Figure 1.
Stochastic channel gating contributes to BVR in a computational model of the canine ventricular myocyte.
A. 5 consecutive APs in a representative canine ventricular midmyocardial cell, the deterministic computational model, or the model with a stochastic Markov formulation of IKr (top to bottom) at 1000-ms pacing CL. APD (ms) is indicated below each beat. B. Poincaré plot of 45 consecutive APDs for the conditions in (A). The white circle in each panel indicates the steady-state APD of the deterministic model.
Figure 2.
Contribution of channel density of stochastic ion currents to BVR and its rate dependence.
A. STV magnitude induced by stochastic channel gating of individual currents in an otherwise deterministic model or stochastic channel gating of all 13 currents/fluxes combined (right-most bars) at CL of 500 ms, 1000 ms, or 2000 ms. Top panel shows 5-fold reduction in channel density (with 5-fold increase in single-channel conductance), middle panel shows channel density based on estimates from experimental data (Section 2.5 in the Supplemental Information), and bottom panel shows 5-fold increase in channel density with reduced single-channel conductance. B. Rate dependence of average APD (left), STV (middle) and LTV (right) in experiments (symbols) and model (lines) with stochastic gating of all 13 targets combined at 100% channel density.
Figure 3.
Contribution of currents to BVR determined via linear regression of 200 unique virtual myocytes.
A. Relative changes in the maximal conductance (Gx) of the 13 currents/fluxes (lanes correspond to the column pairs in panel B) for 100 (out of 200) trials (left panel) and corresponding changes in outputs (APD, STV and LTV) during steady-state pacing at CL = 1000 ms (right panel). Middle panel shows the coefficients that indicate the contribution of each current to every output measure as determined via linear regression. B. Bar plot of the magnitude of the coefficients from panel A regarding their impact on APD (white bars) or STV (shaded bars). IKr and INa have a large impact on both APD and BVR, consistent with the results from Figure 2. In addition, INaK also strongly affects STV. LTV showed similar pattern as STV and is not shown for clarity.
Figure 4.
Effect of AP morphology on BVR.
A. Overlay of 30 APs (top panel) and Poincaré plot of corresponding APDs (bottom panel) for the control myocyte, without alterations in ion currents, simulated with deterministic ICaL, IK1, IKur, and ITo and stochastic gating of the remaining 9 currents. APs with the shortest and longest duration are shown in black, others in grey. Average APD and STV are indicated below the APs. B. Similar to panel A for a triangular AP morphology obtained by reducing IK1 and ITo (by 70% and 60%, respectively) and increasing IKur (by 275%). C. Similar to panels A and B for a square AP morphology obtained by increasing IK1 and IKur (by 20% each) and decreasing ICaL and ITo (by 75% and 20%), respectively.
Figure 5.
Effect of cell-to-cell coupling on BVR.
A. APD (top panel) and STV (bottom panel) of two identical cells for various degrees of electrical coupling. Normal coupling (left vertical dashed line) and critical coupling for successful conduction in a one-dimensional strand of virtual myocytes (right vertical dashed line) are indicated. Both cells received external stimulation. B. Similar to panel A for two cells of which one is prolonged via current injection (−0.1 pA/pF). Cell-to-cell coupling causes a mild decrease in average STV (1.1 ms) that is more pronounced in the case of an asymmetrical cell pair (1.9 ms; inset). C. Effect of strand length on temporal (solid line) and spatial (dashed line) dispersion of repolarization in an asymmetrical one-dimensional strand. Half of the strand received additional current injection to prolong APD, similar to panel B. BVR decreased with increasing strand length, whereas spatial dispersion of repolarization increased for longer strands.
Figure 6.
Role of APD and stochastic gating in BVR reverse rate dependence.
A. Magnitude of channel gating stochastics (assessed by Std(Im) for 50 beats) over time for CL of 350–4000 ms using the fully stochastic model under control conditions. B. Rate dependence of total magnitude of Im fluctuations (given by area under Std(Im) curve). C. STV rate dependence in the fully stochastic model during fixed-CL pacing (solid line) or fixed-DI pacing (dash-dotted line), or in the deterministic model during fixed-CL pacing with a CL-independent stochastic term (see Results, section “BVR rate dependence”) added to Im (dashed line). CL-independent stochastic behavior results in a blunted STV rate dependence. D. STV vs. APD relationship at CLs of 500 ms (dark grey symbols), 1000 ms (white symbols), or 2000 ms (light grey symbols). APD was varied through injection of a deterministic stimulus current between −0.1 and 0.1 pA/pF for the duration of the AP.
Figure 7.
BVR in simulated LQT syndrome types 1–3 in the absence or presence of βARS.
A. Overlay of 30 consecutive APs in the absence (−βARS) or presence (+βARS) of β-adrenergic receptor stimulation under control conditions (top-left panel) or simulated LQT1 (top-right panel), LQT2 (bottom-left panel), or LQT3 (bottom-right panel) at 1000-ms CL. Shortest and longest APs are shown in black, intermediate APs in grey. A Poincaré plot of the 30 APDs is shown below. B. Quantification of BVR in LQT1-3 at CL of 500, 1000, or 2000 ms in the absence or presence of βARS. HMR indicates simulation of the IKs blocker HMR1556 (simulated LQT1), Dof simulation of the IKr blocking drug dofetilide (LQT2) and ATXII indicates simulations with enhanced persistent INa (LQT3). βARS reduces BVR significantly in LQT2 and LQT3, but not in LQT1, consistent with experimental results [8].
Figure 8.
Role of APD in the observed increase in BVR under simulated LQT2 conditions.
A. Overlay of 30 consecutive APs in the model using control conditions, simulated LQT2, simulated LQT2 with deterministic IKr, or simulated LQT2 with reduced APD due to injection of a deterministic stimulus current. Shortest and longest APs are shown in black, intermediate APs in grey. APD, STV, and Poincaré plots are shown below each overlay. B. STV vs. APD relationship under control conditions (left panel) or LQT2 conditions (right panel) in individual canine ventricular myocytes (filled symbols) or individual model cells (open symbols; based on whole-cell conductances drawn from a Gaussian distribution, as in Figure 3A). Data were fit with a monoexponential function (lines). C. Parameters of the monoexponential fits of panel B under control and LQT2 conditions in experiments (grey bars) and model (white bars). The model shows a quantitatively similar STV vs. APD relationship as experiments, and this relationship is not different between control and LQT2 conditions.
Figure 9.
Mechanisms underlying increased BVR under LQT1 conditions with SR Ca2+ overload.
A. STV vs. APD relationship under control (open symbols) or LQT1 conditions (filled symbols) in individual canine ventricular myocytes (left panel). Right panel shows the parameters of the non-linear fit of the STV vs. APD relationship under control or LQT1 conditions (solid and dashed lines in left panel, respectively), or under LQT2 conditions (from Figure 8). B. Consecutive APDs (top panel) and Ca2+-transient amplitudes (middle panel) during simulated application of 1.0 µmol/L isoproterenol (ISO) at a 500-ms CL in the deterministic model. Membrane potential and intracellular [Ca2+] for the beats indicated by the black vertical boxes are shown in the bottom panel. APD (in ms) is indicated below each beat and a Poincaré plot is shown on the right. Simulations were performed with 100% IKs inhibition to simulate LQT1 conditions and with 10% inhibition of INaK, resulting in increased [Na+]i and reduced Ca2+ extrusion via INaCa, to promote Ca2+-handling abnormalities. C. Similar to panel B for the stochastic model with a single domain. D. Similar to panel B for the stochastic model divided into four identical domains connected via Ca2+-diffusion terms with time constant τ = 20 ms.