Nonlinear mixed-effects models to analyze actin dynamics in dendritic spines

Fluorescence recovery after photobleaching (FRAP) allows to study actin-turnover in dendritic spines by providing recovery trajectories over time within a nested data structure (i.e. spine/neuron/culture). Statistical approaches to FRAP usually consider one-phase association models to estimate recovery-curve-specific parameters and test statistical hypotheses on curve parameters either at the spine or neuron level, ignoring the nested data structure. However, this approach leads to pseudoreplication concerns. We propose a nonlinear mixed-effects model to integrate the one-phase association model estimate with the nested data structure of FRAP experiments; this also allows us to model heteroscedasticity and time dependence in the data. We used this approach to evaluate the effect of the downregulation of the actin-binding protein CAP2 on actin dynamics. Our model allows the additional modelling of the variance function across experimental conditions, which may represent a novel parameter of interest in FRAP experiments. Indeed, the detected differential effect of the experimental condition on the variance component captures the increased instability of time-specific observations around the spine-specific trajectory for the CAP2-downregulated spines compared to the control spines. We hypothesise that this parameter reflects the increased instability of the actin cytoskeleton in dendritic spines upon CAP2 downregulation. We developed an R-based Shiny application, termed FRApp, to fit the statistical models introduced without requiring programming expertise.