include the size of R jc , the transverse resistance of the junctional cleft. This results in excitation of the postjunctional cell, after a brief junctional delay. The total propagation time consists primarily of the summed junctional delays. This results in a staircase-shaped propagation, the surface sarcolemma of each cell firing almost simultaneously [ 2 ]. There are no low-resistance connections between the cells in several different cardiac muscle and smooth muscle preparations (reviewed in [ 3 , 4 ]. Propagation by mechanisms not requiring low-resistance connections have also been proposed by others [ 5 - 8 ]. Propagation has been demonstrated to be discontinuous (or saltatory) in cardiac muscle [ 9 - 12 ]. Fast Na +  channels are localized in the junctional membranes of the intercalated discs of cardiac muscle [ 13 - 15 ] Sperelakis, 1995, a requirement for the EF mechanism to work [ 3 , 4 , 1 , 2 , 13 ]. In connexin-43 and Cx40 knockout mice, propagation in the heart still occurs, but it is slowed [ 15 - 19 ], as predicted by our PSpice simulation study [ 20 ]. It was reported that the anisotropic conduction velocity observed in the heart is not a result of cell geometry [ 21 ]. Subsequently, we published a series of papers on the longitudinal and transverse propagation of action potentials in cardiac muscle and smooth muscle using PSpice analysis [ 22 , 20 , 24 ]. In the review process for our recent paper [ 24 ], one of the referees asked us to determine the effect of introducing strong cell coupling via gap-junction (g-j) channels between cells within each chain on the transverse propagation in our 5 × 5 model (5 parallel chains of 5 cells each). Unexpectedly, we found that strong cell coupling (10,000 or 1,000 g-j channels per junction) actually  inhibited  transverse propagation. This fact was briefly mentioned as an unpublished observation in that paper. The purpose of the present study was to do a thorough investigation of that strange phenomenon. The results showed that, in cardiac muscle, transverse propagation was inhibited when many g-j channels were added between cells of each chain. This was true when either a single cell in the first chain was stimulated (cell A1) or the entire chain (A-chain) was stimulated simultaneously.
Introduction
We have developed an electric field hypothesis for the mechanism of transmission of excitation from one cell to the next that does not require gap-junction channels [ 1 - 4 ]. In the electric field hypothesis, the electrical voltage that develops in the narrow junctional cleft (V jc ) when the prejunctional membrane generates an action potential, serves to depolarize the postjunctional membrane its threshold, by a patch-clamp-like effect. The parameters that affect the magnitude of Vjc include the size of R jc , the transverse resistance of the junctional cleft. This results in excitation of the postjunctional cell, after a brief junctional delay. The total propagation time consists primarily of the summed junctional delays. This results in a staircase-shaped propagation, the surface sarcolemma of each cell firing almost simultaneously [ 2 ].There are no low-resistance connections between the cells in several different cardiac muscle and smooth muscle preparations (reviewed in [ 3 , 4 ]. Propagation by mechanisms not requiring low-resistance connections have also been proposed by others [ 5 - 8 ]. Propagation has been demonstrated to be discontinuous (or saltatory) in cardiac muscle [ 9 - 12 ]. Fast Na +  channels are localized in the junctional membranes of the intercalated discs of cardiac muscle [ 13 - 15 ] Sperelakis, 1995, a requirement for the EF mechanism to work [ 3 , 4 , 1 , 2 , 13 ]. In connexin-43 and Cx40 knockout mice, propagation in the heart still occurs, but it is slowed [ 15 - 19 ], as predicted by our PSpice simulation study [ 20 ]. It was reported that the anisotropic conduction velocity observed in the heart is not a result of cell geometry [ 21 ].Subsequently, we published a series of papers on the longitudinal and transverse propagation of action potentials in cardiac muscle and smooth muscle using PSpice analysis [ 22 , 20 , 24 ]. In the review process for our recent paper [ 24 ], one of the referees asked us to determine the effect of introducing strong cell coupling via gap-junction (g-j) channels between cells within each chain on the transverse propagation in our 5 × 5 model (5 parallel chains of 5 cells each). Unexpectedly, we found that strong cell coupling (10,000 or 1,000 g-j channels per junction) actually  inhibited  transverse propagation. This fact was briefly mentioned as an unpublished observation in that paper. The purpose of the present study was to do a thorough investigation of that strange phenomenon. The results showed that, in cardiac muscle, transverse propagation was inhibited when many g-j channels were added between cells of each chain. This was true when either a single cell in the first chain was stimulated (cell A1) or the entire chain (A-chain) was stimulated simultaneously.inhibitedMethods Details of the methods used and modeling of the PSpice analysis were given in our previous papers, including the limitations [ 21 - 24 ]. The full version of the PSpice software for circuit analysis/design was obtained from the Cadence Co. (Portland, OR). The assumptions made were given previously, including the entire circuit that was used [ 22 ]. An abbreviated version of the circuitry is given in the first two figures. The surface membrane of each myocardial cell was represented by 2 units and each junctional membrane by 1 unit (Figs.  1 ,  2 ). The values for the circuit parameters used under standard conditions were given previously for both the surface units and junctional units in cardiac muscle [ 22 ]. The myocardial cell was assumed to be a cylinder 150 μm long and 16 μm in diameter. The myocardial cell capacitance was assumed to be 100 pF, and the input resistance to be 20 MΩ. A junctional tortuosity (interdigitation) factor of 4 was assumed for the cell junction. Figure 1 The 5 × 5 model for cardiac muscle, consisting of 5 parallel strands (A-E) of 5 cells each (1–5) (total of 25 cells). Each muscle cell was represented by a block of 4 basic units: 2 units representing the surface membrane (one upward-facing and one downward-facing) and one unit for each of the two junctional membranes. For simplicity, the lumped resistance of the gap-junctions is not indicated here, but is shown in Fig. 2. Transverse propagation is sequential activation of chains A to B to C to D to E. Figure 2 Blow-up of a small portion of the 5 × 5 model to show the electrical circuit for each basic unit, including the "black-box" required for excitability. R ol2  represents the longitudinal resistance of the interstitial fluid between the parallel chains; the higher the resistance, the tighter the packing of the chains. Depolarizing current (0.25 nA) is applied to the interior of either the first cell or the entire chain (A-chain) simultaneously. When gap-junction channels were added, a resistor (R gj ) was inserted across each cell junction, from the interior of one cell to the interior of the next one. The circuit used for each unit was kept as simple as possible, using only those ion channels that set the resting potential (RP) and predominate during the rising phase of the AP. We wanted to only inscribe the rising phase of the APs to study propagation in the 2-dimensional sheet of myocardial cells. It was not possible to insert a second or third "black-box" into the basic excitable units, because the system became erratic, therefore the dynamic behavior of the cardiac cell membrane was an approximation. The RP was -80 mV, and the overshoot potential was +30 mV (AP amplitude of 110 mV). Propagation velocity was calculated from the measured total propagation time (TPT) (measured as the difference between when the APs of the first cell and last cell crossed -20 mV) and cell length. Because the PSpice program does not have a V-dependent resistance to represent the increase in conductance for Na +  ions in myocardial cells during depolarization and excitation, this function had to be simulated by a V-controlled current source (our "black-box") in each of the basic circuit units (Fig.  2 ). The current outputs of the black-box, at various membrane voltages, were calculated assuming a sigmoidal relationship between membrane voltage and resistance between -60 mV and -30 mV. The V values used in the GTABLE were those recorded  directly across  the membrane. The excitabilities of the basic units were the same as in our previous papers [ 21 - 24 ]. The upper chain of cells was assumed to be bathed in a large volume of Ringer solution connected to ground. The external resistance (R o ) of this fluid was divided into two components: a radial (or transverse) resistance (R or ) and a longitudinal resistance (R ol ). The longitudinal resistance values (R ol2 ) between the upper chain and interior chains were increased over a wide range to reflect packing of parallel chains into a bundle of fibers, with different degrees of tightness of the packing (Fig.  1 ). The higher the R ol2  value, the tighter the packing of the chains, i.e., the lower the cross-sectional area of the ISF space. The applicable equation is R ol2  = ρ (Ω-cm) × L (cm) /Ax (cm 2 ), where ρ is the resistivity of the ISF, L is the length, and A x  is the cross-sectional area of the ISF space. The transverse resistance of the interstitial fluid (ISF) space (R or2 ) also reflects the closeness between the chains; the lower the R or2  value, the closer the chains are packed. In the present 5 × 5 model, there were five parallel chains (chains A, B, C, D, and E) of five cells each (cells 1–5). Electrical stimulation (rectangular current pulses of 0.25 nA and 0.50 ms duration) was applied to the inside of either the first cell of chain A (cell A1) or all 5 cells of the A-chain. Under initial conditions, the cells in each chain were not interconnected by low-resistance pathways (gap junction channels), so that transmission of excitation from one cell to the next had to be by the EF developed in the narrow junctional cleft. Then gj-channels were added (100, 1,000 and 10,000 channels per junction) to determine what effect they would have on transverse propagation. Since the number of functional gj-channels per junction have been estimated to be about a 1000 [ 12 ], we varied the number over a very wide range. The resistances of the gap-junction channels were lumped into one equivalent resistances because they are all in parallel. As shown in Figure  1 , there were two surface membrane units in each cell (one facing upwards and one inverted) and one unit for each of the junctional membranes (intercalated disks of cardiac muscle). To improve clarity, in some runs the V-recording markers were placed on only one chain at a time. When all cells in a model were being recorded simultaneously (25 cells), the V markers were removed from most of the basic units to minimize confusion. That is, the voltage was recorded from only one surface unit (upward-facing) in each cell. The junctional cleft potential (V jc ) was recorded across R jc , the radial (or transverse) resistance of the narrow and tortuous junctional cleft. Under standard conditions, R ol2  was 200 KΩ, R or2  was 100 Ω, and R jc  and was 25 MΩ (50 MΩ ÷ 2).
Methods
Details of the methods used and modeling of the PSpice analysis were given in our previous papers, including the limitations [ 21 - 24 ]. The full version of the PSpice software for circuit analysis/design was obtained from the Cadence Co. (Portland, OR). The assumptions made were given previously, including the entire circuit that was used [ 22 ]. An abbreviated version of the circuitry is given in the first two figures. The surface membrane of each myocardial cell was represented by 2 units and each junctional membrane by 1 unit (Figs.  1 ,  2 ). The values for the circuit parameters used under standard conditions were given previously for both the surface units and junctional units in cardiac muscle [ 22 ]. The myocardial cell was assumed to be a cylinder 150 μm long and 16 μm in diameter. The myocardial cell capacitance was assumed to be 100 pF, and the input resistance to be 20 MΩ. A junctional tortuosity (interdigitation) factor of 4 was assumed for the cell junction.The circuit used for each unit was kept as simple as possible, using only those ion channels that set the resting potential (RP) and predominate during the rising phase of the AP. We wanted to only inscribe the rising phase of the APs to study propagation in the 2-dimensional sheet of myocardial cells. It was not possible to insert a second or third "black-box" into the basic excitable units, because the system became erratic, therefore the dynamic behavior of the cardiac cell membrane was an approximation. The RP was -80 mV, and the overshoot potential was +30 mV (AP amplitude of 110 mV). Propagation velocity was calculated from the measured total propagation time (TPT) (measured as the difference between when the APs of the first cell and last cell crossed -20 mV) and cell length.Because the PSpice program does not have a V-dependent resistance to represent the increase in conductance for Na +  ions in myocardial cells during depolarization and excitation, this function had to be simulated by a V-controlled current source (our "black-box") in each of the basic circuit units (Fig.  2 ). The current outputs of the black-box, at various membrane voltages, were calculated assuming a sigmoidal relationship between membrane voltage and resistance between -60 mV and -30 mV. The V values used in the GTABLE were those recorded  directly across  the membrane. The excitabilities of the basic units were the same as in our previous papers [ 21 - 24 ].directly acrossThe upper chain of cells was assumed to be bathed in a large volume of Ringer solution connected to ground. The external resistance (R o ) of this fluid was divided into two components: a radial (or transverse) resistance (R or ) and a longitudinal resistance (R ol ). The longitudinal resistance values (R ol2 ) between the upper chain and interior chains were increased over a wide range to reflect packing of parallel chains into a bundle of fibers, with different degrees of tightness of the packing (Fig.  1 ). The higher the R ol2  value, the tighter the packing of the chains, i.e., the lower the cross-sectional area of the ISF space. The applicable equation is R ol2  = ρ (Ω-cm) × L (cm) /Ax (cm 2 ), where ρ is the resistivity of the ISF, L is the length, and A x  is the cross-sectional area of the ISF space. The transverse resistance of the interstitial fluid (ISF) space (R or2 ) also reflects the closeness between the chains; the lower the R or2  value, the closer the chains are packed. In the present 5 × 5 model, there were five parallel chains (chains A, B, C, D, and E) of five cells each (cells 1–5). Electrical stimulation (rectangular current pulses of 0.25 nA and 0.50 ms duration) was applied to the inside of either the first cell of chain A (cell A1) or all 5 cells of the A-chain. Under initial conditions, the cells in each chain were not interconnected by low-resistance pathways (gap junction channels), so that transmission of excitation from one cell to the next had to be by the EF developed in the narrow junctional cleft. Then gj-channels were added (100, 1,000 and 10,000 channels per junction) to determine what effect they would have on transverse propagation. Since the number of functional gj-channels per junction have been estimated to be about a 1000 [ 12 ], we varied the number over a very wide range. The resistances of the gap-junction channels were lumped into one equivalent resistances because they are all in parallel.As shown in Figure  1 , there were two surface membrane units in each cell (one facing upwards and one inverted) and one unit for each of the junctional membranes (intercalated disks of cardiac muscle). To improve clarity, in some runs the V-recording markers were placed on only one chain at a time. When all cells in a model were being recorded simultaneously (25 cells), the V markers were removed from most of the basic units to minimize confusion. That is, the voltage was recorded from only one surface unit (upward-facing) in each cell. The junctional cleft potential (V jc ) was recorded across R jc , the radial (or transverse) resistance of the narrow and tortuous junctional cleft. Under standard conditions, R ol2  was 200 KΩ, R or2  was 100 Ω, and R jc  and was 25 MΩ (50 MΩ ÷ 2).Results The 5 × 5 model (5 parallel chains of 5 cells each) of cardiac muscle was used to examine whether addition of gap-junction (gj) channels between the cells in each chain would affect transverse propagation of simulated (PSpice) action potentials. The number of gj-channels was increased from zero (standard conditions; resistance of the gap junction (R gj ) of infinite) to 100 (R gj  = 100 MΩ), 1000 (R gj  = 10 MΩ), and 10,000 (R gj  = 1.0 MΩ). Experiments were done with electrical stimulation (0.5 nA, 0.5 ms) of only the first cell of the first chain (A; cell A1) and with simultaneous stimulation of all 5 cells of the A-Chain (each cell receiving 0.5 nA current). This second method of stimulation was done to obtain a more accurate assessment of strictly transverse propagation. Figure  3  illustrates some of the results with stimulation of only cell A1.  Panel A  shows the standard conditions: R gj  = ∞ (0 gj-channels) and R ol2  of 200 KΩ (the longitudinal resistance of the interstitial space between the chains). As shown, all 5 chains (25 cells) responded. The total propagation time (TPT) was 4.2 ms (measured as the elapsed time between when the first and last APs crossed -20 mV). When 10,000 g-j channels were inserted into the cells of each chain (R gj  = 1.0 MΩ), then the last 2 chains (D and E) failed to respond ( panel B ). The 5 cells of each chain (A, B, and C) that responded now fired simultaneously because of the high degree of cell coupling, thereby giving only three AP traces, as shown. However, raising R ol2  to 10 MΩ allowed all 5 chains to respond ( Panel C ), and propagation velocity was increased. These data are summarized in Table  1 ,  part A . Hence greatly elevating R ol2  could overcome the impaired transverse propagation caused by the gj-channels. Figure 3 Transverse propagation of simulated action potentials (APs; rising phase) for cardiac muscle (5 × 5 models) with stimulation of one cell only (cell A1; first cell of the A-chain).  A : R gj  = ∞ (0 channels). R ol2  = 200 KΩ. Standard conditions. All 25 cells responded.  B:  R gj  = 1.0 MΩ (10,000 channels). R ol2  kept unchanged. The last 2 chains (D, E) failed to respond. All 5 cells of each chain that responded (A, B, C) fired simultaneously because of the strong cell coupling.  C:  With R gj  held at 1.0 MΩ, raising R ol2  to 10 MΩ (representing tighter packing of the parallel chains) now allowed all 5 chains to respond. Thus, adding gj-channels inhibited transverse propagation, but this inhibition could be overcome by raising R ol2 . Table 1 Summary of simulation data on cardiac muscle with stimulation either of single cell or entire chain. R gj  (MΩ) R ol2  (MΩ) TPT 5c  (ms) TPT 4c  (ms) TPT 3c  (ms) TPT 2G  (ms) # of chains responding ∞ 0.2 4.2 3.5 2.7 5 100 0.2 2.4 2.3 2.2 5 10 0.2 ---- ---- 2.1 3 1.0 0.2 ---- ---- 2.1 3 ∞ 1.0 3.8 3.2 2.6 5 100 1.0 3.6 3.1 1.9 5 10 1.0 ---- ---- 1.6 3 1.0 1.0 ---- ---- 1.5 3 ∞ 5.0 2.7 2.6 2.3 5 100 5.0 2.0 1.6 1.2 5 10 5.0 ---- ---- 1.0 3 1.0 5.0 ---- ---- 0.9 3 ∞ 10 2.4 2.2 2.0 5 100 10 1.5 1.3 1.0 5 10 10 2.6 1.2 0.8 5 1.0 10 2.9 1.3 0.8 5 ∞ 0.2 3.6 2.7 2.0 1.2 5 100 0.2 2.5 2.4 2.4 1.2 5 10 0.2 ---- ---- ---- 1.1 2 1.0 0.2 ---- ---- ---- 1.1 2 ∞ 1.0 2.6 2.1 1.5 0.9 5 100 1.0 2.7 2.6 1.6 0.8 5 10 1.0 ---- ---- 1.6 0.8 3 1.0 1.0 ---- ---- 1.6 0.7 3 ∞ 5.0 1.7 1.4 0.9 0.6 5 100 5.0 1.6 1.4 0.9 0.6 5 10 5.0 ---- 1.3 0.8 0.5 4 1.0 5.0 ---- 1.3 0.8 0.5 4 ∞ 10 1.4 1.1 0.8 0.6 5 100 10 1.3 1.0 0.8 0.5 5 10 10 1.2 0.9 0.7 0.4 5 1.0 10 1.2 0.9 0.7 0.4 5 Figure  4  illustrates some of the results with simultaneous stimulation of all 5 cells of the A-chain.  Panel A  shows the standard conditions: R gj  = ∞ and R ol2  = 200 KΩ. As shown, all 5 chains responded (TPT was 3.6 ms). Note that all 5 cells of the B – E chains did not respond simultaneously. When 10,000 gj-channels were added to the contiguous cells of each chain (R gj  = 1.0 MΩ), then the last 3 chains (C, D, and E) failed to respond ( Panel B ). The 5 cells of each chain that responded (A, B) now fired simultaneously because of the strong coupling. However, elevating R ol2  to 10 MΩ allowed all 5 chains to respond ( Panel C ). These data are summarized in Table  1 , part B. Figure 4 Transverse propagation of simulated APs for cardiac muscle with stimulation simultaneously of the entire A-chain. This was done as a better assessment of transverse propagation for comparison with stimulation of only one cell of the A-chain.  A:  R gj  = ∞ (0 channels). R ol2  = 200 KΩ. Standard conditions. All 5 chains responded.  B:  R gj  = 1.0 MΩ (10,000 channels). With R ol2  kept at 200 KΩ, chains C, D, and E failed to respond.  C : With R gj  held at 1.0 MΩ, raising R ol2  to 10 MΩ (representing tighter packing of the chains) now allowed all 5 chains to respond. All 5 cells of each chain responded simultaneously because of the strong coupling. Thus, adding gj-channels inhibited transverse propagation, but this inhibition was overcome by raising R ol2 . Figure  5  is a graphic summary of the results for both stimulation of only one cell (A1) ( Panel A ) and stimulation of the entire A-chain ( Panel B ). The data include R gj  values and R ol2  values not illustrated in Figures  3  and  4 . As such, this figure is complementary to Table  1 , but Table  1  lists the TPT values as well. As shown, progressive addition of gj- channels reduces the number of chains that respond, with both ways of stimulation, and progressive elevation of R ol2  reverses this inhibition. Figure 5 Summary of the transverse propagation experiments. Graphic plot of the number of chains responding as a function of R gj  for cardiac muscle, with stimulation of only one cell (cell A1) ( panel A ) or with stimulation of the entire A-chain ( panel B ). Data for various R ol2  values (0.2, 1.0, 5.0, and 10 MΩ) are indicated. Four different R gj  values were tested: ∞ (0 channels), 100 MΩ (100 channels), 10 MΩ (1,000 channels), and 1.0 MΩ (10,000 channels). Thus, transverse propagation was depressed when there were many gj-channels (1000 or 10,000), but elevation of R ol2  could overcome this depression.
Results
The 5 × 5 model (5 parallel chains of 5 cells each) of cardiac muscle was used to examine whether addition of gap-junction (gj) channels between the cells in each chain would affect transverse propagation of simulated (PSpice) action potentials. The number of gj-channels was increased from zero (standard conditions; resistance of the gap junction (R gj ) of infinite) to 100 (R gj  = 100 MΩ), 1000 (R gj  = 10 MΩ), and 10,000 (R gj  = 1.0 MΩ). Experiments were done with electrical stimulation (0.5 nA, 0.5 ms) of only the first cell of the first chain (A; cell A1) and with simultaneous stimulation of all 5 cells of the A-Chain (each cell receiving 0.5 nA current). This second method of stimulation was done to obtain a more accurate assessment of strictly transverse propagation.Figure  3  illustrates some of the results with stimulation of only cell A1.  Panel A  shows the standard conditions: R gj  = ∞ (0 gj-channels) and R ol2  of 200 KΩ (the longitudinal resistance of the interstitial space between the chains). As shown, all 5 chains (25 cells) responded. The total propagation time (TPT) was 4.2 ms (measured as the elapsed time between when the first and last APs crossed -20 mV). When 10,000 g-j channels were inserted into the cells of each chain (R gj  = 1.0 MΩ), then the last 2 chains (D and E) failed to respond ( panel B ). The 5 cells of each chain (A, B, and C) that responded now fired simultaneously because of the high degree of cell coupling, thereby giving only three AP traces, as shown. However, raising R ol2  to 10 MΩ allowed all 5 chains to respond ( Panel C ), and propagation velocity was increased. These data are summarized in Table  1 ,  part A . Hence greatly elevating R ol2  could overcome the impaired transverse propagation caused by the gj-channels.Panel Apanel BPanel Cpart ASummary of simulation data on cardiac muscle with stimulation either of single cell or entire chain.Figure  4  illustrates some of the results with simultaneous stimulation of all 5 cells of the A-chain.  Panel A  shows the standard conditions: R gj  = ∞ and R ol2  = 200 KΩ. As shown, all 5 chains responded (TPT was 3.6 ms). Note that all 5 cells of the B – E chains did not respond simultaneously. When 10,000 gj-channels were added to the contiguous cells of each chain (R gj  = 1.0 MΩ), then the last 3 chains (C, D, and E) failed to respond ( Panel B ). The 5 cells of each chain that responded (A, B) now fired simultaneously because of the strong coupling. However, elevating R ol2  to 10 MΩ allowed all 5 chains to respond ( Panel C ). These data are summarized in Table  1 , part B.Panel APanel BPanel CFigure  5  is a graphic summary of the results for both stimulation of only one cell (A1) ( Panel A ) and stimulation of the entire A-chain ( Panel B ). The data include R gj  values and R ol2  values not illustrated in Figures  3  and  4 . As such, this figure is complementary to Table  1 , but Table  1  lists the TPT values as well. As shown, progressive addition of gj- channels reduces the number of chains that respond, with both ways of stimulation, and progressive elevation of R ol2  reverses this inhibition.Panel APanel BDiscussion The results demonstrated that, in a cardiac muscle model, the insertion of many gj- channels, between abutting cells in each longitudinal chain of cells, actually inhibited transverse propagation of excitation between the parallel chains. This was true both for stimulation of only a single cell of the first chain (A-chain; cell A1) and for stimulation simultaneously of the entire 5 cells of the A-chain. The inhibition produced by the gj-channels could be overcome by greatly increasing the value of R ol2  (the longitudinal resistance of the narrow interstitial space between the parallel chains), reflecting tighter packing of the chains. This finding surprised us at first. We were expecting either that there would be no effect on transverse transmission of excitation or that transverse transfer of excitation would be enhanced. But on further refection, the inhibition produced might be predicted. This is based on the fact that, with strong longitudinal coupling between cells, the entire chain of 5 cells must be simultaneously stimulated to threshold. Therefore, if the transverse transfer energy available is limited and is near threshold for a give chain, it is likely that some chains will fail to fire. Thus, the problem of strong coupling is not in the chains that are already excited, but rather in the quiescent adjacent chain which is in process of trying to become excited (D-chain in case of Fig.  3  and C-chain in Fig.  4 ). Strong coupling in the "in-process" chain requires more energy transfer from the "already-activated" chain. If the "in-process" chain were not coupled by gj-channels, then if only one cell of the chain received enough stimulating energy to become activated, excitation would spread from it to the remaining cells of that chain. This idea was tested, and the results shown in Figure  6  are consistent with the mechanism proposed above. In  panel A , in which R gj  was 1.0 MΩ (10,000 gj-channels) uniformly in all 5 chains, chains D and E failed to fire. When R gj  of just chains D and E were changed to infinity (0 channels), then all 5 chains fired ( panel B ). Therefore, the inhibition of transverse propagation can be reversed by uncoupling the cells of the chains that failed. Figure 6 Special experiment to test why presence of many gap-junction channels inhibits transverse propagation. Stimulated Cell A1 only. R ol2  of 1.0 MΩ.  A:  Uniform value for R gj  of 1.0 MΩ (10,000 channels) in all 5 chains. Chains D and E failed to respond. Compare with Fig. 3B for the standard R ol2  of 0.2 MΩ.  B:  The R gj  values in chains D and E only were changed to infinity (0 channels). Now chains D and E responded. See text for details. This demonstrates that removing the gj-channels in the two chains awaiting excitation (D, E) increased the safety factor for transverse propagation. Consistent with the argument presented in the paragraph above, the transverse propagation velocity was not inhibited by insertion of gj-channels, up through the last chain activated (C-chain in case of Fig.  3  and B-chain in Fig.  4 ). If anything, the transverse velocity was increased slightly (TPT lowered). The TPT values (for differing amount of transverse spread of excitation, e.g. 2-chains, 3-chains, 4-chains, or all 5-chains) are listed in Table  1  for different degrees of cell coupling. Note that, in part A, the largest change in TPT value is between R gj  of ∞ (0 channels) and R gj  of 100 MΩ (100 channels); adding more channels (Rgj of 10 MΩ (1000 channels) or 1.0 MΩ (10,000 channels)) did not further decrease TPT. Similar results were found when the entire A-chain was simulated (part B of Table  1 ). The reader should be alerted to the limitations of the PSpice program. It was not possible to insert a second or third "black-box" in the basic excitable units (because the system went berserk). Therefore, the dynamic behavior of the cardiac cell membrane was only a close approximation. We previously found (unpublished observation) that the transverse velocity was greater when size of the model was increased (eg, 3 × 4, 5 × 5, 7 × 7) up to a presumed maximum, indicating that the boundary conditions affected behavior of the model. Therefore, the present experiments should be repeated on larger-sized models. But we believe that the qualitative findings would be much the same. In addition, 2-dimensional activation maps should be made in the future to better elucidate how the wavefront spreads. These findings might have important clinical implications, especially for the genesis of arrhythmias in pathophysiological situations. Any pathology that altered the number of functioning gj-channels, not only would affect longitudinal velocity of propagation, but also the transverse propagation ability and velocity. Therefore, the genesis of some arrhythmias, e.g., the reentrant type, could be promoted under such conditions.
Discussion
The results demonstrated that, in a cardiac muscle model, the insertion of many gj- channels, between abutting cells in each longitudinal chain of cells, actually inhibited transverse propagation of excitation between the parallel chains. This was true both for stimulation of only a single cell of the first chain (A-chain; cell A1) and for stimulation simultaneously of the entire 5 cells of the A-chain. The inhibition produced by the gj-channels could be overcome by greatly increasing the value of R ol2  (the longitudinal resistance of the narrow interstitial space between the parallel chains), reflecting tighter packing of the chains.This finding surprised us at first. We were expecting either that there would be no effect on transverse transmission of excitation or that transverse transfer of excitation would be enhanced. But on further refection, the inhibition produced might be predicted. This is based on the fact that, with strong longitudinal coupling between cells, the entire chain of 5 cells must be simultaneously stimulated to threshold. Therefore, if the transverse transfer energy available is limited and is near threshold for a give chain, it is likely that some chains will fail to fire. Thus, the problem of strong coupling is not in the chains that are already excited, but rather in the quiescent adjacent chain which is in process of trying to become excited (D-chain in case of Fig.  3  and C-chain in Fig.  4 ). Strong coupling in the "in-process" chain requires more energy transfer from the "already-activated" chain. If the "in-process" chain were not coupled by gj-channels, then if only one cell of the chain received enough stimulating energy to become activated, excitation would spread from it to the remaining cells of that chain. This idea was tested, and the results shown in Figure  6  are consistent with the mechanism proposed above. In  panel A , in which R gj  was 1.0 MΩ (10,000 gj-channels) uniformly in all 5 chains, chains D and E failed to fire. When R gj  of just chains D and E were changed to infinity (0 channels), then all 5 chains fired ( panel B ). Therefore, the inhibition of transverse propagation can be reversed by uncoupling the cells of the chains that failed.panel Apanel BConsistent with the argument presented in the paragraph above, the transverse propagation velocity was not inhibited by insertion of gj-channels, up through the last chain activated (C-chain in case of Fig.  3  and B-chain in Fig.  4 ). If anything, the transverse velocity was increased slightly (TPT lowered). The TPT values (for differing amount of transverse spread of excitation, e.g. 2-chains, 3-chains, 4-chains, or all 5-chains) are listed in Table  1  for different degrees of cell coupling. Note that, in part A, the largest change in TPT value is between R gj  of ∞ (0 channels) and R gj  of 100 MΩ (100 channels); adding more channels (Rgj of 10 MΩ (1000 channels) or 1.0 MΩ (10,000 channels)) did not further decrease TPT. Similar results were found when the entire A-chain was simulated (part B of Table  1 ).The reader should be alerted to the limitations of the PSpice program. It was not possible to insert a second or third "black-box" in the basic excitable units (because the system went berserk). Therefore, the dynamic behavior of the cardiac cell membrane was only a close approximation.We previously found (unpublished observation) that the transverse velocity was greater when size of the model was increased (eg, 3 × 4, 5 × 5, 7 × 7) up to a presumed maximum, indicating that the boundary conditions affected behavior of the model. Therefore, the present experiments should be repeated on larger-sized models. But we believe that the qualitative findings would be much the same. In addition, 2-dimensional activation maps should be made in the future to better elucidate how the wavefront spreads.These findings might have important clinical implications, especially for the genesis of arrhythmias in pathophysiological situations. Any pathology that altered the number of functioning gj-channels, not only would affect longitudinal velocity of propagation, but also the transverse propagation ability and velocity. Therefore, the genesis of some arrhythmias, e.g., the reentrant type, could be promoted under such conditions.


The hypothesis that human cancers express antigens that can be specifically targeted by cell mediated immunity has become a scientifically justifiable rationale for the design and clinical testing of novel tumor-associated antigens (TAA). Although a number of TAA have been recognized and it has been suggested that they could be useful in the immunological treatment of cancer, the complexity of human beings leads us to reflect on the need to establish new criteria for validating their real applicability. Herein, we show a system level-based approach that includes morphological and molecular techniques, which is specifically required to improve the capacity to produce desired results and to allow cancer immunotherapy to re-emerge from the mist in which it is currently shrouded.

Introduction Although considerable advances have been made in terms of our molecular and cellular knowledge, for most human disease states a fundamental understanding of causal disease onset, disease mechanism and progression, and optimal treatment is still significantly limited. In part, this advancement has been hampered by our inability to fully and rapidly delineate complex cellular metabolic processes and molecular pathways. Organisms are complex self-organizing entities made up of such parts: organs, tissues, cells, organelles and ultimately molecules and atoms. One question that arises, concerns the relationship between the whole and its component parts. The issue at stake is sometimes called "the question of reduction" or "the problem of reductionism" [ 1 ]. The inefficacy of contemporary science to describe biological systems, consisting of non-identical parts that have different and non-local interactions has tended to limit progress in the human healthcare. Many biological systems remain incomprehensible because their multifarious nature has been combined with a reductionist approach based on the linear conception of  cause  and  effect . The use, however, of a more  holistic  multidimensional system level-based approach may provide new insights into the understanding of disease processes and mechanisms of action of therapeutical agents [ 2 ]. Herein we aim to introduce a system level-based approach that includes morphological and molecular techniques for validating the appropriateness of using novel tumor-associated antigens (TAA) for clinical purposes. This approach might be easily implemented for identifying prognostic, diagnostic and alternative biomarkers. Finally, this type of analysis of appropriately designed cohorts might also provide a key to understanding the differences in patients who do or do not respond to any particular therapy. This information may be helpful for a more effective (and therefore more  cost-effective ) design of clinical trials [ 2 ].
Introduction
Although considerable advances have been made in terms of our molecular and cellular knowledge, for most human disease states a fundamental understanding of causal disease onset, disease mechanism and progression, and optimal treatment is still significantly limited.In part, this advancement has been hampered by our inability to fully and rapidly delineate complex cellular metabolic processes and molecular pathways.Organisms are complex self-organizing entities made up of such parts: organs, tissues, cells, organelles and ultimately molecules and atoms. One question that arises, concerns the relationship between the whole and its component parts. The issue at stake is sometimes called "the question of reduction" or "the problem of reductionism" [ 1 ].The inefficacy of contemporary science to describe biological systems, consisting of non-identical parts that have different and non-local interactions has tended to limit progress in the human healthcare. Many biological systems remain incomprehensible because their multifarious nature has been combined with a reductionist approach based on the linear conception of  cause  and  effect .causeeffectThe use, however, of a more  holistic  multidimensional system level-based approach may provide new insights into the understanding of disease processes and mechanisms of action of therapeutical agents [ 2 ].holisticHerein we aim to introduce a system level-based approach that includes morphological and molecular techniques for validating the appropriateness of using novel tumor-associated antigens (TAA) for clinical purposes. This approach might be easily implemented for identifying prognostic, diagnostic and alternative biomarkers.Finally, this type of analysis of appropriately designed cohorts might also provide a key to understanding the differences in patients who do or do not respond to any particular therapy. This information may be helpful for a more effective (and therefore more  cost-effective ) design of clinical trials [ 2 ].cost-effectiveImmunotherapy and the human complexity The recognition and characterization of novel TAA is fundamental to the advance of cancer immunotherapy. The original hypothesis of Boon [ 3 ] and Rosenberg [ 4 ] that human cancers express antigens that can be specifically targeted by cell mediated immunity has become a scientifically justifiable rationale for the design and clinical testing of novel TAA based immunotherapies and therapeutic vaccines [ 5 - 7 ]. However, although a number of TAA have been discovered and it has been suggested that they could be useful in the immunological treatment of cancer, the  complexity  of human beings leads us to reflect on the need to establish compelling new criteria for validating their real applicability.  Biological complexity  can be intuitively appreciated – at least in terms of morphological or behavioral complexity, or the variety of cell types in an organism – but the term itself is notoriously difficult to define [ 8 ]. Human beings are  complex hierarchical system s consisting of a number of  levels of anatomical organization  (genes, cells, tissues, organs, apparatuses, and organism) that interrelate differently with each other to form networks of growing complexity. The concept of anatomical entities as hierarchy of graduated forms, and the increasing number of known structural variables, have highlighted new properties of organized biological matter and raised a series of intriguing questions. In order to understand biology at the system  level , we need to examine the structure and dynamics of the functions of organisms rather than the characteristics of their constitutive isolated parts [ 8 - 13 ]. The expression of TAA in biological materials has mainly been studied at the level of gene expression and gene level measurement by Reverse Transcriptase-Polymerase Chain Reaction (RT-PCR) analysis and the Quantitative real-time PCR (qrt-PCR) technology [ 14 - 17 ]. However, the  information  provided by these approaches is limited by the fact that the phenomena observed at each level of anatomical organization have properties that do not exist at a lower or higher level: RT-PCR and qrt-PCR may offer a satisfactory  qualitative/quantitative  description of  small-scale structures , but this is likely to be irrelevant when it comes to  large-scale features . The above considerations, in conjunction with the  complexity of tumor-host interactions  within the tumor microenvironment caused by temporal changes in tumor phenotypes and an array of immune mediators expressed in the tumor microenvironment [ 18 ] might clarify the limited reliability and applicability of current immunotherapeutic approaches. Here, we suggest a  system level-based  approach (Figure  1 ) for validating the appropriateness of using TAA for clinical purposes, which includes the following never defined before key points: Figure 1 System level-based approach for validating candidate TAA for clinical application. Aside from the well defined experimental procedure, the method presented here is based on the  complex hierarchical nature  of the human beings. The analysis begins at level of gene expression and then continues to higher levels of anatomical organization, (cell, tissue, organ, apparatuses and organism). This approach includes both morphological and molecular techniques. It also introduces the concept of dynamics of TAA expression at the level of the  cell cycle , the  physiological status of the organism  and the  process of aging . •  Discriminating  the  cell types  expressing the candidate antigen on the basis of the morphological visualization of all of the parts making up the  organ  under investigation. •  Discriminating  the candidate antigen's sub-cellular localization (at the level of cell  nucleus ,  cytoplasm  and/or  plasma membrane ) by ultra-structural morphological visualizations. •  Mapping  candidate antigen expression in all of the  organs  making up the  apparatuses . •  Mapping  candidate antigen expression in all of the  apparatuses  making up the living  organism . •  Estimating  the percentage of normal cells and their neoplastic counterparts expressing the candidate antigen. •  Evaluating  the  dynamics  of candidate antigen expression at the level of the  cell cycle , the  physiological status of the organism  ( i.e.  the woman's menstrual cycle) and the  process of aging . In order to advance our knowledge in a currently widely debated field of investigation, a clearer distinction must be made between  in vitro  laboratory results (the discovery and validation of target antigens) and their  in vivo  application ( in vivo  validation), and it is necessary to adopt a more complete experimental approach that forcefully includes both morphological and molecular techniques [ 19 ].
Immunotherapy and the human complexity
The recognition and characterization of novel TAA is fundamental to the advance of cancer immunotherapy. The original hypothesis of Boon [ 3 ] and Rosenberg [ 4 ] that human cancers express antigens that can be specifically targeted by cell mediated immunity has become a scientifically justifiable rationale for the design and clinical testing of novel TAA based immunotherapies and therapeutic vaccines [ 5 - 7 ].However, although a number of TAA have been discovered and it has been suggested that they could be useful in the immunological treatment of cancer, the  complexity  of human beings leads us to reflect on the need to establish compelling new criteria for validating their real applicability.  Biological complexity  can be intuitively appreciated – at least in terms of morphological or behavioral complexity, or the variety of cell types in an organism – but the term itself is notoriously difficult to define [ 8 ]. Human beings are  complex hierarchical system s consisting of a number of  levels of anatomical organization  (genes, cells, tissues, organs, apparatuses, and organism) that interrelate differently with each other to form networks of growing complexity. The concept of anatomical entities as hierarchy of graduated forms, and the increasing number of known structural variables, have highlighted new properties of organized biological matter and raised a series of intriguing questions. In order to understand biology at the system  level , we need to examine the structure and dynamics of the functions of organisms rather than the characteristics of their constitutive isolated parts [ 8 - 13 ].complexityBiological complexitycomplex hierarchical systemlevels of anatomical organizationlevelThe expression of TAA in biological materials has mainly been studied at the level of gene expression and gene level measurement by Reverse Transcriptase-Polymerase Chain Reaction (RT-PCR) analysis and the Quantitative real-time PCR (qrt-PCR) technology [ 14 - 17 ]. However, the  information  provided by these approaches is limited by the fact that the phenomena observed at each level of anatomical organization have properties that do not exist at a lower or higher level: RT-PCR and qrt-PCR may offer a satisfactory  qualitative/quantitative  description of  small-scale structures , but this is likely to be irrelevant when it comes to  large-scale features . The above considerations, in conjunction with the  complexity of tumor-host interactions  within the tumor microenvironment caused by temporal changes in tumor phenotypes and an array of immune mediators expressed in the tumor microenvironment [ 18 ] might clarify the limited reliability and applicability of current immunotherapeutic approaches.informationqualitative/quantitativesmall-scale structureslarge-scale featurescomplexity of tumor-host interactionsHere, we suggest a  system level-based  approach (Figure  1 ) for validating the appropriateness of using TAA for clinical purposes, which includes the following never defined before key points:system level-based•  Discriminating  the  cell types  expressing the candidate antigen on the basis of the morphological visualization of all of the parts making up the  organ  under investigation.Discriminatingcell typesorgan•  Discriminating  the candidate antigen's sub-cellular localization (at the level of cell  nucleus ,  cytoplasm  and/or  plasma membrane ) by ultra-structural morphological visualizations.Discriminatingnucleuscytoplasmplasma membrane•  Mapping  candidate antigen expression in all of the  organs  making up the  apparatuses .Mappingorgansapparatuses•  Mapping  candidate antigen expression in all of the  apparatuses  making up the living  organism .Mappingapparatusesorganism•  Estimating  the percentage of normal cells and their neoplastic counterparts expressing the candidate antigen.Estimating•  Evaluating  the  dynamics  of candidate antigen expression at the level of the  cell cycle , the  physiological status of the organism  ( i.e.  the woman's menstrual cycle) and the  process of aging .Evaluatingdynamicscell cyclephysiological status of the organismi.e.process of agingIn order to advance our knowledge in a currently widely debated field of investigation, a clearer distinction must be made between  in vitro  laboratory results (the discovery and validation of target antigens) and their  in vivo  application ( in vivo  validation), and it is necessary to adopt a more complete experimental approach that forcefully includes both morphological and molecular techniques [ 19 ].in vitroin vivoin vivoConclusions Translational science which is aimed to test, in humans, novel therapeutic strategies developed through experimentation [ 20 ] should begin to consider the role of  emergence  in other words the appearance of  unexpected structures  and/or the occurrence of  surprising behaviors  in large systems composed from microscopic parts, whether physical or biological. By unexpected and surprising we mean structures and behaviors which are not  intuitive  and are not simply  predictable . Since our understanding of complex human disease such as cancer, is still limited and pre-clinical models have shown a discouraging propensity [ 2 , 6 ] to fail when applied to humans, a new way of thinking is strongly needed that unites physicians, biologists, mathematicians and epidemiologists, in order to develop a better theoretical framework of tumor development, progression and tumor-host interactions. Although the model presented here is based on a multidisciplinary system-level approach probably within the reach of only very large and multi-talented laboratories, it is aimed to introduce a different way of investigating  human cancer,  which takes into account the complexity of the human being as a system. The use of a holistic approach, which enables a more accurate selection of immunotherapeutic target antigens in the first phase of the experimental research, will reduce the notable fragmentation of the biological information in the post-genomic era, and will facilitate a more accurate transfer of the acquired knowledge to the bedside. Further, this new multidisciplinary approach is specifically required to improve the capacity to produce desired results with a minimum expenditure of  energy ,  time , or  resources  for immunotherapeutic treatments and to allow cancer immunotherapy to re-emerge from the mist in which it is currently shrouded.
Conclusions
Translational science which is aimed to test, in humans, novel therapeutic strategies developed through experimentation [ 20 ] should begin to consider the role of  emergence  in other words the appearance of  unexpected structures  and/or the occurrence of  surprising behaviors  in large systems composed from microscopic parts, whether physical or biological. By unexpected and surprising we mean structures and behaviors which are not  intuitive  and are not simply  predictable .emergenceunexpected structuressurprising behaviorsintuitivepredictableSince our understanding of complex human disease such as cancer, is still limited and pre-clinical models have shown a discouraging propensity [ 2 , 6 ] to fail when applied to humans, a new way of thinking is strongly needed that unites physicians, biologists, mathematicians and epidemiologists, in order to develop a better theoretical framework of tumor development, progression and tumor-host interactions.Although the model presented here is based on a multidisciplinary system-level approach probably within the reach of only very large and multi-talented laboratories, it is aimed to introduce a different way of investigating  human cancer,  which takes into account the complexity of the human being as a system.human cancer,The use of a holistic approach, which enables a more accurate selection of immunotherapeutic target antigens in the first phase of the experimental research, will reduce the notable fragmentation of the biological information in the post-genomic era, and will facilitate a more accurate transfer of the acquired knowledge to the bedside.Further, this new multidisciplinary approach is specifically required to improve the capacity to produce desired results with a minimum expenditure of  energy ,  time , or  resources  for immunotherapeutic treatments and to allow cancer immunotherapy to re-emerge from the mist in which it is currently shrouded.energytimeresources