In eukaryotes, genomes are spatially organized within the nucleus. Chromosomes occupy distinct subnuclear ‘territories’, heterochromatin is segregated from euchromatin, and individual genes show non-random positioning relative to nuclear structures and other genes (Misteli, 2020). Gene positioning reflects physical interactions of chromosomal loci with nuclear structures like the nuclear lamina, nuclear pore complexes (NPCs), or nuclear bodies, and changes in gene expression are often accompanied by changes in gene positioning (Brickner, 2017). The positioning of genes can impact their transcription, mRNA processing, or chromatin modifications.

One model for such phenomena is the recruitment of genes to the nuclear periphery through interaction with the NPC. Many genes in budding yeast, Caenorhabditis elegans, Drosophila, and mammals physically interact with NPCs, suggesting that the NPC plays an important role in determining the spatial arrangement of eukaryotic genomes (Brown et al., 2008a; Capelson et al., 2010; Casolari et al., 2004; Casolari et al., 2005; Ibarra et al., 2016; Jacinto et al., 2015; Liang et al., 2013; Pascual-Garcia et al., 2017; Rohner et al., 2013; Toda et al., 2017). This is particularly apparent in budding yeast where hundreds of genes interact with the NPC and inducible genes rapidly reposition to the nuclear periphery upon activation (Brickner and Walter, 2004; Casolari et al., 2005; Casolari et al., 2004; Van de Vosse et al., 2013). Interaction with the NPC and localization to the nuclear periphery require specific transcription factors (TFs) and nuclear pore proteins (Brickner et al., 2019; Brickner et al., 2012; Brickner et al., 2007; Cabal et al., 2006; Dieppois et al., 2006; Dilworth et al., 2005; D'Urso et al., 2016; Lapetina et al., 2017; Luthra et al., 2007; Randise-Hinchliff et al., 2016; Texari et al., 2013; Van de Vosse et al., 2013). A majority of yeast TFs can mediate interaction with the NPC (Brickner et al., 2019), suggesting that the yeast genome encodes spatial organization through cis-acting TF binding sites. Such cis-acting DNA zip codes are both necessary and sufficient to mediate interaction with the NPC and positioning to the nuclear periphery (Ahmed et al., 2010; Brickner et al., 2019; Brickner et al., 2012; Light et al., 2010; Randise-Hinchliff et al., 2016). Furthermore, interaction with the NPC frequently leads to inter-chromosomal clustering of co-regulated genes, suggesting that it influences the spatial organization of the yeast genome at multiple levels (Brickner et al., 2016; Brickner et al., 2012; Kim et al., 2019; Kim et al., 2017; Mirkin et al., 2013; Randise-Hinchliff et al., 2016).

Much of the work on gene recruitment to the nuclear periphery has utilized static population measurements such as microscopy, chromatin immunoprecipitation, or HiC. Although these studies have revealed important players necessary for gene positioning to the nuclear periphery, there are questions that cannot be answered using static methods. For example, while some loci interact very stably with the nuclear envelope (e.g., telomeres and centromeres; Heun et al., 2001; Jin et al., 2000), leading to ~85% of cells showing colocalization of these loci with the nuclear envelope, genes that interact with the NPC show lower levels (~50–65%; Brickner and Walter, 2004; Casolari et al., 2004). This has been suggested to reflect transient interaction with the nuclear periphery (Brickner and Walter, 2004), cell-cycle regulation of peripheral localization (Brickner and Brickner, 2010), or, perhaps, two distinct populations, one that stably associates with the NPC and the other that does not (Brickner and Walter, 2004; Cabal et al., 2006). Likewise, the repositioning of inducible genes from the nucleoplasm to the nuclear periphery is not well-understood. Some data – including the involvement of nuclear actin and myosin – has suggested that repositioning to the NPC could involve directed, super-diffusive movement (Guet et al., 2015; Wang et al., 2020). Finally, while inter-chromosomal clustering is a widespread phenomenon (Apostolou and Thanos, 2008; Brickner et al., 2012; Brown et al., 2006; Homouz and Kudlicki, 2013; Kim et al., 2017; Lin et al., 2009; Noma et al., 2006; Schoenfelder et al., 2010; Thompson et al., 2003), relatively few studies have explored the dynamics of clustering over time and it is unclear if clustering reflects a stable physical interaction (Brickner et al., 2016; Dai et al., 2018). High-resolution, quantitative dynamics of chromatin diffusion are required to address each of these questions.

Chromatin is a mobile polymer, and individual loci exhibit constrained or anomalous diffusion (Bystricky et al., 2004; Gasser, 2002; Hajjoul et al., 2013; Heun et al., 2001; Marshall et al., 1997). Chromatin motion can reveal important aspects of the nuclear environment and the biophysical mechanisms that control the spatial organization of the genome. Repositioning to the NPC in budding yeast is an intriguing model for such studies because it is inducible, relatively rapid, controlled by well-understood DNA elements, and induces both a change in position and inter-chromosomal clustering.

Here we show that repositioning to the nuclear periphery is continuous and dynamic but uniform within the population, suggesting that, within each cell, localization to the periphery it is a probabilistic process. Localization at the nuclear periphery correlates with more constrained diffusion, as suggested by previous work (Backlund et al., 2014; Cabal et al., 2006). Using mean-squared displacement (MSD) analysis and molecular genetics, we pinpoint this effect to the interaction with the NPC. The parameters of sub-diffusion derived from MSD of nucleoplasmic loci were used to develop a computational simulation that faithfully recapitulates the behavior of such genes. This simulation was also adapted to model repositioning to the nuclear periphery through random sub-diffusion and transient capture at the nuclear envelope. The repositioning predicted by the simulation was then compared with several rapid repositioning experiments to determine whether it is vectorial or super-diffusive. The simulation matched the observed behavior of loci in cells, suggesting that repositioning from the nucleoplasm to the nuclear periphery does not require directed movement.

Finally, we monitored the dynamics of inter-chromosomal clustering. Unlike pairs of simulated paths, genes that exhibit clustering remain near each other for tens of seconds and show correlated movement. Simulated interaction with the NPC, while sufficient to recapitulate the chromatin dynamics of individual loci, is not sufficient to recapitulate this correlated movement. Therefore, we propose that inter-chromosomal clustering relies on a distinct physical interaction between genes that can extend hundreds of nanometers.

Tracking yeast NPC-associated chromatin over time revealed a frequent exchange between the nucleoplasm and periphery (Figure 1), suggesting that the interaction with the NPC is continuously re-established and that the population averages reflect this dynamism, rather than distinct, stable sub-populations. In other words, localization to the nuclear periphery is less well described as tethering than as a change in the steady-state positioning through continuous binding and dissociation. As interaction with the NPC enhances transcription (Ahmed et al., 2010; Brickner et al., 2019; Brickner et al., 2016; Brickner et al., 2012; Capelson et al., 2010; Jacinto et al., 2015; Liang et al., 2013; Pascual-Garcia et al., 2014; Taddei et al., 2006), it is intriguing that the periodic and transient interaction with the NPC is reminiscent of the widespread phenomenon of transcriptional ‘bursting’ (Femino et al., 1998; Rodriguez and Larson, 2020). Transcriptional bursting leads to heterogeneity in the transcription between cells within a population (Zenklusen et al., 2008) and disrupting the interaction of the GAL1-10 promoter with the NPC leads to a decrease in the number of cells expressing these genes without affecting the amount of transcript produced at the site of transcription (Brickner et al., 2016). Perhaps interaction with the yeast NPC functions with other transcriptional regulators to stimulate transcriptional bursts. Exploring this connection will require assessing the dynamics of chromatin positioning and transcription simultaneously in live cells.

Chromatin undergoes anomalous sub-diffusive movement during interphase (Hajjoul et al., 2013; Marshall et al., 1997). The physical interaction between chromatin and the NPC, though transient, reduces chromatin sub-diffusion (Figure 2; Backlund et al., 2014; Cabal et al., 2006), independent of changes in transcription (Figures 2 and 3). Using the parameters derived from MSD, we developed computational simulations for yeast chromatin sub-diffusion in the nucleoplasm and at the nuclear periphery. The anticorrelation between successive steps of chromatin and can be modeled as FBM (a.k.a. overdamped fractional Langevin motion; Lucas et al., 2014). Sub-diffusion of yeast chromosomal loci is determined by the elastic response from the chromatin polymer and the viscous interaction between the polymer and the nucleoplasm. While we do not explicitly simulate the total chromatin polymer or other nuclear occupants, FBM captures their net effects, recapitulating the MSD behavior of a nucleoplasmic locus (Figure 4). However, the FBM model leads to exclusion near boundaries, leading to non-random positioning of loci, a phenomenon that is not consistent with experimental observations. This likely reflects the fact that, while the motion of a segment of chromatin can be modeled as an FBM particle, it is part of a polymer and is not an FBM particle. Our solution to this shortcoming of the FBM model, recalculating the path upon collision with the nuclear boundary (see detailed explanation in Materials and methods), produced localization patterns and MSD behaviors that are consistent with experimental observations. However, additional theoretical and experimental work will help clarify the biological and physical significance of this modification.

To simulate the interaction of chromatin with the NPC, we allowed loci in an area within 50 nm of the nuclear boundary to ‘bind’ to the nuclear periphery, assuming the mobility of the SPB. The width of this annulus is roughly equal to the height of the NPC nuclear basket (Vallotton et al., 2019), whose components are required for chromatin association with the NPC (Ahmed et al., 2010). We independently optimized the probability of binding and of remaining bound by comparing the positioning and MSD of simulated paths with that conferred by a DNA zip code. This simple modification of the simulation was able to reliably recreate the peripheral localization and constraint on chromatin sub-diffusion caused by interaction with the NPC (Figure 4). Thus, the work described here provides a straightforward and powerful theoretical framework for modeling the biophysical nature of gene positioning through association with any stable nuclear structure.

Repositioning of genes to the NPC during transcriptional activation occurs over a wide range of timescales, depending on the stimulus and gene (Randise-Hinchliff et al., 2016), making it difficult to test whether it involves super-diffusive or vectorial movement. Our simulated trajectories offer an important insight; starting from random positions within the center of the yeast nucleus, the population shifted from a random distribution to a peripheral distribution within ~2 min by random sub-diffusion (Figure 5G). This timescale is comparable to the experimental models for peripheral repositioning (Figure 5), arguing that active mechanism(s) are unnecessary to explain the observed rate of repositioning. More importantly, experimental analysis of the speed and vector of individual steps preceding contact with the nuclear envelope showed non-vectorial sub-diffusive movement that was indistinguishable from that captured by the simulation (Figure 5). Furthermore, there was also no difference between experimental cells and negative control cells for these components. These results indicate that zip code-dependent gene localization results from random sub-diffusive chromatin movement, collision with the NPC, leading to dynamic binding. The recently discovered role for actin and Myo3 in localization of INO1 at the nuclear periphery (Wang et al., 2020), raises an important question: how do these factors impact peripheral repositioning through a sub-diffusive mechanism? Our results suggest that loss of Myo3 delays arrival of some loci at the nuclear periphery but does not disrupt localization once it is established (Figure 5—figure supplement 1). Perhaps, like actin (Kapoor et al., 2013), Myo3 impacts the function of chromatin remodeling complexes or histone-modifying enzymes, which regulate binding of transcription factors to DNA zip codes (Randise-Hinchliff et al., 2016). Alternatively, perhaps actin/Myo3 act at the NPC to facilitate capture. A better biochemical and biophysical understanding of these processes will illuminate such possible roles.

Interaction with nuclear pore proteins plays a conserved role in promoting transcription. However, while interaction of yeast genes with nuclear pore proteins occurs at the nuclear periphery in association with the NPC, many genes in mammalian cells and Drosphila interact with soluble nuclear pore proteins in the nucleoplasm (Capelson et al., 2010; Liang et al., 2013; Light et al., 2013). Sub-diffusion for mammalian chromatin (which has been suggested to be less mobile than in yeast; Chubb et al., 2002) in a nucleus with a radius of 5 µm would make it impossible (on a biologically meaningful timescale) for loci in the center of the nucleus to reach the periphery. In larger nuclei, recruitment of nuclear pore proteins to sites of action, regardless of their position, likely overcomes this obstacle.

Inter-chromosomal clustering is a widespread phenomenon in eukaryotes (Bantignies et al., 2011; Brickner et al., 2012; Brown et al., 2008b; Cook and Marenduzzo, 2018; Eskiw et al., 2010; Gehlen et al., 2012; Haeusler et al., 2008; Noma et al., 2006; Ramos et al., 2006; Taddei et al., 2009; Thompson et al., 2003; Xu and Cook, 2008). Genes that interact with the NPC through shared transcription factors exhibit inter-chromosomal clustering (Brickner et al., 2015; Brickner et al., 2016; Brickner et al., 2012; Kim et al., 2019; Kim et al., 2017; Randise-Hinchliff et al., 2016). Such clustering requires transcription factor(s) and nuclear pore proteins (Brickner et al., 2012; Chowdhary et al., 2017; Kim et al., 2019) but is also mechanistically distinguishable from interaction with the NPC (Brickner et al., 2016). Clustering persisted for 20–40 s (Figure 6) and led to correlated movement between pairs of loci that were within 550 nm (Figure 7). Importantly, independently correlating step size and step angle is sensitive to correlations among pairs of loci in a subset of the cells in the population. Such correlated movement, averaged over the entire population, would be more difficult to appreciate. This may explain why previous work tracking movement of pairs of active GAL1-10 alleles in yeast found little correlation in aggregate (Backlund et al., 2014).

Pairs of paths generated by either the simulation or the simulation+zip code do not lead to inter-chromosomal clustering, consistent with the observation that genes that interact with the NPC through different transcription factors do not exhibit clustering (Brickner et al., 2012). Therefore, while clustering requires transcription factors and interaction with the NPC, it represents a distinct physical interaction. Surprisingly, correlated movement was observed between loci separated by hundreds of nanometers, suggesting that it reflects a large molecular complex, or more likely, an environment. Physical interactions that lead to phase separation could encompass groups of genes to create a (perhaps transient) nuclear sub-compartment (Hult et al., 2017). This is reminiscent of superenhancers, which exist within phase-separated droplets (Hnisz et al., 2017; Sabari et al., 2018) and are strongly associated with nuclear pore proteins (Ibarra et al., 2016). It is possible that phase separation is facilitated by multivalent interactions between natively unstructured nuclear pore proteins, which are capable of forming phase-separated droplets in vitro (Frey et al., 2006; Frey and Görlich, 2007). Such conditional phase separation would be regulated and specified by transcription factors, and potentially other transcriptional complexes such as mediator or RNA polymerase II, to functionally compartmentalize the nucleus.

All tracking data will be included as Source Data. All Scripts are publicly available from Github https://github.com/MCnu/R_sim_scripts copy archived at https://archive.softwareheritage.org/swh:1:rev:6440995193e1245c44d2c9a9e0b21b161d98e788.

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Author details

1. Michael Chas Sumner

   Department of Molecular Biosciences, Northwestern University, Evanston, United States

   Contribution

   Conceptualization, Resources, Data curation, Software, Formal analysis, Supervision, Funding acquisition, Investigation, Visualization, Methodology, Writing - original draft, Project administration, Writing - review and editing

   Competing interests

   No competing interests declared

2. Steven B Torrisi

   Department of Physics, Harvard University, Cambridge, United States

   Contribution

   Conceptualization, Software, Formal analysis, Investigation, Visualization, Methodology, Writing - original draft, Writing - review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-4283-8077

3. Donna G Brickner

   Department of Molecular Biosciences, Northwestern University, Evanston, United States

   Contribution

   Conceptualization, Data curation, Software, Formal analysis, Investigation, Visualization, Methodology, Writing - original draft, Writing - review and editing

   Competing interests

   No competing interests declared

4. Jason H Brickner

   Department of Molecular Biosciences, Northwestern University, Evanston, United States

   Contribution

   Conceptualization, Resources, Software, Formal analysis, Supervision, Funding acquisition, Visualization, Methodology, Writing - original draft, Project administration, Writing - review and editing

   For correspondence

   j-brickner@northwestern.edu

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-8019-3743

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