  Aerotaxis is the particular form of chemotaxis in which oxygen plays the role
of both the attractant and the repellent. Aerotaxis occurs without methylation
adaptation, and it leads to fast and complete aggregation toward the most
favorable oxygen concentration. Biochemical pathways of aerotaxis remain
largely elusive, however, aerotactic pattern formation is well documented. This
allows mathematical modeling to test plausible hypotheses about the biochemical
mechanisms. Our model demonstrates that assuming fast, non-methylation
adaptation produces theoretical results that are consistent with experimental
observations. We obtain analytical estimates for parameter values that are
difficult to obtain experimentally.
  Chemotaxis in growth cones differs from gradient sensing in other animal
cells, because growth cones can change their attractive or repulsive response
to the same chemical gradient based on their internal calcium or cAMP levels.
We create two models describing different aspects of growth cone guidance. One
model describes the internal switch that determines the direction of movement.
However, this model allows chemotaxis under certain conditions only, so a
second model is created to propose a mechanism that allows growth cone guidance
in any environment.
  Endothelial cells go through extensive morphological changes when exposed to
shear stress due to blood flow. These morphological changes are thought to be
at least partially the result of mechanical signals, such as deformations,
transmitted to the cell structures. Our model describes an endothelial cell as
a network of viscoelastic Kelvin bodies with experimentally obtained
parameters. Qualitative predictions of the model agree with experiments.
