Random walk is a fundamental concept with applications ranging from quantum physics to
econometrics. Remarkably, one specific model of random walks appears to be ubiquitous …

T cell migration is essential for T cell responses; it allows for the detection of cognate antigen
at the surface of antigen-presenting cells and for interactions with other cells involved in the …

We review theoretical models of individual motility as well as collective dynamics and
pattern formation of active particles. We focus on simple models of active dynamics with a …

The mechanism by which cells control directional persistence during migration is a major
question. However, the common index measuring directional persistence, namely the ratio …

Collective cell migration in tissues occurs throughout embryonic development, during wound
healing, and in cancerous tumor invasion, yet most detailed knowledge of cell migration …

Cell motility is central to tissue homeostasis in health and disease, and there is hardly any
cell in the body that is not motile at a given point in its life cycle. Important physiological …

It is well established that a wide variety of phenomena in cellular and molecular biology
involve anomalous transport eg the statistics for the motility of cells and molecules are …

Single particle tracking of mRNA molecules and lipid granules in living cells shows that the
time averaged mean squared displacement δ 2¯ of individual particles remains a random …

In this chapter we have presented mathematical modeling approaches to biological pattern
formation. While reaction-diffusion models are appropriate to describe the spatio-temporal …

Cell migration through connective tissue, or cell invasion, is a fundamental biomechanical
process during metastasis formation. Cell invasion usually requires cell adhesion to the …