Heterogeneous flexibility can contribute to chromatin segregation in the cell nucleus.

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.

Induced phase transformation in ionizable colloidal nanoparticles.

Acid-base equilibria directly influence the functionality and behavior of particles in a system. Due to the ionizing effects of acid-base functional groups, particles will undergo charge exchange. The degree of ionization and their intermolecular and electrostatic interactions are controlled by varying the pH and salt concentration of the solution in a system. Although the pH can be tuned in experiments, it is hard to model this effect using simulations or theoretical approaches. This is due to the difficulty in treating charge regulation and capturing the cooperative effects in a colloidal suspension with Coulombic interaction. In this work, we analyze a suspension of ionizable colloidal particles via molecular dynamics (MD) simulations, along with Monte Carlo simulations for charge regulation (MC-CR) and derive a phase diagram of the system as a function of pH. It is observed that as pH increases, particles functionalized with acid groups change their arrangement from face-centered cubic (FCC) packing to a disordered state. We attribute these transitions to an increase in the degree of charge polydispersity arising from an increase in pH. Our work shows that charge regulation leads to amorphous solids in colloids when the mean nanoparticle charge is sufficiently high.

Colloidal Clusters and Networks Formed by Oppositely Charged Nanoparticles with Varying Stiffnesses.

Colloidal clusters and gels are ubiquitous in science and technology. Particle softness has a strong effect on interparticle interactions; however, our understanding of the role of this factor in the formation of colloidal clusters and gels is only beginning to evolve. Here, we report the results of experimental and simulation studies of the impact of particle softness on the assembly of clusters and networks from mixtures of oppositely charged polymer nanoparticles (NPs). Experiments were performed below or above the polymer glass transition temperature, at which the interaction potential and adhesive forces between the NPs were significantly varied. Hard NPs assembled in fractal clusters that subsequently organized in a kinetically arrested colloidal gel, while soft NPs formed dense precipitating aggregates, due to the NP deformation and the decreased interparticle distance. Importantly, interactions of hard and soft NPs led to the formation of discrete precipitating NP aggregates at a relatively low volume fraction of soft NPs. A phenomenological model was developed for interactions of oppositely charged NPs with varying softnesses. The experimental results were in agreement with molecular dynamics simulations based on the model. This work provides insight on interparticle interactions before, during, and after the formation of hard-hard, hard-soft, and soft-soft contacts and has impact for numerous applications of reversible colloidal gels, including their use as inks for additive manufacturing.

Microporous water with high gas solubilities.

Liquids with permanent microporosity can absorb larger quantities of gas molecules than conventional solvents1, providing new opportunities for liquid-phase gas storage, transport and reactivity. Current approaches to designing porous liquids rely on sterically bulky solvent molecules or surface ligands and, thus, are not amenable to many important solvents, including water2-4. Here we report a generalizable thermodynamic strategy to preserve permanent microporosity and impart high gas solubilities to liquid water. Specifically, we show how the external and internal surface chemistry of microporous zeolite and metal-organic framework (MOF) nanocrystals can be tailored to promote the formation of stable dispersions in water while maintaining dry networks of micropores that are accessible to gas molecules. As a result of their permanent microporosity, these aqueous fluids can concentrate gases, including oxygen (O2) and carbon dioxide (CO2), to much higher densities than are found in typical aqueous environments. When these fluids are oxygenated, record-high capacities of O2 can be delivered to hypoxic red blood cells, highlighting one potential application of this new class of microporous liquids for physiological gas transport.

Origin of Proteolytic Stability of Peptide-Brush Polymers as Globular Proteomimetics.

Peptide-brush polymers (PBPs), wherein every side-chain of the polymers is peptidic, represent a new class of proteomimetic with unusually high proteolytic resistance while maintaining bioactivity. Here, we sought to determine the origin of this behavior and to assess its generality via a combined theory and experimental approach. A series of PBPs with various polymer backbone structures were prepared and examined for their proteolytic stability and bioactivity. We discovered that an increase in the hydrophobicity of the polymer backbones is predictive of an elevation in proteolytic stability of the side-chain peptides. Computer simulations, together with small-angle X-ray scattering (SAXS) analysis, revealed globular morphologies for these polymers, in which pendant peptides condense around hydrophobic synthetic polymer backbones driven by the hydrophobic effect. As the hydrophobicity of the polymer backbones increases, the extent of solvent exposure of peptide cleavage sites decreases, reducing their accessibility to proteolytic enzymes. This study provides insight into the important factors driving PBP aqueous-phase structures to behave as globular, synthetic polymer-based proteomimetics.

Quincke Oscillations of Colloids at Planar Electrodes.

Dielectric particles in weakly conducting fluids rotate spontaneously when subject to strong electric fields. Such Quincke rotation near a plane electrode leads to particle translation that enables physical models of active matter. In this Letter, we show that Quincke rollers can also exhibit oscillatory dynamics, whereby particles move back and forth about a fixed location. We explain how oscillations arise for micron-scale particles commensurate with the thickness of a field-induced boundary layer in the nonpolar electrolyte. This work enables the design of colloidal oscillators.

Fast and programmable locomotion of hydrogel-metal hybrids under light and magnetic fields.

The design of soft matter in which internal fuels or an external energy input can generate locomotion and shape transformations observed in living organisms is a key challenge. Such materials could assist in productive functions that may range from robotics to smart management of chemical reactions and communication with cells. In this context, hydrated matter that can function in aqueous media would be of great interest. Here, we report the design of hydrogels containing a scaffold of high-aspect ratio ferromagnetic nanowires with nematic order dispersed in a polymer network that change shape in response to light and experience torques in rotating magnetic fields. The synergistic response enables fast walking motion of macroscopic objects in water on either flat or inclined surfaces and also guides delivery of cargo through rolling motion and light-driven shape changes. The theoretical description of the response to the external energy input allowed us to program specific trajectories of hydrogel objects that were verified experimentally.

Strain-Dependent Nanowrinkle Confinement of Block Copolymers.

This paper describes an all-soft, templated assembly of block copolymers (BCPs) with programmable alignment. Using polymeric nanowrinkles as a confining scaffold, poly(styrene)-block-poly(dimethylsiloxane) (PS-b-PDMS) BCPs were assembled to be parallel or perpendicular to the wrinkle orientation by manipulating the substrate strain. Self-consistent field theory modeling revealed that wrinkle curvature and surface affinity govern the BCP structural formation. Furthermore, control of BCP alignment was demonstrated for complex wrinkle geometries, various copolymer molecular weights, and functional wrinkle skin layers. This integration of BCP patterning with flexible 3D architectures offers a promising nanolithography approach for next-generation soft electronics.

Single-chain heteropolymers transport protons selectively and rapidly.

Precise protein sequencing and folding are believed to generate the structure and chemical diversity of natural channels1,2, both of which are essential to synthetically achieve proton transport performance comparable to that seen in natural systems. Geometrically defined channels have been fabricated using peptides, DNAs, carbon nanotubes, sequence-defined polymers and organic frameworks3-13. However, none of these channels rivals the performance observed in their natural counterparts. Here we show that without forming an atomically structured channel, four-monomer-based random heteropolymers (RHPs)14 can mimic membrane proteins and exhibit selective proton transport across lipid bilayers at a rate similar to those of natural proton channels. Statistical control over the monomer distribution in an RHP leads to segmental heterogeneity in hydrophobicity, which facilitates the insertion of single RHPs into the lipid bilayers. It also results in bilayer-spanning segments containing polar monomers that promote the formation of hydrogen-bonded chains15,16 for proton transport. Our study demonstrates the importance of the adaptability that is enabled by statistical similarity among RHP chains and of the modularity provided by the chemical diversity of monomers, to achieve uniform behaviour in heterogeneous systems. Our results also validate statistical randomness as an unexplored approach to realize protein-like behaviour at the single-polymer-chain level in a predictable manner.

The Importance of Salt-Enhanced Electrostatic Repulsion in Colloidal Crystal Engineering with DNA.

Realizing functional colloidal single crystals requires precise control over nanoparticles in three dimensions across multiple size regimes. In this regard, colloidal crystallization with programmable atom equivalents (PAEs) composed of DNA-modified nanoparticles allows one to program in a sequence-specific manner crystal symmetry, lattice parameter, and, in certain cases, crystal habit. Here, we explore how salt and the electrostatic properties of DNA regulate the attachment kinetics between PAEs. Counterintuitively, simulations and theory show that at high salt concentrations (1 M NaCl), the energy barrier for crystal growth increases by over an order of magnitude compared to low concentration (0.3 M), resulting in a transition from interface-limited to diffusion-limited crystal growth at larger crystal sizes. Remarkably, at elevated salt concentrations, well-formed rhombic dodecahedron-shaped microcrystals up to 21 µm in size grow, whereas at low salt concentration, the crystal size typically does not exceed 2 µm. Simulations show an increased barrier to hybridization between complementary PAEs at elevated salt concentrations. Therefore, although one might intuitively conclude that higher salt concentration would lead to less electrostatic repulsion and faster PAE-to-PAE hybridization kinetics, the opposite is the case, especially at larger inter-PAE distances. These observations provide important insight into how solution ionic strength can be used to control the attachment kinetics of nanoparticles coated with charged polymeric materials in general and DNA in particular.

Correction: Electrostatics at the nanoscale.

Correction for 'Electrostatics at the nanoscale' by David A. Walker et al., Nanoscale, 2011, 3, 1316-1344.

Controlled Symmetry Breaking in Colloidal Crystal Engineering with DNA.

The programmed crystallization of particles into low-symmetry lattices represents a major synthetic challenge in the field of colloidal crystal engineering. Herein, we report an approach to realizing such structures that relies on a library of low-symmetry Au nanoparticles, with synthetically adjustable dimensions and tunable aspect ratios. When modified with DNA ligands and used as building blocks for colloidal crystal engineering, these structures enable one to expand the types of accessible lattices and to answer mechanistic questions about phase transitions that break crystal symmetry. Indeed, crystals formed from a library of elongated rhombic dodecahedra yield a rich phase space, including low-symmetry lattices (body-centered tetragonal and hexagonal planar). Molecular dynamics simulations corroborate and provide insight into the origin of these phase transitions. In particular, we identify an unexpected asymmetry in the DNA shell, distinct from both the particle and lattice symmetries, which enables directional, nonclose-packed interactions.

Effects of electrostatic interactions on ligand dissociation kinetics.

We study unbinding of multivalent cationic ligands from oppositely charged polymeric binding sites sparsely grafted on a flat neutral substrate. Our molecular dynamics simulations are suggested by single-molecule studies of protein-DNA interactions. We consider univalent salt concentrations spanning roughly a 1000-fold range, together with various concentrations of excess ligands in solution. To reveal the ionic effects on unbinding kinetics of spontaneous and facilitated dissociation mechanisms, we treat electrostatic interactions both at a Debye-Hückel (DH) (or implicit ions, i.e., use of an electrostatic potential with a prescribed decay length) level and by the more precise approach of considering all ionic species explicitly in the simulations. We find that the DH approach systematically overestimates unbinding rates, relative to the calculations where all ion pairs are present explicitly in solution, although many aspects of the two types of calculation are qualitatively similar. For facilitated dissociation (FD) (acceleration of unbinding by free ligands in solution) explicit-ion simulations lead to unbinding at lower free-ligand concentrations. Our simulations predict a variety of FD regimes as a function of free-ligand and ion concentrations; a particularly interesting regime is at intermediate concentrations of ligands where nonelectrostatic binding strength controls FD. We conclude that explicit-ion electrostatic modeling is an essential component to quantitatively tackle problems in molecular ligand dissociation, including nucleic-acid-binding proteins.

Orbitals for classical arbitrary anisotropic colloidal potentials.

Coarse-grained potentials are ubiquitous in mesoscale simulations. While various methods to compute effective interactions for spherically symmetric particles exist, anisotropic interactions are seldom used, due to their complexity. Here we describe a general formulation, based on a spatial decomposition of the density fields around the particles, akin to atomic orbitals. We show that anisotropic potentials can be efficiently computed in numerical simulations using Fourier-based methods. We validate the field formulation and characterize its computational efficiency with a system of colloids that have Gaussian surface charge distributions. We also investigate the phase behavior of charged Janus colloids immersed in screened media, with screening lengths comparable to the colloid size. The system shows rich behaviors, exhibiting vapor, liquid, gel, and crystalline morphologies, depending on temperature and screening length. The crystalline phase only appears for symmetric Janus particles. For very short screening lengths, the system undergoes a direct transition from a vapor to a crystal on cooling; while, for longer screening lengths, a vapor-liquid-crystal transition is observed. The proposed formulation can be extended to model force fields that are time or orientation dependent, such as those in systems of polymer-grafted particles and magnetic colloids.

Morphology-enhanced conductivity in dry ionic liquids.

Ionic liquids exhibit fascinating nanoscale morphological phases and are promising materials for energy storage applications. Liquid crystalline order emerges in ionic liquids with specific chemical structures. Here, we investigate the phase behaviour and related ionic conductivities of dry ionic liquids, using extensive molecular dynamics simulations. Temperature dependence, properties of polymeric tail and excluded volume symmetry of the amphiphilic ionic liquid molecules are investigated in large scale systems with both short and long-range Coulomb interactions. Our results suggest that by adjusting stiffness and steric interactions of the amphiphilic molecules, lamellar or 3D continuous phases result in these molecular salts. The resulting phases are composed of ion rich and ion pure domains. In 3D phases, ion rich clusters form ionic channels and have significant effects on the conductive properties of the observed nano-phases. If there is no excluded-volume asymmetry along the molecules, mostly lamellar phases with anisotropic conductivities emerge. If the steric interactions become asymmetric, lamellar phases are replaced by complex 3D continuous phases. Within the temperature ranges for which morphological phases are observed, conductivities exhibit low-temperature maxima in accord with experiments on ionic liquid crystals. Stiffer molecules increase the high-conductivity interval and strengthen temperature-resistance of morphological phases. Increasing the steric interactions of cation leads to higher conductivities. Moreover, at low monomeric volume fractions and at low temperatures, cavities are observed in the nano-phases of flexible ionic liquids. We also demonstrate that, in the absence of electrostatic interactions, the morphology is distorted. Our findings inspire new design principles for room temperature ionic liquids and help explain previously-reported experimental data.

Energy landscapes and functions of supramolecular systems.

By means of two supramolecular systems--peptide amphiphiles engaged in hydrogen-bonded ß-sheets, and chromophore amphiphiles driven to assemble by π-orbital overlaps--we show that the minima in the energy landscapes of supramolecular systems are defined by electrostatic repulsion and the ability of the dominant attractive forces to trap molecules in thermodynamically unfavourable configurations. These competing interactions can be selectively switched on and off, with the order of doing so determining the position of the final product in the energy landscape. Within the same energy landscape, the peptide-amphiphile system forms a thermodynamically favoured product characterized by long bundled fibres that promote biological cell adhesion and survival, and a metastable product characterized by short monodisperse fibres that interfere with adhesion and can lead to cell death. Our findings suggest that, in supramolecular systems, functions and energy landscapes are linked, superseding the more traditional connection between molecular design and function.

Vesicle Geometries Enabled by Dynamically Trapped States.

Understanding and controlling vesicle shapes is a fundamental challenge in biophysics and materials design. In this paper, we design dynamic protocols for enlarging the shape space of both fluid and crystalline vesicles beyond the equilibrium zone. By removing water from within the vesicle at different rates, we numerically produced a series of dynamically trapped stable vesicle shapes for both fluid and crystalline vesicles in a highly controllable fashion. In crystalline vesicles that are continuously dehydrated, simulations show the initial appearance of small flat areas over the surface of the vesicles that ultimately merge to form fewer flat faces. In this way, the vesicles transform from a fullerene-like shape into various faceted polyhedrons. We perform analytical elasticity analysis to show that these salient features are attributable to the crystalline nature of the vesicle. The potential to use dynamic protocols, such as those used in this study, to engineer vesicle shape transformations is helpful for exploiting the richness of vesicle geometries for desired applications.

DNA-Segment-Facilitated Dissociation of Fis and NHP6A from DNA Detected via Single-Molecule Mechanical Response.

The rate of dissociation of a DNA-protein complex is often considered to be a property of that complex, without dependence on other nearby molecules in solution. We study the kinetics of dissociation of the abundant Escherichia coli nucleoid protein Fis from DNA, using a single-molecule mechanics assay. The rate of Fis dissociation from DNA is strongly dependent on the solution concentration of DNA. The off-rate (k(off)) of Fis from DNA shows an initially linear dependence on solution DNA concentration, characterized by an exchange rate of k(ex)≈9×10(-4) (ng/µl)(-1) s(-1) for 100 mM univalent salt buffer, with a very small off-rate at zero DNA concentration. The off-rate saturates at approximately k(off,max)≈8×10(-3) s(-1) for DNA concentrations above ≈20 ng/µl. This exchange reaction depends mainly on DNA concentration with little dependence on the length of the DNA molecules in solution or on binding affinity, but this does increase with increasing salt concentration. We also show data for the yeast HMGB protein NHP6A showing a similar DNA-concentration-dependent dissociation effect, with faster rates suggesting generally weaker DNA binding by NHP6A relative to Fis. Our results are well described by a model with an intermediate partially dissociated state where the protein is susceptible to being captured by a second DNA segment, in the manner of "direct transfer" reactions studied for other DNA-binding proteins. This type of dissociation pathway may be important to protein-DNA binding kinetics in vivo where DNA concentrations are large.

Coulomb energy of uniformly charged spheroidal shell systems.

We provide exact expressions for the electrostatic energy of uniformly charged prolate and oblate spheroidal shells. We find that uniformly charged prolate spheroids of eccentricity greater than 0.9 have lower Coulomb energy than a sphere of the same area. For the volume-constrained case, we find that a sphere has the highest Coulomb energy among all spheroidal shells. Further, we derive the change in the Coulomb energy of a uniformly charged shell due to small, area-conserving perturbations on the spherical shape. Our perturbation calculations show that buckling-type deformations on a sphere can lower the Coulomb energy. Finally, we consider the possibility of counterion condensation on the spheroidal shell surface. We employ a Manning-Oosawa two-state model approximation to evaluate the renormalized charge and analyze the behavior of the equilibrium free energy as a function of the shell's aspect ratio for both area-constrained and volume-constrained cases. Counterion condensation is seen to favor the formation of spheroidal structures over a sphere of equal area for high values of shell volume fractions.