Enhancing fluorescence correlation spectroscopy with machine learning to infer anomalous molecular motion

The random motion of molecules in living cells has consistently been reported to deviate from standard Brownian motion, a behavior coined as "anomalous diffusion." To study this phenomenon in living cells, fluorescence correlation spectroscopy (FCS) and single-particle tracking (SPT) are the two main methods of reference. In opposition to SPT, FCS, with its classical analysis methodology, cannot consider models of motion for which no analytical expression of the auto-correlation function is known. This excludes, for instance, anomalous continuous-time random walks and random walk on fractal. Moreover, the whole acquisition sequence of the classical FCS methodology takes several tens of minutes. Here, we propose a new analysis approach that frees FCS of these limitations. Our approach associates each individual FCS recording with a vector of features based on an estimator of the auto-correlation function and uses machine learning to infer the underlying model of motion and to estimate the values of the motion parameters. Using simulated recordings, we show that this approach endows FCS with the capacity to distinguish between a range of standard and anomalous random motions, including continuous-time random walk and random walk on fractal. Our approach exhibits performances comparable to the best-in-class state-of-the-art algorithms for SPT and can be used with a range of FCS setup parameters. Since it can be applied on individual recordings of short duration, we show that, with our method, FCS can be used to monitor rapid changes of the motion parameters. Finally, we apply our method on experimental FCS recordings of calibrated fluorescent beads in increasing concentrations of glycerol in water. Our results accurately predict that the beads follow Brownian motion with a diffusion coefficient and anomalous exponent, which agree with classical predictions from Stokes-Einstein law even at large glycerol concentrations. Taken together, our approach significantly augments the analysis power of FCS to capacities that are similar to state-of-the-art SPT approaches.