Optimal estimation of diffusion coefficients from single-particle trajectories

Flyvbjerg, H. (Invited speaker)

    Activity: Talks and presentationsConference presentations

    Description

    Given a theoretical model for a self-propelled micro-organism, how does one optimally determine the parameters of the model from experimental data in the form of a time-lapse recorded trajectory? For very long trajectories, one has very good statistics, and optimality may matter little. However, for biological micro-organisms, one may not control the duration of recordings, and then optimality may matter. Especially if one is interested in individuality and hence does not wish to improve statistics by taking population averages over many trajectories. One can learn much about this problem by studying its simplest case, pure diffusion with no self-propagation. This turns out to be an interesting problem also in its own right and for the very same reasons. I address this latter issue in my talk [1] and will indicate which conclusions are valid also for self-propelled particles [2].

    So now the question is: How does one optimally determine the diffusion coefficient of a diffusing particle from a single time-lapse recorded trajectory of the particle? We answer this question with an explicit, unbiased, and practically optimal covariance-based estimator (CVE). This estimator is regression-free and is far superior to commonly used methods based on measured mean squared displacements. In experimentally relevant parameter ranges, it also outperforms the analytically intractable and computationally more demanding maximum likelihood estimator (MLE). For the case of diffusion on a flexible and fluctuating substrate, the CVE is biased by substrate motion. However, given some long time series and a substrate under some tension, an extended MLE can separate particle diffusion on the substrate from substrate motion in the laboratory frame. This provides benchmarks that allow removal of bias caused by substrate fluctuations in CVE. The resulting unbiased CVE is optimal also for short time series on a fluctuating substrate. We have applied our estimators to human 8-oxoguanine DNA glycolase proteins diffusing on flow-stretched DNA, a fluctuating substrate, and found that diffusion coefficients are severely overestimated if substrate fluctuations are not accounted for [1].
    Period22 Sep 201426 Sep 2014
    Event title27th Marian Smoluchowski Symposium on Statistical Physics
    Event typeConference
    LocationZakopane, Poland