Viscoelasticity of model interphase chromosomes

Interplay of chromatin organization and mechanics of the cell nucleus

The nucleus of eukaryotic cells is constantly subjected to different kinds of mechanical stimuli, which can impact the organization of chromatin and, subsequently, the expression of genetic information. Experiments from different groups showed that nuclear deformation can lead to transient or permanent condensation or decondensation of chromatin and the mechanical activation of genes, thus altering the transcription of proteins. Changes in chromatin organization, in turn, change the mechanical properties of the nucleus, possibly leading to an auxetic behavior. Here, we model the mechanics of the nucleus as a chemically active polymer gel in which the chromatin can exist in two states: a self-attractive state representing the heterochromatin and a repulsive state representing euchromatin. The model predicts reversible or irreversible changes in chromatin condensation levels upon external deformations of the nucleus. We find an auxetic response for a broad range of parameters under small and large deformations. These results agree with experimental observations and highlight the key role of chromatin organization in the mechanical response of the nucleus.

The Material Properties of the Cell Nucleus: A Matter of Scale

Chromatin regulatory processes physically take place in the environment of the cell nucleus, which is filled with the chromosomes and a plethora of smaller biomolecules. The nucleus contains macromolecular assemblies of different sizes, from nanometer-sized protein complexes to micrometer-sized biomolecular condensates, chromosome territories, and nuclear bodies. This multiscale organization impacts the transport processes within the nuclear interior, the global mechanical properties of the nucleus, and the way the nucleus senses and reacts to mechanical stimuli. Here, we discuss recent work on these aspects, including microrheology and micromanipulation experiments assessing the material properties of the nucleus and its subcomponents. We summarize how the properties of multiscale media depend on the time and length scales probed in the experiment, and we reconcile seemingly contradictory observations made on different scales. We also revisit the concept of liquid-like and solid-like material properties for complex media such as the nucleus. We propose that the nucleus can be considered a multiscale viscoelastic medium composed of three major components with distinct properties: the lamina, the chromatin network, and the nucleoplasmic fluid. This multicomponent organization enables the nucleus to serve its different functions as a reaction medium on the nanoscale and as a mechanosensor and structural scaffold on the microscale.

The Physical Behavior of Interphase Chromosomes: Polymer Theory and Coarse-Grain Computer Simulations

Fluorescence in situ hybridization and chromosome conformation capture methods point to the same conclusion: that chromosomes appear to the external observer as compact structures with a highly nonrandom three-dimensional organization. In this work, we recapitulate the efforts made by us and other groups to rationalize this behavior in terms of the mathematical language and tools of polymer physics. After a brief introduction dedicated to some crucial experiments dissecting the structure of interphase chromosomes, we discuss at a nonspecialistic level some fundamental aspects of theoretical and numerical polymer physics. Then, we inglobe biological and polymer aspects into a polymer model for interphase chromosomes which moves from the observation that mutual topological constraints, such as those typically present between polymer chains in ordinary melts, induce slow chain dynamics and "constraint" chromosomes to resemble double-folded randomly branched polymer conformations. By explicitly turning these ideas into a multi-scale numerical algorithm which is described here in full details, we can design accurate model polymer conformations for interphase chromosomes and offer them for systematic comparison to experiments. The review is concluded by discussing the limitations of our approach and pointing to promising perspectives for future work.

Nanorheology of active-passive polymer mixtures differentiates between linear and ring polymer topology

We study the motion of dispersed nanoprobes in entangled active-passive polymer mixtures. By comparing the two architectures of linear vs. unconcatenated and unknotted circular polymers, we demonstrate that novel, rich physics emerge. For both polymer architectures, nanoprobes of size smaller than the entanglement threshold of the solution move faster as activity is increased and more energy is pumped in the system. For larger nanoprobes, a surprising phenomenon occurs: while in linear solutions they move qualitatively as before, in active-passive ring solutions nanoprobes decelerate with respect to the purely passive conditions. We rationalize this effect in terms of the non-equilibrium, topology-dependent association (clustering) of nanoprobes to the cold component of the ring mixture reminiscent of the recently discovered [Weber et al., Phys. Rev. Lett., 2016, 116, 058301] phase separation in scalar active-passive mixtures. We conclude with a potential connection to the microrheology of the chromatin in the nuclei of the cells.

Microrheology for Hi-C Data Reveals the Spectrum of the Dynamic 3D Genome Organization

The one-dimensional information of genomic DNA is hierarchically packed inside the eukaryotic cell nucleus and organized in a three-dimensional (3D) space. Genome-wide chromosome conformation capture (Hi-C) methods have uncovered the 3D genome organization and revealed multiscale chromatin domains of compartments and topologically associating domains (TADs). Moreover, single-nucleosome live-cell imaging experiments have revealed the dynamic organization of chromatin domains caused by stochastic thermal fluctuations. However, the mechanism underlying the dynamic regulation of such hierarchical and structural chromatin units within the microscale thermal medium remains unclear. Microrheology is a way to measure dynamic viscoelastic properties coupling between thermal microenvironment and mechanical response. Here, we propose a new, to our knowledge, microrheology for Hi-C data to analyze the dynamic compliance property as a measure of rigidness and flexibility of genomic regions along with the time evolution. Our method allows the conversion of an Hi-C matrix into the spectrum of the dynamic rheological property along the genomic coordinate of a single chromosome. To demonstrate the power of the technique, we analyzed Hi-C data during the neural differentiation of mouse embryonic stem cells. We found that TAD boundaries behave as more rigid nodes than the intra-TAD regions. The spectrum clearly shows the dynamic viscoelasticity of chromatin domain formation at different timescales. Furthermore, we characterized the appearance of synchronous and liquid-like intercompartment interactions in differentiated cells. Together, our microrheology data derived from Hi-C data provide physical insights into the dynamics of the 3D genome organization.

Microrheology of interphase chromosomes with spatial constraints: a computational study

Chromatin fibers within the interior of the nucleus of the cell make stable interactions with the nucleoskeleton, an ensemble of 'extra-chromatin' structures which help ensuring genome stability. Although the role of these interactions appears crucial to the correct behavior of the cell, their impact on chromatin structure and dynamics remains to be elucidated. In order to tackle this important issue, in this work we introduce a simple polymer model for chromatin fibers in interphase which takes into account the two generic properties of chain-versus-chain mutual uncrossability and the presence of stable binding interactions to an extra-chromatin nuclear matrix. To study how these constraints affect chromatin structure from small to large scales, we employ extensive molecular dynamics computer simulations and we monitor the motion of nanoprobes of different sizes embedded within the polymer medium. Our results demonstrate that nanoprobes show hampered motion whenever their linear size becomes larger than chromatin stiffness. This transition is also displaying features which usually belong to the realm of glassy systems, namely long-tail correlations in the distribution functions of nanoprobe spatial displacements and heterogeneous behavior accompanied by ergodicity breaking.

Advances in the microrheology of complex fluids

New developments in the microrheology of complex fluids are considered. Firstly the requirements for a simple modern particle tracking microrheology experiment are introduced, the error analysis methods associated with it and the mathematical techniques required to calculate the linear viscoelasticity. Progress in microrheology instrumentation is then described with respect to detectors, light sources, colloidal probes, magnetic tweezers, optical tweezers, diffusing wave spectroscopy, optical coherence tomography, fluorescence correlation spectroscopy, elastic- and quasi-elastic scattering techniques, 3D tracking, single molecule methods, modern microscopy methods and microfluidics. New theoretical techniques are also reviewed such as Bayesian analysis, oversampling, inversion techniques, alternative statistical tools for tracks (angular correlations, first passage probabilities, the kurtosis, motor protein step segmentation etc), issues in micro/macro rheological agreement and two particle methodologies. Applications where microrheology has begun to make some impact are also considered including semi-flexible polymers, gels, microorganism biofilms, intracellular methods, high frequency viscoelasticity, comb polymers, active motile fluids, blood clots, colloids, granular materials, polymers, liquid crystals and foods. Two large emergent areas of microrheology, non-linear microrheology and surface microrheology are also discussed.

Large Scale Chromosome Folding Is Stable against Local Changes in Chromatin Structure

Characterizing the link between small-scale chromatin structure and large-scale chromosome folding during interphase is a prerequisite for understanding transcription. Yet, this link remains poorly investigated. Here, we introduce a simple biophysical model where interphase chromosomes are described in terms of the folding of chromatin sequences composed of alternating blocks of fibers with different thicknesses and flexibilities, and we use it to study the influence of sequence disorder on chromosome behaviors in space and time. By employing extensive computer simulations, we thus demonstrate that chromosomes undergo noticeable conformational changes only on length-scales smaller than 10⁵ basepairs and time-scales shorter than a few seconds, and we suggest there might exist effective upper bounds to the detection of chromosome reorganization in eukaryotes. We prove the relevance of our framework by modeling recent experimental FISH data on murine chromosomes.

A key determining factor in many important cellular processes as DNA transcription, for instance, the specific composition of the chromatin fiber sequence has a major influence on chromosome folding during interphase. Yet, how this is achieved in detail remains largely elusive. In this work, we explore this link by means of a novel quantitative computational polymer model for interphase chromosomes where the associated chromatin filaments are composed of mixtures of fibers with heterogeneous physical properties. Our work suggests a scenario where chromosomes undergo only limited reorganization, namely on length-scales below 10⁵ basepairs and time-scales shorter than a few seconds. Our conclusions are supported by recent FISH data on murine chromosomes.