Excluded Volume Interactions Research Articles

Stars, combs and bottlebrushes of elastic single-chain nanoparticles

Hierarchical self-assembly of structural elements gives rise to superstructures often with outstanding properties when compared to individual elements, as first observed in nature. While folding of individual synthetic chains leads to discrete single-chain nanoparticles (SCNPs) of significant interest for a number of applications, its full potential utility through integration into well-defined superstructures is recently being recognized. Remarkably, SCNPs in good solvent resemble randomly branched polymers with ideal connectivity in a theta-solvent or percolating clusters with screened excluded-volume interactions. Herein we consider the integration of SCNPs into star, comb and bottlebrush topologies and investigate the dimensions of the resulting superstructures under different conditions (good solvent, ideal conformations, 1D- and 2D-confinement in nanopores and nanoslits, anchored to flat surfaces). A detailed comparison of the equilibrium conformational properties of star, comb and bottlebrush polymers composed of elastic SCNPs to those of equivalent topologies based on linear chains is provided. This analysis reveals the effect of hierarchical topology on superstructure dimensions in several relevant environments, as well as how the structural parameters of the SCNPs influence the location of the comb-to-bottlebrush transition as a function of grafting density. The degree of intra-chain cross-linking arises as an additional parameter for controlling the local and global dimensions of stars, combs and bottlebrushes of SCNPs. • Integration of single-chain nanoparticles (SCNPs) into superstructures. • Dimensions of stars, combs and bottlebrushes composed of SCNPs. • Equilibrium size in good solvent and ideal conformations. • Effect of 1D and 2D-confinement on conformational properties.

Dissipative Particle Dynamics Simulation of Nanoparticle Diffusion in a Crosslinked Polymer Network.

Dissipative particle dynamics simulation is conducted to investigate the diffusion of a nanoparticle in a crosslinked polymer network based on a bead-spring model. Focusing on cases where the particle is comparable in size to the network mesh, we find from rigid networks that the excluded-volume and hydrodynamic interaction effects associated with solvent beads lead to lubricity, which assists the particle to slip through an opening into the adjacent cell. For flexible networks, the hopping mechanism for particle escape becomes less pronounced with higher network flexibility due to either a smaller spring constant or slacker strands, each consisting of more beads. This behavior could be explained by the larger cell size fluctuation and its slower relaxation, whereby large enough openings temporarily formed are longer-lived, increasing the chance for particle hopping.

Electric double layer of spherical pH-responsive polyelectrolyte brushes in an electrolyte solution: A strong stretching theory accounting for excluded volume interaction and mass action law

In this paper, we study the electrostatics of pH-responsive polyelectrolyte-grafted spherical particles by using a strong stretching theory that takes into account the excluded volume interaction and the density of chargeable sites on the polyelectrolyte molecules. Based on free energy formalism, we obtain self-consistent field equations for determining the structure and electrostatics of spherical polyelectrolyte brushes. First, we find that the smaller the radius of the inner core, the longer the height of the polyelectrolyte brush. Then, we also prove that an increase in the excluded volume interaction yields a swelling of the polyelectrolyte brush height. In addition, we demonstrate how the effect of pH, bulk ionic concentration, and lateral separation between adjacent polyelectrolyte chains on the electrostatic properties of a spherical polyelectrolyte brush is affected by the radius of the inner core, the excluded volume interaction, and the chargeable site density.

Structural and electrostatic properties between pH-responsive polyelectrolyte brushes studied by augmented strong stretching theory.

In this paper, we study electrostatic and structural properties between pH-responsive polyelectrolyte brushes by using a strong stretching theory accounting for excluded volume interactions, the density of polyelectrolyte chargeable sites, and the Born energy difference between the inside and outside of the brush layer. In a free energy framework, we obtain self-consistent field equations to determine electrostatic properties between two pH-responsive polyelectrolyte brushes. We elucidate that in the region between two pH-responsive polyelectrolyte brushes, electrostatic potential at the centerline and osmotic pressure increase not only with excluded volume interaction but also with the density of chargeable sites on a polyelectrolyte molecule. Importantly, we clarify that when two pH-responsive polyelectrolyte brushes approach each other, the brush thickness becomes short and that a large excluded volume interaction and a large density of chargeable sites yield the enhanced contract of polyelectrolyte brushes. In addition, we also demonstrate how the influence of such quantities as pH, the number of Kuhn monomers, the density of charged sites, the lateral separation between adjacent polyelectrolyte brushes, and Kuhn length on the electrostatic and structural properties between the two polyelectrolyte brushes is affected by the exclusion volume interaction. Finally, we investigate the influence of the Born energy difference on the thickness of polyelectrolyte brushes and the osmotic pressure between two pH-responsive polyelectrolyte brushes.

Partitioning of ribonucleoprotein complexes from the cellular actin cortex.

The cell cortex plays a crucial role in cell mechanics, signaling, and development. However, little is known about the influence of the cortical meshwork on the spatial distribution of cytoplasmic biomolecules. Here, we describe a fluorescence microscopy method with the capacity to infer the intracellular distribution of labeled biomolecules with subresolution accuracy. Unexpectedly, we find that RNA binding proteins are partially excluded from the cytoplasmic volume adjacent to the plasma membrane that corresponds to the actin cortex. Complementary diffusion measurements of RNA-protein complexes suggest that a rudimentary model based on excluded volume interactions can explain this partitioning effect. Our results suggest the actin cortex meshwork may play a role in regulating the biomolecular content of the volume immediately adjacent to the plasma membrane.

Forced microrheology of active colloids

Particle-tracking microrheology of dilute active (self-propelled) colloidal suspensions is studied by considering the external force required to maintain the steady motion of an immersed constant-velocity colloidal probe. If the probe speed is zero, the suspension microstructure is isotropic but exhibits a boundary accumulation of active bath particles at contact due to their self-propulsion. As the probe moves through the suspension, the microstructure is distorted from the nonequilibrium isotropic state, which allows us to define a microviscosity for the suspension using the Stokes drag law. For a slow probe, we show that active suspensions exhibit a swim-thinning behavior in which their microviscosity is gradually lowered from that of passive suspensions as the swim speed increases. When the probe speed is fast, the suspension activity is obscured by the rapid advection of the probe and the measured microviscosity is indistinguishable from that of passive suspensions. Generally for finite activity, the suspension exhibits a velocity-thinning behavior—though with a zero-velocity plateau lower than passive suspensions—as a function of the probe speed. These behaviors originate from the interplay between the suspension activity and the hard-sphere excluded-volume interaction between the probe and a bath particle.

Computing time-periodic steady-state currents via the time evolution of tensor network states.

We present an approach based upon binary tree tensor network (BTTN) states for computing steady-state current statistics for a many-particle 1D ratchet subject to volume exclusion interactions. The ratcheted particles, which move on a lattice with periodic boundary conditions subject to a time-periodic drive, can be stochastically evolved in time to sample representative trajectories via a Gillespie method. In lieu of generating realizations of trajectories, a BTTN state can variationally approximate a distribution over the vast number of many-body configurations. We apply the density matrix renormalization group algorithm to initialize BTTN states, which are then propagated in time via the time-dependent variational principle (TDVP) algorithm to yield the steady-state behavior, including the effects of both typical and rare trajectories. The application of the methods to ratchet currents is highlighted, but the approach extends naturally to other interacting lattice models with time-dependent driving. Although trajectory sampling is conceptually and computationally simpler, we discuss situations for which the BTTN TDVP strategy can be beneficial.

Arrested-motility states in populations of shape-anisotropic active Janus particles.

The emergence of large-scale collective phenomena from simple interactions between individual units is a hallmark of active matter systems. Active colloids with alignment-dominated interparticle interactions tend to develop orientational order and form motile coherent states, such as flocks and swarms. Alternatively, a combination of self-propulsion and excluded-volume interactions results in self-trapping and active phase separation into dense clusters. Here, we reveal unconventional arrested-motility states in ensembles of active discoidal particles powered by induced-charge electrophoresis. Combining experiments and computational modeling, we demonstrate that the shape asymmetry of the particles promotes the hydrodynamically assisted formation of active particles' bound states in a certain range of excitation parameters, ultimately leading to a spontaneous collective state with arrested motility. Unlike the jammed clusters obtained through self-trapping, the arrested-motility phase remains sparse, dynamic, and reconfigurable. The demonstrated mechanism of phase separation seeded by bound state formation in ensembles of oblate active particles is generic and should be applicable to other active colloidal systems.

Electrostatic Repulsion Slows Relaxations of Polyelectrolytes in Semidilute Solutions

We investigate the structure and dynamics of unentangled semidilute solutions of sodium polystyrenesulfonate (NaPSS) using small-angle neutron scattering (SANS) and neutron spin-echo (NSE) spectroscopy. The effects of electrostatic interactions and chain structure are examined as a function of ionic strength and polymer concentration, respectively. The SANS profiles exhibit a characteristic structural peak, signature of polyelectrolyte solutions, that can be fit with a combination of a semiflexible chain with excluded volume interactions form factor and a polymer reference interaction site model (PRISM) structure factor. We confirm that electrostatic interactions vary with ionic strength across solutions with similar geometries. The segmental relaxations from NSE deviate from theoretical predictions from Zimm and exhibit two scaling behaviors, with the crossover between the two regimes taking place around the characteristic structural peak. The chain dynamics are suppressed across the length scale of the correlation blob, and inversely related to the structure factor. These observations suggest that the highly correlated nature of polyelectrolytes presents an additional energy barrier that leads to de Gennes narrowing behavior.

Size-Dependent Interplay of Volume Exclusion Versus Soft Interactions: Cytochrome c in Macromolecular Crowded Environment.

Even though there are a great number of possible conformational states, how a protein generated as a linear unfolded polypeptide efficiently folds into its physiologically active form remained a fascinating and unanswered enigma inside crowded conditions of cells. In this study, various spectroscopic techniques have been exploited to know and understand the effect and mechanism of action of two different sizes of polyethylene glycols, or PEGs (molecular mass ∼10 and ∼20kilo Daltons, kDa), on cytochrome c (cyt c). The outcomes showed that small size of the PEG leads to perturbation of the protein structure, and conversely, large size of the PEG has stabilizing effect on cyt c. Moreover, binding measurements showed that small size of PEG interacts strongly via soft interactions compared to the larger size of PEG, the latter being governed more by excluded volume effect or preferential exclusion from the protein. Overall, this finding suggests that conformations of protein may be influenced in cellular crowded conditions via interactions which depend upon the size of molecule in the environment. This study proposes that both volume exclusion and soft (chemical) interactions governs the protein's conformation and functional activities. The cellular environment's internal architecture as evident from crowder size and shape in this study has a significant role.

Effects of Non-Ionic Micelles on the Acid-Base Equilibria of a Weak Polyelectrolyte.

Weak polyelectrolytes (WPEs) are widely used as pH-responsive materials, pH modulators and charge regulators in biomedical and technological applications that involve multi-component fluid environments. In these complex fluids, coupling between (often weak) interactions induced by micelles, nanoparticles and molecular aggregates modify the pKa as compared to that measured in single component solutions. Here we investigated the effect of coupling between hydrogen bonding and excluded volume interactions on the titration curves and pKa of polyacrylic acid (PAA) in solutions comprising PEO-based micelles (Pluronics and Brij-S20) of different size and volume fraction. Titration experiments of dilute, salt-free solutions of PAA (5 kDa, 30 kDa and 100 kDa) at low degree of polymer ionization (α < 0.25) drive spatial re-organization of the system, reduce the degree of ionization and consequentially increase the pKa by up to ~0.7 units. These findings indicate that the actual degree of ionization of WPEs measured in complex fluids is significantly lower (at a given pH) than that measured in single-component solutions.

Evaluation of loop formation dynamics in a chromatin fiber during chromosome condensation

Abstract Chromatin fibers composed of DNA and proteins fold into consecutive loops to form rod-shaped chromosomes in mitosis. Although the loop growth dynamics has been investigated in several studies, its detailed processes are unclear. Here, we describe the time evolution of the loop length for thermal-driven loop growth processes as an iterative map by calculating the physical quantities involved in the processes. We quantify the energy during the chromatin loop formation by calculating the free energies of unlooped and looped chromatins using the Domb–Joyce model of a lattice polymer chain incorporating the bending elasticity for thermal-driven loop growth processes. The excluded volume interaction among loops is integrated by employing the mean-field theory. We compare the loop formation energy with the thermal energy and evaluate the growth of the loop length via thermal fluctuation. By assuming the dependence of the excluded volume parameter on the loop length, we construct an iterative map for the loop growth dynamics. The map demonstrates that the growth length of the loop for a single reaction cycle decreases with time to reach the condensin size, where the loop growth dynamics can be less stochastic and be regarded as the direct power stroke of condensin as a kind of motor protein.

Physics-constrained Bayesian inference of state functions in classical density-functional theory.

We develop a novel data-driven approach to the inverse problem of classical statistical mechanics: Given the experimental data on the collective motion of a classical many-body system, how does one characterize the free energy landscape of that system? By combining non-parametric Bayesian inference with physically motivated constraints, we develop an efficient learning algorithm that automates the construction of approximate free-energy functionals. In contrast to optimization-based machine learning approaches, which seek to minimize a cost function, the central idea of the proposed Bayesian inference is to propagate a set of prior assumptions through the model, derived from physical principles. The experimental data are used to probabilistically weigh the possible model predictions. This naturally leads to humanly interpretable algorithms with full uncertainty quantification of predictions. In our case, the output of the learning algorithm is a probability distribution over a family of free energy functionals, consistent with the observed particle data. We find that surprisingly small data samples contain sufficient information for inferring highly accurate analytic expressions of the underlying free-energy functionals, making our algorithm highly data efficient. In particular, we consider classical particle systems with excluded volume interactions, which are ubiquitous in nature, while being highly challenging in terms of free energy modeling. We validate our approach on the paradigmatic case of one-dimensional fluid and develop inference algorithms for the canonical and grand-canonical statistical-mechanical ensembles. Extensions to higher dimensional systems are conceptually straightforward, while standard coarse-graining techniques allow one to easily incorporate attractive interactions.

Interface topology and evolution of particle patterns on deformable drops in turbulence

The capture of neutrally buoyant, sub-Kolmogorov particles at the interface of deformable drops in turbulent flow and the subsequent evolution of particle surface distribution are investigated. Direct numerical simulation of turbulence, phase-field modelling of the drop interface dynamics and Lagrangian particle tracking are used. Particle distribution is obtained considering excluded-volume interactions, i.e. by enforcing particle collisions. Particles are initially dispersed in the carrier flow and are driven in time towards the surface of the drops by jet-like turbulent fluid motions. Once captured by the interfacial forces, particles disperse on the surface. Excluded-volume interactions bring particles into long-term trapping regions where the average surface velocity divergence sampled by the particles is zero. These regions correlate well with portions of the interface characterized by higher-than-mean curvature, indicating that modifications of the surface tension induced by the presence of very small particles will be stronger in the highly convex regions of the interface.

Molecular dynamics studies of entropic elasticity of condensed lattice networks connected with uniform functionality f = 4.

To study the linear region of entropic elasticity, we considered the simplest physical model possible and extracted the linear entropic regime by using the least squares fit and the minimum of the mean absolute error. With regard to the effect of the fluctuation of the strand length Ns, the strand length with fluctuation was set to a form proportional to (1.0 + C (R - 0.5)), where R is a uniform random number between 0 and 1 and C is the amplitude of fluctuation. This form enabled us to analytically calculate the fluctuation dependence of the elastic modulus G. To reveal the linear regions of entropic elasticity as a function of the strand length between neighboring nodes in lattices, molecular dynamics (MD) simulations of condensed lattice networks with harmonic bonds without the excluded volume interactions were performed. Stress-strain curves were estimated by performing uniaxial stretching MD simulations under periodic boundary conditions with a bead number density of 0.85. First, we used a diamond lattice with functionality f = 4. The linear region of the entropic elasticity was found to become larger with the increasing number of beads in a strand Ns. For Ns = 100, the linear region had a strain of up to 8 for a regular diamond lattice. We investigated the effect of strand length fluctuation on the diamond lattice, and we confirmed that the equilibrium shear modulus G increases as the obtained analytical prediction and the linear entropic region in the stress-strain curves becomes narrower with increasing fluctuation of Ns. To investigate the difference in network topology with the same functionality f and uniform strand length Ns, we performed MD simulations on regular networks of the BC-8 structure with f = 4 prepared from the ab initio DFT calculations of carbon at high pressure. We found that the elastic behavior depends on the network connectivity (i.e., topology). This indicates that the network topology plays an important role in the emergence of nonlinearity owing to the crossover from entropic to energetic elasticity.

Design of self-assembling mesoscopic Goldberg polyhedra.

Palladium ions complexed with nonlinear bidentate ligands have been shown to form hollow, spherical shells with high symmetries. We show that such structures can be reproduced using model anisotropic mesoscale building blocks featuring excluded volume and long-range ionic interactions. A linear building block with a central charged particle, in combination with a bent 'ligand' particle with opposite charges at the ends is sufficient to drive the system towards planar coordination, and the charge ratio determines the coordination number. Similar to the molecular systems, the bend in the 'ligand' particle determines the curvature of the shells that these building blocks prefer. Besides reproducing exotic structures such as M30L60 and M48L96 tetravalent Goldberg polyhedra, we identify highly cooperative single transition state rearrangements between low-energy competing structures as well, corresponding to rotatory motions of a planar subunit within the spherical shell.

Simulation of Different Three-Dimensional Models of Whole Interphase Nuclei Compared to Experiments- A Consistent Scale-Bridging Simulation Framework for Genome Organization.

The three-dimensional architecture of chromosomes, their arrangement, and dynamics within cell nuclei are still subject of debate. Obviously, the function of genomes-the storage, replication, and transcription of genetic information-has closely coevolved with this architecture and its dynamics, and hence are closely connected. In this work a scale-bridging framework investigates how of the 30nm chromatin fibre organizes into chromosomes including their arrangement and morphology in the simulation of whole nuclei. Therefore, mainly two different topologies were simulated with corresponding parameter variations and comparing them to experiments: The Multi-Loop-Subcompartment (MLS) model, in which (stable) small loops form (stable) rosettes, connected by chromatin linkers, and the Random-Walk/Giant-Loop (RW/GL) model, in which large loops are attached to a flexible non-protein backbone, were simulated for various loop and linker sizes. The 30nm chromatin fibre was modelled as a polymer chain with stretching, bending and excluded volume interactions. A spherical boundary potential simulated the confinement to nuclei with different radii. Simulated annealing and Brownian Dynamics methods were applied in a four-step decondensation procedure to generate from metaphase decondensated interphase configurations at thermodynamical equilibrium. Both the MLS and the RW/GL models form chromosome territories, with different morphologies: The MLS rosettes result in distinct subchromosomal domains visible in electron and confocal laser scanning microscopic images. In contrast, the big RW/GL loops lead to a mostly homogeneous chromatin distribution. Even small changes of the model parameters induced significant rearrangements of the chromatin morphology. The low overlap of chromosomes, arms, and subchromosomal domains observed in experiments agrees only with the MLS model. The chromatin density distribution in CLSM image stacks reveals a bimodal behaviour in agreement with recent experiments. Combination of these results with a variety of (spatial distance) measurements favour an MLS like model with loops and linkers of 63 to 126kbp. The predicted large spaces between the chromatin fibres allow typically sized biological molecules to reach nearly every location in the nucleus by moderately obstructed diffusion and is in disagreement with the much simplified assumption that defined channels between territories for molecular transport as in the Interchromosomal Domain (ICD) hypothesis exist and are necessary for transport. All this is also in agreement with recent selective high-resolution chromosome interaction capture (T2C) experiments, the scaling behaviour of the DNA sequence, the dynamics of the chromatin fibre, the diffusion of molecules, and other measurements. Also all other chromosome topologies can in principle be excluded. In summary, polymer simulations of whole nuclei compared to experimental data not only clearly favour only a stable loop aggregate/rosette like genome architecture whose local topology is tightly connected to the global morphology and dynamics of the cell nucleus and hence can be used for understanding genome organization also in respect to diagnosis and treatment. This is in agreement with and also leads to a general novel framework of genome emergence, function, and evolution.

Brownian simulations for tetra-gel-type phantom networks composed of prepolymers with bidisperse arm length.

We studied the effect of arm length contrast of prepolymers on the mechanical properties of tetra-branched networks via Brownian dynamics simulations. We employed a bead-spring model without the excluded volume interactions, and we did not consider the solvent explicitly. Each examined 4-arm star branch prepolymer has uneven arm lengths to attain two-against-two (2a2) or one-against-three (1a3) configurations. The arm length contrast was varied from 38-2 to 20-20 for 2a2, and from 5-25 to 65-5 for 1a3, with the fixed total bead number of 81, including the single bead located at the branch point for prepolymers. We distributed 400 molecules in the simulation box with periodic boundary conditions, and the bead number density was fixed at 4. We created polymer networks by cross-end-coupling of equilibrated tetra-branched prepolymers. To mimic the experiments of tetra gels, we discriminated the molecules into two types and allowed the reaction only between different types of molecules at their end beads. The final conversion ratio was more than 99%, at which unreacted dangling ends are negligible. We found that the fraction of double linkage, in which two of the four arms connect a pair of branch points, increases from 3% to 15% by increasing the arm length contrast. We stretched the resultant tetra-type networks to obtain the ratio of mechanically effective strands. We found that the ratio is 96% for the monodisperse system, decreasing to 90% for high arm length contrast. We introduced bond scission according to the bond stretching to observe the network fracture under sufficiently slow elongation. The fracture behavior was not correlated with the fraction of double linkage because the scission occurs at single linkages.

Excluded volume interactions and phase stability in mixtures of hard spheres and hard rods.

In this paper we study excluded volume interactions, the free volume fraction available, and the phase behaviour, in mixtures of hard spheres (HS) and hard rods, modeled as spherocylinders. We use free volume theory (FVT) to predict various physical properties and compare to Monte Carlo computer simulations. FVT is used at two levels. We use the original FVT approach in which it is assumed that the correlations of the HS are not affected by the rods. This is compared to a recent, more rigorous, FVT approach which includes excluded volume interactions between the different components at all levels. We find that the novel rigorous FVT approach agrees well with computer simulation results at the level of free volume available, as well as for the phase stability. The FVT predictions show significant quantitative and qualitative deviations with respect to the original FVT approach. The phase transition curves are systematically at higher rod concentrations than previously predicted. Furthermore, the calculations revealed that a certain asphericity is required to induce isostructural fluid-fluid coexistence and the stability region is highly dependent on the size ratio between the rods and the spheres.

Binding of anisotropic curvature-inducing proteins onto membrane tubes.

Bin/Amphiphysin/Rvs superfamily proteins and other curvature-inducing proteins have anisotropic shapes and anisotropically bend biomembranes. Here, we report how the anisotropic proteins bind the membrane tube and are orientationally ordered using mean-field theory including an orientation-dependent excluded volume. The proteins exhibit a second-order or first-order nematic transition with increasing protein density depending on the radius of the membrane tube. The tube curvatures for the maximum protein binding and orientational order are different and varied by the protein density and rigidity. As the external force along the tube axis increases, a first-order transition from a large tube radius with low protein density to a small radius with high density occurs once, and subsequently, the protein orientation tilts to the tube-axis direction. When an isotropic bending energy is used for the proteins with an elliptic shape, the force-dependence curves become symmetric and the first-order transition occurs twice. This theory quantitatively reproduces the results of meshless membrane simulation for short proteins, whereas deviations are seen for long proteins owing to the formation of protein clusters.