A Comparison of Computational Methods for Modeling Stochastic Collaborative DNA Methylation Dynamics

The methylation of cytosine-phosphate-guanine (CpG) dinucleotides in DNA is linked to gene expression, cancer, and aging. The methylation levels of nearby CpG sites influence many enzymatic reactions governing DNA methy-lation. However, efficiently modeling this influence, known as "collaborative" DNA methylation, is computationally challenging. We compare the efficiency and accuracy of three collaborative DNA methylation modeling approaches: a stochastic simulation algorithm (SSA), an exact Chemical Master Equa-tion (CME), and a mean-field CME. The exact CME model provides high accuracy but is limited to small system sizes due to its exponential state-space growth of 3N for N CpG sites. In the neighbor-dependent mean-field CME model, qualitative methylation patterns are accurately captured, but runtimes scale as Nk, 4 < k < 6, for N CpG sites. The SSA model is accu-rate and its runtime scales as Nl, 1.6 < l < 2.5, but for smaller system sizes (N < 100), it is inefficient compared to the mean-field CME method. Across all three methods, bimodality is achieved when sufficiently strong collabo-ration among CpGs promotes balanced net methylating and demethylating flux, in concert with reactions that occur independently at individual sites. Our findings provide insight into both symmetric and asymmetric parameter regimes, the influence of CpG density, and the trade-off between accuracy and efficiency in modeling collaborative DNA methylation dynamics, paving the way for future analysis.