Analysis of Single Locus Trajectories for Extracting In Vivo Chromatin Tethering Interactions

Abstract

Is it possible to extract tethering forces applied on chromatin from the statistics of a single locus trajectories imaged in vivo? Chromatin fragments interact with many partners such as the nuclear membrane, other chromosomes or nuclear bodies, but the resulting forces cannot be directly measured in vivo. However, they impact chromatin dynamics and should be reflected in particular in the motion of a single locus. We present here a method based on polymer models and statistics of single trajectories to extract the force characteristics and in particular when they are generated by the gradient of a quadratic potential well. Using numerical simulations of a Rouse polymer and live cell imaging of the MAT-locus located on the yeast Saccharomyces cerevisiae chromosome III, we recover the amplitude and the distance between the observed and the interacting monomer. To conclude, the confined trajectories we observed in vivo reflect local interaction on chromatin.

Encounter times of chromatin loci influenced by polymer decondensation

“…Chromatin strands are well localized [24] in the nucleus due to local interactions [25] imposed by the binding molecules such as Lamin A [26]. In this last section, we study the influence of local tethering forces on the search time.…”

“…3(a)]. The consequence of this resulting force is to confine the locus motion [25].We simulated the motion of several monomers, restricted by potential wells [ Fig. 3(b)], where the energy for an interacting of monomer i is…”

“…We recall that the resulting force on a tracked locus [red bead in Fig. 3(a) is computed [25] by the formulawhere E{·|R c = x} is the average over all polymer configurations under the condition that the tagged monomer is at position R c = x. When only one monomer n is interacting with a potential [Eq.…”

Commentary: New mathematical physics needed for life sciences

“…That modeling led to the discovery of local wells; their origin is still unknown, 3 but they appear to regulate molecular trafficking in several microdomains. Other theoretical problems raised by large data sets 4 are the reconstruction of a cell's surface and its local structure from the planar projections of trajectories of diffusing molecules, solved by deriving new nonlinear partial differential equations. Models are needed to describe how cells move and grow based on molecular trafficking, how a cell can repair itself, or how viruses and their DNA or RNA find targets inside a cell.…”

“…Apparently, neither they nor any others noticed that result until we recently discovered it. 4 Muller's and Stern's approaches survive in the LNT model of today, which says that low-dose radiation increases cancer risk. However, while linearitythe "L" in LNT-was demonstrated only at high doses, the absence of a threshold has never been demonstrated.…”