q-bio.QMMay 23, 2025

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

Authors: Aurora Poggi, Giuseppe Alessio D'Inverno, Hjalmar Brismar, Ozan Öktem, Matthieu Barreau, Kateryna Morozovska

Organizations: KTH Royal Institute of Technology, Department of Mathematics, Stockholm, Sweden · International School for Advanced Studies (SISSA), Trieste, Italy · KTH Royal Institute of Technology, Department of Biophysics, Stockholm, Sweden · KTH Royal Institute of Technology, Department of Intelligent Systems, Stockholm, Sweden

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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.

Figures & tables

Figure 1: Structure of PINNs for inverse problems.
Figure 2: First frame of cell culture showing calcium signaling.
Figure 3: Frame 145 containing a hot pixel, leading to artifacts in the image.
Figure 4: Before and after median filter is applied to a frame containing a hot pixel.
Figure 5: Results obtained with cellpose segmentation on a selected frame.
Figure 6: Resulting polygons obtain for frame 10.
Figure 7: Resulting graph for frame 10.
Figure 8: Setup modeling one cell.
Figure 9: Cell 68, MSE = 0.0012.
Figure 10: Cell 73, MSE = 0.0029.
Figure 11: Cell 68 parameter identification via CRLSM, MSE = 0.0075.
Figure 12: Cell 73 parameter identification via CRLSM, MSE = 0.0029.
Figure 13: Resulting segmentation of different setup modelling groups of cells.
Figure 14: Error propagation for the 3 different setup.
Figure 15: Results obtained with the 3 different setups for the same cell.
Figure 16: Results obtained with 3 different setups for cell 43.
SetupMSE
I0.0023
II0.0011
III0.0013
Table I : MSE of the CRLSM applied to the 3 different setup for cell 43.
Figure 17: Total Loss during training over two different cells.
Figure 18: Cell 68 parameter identification via PINN, MSE = 0.0067.
Figure 19: Results obtained from CRLSM on different cells.
Figure 20: Losses of PINN over 3 setups.
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