Characterising Epigenetic Tipping Points using a Spectral Dimension Reduction Approach

Epigenetic landscapes (ELs) are defined by the pattern of epigenetic marks (acetylation, methylation, etc.) layed over large chromatin regions. The information contained in the ELs is essential to sustain the patterns of gene expression that shape cell fate and identity. EL maintenance requires the precise regulation of chromatin-modifying enzymes (ChME) and their metabolic cofactors (McF). Competition for ChME or dysregulation of McF abundance can lead to degradation of ELs, triggering large-scale changes in the cell fate information contained in EL. Thus, predicting impending epigenetic tipping points (ETPs) by identifying early warning signals (EWS) may help to anticipate the onset of cell identity loss during aging and cancer. Since ELs are formed (and maintained) by a systems of writer/eraser enzymes that interact both in cis (local) and trans (long-range) modes, their mathematical description involves a high-dimensional dynamical system, where identifying ETPs and characterising the biological mechanisms that control them remains challenging. Here, we develop a general mathematical framework that incorporates different connectivity patterns generated by the 3D chromatin folding structure to analyze competition-induced ETP in large EL. This framework allows us to measure the sensitivity and robustness of ETP to the availability of metabolic cofactors and to identify potential EWS. Using a dimension reduction method, we derived coarse-grained (CG) equations for the collective observables associated with chromatin modifications. Analysis of the CG system allows the prediction of global transitions that shape the large-scale features of EL, accurately reproduce the corresponding microscopic benchmarks, and reveal the existence of tipping points under conditions of ChME competition. We applied the CG method to predict ETP under different connectivity patterns, including heterogeneous profiles such as those found in Hi-C data. Although a robustness measure for stable EL was derived from the CG dynamics in bistable regimes, sensitivity analysis revealed that metabolic cofactors have the greatest impact on EL robustness. In particular, we identified the metabolic cofactors SAM and acetyl-CoA as potential EWS for the catastrophic loss of hyperacetylated EL induced by ChME competition. The ability to predict global ETP can facilitate the discovery of predictive biomarkers and inform metabolic interventions aimed at limiting and reversing pathological cell fate decisions.