Structured neighboring-sarcomere switching is coupled to variable-reach internal length redistribution during hyperthermal sarcomeric oscillations in living cardiomyocytes

Figures

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  Figure 1. Primary sarcomere-length time-series context before warming and during HSOs. A, Full-trace local five-sarcomere mean trace for an exemplar cell, with a low-pass mean overlaid. Shaded windows indicate the before-warming and HSO segments shown below. B, Representative before-warming window. The upper panel shows sarcomere-length traces of five consecutive sarcomeres and their local mean; the lower panel shows high-frequency internal components after subtraction of the instantaneous local mean. C, Representative HSO window shown in the same format. During HSO, the beat-scale envelope remains visible while fast internal sarcomere oscillations become sustained.

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  Figure 2. Definition of the local phase state during a representative HSO segment. A, Local five-sarcomere mean trace and its low-pass component. B, HSO-band internal signals for the five sarcomeres. C, Normalized high-frequency envelope and hysteresis thresholds that define the phase-valid gate; the upper and lower dashed lines mark the high and low thresholds of the hysteresis gate. D, Phase-locking value for the four neighboring pairs. E, Binary neighboring-pair states for pairs 1–2, 2–3, 3–4, and 4–5. Blue indicates in-phase (I), and orange indicates anti-phase (A). The segment is shown with the refined visualization gate for display continuity; quantitative statistics use the fixed primary gate.

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  Figure 3. HSOs reveal a constrained local phase topology. A, Paired values for the fraction of time in which local phase tracking was valid before warming and during HSO. B, Paired values for time spent in anti-phase-rich states, defined as states with three or more anti-phase neighboring pairs. C, Pooled transition topology before warming and during HSO. The HSO phase-topology analysis used 230 valid dwell-to-dwell HSO phase transitions from seven cells, including 216 one-link transitions. Numbers inside the bars indicate the count of one-link transitions relative to all detected transitions. A one-link transition means that only one of the four neighboring-pair relations changed between successive patterns. D, HSO transition network restricted to one-link edges. State labels encode the four neighboring pairs from 1–2 to 4–5, with I for in-phase and A for anti-phase. Edge width scales with pooled HSO transition count.

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  Figure 4. The same IAAI-to-IAII phase switch is coupled to different internal redistribution reaches. A–D, Short-reach example. A, Raw sarcomere lengths of five consecutive sarcomeres. B, HSO-band internal length traces after subtraction of the five-sarcomere mean. C, Binary I/A state of the four local links; the dashed line marks the update time. D, Post-minus-pre internal change vector. Orange bars indicate relative lengthening, and blue bars indicate relative shortening; the compensation reach is S=1.29. E–H, Cross-chain example with the same directed IAAI-to-IAII switch. E, Raw sarcomere lengths. F, HSO-band internal length traces. G, Local-link I/A state. H, Post-minus-pre internal change vector. Relative lengthening and shortening are placed across a wider part of the observed chain, giving S=2.88. Cross-chain refers to the observed five-sarcomere chain.

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  Figure 5. Compensation reach measures a population-level axis that expands in I-rich pre-event states. A, Distribution of compensation reach, S, across 248 reach-qualified one-link HSO events from seven cells. Events were included when the post-minus-pre internal change vector contained both relative shortening and relative lengthening, allowing S to be calculated. The background bands show adjacent-reach, chain-spread, and cross-chain regimes. The vertical line marks the median. B, Compensation reach grouped by the pre-event I-link count, MI. Points represent events, box plots summarize group distributions, and the orange line links group medians. C, Dominant source-sink map showing the dominant relative shortening site and dominant relative lengthening site. D, Reach variation within major directed transitions. Points indicate median S and horizontal lines indicate the range within each transition.

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  Figure 6. Cell-aware and coordinate controls for compensation reach. Unless otherwise indicated, controls used the 248 reach-qualified one-link HSO events used for the compensation-reach analysis. A, Cell-blocked permutation analysis. Pre-event I-link counts were shuffled within each cell, and the slope linking MI to S was recomputed. The orange line marks the observed slope. B, Cell-cluster bootstrap analysis. Cells were resampled with replacement, and the dashed lines show the 95% bootstrap interval for the slope. C, Comparison of compensation reach computed from raw internal coordinates and HSO-band internal coordinates. The positive correlation indicates that HSO-band reach tracks length redistribution present in the measured internal coordinate. D, Compensation reach grouped by the flipped adjacent link. The overlapping distributions and flipped-link-adjusted slope show that the pre-event I-link load is associated with reach across switched-pair positions.