Transverse propagation in an expanded PSpice model for cardiac muscle with gap-junction ion channels

Transverse propagation was previously found to occur in a two-dimensional model of cardiac muscle using the PSpice software program for electronic circuit design and analysis. Longitudinal propagation within each chain, and transverse propagation between parallel chains, occurred even when there were no gap-junction (g-j) channels inserted between the simulated myocardial cells either longitudinally or transversely. In those studies, there were pronounced edge (boundary) effects and end-effects even within single chains. Transverse velocity increased with increase in model size. The present study was performed to examine boundary effects on transverse propagation velocity when the length of the chains was held constant at 10 cells and the number of parallel chains was varied from 3 to 5, to 7, to 10, and to 20. The number of g-j channels was either zero, both longitudinally and transversely (0/0), or 100/100. Some experiments were also made at 100/0, 1/1, and 10/10. Transverse velocity and overall velocity (both longitudinal and transverse components) was calculated from the measured total propagation time (TPT), i.e., the elapsed time between when the first action potential (AP) and the last AP crossed the zero potential level. The transverse g-j channels were placed only at the ends of each chain, such that propagation would occur in a zigzag pattern. Electrical stimulation was applied intracellularly between cells A1 and A2. It was found that, with no g-j channels (0/0), overall velocity increased almost linearly when more and more chains were placed in parallel. In contrast, with many g-j channels (100/100), there was a much flatter relationship between overall velocity and number of parallel chains. The difference in velocities with 0/0 channels and 100/100 channels was reduced as the number of chains was increased. In conclusion, edges have important effects on propagation velocity (overall and transverse) in cardiac muscle simulations.     

Gap-junction channels inhibit transverse propagation in cardiac muscle

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.     

Transverse propagation of action potentials between parallel chains of cardiac muscle and smooth muscle cells in PSpice simulations

Background  

We previously examined transverse propagation of action potentials between 2 and 3 parallel chain of cardiac muscle cells (CMC) simulated using the PSpice program. The present study was done to examine transverse propagation between 5 parallel chains in an expanded model of CMC and smooth muscle cells (SMC).     

Transverse propagation of action potentials between parallel chains of cardiac muscle and smooth muscle cells in PSpice simulations

Background  

The goal of our study is to examine the effect of stimulating a two-dimensional sheet of myocardial cells. We assume that the stimulating electrode is located in a bath perfusing the tissue.     

Propagation of action potentials between parallel chains of cardiac muscle cells in PSpice simulation

Propagation of action potentials between parallel chains of cardiac muscle cells was simulated using the PSpice program. Excitation was transmitted from cell to cell along a strand of three or four cells not connected by low-resistance tunnels (gap-junction connexons) in parallel with one or two similar strands. Thus, two models were used: a 2 x 3 model (two parallel chains of three cells each) and a 3 x 4 model (three parallel chains of four cells each). The entire surface membrane of each cell fired nearly simultaneously, and nearly all the propagation time was spent at the cell junctions, thus giving a staircase-shaped propagation profile. The junctional delay time between contiguous cells in a chain was about 0.2-0.5 ms. A significant negative cleft potential develops in the narrow junctional clefts, whose magnitude depends on several factors, including the radial cleft resistance (Rjc). The cleft potential (Vjc) depolarizes the postjunctional membrane to threshold by a patch-clamp action. Therefore, one mechanism for the transfer of excitation from one cell to the next is by the electric field (EF) that is generated in the junctional cleft when the prejunctional membrane fires. Propagation velocity increased with elevation of Rjc. With electrical stimulation of the first cell of the first strand (cell A1), propagation rapidly spread down that chain and then jumped to the second strand (B chain), followed by jumping to the third strand (C chain) when present. The rapidity by which the parallel chains became activated depended on the longitudinal resistance of the narrow extracellular cleft between the parallel strands (Rol2). The higher the Rol2 resistance, the faster the propagation (lower propagation time) over the cardiac muscle sheet (2-dimensional). The transverse resistance of the cleft had no effect. When the first cell of the second strand (cell B1) was stimulated, propagation spread down the B chain and jumped to the other two strands (A and C) nearly simultaneously. When cell C1 was stimulated, propagation traveled down the C chain and jumped to the B chain, followed by excitation of the A chain. Thus, there was transverse propagation of excitation as longitudinal propagation was occurring. Therefore, transmission of excitation by the EF mechanism can occur between myocardial cells lying closely parallel to one another without the requirement of a specialized junction.     

Propagation velocity profile in a cross-section of a cardiac muscle bundle from PSpice simulation

Background  

The effect of depth on propagation velocity within a bundle of cardiac muscle fibers is likely to be an important factor in the genesis of some heart arrhythmias.     

Repolarization of the action potential enabled by Na<Superscript>+</Superscript> channel deactivation in PSpice simulation of cardiac muscle propagation

Background  

In previous studies on propagation of simulated action potentials (APs) in cardiac muscle using PSpice modeling, we reported that a second black-box (BB) could not be inserted into the K⁺ leg of the basic membrane unit because that caused the PSpice program to become very unstable. Therefore, only the rising phase of the APs could be simulated. This restriction was acceptable since only the mechanism of transmission of excitation from one cell to the next was being investigated.     

Stochastic 16-state model of voltage gating of gap-junction channels enclosing fast and slow gates

Gap-junction (GJ) channels formed of connexin (Cx) proteins provide a direct pathway for electrical and metabolic cell-cell interaction. Each hemichannel in the GJ channel contains fast and slow gates that are sensitive to transjunctional voltage (Vj). We developed a stochastic 16-state model (S16SM) that details the operation of two fast and two slow gates in series to describe the gating properties of homotypic and heterotypic GJ channels. The operation of each gate depends on the fraction of Vj that falls across the gate (VG), which varies depending on the states of three other gates in series, as well as on parameters of the fast and slow gates characterizing 1), the steepness of each gate's open probability on VG; 2), the voltage at which the open probability of each gate equals 0.5; 3), the gating polarity; and 4), the unitary conductances of the gates and their rectification depending on VG. S16SM allows for the simulation of junctional current dynamics and the dependence of steady-state junctional conductance (gj,ss) on Vj. We combined global coordinate optimization algorithms with S16SM to evaluate the gating parameters of fast and slow gates from experimentally measured gj,ss-Vj dependencies in cells expressing different Cx isoforms and forming homotypic and/or heterotypic GJ channels.     

Properties of calcium channels in cardiac muscle and vascular smooth muscle

The voltage-dependent slow channels in the myocardial cell membrane are the major pathway by which Ca²⁺ ions enter the cell during excitation for initiation and regulation of the force of contraction of cardiac muscle. The slow channels have some special properties, including functional dependence on metabolic energy, selective blockade by acidosis, and regulation by the intracellular cyclic nucleotide levels. Because of these special properties of the slow channels, Ca²⁺ influx into the myocardial cell can be controlled by extrinsic factors (such as autonomic nerve stimulation or circulating hormones) and by intrinsic factors (such as cellular pH or ATP level). The slow Ca²⁺ channels of the heart are regulated by cAMP in a stimulatory fashion. Elevation of cAMP produces a very rapid increase in number of slow channels available for voltage activation during excitation. The probability of a slow channel opening and the mean open time of the channel are increased. Therefore, any agent that increases the cAMP level of the myocardial cell will tend to potentiate I_si, Ca²⁺ influx, and contraction. The myocardial slow Ca²⁺ channels are also regulated by cGMP, in a manner that is opposite to that of CAMP. The effect of cGMP is presumably mediated by means of phosphorylation of a protein, as for example, a regulatory protein (inhibitory-type) associated with the slow channel. Preliminary data suggest that calmodulin also may play a role in regulation of the myocardial slow Ca²⁺ channels, possibly mediated by the Ca²⁺-calmodulin-protein kinase and phosphorylation of some regulatory-type of protein. Thus, it appears that the slow Ca²⁺ channel is a complex structure, including perhaps several associated regulatory proteins, which can be regulated by a number of extrinsic and intrinsic factors.VSM cells contain two types of Ca²⁺ channels: slow (L-type) Ca²⁺ channels and fast (T-type) Ca²⁺ channels. Although regulation of voltage-dependent Ca²⁺ slow channels of VSM cells have not been fully clarified yet, we have made some progress towards answering this question. Slow (L-type, high-threshold) Ca²⁺ channels may be modified by phosphorylation of the channel protein or an associated regulatory protein. In contrast to cardiac muscle where cAMP and cGMP have antagonistic effects on Ca²⁺ slow channel activity, in VSM, cAMP and cGMP have similar effects, namely inhibition of the Ca²⁺ slow channels. Thus, any agent that elevates cAMP or cGMP will inhibit Ca²⁺ influx, and thereby act to produce vasodilation. The Ca²⁺ slow channels require ATP for activity, with a K_0.5 of about 0.3 mM. C-kinase may stimulate the Ca²⁺ slow channels by phosphorylation. G-protein may have a direct action on the Ca²⁺ channels, and may mediate the effects of activation of some receptors. These mechanisms of Ca²⁺ channel regulation may be invoked during exposure to agonists or drugs, which change second messenger levels, thereby controlling vascular tone.     

Boundary effects influence velocity of transverse propagation of simulated cardiac action potentials

Background  

We previously demonstrated that transverse propagation of excitation (cardiac action potentials simulated with PSpice) could occur in the absence of low-resistance connections (gap – junction channels) between parallel chains of myocardial cells. The transverse transmission of excitation between the chains was strongly dependent on the longitudinal resistance of the interstitial fluid space between the chains: the higher this resistance, the closer the packing of the parallel chains within the bundle. The earlier experiments were carried out with 2-dimensional sheets of cells: 2 × 3, 3 × 4, and 5 × 5 models (where the first number is the number of parallel chains and the second is the number of cells in each chain). The purpose of the present study was to enlarge the model size to 7 × 7, thus enabling the transverse velocities to be compared in models of different sizes (where all circuit parameters are identical in all models). This procedure should enable the significance of the role of edge (boundary) effects in transverse propagation to be determined.     

Monovalent ion current through single calcium channels of skeletal muscle transverse tubules.

Akali monovalents, Li, Na, K, Cs, and organic monovalents of molecular cross section less than 20 A2, ammonium, methylammonium, hydrazinium, guanidinium, are shown to have a measurable conductance through Ca channels of muscle transverse tubules reconstituted into planar bilayers. For the alkali series, single channel conductances follow the sequence Cs approximately equal to K greater than Na greater than Li with a conductance ratio [g(Cs)/g(Li)] = 1.7. For permeability ratios, the sequence is Li greater than Na greater than K approximately equal to Cs with [P(Li)/P(Cs)] = 1.5. Monovalent current is only unmasked when Ba ions are not present. In mixtures of Cs and Ba, single channel current reverses close to the Ba equilibrium potential and more than 100 mV away from the Cs equilibrium potential. A cutoff in conduction is found for organic cations larger than trimethylammonium; this suggests an apparent pore aperture of about 5 X 5 A. Even in such a large pore, the fact that the alkali cation permeability sequence and conductance sequence are inverted rules out molecular sieving as the mechanism of selection among monovalents.     

A model for propagation of action potentials in smooth muscle

A modified Hodgkin & Huxley (1952) model for axons was used to simulate smooth muscle action potentials. The modifications were such as to match our own experimental results and published data on the passive and active behavior of smooth muscle.A brief account of the modifications introduced to the HH model is as follows. The resting ionic conductances were obtained from the data of Casteels (1969). Chloride conductance was replaced by an ad hoc leakage conductance ($\text{g}\text{?}{}_{\mathrm{L}}$) in order to obtain a resting membrane resistance of about 11 kΩcm². The ionic equilibrium potentials were according to Kao & Nishiyama (1969). The rate constants m, n and h have similar form to those in axons, but their different numerical values produce action potentials that match the duration of the smooth muscle action potential (about 16 ms) at half its maximum amplitude. The effective membrane capacitance was taken as 2.5 μF/cm².The results obtained by implementing those smooth muscle parameters in the HH formulation include: (a) a membrane potential that matches the main characteristics of experimentally recorded action potentials in uterine smooth muscle and guinea-pig taenia-coli, and (b) a propagated action potential which, on a cable diameter of 5 μm (similar to the diameter of a single smooth muscle cell), has a speed of propagation within the range of the values experimentally recorded in smooth muscle. This observed velocity of propagation is not compatible with a large cable and it is concluded that “functional units” are not required to sustain propagation of action potentials in smooth muscle.     

A hill-type muscle model expansion accounting for effects of varying transverse muscle load

Recent studies demonstrated that uniaxial transverse loading (F_G) of a rat gastrocnemius medialis muscle resulted in a considerable reduction of maximum isometric muscle force (ΔF_im). A hill-type muscle model assuming an identical gearing G between both ΔF_im and F_G as well as lifting height of the load (Δh) and longitudinal muscle shortening (Δl_CC) reproduced experimental data for a single load.Here we tested if this model is able to reproduce experimental changes in ΔF_im and Δh for increasing transverse loads (0.64 N, 1.13 N, 1.62 N, 2.11 N, 2.60 N). Three different gearing ratios were tested: (I) constant G_c representing the idea of a muscle specific gearing parameter (e.g. predefined by the muscle geometry), (II) G_exp determined in experiments with varying transverse load, and (III) G_f that reproduced experimental ΔF_im for each transverse load.Simulations using G_c overestimated ΔF_im (up to 59%) and Δh (up to 136%) for increasing load. Although the model assumption (equal G for forces and length changes) held for the three lower loads using G_exp and G_f, simulations resulted in underestimation of ΔF_im by 38% and overestimation of Δh by 58% for the largest load, respectively. To simultaneously reproduce experimental ΔF_im and Δh for the two larger loads, it was necessary to reduce F_im by 1.9% and 4.6%, respectively. The model seems applicable to account for effects of muscle deformation within a range of transverse loading when using a linear load-dependent function for G.     

Effect of transverse thoracic muscle plane block on postoperative cognitive dysfunction after open cardiac surgery: A randomized clinical trial

The transversus thoracis muscle plane (TTMP) block provides effective analgesia in cardiac surgery patients. The aim of this study was to assess whether bilateral TTMP blocks can reduce the incidence of postoperative cognitive dysfunction (POCD) in patients undergoing cardiac valve replacement. A group of 103 patients were randomly divided into the TTM group (n = 52) and the PLA (placebo) group (n = 51). The primary endpoint was the incidence of POCD at 1 week after surgery. Secondary outcome measures included a reduction of intraoperative mean arterial pressure (MAP) >20% from baseline, intraoperative and postoperative sufentanil consumption, length of stay in the ICU, incidence of postoperative nausea and vomiting (PONV), time to first faeces, postoperative pain at 24 h after surgery, time to extubation and the length of hospital stay. Interleukin (IL)-6, TNF-α, S-100β, insulin, glucose and insulin resistance were measured at before induction of anaesthesia, 1, 3and 7 days after surgery. The MoCA scores were significantly lower and the incidence of POCD decreased significantly in TTM group compared with PLA group at 7 days after surgery. Perioperative sufentanil consumption, the incidence of PONV and intraoperative MAP reduction >20% from baseline, length of stay in the ICU, postoperative pain at 24 h after surgery, time to extubation and the length of hospital stay were significantly decreased in the TTM group. Postoperatively, IL-6, TNF-α, S-100β, HOMA-IR, insulin, glucose levels increased and the TTM group had a lower degree than the PLA group at 1, 3 and 7 days after surgery. In summary, bilateral TTMP blocks could improve postoperative cognitive function in patients undergoing cardiac valve replacement.     

Voltage-dependent calcium channels in skeletal muscle transverse tubules. Measurements of calcium efflux in membrane vesicles

Transverse tubule membranes isolated from rabbit skeletal muscle consist mainly of sealed vesicles that are oriented primarily inside out. These membranes contain a high density of binding sites for 1,4-dihydropyridine calcium channel antagonists. The presence of functional voltage-dependent calcium channels in these membranes has been demonstrated by their ability to mediate 45Ca2+ efflux in response to changes in membrane potential. Fluorescence changes of the voltage-sensitive dye, 3,3'-dipropyl-2,2'-thiadicarbocyanine, have shown that transverse tubule vesicles may generate and maintain membrane potentials in response to establishing potassium gradients across the membrane in the presence of valinomycin. A two-step procedure has been developed to measure voltage-dependent calcium fluxes. Vesicles loaded with 45Ca2+ are first diluted into a buffer designed to generate a membrane potential mimicking the resting state of the cell and to reduce the extravesicular Ca2+ to sub-micromolar levels. 45Ca2+ efflux is then measured upon subsequent depolarization. Flux responses are modulated with appropriate pharmacological specificity by 1,4-dihydropyridines and are inhibited by other calcium channel antagonists such as lanthanum and verapamil.     

Effect of thapsigargin on cardiac muscle cells.

The effect of thapsigargin on the activity of various enzymes involved in the Ca(2+)-homeostasis of cardiac muscle and on the contractile activity of isolated cardiomyocytes was investigated. Thapsigargin was found to be a potent and specific inhibitor of the Ca(2+)-pump of striated muscle SR (IC50 in the low nanomolar range). A strong reduction of the Vmax of the Ca(2+)-pump was observed while the Km (Ca2+) was only slightly affected. Reduction of the Vmax was caused by the inability of the ATPase to form the Ca(2+)-dependent acylphosphate intermediate. Thapsigargin did not change the passive permeability characteristics nor the function of the Ca(2+)-release channels of the cisternal compartments of the SR. In addition, no significant effects of thapsigargin on other ATPases, such as the Ca(2+)-ATPase and the Na+/K(+)-ATPase of the plasma membrane as well as the actomyosin ATPase could be detected. The contractile activity of paced adult rat cardiomyocytes was completely abolished by 300 nM thapsigargin. At lower concentrations the drug prolonged considerably the contraction-relaxation cycle, in particular the relaxation phase. The intracellular Ca(2+)-transients elicited by electrical stimulation (as measured by the changes in Fluo-3 fluorescence) decreased in parallel and the time needed to lower free Ca2+ down to the resting level increased. In conclusion, the results indicate that selective inhibition of the Ca(2+)-pump of the SR by thapsigargin accounts for the functional degeneration of myocytes treated with the drug.     

Biochemical analysis of L-type calcium channels from skeletal and cardiac muscle

The development of specific pharmacological agents that modulate different types of ion channels has prompted an extensive effort to elucidate the molecular structure of these important molecules. The calcium channel blockers that specifically modulate the L-type calcium channel activity have aided in the purification and reconstitution of this channel from skeletal muscle transverse tubules. The L-type calcium channel from skeletal muscle is composed of five subunits designated alpha 1, alpha 2, beta, gamma, and sigma. The alpha 1-subunit is the pore-forming polypeptide and contains the ligand binding and phosphorylation sites through which channel activity can be modulated. The role of the other subunits in channel function remains to be studied. The calcium channel components have also been partially purified from cardiac muscle. The channel consists of at least three subunits that have properties related to the subunits of the calcium channel from skeletal muscle. A core polypeptide that can form a channel and contains ligand binding and phosphorylation sites has been identified in cardiac preparations. Here we summarize recent biochemical and molecular studies describing the structural features of these important ion channels.     

Action potential repolarization enabled by Ca<Superscript>++</Superscript> channel deactivation in PSpice simulation of smooth muscle propagation

Background  

Previously, only the rising phase of the action potential (AP) in cardiac muscle and smooth muscle could be simulated due to the instability of PSpice upon insertion of a second black box (BB) into the K⁺ leg of the basic membrane unit. This restriction was acceptable because only the transmission of excitation from one cell to the next was investigated.     

Effect of exercise on cardiac muscle performance in aged rats

Most investigations of a direct impact of chronic physical conditioning on cardiac muscle physiology and biochemistry have utilized relatively young animal models. Some, but not all, of these studies have demonstrated beneficial effect of relatively modest magnitude. With advancing age, i.e., with the onset of senescence, characteristic changes in many aspects of cardiac physiology and biochemistry in rodent models have been noted to occur. In general, these consist of a reduction in the kinetics of events that determine myocardial excitation-contraction relaxation and energetics. Recently it has been shown that several of these apparent age-related functional declines can be reversed by chronic physical conditioning, which in some instances have no effect on cardiac muscle of younger animals. This suggests that the relative efficacy of chronic exercise to modulate myocardial performance may, in part, be determined by the level of function present before the intervention, as is the case for other modulators of cardiac muscle function. In addition, that apparent age-related deficits in myocardial function can be reversed by conditioning suggests an interaction between life-style and aging.