A machine learning based model accurately predicts cellular response to electric fields in multiple cell types

Abstract

Many cell types migrate in response to naturally generated electric fields. Furthermore, it has been suggested that the external application of an electric field may be used to intervene in and optimize natural processes such as wound healing. Precise cell guidance suitable for such optimization may rely on predictive models of cell migration, which do not generalize. Here, we present a machine learning model that can forecast directedness of cell migration given a timeseries of previous directedness and electric field values. This model is trained using time series galvanotaxis data of mammalian cranial neural crest cells obtained through time-lapse microscopy of cells cultured at 37 °C in a galvanotaxis chamber at ambient pressure. Next, we show that our modeling approach can be used for a variety of cell types and experimental conditions with very limited training data using transfer learning methods. We adapt the model to predict cell behavior for keratocytes (room temperature, ~ 18-20 °C) and keratinocytes (37 °C) under similar experimental conditions with a small dataset (~ 2-5 cells). Finally, this model can be used to perform in silico studies by simulating cell migration lines under time-varying and unseen electric fields. We demonstrate this by simulating feedback control on cell migration using a proportional-integral-derivative (PID) controller. This data-driven approach provides predictive models of cell migration that may be suitable for designing electric field based cellular control mechanisms for applications in precision medicine such as wound healing.

Figure 1

The image processing and cell directedness prediction pipeline. Time-lapse microscope images are used to manually track a number of cells. The tracking data is used to create timeseries of our two features (cell directedness and EF), which are used as inputs to our blackbox LSTM model to make predictions about the next directedness value.

Figure 2

(a) Quantifying directional movement of cells by directedness. (b) Trained LSTM model takes in directedness and EF values from the past 20 times steps and outputs directedness at current time step. (c) Reconstruction of single-cell trajectories from directedness assuming constant cell speed.

Figure 3

(a) Average predicted directedness and distribution across 50 models compared to ground truth measurements at each EF. A timestep unit is 5 min (the interval at which images were taken). The first 19 time steps are used to initiate predictions. (b) Comparison of LSTM model to naïve predictors. Root mean square error (RMSE) values computed based on predicted directedness and measured directedness. The boxes represent the middle 50% of error values and the whiskers extend to the minimum and maximum error values.

Figure 4

(a) Distributions of cell-level test set RMSE values of the base model and a model with identical architecture which was trained with a modified training set from which the 30 mV/mm instances were removed. Error distributions shown for both the complete testing set and for the 30 mV/mm test instances. (b) Distributions of cell-level test set RMSE values of the base model and a model with identical architecture which was trained with a modified training set from which the 200 mV/mm instances were removed. Error distributions shown for both the complete testing set and for the 200 mV/mm test instances. The boxes represent the middle 50% of error values and the whiskers extend to the minimum and maximum error values.

Figure 5

(a) Diagram comparing the traditional machine learning training approach, which involves training a separate randomly initialized model for each learning task, with the transfer learning approach, which involves training a model for one task and then retraining that model on another dataset to perform a related task. (b) Distributions of cell-level RMSE values for the base model, a model training only on the reversal dataset, and a model which uses transfer learning to retrain the base model for the polarity reversal task. The boxes represent the middle 50% of error values and the whiskers extend to the minimum and maximum error values. (c) Plot of average directedness over time for the polarity reversal dataset, with error bars representing standard error of the mean for each timestep to illustrate the spread of directedness values at each step.

Figure 6

Distributions of RMSE values for the base model on the CNCC test set (benchmark), the keratocyte model on the keratocyte test set, and the transfer learning model on the keratocyte test set. Distributions of RMSE values for the base model on the CNCC test set (benchmark), the target cell models without transfer learning on the target cell test sets, and the target cell models which used transfer learning with the CNCC source domain on the target cell test sets. The boxes represent the middle 50% of error values and the whiskers extend to the minimum and maximum error values.

Figure 7

Distributions of final directedness values of cells in both ground truth data and synthetic data generated by simulations. The boxes represent the middle 50% of cell directedness values and the whiskers extend to the minimum and maximum directedness values for each distribution. For simulations, these distributions are over 50 trained models to ensure that these results are not dependent on the random initialization of any one model; see “Materials and methods” subsection “Recurrent model architecture” for more details. See Table S7 for mean and median values of final directedness values for both ground truth and synthetic data.

Figure 8

Directional plots for cell migration at various EF for ground truth measurements and in silico simulations with added noise on computed directedness at each time step.

Figure 9

(a) The top figure depicts the closed loop design. A reference value/trajectory is picked. The error is evaluated and fed to the PID. The PID uses this value to determine the appropriate EF in order to guide the average directedness towards the reference. This EF is applied to the model of cell migration. (b) (Bottom upper left) The average directedness of all the cells (the dashed red line indicates the reference value). (Bottom upper right) The directedness of individual cells. (Bottom lower left) The voltage being applied throughout the simulation to get the appropriate response. (Bottom lower right) The error of the average directedness in relation to the reference value.