Fig 1.
Workflow diagram: Our approach processes diverse dynamical patterns of intracellular calcium (Ca2+) dynamics in simulated trajectories as well as experimental traces.
Simulated data are generated by the interplay between the mechanisms of Ca2+-induced Ca2+-release (CICR) and Ca2+-activated 1,4,5-trisphosphate (InsP3) degradation inside a biological cell as illustrated in (a). See Methods section for detailed descriptions of the intracellular Ca2+ oscillation model. Experimental traces of Ca2+ concentration are obtained from different cells (see the Main text). First, we generate simulated cytosolic Ca2+ concentration trajectories from the intracellular Ca2+ oscillation model or obtain experimental traces from publicly available datasets (two representative traces shown in (b)). We then feed the simulated trajectories or experimental traces to the large kernel convolutional neural network (LKCNN) model (as shown in (c)), which classifies the diverse dynamical patterns of cytosolic Ca2+ concentration into correct labels (d).
Fig 2.
Various dynamical states of cytosolic Ca2+ concentration: (a) Steady state, (b) oscillating state, (c) bursting, (d) chaotic state, sequences of (e) period-2, (f) period-3, (g) period-4, and (h) quasiperiodic oscillations.
For each panel, the three rows correspond to deterministic or noiseless (top), noisy with V = 105 (middle), and V = 103 (bottom).
Table 1.
Parameter values used in the numerical simulation of the intracellular calcium oscillation model (1). Each region exhibits distinct dynamical behaviors: Region 1 (Bursting, Oscillatory, Steady State), Region 2 (Chaotic, Period-2, Period-3, Period-4, Steady State, Oscillatory), and Region 3 (Quasiperiodic, Steady State, Oscillatory). Within each region, 1000 synthetic trajectories were generated per dynamical pattern, each for training and testing the LKCNN classifier.
Fig 3.
Classification accuracy of LKCNNs over a range of kernel size for noiseless (blue circles) and noisy (orange squares) trajectories of cytosolic Ca2+ dynamics.
For noisy trajectories, we train the LKCNN on data with noise levels and test on data with
. The solid lines indicate the mean accuracy averaged over a set of 20 distinct randomly generated seeds for each kernel size. The shaded envelopes denote one standard deviation (
) calculated from the multiple realizations.
Table 2.
Precision, recall, and F1 score for noiseless simulated trajectories of cytosolic Ca2+ concentration.
Fig 4.
Confusion matrix showing the result of multi-class classification performance of our LKCNN model for the noiseless case.
Diagonal entries denote the percentage of correctly predicted dynamical states of cytosolic Ca2+. Labels indicate steady state, bursting, oscillatory, period-2, period-3, period-4, chaotic state, and quasiperiodic oscillation.
Fig 5.
Classification accuracy of LKCNN versus system size V for the simulated cytosolic Ca2+ dynamics.
Noise in the trajectories scales inversely as the system size as , i.e., the smaller the system size V, the larger the noise in the trajectory data. The green circles denote the mean accuracy averaged over a set of 20 distinct randomly generated seeds for each noise level. The shaded green region indicates the corresponding standard deviation (
) from multiple realizations.
Table 3.
Precision, recall, and F1 score for noisy simulated trajectories of cytosolic Ca2+ concentration.
Fig 6.
Confusion matrix showing the result of multi-class classification performance of our LKCNN model for the case of realistic noise levels.
Diagonal entries denote the percentage of correctly predicted dynamical states of cytosolic Ca2+. Labels indicate steady state, bursting, oscillatory, period-2, period-3, period-4, chaotic state, and quasiperiodic oscillation.
Fig 7.
A sample of experimental trajectories with the LKCNN predicted class.
Correctly classified (a) Bursting, (b) Steady States, (c) Oscillatory states. (d) Misclassified states where the first state was manually labelled as Bursting, while the other three were labelled as Others.
Fig 8.
Confusion matrix showing the classification performance of our LKCNN model for the experimental dataset.
Diagonal entries denote the percentage of correctly predicted dynamical states based on human annotation. Labels indicate three representative classes: Bursting, Steady State, and Others.
Fig 9.
Comparison of LKCNN against conventional baselines and robustness to spike-like corruption.
(a) Classification accuracy (%) of LKCNN versus two conventional classifiers, namely, linear-kernel SVM and Random Forest (see legend at the top of the figure) on noiseless synthetic trajectories, noisy synthetic trajectories, and experimental Ca2+ traces. SVM and RF operate on FFT-based features of the trajectories. (b) Accuracy drop (%) after adding sparse, large-amplitude impulsive noise to the synthetic test trajectories. Accuracy drop is computed relative to the corresponding uncorrupted test set.