Stretch-activated current in human atrial myocytes and Na+ current and mechano-gated channels’ current in myofibroblasts alter myocyte mechanical behavior: a computational study

Background The activation of stretch-activated channels (SACs) in cardiac myocytes, which changes the phases of action potential repolarization, is proven to be highly efficient for the conversion of atrial fibrillation. The expression of Na+ current in myofibroblasts (Mfbs) regenerates myocytes’ action potentials, suggesting that Mfbs play an active role in triggering cardiac rhythm disturbances. Moreover, the excitation of mechano-gated channels (MGCs) in Mfbs depolarizes their membrane potential and contributes to the increased risk of post-infarct arrhythmia. Although these electrophysiological mechanisms have been largely known, the roles of these currents in cardiac mechanics are still debated. In this study, we aimed to investigate the mechanical influence of these currents via mathematical modeling. A novel mathematical model was developed by integrating models of human atrial myocyte (including the stretch-activated current, Ca2+–force relation, and mechanical behavior of a single segment) and Mfb (including our formulation of Na+ current and mechano-gated channels’ current). The effects of the changes in basic cycle length, number of coupled Mfbs and intercellular coupling conductance on myocyte mechanical properties were compared. Results Our results indicated that these three currents significantly regulated myocyte mechanical parameters. In isosarcometric contraction, these currents increased segment force by 13.8–36.6% and dropped element length by 12.1–31.5%. In isotonic contraction, there are 2.7–5.9% growth and 0.9–24% reduction. Effects of these currents on the extremum of myocyte mechanical parameters become more significant with the increase of basic cycle length, number of coupled Mfbs and intercellular coupling conductance. Conclusions The results demonstrated that stretch-activated current in myocytes and Na+ current and mechano-gated channels’ current in Mfbs significantly influenced myocyte mechanical behavior and should be considered in future cardiac mechanical mathematical modeling.

Synergistic plasticity of intrinsic conductance and electrical coupling restores synchrony in an intact motor network

Motor neurons of the crustacean cardiac ganglion generate virtually identical, synchronized output despite the fact that each neuron uses distinct conductance magnitudes. As a result of this variability, manipulations that target ionic conductances have distinct effects on neurons within the same ganglion, disrupting synchronized motor neuron output that is necessary for proper cardiac function. We hypothesized that robustness in network output is accomplished via plasticity that counters such destabilizing influences. By blocking high-threshold K+ conductances in motor neurons within the ongoing cardiac network, we discovered that compensation both resynchronized the network and helped restore excitability. Using model findings to guide experimentation, we determined that compensatory increases of both GA and electrical coupling restored function in the network. This is one of the first direct demonstrations of the physiological regulation of coupling conductance in a compensatory context, and of synergistic plasticity across cell- and network-level mechanisms in the restoration of output.

Effects of Na+Current and Mechanogated Channels in Myofibroblasts on Myocyte Excitability and Repolarization

Fibrotic remodeling, characterized by fibroblast phenotype switching, is often associated with atrial fibrillation and heart failure. This study aimed to investigate the effects on electrotonic myofibroblast-myocyte (Mfb-M) coupling on cardiac myocytes excitability and repolarization of the voltage-gated sodium channels (VGSCs) and single mechanogated channels (MGCs) in human atrial Mfbs. Mathematical modeling was developed from a combination of (1) models of the human atrial myocyte (including the stretch activated ion channel current,ISAC) and Mfb and (2) our formulation of currents through VGSCs (INa_Mfb) and MGCs (IMGC_Mfb) based upon experimental findings. The effects of changes in the intercellular coupling conductance, the number of coupled Mfbs, and the basic cycle length on the myocyte action potential were simulated. The results demonstrated that the integration ofISAC,INa_Mfb, andIMGC_Mfbreduced the amplitude of the myocyte membrane potential(Vmax)and the action potential duration (APD), increased the depolarization of the resting myocyte membrane potential(Vrest), and made it easy to trigger spontaneous excitement in myocytes. For Mfbs, significant electrotonic depolarizations were exhibited with the addition ofINa_MfbandIMGC_Mfb. Our results indicated thatISAC,INa_Mfb, andIMGC_Mfbsignificantly influenced myocytes and Mfbs properties and should be considered in future cardiac pathological mathematical modeling.

Extending Cable Theory to Heterogeneous Dendrites

Dendrites may exhibit many types of electrical and morphological heterogeneities at the scale of a few micrometers. Models of neurons, even so-called detailed models, rarely consider such heterogeneities. Small-scale fluctuations in the membrane conductances and the diameter of dendrites are generally disregarded and spines merely incorporated into the dendritic shaft. Using the two-scales method known as homogenization, we establish explicit expressions for the small-scale fluctuations of the membrane voltage, and we derive the cable equation satisfied by the voltage when these fluctuations are averaged out. This allows us to rigorously establish under what conditions a heterogeneous dendrite can be approximated by a homogeneous cable. We consider different distributions of synapses, orderly or random, on a passive dendrite, and we investigate when replacing excitatory and inhibitory synaptic conductances by their local averages leads to a small error in the voltage. This indicates in which regimes the approximations made in compartmental models are justified. We extend these results to active membranes endowed with voltage-dependent conductances or NMDA receptors. Then we examine under which conditions a spiny dendrite behaves as a smooth dendrite. We discover a new regime where this holds true, namely, when the conductance of the spine neck is small compared to the conductance of the synapses impinging on the spine head. Spines can then be taken into account by an effective excitatory current, the capacitance of the dendrite remaining unchanged. In this regime, the synaptic current transmitted from a spine to the dendritic shaft is strongly attenuated by the weak coupling conductance, but the total current they deliver can be quite substantial. These results suggest that pedunculated spines and stubby spines might play complementary roles in synaptic integration. Finally, we analyze how varicosities affect voltage diffusion in dendrites and discuss their impact on the spatiotemporal integration of synaptic input.

Connections Between Connexins, Calcium, and Cataracts in the Lens

There is a good deal of evidence that the lens generates an internal micro circulatory system, which brings metabolites, like glucose, and antioxidants, like ascorbate, into the lens along the extracellular spaces between cells. Calcium also ought to be carried into the lens by this system. If so, the only path for Ca2+ to get out of the lens is to move down its electrochemical gradient into fiber cells, and then move by electrodiffusion from cell to cell through gap junctions to surface cells, where Ca-ATPase activity and Na/Ca exchange can transport it back into the aqueous or vitreous humors. The purpose of the present study was to test this calcium circulation hypothesis by studying calcium homeostasis in connexin (Cx46) knockout and (Cx46 for Cx50) knockin mouse lenses, which have different degrees of gap junction coupling. To measure intracellular calcium, FURA2 was injected into fiber cells, and the gradient in calcium concentration from center to surface was mapped in each type of lens. In wild-type lenses the coupling conductance of the mature fibers was ∼0.5 S/cm2 of cell to cell contact, and the best fit to the calcium concentration data varied from 700 nM in the center to 300 nM at the surface. In the knockin lenses, the coupling conductance was ∼1.0 S/cm2 and calcium varied from ∼500 nM at the center to 300 nM at the surface. Thus, when the coupling conductance doubled, the concentration gradient halved, as predicted by the model. In knockout lenses, the coupling conductance was zero, hence the efflux path was knocked out and calcium accumulated to ∼2 μM in central fibers. Knockout lenses also had a dense central cataract that extended from the center to about half the radius. Others have previously shown that this cataract involves activation of a calcium-dependent protease, Lp82. We can now expand on this finding to provide a hypothesis on each step that leads to cataract formation: knockout of Cx46 causes loss of coupling of mature fiber cells; the efflux path for calcium is therefore blocked; calcium accumulates in the central cells; at concentrations above ∼1 μM (from the center to about half way out of a 3-wk-old lens) Lp82 is activated; Lp82 cleaves cytoplasmic proteins (crystallins) in central cells; and the cleaved proteins aggregate and scatter light.

Gap Junctional Coupling in Lenses from α8 Connexin Knockout Mice

Lens fiber cell gap junctions contain α3 (Cx46) and α8 (Cx50) connexins. To examine the roles of the two different connexins in lens physiology, we have genetically engineered mice lacking either α3 or α8 connexin. Intracellular impedance studies of these lenses were used to measure junctional conductance and its sensitivity to intracellular pH. In Gong et al. 1998, we described results from α3 connexin knockout lenses. Here, we present original data from α8 connexin knockout lenses and a comparison with the previous results. The lens has two functionally distinct domains of fiber cell coupling. In wild-type mouse lenses, the outer shell of differentiating fibers (see 1, DF) has an average coupling conductance per area of cell–cell contact of ∼1 S/cm2, which falls to near zero when the cytoplasm is acidified. In the inner core of mature fibers (see 1, MF), the average coupling conductance is ∼0.4 S/cm2, and is insensitive to acidification of the cytoplasm. Both connexin isoforms appear to contribute about equally in the DF since the coupling conductance for either heterozygous knockout (+/−) was ∼70% of normal and 30–40% of the normal for both −/− lenses. However, their contribution to the MF was different. About 50% of the normal coupling conductance was found in the MF of α3 +/− lenses. In contrast, the coupling of MF in the α8 +/− lenses was the same as normal. Moreover, no coupling was detected in the MF of α3 −/− lenses. Together, these results suggest that α3 connexin alone is responsible for coupling MF. The pH- sensitive gating of DF junctions was about the same in wild-type and α3 connexin −/− lenses. However, in α8 −/− lenses, the pure α3 connexin junctions did not gate closed in the response to acidification. Since α3 connexin contributes about half the coupling conductance in DF of wild-type lenses, and that conductance goes to zero when the cytoplasmic pH drops, it appears α8 connexin regulates the gating of α3 connexin. Both connexins are clearly important to lens physiology as lenses null for either connexin lose transparency. Gap junctions in the MF survive for the lifetime of the organism without protein turnover. It appears that α3 connexin provides the long-term communication in MF. Gap junctions in DF may be physiologically regulated since they are capable of gating when the cytoplasm is acidified. It appears α8 connexin is required for gating in DF.

Fast pacing facilitates discontinuous action potential propagation between rabbit atrial cells

We examined the critical coupling conductance ( G C) for propagation at different pacing cycle lengths (CLs) (1,000 and 400 ms). As G C was progressively reduced, propagation failed at a CL of 1,000 ms, whereas propagation succeeded at a CL of 400 ms over a range of G C values before failing at a CL of 400 ms at a lower G C, showing facilitation of propagation at the shorter CL. Critical G C was (means ± SE) 0.8 ± 0.1 nS for a CL of 400 ms and 1.3 ± 0.1 nS for a CL of 1,000 ms (a 63% increase, P < 0.002, n = 9 cell pairs). In 14 uncoupled cells, action potential duration at 30% repolarization (APD30) increased from 19.9 ± 2.5 to 41.8 ± 2.6 ms ( P < 0.001) as CL decreased from 1,000 to 400 ms. In five cell pairs, critical G Cwith 4-aminopyridine (4-AP) was reduced to 0.4 ± 0.1 nS at a CL of 1,000 ms ( P < 0.05 compared with control solution), and critical G C in 4-AP was unchanged by decreasing CL to 400 ms. It is possible that the “remodeling” of atrial cells due to atrial fibrillation or tachycardia, which has been shown to produce a decrease in the transient outward current, may result in an enhanced ability to propagate, possibly facilitating further development of fibrillation under conditions of decreased cellular coupling.