Do calcium channel blockers applied to cardiomyocytes cause increased channel expression resulting in reduced efficacy?

The study examines whether calcium channel blockers (CCBs), specifically nifedipine, trigger compensatory increases in calcium channel expression in cardiomyocytes, thereby reducing drug efficacy over hours. Excitable cells maintain electrophysiological homeostasis despite constant protein turnover, raising the question of how ion channel expression is regulated to preserve function. Prior work (notably by Marder and colleagues and O’Leary et al.) posits that intracellular calcium acts as a feedback signal controlling ion channel expression to maintain a target calcium level. Given that CCBs acutely reduce calcium influx and intracellular calcium, the authors hypothesize that this reduction activates a homeostatic program that upregulates L-type channel density, partially reversing the drug effect over time. The purpose is to combine mathematical modeling with hiPSC-CM measurements to test this time-dependent efficacy hypothesis and to refine models to prevent unrealistic unlimited channel growth.

Foundational studies by Marder and colleagues established activity-dependent regulation of neuronal conductances and homeostatic network stability. O’Leary et al. proposed a biologically plausible model where intracellular calcium relative to a target level drives the transcriptional and translational regulation of ion channels, leading to correlated channel expression. This framework has been extended to cardiac pacemaker cells (Moise and Weinberg) and discussed more broadly in calcium regulation literature. Clinically, CCBs are well-established for hypertension, angina, and arrhythmias; by blocking L-type Ca2+ channels, they reduce calcium entry and downstream calcium-induced calcium release (graded release). Prior models suggested calcium could regulate multiple channels, pumps, and exchangers, but the present work focuses on L-type channels for parsimony, given complex and sometimes opposing effects of other currents on intracellular calcium. Reports indicate time-dependent recovery of calcium currents after chronic CCB exposure in some iPSC-CM lines, motivating a mechanistic explanation via gene expression dynamics.

Modeling framework: The authors start from a two-variable ODE model for ion channel expression dynamics inspired by O’Leary et al., with m representing relative mRNA abundance and n representing relative channel protein abundance. The dynamics are driven by the deviation of cytosolic calcium (c) from a target value (c*): dm/dt ∝ (c* − c) with time constant τm, and dn/dt ∝ (m − n) with time constant τr. The number of L-type channels is dynamic (proportional to n), while other channel types are held constant. Calcium current formulation: The whole-cell L-type calcium current I_CaL is computed from single-channel current and open probability scaled by the number of channels per area and membrane capacitance. Drug block is incorporated by a factor b(D) (fraction of current remaining), with b(0)=1 and smaller values indicating stronger block (e.g., 0.1 for 90% block). Only I_CaL is directly affected by nifedipine in the model. Reduction and constraints: Simulations reveal m≈n, motivating reduction to a scalar model for n. To prevent unrealistic unlimited channel growth under sustained low calcium (as occurs with strong CCB block), the authors impose lower and upper bounds on n via a smooth bounding function H(c,n), so that dn/dt = (c* − c) H(c,n)/τr. This effectively limits n within a plausible physiological range (on the order of ~0.1 to ~3 relative to baseline), while allowing regulation toward c*. Parameter choices used for demonstrations include τm=400 ms and τr=1000 ms for initial explorations, with τr tuned around several hundred milliseconds in the reduced/bounded model; small smoothing parameter ε≈0.01; calcium threshold parameter on the order of 10^−7 mM. The target c* is the average cytosolic calcium over one action potential (AP) cycle in the default model (n=1). Electrophysiology model: The regulation model is embedded in a hiPSC-CM action potential model (ref. 10) to compute APs, I_CaL waveforms, and cytosolic calcium dynamics. Demonstration simulations initialize n and m at 0.1, then track m,n and electrophysiological outputs over hours, contrasting control (no drug) against drug block. Drug dosing in simulations: Two nifedipine conditions are modeled: 0.1 μM as 55% I_CaL block (b=0.45) and 1 μM as 88% block (b=0.12), aligned with literature. Numerical methods: All ODE systems are integrated using MATLAB’s stiff solver ode15s. Experimental measurements: Cardiac microtissues of hiPSC-CMs (35,000 cells/well) were formed in 384-well plates and used at day 29. Voltage-sensitive dye (Hypo1) was used for optical AP recordings. Nifedipine dilutions were prepared from a 10 mM DMSO stock and added to achieve 0.1 or 1 μM. Repeated recordings were performed at 2, 4, 6, 8, 13, and 16 hours post-addition in an incubated microscope (ImageXpress Micro). Fluorescence was recorded (512–525 nm excitation) at 85 ms/frame with a 40× objective and 2× binning. Videos were segmented to extract single-tissue voltage traces, and biomarkers APD50, APD90 (and APD80 in model plots) and beat rate were computed as described in Supplementary Note 4. Experimental protocols were approved by the UC Berkeley IRB and used commercial iCell cardiomyocytes. Data and code are publicly available on Zenodo.

- The unbounded original expression model predicts that sustained CCB block (e.g., 90%) lowers cytosolic calcium, which in turn drives a compensatory increase in L-type channel expression (n→large). Over hours, this upregulation can fully restore I_CaL and AP properties to near-control levels, effectively nullifying the drug effect in silico. - Introducing physiological bounds on channel density yields a stable equilibrium where drug effects are attenuated but not eliminated. The bounded model prevents unlimited channel growth and maintains a reduced, yet significant, block at equilibrium. - Simulations of 0.1 μM nifedipine (modeled as 55% I_CaL block, b=0.45) show an initial drop in intracellular calcium, reduced APD, and increased beat rate, followed by a gradual rise in n and partial recovery of I_CaL and calcium. By ~16 hours, model outputs (APD and beat rate) approach control values, indicating substantial attenuation of the drug effect. - For 1 μM nifedipine (88% block, b=0.12), n increases but reaches the imposed upper limit before full recovery of I_CaL. Consequently, a considerable drug effect persists at 16 hours, though less pronounced than at 2 hours. - Sensitivity analyses show that increasing Na or If channel densities also increases intracellular calcium, whereas increasing certain K+ channels (IKr, IK1) or SERCA tends to decrease intracellular calcium, underscoring that multi-protein regulation could produce complex calcium responses. - Overall, both modeling and hiPSC-CM measurements support a time-dependent attenuation of CCB effects at the whole-cell level over hours, consistent with calcium-driven homeostatic regulation of channel expression.

The findings support the hypothesis that CCB-induced reductions in intracellular calcium activate a homeostatic program that upregulates L-type channel expression, thereby attenuating the whole-cell drug effect over hours. This mechanism explains experimental observations of time-varying APD and beat rate responses to nifedipine in hiPSC-CM microtissues. The original unbounded model demonstrates the potential for complete compensation, highlighting the need for biologically plausible constraints; the bounded model aligns better with observed partial recovery. These results emphasize that assessments of CCB efficacy should consider time-dependent cellular adaptation, especially in whole-cell measurements where gene expression changes can occur on multi-hour timescales. Importantly, the authors do not expect time-dependent changes at the single-channel level; rather, the temporal effects arise from altered channel density. While intracellular calcium likely regulates multiple membrane proteins, the present focus on L-type channels provides a parsimonious explanation consistent with data; extending regulation to additional currents may be necessary when datasets demand it.

The study integrates a calcium homeostasis-driven expression model with hiPSC-CM electrophysiology and experiments to show that nifedipine’s whole-cell effects diminish over hours due to compensatory upregulation of L-type channel density. By constraining the model to physiologically plausible channel ranges, the authors reconcile simulations with measurements: modest block (0.1 μM) largely attenuates by ~16 hours, whereas strong block (1 μM) remains significant but reduced. The work underscores the importance of timing in interpreting CCB responses and suggests that calcium-driven gene expression dynamics can confound acute pharmacological assessments. Future research should refine constraints on expression dynamics, explore co-regulation of multiple currents and calcium handling proteins, and extend validation across cell models and longer timescales to better predict time-dependent drug efficacy.

- The expression model abstracts complex gene regulation (transcription, translation, trafficking) into simplified ODEs and a scalar reduction; biological processes are coarsely represented. - Upper and lower bounds on channel density and several parameters were hand-tuned to fit data; physiological ranges and kinetics may vary across preparations and cell lines. - Only L-type calcium channel density was regulated; other channels, pumps, and exchangers were held fixed despite evidence that intracellular calcium could regulate multiple proteins with potentially opposing effects. - Experimental observations are limited to hiPSC-CM microtissues and a 16-hour window post-drug; generalizability to adult human cardiomyocytes and longer-term/chronic exposure remains to be established. - The model assumes drug effects act only on single-channel current amplitude (via b(D)) and not on gating kinetics or other cellular processes, which may be an oversimplification for some contexts.