The cell nucleus is a mechanically responsive structure that governs how external forces affect chromosomes. Chromatin, particularly transcriptionally inactive heterochromatin, resists nuclear deformations through its mechanical response. However, chromatin also exhibits liquid-like properties, casting ambiguity on the physical mechanisms of chromatin-based nuclear elasticity. To determine how heterochromatin strengthens nuclear mechanical response, we performed polymer physics simulations of a nucleus model validated by micromechanical measurements and chromosome conformation capture data. The attachment of peripheral heterochromatin to the lamina is required to transmit forces directly to the chromatin and elicit its elastic response. Thus, increases in heterochromatin levels increase nuclear rigidity by increasing the linkages between chromatin and the lamina. Crosslinks within heterochromatin, such as HP1 α proteins, can also stiffen nuclei, but only if chromatin is peripherally tethered. In contrast, heterochromatin affinity interactions that may drive liquid-liquid phase separation do not contribute to nuclear rigidity. When the nucleus is stretched, gel-like peripheral heterochromatin can bear stresses and deform, while the more fluid-like interior euchromatin is less perturbed. Thus, heterochromatin's internal structure and stiffness may regulate nuclear mechanics via peripheral attachment to the lamina, while also enabling nuclear mechanosensing of external forces and external measurement of the nucleus' internal architecture.

One of the key structural proteins in the eukaryotic cell nucleus is lamin. Lamins can assemble into a two-dimensional protein meshwork at the nuclear periphery, known as the nuclear lamina, which provides rigidity and shape to the nucleus. Mutations in lamin proteins that alter the structure of the nuclear lamina underlie laminopathic diseases, including Hutchinson-Gilford Progeria Syndrome (HGPS). Experiments have shown that, compared to healthy cells, lamin supramolecular structures (e.g., protofilaments) assemble into a thicker lamina in HGPS, where they form highly stable nematic microdomains at the nuclear periphery, reminiscent of liquid crystals. This significantly alters the morphological and mechanical properties of the nucleus. In this study, we investigate the aggregation of lamin fibrous structures and their dissociation kinetics from the nuclear periphery by modeling them as coarse-grained, rod-like polymer chains confined within a rigid spherical shell. Our model reproduces the formation of multidirectional nematic domains at the nuclear surface and the reduced lamin dissociation observed in HGPS nuclei by adjusting lamin concentration, lamin-lamin (head-tail), and lamin-shell association strengths. While nematic phase formation requires relatively strong lamin-shell affinity under any non-vanishing inter-lamin attraction, the thickness of the lamina layer is primarily controlled by the head-tail association strength in the model. Furthermore, the unbinding kinetics of lamin chains from the lamina exhibit a concentration-dependent facilitated dissociation, suppressed by strong intra-lamin interactions, reminiscent of diseased nuclei. Overall, our calculations reveal the physical mechanisms by which mutations affecting native lamin interactions and concentration could lead to an abnormal nuclear lamina in laminopathic diseases.

Topological modification of block copolymer (BCP) conformations offers a promising approach for developing self-assembled periodic nanostructured materials with smaller domain sizes, which are essential for a range of technological applications. Cyclic polymers, with their inherently more compact conformations, present an effective strategy for achieving this miniaturization. In this work, through a combination of analytical theory and coarse-grained molecular dynamics simulations, we establish a relationship between different nonlinear topologies and the corresponding domain size of lamella-forming BCPs. Our investigations includes BCP architectures with one or two cyclic segments such as tadpoles, diblock and triblock 8-shaped polymers, and diblock nonconcatenated and concatenated rings. We demonstrate that the primary reduction in lamellar domain size is driven by the more compact arrangement of monomers in the cyclic architectures, with an additional contribution from the nonconcatenation of cyclic segments. This is corroborated by theoretical predictions for both domain size reduction and BCP conformations across different architectures. Moreover, consistent with theoretical expectations, the nonconcatenation of rings reduces the interpenetration of opposing brushes, thereby lowering friction between lamellae.

Polyelectrolyte hydrogels can deform under electric fields due to their unique nature combining polymer elasticity and electrostatics within a single structure. While the response of hydrogels to electric fields is relatively well-characterized at the macroscale, at the mesoscale-where the behaviour of the constituent chains becomes significant-the effect of external electric potentials on the hydrogel structure is poorly understood. In this study, we explored the mechanical response of a semi-infinite polyelectrolyte hydrogel slab to transient, sinusoidal electric fields using extensive coarse-grained molecular dynamics simulations with both short and long-range electrostatics. Our simulations show that when the electric field is applied to a small volumetric section of the hydrogel slab spatially nonuniformly, the entire slab contracts reversibly and in a direction perpendicular to the field. The hydrogel contracts to almost half of its initial, field-free length before retracting to its original size, with its size fluctuations eventually decaying similar to an underdamped oscillator. Contraction is maximized if the electric field is applied to the central region of the slab, away from the slab's interfaces. Additionally, tuning the electric field frequency and amplitude controls both contraction times and contraction efficiency. Further analyses using implicit solvent simulations across various electrostatic parameters and salt concentrations confirm the robustness of the phenomenon while highlighting the importance of hydrodynamics. Our results demonstrate the effectiveness of electric fields applied spatially nonuniformly on homogeneous hydrogel structures, with potential applications in electro-mechanochemistry.

Using scaling arguments to model peripheral chromatin localized near the inner surface of the nuclear envelope (NE) as a flexible polymer chain, we discuss the structural properties of the peripheral chromatin composed of alternating lamin-associated domains (LADs) and inter-LADs. Modeling the attraction of LADs to NE by de Gennes' self-similar carpet, which treats the chromatin layer as a polymer fractal, explains two major experimental observations: (i) The high density of chromatin close to the nuclear periphery decays to a constant density as the distance to the periphery increases. (ii) Due to the decreasing mesh size towards the nuclear periphery, the chromatin carpet inside NE excludes molecules (via non-specific interactions) above a threshold size that depends on the distance from the nuclear periphery.

The highly and slightly condensed forms of chromatin, heterochromatin and euchromatin, respectively, segregate in the cell nucleus. Heterochromatin is more abundant in the nucleus periphery. Here we study the mechanism of heterochromatin segregation by modeling interphase chromosomes as diblock ring copolymers confined in a rigid spherical shell using molecular dynamics simulations. In our model, heterochromatin and euchromatin are distinguished by their bending stiffnesses only, while an interaction potential between the spherical shell and chromatin is used to model lamin-associated proteins. Our simulations indicate that in the absence of attractive interactions between the nuclear shell and the chromatin, most heterochromatin segregates towards the nuclear interior due to the depletion of less flexible heterochromatin segments from the nuclear periphery. This inverted chromatin distribution,which is opposite to the conventional case with heterochromatin dominating at the periphery, is in accord with experimental observations in rod cells. This "inversion" is also found to be independent of the heterochromatin concentration and chromosome number. The chromatin distribution at the periphery found in vivo can be recovered by further increasing the bending stiffness of heterochromatin segments or by turning on attractive interactions between the nuclear shell and heterochromatin. Our results indicate that the bending stiffness of chromatin could be a contributor to chromosome organization along with differential effects of HP1α-driven phase segregation and of loop extruders and interactions with the nuclear envelope and topological constraints.

We use nonequilibrium atomistic molecular dynamics simulations of unentangled melts of linear and star oligomer chains (C25H52) to study the steady-state viscoelastic response under confinement within nanoscale hematite (α−Fe2O3) channels. We report (i) the negative (positive) first (second) normal stress difference and (ii) the presence of viscoelastic tension at low Wi. With the aim of uncovering the molecular mechanism of viscoelasticity, we link these effects to bond alignment such that absorbed chains near the surface can carry the elastic force exerted on the walls, which decays as the chains become more aligned in the flow direction. This alignment is observed to be independent of the film thickness but enhanced as the shear rate increases or the surface attraction weakens.

Abnormal cell nuclear shapes are hallmarks of diseases, including progeria, muscular dystrophy, and many cancers. Experiments have shown that disruption of heterochromatin and increases in euchromatin lead to nuclear deformations, such as blebs and ruptures. However, the physical mechanisms through which chromatin governs nuclear shape are poorly understood. To investigate how heterochromatin and euchromatin might govern nuclear morphology, we studied chromatin microphase separation in a composite coarse-grained polymer and elastic shell simulation model. By varying chromatin density, heterochromatin composition, and heterochromatin-lamina interactions, we show how the chromatin phase organization may perturb nuclear shape. Increasing chromatin density stabilizes the lamina against large fluctuations. However, increasing heterochromatin levels or heterochromatin-lamina interactions enhances nuclear shape fluctuations by a "wetting"-like interaction. In contrast, fluctuations are insensitive to heterochromatin's internal structure. Our simulations suggest that peripheral heterochromatin accumulation could perturb nuclear morphology, while nuclear shape stabilization likely occurs through mechanisms other than chromatin microphase organization.

Hydrogel-integrated optical fiber sensors have garnered momentous interest due to their optical properties, biocompatibility, and biodegradability.

Rotaxanes can exhibit stimuli-responsive behavior by allowing positional fluctuations of their rota groups in response to physiochemical conditions such as the changes in solution pH. However, ionic strength of the solution also affects the molecular conformation by altering the charge state of the entire molecule, coupling the stimuli-responsiveness of rotaxanes with their conformation. A molecular-scale investigation on a model system can allow the decoupling and identification of various effects and can greatly benefit applications of such molecular switches. By using atomistic molecular dynamics simulations, we study equilibrium and kinetics properties of various charge states of the [5]rotaxane, which is a supramolecular moiety with four rotaxanes bonded to a porphyrin core. We model various physiochemical charge states, each of which can be realized at various solution pH levels as well as several exotic charge distributions. By analyzing molecular configurations, hydrogen bonding, and energetics of single molecules in salt-free water and its polyrotaxanated network at the interface of water and chloroform, we demonstrate that charge-neutral and negatively charged molecules often tend to collapse in a way that they can expose their porphyrin core. Contrarily, positively charged moieties tend to take more extended molecular configurations blocking the core. Further, sudden changes in the charge states emulating the pH alterations in solution conditions lead to rapid, sub-10 ns level, changes in the molecular conformation of [5]rotaxane via shuttling motion of CB6 rings along axles. Finally, simulations of 2D [5]rotaxane network structures support our previous findings on a few nanometer-thick film formation at oil-water interfaces. Overall, our results suggest that rotaxane-based structures can exhibit a rich spectrum of molecular configurations and kinetics depending on the ionic strength of the solution.

The transcription process is regulated by temporal interactions of transcription factors with DNA. In the last decade, computational and experimental studies revealed the residence times of transcription factors on DNA correlate with transcriptional output. Biochemical studies suggest that transcription factors exhibit bi-exponential dynamics, attributed to the binary affinity model composed of nonspecific and specific protein-DNA bindings. Recently, transcription factor residence times were shown to display a power-law pattern implicating proteinDNA affinity levels are rather continuous. Elucidating the underlying mechanisms of transcription factor residence distributions, beyond protein-DNA interaction strength, is crucial to construct a more complete understanding of transcriptional regulation. Here, by using molecular dynamics simulations of DNA and dimeric proteins, we demonstrate residence time behaviors of generic homodimeric transcription factors follow a multi-exponential pattern even with single and binary affinity levels between DNA and proteins, indicating the existence of emergent behavior. Our simulations reveal that DNA-protein clusters of various sizes contribute to this multi-exponential behavior. These findings add another layer to transcriptional regulation and, consequently, to gene expression by connecting protein concentration, DNA-protein clusters, and DNA residence times of transcription factors.

Interphase chromosomes are known to organize non-randomly in the micron-sized eukaryotic cell nucleus and occupy certain fraction of nuclear volume, often without mixing. Using extensive coarse-grained simulations, we model such chromosome structures as colloidal particles whose surfaces are grafted by cyclic polymers. This model system is known as Rosetta. The cyclic polymers, with varying polymerization degrees, mimic chromatin loops present in interphase chromosomes, while the rigid core models the chromocenter section of the chromosome. Our simulations show that the colloidal chromosome model provides a well-separated particle distribution without specific attraction between the chain monomers. As the polymerization degree of the grafted cyclic chains decreases while maintaining the total chromosomal length (e.g. the more potent activity of condensin-family proteins), the average chromosomal volume becomes smaller, inter-chromosomal contacts decrease, and chromocenters organize in a quasi-crystalline order reminiscent of a glassy state. This order weakens for polymer chains with a characteristic size on the order of the confinement radius. Notably, linear-polymer grafted particles also provide the same chromocenter organization scheme. However, unlike linear chains, cyclic chains result in less contact between the polymer layers of neighboring chromosome particles, demonstrating the effect of DNA breaks in altering genome-wide contacts. Our simulations show that polymer-grafted colloidal systems could help decipher 3D genome architecture along with the fractal globular and loop-extrusion models.

Cyclic polymers display unique physical behaviors in comparison to their linear counterparts. Theoretical, computational and experimental studies have revealed that some of their distinctive properties are also observed in charged variants of cyclic polymers, known as cyclic polyelectrolytes (PEs), especially in terms of their structural responses to variations in the strength of electrostatic interactions. In this study, we investigate the impact of cyclic topology on the conformations of PE chains in dilute good solvent using scaling analysis and coarse-grained bead-spring molecular dynamics simulations. Our observations indicate that, in contrast to linear PE chains, cyclic topology results in more compact conformations at low and intermediate Bjerrum lengths. Moreover, two structural metrics, asphericity and prolateness, which quantify deviations from spherical and flat molecular shapes, exhibit non-monotonic behaviors for cyclic PEs. This stands in contrast to linear PEs, where these shape characteristics exhibit a monotonic trend with increasing Bjerrum length. A feasible analytical theory, developed to account for ionic distributions around cyclic PE chains, suggests that the fundamental difference between linear and cyclic chain conformations may be attributed to topological effects influencing long-range electrostatic interactions.

Polyelectrolyte gels can generate electric potentials under mechanical deformation. While the underlying mechanism of such a response is often attributed to changes in counterion-condensation levels or alterations in the ionic conditions in the pervaded volume of the hydrogel, the exact molecular origins are largely unknown. By using all-atom molecular dynamics simulations of a polyacrylic acid hydrogel in explicit water as a model system, we simulate the uniaxial compression and uniaxial stretching of weakly to highly swollen (i.e., between 60-90% solvent content) hydrogel networks and calculate the microscopic condensation levels of counterions around the hydrogel chains. The counterion condensation under deformation is highly non-monotonic. Ionic condensation around the constituting chains of the deformed hydrogel tends to increase as the chains are stretched. This increase reaches a maximum and decreases as the chains are strongly stretched. The condensation around the collapsed chains of the hydrogel is weakly affected by the deformation. As a result, both compressing and stretching the model hydrogel lead to an overall increase in the counterion condensation. The effect vanishes for weakly swollen hydrogels, for which most ions are already condensed. The simulations with single, stretched polyelectrolyte chains show a qualitatively similar response, suggesting the effect of chain elongation on the ionic distribution throughout the hydrogel. Notably, this deformation-induced counterion condensation phenomenon does not occur in a polyelectrolyte solution at its critical concentration, indicating the role of hydrogel topology constraining the chain ends. Our results indicate that counterion condensation in a deforming polyelectrolyte hydrogel can be highly heterogeneous and exhibit a rich behaviour of electrostatic responses.

DNA is the ultimate molecule that encodes life through genes. Genes positioned along the meter-long DNA molecule have to be expressed at the right time and in the right amount via strict regulatory processes. Regulation of a gene starts with the binding of a DNA-binding protein known as a transcription factor (TF) to a target regulatory element along the double-stranded DNA molecule. Often, TFs attach to DNA in a sequence-specific manner and can target DNA motifs of various lengths, yet some TFs can also interact with DNA nonspecifically. The resulting DNA-TF complexes can control gene expression directly via controlling the recruitment of RNA polymerase on the target DNA sequence. Recent single-molecule experiments have added a new dimension to such control mode; the lifetime of a DNA-TF complex (i.e., the residence time of the protein on its DNA site) can function as a regulatory component. This breakthrough inevitably suggests that any physiochemical constituent that can alter the residence time of a DNA-binding protein can also be involved in gene regulation. In this perspective, we argue that a TF protein’s cellular concentration can contribute to the cell-scale transcription activity by modulating the DNA-residence time of the protein. Cells can achieve this either by enabling a concentration-dependent dissociation mechanism or by promoting the formation of multiprotein-DNA complexes. While our discussion here will consider examples from prokaryotic cells, we will also briefly argue that similar mechanisms could also be functional in eukaryotic cells.

Surface plasmon resonance (SPR) is a real-time kinetic measurement principle that can probe the kinetic interactions between ligands and their binding sites, and lies at the backbone of pharmaceutical, biosensing, and biomolecular research. The extraction of dissociation rates from SPR-response signals often relies on several commonly adopted assumptions, one of which is the exponential decay of the dissociation part of the response signal. However, certain conditions, such as high density of binding sites or high concentration fluctuations near the surface as compared to the bulk, can lead to non-exponential decays via ligand rebinding or facilitated dissociation. Consequently, fitting the data with an exponential function can underestimate or overestimate the measured dissociation rates. Here, we describe a set of alternative fit functions that can take such effects into consideration along with plasmonic sensor design principles with key performance metrics, thereby suggesting methods for error-free high-precision extraction of the dissociation rates.

Transcription machinery depends on the temporal formation of protein-DNA complexes. Recent experiments demonstrated that lifetime of the complex can also affect transcription. In parallel, in vitro single-molecule studies showed that nucleoid-associated proteins (NAPs) leave the DNA rapidly as the bulk concentration of the protein increases via facilitated dissociation (FD). Never-theless, whether such concentration-dependent mechanism is functional in a bacterial cell, in which NAP levels and the 3D chromosomal structure are often coupled, is not clear a priori . Here, by using extensive coarse-grained molecular simulations, we model the unbinding of specific and nonspecific dimeric NAPs from a high-molecular-weight circular DNA molecule in a cylindrical structure mimicking the cellular confinement of a bacterial chromosome. Our simulations show that physiologically relevant peak protein levels (tens of micromolar) lead to highly compact chromosomal structures. This compaction results in rapid off rates (shorter DNA-residence times) but only for specifically DNA-binding NAPs such as the factor for inversion stimulation (Fis). Contrarily, for nonspecific NAPs, the off rates decrease as the protein levels increase, suggesting an inverse FD pattern. The simulations with restrained chromosome models reveal that this inverse response is due to DNA-segmental fluctuations, and that chromosomal compaction is in favor of faster protein dissociation. Overall, our results indicate that cellular-concentration level of a structural DNA-binding protein can be highly intermingled with its DNA-residence time.

Using molecular dynamics simulations and scaling arguments, we analyzed the interactions between two identical molten polymer brushes intermediately and strongly compressed towards each other at melt conditions. The width of the overlap region, in which monomers of the linear chains composing the two brushes interact, increases as the polymer-grafted surfaces are brought closer. If two-brush coated surfaces are as close as the characteristics size of the grafted chains, the overlap region is directly controlled by intersurface distance. At intermediate compression, the width of the overlap region scales with the end-to-end size of chain sections within the overlap region. This result is consistent with the scaling regimes in the literature. As the intersurface distance is decreased, the number fraction of chains (chains with their free ends in the overlap region) decreases with a power law. Our results could be useful for studies on tribological behavior of polymer-grafted surfaces as well as for the self-assembly of polymer coated colloids.

While there is a prevalent genome organization in eukaryotic cells, with heterochromatin concentrated at the nuclear periphery, anomalous cases do occur. Deviations of chromatin distribution are frequent, for example, upon aging, under malignant diseases, or even naturally in rod cells of nocturnal mammals. Using molecular dynamic simulations, we study the segregation of heterochromatin in the cell nucleus by modeling interphase chromosomes as diblock ring copolymers confined in a rigid spherical shell. In our model, heterochromatin and euchromatin are distinguished by their bending stiffnesses, while an interaction potential between the spherical shell and chromatin is used as a proxy for lamin-associated proteins. Our simulations indicate that in the absence of attractive interactions between the nuclear shell and the chromatin, the majority of heterochromatin segregates towards the nuclear interior due to depletion of less flexible heterochromatin segments from the nuclear periphery. This inverted chromatin distribution is in accord with experimental observations in rod cells. This “inversion” is also found to be independent of the heterochromatin concentration and chromosome number, and is further enhanced by additional attractive interactions between heterochromatin segments. as well as by allowing bond-crossing to emulate topoisomerase activity. The usual chromatin distribution, with heterochromatin at the periphery, can be recovered by further increasing the bending stiffness of heterochromatin segments or by turning on attractive interactions between the nuclear shell and heterochromatin. Overall, our results indicate that bending stiffness of chromatin could be a contributor to chromosome organization along with differential effects of HP1 α -driven phase segregation and of loop extruders, and interactions with the nuclear envelope and topological constraints.

Hybrid systems based on covalent polymers and supramolecular assemblies offer unique opportunities for functional materials based on the pathway-dependent dynamic structures of supramolecular assemblies and the mechanical stability of covalent polymers. We report here on the synthesis of functional hybrid hydrogels containing self-assembling chromophore amphiphiles and polyelectrolytes. Chromophore amphiphiles were introduced into non-aqueous solvent swollen polymer matrices and self-assembly of the chromophore amphiphiles into crystalline nanostructures was triggered in the confined environment of the covalent network upon solvent exchange for water. Opposite charges in the covalent polyelectrolyte and the chromophore amphiphiles and sterics entrap the supramolecular assemblies within the mechanically stable network. However, molecular components necessary for catalysis, byproducts from photocatalysis, and the hydrogen produced are able to diffuse in or out of the covalent network to create a reusable robust host for photocatalysis. By varying the monomer and crosslinker composition in the feed, we can tune the porosity of the network as well as the chemical environment in which supramolecular crystallization of the chromophore amphiphiles takes place. This allows optimization of the hydrogel mechanical properties, retention of the chromophore amphiphile assemblies, and the photocatalytic reaction efficiency. Coarse-grained molecular dynamics simulations revealed that the chromophore amphiphile assembly is guided by the polyelectrolyte network via ionic interactions. We also demonstrate successful photocatalytic hydrogen production from catalyst-laden hybrid hydrogels with the turnover frequency approaching that of the supramolecular hydrogel system, and also show that the hybrid hydrogels can be reused over multiple cycles as photosensitizers.