  We investigate a quantitative network of gene expression dynamics describing
the competence development in Bacillus subtilis. First, we introduce an
Onsager-Machlup approach to quantify the most probable transition pathway for
both excitable and bistable dynamics. Then, we apply a machine learning method
to calculate the most probable transition pathway via the Euler-Lagrangian
equation. Finally, we analyze how the noise intensity affects the transition
phenomena.
