HYBRID LOGICAL–STOCHASTIC MODELING OF CELL DIFFERENTIATION IN ANGIOGENESIS

Understanding cellular signaling networks requires approaches that capture both the qualitative logic of interactions and the quantitative stochastic dynamics of molecular populations. We present a hybrid modeling framework that combines logical models with a stochastic formulation based on the Chemical Master Equation (CME). The logical model identifies stable states and qualitative phenotypic patterns, while the stochastic model describes temporal evolution and fluctuations in protein populations, revealing dynamic features not accessible through deterministic or qualitative methods. We apply this framework to endothelial cell differentiation in angiogenesis, focusing on the transition between tip and stalk cells. Angiogenesis, the growth of new blood vessels from existing ones, is essential for tissue development and repair, but is also exploited by tumors to promote growth and metastasis. The model reproduces multiple stable states and distinct dynamics under different environmental and molecular conditions. The logical and stochastic approaches show overall agreement, but each highlights different aspects: the logical model emphasizes the network structure and phenotypic attractors, while the stochastic model adds temporal and probabilistic detail, including variability in phenotype switching. This work demonstrates how hybrid logical–stochastic modeling can be applied to explain cell fate decisions in angiogenesis. The approach is versatile and can be extended to investigate other complex biological systems, offering a framework to connect qualitative regulatory logic with quantitative molecular dynamics.

This work was supported by Conselho Nac. Des. Cient. Tecnologico (CNPq  107099-2023-3)