Low-frequency ERK and Akt activity dynamics are predictive of stochastic cell division events

Understanding the dynamics of intracellular signaling pathways, such as ERK1/2 (ERK) and Akt1/2 (Akt), in the context of cell fate decisions is important for advancing our knowledge of cellular processes and diseases, particularly cancer. While previous studies have established associations between ERK and Akt activities and proliferative cell fate, the heterogeneity of single-cell responses adds complexity to this understanding. This study employed a data-driven approach to address this challenge, developing machine learning models trained on a dataset of growth factor-induced ERK and Akt activity time courses in single cells, to predict cell division events. The most predictive models were developed by applying discrete wavelet transforms (DWTs) to extract low-frequency features from the time courses, followed by using Ensemble Integration, a data integration and predictive modeling framework. The results demonstrated that these models effectively predicted cell division events in MCF10A cells (F-measure=0.524, AUC=0.726). ERK dynamics were found to be more predictive than Akt, but the combination of both measurements further enhanced predictive performance. The ERK model`s performance also generalized to predicting division events in RPE cells, indicating the potential applicability of these models and our data-driven methodology for predicting cell division across different biological contexts. Interpretation of these models suggested that ERK dynamics throughout the cell cycle, rather than immediately after growth factor stimulation, were associated with the likelihood of cell division. Overall, this work contributes insights into the predictive power of intra-cellular signaling dynamics for cell fate decisions, and highlights the potential of machine learning approaches in unraveling complex cellular behaviors.


Cross-validated performance analysis and model selection
We partitioned the High-dose (train) dataset into 10 folds that were kept consistent in the evaluation of all methods tested.To reduce the effects of class imbalance, we undersampled all training folds to equalize the sizes of the divided and non-divided classes.Our analysis considered three separate cases, using (i) only ERK time courses, (ii) only Akt time courses, and (iii) both ERK and Akt time courses, with the aim of building three final models to evaluate on our test datasets.Classification algorithms were trained on each set of nine training folds, and used to make predictions on the remaining test fold.Predictions across all test folds were concatenated before being evaluated.Evaluation of classification performance was based on the F max score associated with the minority divided class.This measure, which is the maximum value of the F-measure across all classification thresholds, has been suggested to be more reliable than other more commonly used evaluation metrics for unbalanced class scenarios like ours [1,2].We also calculated the area under the receiver operating curve, and for reference, the performance of a random classifier in our results (Fig. 2B-D).
At the beginning of the above evaluation process, a number of transformations were evaluated by assessing the predictive performance of classifiers built using Ensemble Integration (EI) [3].Transformations were applied to ERK and Akt modalities separately to generate features which were used as input to EI, which carried out the above cross-validation process internally, and generated performance scores for each ensemble method considered, forming a distribution of performance scores (Fig. 2B).The most effective transformation was identified as the one with the highest median EI performance across cases (i)-(iii), and selecting the most frequent one.The final transformation + ensemble method for each course was determined to be the one with the highest F max .This best-performing method was compared to two benchmark algorithms: an LSTM-based [4] deep learning algorithm, and XGBoost [5].In the case of the LSTM model, we further partitioned each (outer) training fold into 10 inner folds (nested cross validation) to optimize the number of training epochs and avoid overfitting (a common issue with neural networks especially with a small number of samples).For each outer fold, inner test folds were used to track the validation loss at each successive epoch, and the epoch with the lowest loss was stored.The median of these epoch values was then taken across the inner folds.An LSTM model was then trained (with this median epoch value) and evaluated on each time course and their combination in the same cross-validation setup as described above.
For the best performing methods for cases (i)-(iii), we trained final models on the full High-dose (train) dataset (all ten folds).We then evaluated these models on the held out test sets (Table 1).A more detailed overview of the analysis performed in this study is shown in Supplementary Fig. 2.

LSTM benchmark
There is substantial flexibility when constructing LSTM architectures, but we found that configurations with large numbers of parameters were prone to overfitting, which was likely due to the relatively small amount of training data available for this task.For this reason, we limited the number of layers in our LSTM benchmark, as well as the number of units in each layer.This benchmark consisted of two hidden layers: a bi-directional LSTM layer, followed by a fully connected layer with ReLU activation.Each of these layers contained 64 units.
We also used heavy dropout to regularize the network to further control overfitting.
We optimized the binary cross-entropy loss used in the benchmark using Adam optimization [9].Full details of the method used can be found in the GitHub repository.