  We develop an agent-based model of the motion and pattern formation of
vesicles. These intracellular particles can be found in four different modes of
(undirected and directed) motion and can fuse with other vesicles. While the
size of vesicles follows a log-normal distribution that changes over time due
to fusion processes, their spatial distribution gives rise to distinct
patterns. Their occurrence depends on the concentration of proteins which are
synthesized based on the transcriptional activities of some genes. Hence,
differences in these spatio-temporal vesicle patterns allow indirect
conclusions about the (unknown) impact of these genes.
  By means of agent-based computer simulations we are able to reproduce such
patterns on real temporal and spatial scales. Our modeling approach is based on
Brownian agents with an internal degree of freedom, $\theta$, that represents
the different modes of motion. Conditions inside the cell are modeled by an
effective potential that differs for agents dependent on their value $\theta$.
Agent's motion in this effective potential is modeled by an overdampted
Langevin equation, changes of $\theta$ are modeled as stochastic transitions
with values obtained from experiments, and fusion events are modeled as
space-dependent stochastic transitions. Our results for the spatio-temporal
vesicle patterns can be used for a statistical comparison with experiments. We
also derive hypotheses of how the silencing of some genes may affect the
intracellular transport, and point to generalizations of the model.
