Plastid and peroxisome movement tracks in the root cells of Arabidopsis thaliana

In movement analysis, correlated random walk (CRW) models often use
so-called turning angles, which are measured relative to the previous
movement direction. To segregate between different movement modes, hidden
Markov models (HMMs) describe movements as piecewise stationary CRWs in
which the distributions of turning angles and step sizes depend on the
underlying state. This typically allows for the segregation of movement
modes that show different movement speeds.  We show that in some
cases, it may be interesting to investigate absolute angles, i.e., biased
random walks (BRWs) instead of turning angles. In particular, while
discrimination between states in the turning angle setting can only rely
on movement speed, models with absolute angles can be used to discriminate
between sections of different movement directions. A preprocessing
algorithm is provided that enables the analysis of absolute angles in the
existing R package moveHMM. In a data set of movements of cell
organelles, models using not the turning angle but the absolute angle
could capture interesting additional properties. Goodness of fit was
increased for HMMs with absolute angles, and HMMs with absolute angles
tended to choose a higher number of states, suggesting the existence and
relevance of prominent directional changes in the present data
set. These results suggest that models with absolute angles can
provide important information in the analysis of movement patterns if the
existence and frequency of directional changes is of biological
importance.