Live-cell micromanipulation of a genomic locus reveals interphase chromatin mechanics

Our understanding of the physical principles organizing the genome in the nucleus is limited by the lack of tools to directly exert and measure forces on interphase chromosomes in vivo and probe their material nature. Here, we introduce an approach to actively manipulate a genomic locus using controlled magnetic forces inside the nucleus of a living human cell. We observed viscoelastic displacements over micrometers within minutes in response to near-piconewton forces, which are consistent with a Rouse polymer model. Our results highlight the fluidity of chromatin, with a moderate contribution of the surrounding material, revealing minor roles for cross-links and topological effects and challenging the view that interphase chromatin is a gel-like material. Our technology opens avenues for future research in areas from chromosome mechanics to genome functions. Description A new force in chromatin research Fundamental questions about the physical nature of chromosomes remain unanswered, largely due to the absence of direct mechanical measurements inside the nuclei of living cells. Keizer et al. developed a technique to measure how a genomic locus, in its native nuclear context, responds to a point force of physiological magnitude (see the Perspective by So and Tanner). Interphase chromatin was found to be liquid like, with moderate hindrance and topological effects, contrasting with the common view of a crowded and entangled nuclear environment. Ultimately, these measurements allow a deeper understanding of how genomic elements can move under active biological forces and provide a basis for developing new physical models of chromosomes. —DJ An approach for probing the force response of interphase chromosomes in living cells reveals their material nature.

R ecent progress in observing and perturbing chromosome conformation has led to an unprecedented understanding of the physical principles at play in shaping the genome in four dimensions (4D) (1). From genomic loops and topologically associating domains to spatially segregated A/B compartments and chromosome territories, the different levels of organization of the eukaryotic genome are thought to arise from various physical phenomena, including phase separation (2)(3)(4), ATP-dependent motors (4,5), and polymer topological effects (6). Nonetheless, the physical nature of chromatin and chromosomes inside the nucleus and its functional implications for mechanotransduction remain an active area of investigation (7,8). Observationbased studies assessing the mobility of the genome in living cells, from single loci (9)(10)(11) and small regions (12) to large domains (13), underline the possible existence of different material states of chromatin (e.g., liquid, solid, and gel-like). Extranuclear mechanical perturbations, including whole-nucleus stretching (14,15), micropipette aspiration (16), and application of local pressures (16,17) or torques (18) onto a cell, all affect the overall geometry of the nucleus and reveal global viscoelastic properties. Conversely, intranuclear mechanical manipulation of the genome is rare and technically challenging (8). Viscoelasticity measurements using a microinjected 1-mm bead suggested that interphase chromatin may be a cross-linked polymer network (i.e., a gel) (19). Recently, intranuclear mechanics were elegantly probed by monitoring the fusion of both artificial (20) and naturally occurring (21) droplet-like structures. Active mechanical manipulation of an intranuclear structure was recently achieved using an optical tweezer to displace a whole nucleolus in oocytes (22) and using optically induced thermophoretic flows within prophase (23) or interphase (24) nuclei. However, these approaches are limited to the manipulation of large structures or do not apply forces directly on chromatin. These limitations have made it difficult to disentangle various effects (e.g., mechanical response of the nucleus versus chromatin itself or hydrodynamics versus polymer viscoelasticity), leading to contradictory results. Therefore, an approach for the direct and active mechanical manipulation of specific genomic loci inside living cells is needed. To meet this need, we developed a technique for targeted micromanipulation of a specific genomic locus in the nucleus of a living cell, allowing us to probe the physical properties of an interphase chromosome by measuring its response to a controlled point force.

Mechanical manipulation of a genomic locus in a living cell
Our approach relies on tethering magnetic nanoparticles (MNPs) to a genomic locus and applying an external magnetic field (Fig. 1A). We chose ferritin MNPs for their small size (25,26): 12 nm in diameter for ferritin (PDB 1GWG) and 28 nm for the full MNP (26). We produced ferritin MNPs by synthesizing in vitro recombinant enhanced green fluorescent protein (eGFP)-labeled ferritin cages and loading them with a magnetic core (see the materials and methods). We microinjected MNPs into the nuclei of living human U-2 OS cells previously engineered to contain an artificial array inserted at a single genomic location in a subtelomeric region of chromosome 1 (band 1p36) (27). This genomic array contains~200 copies of a 20-kb genetic construct, each including 96 tetO binding sites and a transgene. It has been extensively used in the past to study the function of several chromatin modifications, RNA polymerase II (Pol II) recruitment, and RNA synthesis during induction of the transgene (27)(28)(29). Therefore, although we used it here uninduced, this array can recapitulate functional chromatin-based processes such as transcriptional activation. MNPs were targeted to the array using a constitutively expressed fusion protein (TetR, mCherry, and anti-GFP nanobody) serving as a tether (Fig.  1A). Upon injection, MNPs diffused through the nucleus and accumulated at the array, forming a fluorescent spot in both eGFP and mCherry channels (figs. S1A and S2A). Quantification of the fluorescence signals indicated that MNPs were at nanomolar concentrations in the nucleus after injection and accumulated at the genomic locus in the range of hundreds to thousands of MNPs (median 1500 MNPs; figs. S1B and S3, movie S1, table S1, and materials and methods). The locus should be regarded as a condensed and heterochromatic 4-Mb region (1.6% of chromosome 1) residing in a euchromatic genomic context, as previously reported (27), with small MNPs (each being ∼2 to 3 times (26) the size of a nucleosome) sparsely decorating chromatin (1 MNP per ∼2.7 kb). Consistently, we observed that the locus typically resided in low to intermediate DNA density regions and was itself relatively condensed ( fig. S4, A . S5). Therefore, ON/OFF modulation of the local force field could be achieved while imaging by placing and removing an external magnet on the microscope stage. The shape and orientation of the pillars were chosen to maximize the magnetic field gradient and hence the force. We performed magnetic simulations and experimental calibrations using two independent methods (see the materials and methods, figs. S6 and S7, and movie S2) to determine the magnitude and orientation of the force applied onto the genomic locus as a function of the number of MNPs bound to it and its position relative to the magnetic pillar (Fig. 1B). The typical forces applied onto the locus were in the subpiconewton (pN) range, occasionally reaching a few piconewtons (table S1;     forces exerted by molecular motors in the nucleus, e.g., comparable to the stalling force of ∼0.5 pN for the structural maintenance of chromosomes (SMC) complex condensin (32) and a few piconewtons for Pol II (33).

Force-induced movement of a genomic locus reveals viscoelastic properties of chromatin
We first applied the magnetic force for 30 min and released it for another 30 min while performing low-illumination three-dimensional imaging with a 2-min interval (30′-PR scheme). We observed a clear motion of the locus toward the magnet upon application of the force and a slow and partial recoil when the force stopped ( Fig. 1, C and D, and movie S3). This indicates that a sub-piconewton force, when applied in a sustained and unidirectional manner on a genomic locus, elicits a displacement of that locus by several micrometers over minutes. It also shows that the chromosomal locus can move across the nuclear environment, which is believed to be crowded and entangled. We also applied the force periodically, pulling for 100 s, releasing for 100 s, and repeating this cycle 10 times (100′′-PR scheme) while performing fast two-dimensional imaging with a 5-s interval (Fig. 1, E and F, and movie S4). Several observations from these two experiments hinted at the material properties of chromatin. First, the trajectories showed recoils during release periods and a gradual slowdown during both pulls and releases, characteristic of a viscoelastic material. Second, spatial heterogeneities in the trajectories were visible and appeared to relate to the spatial distribution of DNA density (the motion of the locus was occasionally hindered where the DNA density varied; Fig. 1, D and F, white arrows). Third, recoil after force release was seen even after collision with the nuclear periphery, indicating that the material there (peripheral heterochromatin and the nuclear lamina) was not sticky enough to fully retain the locus. Fourth, the spatial distribution of DNA density in the nucleus did not show large-scale deformations, indicating that the locus did not drag along large amounts of material (movies S3 and S4). The force-induced displacements that we observed are consistent with viscoelastic and nonconfining chromatin and constitute a basis to further develop and test physical models of interphase chromosomes.

Quantitative force-response and scaling laws of interphase chromatin mechanics
To quantify the viscoelastic properties of chromatin, we analyzed the trajectories of the locus in 35 cells undergoing the 30′-PR scheme (corrected for cell motion and force orientation; see the materials and methods). We observed a range of behaviors in both pulls and releases regarding initial speed, total distance traveled, and shape of time profiles (Fig. 2, A   and B, and fig. S8). Most traces showed a displacement that was clearly distinguishable from diffusion (Fig. 2, A and B, hatched areas; see the materials and methods). Collision with the nuclear periphery (Fig. 2, A and B, open symbols, and fig. S8, open symbols) was seen in nine of 35 traces, so the total displacement during the pull is most often not limited by the nuclear periphery. The initial force applied onto the locus largely predicted the variability seen in the initial motion ( Fig. 2C and fig.  S9A). The recoil motion after force release was in part predicted by the total distance over which the locus had been displaced during the pull ( Fig. 2D and fig. S9B), with a simple linear relationship highlighting the elastic nature of chromatin. Deviations from these simple proportionality relationships indicate that the specific nuclear context or the state of the genomic locus might influence its response. In particular, we observed that when the locus moved more slowly than expected, it was less DNA dense, and when the locus moved faster than expected, it was more DNA dense ( fig.  S4C), suggesting that the compaction state of the locus itself affected its response to the force. The absolute nuclear position of the locus did not correlate with its response to the force, but if the locus reached the periphery during the pull, it often recoiled more slowly than expected ( fig. S10). Despite the variability between traces, log-log plots of all the pulls and releases from the 30′-PR and 100′′-PR trajectories, together with three additional high-frame-rate (dt = 0.5′′) pull-release trajectories, revealed linear portions in the curves with a slope of 0.5 over more than three orders of magnitude in time (Fig. 2E). This behavior suggests that the different levels of the hierarchical genome organization are not characterized by vastly distinct mechanical properties. In addition, displacements that scale with time as t 1/2 can be empirically described by a "fractional speed," i.e., a single value in mm/s 1/2 capturing how the motion evolves over time (Fig. 2, C and D, and fig. S9, right axes). The first pull of the 100′′-PR trace, represented in this unit, indeed followed the same relationship as the 30′-PR traces (Fig. 2C, dark green triangle), and the slope of the resulting forcedisplacement plot yielded a unique factor of 0.158 (±0.014) mm/s 1/2 /pN, characterizing the dynamic response of chromatin to force. These results indicate that a large part of the response of chromatin to force can be described by simple laws.
The chromatin force response is well described by a free polymer model (Rouse chain) We then sought a model of chromatin that best explains our quantitative measurement of force-induced locus displacement. Several features in our data suggested a classical polymer model known as a Rouse polymer (34) as a first approximation to describe the response of chromatin to forces. The Rouse model represents a polymer in which each monomer diffuses by thermal motion in a viscous medium and is connected to its two neighbors by elastic bonds. Rouse ignores steric effects (contact, hindrance), cross-links (affinity, stickiness), and topological effects (fibers can pass through each other). This model is frequently invoked for chromatin dynamics because it predicts the characteristic power-law scalingthat is, a linear relationship on a log-log plot-of the mean squared displacement (MSD) versus time with exponent 0.5, as observed here (fig. S11, A and E) and for other genomic loci in eukaryotes (35)(36)(37). We extended Rouse theory to study how a polymer responds to a point force (see the materials and methods and the supplementary text). Our calculations predict a power-law behavior with exponent 0.5 for displacements and recoils in response to force, consistent with our experimental observations (Fig. 2E). These two power laws have the same physical origin, so the diffusion coefficient obtained independently from the MSD (1627 ± 19 nm 2 s -1/2 ; fig. S11A) directly relates to-and predicts-the slope of the force-displacement plot (Fig. 2C, red line): 1627 nm 2 s -1/2 /2k B T = 0.190 ± 0.003 mm/s 1/2 /pN (see the materials and methods). This agreement between two independent passive and active measurements (Fig. 2C and fig. S9A, red and gray lines, representing diffusion and force response, respectively) supports the Rouse model to explain our chromatin dynamics data. Inspected on a cell-by-cell basis, the force-free MSD of the locus before and after the pull-release experiments appeared very moderately reduced in most cases ( fig. S11B). Its natural variability between cells does not appear to explain the variability of the response to force (fig. S11C). After force release, the Rouse model also predicted a recoil proportional to the total displacement during the pull. However, in many cases, the locus recoiled somewhat more slowly than predicted by the Rouse theory. Instead, the theoretical prediction appears to define an upper bound for the recoils (Fig. 2D and fig. S9B, red lines), and deviations from Rouse theory were more pronounced at the nuclear periphery ( fig. S10B). This analysis suggests that the dynamic response of the chromosome to the force can be described by the Rouse polymer model, with additional effects from the nuclear environment.

Model-based trajectory analysis reveals moderate hindrance by surrounding chromatin
To further understand the physical nature of chromatin, we investigated how alternative polymer models are able to capture the 100′′-PR trace (Fig. 3, A to D). Our approach was to use the displacement trajectory and infer, assuming a given polymer model, the time profile of the force that produced the measured trajectory (see the materials and methods, supplementary text, and fig. S12, A to C). Disagreement between inferred and actual force profiles indicates when models are incorrect or incomplete, allowing one to select and refine the best model(s). With this approach, we compared a series of models ( fig. S12C). First, a simple Rouse model without any adjustable parameters (i.e., calibrated using the MSD versus time plot; fig. S11A) predicted well the first pull and all of the release periods (Fig.  3B). However, the prediction leaves some of the applied force unexplained (Fig. 3B, gray area between curves), suggesting a missing component in the model that would additionally slow down or hinder the progression of the locus. This residual unexplained force did not scale with speed and thus could not be explained as an additional viscous drag on the locus (fig. S12D). Instead, it increased progressively across successive pulls, suggest-ing an accumulation of hindrance as the locus moved through the nucleus. To represent this, we added a capacity for the locus to interact with the surrounding chromatin, represented as extra Rouse chains that are either attached to or pushed by the locus along its path ( Fig.  3C and fig. S12C). These models better predicted the force profile throughout the trajectory compared with a pure Rouse model. The only free parameter used for the inference shown in Fig. 3C is the frequency at which the locus interacts with other polymers, which we found to be very low ( fig. S12C), indicating that the interaction with the surrounding chromatin was moderate. This is also consistent with the small but detectable reduction in mobility of the locus before and after pull-release experiments (fig. S11B) and the subtle redistribution of DNA densities around the pulled locus ( fig.  S4D). These modeling results suggest that, upon force application and release on our genomic locus, chromatin is well described as a Rouse polymer (i.e., a free polymer in a viscous environment), with moderate interactions from the surrounding chromatin, indicating that hindrance, cross-links, and topological effects play a minor role.

Interphase chromatin does not behave as a gel in force-response experiments
Interphase chromatin has been proposed to be a gel-like material (11,12,19). A gel is a highly cross-linked polymer, which means that unlike a linear polymer, in which monomers are linked to two neighbors, extra links between nonadjacent monomers form an interconnected mesh, giving the gel solid-like properties. For chromatin, this could in principle arise from affinity between nucleosomes, as well as loops or bridges formed by proteins, complexes, and condensates and topological entanglement between chromatin fibers. However, in such an interconnected mesh structure, short paths effectively linking the pulled locus to all other loci in the nucleus would result in long-range deformation of the spatial pattern of DNA density, which we did not observe (Fig. 1, D and F, and movies S3 and S4). Further, if the chromatin surrounding the locus were gel-like, then it would effectively act as a viscoelastic medium. This assumption does not recapitulate well the experimental data (even with two free parameters; Fig. 3D and  fig. S12C) and is inconsistent with the observed scaling of 0.5 in the MSD (fig. S11, A and E), which argues for a simply viscous and nonelastic medium. Finally, if the locus were part of an interconnected mesh, then short series of links would tether it to large structures (e.g., the periphery and nucleoli). A Rouse model that includes a finite tether does not recapitulate the experimental data (fig. S12C) and is inconsistent with the linear behavior observed in Fig. 2E up to several micrometers. These results suggest again minor effects of cross-links and topological constraints and argue against the view that interphase chromatin behaves like a gel at the spatial and temporal scale of our observations. Heterogeneities in the trajectory reveal obstacles in the nuclear interior and a soft elastic material at the nuclear periphery Even the models that best capture the data leave part of the force unexplained (Fig. 3C, gray area). We plotted this residual unexplained force as a function of spatial position (Fig. 3E). This revealed an accumulation of non-null residual forces at specific locations, matching visible features in the trajectory and in the spatial distribution of DNA density in the nucleus. First, the residual force in pulls P3 to P5 corresponds to an apparent obstacle in the trajectory (Fig. 3, A and C, asterisks) occurring at a high-to-low transition of DNA density (Figs. 3F and 1F). It appears as a spatially defined barrier of residual force (Fig. 3E), requiring an energy of ≈ 46 k B T to overcome. This suggests that, whereas DNA dense regions are not obstacles per se, the interface between high-and low-density regions may constitute a barrier. The energy that we estimated suggests that such barriers may be overcome by ATP-dependent molecular motors (32, 33) but not likely by spontaneous thermal fluctuations. Second, the residual force in pulls P8 to P10 (Fig. 3, A and C, hash marks) corresponds to the collision with structures near the nuclear periphery (Figs. 1F and 3F, hash marks). The observed linear force-distance relationship (Fig. 3E) indicates a solid-like elastic behavior for these structures over at least 600 nm and with a spring constant of 4.81 pN/mm. This is much softer than what was measured by whole-nucleus stretching experiments (14,15), which could be explained by the small size of the locus and/or the existence of a soft layer of Keizer  elastic peripheral components (e.g., heterochromatin and nuclear lamina) rather than the material directly contributing to the structural rigidity of the nucleus.

Lateral mobility of the locus reflects transient collisions with obstacles in the nucleoplasm
To further investigate the material encountered by the locus, we analyzed the lateral motion of the locus as it was being pulled and released (Fig. 3A, blue curve). We hypothesized that collisions with obstacles could increase lateral mobility or, conversely, that the locus being dragged into a more constraining and entangled environment could result in a reduction of its mobility (Fig. 3G). After computing the MSD of the lateral motion as a function of both time delay t and velocity u y along the direction of the force (Fig. 3, H and  I, and fig. S11, F and G), we observed a clear increase of lateral mobility when the locus moved (for both forward and backward movements; Fig. 3I), suggesting the existence of obstacles that deflected the motion. This additional mobility in the MSD is captured by a term proportional to u y , as would be expected for collisions, and proportional to t (not t 0.5 ), as would be expected if the force due to the collision with obstacles persists in the same direction across several frames, indicating the existence of large obstacles. Indeed, in P3 for instance, the lateral motion clearly shows a directional behavior (Figs. 1E and 3A). However, the relationships that we observed (Fig. 3, H and I) held even when excluding all of the time points before P4 (fig. S11, H and I), indicating that the collision with obstacles was widespread throughout the nucleus. These results, together with our observation that very few chromatin fibers appeared to be carried along with the locus, indicate that obstacles are frequently encountered by the locus, but most interactions are weak and transient.

Discussion
Our measurements of how a genomic locus inside the nucleus of a living cell responds to a point force indicates that interphase chromatin has fluid-like properties and behaves as a free polymer. This contrasts with previous studies depicting chromatin as a stiff, crosslinked polymer gel with solid-like properties (11,12,19). Our observation that near-piconewton forces can easily move a genomic locus across the nucleus over a few minutes (Fig. 1, D and F) also contrasts with a previous study reporting confined submicrometer displacements over seconds upon application of 65 to 110 pN forces to a 1-mm bead (19). We propose that our results may be reconciled with previous experiments in several ways. First, unlike a micrometer-sized bead, the locus used in our experiments is small and may be deformable enough to pass through the surrounding chromatin. Second, chromatin may contain many small, gel-like patches embedded in a structure with liquid, Rouse-like properties at a larger scale. This is also consistent with our observation that the transiting locus frequently encounters obstacles. Third, chromatin may be a weak gel, i.e., a gel with short-lived cross-links (11). Such a gel could continuously maintain a stiff, globally connected network that resists stresses over large length scales while permitting fluid-like motions at smaller scales. Future experiments perturbing chromatin state and chromatin associated proteins will be important to reconcile observed microand mesoscale mechanics.
Organization of chromosomes that allows movement of genomic loci across large distances by weak forces could have implications for a range of genome functions. For example, large-scale movements of chromosomes occur during nuclear inversion in rod cell differentiation for nocturnal mammals (38). Specific genes undergo long-range directional motion upon transcriptional activation (39,40). Long and highly transcribed genes can form ∼5-mm giant loops, believed to be due to chromosome fiber stiffening (41). Certain double-strand break sites undergo large-scale, nuclear F-actin dependent relocation to the nuclear periphery (42). These DNA-based biological processes require a nuclear organization in which such movements are possible. Our results reveal the mechanical properties of chromatin in which such large-scale movements would only require weak (near piconewton) forces. Although sustained unidirectional forces are unlikely to occur naturally in the nucleus, the magnitude of the forces and the time scale of force exertion in our experiments are comparable to those of molecular motors such as SMC complexes and Pol II; that is, in the sub-piconewton (32) or low-piconewton (33) ranges and applied over minutes (e.g., 10 min for Pol II to elongate through a 25-kb gene, 5-30 min for SMC complexes). Therefore, some molecular motors in the nucleus operate in a force range that is sufficient to substantially reorganize the genome in space.
Future work will be important to expand and complement our results. Although the genomic array that we used here is known to be chromatinized and has been used extensively to recapitulate and study functional chromatinbased processes (27)(28)(29), we cannot exclude that its repetitive and artificial nature might prevent some of our measurements from being applicable to nonrepetitive and native regions. Manipulating loci other than a subtelomeric locus on the longest chromosome (chromosome 1) in other genomic contexts (e.g., heterochromatin or euchromatin) and in different cell types will be important to assess the generalizability of our findings in various biological contexts.
Our approach to mechanically manipulate and relocate genomic loci in the nuclear space opens many avenues for future research, from the study of interphase chromosome mechanics to the perturbation of genome functions, including transcription, replication, DNA damage repair, and chromosome segregation. By giving access to physical parameters and revealing fundamental scaling laws to describe chromatin mechanics, our work provides a foundation for future theories of genome organization.