Reconstruction of ensemble of single-cell time trajectories from discrete-time fluorescence data: Oscillatory MAPK dynamics

Abstract

Abstract: Continuous time profiles of intracellular protein levels in a collection of isogenic cells is needed to achieve quantitative prediction of heterogeneity in cellular systems. However, intracellular staining based quantitative single-cell detection of protein levels, reported by emitted fluorescence, using confocal microscopy or flow cytometry can only result in discrete time series due to arresting of cell state to enable entry of reporters - antibody - into the cell. We propose a method to reconstruct the time-series of oscillatory dynamics of phosphorylated ERK (pERK), the terminal protein in the ubiquitously found MAPK cascades, based on the discrete time series data consisting of a distribution of fluorescence emitted by different ensemble of cells at different time points post-stimulation. This method employs a model autocorrelation function to predict the fluorescence from the experimental data that will correspond to a specific time point in a randomly reconstructed trajectory. We validate the method using the single-cell pERK oscillatory dynamics data consisting of 12100 data points measured in transfected cells across 121 time points by pairing reconstructed trajectories with those from original based on the constraint that the pair satisfied a certain cut-off for both mutual information score and Euclidean distance between them. Out of the 100 trajectories in the original data, our algorithm was able to reconstruct ~30 of them capturing a reasonable fraction of the amplitudes of the Fast fourier transform modes present in the original trajectory. Using the developed method, we reconstructed 2471 trajectories from pERK discrete dynamics data set consisting of distribution of fluorescence data across 16 time points obtained from single-cell flow cytometry. The dynamics of the standard deviation of the reconstructed trajectories is comparable to that of the original fluorescence data.