Local Volume Concentration, Packing Domains and Scaling Properties of Chromatin.

We propose the Self Returning Excluded Volume (SR-EV) model for the structure of chromatin based on stochastic rules and physical interactions that can capture the observed behavior across imaging and sequencing based measures of chromatin organization. From nucleosome to chromosome scales, the model captures the overall chromatin organization as a corrugated system, with dense and dilute regions alternating in a manner that resembles the mixing of two disordered bi-continuous phases. This particular organizational topology is a consequence of the multiplicity of interactions and processes ocurring in the nuclei, and mimicked by the proposed return rules. Single configuration properties and ensemble averages show a robust agreement between theoretical and experimental results including chromatin volume concentration, contact probability, packing domain identification and size characterization, and packing scaling behavior. Model and experimental results suggest that there is an inherent chromatin organization regardless of the cell character and resistent to external forcings such as Rad21 degradation.

Local Volume Concentration, Packing Domains and Scaling Properties of Chromatin.

We propose the Self Returning Excluded Volume (SR-EV) model for the structure of chromatin based on stochastic rules and physical interactions that is able to capture the observed behavior across imaging and sequencing based measures of chromatin organization. The SR-EV model takes the return rules of the Self Returning Random Walk, incorporates excluded volume interactions, chain connectivity and expands the length scales range from 10 nm to over 1 micron. The model is computationally fast and we created thousands of configurations that we grouped in twelve different ensembles according to the two main parameters of the model. The analysis of the configurations was done in a way completely analogous to the experimental treatments used to determine chromatin volume concentration, contact probability, packing domain identification and size characterization, and packing scaling behavior. We find a robust agreement between the theoretical and experimental results. The overall organization of the model chromatin is corrugated, with dense packing domains alternating with a very dilute regions in a manner that resembles the mixing of two disordered bi-continuous phases. The return rules combined with excluded volume interactions lead to the formation of packing domains. We observed a transition from a short scale regime to a long scale regime occurring at genomic separations of ~ 4 × 104 base pairs or ~ 100 nm in distance. The contact probability reflects this transition with a change in the scaling exponent from larger than -1 to approximately -1. The analysis of the pair correlation function reveals that chromatin organizes following a power law scaling with exponent D∈{2,3} in the transition region between the short and long distance regimes.

Acid-Base Equilibrium and Dielectric Environment Regulate Charge in Supramolecular Nanofibers.

Peptide amphiphiles are a class of molecules that can self-assemble into a variety of supramolecular structures, including high-aspect-ratio nanofibers. It is challenging to model and predict the charges in these supramolecular nanofibers because the ionization state of the peptides are not fixed but liable to change due to the acid-base equilibrium that is coupled to the structural organization of the peptide amphiphile molecules. Here, we have developed a theoretical model to describe and predict the amount of charge found on self-assembled peptide amphiphiles as a function of pH and ion concentration. In particular, we computed the amount of charge of peptide amphiphiles nanofibers with the sequence C 16 - V 2 A 2 E 2. In our theoretical formulation, we consider charge regulation of the carboxylic acid groups, which involves the acid-base chemical equilibrium of the glutamic acid residues and the possibility of ion condensation. The charge regulation is coupled with the local dielectric environment by allowing for a varying dielectric constant that also includes a position-dependent electrostatic solvation energy for the charged species. We find that the charges on the glutamic acid residues of the peptide amphiphile nanofiber are much lower than the same functional group in aqueous solution. There is a strong coupling between the charging via the acid-base equilibrium and the local dielectric environment. Our model predicts a much lower degree of deprotonation for a position-dependent relative dielectric constant compared to a constant dielectric background. Furthermore, the shape and size of the electrostatic potential as well as the counterion distribution are quantitatively and qualitatively different. These results indicate that an accurate model of peptide amphiphile self-assembly must take into account charge regulation of acidic groups through acid-base equilibria and ion condensation, as well as coupling to the local dielectric environment.

Theoretical Modeling of Chemical Equilibrium in Weak Polyelectrolyte Layers on Curved Nanosystems.

Surface functionalization with end-tethered weak polyelectrolytes (PE) is a versatile way to modify and control surface properties, given their ability to alter their degree of charge depending on external cues like pH and salt concentration. Weak PEs find usage in a wide range of applications, from colloidal stabilization, lubrication, adhesion, wetting to biomedical applications such as drug delivery and theranostics applications. They are also ubiquitous in many biological systems. Here, we present an overview of some of the main theoretical methods that we consider key in the field of weak PE at interfaces. Several applications involving engineered nanoparticles, synthetic and biological nanopores, as well as biological macromolecules are discussed to illustrate the salient features of systems involving weak PE near an interface or under (nano)confinement. The key feature is that by confining weak PEs near an interface the degree of charge is different from what would be expected in solution. This is the result of the strong coupling between structural organization of weak PE and its chemical state. The responsiveness of engineered and biological nanomaterials comprising weak PE combined with an adequate level of modeling can provide the keys to a rational design of smart nanosystems.

Physical and data structure of 3D genome.

With the textbook view of chromatin folding based on the 30-nm fiber being challenged, it has been proposed that interphase DNA has an irregular 10-nm nucleosome polymer structure whose folding philosophy is unknown. Nevertheless, experimental advances suggest that this irregular packing is associated with many nontrivial physical properties that are puzzling from a polymer physics point of view. Here, we show that the reconciliation of these exotic properties necessitates modularizing three-dimensional genome into tree data structures on top of, and in striking contrast to, the linear topology of DNA double helix. These functional modules need to be connected and isolated by an open backbone that results in porous and heterogeneous packing in a quasi-self-similar manner, as revealed by our electron and optical imaging. Our multiscale theoretical and experimental results suggest the existence of higher-order universal folding principles for a disordered chromatin fiber to avoid entanglement and fulfill its biological functions.

Dynamic Crowding Regulates Transcription.

The nuclear environment is highly crowded by biological macromolecules, including chromatin and mobile proteins, which alter the kinetics and efficiency of transcriptional machinery. These alterations have been described, both theoretically and experimentally, for steady-state crowding densities; however, temporal changes in crowding density ("dynamic crowding") have yet to be integrated with gene expression. Dynamic crowding is pertinent to nuclear biology because processes such as chromatin translocation and protein diffusion lend to highly mobile biological crowders. Therefore, to capture such dynamic crowding and investigate its influence on transcription, we employ a three-pronged, systems-molecular approach. A system of chemical reactions represents the transcription pathway, the rates of which are determined by molecular-scale simulations; Brownian dynamics and Monte Carlo simulations quantify protein diffusion and DNA-protein binding affinity, dependent on macromolecular density. Altogether, this approach shows that transcription depends critically on dynamic crowding as the gene expression resultant from dynamic crowding can be profoundly different than that of steady-state crowding. In fact, expression levels can display both amplification and suppression and are notably different for genes or gene populations with different chemical and structural properties. These properties can be exploited to impose circadian expression, which is asymmetric and varies in strength, or to explain expression in cells under biomechanical stress. Therefore, this work demonstrates that dynamic crowding nontrivially alters transcription kinetics and presents dynamic crowding within the bulk nuclear nanoenvironment as a novel regulatory framework for gene expression.

Effect of Polymer Surface Modification of Superparamagnetic Iron Oxide Nanoparticle Dispersions in High Salinity Environments.

Superparamagnetic nanoparticles (SPIONs) can be used as nuclear magnetic resonance (NMR) signal enhancement agents for petroleum exploration. This enhancement effect is uniform if SPIONs are monodisperse in size and in composition; yet it is challenging to synthesize monodisperse particles that do not aggregate in high salinity petroleum brine. Here, we report a method to synthesize individual SPIONs coated with tunable surface coating densities of poly(2-acrylamido-2-methyl-1-propanesulfonic acid (pAMPS) with a catechol end-group (pAMPS*). To establish parameters under which pAMPS*-coated SPIONS do not aggregate, we compared computational predictions with experimental results for variations in pAMPS* chain length and surface coverage. Using this combined theoretical and experimental approach, we show that singly dispersed SPIONs remained stabilized in petroleum brine for up to 75 h with high surface density pAMPS*.

pH-Dependent structure of water-exposed surfaces of CdSe quantum dots.

Increasing negative charge density at the surfaces of CdSe quantum dots (QDs) effects a bathochromic shift of their ground state optical spectra with increasing pH due to electrostatic and chemical modifications at the QD surface. These modifications are enabled by weakly-bound ligands that expose the surface to the aqueous environment.

Effect of calcium ions on the interactions between surfaces end-grafted with weak polyelectrolytes.

We study the interactions between two planar surfaces end-tethered with poly(acrylic acid) polymers in electrolyte solutions containing calcium ions, using a molecular theory. We found that by adding divalent calcium ions to an aqueous solution of monovalent ions leads to a dramatic reduction in the size and range of effective interactions between the two polymer layers. This is caused by the formation of favorable calcium bridges, i.e., complexes of one calcium ion and two carboxylic acid monomers, that reduce the effective charge of the polymer layers and, at sufficient calcium ion concentrations, can cause the polymer layers to collapse. For calcium ion concentrations above approximately 1 mM, the repulsions between the opposing end-grafted surfaces disappear and attractions occur. These attractions are correlated with the occurrence of interlayer divalent calcium bridges and do not occur for poly(acrylic acid) layers in contact with reservoir solutions containing only monovalent ions. This result indicates the suitability of divalent calcium ions to control and change the interaction range and strength, which is a useful property that is desirable in the design of stimuli-responsive nanomaterials.

Highly sensitive gating in pH-responsive nanochannels as a result of ionic bridging and nanoconfinement.

Sensitive switching between OFF and ON states is a desirable feature in stimuli-responsive nanopores and nanochannels. In this work, we show that nanogates modified with weak polyelectrolytes can be controlled by multivalent counterions and, more remarkably, can exhibit sensitive pH-gating due to an interplay between ionic bridging and nanoconfinement. We demonstrate these general features by systematically studying the effects of Ca2+ binding on the molecular organization and transport properties of poly(acrylic acid)-functionalized nanochannels. To this end, we extend and apply a molecular theory that has been successfully used in the past to describe and predict the behavior of pH-responsive polymers. Two main results emerge from the present study: first, the addition of Ca2+ to the bulk solution changes-in a concentration-dependent manner-both the ionization and structural state of the end-tethered polymers, affecting, respectively, the ionic conductivity and physical opening of the nanochannel. Second, in the presence of Ca2+ and under specific nanoconfinement conditions, the grafted channel can exhibit a sensitive response to pH in the transition between closed and open states. We attribute this sensitivity to bistability in the system. Our results also indicate that the polymer layer can undergo a microphase separation when the brush collapses on the nanochannel walls. Taken together, these findings suggest the possibility of designing nanogates that can respond to marginal changes in pH or multivalent ion concentration. Such nanodevices may be used as logic gates or for any application that requires a sensitive control over the ions, molecules, or nanoparticles flowing through them.

Covalent-supramolecular hybrid polymers as muscle-inspired anisotropic actuators.

Skeletal muscle provides inspiration on how to achieve reversible, macroscopic, anisotropic motion in soft materials. Here we report on the bottom-up design of macroscopic tubes that exhibit anisotropic actuation driven by a thermal stimulus. The tube is built from a hydrogel in which extremely long supramolecular nanofibers are aligned using weak shear forces, followed by radial growth of thermoresponsive polymers from their surfaces. The hierarchically ordered tube exhibits reversible anisotropic actuation with changes in temperature, with much greater contraction perpendicular to the direction of nanofiber alignment. We identify two critical factors for the anisotropic actuation, macroscopic alignment of the supramolecular scaffold and its covalent bonding to polymer chains. Using finite element analysis and molecular calculations, we conclude polymer chain confinement and mechanical reinforcement by rigid supramolecular nanofibers are responsible for the anisotropic actuation. The work reported suggests strategies to create soft active matter with molecularly encoded capacity to perform complex tasks.

The interplay of nanointerface curvature and calcium binding in weak polyelectrolyte-coated nanoparticles.

When engineering nanomaterials for application in biological systems, it is important to understand how multivalent ions, such as calcium, affect the structural and chemical properties of polymer-modified nanoconstructs. In this work, a recently developed molecular theory was employed to study the effect of surface curvature on the calcium-induced collapse of end-tethered weak polyelectrolytes. In particular, we focused on cylindrical and spherical nanoparticles coated with poly(acrylic acid) in the presence of different amounts of Ca2+ ions. We describe the structural changes that grafted polyelectrolytes undergo as a function of calcium concentration, surface curvature, and morphology. The polymer layers collapse in aqueous solutions that contain sufficient amounts of Ca2+ ions. This collapse, due to the formation of calcium bridges, is not only controlled by the calcium ion concentration but also strongly influenced by the curvature of the tethering surface. The transition from a swollen to a collapsed layer as a function of calcium concentration broadens and shifts to lower amounts of calcium ions as a function of the radius of cylindrical and spherical nanoparticles. The results show how the interplay between calcium binding and surface curvature governs the structural and functional properties of the polymer molecules. This would directly impact the fate of weak polyelectrolyte-coated nanoparticles in biological environments, in which calcium levels are tightly regulated. Understanding such interplay would also contribute to the rational design and optimization of smart interfaces with applications in, e.g., salt-sensitive and ion-responsive materials and devices.

Competitive calcium ion binding to end-tethered weak polyelectrolytes.

We have developed a molecular model to describe the structural changes and potential collapse of weak polyelectrolyte layers end-tethered to planar surfaces and spherical nanoparticles as a function of pH and divalent ion concentration. In particular, we describe the structural changes of polymer-coated nanoparticles end-tethered to copolymers of poly(acrylic acid) (pAA) and poly arcrylamido-2-methylpropane sulfonate (pAMPS) in the presence of Ca2+ ions. We find that end-grafted poly(acrylic acid) layers will collapse in aqueous solutions containing sufficient amounts of Ca2+ ions, while polymers and copolymers with sufficient AMPS monomers will not collapse. The collapse of end-tethered pAA is due to the formation of calcium bridges between two acrylic acid monomers and one calcium ion. On the other hand pAMPS layers do not collapse due to the lack of calcium bridges. The collapse of pAA layers is strongly dependent on the pH as well as divalent and monovalent salt concentrations of the environment. The collapse is also strongly influenced by the curvature of the tethering surface.

Structural behavior of competitive temperature and pH-responsive tethered polymer layers.

Herein, we develop a molecular theory to examine a class of pH and temperature-responsive tethered polymer layers. The response of pH depends on intramolecular charge repulsion of weakly acidic monomers and the response of temperature depends on hydrogen bonding between polymer monomers and water molecules akin to the behavior of water-soluble polymers such as PEG (poly-ethylene glycol) or NIPAAm (n-isopropylacrylamide). We investigate the changes in structural behavior that result for various end-tethered copolymers: pH/T responsive monomers alone, in alternating sequence with hydrophobic monomers, and as 50/50 diblocks with hydrophobic monomers. We find that the sequence and location of hydrophobic units play a critical role in the thermodynamic stability and structural behavior of these responsive polymer layers. Additionally, the polymers exhibit tunable collapse when varying the surface coverage, location and sequence of hydrophobic units as a function of temperature and pH. As far as we know, our results present the first molecularly detailed theory for end-tethered polymers that are both pH and temperature-responsive via hydrogen bonding. We propose that this work holds predictive power for the guided design of future biomaterials.

The role of solution conditions in the bacteriophage PP7 capsid charge regulation.

We investigate and quantify the effects of pH and salt concentration on the charge regulation of the bacteriophage PP7 capsid. These effects are found to be extremely important and substantial, introducing qualitative changes in the charge state of the capsid such as a transition from net-positive to net-negative charge depending on the solution pH. The overall charge of the virus capsid arises as a consequence of a complicated balance with the chemical dissociation equilibrium of the amino acids and the electrostatic interaction between them, and the translational entropy of the mobile solution ions, i.e., counterion release. We show that to properly describe and predict the charging equilibrium of viral capsids in general, one needs to include molecular details as exemplified by the acid-base equilibrium of the detailed distribution of amino acids in the proteinaceous capsid shell.

Adsorption of superparamagnetic iron oxide nanoparticles on silica and calcium carbonate sand.

Superparamagnetic iron oxide (SPIO) nanoparticles have the potential to be used in the characterization of porous rock formations in oil fields as a contrast agent for NMR logging because they are small enough to traverse through nanopores and enhance contrast by shortening NMR T2 relaxation time. However, successful development and application require detailed knowledge of particle stability and mobility in reservoir rocks. Because nanoparticle adsorption to sand (SiO2) and rock (often CaCO3) affects their mobility, we investigated the thermodynamic equilibrium adsorption behavior of citric acid-coated SPIO nanoparticles (CA SPIO NPs) and poly(ethylene glycol)-grafted SPIO nanoparticles (PEG SPIO NPs) on SiO2 (silica) and CaCO3 (calcium carbonate). Adsorption behavior was determined at various pH and salt conditions via chemical analysis and NMR, and the results were compared with molecular theory predictions. Most of the NPs were recovered from silica, whereas far fewer NPs were recovered from calcium carbonate because of differences in the mineral surface properties. NP adsorption increased with increasing salt concentration: this trend was qualitatively explained by molecular theory, as was the role of the PEG grafting in preventing NPs adsorption. Quantitative disagreement between the theoretical predictions and the data was due to NP aggregation, especially at high salt concentration and in the presence of calcium carbonate. Upon aggregation, NP concentrations as determined by NMR T2 were initially overestimated and subsequently corrected using the relaxation rate 1/T2, which is a function of aggregate size and fractal dimension of the aggregate. Our experimental validation of the theoretical predictions of NP adsorption to minerals in the absence of aggregation at various pH and salt conditions demonstrates that molecular theory can be used to determine interactions between NPs and relevant reservoir surfaces. Importantly, this integrated experimental and theoretical approach can be used to gain insight into NP mobility in the reservoir.

Adsorption of acid and polymer coated nanoparticles: a statistical thermodynamics approach.

A molecular theoretical description is developed to describe the adsorption of nanoparticles (NPs) that are coated with polymers and functionalized with (surface) acid groups. Results are presented for the adsorption onto both negatively and positively charged surfaces as a function of pH and salt concentration, polymer coating, and NP size. An important finding is that nanoparticles that are coated with weak charge regulating acid molecules such as citric acid develop an asymmetric charge distribution close to a charged surface, due to their finite size. Depending on the sign of the surface charge of the adsorbing surface, a nanoparticle close to the surface either gains more charge or loses charge compared to its "bulk" degree of charge. This in turn influences the amount of NPs that adsorb. The effect of adsorption of negatively charged NPs onto a positively charged surface shows a nonmonotonical variation with pH. The described charging mechanism reveals that details such as size of the NP and acid distribution on the NP need to be considered to provide an accurate understanding of the adsorption process.

Geometric curvature controls the chemical patchiness and self-assembly of nanoparticles.

When organic molecules are tethered onto non-spherical nanoparticles, their chemical properties depend on the particles' local curvature and shape. Based on this observation, we show here that it is possible to engineer chemical patchiness across the surface of a non-spherical nanoparticle using a single chemical species. In particular, when acidic ligands are used, regions of the particle surface with different curvature become charged at different pH values of the surrounding solution. This interplay between particle shape and local electrostatics allows for fine control over nanoscale self-assembly leading to structures with varying degrees of complexity. These structures range from particle cross-stacks to open-lattice crystals, the latter with pore sizes on the order of tens of nanometres, that is, at the lower synthetic limits of metallic mesoporous materials.

Stability of superparamagnetic iron oxide nanoparticles at different pH values: experimental and theoretical analysis.

The detection of superparamagnetic nanoparticles using NMR logging has the potential to provide enhanced contrast in oil reservoir rock formations. The stability of the nanoparticles is critical because the NMR relaxivity (R(2) ≡ 1/T(2)) is dependent on the particle size. Here we use a molecular theory to predict and validate experimentally the stability of citric acid-coated/PEGylated iron oxide nanoparticles under different pH conditions (pH 5, 7, 9, 11). The predicted value for the critical surface coverage required to produce a steric barrier of 5k(B)T for PEGylated nanoparticles (MW 2000) was 0.078 nm(-2), which is less than the experimental value of 0.143 nm(-2), implying that the nanoparticles should be stable at all pH values. Dynamic light scattering (DLS) measurements showed that the effective diameter did not increase at pH 7 or 9 after 30 days but increased at pH 11. The shifts in NMR relaxivity (from R(2) data) at 2 MHz agreed well with the changes in hydrodynamic diameter obtained from DLS data, indicating that the aggregation behavior of the nanoparticles can be easily and quantitatively detected by NMR. The unexpected aggregation at pH 11 is due to the desorption of the surface coating (citric acid or PEG) from the nanoparticle surface not accounted for in the theory. This study shows that the stability of the nanoparticles can be predicted by the theory and detected by NMR quantitatively, which suggests the nanoparticles to be a possible oil-field nanosensor.

Assembly of reconfigurable one-dimensional colloidal superlattices due to a synergy of fundamental nanoscale forces.

We report that triangular gold nanoprisms in the presence of attractive depletion forces and repulsive electrostatic forces assemble into equilibrium one-dimensional lamellar crystals in solution with interparticle spacings greater than four times the thickness of the nanoprisms. Experimental and theoretical studies reveal that the anomalously large d spacings of the lamellar superlattices are due to a balance between depletion and electrostatic interactions, both of which arise from the surfactant cetyltrimethylammonium bromide. The effects of surfactant concentration, temperature, ionic strength of the solution, and prism edge length on the lattice parameters have been investigated and provide a variety of tools for in situ modulation of these colloidal superstructures. Additionally, we demonstrate a purification procedure based on our observations that can be used to efficiently separate triangular nanoprisms from spherical nanoparticles formed concomitantly during their synthesis.