Data-driven multi-agent modelling of calcium interactions in cell culture: PINN vs Regularized Least-squares

2025-05-23

AI Summary

Modeling calcium signaling dynamics in cell cultures lacks sufficient prior knowledge, posing challenges for data-driven ordinary differential equation (ODE) system identification and parameter discovery. Method: This study systematically compares constrained regularized least-squares minimization (CRLSM) and physics-informed neural networks (PINNs) for ODE inference and parameter estimation. CRLSM is introduced for the first time to multi-cell calcium dynamics modeling—eliminating reliance on predefined candidate function libraries—while standard PINNs exhibit substantial parameter bias and poor fit accuracy in small-scale biological ODE identification. Results: CRLSM achieves high-precision parameter estimation and superior data fidelity, validated via multi-agent consensus dynamics simulations. In contrast, PINNs’ limitations highlight hyperparameter optimization and uncertainty quantification as critical avenues for improvement. This work establishes an interpretable, robust paradigm for data-driven biodynamic modeling.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

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.

Problem

• Compare CRLSM and PINN for calcium dynamics modeling
• Evaluate parameter estimation in cell culture ODEs
• Assess data-driven methods for biological system identification

Innovation

• Data-driven multi-agent modeling of calcium interactions
• Comparison of CRLSM and PINN for ODEs
• CRLSM outperforms PINN in parameter estimation