Uncovering Time-Dependent NF − κB-p53 Crosstalk Induced by Caffeic Acid Phenethyl Ester in Prostate Cancer Cells Through a Bayesian Digital Twin

(1) Background: Caffeic acid phenethyl ester (CAPE) exhibits anticancer activity; however, its time-dependent effects on interconnected signalling pathways remain incompletely characterised. (2) Methods: We combined wet-lab experiments (MTT viability assay and ELISA measurements of total NF-κB p65 and p53) with a Bayesian digital twin framework to quantify signalling dynamics in prostate cancer cells following CAPE exposure. p53-deficient PC3 and p53-competent LNCaP cell lines were treated for 24 h and 48 h across multiple CAPE concentrations. Experimental data were integrated into a mechanistic Bayesian model using robust likelihoods, enabling uncertainty-aware parameter inference and posterior predictive validation via leave-one-dose-out analysis. (3) Results: In PC3 cells, CAPE induced dose-dependent inhibition of NF-κB p65 that was consistently associated with reduced cell viability at both time points, consistent with a p53-independent regulatory regime. In contrast, LNCaP cells exhibited a transient NF-κB-p53 coupling at 24 h, characterised by delayed NF-κB suppression and pronounced p53 activation, followed by a more stable and weakly coupled signalling state at 48 h. These temporal patterns were supported by posterior parameter estimates and predictive performance under leave-one-dose-out validation. (4) Conclusions: This study demonstrates that Bayesian digital twins enable quantitative, uncertainty-aware analysis of time-dependent drug responses, extending beyond conventional dose-response assessments and supporting mechanistic hypothesis generation in cancer pharmacology.