FCSNet and ImFCSNet, convolutional neural network approaches to FCS data analysis

Fluorescence Correlation Spectroscopy (FCS) is a widely used tool to analyse molecular dynamics in biological samples. It analyses the correlation function of the fluorescence fluctuations in a defined observation volume to extract information about the underlying molecular processes. However, FCS faces a number of challenges. First, it requires the use of theoretical fit models that often cannot be solved exactly and thus require approximations. Second, the measurement times for FCS are comparatively long, on the order of a minute, to obtain accurate parameter estimates. Third, the data analysis can be computationally quite time consuming. We therefore explore deep learning approaches to address these issues. For this purpose, we focus on Imaging FCS, a camera-based FCS modality, that provides correlation functions at or between any pixels on a camera, without loss of generality. We developed two convolutional neural networks (CNNs). FCSNet and ImFCSNet use either correlation functions or raw intensity traces as input, respectively. Both networks are trained on simulated, synthetic data, as it is difficult to obtain ground truth data for FCS over wide parameter ranges. More importantly, it allows us to use arbitrary experimental geometries and molecular processes, even when analytic models are not available for conventional fitting, thus solving the first problem. We demonstrate that the two CNNs perform well on synthetic and experimental data and outperform conventional nonlinear least squares (NLS) fits by a) requiring about one order of magnitude less data, b) providing higher precision for parameter estimates, and c) being two orders of magnitude faster. To demonstrate the power of CNNs we present comparisons of data evaluations by conventional NLS fitting on lipid bilayers and cells and on data recorded on total internal reflection and light sheet microscopes.