Hybrid Physics-Informed and Bayesian Modeling of Single-Nanoparticle–Cell Adhesion Kinetics under Cytoskeletal Perturbation

Understanding the dynamic mechanical interaction between nanoparticles and cell membranes is essential for advancing nanomedicine, yet modeling these kinetics is often hindered by biological variability, experimental noise, and the limitations of traditional equilibrium-based frameworks. In this study, we present an advanced hybrid Physics-Informed Neural Network (PINN) framework designed to capture the early-stage adhesion dynamics. Our architecture integrates an analytical Standard Linear Solid model as a mechanistic backbone to represent baseline viscoelasticity, augmented by a neural residual term that captures nonlinear, stochastic, and nonequilibrium deviations. To handle heterogeneous experimental data, we incorporate an adaptive, uncertainty-aware loss weighting scheme and a physics-informed Bayesian framework utilizing a heteroscedastic likelihood for robust parameter inference. We validated this approach using single-nanoparticle force measurements on fibroblasts and MiaPaCa-2 cancer cells under a range of pharmacological treatments (Chlorpromazine, Genistein, and Nocodazole). Validated via leave-one-out cross-validation, the hybrid model demonstrates condition-dependent predictive improvements over classical models, most pronounced in severely perturbed biological states where cytoskeletal disruption renders adhesion dynamics highly irregular. This approach offers a framework for cross-condition phenotyping, providing physically consistent parameter estimates across the full spectrum of cytoskeletal perturbation severity studied here. This work introduces an interpretable approach for modeling complex biophysical adhesion processes and offers a potentially generalizable framework for analyzing noisy, heterogeneous biological systems.