Polymer folding through active processes recreates features of genome organization

Delayed Excitations Induce Polymer Looping and Coherent Motion

We consider inhomogeneous polymers driven by energy-consuming active processes which encode temporal patterns of athermal kicks. We find that such temporal excitation programs, propagated by tension along the polymer, can effectively couple distinct polymer loci. Consequently, distant loci exhibit correlated motions that fold the polymer into specific conformations, as set by the local actions of the active processes and their distribution along the polymer. Interestingly, active kicks that are canceled out by a time-delayed echo can induce strong compaction of the active polymer.

OpenNucleome for high-resolution nuclear structural and dynamical modeling

The intricate structural organization of the human nucleus is fundamental to cellular function and gene regulation. Recent advancements in experimental techniques, including high-throughput sequencing and microscopy, have provided valuable insights into nuclear organization. Computational modeling has played significant roles in interpreting experimental observations by reconstructing high-resolution structural ensembles and uncovering organization principles. However, the absence of standardized modeling tools poses challenges for furthering nuclear investigations. We present OpenNucleome-an open-source software designed for conducting GPU-accelerated molecular dynamics simulations of the human nucleus. OpenNucleome offers particle-based representations of chromosomes at a resolution of 100 KB, encompassing nuclear lamina, nucleoli, and speckles. This software furnishes highly accurate structural models of nuclear architecture, affording the means for dynamic simulations of condensate formation, fusion, and exploration of non-equilibrium effects. We applied OpenNucleome to uncover the mechanisms driving the emergence of 'fixed points' within the nucleus-signifying genomic loci robustly anchored in proximity to specific nuclear bodies for functional purposes. This anchoring remains resilient even amidst significant fluctuations in chromosome radial positions and nuclear shapes within individual cells. Our findings lend support to a nuclear zoning model that elucidates genome functionality. We anticipate OpenNucleome to serve as a valuable tool for nuclear investigations, streamlining mechanistic explorations and enhancing the interpretation of experimental observations.

Shear flow as a tool to distinguish microscopic activities of molecular machines in a chromatin loop

Several types of molecular machines move along biopolymers like chromatin. However, the details about the microscopic activity of these machines and how to distinguish their modes of action are not well understood. We propose that the activity of such machines can be classified by studying looped chromatin under shear flow. Our simulations show that a chromatin-like polymer with two types of activities-constant (type-I) or local curvature-dependent tangential forces (type-II)-exhibits very different behavior under shear flow. We show that one can distinguish both activities by measuring the nature of a globule-to-extended coil transition, tank treading, and tumbling dynamics.

Motorized chain models of the ideal chromosome

An array of motor proteins consumes chemical energy in setting up the architectures of chromosomes. Here, we explore how the structure of ideal polymer chains is influenced by two classes of motors. The first class which we call "swimming motors" acts to propel the chromatin fiber through three-dimensional space. They represent a caricature of motors such as RNA polymerases. Previously, they have often been described by adding a persistent flow onto Brownian diffusion of the chain. The second class of motors, which we call "grappling motors" caricatures the loop extrusion processes in which segments of chromatin fibers some distance apart are brought together. We analyze these models using a self-consistent variational phonon approximation to a many-body Master equation incorporating motor activities. We show that whether the swimming motors lead to contraction or expansion depends on the susceptibility of the motors, that is, how their activity depends on the forces they must exert. Grappling motors in contrast to swimming motors lead to long-ranged correlations that resemble those first suggested for fractal globules and that are consistent with the effective interactions inferred by energy landscape analyses of Hi-C data on the interphase chromosome.

Activity-induced stiffness, entanglement network and dynamic slowdown in unentangled semidilute polymer solutions

Active polymers possess numerous unique properties that are quite different from those observed in the system of small active molecules due to the intricate interplay between their activity and topological constraints. This study focuses on the conformational changes induced by activity, impacting effective stiffness and crucially influencing entanglement and dynamics. When the two terminals of a linear chain undergo active modification through coupling to a high-temperature thermal bath, there is a substantial increase in chain size, indicating a notable enhancement in effective stiffness. Unlike in passive semiflexible chains where stiffness predominantly affects local bond angles, activity-induced stiffness manifests at the scale of tens of monomers. While activity raises the ambient temperature, it significantly decreases diffusion by over an order of magnitude. The slowdown of the dynamics observed can be attributed to increased entanglement due to chain elongation.

From Nucleosomes to Compartments: Physicochemical Interactions Underlying Chromatin Organization

Chromatin organization plays a critical role in cellular function by regulating access to genetic information. However, understanding chromatin folding is challenging due to its complex, multiscale nature. Significant progress has been made in studying in vitro systems, uncovering the structure of individual nucleosomes and their arrays, and elucidating the role of physicochemical forces in stabilizing these structures. Additionally, remarkable advancements have been achieved in characterizing chromatin organization in vivo, particularly at the whole-chromosome level, revealing important features such as chromatin loops, topologically associating domains, and nuclear compartments. However, bridging the gap between in vitro and in vivo studies remains challenging. The resemblance between in vitro and in vivo chromatin conformations and the relevance of internucleosomal interactions for chromatin folding in vivo are subjects of debate. This article reviews experimental and computational studies conducted at various length scales, highlighting the significance of intrinsic interactions between nucleosomes and their roles in chromatin folding in vivo.

Polymer Collapse & Liquid-Liquid Phase-Separation are Coupled in a Generalized Prewetting Transition

The three-dimensional organization of chromatin is thought to play an important role in controlling gene expression. Specificity in expression is achieved through the interaction of transcription factors and other nuclear proteins with particular sequences of DNA. At unphysiological concentrations many of these nuclear proteins can phase-separate in the absence of DNA, and it has been hypothesized that, in vivo, the thermodynamic forces driving these phases help determine chromosomal organization. However it is unclear how DNA, itself a long polymer subject to configurational transitions, interacts with three-dimensional protein phases. Here we show that a long compressible polymer can be coupled to interacting protein mixtures, leading to a generalized prewetting transition where polymer collapse is coincident with a locally stabilized liquid droplet. We use lattice Monte-Carlo simulations and a mean-field theory to show that these phases can be stable even in regimes where both polymer collapse and coexisting liquid phases are unstable in isolation, and that these new transitions can be either abrupt or continuous. For polymers with internal linear structure we further show that changes in the concentration of bulk components can lead to changes in three-dimensional polymer structure. In the nucleus there are many distinct proteins that interact with many different regions of chromatin, potentially giving rise to many different Prewet phases. The simple systems we consider here highlight chromatin's role as a lower-dimensional surface whose interactions with proteins are required for these novel phases.

Polymer Collapse & Liquid-Liquid Phase-Separation are Coupled in a Generalized Prewetting Transition

The three-dimensional organization of chromatin is thought to play an important role in controlling gene expression. Specificity in expression is achieved through the interaction of transcription factors and other nuclear proteins with particular sequences of DNA. At unphysiological concentrations many of these nuclear proteins can phase-separate in the absence of DNA, and it has been hypothesized that, in vivo, the thermodynamic forces driving these phases help determine chromosomal organization. However it is unclear how DNA, itself a long polymer subject to configurational transitions, interacts with three-dimensional protein phases. Here we show that a long compressible polymer can be coupled to interacting protein mixtures, leading to a generalized prewetting transition where polymer collapse is coincident with a locally stabilized liquid droplet. We use lattice Monte-Carlo simulations and a mean-field theory to show that these phases can be stable even in regimes where both polymer collapse and coexisting liquid phases are unstable in isolation, and that these new transitions can be either abrupt or continuous. For polymers with internal linear structure we further show that changes in the concentration of bulk components can lead to changes in three-dimensional polymer structure. In the nucleus there are many distinct proteins that interact with many different regions of chromatin, potentially giving rise to many different Prewet phases. The simple systems we consider here highlight chromatin's role as a lower-dimensional surface whose interactions with proteins are required for these novel phases.

The scales, mechanisms, and dynamics of the genome architecture

Even when split into several chromosomes, DNA molecules that make up our genome are too long to fit into the cell nuclei unless massively folded. Such folding must accommodate the need for timely access to selected parts of the genome by transcription factors, RNA polymerases, and DNA replication machinery. Here, we review our current understanding of the genome folding inside the interphase nuclei. We consider the resulting genome architecture at three scales with a particular focus on the intermediate (meso) scale and summarize the insights gained from recent experimental observations and diverse computational models.

OpenNucleome for high resolution nuclear structural and dynamical modeling

The intricate structural organization of the human nucleus is fundamental to cellular function and gene regulation. Recent advancements in experimental techniques, including high-throughput sequencing and microscopy, have provided valuable insights into nuclear organization. Computational modeling has played significant roles in interpreting experimental observations by reconstructing high-resolution structural ensembles and uncovering organization principles. However, the absence of standardized modeling tools poses challenges for furthering nuclear investigations. We present OpenNucleome-an open-source software designed for conducting GPU-accelerated molecular dynamics simulations of the human nucleus. OpenNucleome offers particle-based representations of chromosomes at a resolution of 100 KB, encompassing nuclear lamina, nucleoli, and speckles. This software furnishes highly accurate structural models of nuclear architecture, affording the means for dynamic simulations of condensate formation, fusion, and exploration of non-equilibrium effects. We applied OpenNucleome to uncover the mechanisms driving the emergence of "fixed points" within the nucleus-signifying genomic loci robustly anchored in proximity to specific nuclear bodies for functional purposes. This anchoring remains resilient even amidst significant fluctuations in chromosome radial positions and nuclear shapes within individual cells. Our findings lend support to a nuclear zoning model that elucidates genome functionality. We anticipate OpenNucleome to serve as a valuable tool for nuclear investigations, streamlining mechanistic explorations and enhancing the interpretation of experimental observations.

Transcription-induced active forces suppress chromatin motion

The organization of interphase chromosomes in a number of species is starting to emerge thanks to advances in a variety of experimental techniques. However, much less is known about the dynamics, especially in the functional states of chromatin. Some experiments have shown that the motility of individual loci in human interphase chromosome decreases during transcription and increases upon inhibiting transcription. This is a counterintuitive finding because it is thought that the active mechanical force (F) on the order of ten piconewtons, generated by RNA polymerase II (RNAPII) that is presumably transmitted to the gene-rich region of the chromatin, would render it more open, thus enhancing the mobility. We developed a minimal active copolymer model for interphase chromosomes to investigate how F affects the dynamical properties of chromatin. The movements of the loci in the gene-rich region are suppressed in an intermediate range of F and are enhanced at small F values, which has also been observed in experiments. In the intermediate F, the bond length between consecutive loci increases, becoming commensurate with the distance at the minimum of the attractive interaction between nonbonded loci. This results in a transient disorder-to-order transition, leading to a decreased mobility during transcription. Strikingly, the F-dependent change in the locus dynamics preserves the organization of the chromosome at [Formula: see text]. Transient ordering of the loci, which is not found in the polymers with random epigenetic profiles, in the gene-rich region might be a plausible mechanism for nucleating a dynamic network involving transcription factors, RNAPII, and chromatin.

Polycomb repression of Hox genes involves spatial feedback but not domain compaction or phase transition

Polycomb group proteins have a critical role in silencing transcription during development. It is commonly proposed that Polycomb-dependent changes in genome folding, which compact chromatin, contribute directly to repression by blocking the binding of activating complexes. Recently, it has also been argued that liquid-liquid demixing of Polycomb proteins facilitates this compaction and repression by phase-separating target genes into a membraneless compartment. To test these models, we used Optical Reconstruction of Chromatin Architecture to trace the Hoxa gene cluster, a canonical Polycomb target, in thousands of single cells. Across multiple cell types, we find that Polycomb-bound chromatin frequently explores decompact states and partial mixing with neighboring chromatin, while remaining uniformly repressed, challenging the repression-by-compaction or phase-separation models. Using polymer simulations, we show that these observed flexible ensembles can be explained by 'spatial feedback'-transient contacts that contribute to the propagation of the epigenetic state (epigenetic memory), without inducing a globular organization.

Effect of local active fluctuations on structure and dynamics of flexible biopolymers

Active fluctuations play a significant role in the structure and dynamics of biopolymers (e.g. chromatin and cytoskeletal proteins) that are instrumental in the functioning of living cells. For a large range of experimentally accessible length and time scales, these polymers can be represented as flexible chains that are subjected to spatially and temporally varying fluctuating forces. In this work, we introduce a mathematical framework that correlates the spatial and temporal patterns of the fluctuations to different observables that describe the dynamics and conformations of the polymer. We demonstrate the power of this approach by analyzing the case of a point fluctuation on the polymer with an exponential decay of correlation in time with a finite time constant. Specifically, we identify the length and time scale over which the behavior of the polymer exhibits a significant departure from the behavior of a Rouse chain and the range of impact of the fluctuation along the chain. Furthermore, we show that the conformation of the polymer retains the memory of the active fluctuation from earlier times. Altogether, this work sets the basis for understanding and interpreting the role of spatio-temporal patterns of fluctuations in the dynamics, conformation, and functionality of biopolymers in living cells.

Explicit ion modeling predicts physicochemical interactions for chromatin organization

Molecular mechanisms that dictate chromatin organization in vivo are under active investigation, and the extent to which intrinsic interactions contribute to this process remains debatable. A central quantity for evaluating their contribution is the strength of nucleosome-nucleosome binding, which previous experiments have estimated to range from 2 to 14 kBT. We introduce an explicit ion model to dramatically enhance the accuracy of residue-level coarse-grained modeling approaches across a wide range of ionic concentrations. This model allows for de novo predictions of chromatin organization and remains computationally efficient, enabling large-scale conformational sampling for free energy calculations. It reproduces the energetics of protein-DNA binding and unwinding of single nucleosomal DNA, and resolves the differential impact of mono- and divalent ions on chromatin conformations. Moreover, we showed that the model can reconcile various experiments on quantifying nucleosomal interactions, providing an explanation for the large discrepancy between existing estimations. We predict the interaction strength at physiological conditions to be 9 kBT, a value that is nonetheless sensitive to DNA linker length and the presence of linker histones. Our study strongly supports the contribution of physicochemical interactions to the phase behavior of chromatin aggregates and chromatin organization inside the nucleus.

Characteristic features of self-avoiding active Brownian polymers under linear shear flow

We present Brownian dynamics simulation results of a flexible linear polymer with excluded-volume interactions under shear flow in the presence of active noise. The active noise strongly affects the polymer's conformational and dynamical properties, such as the stretching in the flow direction and compression in the gradient direction, shear-induced alignment, and shear viscosity. In the asymptotic limit of large activities and shear rates, the power-law scaling exponents of these quantities differ significantly from those of passive polymers. The chain's shear-induced stretching at a given shear rate is reduced by active noise, and it displays a non-monotonic behavior, where an initial polymer compression is followed by its stretching with increasing active force. The compression of the polymer in the gradient direction follows the relation ∼WiPe-3/4 as a function of the activity-dependent Weissenberg number WiPe, which differs from the scaling observed in passive systems ∼WiPe-1/2. The flow-induced alignment at large Péclet numbers Pe ≫ 1, where Pe is the Péclet number, and large shear rates WiPe ≫ 1 displays the scaling behavior WiPe-1/2, with an exponent differing from the passive value -1/3. Furthermore, the polymer's zero-shear viscosity displays a non-monotonic behavior, decreasing in an intermediate activity regime due to excluded-volume interactions and increasing again for large Pe. Shear thinning appears with increasing Weissenberg number with the power-laws WiPe-1/2 and WiPe-3/4 for passive and active polymers, respectively. In addition, our simulation results are compared with the results of an analytical approach, which predicts quantitatively similar behaviors for the various aforementioned physical quantities.

Explicit Ion Modeling Predicts Physicochemical Interactions for Chromatin Organization

Molecular mechanisms that dictate chromatin organization in vivo are under active investigation, and the extent to which intrinsic interactions contribute to this process remains debatable. A central quantity for evaluating their contribution is the strength of nucleosome-nucleosome binding, which previous experiments have estimated to range from 2 to 14 kBT. We introduce an explicit ion model to dramatically enhance the accuracy of residue-level coarse-grained modeling approaches across a wide range of ionic concentrations. This model allows for de novo predictions of chromatin organization and remains computationally efficient, enabling large-scale conformational sampling for free energy calculations. It reproduces the energetics of protein-DNA binding and unwinding of single nucleosomal DNA, and resolves the differential impact of mono and divalent ions on chromatin conformations. Moreover, we showed that the model can reconcile various experiments on quantifying nucleosomal interactions, providing an explanation for the large discrepancy between existing estimations. We predict the interaction strength at physiological conditions to be 9 kBT, a value that is nonetheless sensitive to DNA linker length and the presence of linker histones. Our study strongly supports the contribution of physicochemical interactions to the phase behavior of chromatin aggregates and chromatin organization inside the nucleus.

Leveraging polymer modeling to reconstruct chromatin connectivity from live images

Chromosomal dynamics plays a central role in a number of critical biological processes, such as transcriptional regulation, genetic recombination, and DNA replication. However, visualization of chromatin is generally limited to live imaging of a few fluorescently labeled chromosomal loci or high-resolution reconstruction of multiple loci from a single time frame. To aid in mapping the underlying chromosomal structure based on parsimonious experimental measurements, we present an exact analytical expression for the evolution of the polymer configuration based on a flexible-polymer model, and we propose an algorithm that tracks the polymer configuration from live images of chromatin marked with several fluorescent marks. Our theory identifies the resolution of microscopy needed to achieve high-accuracy tracking for a given spacing of markers, establishing the statistical confidence in the assignment of genome identity to the visualized marks. We then leverage experimental data of locus-tracking measurements to demonstrate the validity of our modeling approach and to establish a basis for the design of experiments with a desired resolution. Altogether, this work provides a computational approach founded on polymer physics that vastly improves the interpretation of in vivo measurements of biopolymer dynamics.

Model chromatin flows: numerical analysis of linear and nonlinear hydrodynamics inside a sphere

We solve a hydrodynamic model of active chromatin dynamics, within a confined geometry simulating the cell nucleus. Using both analytical and numerical methods, we describe the behavior of the chromatin polymer driven by the activity of motors having polar symmetry, both in the linear response regime as well as in the long-term, fully nonlinear regime of the flows. The introduction of a boundary induces a particular geometry in the flows of chromatin, which we describe using vector spherical harmonics, a tool which greatly simplifies both our analytical and numerical approaches. We find that the long-term behavior of this model in confinement is dominated by steady, transverse flows of chromatin which circulate around the spherical domain. These circulating flows are found to be robust to perturbations, and their characteristic size is set by the size of the domain. This gives us further insight into active chromatin dynamics in the cell nucleus, and provides a foundation for development of further, more complex models of active chromatin dynamics.

Activity-Driven Phase Transition Causes Coherent Flows of Chromatin

We discover a new type of nonequilibrium phase transition in a model of chromatin dynamics, which accounts for the coherent motions that have been observed in experiment. The coherent motion is due to the long-range cooperation of molecular motors tethered to chromatin. Cooperation occurs if each motor acts simultaneously on the polymer and the surrounding solvent, exerting on them equal and opposite forces. This drives the flow of solvent past the polymer, which in turn affects the orientation of nearby motors and, if the drive is strong enough, an active polar ("ferromagnetic") phase of motors can spontaneously form. Depending on boundary conditions, either transverse flows or sustained longitudinal oscillations and waves are possible. Predicted length scales are consistent with experiments. We now have in hand a coarse-grained description of chromatin dynamics which reproduces the directed coherent flows of chromatin seen in experiments. This field-theoretic description can be analytically coupled to other features of the nuclear environment such as fluctuating or porous boundaries, local heterogeneities in the distribution of chromatin or its activity, leading to insights on the effects of activity on the cell nucleus and its contents.

Polymer folding through active processes recreates features of genome organization

From proteins to chromosomes, polymers fold into specific conformations that control their biological function. Polymer folding has long been studied with equilibrium thermodynamics, yet intracellular organization and regulation involve energy-consuming, active processes. Signatures of activity have been measured in the context of chromatin motion, which shows spatial correlations and enhanced subdiffusion only in the presence of adenosine triphosphate. Moreover, chromatin motion varies with genomic coordinate, pointing toward a heterogeneous pattern of active processes along the sequence. How do such patterns of activity affect the conformation of a polymer such as chromatin? We address this question by combining analytical theory and simulations to study a polymer subjected to sequence-dependent correlated active forces. Our analysis shows that a local increase in activity (larger active forces) can cause the polymer backbone to bend and expand, while less active segments straighten out and condense. Our simulations further predict that modest activity differences can drive compartmentalization of the polymer consistent with the patterns observed in chromosome conformation capture experiments. Moreover, segments of the polymer that show correlated active (sub)diffusion attract each other through effective long-ranged harmonic interactions, whereas anticorrelations lead to effective repulsions. Thus, our theory offers nonequilibrium mechanisms for forming genomic compartments, which cannot be distinguished from affinity-based folding using structural data alone. As a first step toward exploring whether active mechanisms contribute to shaping genome conformations, we discuss a data-driven approach.