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Generalised Langevin dynamics for movement data analysis

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MMVW01 - Summer School on Mathematics of Movement

I briefly review the concept of Langevin dynamics, which originates from modeling the Brownian motion of a passive tracer particle in a fluid. However, for describing active biological motion this equation has to be suitably modified. I then show how such suggested modifications are obtained in stochastic models constructed from experimental data. First, I discuss migration of neutrophil cells along a chemical gradient [1]. Extracting moments of the positions, position probability distributions and velocity autocorrelation functions from experimental data suggests a simple stochastic model in the form of an overdamped generalised Langevin equation that well reproduces the data. Notably, cells move asymmetrically superdiffusively in both directions. Biological activity is represented by power law correlation decay. Second, experimental data of bumblebee flights is analysed for constructing a Langevin-type generalised correlated random walk model, again well reproducing the data [2]. Biological activity shows up both in the friction coefficient of the speed and in non-trivial correlation decay. [1] P.Dieterich et al., PLoS Comput Biol 18, e1010089 (2022)[2] F.Lenz, A.V.Chechkin, RK, PLoS ONE 8 , e59036 (2013)

This talk is part of the Isaac Newton Institute Seminar Series series.

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