# Interphase chromatin biophysics and mechanics: new perspectives and open questions

Antoine Coulon

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Antoine Coulon. Interphase chromatin biophysics and mechanics: new perspectives and open questions. Current Opinion in Genetics and Development, 2025, 90, pp.102296. 10.1016/j.gde.2024.102296. hal-05015142

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Review

# Interphase chromatin biophysics and mechanics: new perspectives and open questions

Antoine Coulon

<figure><img src="image_3.png" /></figure>

The physical organization and properties of chromatin within the interphase nucleus are intimately linked to a wide range of functional DNA-based processes. In this context, interphase chromatin mechanics — that is, how chromatin, physically, responds to forces — is gaining increasing attention. Recent methodological advances for probing the force-response of chromatin *in cellulo* open new avenues for research, as well as new questions. This review discusses emerging views from these approaches and others, including recent *in vitro* single-molecule studies of cohesin and condensin motor activities, providing insights into physical and material aspects of chromatin, its plasticity in the context of functional processes, its nonequilibrium or ‘active matter’ properties, and the importance of factors such as chromatin fiber tension and stiffness. This growing field offers exciting opportunities to better understand the interplay between interphase chromosome structure, dynamics, mechanics, and functions.

Address

Institut Curie, PSL Research University, Sorbonne Université, CNRS UMR3664 Laboratoire Dynamique du Noyau, CNRS UMR168 Laboratoire Physique des Cellules et Cancer, 75005 Paris, France

Corresponding author: Coulon, Antoine (antoine.coulon@curie.fr)

Current Opinion in Genetics & Development 2025, 90:102296

This review comes from a themed issue on **Genome Architecture and Expression**

Edited by Anders Sejr Hansen and Marcelo Nollmann

Available online 25 December 2024

https://doi.org/10.1016/j.gde.2024.102296

0959-437X/© 2024 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Our understanding of genome organization and nuclear architecture has greatly progressed, in the past decades, thanks to advances in sequencing-based technologies to map chromosomal contacts and in microscopy-based technologies for visualizing chromosome folding and dynamics [1]. Beyond visualization, the ability to physically manipulate chromosomes inside a living cell holds great potentials

to reveal what passive visualization cannot. Recently, novel approaches have been developed to physically — or mechanically — act on chromatin, opening new avenues for research. As we will review here, mechanical manipulation of chromatin is unique because it sheds new light onto the physical state and properties of chromatin as a material [2,3] and helps understanding how chromatin reacts to the force-generating biological processes happening on it [4–6] (Figure 1). While out of the scope of this review, by allowing direct perturbations of 3D genome organization, these technologies will also be unparalleled tools in the coming years to assess the causal links between structure and function, often hard to establish for the 3D genome [7–10], as well as to understand the physiological responses of chromatin to extranuclear forces in the field of mechanobiology [11].

Intranuclear manipulation of interphase chromatin — past, present, future

Many approaches to mechanically perturb chromatin inside an interphase nucleus rely on the transmission of extracellular or extranuclear forces to the nucleus — using micropipettes, cantilevers, nanoneedles, optical or magnetic tweezer, constrictions or confinements, and engineered cell substrates [12]. Here, the measured response reflects the properties of a heterogenous set of mechanical components, and chromatin itself is revealed either by visualizing how it deforms within the nucleus [13] or by observing how perturbing its biochemical state affects the mechanical properties measured externally [14].

Intranuclear manipulation, on the other hand, offers a direct handle onto chromatin for probing its mechanics (see Table 1 for existing methods). Pioneering studies have used micron-sized magnetic objects (beads, rods) in the nucleoplasm to perform active microrheology measurements [15–17]. More recently, multiple new techniques have emerged. Several groups have exploited the forces generated by phase-separated condensates, either by monitoring nucleoli fusion [18] or using optogenetics to control the nucleation and fusion of artificial liquid condensates at specific genomic loci [19,20]. Optical trapping, which can manipulate large objects with a strong refractive index contrast, has been employed to displace nucleoli in oocytes [21]. An approach using a laser-induced local temperature gradient was used to deform chromatin [22]. Our group and collaborators targeted magnetic nanoparticles to a specific genomic
<figure><img src="image_4.png" /><figcaption>Figure 1</figcaption></figure>

Research avenues opened by intranuclear mechanical manipulation technologies.

locus and displaced it using a controlled magnetic force [2]. These techniques started uncovering how chromatin reacts to forces of various types, providing unprecedented insight into interphase chromosomes as physical objects.

## Characteristic timescales in chromatin mechanics?

Collectively, these studies have revealed viscoelastic properties of chromatin, with different degrees of deformation reversibility and a broad variety of characteristic timescales reported across studies — from sub-second to several minutes, detailed in Table 1. It is possible that this discrepancy — or even the existence of an apparent characteristic timescale — arises from the use, in most approaches, of large (≥1 µm) force-generating probes (bead, rod, condensates; Figure 2a), which cannot interpenetrate the chromatin mesh (30–200 nm [23,24]) and moves large volumes of nucleoplasm when displaced — two effects likely to result in a characteristic timescale in the mechanical response.

Complementary to other methods, our magnetic manipulation approach introduces a potentially key difference by utilizing many probes of nanometric size (Figure 2b). Specifically, this technique relies on targeting hundreds or thousands of ferritin-Green Fluorescent Protein (GFP) magnetic nanoparticles, each 28 nm in diameter [25], to a specific genomic locus. This locus, located on chromosome 1 and spanning 4 Mb, is small compared to the entire chromosome (1.6% of 250 Mb) but large enough to be only sparsely decorated by nanoparticles (on average one particle per ~15 nucleosomes). Like in other approaches (Table 1), the

<table><caption>Table 1
Summary of current intranuclear mechanical manipulation approaches.</caption><thead><tr><th rowspan="2">Approach</th><th rowspan="2">Genomic targeting</th><th colspan="2">Force-generating object</th><th rowspan="2">Force range</th><th rowspan="2">Characteristic timescales of chromatin response</th><th rowspan="2">Refs</th><th rowspan="2">Comments, limitations</th></tr><tr><th>size</th><th>nature</th></tr></thead><tbody><tr><td rowspan="3">Magnetic beads or rods in nucleoplasm</td><td>No</td><td>1 µm</td><td>Hard</td><td>~100 pN</td><td>0.1 sec</td><td>[15]</td><td rowspan="3">Requires microinjection</td></tr><tr><td>No</td><td>1 µm</td><td>Hard</td><td>~100 pN</td><td>N/A</td><td>[17]</td></tr><tr><td>No</td><td>1.5 µm</td><td>Hard</td><td>N/A</td><td>1 – 3 sec</td><td>[16]</td></tr><tr><td>Optical trap</td><td>Nucleolus</td><td>~8 µm</td><td>Bulk, deformable</td><td>≤ 10 pN</td><td>1 – 20 sec</td><td>[21]</td><td>Limited to high refractive index mismatch objects</td></tr><tr><td rowspan="3">Formation or fusion of liquid condensates</td><td>Nucleolus</td><td>1 – 4 µm</td><td>Bulk, deformable</td><td>N/A</td><td rowspan="3">Minutes</td><td rowspan="3">[24]</td><td rowspan="3">Limited targeting capacity.</td></tr><tr><td>Telomeres, endogenous repeats (dCas9)</td><td>1 – 2 µm</td><td>Bulk, deformable</td><td>0.1 – 1 pN</td></tr><tr><td></td><td>1 – 2 µm</td><td>Bulk, deformable</td><td>0.1 – 1 pN</td></tr><tr><td>Light-induced temperature gradient</td><td>No</td><td>Probe-free, ~7 µm (gradient length)</td><td>N/A</td><td>N/A</td><td>1 – 5 sec</td><td>[22]</td><td>Local heating by 2 to 6 °C. Unclear force-generating mechanism.</td></tr><tr><td>Magnetic nanoparticles targeted to genomic locus</td><td>Specific genomic locus (exogenous)</td><td>Particles: 28 nm Locus: ~1 µm</td><td>Locus: permeable, deformable</td><td>0.1 – 5 pN</td><td>Scale-free (no characteristic time from 0.5 sec to 30 min)</td><td>[2]</td><td>Requires microinjection. Limited targeting capacity. Limited throughput.</td></tr></tbody></table>
<figure><img src="image_5.png" /><figcaption>Figure 2</figcaption></figure>

Intranuclear mechanical manipulation of chromatin. (a) Technologies using micron-sized force-generating probes likely reflect aspects of chromatin mechanics that depend on their size — in particular, relative to the chromatin mesh — and reflecting their (partially) impenetrable nature — displacing both chromatin and nucleoplasm. (b) Using many nanoparticles provides a complementary standpoint since the force is applied in a distributed manner onto a portion of chromatin, by nanoparticles that occupy a small volume fraction, leaving it presumably penetrable and accessible to the nucleoplasmic machinery. Its accessibility to topoisomerase II, in particular, is one hypothesis to explain the ‘phantom-chain’ behavior observed in these experiments. (c) Applying a force to a small portion (1.6%) of chromosome with the latter approach yields a straight-line trajectory on a log-log displacement versus time plot (or a square root function in linear scales), indicating that the response is scale free (no intrinsic timescale) and pointing to a ‘phantom-chain’ polymer model, called the Rouse model. (d) Pulling a chromosomal locus from a DNA-dense to a DNA-poor region was observed to coincide with a measurable energy barrier, yielding measurement that can be interpreted as reflecting the force and energy needed to traverse an interface between two types of chromatin, such as heterochromatin and euchromatin.

manipulated object (the locus) remains here in the micro-
metric range (typically 1 µm), but it is of a very different
nature: it is itself a portion of chromatin, within which
magnetic nanoparticles only occupy 3–5% of the volume.
While better characterization is needed, this likely makes
the locus a deformable and boundary-less object, permeable
to the solvent, and accessible to enzymes, including topo-
somerase II (known to let chromatin fibers pass through one
another). Although speculative, these key differences from
other approaches may explain our surprising findings: the
trajectories of the locus under force exhibit a scale-free beh-
vior, that is, a straight line on the log-log plot representing
the distance traveled by the locus as a function of time
(Figure 2c), indicating the absence of any characteristic
timescale in the mechanical response of chromatin — from
subseconds to tens of minutes and across several microns.
The properties of this scaling behavior also suggest polymer
models with unexpected properties, as we will discuss
further.

**Future technical developments**

In the coming years, combining dCas9-based locus
targeting [19,20] with our magnetic manipulation

approach will address a current limitation of our work,
which has so far relied on *tetO/TetR* targeting and
hence been restricted to a single exogenous, repetitive,
and relatively large locus. Improving the magnetic
properties of nanoparticles may produce a stronger
force per particle, allowing the targeting of smaller
genomic regions, hence expanding the range of appli-
cations. We also expect modifications of our micro-
fabricated magnetic device to increase the throughput
and flexibility of the approach, making it more widely
applicable.

The temperature gradient approach [22] is very powerful
in that it is a probe-free method, hence not necessitating
any cell line engineering. However, the physical me-
chanism by which forces are generated remains to be
clarified. Another promising approach involving laser-
based local heating consists in creating flows through a
thermophoretic effect [26], requiring smaller tempera-
ture increase and relying on a well-understood physical
principle. Only applied in the cytoplasm so far, it may be
adapted for use within the interphase nucleus in the
future.
## The two-way relationship between structure and function

Our work using magnetic nanoparticles reveals that the genome can be rearranged substantially with surprisingly low forces: namely, a genomic locus moves several microns in a few minutes under forces on the order of a piconewton (0.2–5 pN) [2]. This is the typical force range naturally exerted by the nuclear machinery. Indeed, structural maintenance of chromosomes (SMC) complexes, capable of modulating chromatin conformation to form topologically associating domains (TADs) [27,28] or to compact chromosomes for mitosis [29,30], operate at near-pN forces [5,31,32]. Polymerases typically exert forces in the range of a few pN [33]. Although these physiological forces are not sustained and uni-directional as in Ref. [2], this nonetheless indicates that the mere transcription of a gene generates forces that are in principle sufficient to substantially alter chromatin conformation. What such forces between DNA and an elongating polymerase would be applied against remains open. If polymerases or nascent transcripts have a propensity to self-interact [34,35], even transiently or indirectly, this would provide several genomic anchor points, potentially leading to intra- and inter-genic forces. Elongating polymerases, carrying nascent RNAs with large associated complexes, may also associate with nuclear structures [36] and have been proposed to exert a drag force onto the nucleoplasm [37]. Additionally, the mechanical work produced by elongation may also result into different type of forces, including torques due to supercoiling [38] or dynamics changes in chromatin fiber stiffness. The latter hypothesis stems from the observation of long and highly transcribed genes, which revealed that transcription can lead to major spatial re-organization, consistent with a local stiffening of the chromatin fiber over gene bodies [4]. In this scenario, the mechanical work produced by the increased stiffness of the chromatin fiber would originate from the elongating polymerases straightening the fiber by pushing against each other. Although yet unobserved, a similar mechanical effect may occur at a smaller scale on other genes, especially considering that most human genes are transcribed in bursts, that is, brief periods of intense transcription [39,40], potentially leading to dense convulsions of polymerases. Altogether, while structure is often thought to drive function, the effect of pN forces on chromatin conformation suggests that a dynamic interplay where structure and function influence each other may be more prevalent than typically recognized.

Also highlighting the plasticity of interphase chromatin organization is the energy barrier we measured when pulling a genomic locus from a DNA-dense to a DNA-poor region of the nucleus [2], which can be viewed as crossing an interface between two chromatin types (e.g. heterochromatin and euchromatin) in affinity-based models of chromatin compartmentalization [41,42]. The

energy we measured (a few tens of $k_BT$, where $k_B$ is the Boltzmann constant and T is the temperature) indicates that a locus is unlikely to spontaneously cross such an interface by thermally driven diffusion but only requires a few ATP hydrolyses to be pulled out by an energy-dependent motor (e.g. polymerase, cohesin). In other words, the 3D compartmentalization of the genome appears thermally stable but highly malleable by the nuclear machinery.

## When chromatin mechanics affects function

### Supercoiling, nucleosomes, and transcription

Mechanical aspects of chromosomes and DNA can affect functional processes. A canonical example is supercoiling, that is, the torsional stress on DNA induced by processes like transcription and replication, long thought to potentially affect these processes in return (since negative and positive supercoils respectively facilitate or impede the opening of the double helix). This has been proposed to be involved in the coordinated activity between neighboring genes [43] and in transcriptional bursting [44] in prokaryotes. In eukaryotes, nucleosome assembly and eviction can absorb, respectively, negative and positive supercoils, leading to another layer of complexity whereby transcription, nucleosomes, and chromatin mechanics may influence each other [45,46]. One can expect a nontrivial coupling since negative supercoils, for instance, may facilitate transcription by destabilizing the double helix but may also impede it by favoring nucleosome assembly. These two opposite effects may occur at different timescales and could in principle propagate locally along the chromatin fiber to affect adjacent genes. Notably, supercoiling-dependent transcriptional coupling between adjacent genes *in cis* has recently been observed experimentally using live single-molecule imaging [47], showing a singular temporal pattern of transcriptional correlation and calling for further investigation.

### Tension, stiffness, and loop extrusion

Recent work has revealed that chromatin tension and stiffness influence key aspects of loop extrusion by SMC complexes, condensin and cohesin. Loop extrusion is the process by which small DNA loops are created and progressively enlarged — or *extruded* — through an energy-dependent mechanism, by condensin [31] and cohesin [48], leading, respectively, to chromosome compaction in prophase [29,30] and to TAD formation in interphase [27,28]. In the latter case, extrusion is known to stop at specific DNA elements, notably sites bound by factor CTCF, thereby defining TAD boundaries and local chromosome contact patterns, potentially with many functional implications [49].

*In vitro* single-molecule experiments revealed that loop extrusion strongly depends on DNA tension, that is, the
force against which condensin or cohesin has to act to
reel in DNA and enlarge the loop. Extrusion slows down
a 2.5-fold from 0.3 to 0.6 pN and is almost fully stalled at
0.8 pN [31,32] (Figure 3a). It occurs through discrete
steps, whose size and frequency also depend on tension,
both decreasing by a threefold from 0.2 to 1 pN [50].
Tension dependency is also seen in the efficiency with
which CTCF blocks extruding cohesins, from no
blocking with relaxed DNA to systematic blocking for a
tension of 0.14 pN [51]. Finally, although cohesin and
condensin can bypass large objects (nucleosomes, RNA
polymerases, or even much larger) [52], cohesin is effi-
ciently blocked by a short stretch of stiff DNA, that is,
DNA made more rigid due to the tight binding of pro-
teins [53] (Figure 3b).

These observations highlight chromatin tension and
stiffness as key parameters modulating loop extrusion
and hence, potentially, downstream functional pro-
cesses. Yet, we have a poor understanding of chromatin
tension and stiffness in *cellulo*, how they distribute along
the genome, and what can modulate it. Tension can be
expected to depend on the activity of motors, such as
extruders or polymerases operating in the pN range.
Stiffness likely depends on chromatin fiber structure and
associated factors. Indeed, modeling suggested that
chromatin fiber stiffness is affected by the regularity of
nucleosome positioning [54], which is notably high
around CTCF-bound sites and gene promoters [55,56].
In the coming year, developing *cellulo* force sensors for
chromatin, using mechanical manipulation tools
[2,20,22], and incorporating tension and stiffness in our

models of loop extrusion will be key to advance our
knowledge.

Understanding chromatin as an active
material

A central question for physicists working on a given
biological system is to understand if and how it operates
away from equilibrium. Beyond the mere statement that
a biological system consumes energy (they virtually all
do), the goal is to understand whether this fundamental
property of life is at play in the observed dynamics,
hence potentially impacting organization, behaviors, and
ultimately functions. Indeed, properties of none-
quilibrium systems have fundamental implications, in
particular, for the reliability of information transmission
(from biochemical or genetic networks [57,58] to the
auditory system [59]) or for large-scale self-organization
and collective behavior (from cytoskeletal components
[60] to bird flocks [61]). In the nucleus, such collective
behavior effects have been proposed to explain observed
multiscale patterns of coherent chromatin motion [62].
This *active matter* field, which has received increasing
attention in the physics community, has developed
concepts and approaches — relying, among others, on
active mechanical manipulations — that could sig-
nificantly benefit nuclear and chromatin biology.

**Challenges and confounding effects**

Extracting signatures of nonequilibrium dynamics is
notoriously difficult [63,64]. It consists of demonstrating
whether observed fluctuations — for example, motion of
chromosomal loci or stochastic association/dissociation of

<figure><img src="image_6.png" /><figcaption>Figure 3</figcaption></figure>

Loop extrusion by cohesin and condensin is tension and stiffness dependent. (a) *In vitro* measurements have shown that the speed of extrusion and the probability of a bound CTCF site to stop extrusion are both strongly dependent on the tension of the DNA substrate [31,32,50,51]. (b) Similar *in vitro* experiments have revealed that large objects can be bypassed [52], while a smaller stretch of stiff and protein-bound DNA constitutes an efficient roadblock [53].
factors to chromatin — are purely thermally driven (equilibrium) or have an energy-consuming component (nonequilibrium). Observing how dynamics is altered following the perturbation of an energy-dependent process (e.g. using drugs or knockdowns), although often insightful, cannot demonstrate nonequilibrium dynamics *per se*. Indeed, such perturbation may do more than just affecting the source of fluctuations, hence sometimes leading to counterintuitive results. For instance, after cohesin depletion, one might expect a reduction of chromatin mobility from the loss of tens of thousands of loop-extruding machines constantly pulling on DNA, but the opposite is observed [65,66], likely reflecting that removing the many cohesin-mediated tethers between loci throughout the genome also makes chromatin less constrained. Another example, while one might expect the motor activity of RNA polymerases to increase chromatin mobility by adding energy-dependent forces to thermal agitation, certain genes show reduced mobility upon activation [67,68], and certain transcription inhibitors increase chromatin mobility [35], possibly revealing that the engagement of the transcription machinery onto chromatin also constrains its motion. Global perturbations such as ATP depletion are likely to have many of such indirect consequences. In sum, evaluating whether fluctuations are influenced by an energy-dependent process is distinct from determining if the driving force behind them is non-thermal.

## Fluctuation-dissipation theorem in the nucleus

Several approaches exist to identify nonequilibrium dynamics, one of which is to use active manipulation to look for deviations from the *fluctuation-dissipation theorem*. This theorem, originating from Einstein's early work in 1905, establishes a relationship between the random fluctuations causing a particle to diffuse and the viscous drag that dissipates its motion (e.g. which one would feel if applying a force), since, in a system at thermal equilibrium, these fluctuations and drag forces are generated by the *same* molecular collisions. Hence, comparing fluctuations and force-response measurements can reveal nonequilibrium dynamics in biological systems [69,70]. Surprisingly, our measurements of chromosomal locus displacement under a range of magnetic forces collectively matched the theorem's predictions based on diffusion measurements without force [2], suggesting that the diffusion of the locus is not dominated by active processes. Put differently, if energy-dependent processes (transcription, loop extrusion, etc) had been driving chromatin mobility, it should have been a lot harder to displace the locus with a force than what we observed. However, several observations warrant further investigation, leaving open the possibility of finding nonequilibrium signatures. First, the force-response was highly variable between cells, with displacements varying up to a fourfold under the same force, possibly due to biological factors (e.g. cell cycle

effects) or to technical factors (e.g. force estimation). Second, while averaged data matched the theorem's predictions, individual cells did not, suggesting that cells may deviate from the fluctuation-dissipation relationship to different extents. Third, our sustained and uni-directional forces produce large displacements and probe many timescales simultaneously, which may mask subtle deviations from equilibrium dynamics that could be better detected with low-strain frequency-dependent methods (i.e. using oscillatory forces) [69,70]. Finally, our measurements were made in a cancer cell line and on an exogenous locus, while other loci or cell types may lead to different results. Future work can be expected to shed further light on the question.

## The arrow of time

Other ways to demonstrate nonequilibrium dynamics consist of looking for signature of *broken detailed balance*. As discovered by Maxwell and Boltzmann, in an equilibrium system, transitions between microscopic states are *balanced*, that is, they occur equally frequently in both directions. This would hold only if interactions between elements (e.g. a factor and its target or an enhancer and a promoter) were *undone the same way they are done*. Therefore, a factor binding and modifying/re-modeling its target before dissociating, or two genomic elements being brought together by loop extrusion but coming apart through diffusion, should result in signatures of broken detailed balance in experimental data. Such signatures include evidence for cyclic behavior [71] or temporal asymmetry [72] in time series and refractory periods in dwell-time distributions [58]. The resulting metrics reveal key information (fluxes, energy consumption, characteristic time/length scales), providing a basis for studying these processes. From a functional point of view, and often underappreciated, the very nature — at equilibrium or not — of molecular events like transcription factor binding and enhancer-promoter encounters may have key implications for the reliability and control of the downstream biological processes [57,58].

## In search of polymer models of interphase chromosome structure, dynamics, and mechanics

A surprising result from our initial study on interphase chromatin mechanics is that the response of an interphase chromosome to a point force is well captured by a *Rouse polymer* model [2]. This is unexpected since this model ignores key factors that seem intuitively relevant for a physical model of chromatin: volume exclusion, steric hindrance, affinities/crosslinks, and topology/entanglement. Instead, a Rouse polymer is essentially an elastic phantom chain in a simple viscous liquid. Indeed, in our experiments, the pulled locus moved across the nucleus with minimal obstruction and deformation of its
surroundings. But one other key argument for the Rouse
model is that the displacements of the pulled locus over
time *t* have the shape of a 'square root' function $\sqrt{t}$
(Figure 2c). In other words, displacement scales as $t^{0.5}$,
making a straight line on a log-log plot (also known as a
*power law* or a *scaling relationship*) with a slope (called the
*exponent*) of 0.5. Such behavior is characteristic of a Rouse
polymer [2], and many other models either do not dis-
play a power law or show a different exponent.

The diffusion dynamics of genomic loci, a measurement
widely used in the field, also suggest a Rouse model for
interphase chromosomes in eukaryotes. Here, the *mean
square displacement* or MSD(*t*), which quantifies how
much space a locus explores in a given amount of time *t*,
often displays a scaling relationship as well, with an
exponent around 0.5 in eukaryotes [65,66,73–75] (espe-
cially when accounting for localization accuracy and cell
motion [65,66]), that is, the hallmark of a Rouse polymer.
This is also what we observed on the very same locus we
used for magnetic manipulation when no force was ap-
plied [2], hence aligning *dynamics* and *mechanics* mea-
surements.

A different picture arises from *structural* measurements,
such as Hi-C and DNA FISH. Here, the contact prob-
abilities between loci decrease as a power law of their
genomic distance with an exponent overall around –1
when observed over many orders of magnitudes [76,77],
matching the exponent around 1/3 seen for 3D distance
[78,79] (since the former is –3× the latter, under a
simple mean field assumption [80]). This reflects the
fact that chromosomes are folded in a way that ‘*fills
space*’, that is, a portion of a chromosome occupies a
volume proportional to its length — also called a *globular*
or *crumpled* organization. To be long-lasting, such 3D
organization typically requires a polymer with steric/vo-
lume exclusion, topological effects, and/or crosslinks/af-
finity — that is the very properties that are ignored by
the Rouse polymer model and that lead to MSD(*t*) ex-
ponents around 0.25–0.4 if incorporated [81,82]. By
comparison, in a Rouse polymer, contact probability
decays with genomic distance with exponent –1.5, that
is, much steeper than experimentally observed.

In sum, measurement of chromatin *dynamics* (locus
tracking) and *mechanics* (force–response) suggests a *Rouse
polymer*, while *structural* measurements (Hi-C, DNA
FISH) suggest a *space-filling* polymer — two fundamen-
tally incompatible views. Recently, such seemingly in-
compatible dynamic and structural scaling relationships
were even measured simultaneously on the very same
biological system [79].

To date, the physical grounds of a polymer model that
would capture structural, dynamical, and mechanical
observations remain unclear. Modeling approaches have

successfully reproduced the observed structural and
dynamical properties [83,84], but at the cost of imposing
an artificial force without a physical justification. Theo-
retical frameworks have also revealed how the three
exponents mentioned above relate to each other and to
additional exponents that further describe the for-
ce-response and the properties of the nucleoplasm
[85,86]. Such theoretical framework also opens avenues
by suggesting new experimental measurements and by
highlighting hydrodynamics [87] and/or nucleoplasm
viscoelasticity [88] as key ingredients for a physical
model of interphase chromosome structure, dynamics,
and mechanics [86].

Perspectives

Recent technical advances have opened exciting new
possibilities to examine the physical and material prop-
erties of interphase chromatin. However, much remains
to be explored and understood. Notably, our initial
findings using intranuclear magnetic micromanipulation
depicted the bulk of chromatin as fluid like, highly
malleable, and best described by a polymer model ig-
noring topology and affinities, with the exception of
peripheral chromatin showing solid-like properties [2].
However, these observations might strongly depend on
the genomic and cellular context of the locus we ex-
amined (longest chromosome, subtelomeric region, eu-
chromatic environment, cancer cells, etc). Indeed, solid-
like behaviors have been observed in certain biological
contexts [89], and it is likely that chromatin operates
close to state transitions [41,90], making its physical state
adaptable to various biological needs. Probing different
genomic contexts (e.g. other chromosomes, heterochro-
matic regions, lamina-associated domains) across cellular
states (e.g. cell cycle, differentiation, pathological pro-
gression) and perturbing specific biological processes
(e.g. transcription, histone modifications, topoisomerase
II, loop extrusion) can be expected to reveal a variety of
behavior and to shed light onto interphase chromatin as
an active and complex material.

Data Availability

No data were used for the research described in the art-
ticle.

Declaration of Competing Interest

The authors declare that they have no known competing
financial interests or personal relationships that could
have appeared to influence the work reported in this
paper.

Declaration of Generative AI and AI-assisted
technologies in the writing process

Occasional use of generative AI during the preparation
of this article served exclusively to reformulate the
author's ideas for enhancing clarity. After using this tool, the author reviewed and edited the resulting text as needed and takes full responsibility for the content of the published article.

## Acknowledgements

I would like to acknowledge discussions and comments from Vittore Scolari, Samuele Lipani, Simon Grosse-Holz, Leonid Mirny, and the members of my group, as well as funding from the Centre National de la Recherche Scientifique (CNRS); the Institut Curie; the LabEx CELL(N) SCALE (ANR-11-LABX-0038) and DEEP (ANR-11-LABX-0044) of PSL (ANR-10-IDEX-0001-02); the Agence Nationale de la Recherche (CHROMAG ANR-18-CE12-0023-01; MechaChrom ANR-22-CE95-0003-01); and the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (grant agreement 757956).

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