Learning Non-Equilibrium Signaling Dynamics in Single-Cell Perturbation Dynamics

Cancer cells exploit non-equilibrium signaling dynamics to develop transient drug resistance through mechanisms that conventional equilibrium-based analyses cannot detect. We present a probabilistic framework integrating live-cell biosensor data with asynchronous multi-omics snapshots to learn these adaptive states. Using data from BRAF-V600E melanoma as a model system, we demonstrate how such learning scheme characterize competing timescales drive resistance mechanisms: rapid post-translational feedback (minutes) versus delayed transcriptional regulation (hours), including RAF dimer rewiring, DUSP-mediated ERK reactivation pulses, and NRAS^Q61K-dependent EGFR recycling. Our approach further combines multi-marginal Schrödinger bridges for distribution alignment with the extracted dynamical patterns from live-cell trajectories. Each step of the algorithm is validated with real-data and further validation is through in silico melanoma models. This framework could help identify therapeutic windows that delay progression to persistent resistant states and targeting adaptive plasticity across cancer types.