Chromatin configuration affects the dynamics and distribution of a transiently interacting protein

Abstract

We present a theoretical study of the interaction between a protein (diffusing particle) with chromatin (polymer chain). Each monomer is a trap where a particle can transiently bind. We derive novel formulas for the transition rate between monomer sites, given a specific polymer configuration, and find that a particle is likely to rapidly rebind many times to its release site, before moving to another. The reattachment probability is larger when the local density around the release site is smaller. Interestingly, for an equilibrated polymer, the transition probability decays as a power-law for close monomer-to-monomer distances and reaches an asymptotic value for faraway ones. By computing the transition rate between monomers, we show that the problem of facilitated search by a protein can be mapped to a continuous time Markov chain, which we solve. Our findings suggest that proteins may be locally trapped for a time much longer than their dissociation time, while their overall motion is ergodic. Our results are corroborated by Brownian simulations.The interaction of proteins with chromatin regulates many cellular functions. Most DNA-binding proteins interact both non-specifically and transiently [1] with many chromatin sites as well as specifically and more stably with cognate binding sites. These interactions and chromatin structure are important in governing protein dynamics [2,3]. However, the effect of these transient interactions on protein motion and distribution has yet been shown from a first principle.Some aspects of protein interactions with DNA have been studied in the context of the search of a gene promoter site by a transcription factor (TF) [4]. It was first noted [5] that the search for a promoter site by a TF would be faster if it involves 3d excursions, as well as sliding of the protein along DNA [6], as was shown in prokaryotes [7]. These different types of motion were observed experimentally, leading to massive interest in models of facilitated diffusion [8][9][10][11][12][13][14][15], and in the impact of a regulating site's position on transcription [16,17]. In current microscopy experiments, it is impossible to examine the search process to its fullest [18]. Thus, we concentrate here on modeling the experimentally observed dynamics of the protein as a diffusing and interacting particle.We will show that proteins are likely to stay in the proximity of a site for a time much longer than their dissociation time from DNA due to reattachment. Moreover, we find that reattachment depends on the local density around the release site and that the precise configuration of the polymer impacts the interacting particle's dynamics. We further find the rates associated with the transition between different monomer sites. Finally, we show that the process as a whole is ergodic; it has no long-time power law distribution of the residence time at a site as has been previously suggested [20]. We consider a point particle (protein) placed at a distance a from monomer n (locus), part of a long flexi- The part...

Guided nuclear exploration increases CTCF target search efficiency

“…We tested this hypothesis by simulating chromatin as self-avoiding polymers confined inside the nucleus (Amitai et al, 2017) (Figure 2- Figure Supplement 1A) and simulated protein motion and interaction with chromatin (see (Amitai, 2018) and Materials and Methods for full details). The protein undergoes Brownian motion inside the nucleus but upon encountering a Transiently Trapping Zone (monomer; TTZ) has a certain probability of becoming absorbed and trapped.…”

“…What is the underlying mechanism of ADTZ? When a protein transiently interacts with chromatin, its dynamics will be governed by rapid reattachment to the release site (Amitai, 2018). Indeed, if a protein is bound to a site for a given time, upon disassociation it is much more likely to re-attach to the same site rather than bind to another site.…”

Force-dependent facilitated dissociation can generate protein-DNA catch bonds

“…Force-dependent facilitated dissociation by competitor DNA may also regulate diffusive searches for target sites. For example, recent theoretical work suggests that protein target searches may be governed by the local chromatin conformation (105). Again, the force dependence of protein dissociation may either assist proteins searching for mechanically relaxed regions of chromatin or inhibit intersegment transfer as observed in vitro (96).…”

Transient DNA Binding Induces RNA Polymerase II Compartmentalization During Herpesviral Infection Distinct From Phase Separation

“…Anisotropy can arise either by imposing reflective boundaries on the particle, or adding the 360 aforementioned "traps" thereby giving the particle a greater probability of revisiting proximal 361 sites before diffusing away (Amitai, 2018). 362…”