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Titel:

Cytoskeletal fluctuations as a stochastic process with four parameters

Abstract:

Information about biochemical processes in the cytoskeleton of living cells can be obtained by attaching microbeads to the cytoskeleton and observing their random motion. Sampling the two-dimensional trajectory in equidistant time intervalls generates a discrete time series (X_n,Y_n). From these raw data, a variety of statistical quantities can be computed, in particular the mean squared displacement (MSD), the velocity autocorrelation (VAC), the power spectral density (PSD), the step width distribution (SWD) and the turning angle distribution (TAD).

We show that all the above spectra and distribution functions can be consistently reproduced by a very simple stochastic process. It consists of a persistent random walk with additive white gaussian noise. The random walk has steps of finite variance, but with long-time (powerlaw) correlated directions. The total process is characterized by only four parameters, which are easily extracted from the data. While under stationary conditions the MSD, VAC and PSD are directly related to each other, it is demonstrated that the SWD is an independent property of the process. The experimentally observed leptocurtic SWD at small lag times is compatible with a Poisson distribution.

Based on the abstract stochastic process, we present a biophysical model of an evolving acto-myosin stress fiber network attached to the bead. Persistent phases of growth or degeneration of remodelling fibers give rise to a superdiffusive bead motion on longer time scales. Within each persistent phase, the discrete adding and removing of fiber building blocks leads to force steps that occur with Poisson statistics and thereby create a non-gaussian SWD. The characterization of bead trajectories by only four key parameters in connection with our biophysical model will be usefull to investigate the effect of pharmacological treatments of the cytoskeleton in the future.

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