Integrated Mathematical Modeling of Epigenetic-Wnt-Notch Crosstalk in Mesenchymal Stem Cell Differentiation: A Stochastic Framework with Gillespie Simulations for Precision Regenerative, Oncotherapeutic, Cardiovascular, and Hepatobiliary Applications

The intricate bidirectional crosstalk between Wnt and Notch signaling pathways, modulated by epigenetic mechanisms, plays a crucial role in regulating mesenchymal stem cell (MSC) differentiation and maintaining tissue homeostasis. This study introduces the Shibah Epigenetic Feedback Model (SEFM 2.0), an advanced stochastic ordinary differential equation (SODE) framework integrated with the Gillespie stochastic simulation algorithm (SSA) and Bayesian inference to quantitatively characterize this crosstalk in MSCs. The model is calibrated using empirical transcriptomic data from NCBI GEO dataset GSE136197, which profiles rat bone marrow-derived MSCs undergoing neural transdifferentiation induced by epidermal growth factor (EGF), basic fibroblast growth factor (bFGF), and insulin-like growth factor-1 (IGF-1), identifying 3,252 differentially expressed genes. Supplemented by ENCODE epigenomic annotations and GTEx expression quantitative trait loci (eQTLs), SEFM 2.0 exhibits high predictive accuracy. Stochastic simulations reveal microenvironmental noise impacts, projecting a 12--18% enhancement in regenerative potential via CRISPR-dCas9-mediated epigenetic interventions. Therapeutic implications extend to targeting glioma stem cells, ameliorating ischemic cardiomyopathy, and treating hepatobiliary conditions such as fibrosis and cirrhosis. Reproducible Python code, accompanied by 95% posterior credible intervals, ensures model falsifiability and verifiability. This integrative approach combines molecular techniques (e.g., RNA-seq, CRISPR-Cas9) with rigorous computational modeling, providing actionable strategies for neurodegeneration, osteoarthritis, oncogenesis, cardiovascular disorders, and liver pathologies, in alignment with Molecular Biology Reports standards.