Constrained neighboring-sarcomere phase topology relates to mean HSO amplitude in living cardiomyocytes

Abstract How neighboring sarcomeres redistribute timing while a cardiomyocyte continues to beat, and whether that coordination during warming-induced hyperthermal sarcomeric oscillations (HSOs) is random or structured, remain unresolved. We reanalyzed sarcomere-length recordings from five consecutive sarcomeres in each of seven living neonatal rat cardiomyocytes and represented each valid time point by the four neighboring-pair phase relations that define a 16-state local phase network. During HSOs, the fraction of time with trackable local phase relations increased from 0.298 before warming to 0.956 (paired Wilcoxon P = 0.0156), enabling direct analysis of local reconfiguration. Successive local states were almost always connected by Hamming-1 edges, meaning that only one neighboring-pair relation changed at a time (34/35, 97.1%, before warming; 216/230, 93.9%, during HSOs). HSOs also increased occupancy of anti-phase-rich states with three or more anti-phase neighboring pairs (0.254 to 0.509, P = 0.0156). These results indicate that HSOs do not reflect unstructured local disorder but a constrained neighboring-sarcomere phase topology. As a complementary cycle-level analysis within the same HSO window, we then asked how the observed fast amplitude of the valid-sarcomere mean trace relates to local amplitude and synchrony measured from the same valid sarcomeres. For each cycle, Yvalid, the peak-to-peak HSO amplitude of the valid-sarcomere mean trace, was closely approximated by the product of mean local HSO amplitude (A) and weighted synchrony (Rw; pooled r = 0.992, normalized mean squared error = 0.015, β1 = 0.948, β0 ≈ 0). A simple state-derived synchrony factor computed from the local phase patterns showed a modest positive association with Rw (cell-adjusted β = 0.197, P = 0.0165), providing a bridge between the binary local-state description and the continuous synchrony summary. In blocked cross-validation, the A × Rw summary was markedly more parsimonious than an additive current-state alternative (pooled normalized mean squared error 0.0138 vs 0.1006), whereas simple history terms changed error only marginally. Thus, the main result is a constrained local phase topology during HSOs, and A × Rw serves as a descriptive cycle-level summary of the mean fast signal in the same observed segment, with local amplitude and synchrony as its two components. Competing Interest Statement The authors have declared no competing interest. Footnotes This revised version refocuses the manuscript around constrained local phase topology as the primary result. The cycle level A x Rw analysis is now presented as a descriptive within segment summary of the observed mean fast signal, not as a standalone predictive rule. Figure 4 and the related main text were revised to clarify this point. The rationale for using Yvalid as the canonical target and for excluding cell 2 sarcomere 2 as a quality control outlier in the complementary cycle level analysis was also clarified. The Supplementary Information was updated to follow the same claim hierarchy, with primary topology results separated from supportive attenuation and cancellation analyses, and with revised target sensitivity, null control, and expanded summary tables.