Fig 1.
Phase response curve for human iPSC-CMs spheroids.
(A) All-optical interrogation of cell spheroid pairs, shown in brightfield (BF), YFP fluorescence (YFP is a reporter tag for the optogenetic actuator ChR2), and BeRST1 (optical voltage sensor). (B) Trace of a full action potential cycle (top) and the phase-response curve (bottom), showing normalized cycle length as a function of the phase of the stimulus within the intrinsic cycle (2.4 s). Black dots show experimental data; the red line is the best fit of a piecewise-defined polynomial equation (S1 Text, RMSE = 0.056). (C) Dot plot showing intervals between stimuli of the HEK spheroid and APs of the hiPSC-CM spheroid. Colors and marker shapes denote interval type: stimulus-stimulus (blue circles); stimulus-AP (red squares); AP-stimulus (green diamonds); AP-AP (purple crosses). (D) Entrainment patterns observed for various pacing frequencies in the experiment (left) and the periodically-forced oscillator model (right). is defined as the ratio of the stimulus cycle length to the intrinsic cycle length of the hiPSC-CMs. For periodic rhythms, locking ratios are given in parentheses in the form N:M, denoting N stimuli per M cycles of the forced oscillator.
Fig 2.
PVC dynamics in a patient with frequent PVCs and corresponding simulations of the modulated parasystole model.
(A) A segment of the patient’s electrocardiogram (top) and associated inter-beat intervals (bottom). N denotes a sinus beat, V an ectopic beat (premature ventricular complex, PVC). The sinus cycle length is denoted by ts, the ectopic cycle length by te and ϕ is the phase of the sinus beat in the ectopic cycle. Intervals are color-coded: NN (blue circle), NV (red square), and VN (green diamond). (B) A representation of the phase response curve of the ectopic focus, inferred from sequences of bigeminy (alternating sinus and ectopic beats, black dots) and trigeminy (two sinus beats between ectopic beats, gray dots) (see S2 Text). (C) Sections of patient ECG recordings (left) and simulations of the modulated parasystole model (right), at five different ratios between sinus and ectopic cycle lengths (). The locking ratio of the model is given in parentheses in the form N:M, denoting N sinus cycles per M ectopic cycles.
Fig 3.
Dynamical regimes observed in experimental and clinical data, explained by bifurcation analysis of mathematical models.
(A) Bifurcation diagram of the periodically-forced oscillator model (Eq. 1) using the experimentally fitted PRC from Fig 1B. Blue dots mark experimental data. The shaded region indicates the range of values observed in the patient data. (B) Cobweb plots for Eq. 1 at selected values of
studied in experiments. The return map is shown in red; model iterations after transients are shown in black; experimental data are overlaid in blue. The identity line, along which
, is shown as a dashed line. (C) Bifurcation diagram of the modulated parasystole model (Eq. 2), using the same experimentally fitted PRC, plotted over the range of
values observed in the patient record. Vertical blue lines indicate specific
values corresponding to the clinical segments shown in Fig 2C. (D) Corresponding cobweb plots for Eq. 2 for each
value. The three regions above the graph indicate different contexts for the sinus beat depending on its phase. V(N), blocked sinus beat preceded by an ectopic beat; (V)N, sinus beat preceded by a blocked ectopic beat; N, single sinus beat. S8 Fig provides an explanation how the cobweb plots in panels B and D relate to the entrainment patterns seen in Figs 1 and 2.
Fig 4.
Phase resetting in a computational model for human iPSC-CMs.
(A) Schematic representation of the ionic currents in the human iPSC-CM model (Paci et al, 2020). (B) Top: Trace of a full action potential cycle (black), overlaid with action potentials evoked by stimuli applied at incrementally increasing times (every 30 ms; traces color-coded by stimulus phase). Bottom: Corresponding phase response curve (PRC). (C) Sensitivity of the PRC discontinuity () to ionic current magnitudes (magnitude of 1 corresponds to default value). Left:
as a function of current magnitude. Right: Change in
following a
change in the conductance of each current (shaded: -30%, opaque: + 30%).
Fig 5.
Locking zones across different models and an implied strategy for suppressing PVCs.
(A) Locking zones in the oscillator model with a piecewise linear PRC, shown as a function of and
. Inset numbers indicate the locking ratio N:M, and colors represent the period N; “Period 0” refers to aperiodicity or N
. The dashed box highlights the region also examined in the ionic model. (B) Locking zones in the ionic model as a function of sodium channel conductance. Similar locking regions appear in the oscillator model with a linear PRC (dashed box). (C) Locking zones in the oscillator model using the empirical PRC. (D) Locking zones in the modulated parasystole model, using the same PRC and other parameters derived from patient data. The white line indicates the range of 𝜏 values observed in the patient record. (E) Percentage of PVCs observed in the modulated parasystole model fit with patient data. (F) Percentage of PVCs averaged over 𝜏, shown as a function of
and
(conduction time into and out of the ectopic focus). The white dot marks parameter values fit to the patient. The white arrow indicates the direction associated with a reduced PVC burden.