  Motor enzymes are remarkable molecular machines that use the energy derived
from the hydrolysis of a nucleoside triphosphate to generate mechanical
movement, achieved through different steps that constitute their kinetic cycle.
These macromolecules, nowadays investigated with advanced experimental
techniques to unveil their molecular mechanisms and the properties of their
kinetic cycles, are implicated in many biological processes, ranging from
biopolymerisation (e.g. RNA polymerases and ribosomes) to intracellular
transport (motor proteins such as kinesins or dyneins). Although the kinetics
of individual motors is well studied on both theoretical and experimental
grounds, the repercussions of their stepping cycle on the collective dynamics
still remains unclear. Advances in this direction will improve our
comprehension of transport process in the natural intracellular medium, where
processive motor enzymes might operate in crowded conditions. In this work, we
therefore extend the current statistical kinetic analysis to study collective
transport phenomena of motors in terms of lattice gas models belonging to the
exclusion process class. Via numerical simulations, we show how to interpret
and use the randomness calculated from single particle trajectories in crowded
conditions. Importantly, we also show that time fluctuations and non-Poissonian
behavior are intrinsically related to spatial correlations and the emergence of
large, but finite, clusters of co-moving motors. The properties unveiled by our
analysis have important biological implications on the collective transport
characteristics of processive motor enzymes in crowded conditions.
