Track papers across labs, topics, and trends.
Search papers, labs, and topics across Lattice.
This paper jointly estimates the Hurst exponent ($H$) and generalized diffusion coefficient ($D_H$) for fractional Brownian motion (fBM) using maximum likelihood estimation (MLE) and neural networks from density measurements with Poisson noise and single-particle trajectories with Gaussian error. It demonstrates that inferring both parameters from a single density measurement is impossible, necessitating multiple time points for precise estimation, and that a neural network approximating the posterior mean of $H$ paired with profile-likelihood for $D_H$ yields the lowest RMSE. Analysis of vesicle trajectories reveals a continuum of $H$ and $D_H$ values within cell types, with a significant proportion of tracks exhibiting switches between subdiffusive and superdiffusive states, challenging the notion of distinct populations with fixed motion characteristics.
Intracellular vesicle motion isn't fixed sub- or superdiffusive populations; cargoes dynamically switch states, a finding enabled by a neural network approximating the fBM posterior mean.
Fractional Brownian motion (fBM) is a model of anomalous diffusion parameterised by a Hurst exponent $H \in (0,1)$ and a generalised diffusion coefficient $D_H>0$. We jointly estimate $H$ and $D_H$ using maximum likelihood (MLE) from density measurements with Poisson counting noise and single-particle trajectory with Gaussian localisation error. We show that one density measurement in time cannot infer both $H$ and $D_H$ and that several time points are needed, which matters most for inference precision. For trajectories, we show that a neural network trained with a squared error loss approximates the posterior mean of $H$, which can be computed exactly at negligible cost. Paired with the profile-likelihood estimate of $D_H$, the posterior mean has the lowest root mean squared error in both $H$ and $D_H$, except near $H=0$ and $H=1$ where MLE estimates $H$ better. In vesicle trajectories from two cell types, $H$ and $D_H$ form a continuum rather than distinct modes of motion. The posterior probability that each window within a track is subdiffusive or superdiffusive shows that $26\%$ of MRC5 fibroblast and $21\%$ of HeLa vesicle trajectories contain both subdiffusive and superdiffusive windows, against $2\%$ and $7\%$ expected from estimation uncertainty alone. Intracellular cargoes therefore switch between subdiffusion and superdiffusion over time rather than forming populations with fixed $H$.