Interpreting biological random walks - the peculiar case of chromatin dynamics

Biological environments are complex and dynamic. Numerous entities constantly interact, diffuse and form structural motifs. Due to their complexity, such systems are commonly studied through the emergent motion of key factors in the system. A canonical example can be found in the cellular nucleus, as accurate expression of various genes demands that DNA interact with functional molecules, undergo packaging modifications and maintain a flexible yet organized structure. Thus, we track the temporal motion of chromatin loci (DNA with its accompanying proteins) across several orders of time. This measurement is performed through single cell in vivo fluorescent microscopy, i.e. a minimally invasive technique allowing us to capture the natural mechanisms in the system.

Once trajectories of biological entities are gathered, it is possible to dive into the stochastic data in order to extract the relevant mathematical and physical picture for the system. Through the implementation of advanced mathematical testing, we have shown that the anomalous diffusion of chromatin can be described as fractional Brownian motion – a framework that can also capture the dynamics of dense viscoelastic media or polymer melts. However, by modifying the expression levels of key nuclear proteins, such as Lamin A, the dynamics of chromatin can be completely transformed. A 'normal' diffusion process emerges, in contradiction to physical theories of polymer dynamics and our current understanding of the nucleus. In another study vector, long range inter locus interactions are found. Surprisingly, these interactions are not isotropic, and reveal three spatial regimes of relative chromatin motion.

These observations lead to a rich and complex picture of chromatin motion that we are only starting to unravel. They serve as an example of the power of dynamic measurements coupled to stochastic analysis in exploring biological systems.