Effect of loops on the mean-square displacement of Rouse-model chromatin.

Chromatin polymer dynamics are commonly described using the classical Rouse model. The subsequent discovery, however, of intermediate-scale chromatin organization known as topologically associating domains (TADs) in experimental Hi-C contact maps for chromosomes across the tree of life, together with the success of loop extrusion factor (LEF) model in explaining TAD formation, motivates efforts to understand the effect of loops and loop extrusion on chromatin dynamics. This paper seeks to fulfill this need by combining LEF-model simulations with extended Rouse-model polymer simulations to investigate the dynamics of chromatin with loops and dynamic loop extrusion. We show that loops significantly suppress the averaged mean-square displacement (MSD) of a gene locus, consistent with recent experiments that track fluorescently labeled chromatin loci. We also find that loops reduce the MSD's stretching exponent from the classical Rouse-model value of 1/2 to a loop-density-dependent value in the 0.45-0.40 range. Remarkably, stretching exponent values in this range have also been observed in recent experiments [Weber et al., Phys. Rev. Lett. 104, 238102 (2010)0031-900710.1103/PhysRevLett.104.238102; Bailey et al., Mol. Biol. Cell 34, ar78 (2023)1059-152410.1091/mbc.E23-04-0119]. We also show that the dynamics of loop extrusion itself negligibly affects chromatin mobility. By studying static "rosette" loop configurations, we also demonstrate that chromatin MSDs and stretching exponents depend on the location of the locus in question relative to the position of the loops and on the local friction environment.

Uncovering diffusive states of the yeast membrane protein, Pma1, and how labeling method can change diffusive behavior.

We present and analyze video-microscopy-based single-particle-tracking measurements of the budding yeast (Saccharomyces cerevisiae) membrane protein, Pma1, fluorescently labeled either by direct fusion to the switchable fluorescent protein, mEos3.2, or by a novel, light-touch, labeling scheme, in which a 5 amino acid tag is directly fused to the C-terminus of Pma1, which then binds mEos3.2. The track diffusivity distributions of these two populations of single-particle tracks differ significantly, demonstrating that labeling method can be an important determinant of diffusive behavior. We also applied perturbation expectation maximization (pEMv2) (Koo and Mochrie in Phys Rev E 94(5):052412, 2016), which sorts trajectories into the statistically optimum number of diffusive states. For both TRAP-labeled Pma1 and Pma1-mEos3.2, pEMv2 sorts the tracks into two diffusive states: an essentially immobile state and a more mobile state. However, the mobile fraction of Pma1-mEos3.2 tracks is much smaller ([Formula: see text]) than the mobile fraction of TRAP-labeled Pma1 tracks ([Formula: see text]). In addition, the diffusivity of Pma1-mEos3.2's mobile state is several times smaller than the diffusivity of TRAP-labeled Pma1's mobile state. Thus, the two different labeling methods give rise to very different overall diffusive behaviors. To critically assess pEMv2's performance, we compare the diffusivity and covariance distributions of the experimental pEMv2-sorted populations to corresponding theoretical distributions, assuming that Pma1 displacements realize a Gaussian random process. The experiment-theory comparisons for both the TRAP-labeled Pma1 and Pma1-mEos3.2 reveal good agreement, bolstering the pEMv2 approach.

Loops and the activity of loop extrusion factors constrain chromatin dynamics.

The chromosomes-DNA polymers and their binding proteins-are compacted into a spatially organized, yet dynamic, three-dimensional structure. Recent genome-wide chromatin conformation capture experiments reveal a hierarchical organization of the DNA structure that is imposed, at least in part, by looping interactions arising from the activity of loop extrusion factors. The dynamics of chromatin reflects the response of the polymer to a combination of thermal fluctuations and active processes. However, how chromosome structure and enzymes acting on chromatin together define its dynamics remains poorly understood. To gain insight into the structure-dynamics relationship of chromatin, we combine high-precision microscopy in living Schizosaccharomyces pombe cells with systematic genetic perturbations and Rouse model polymer simulations. We first investigated how the activity of two loop extrusion factors, the cohesin and condensin complexes, influences chromatin dynamics. We observed that deactivating cohesin, or to a lesser extent condensin, increased chromatin mobility, suggesting that loop extrusion constrains rather than agitates chromatin motion. Our corresponding simulations reveal that the introduction of loops is sufficient to explain the constraining activity of loop extrusion factors, highlighting that the conformation adopted by the polymer plays a key role in defining its dynamics. Moreover, we find that the number of loops or residence times of loop extrusion factors influence the dynamic behavior of the chromatin polymer. Last, we observe that the activity of the INO80 chromatin remodeler, but not the SWI/SNF or RSC complexes, is critical for ATP-dependent chromatin mobility in fission yeast. Taking the data together, we suggest that thermal and INO80-dependent activities exert forces that drive chromatin fluctuations, which are constrained by the organization of the chromosome into loops.

Extrusion of chromatin loops by a composite loop extrusion factor.

Chromatin loop extrusion by structural maintenance of chromosome (SMC) complexes is thought to underlie intermediate-scale chromatin organization inside cells. Motivated by a number of experiments suggesting that nucleosomes may block loop extrusion by SMCs, such as cohesin and condensin complexes, we introduce and characterize theoretically a composite loop extrusion factor (composite LEF) model. In addition to an SMC complex that creates a chromatin loop by encircling two threads of DNA, this model includes a remodeling complex that relocates or removes nucleosomes as it progresses along the chromatin, and nucleosomes that block SMC translocation along the DNA. Loop extrusion is enabled by SMC motion along nucleosome-free DNA, created in the wake of the remodeling complex, while nucleosome rebinding behind the SMC acts as a ratchet, holding the SMC close to the remodeling complex. We show that, for a wide range of parameter values, this collection of factors constitutes a composite LEF that extrudes loops with a velocity, comparable to the velocity of remodeling complex translocation on chromatin in the absence of SMC, and much faster than loop extrusion by an isolated SMC that is blocked by nucleosomes.

Covariance distributions in single particle tracking.

Several recent experiments, including our own experiments in the fission yeast, Schizosaccharomyces pombe, have characterized the motions of gene loci within living nuclei by measuring the locus position over time, then proceeding to obtain the statistical properties of this motion. To address the question of whether a population of such single-particle tracks, obtained from many different cells, corresponds to a single mode of diffusion, we derive theoretical equations describing the probability distribution of the displacement covariance, assuming the displacement itself is a zero-mean multivariate Gaussian random variable. We also determine the corresponding theoretical means, variances, and third central moments. Bolstering the theory is good agreement between its predictions and the results obtained for various simulated and measured data sets, including simulated particle trajectories undergoing simple and anomalous diffusion, and the measured trajectories of an optically trapped bead in water, and in a viscoelastic polymer solution. We also show that, for sufficiently long tracks, each covariance distribution in all of these examples is well-described by a skew-normal distribution with mean, variance, and skewness given by the theory. However, for the experimentally measured motion of a gene locus in S. pombe, we find that the first two covariance distributions are wider than predicted, although the third and subsequent covariance distributions are well-described by theory. This observation suggests that the origin of the theory-experiment discrepancy in this case is associated with localization noise, which influences only the first two covariances. Thus, we hypothesized that the discrepancy is caused by locus-to-locus heterogeneity in the localization noise, of independent measurements of the same tagged site. Indeed, simulations implementing heterogeneous localization noise revealed that the excess covariance widths can be largely recreated on the basis of heterogeneous noise. Thus, we conclude that the motion of gene loci in fission yeast is consistent with a single mode of diffusion.