Lempel-Ziv Complexity and Structural Features of DNA Methylation Reveal Epigenetic Rejuvenation in Mouse...

Background: DNA methylation is a key epigenetic mechanism whose dynamics are closely linked to ageing. Modern epigenetic clocks predict biological age based on the average methylation level. The concept of "epigenetic rejuvenation" posits that at early stages of development, the biological age of the embryo may decrease, reaching a minimum ("ground zero") at the gastrulation stage. However, standard averaging methods may not account for important rearrangements in the internal structure of methylation. Objective: To apply the apparatus of information theory and topological data science to the analysis of scNMT-seq data and to test whether DNA methylation entropy decreases from stage E4.5 to E6.5, which would correspond to an approach towards the biological zero state. Methods: Publicly available scNMT-seq data (GSE121690) were analyzed. Five entropy measures were calculated for each cell (Shannon, Renyi, Tsallis, LZ-complexity, local gradient entropy (entropy of variations in the smoothed histogram of the methylation distribution), and persistent entropy (PE)-a topological complexity measure). For the five-dimensional entropy feature space, a Rips complex was constructed, and persistence diagrams H_0 and H_1 were computed. Results: All five entropy measures decreased significantly, with LZ complexity showing the largest relative reduction (-28.4%) and the strongest independent signal (partial r = -0.181). Among all the complexity measures studied, LZ complexity exhibited the largest relative reduction, underscoring its heightened sensitivity to the progressive ordering of the epigenetic landscape. Notably, the ternary encoding of LZ complexity showed strong correlation with Shannon entropy (r = 0.71), indicating that algorithmic complexity, when accounting for partial methylation states, aligns closely with statistical entropy while retaining sensitivity to spatial order. The consistency of results across binary and ternary encodings confirms the robustness of LZ complexity as a structural biomarker. Persistent entropy confirmed the general dynamics (decrease from 15.91 to 14.89, p = 0.01). Topological analysis of the multidimensional space revealed a qualitative reorganization: at stage E6.5, stable cyclic structures (H₁) emerge, while at E4.5 the space is dominated by a single large-scale cycle. Null model validation confirmed that the observed H₁-cycles are genuine topological features rather than random fluctuations. Comprehensive topological characterization showed that normalized persistent entropy increases from 0.846 to 0.882 (p < 0.001), while maximum persistence decreases from 0.446 to 0.218 (p < 0.001), reflecting a transition from a homogeneous state to structured diversification-multiple, evenly distributed cycles corresponding to distinct cell lineages. Consistent with this, regional disorder (RE/RD) at the single-cell level decreases from E4.5 to E6.5 (RE: -25.5%, RD: -27.4%, p < 10^-13), while global entropy also decreases, together painting a picture of epigenetic rejuvenation as ordered consolidation at the whole-genome scale. An SVM model trained on 15 entropy and structural features achieved stage classification with an accuracy of 93.4% and AUC of 0.981, confirming the diagnostic potential of the approach. Conclusions: The decrease in DNA methylation entropy from E4.5 to E6.5 corresponds to an approach to "ground zero"-the point of minimum biological age in embryogenesis-and supports the hypothesis of a link between decreasing entropy and epigenetic rejuvenation. The addition of topological analysis reveals the hidden organization of epigenetic diversity, showing that ordering does not lead to homogenization but is accompanied by the formation of distinguishable cell lineages.