Data-driven multi-agent modelling of calcium interactions in cell culture: PINN vs Regularized Least-squares
This work addresses the problem of modeling calcium interactions in biological systems for researchers, but it is incremental as it primarily compares existing methods on a specific dataset.
The study compared Constrained Regularized Least-Squares Method (CRLSM) and Physics-Informed Neural Networks (PINN) for identifying calcium signaling dynamics in cell cultures, finding that CRLSM achieved good parameter estimates and data fit, while PINNs underperformed in parameter estimation under the tested configurations.
Data-driven discovery of dynamics in biological systems allows for better observation and characterization of processes, such as calcium signaling in cell culture. Recent advancements in techniques allow the exploration of previously unattainable insights of dynamical systems, such as the Sparse Identification of Non-Linear Dynamics (SINDy), overcoming the limitations of more classic methodologies. The latter requires some prior knowledge of an effective library of candidate terms, which is not realistic for a real case study. Using inspiration from fields like traffic density estimation and control theory, we propose a methodology for characterization and performance analysis of calcium delivery in a family of cells. In this work, we compare the performance of the Constrained Regularized Least-Squares Method (CRLSM) and Physics-Informed Neural Networks (PINN) for system identification and parameter discovery for governing ordinary differential equations (ODEs). The CRLSM achieves a fairly good parameter estimate and a good data fit when using the learned parameters in the Consensus problem. On the other hand, despite the initial hypothesis, PINNs fail to match the CRLSM performance and, under the current configuration, do not provide fair parameter estimation. However, we have only studied a limited number of PINN architectures, and it is expected that additional hyperparameter tuning, as well as uncertainty quantification, could significantly improve the performance in future works.