April 4, 2014
Signature of complex transport dynamics in vitro and in vivo
Since Einstein’s seminal work in 1905, the main means of characterizing stochastic processes has been the mean square displacement (MSD). However, this order parameter fails to capture many features of dynamics at the forefront of science today, ranging from glassy relaxation to active transport in biological cells. Although there have been several studies seeking to go beyond the MSD, such studies have not made full use of the information available in individual trajectories in two (or more) dimensions, as are now commonly obtained in particle tracking experiments. Here, we introduce an approach that quantifies directional properties of complex motions and discover striking correlations in a number of condensed phase systems.
This research is a collaboration between four MRSEC research groups: Margaret Gardel, Stuart Rice, Norbert Scherer, and Aaron Dinner's groups.
Analyses of random walks traditionally use the mean square displacement (MSD) as an order parameter characterizing dynamics. We show that the distribution of relative angles of motion between successive time intervals of random walks in two or more dimensions provides information about stochastic processes beyond the MSD. We illustrate the behavior of this measure for common models and apply it to experimental particle tracking data. For a colloidal system, the distribution of relative angles reports sensitively on caging as the density varies. For transport mediated by molecular motors on filament networks in vitro and in vivo, we discover self-similar properties that cannot be described by existing models and discuss possible scenarios that can lead to the elucidated statistical features.
Fig 1: Schematic of the construction of relative angles. (UpperΔΔLower
Fig 2: Caging and escape in quasi-2D colloidal suspensions. (AΔΔΔB Upper Ø=0.68
Fig 3: Statistical measures of insulin granule transport in a pancreatic cell line (MIN6). (UpperΔ =1Δ =2Δ LowerΘΔΔ =1Δ =5Δ =10Δ =20Δ =40Δ =5024Left Right
Fig 4: Statistical measures of the motion of myosin thick filaments on a disordered actin network. (UpperΔ=5Δ=2Δ=15LowerΔ=1 Δ=3Δ=10Δ=20Δ=30Left Right
Stanislav Burov, S. M. Ali Tabei, Toan Huynh, Michael P. Murrell, Louis H. Philipson, Stuart A. Rice, Margaret L. Gardel, Norbert F. Scherer, and Aaron R. Dinner,