Nonequilibrium switching of segmental states can influence compaction of chromatin.

Knowledge about the dynamic nature of chromatin organization is essential to understand the regulation of processes like DNA transcription and repair. The existing models of chromatin assume that protein organization and chemical states along chromatin are static and the 3D organization is purely a result of protein-mediated intra-chromatin interactions. Here we present a new hypothesis that certain nonequilibrium processes, such as switching of chemical and physical states due to nucleosome assembly/disassembly or gene repression/activation, can also simultaneously influence chromatin configurations. To understand the implications of this inherent nonequilibrium switching, we present a block copolymer model of chromatin, with switching of its segmental states between two states, mimicking active/repressed or protein unbound/bound states. We show that competition between switching timescale Tt, polymer relaxation timescale τp, and segmental relaxation timescale τs can lead to non-trivial changes in chromatin organization, leading to changes in local compaction and contact probabilities. As a function of the switching timescale, the radius of gyration of chromatin shows a non-monotonic behavior with a prominent minimum when Tt ≈ τp and a maximum when Tt ≈ τs. We find that polymers with a small segment length exhibit a more compact structure than those with larger segment lengths. We also find that the switching can lead to higher contact probability and better mixing of far-away segments. Our study also shows that the nature of the distribution of chromatin clusters varies widely as we change the switching rate.

Lipid vesicles induced ordered nanoassemblies of Janus nanoparticles.

Since many advanced applications require specific assemblies of nanoparticles (NPs), considerable efforts have been made to fabricate nanoassemblies with specific geometries. Although nanoassemblies can be fabricated through top-down approaches, recent advances show that intricate nanoassemblies can also be obtained through self-assembly, mediated for example by DNA strands. Here, we show, through extensive molecular dynamics simulations, that highly ordered self-assemblies of NPs can be mediated by their adhesion to lipid vesicles (LVs). Specifically, Janus NPs are considered so that the amount by which they are wrapped by the LV is controlled. The specific geometry of the nanoassembly is the result of effective curvature-mediated repulsion between the NPs and the number of NPs adhering to the LV. The NPs are arranged on the LV into polyhedra which satisfy the upper limit of Euler's polyhedral formula, including several deltahedra and three Platonic solids, corresponding to the tetrahedron, octahedron, and icosahedron.

Collective vortical motion and vorticity reversals of self-propelled particles on circularly patterned substrates.

The collective behavior of self-propelled particles (SPPs) under the combined effects of a circularly patterned substrate and circular confinement is investigated through coarse-grained molecular dynamics simulations of polarized and disjoint ring polymers. The study is performed over a wide range of values of the SPPs packing fraction ϕ[over ¯], motility force F_{D}, and area fraction of the patterned region. At low packing fractions, the SPPs are excluded from the system's center and exhibit a vortical motion that is dominated by the substrate at intermediate values of F_{D}. This exclusion zone is due to the coupling between the driving force and torque induced by the substrate, which induces an outward spiral motion of the SPPs. For high values of F_{D}, the SPPs exclusion from the center is dominated by the confining boundary. At high values of ϕ[over ¯], the substrate pattern leads to reversals in the vorticity, which become quasiperiodic with increasing ϕ[over ¯]. We also found that the substrate pattern is able to separate SPPs based on their motilities.

Sorting of proteins with shape and curvature anisotropy on a lipid bilayer tube.

Curvature induced sorting of lipid membrane bound proteins has been widely studied through experiments that induce curvature variation in a giant unilamellar lipid-bilayer vesicle with adsorbed proteins by pulling thin cylindrical tethers. In the theoretical space, this has been supplemented with models that capture curvature dependent interaction between membrane and idealized protein particles, through free energy contributions. Many membrane proteins such as the BAR domain proteins are known to have extremely anisotropic shapes and soft interacting potentials, whereas the idealizations of protein particles explored in models have only assumed them as hard disk-like particles with curvature anisotropy. Here, we present a model of sorting of the proteins while including the effects of softness in their interaction potentials, shape anisotropy in the protein structure, and curvature anisotropy in the interactions with the membrane. This is based on a clean separation of free energy contributions from non-ideal fluid behavior of soft anisotropic particles and curvature interactions between proteins and membranes. We probe the behavior of the sorting function under limiting conditions and show that it converges to the previously derived models. In addition to this, we present a comparison of the variation in sorting ratio due to the observed variation in the shape parameter values in known membrane proteins. Finally, using published experimental data for membrane proteins, we perform fitting and derive model parameters. We observe that shape anisotropy adversely affects the sorting of proteins to a high curvature region, whereas curvature anisotropy and softer interaction between proteins favor sorting.

Collective motion of cells modeled as ring polymers.

In this article, we use a coarse-grained model of disjoint semi-flexible ring polymers to investigate computationally the spatiotemporal collective behavior of cell colonies. A ring polymer in this model is self-propelled by a motility force along the cell's polarity, which depends on its historical kinetics. Despite the repulsive interaction between the cells, a collective behavior sets in as a result of cells pushing against each other. This cooperative motion emerges as the amplitude of the motility force is increased and/or their areal density is increased. The degree of collectivity, characterized by the average cluster size, the velocity field order parameter, and the polarity field nematic order parameter, is found to increase with increasing the amplitude of the motility force and area coverage of the cells. Furthermore, the degree of alignment exhibited by the cell velocity field within a cluster is found to be stronger than that exhibited by the cell polarity. Comparison between the collective behavior of elongated cells and that of circular cells, at the same area coverage and motility force, shows that elongated cells exhibit a stronger collective behavior than circular cells, in agreement with earlier studies of self-propelled anisotropic particles. An investigation of two-cell collisions shows that while two clustered cells move in tandem, their polarities are misaligned. As such the cells push against each other while moving coherently.

Active Remodeling of Chromatin and Implications for In Vivo Folding.

Building on the observation that chromatin compaction can be locally modulated by activity, we propose a model of in vivo chromatin as an active polymer and study its large scale conformations. In particular, we study an active mechanochemical model of chromosomal folding based on the interplay among polymer elasticity, confinement, topological constraints, and fluctuating active stresses arising from the ATP-dependent action of a variety of chromatin-associated protein machines and chromatin-remodeling proteins and their stochastic turnover. We find that activity drives the chromatin to a nonequilibrium steady state; the statistics of conformations in this nonequilibrium steady state are consistent with recent measurements on intrachromosomal contact probabilities and chromosomal compaction. The contact exponents at steady state show a systematic variation with changes in the nature of activity and the rates of turnover. The steady state configuration of the active chromatin in two dimensions resembles a space-filling Peano curve, which might have implications for the optimization of genome information storage.

Penetrant-Induced Glass-like Transition in Thin Chitosan Films.

We present the water vapor-induced swelling and the emergence of a penetrant-induced glass-like transition in the substrate-supported glassy chitosan thin films. The time evolution of the film thickness under different levels of relative humidity conditions is measured in real-time using a spectroscopic ellipsometer equipped with a humidity cell. In a dry film, the network of chitosan chains is in a glassy state, and upon exposure to water vapor, initially, the film swells by Fickian diffusion of water molecules, which triggers the structural relaxations of the chains. Under higher humidity conditions, a relatively slower evolution of thickness succeeds the initial rapid swelling due to the non-Fickian sorption of water molecules. The swelling characteristics of the polymer films are accounted for by considering the diffusion-relaxation mechanism of chains in the presence of smaller penetrant molecules. The penetrant-induced glass-like transition (Pg), where the polymer film isothermally transits from a glassy to a rubbery state, is determined for pristine and cross-linked chitosan films. Pg is determined from the abrupt change in the rate of swelling observed upon increasing the relative humidity. Chemical crosslinking has an evident influence on the penetrant-induced glass-like transition of the chitosan films. Pg was found to rise sharply for stiffer films with higher cross-linking density.

Conformational behavior and self-assembly of disjoint semi-flexible ring polymers adsorbed on solid substrates.

The conformational behavior and spatial organization of self-avoiding semi-flexible ring polymers, that are fully adsorbed on solid substrates, are investigated via systematic coarse-grained molecular dynamics simulations. Our results show that both conformations and spatial organization of the polymers depend strongly on their bending stiffness, κ, and on their areal number density, ρ. For ρ < ρ*, where ρ* is the overlap density, and for low values of κ, thermal fluctuations lead to weakly anisotropic instantaneous conformations of the polymers. The interplay between thermal fluctuations and polymer stiffness leads to a non-monotonic dependence of the polymers elongation on κ with a maximum elongation at some intermediate κ. Regardless of κ, the polymers elongation is almost independent of ρ for ρ ⪅ ρ*, then increases with ρ. At ρ ≈ ρ* and high κ, the almost circularly-shaped polymers self-assemble into a triangular lattice with quasi-long range order. For ρ above ρ* and high κ, crowding of the polymers leads to their self-assembly into liquid-crystalline phases. In particular, for ρ moderately above ρ* and high κ, the polymer conformations are obround and self-assemble into domains with smectic-A-like order. At higher densities, the polymer have a biconcave geometry and self-assemble into domains with smectic-C-like order.

Binding, unbinding and aggregation of crescent-shaped nanoparticles on nanoscale tubular membranes.

Using molecular dynamics simulations of a coarse-grained implicit solvent model, we investigate the binding of crescent-shaped nanoparticles (NPs) on tubular lipid membranes. The NPs adhere to the membrane through their concave side. We found that the binding/unbinding transition is first-order, with the threshold binding energy being higher than the unbinding threshold, and the energy barrier between the bound and unbound states at the transition that increases with increasing the NP's arclength Lnp or curvature mismatch µ = Rc/Rnp, where Rc and Rnp are the radii of curvature of the tubular membrane and the NP, respectively. Furthermore, we found that the threshold binding energy increases with increasing either Lnp or µ. NPs with curvature larger than that of the tubule (µ > 1) lie perpendicularly to the tubule's axis. However, for µ smaller than a specific arclength-dependent mismatch µ*, the NPs are tilted with respect to the tubule's axis, with the tilt angle that increases with decreasing µ. We also investigated the self-assembly of the NPs on the tubule at relatively weak adhesion strength and found that for µ > 1 and high values of Lnp, the NPs self-assemble into linear chains, and lie side-by-side. For µ < µ* and high Lnp, the NPs also self-assemble into chains, while being tilted with respect to the tubule's axis.

Adhesion and Aggregation of Spherical Nanoparticles on Lipid Membranes.

We present a review of recent results on the adhesion, wrapping and aggregation of spherical nanoparticles (NPs) on lipid membranes via molecular dynamics simulations of an implicit solvent model. We show that the degree of wrapping of small NPs, by tensionless planar membranes, can increase continuously with the adhesion strength. However, the degree of wrapping exhibits a discontinuity for large NPs or short interaction range. The adhesion of NPs to small vesicles, without volume constraint, also exhibits a discontinuity between weakly wrapped states and fully endocytosed states. Multiple spherical NPs, bound to tensionless planar membranes are either in a gas state, at weak adhesion strength, or aggregate, at relatively high adhesion strength, into a multitude of structures, corresponding to in-plane chains, out-of-plane tubes and rings, and out-of-plane single-chain tubes. Annealing scans and free energy calculations show that the gas and tube phases are the predominantly stable phases. In-plane chains are only stable for small aggregates and the out-of-plane bitubes are long-lived metastable states.

Modification of lipid membrane compressibility induced by an electric field.

Changes in membrane deformation and compressibility, induced by an external electric field, are investigated using coarse-grained martini force field simulations in a salt-free environment. We observe changes in the area of the membrane above a critical electric field. Below this value, the membrane compressibility modulus is found to decrease monotonically. For higher electric fields, the membrane projected area remains constant while the net interfacial area increases, with the corresponding compressibility moduli, show the opposite behavior. We find that the mechanical parameters, surface tension and bending modulus, of a freely floating membrane in the absence of explicit ions, are unaffected by the presence of the electric field. We believe these results have a bearing on our understanding of the electroformation of uncharged lipids in a salt-free environment.

Transition from curvature sensing to generation in a vesicle driven by protein binding strength and membrane tension.

The ability of proteins to sense and/or generate membrane curvature is crucial for many biological processes inside the cell. We introduce a model for the binding and unbinding of curvature inducing proteins on vesicles using Dynamic Triangulation Monte Carlo (DTMC) simulations. In our study, the interaction between membrane curvature and protein binding is characterised by the binding affinity parameter µ, which indicates the interaction strength. We demonstrate that both sensing and generation of curvature can be observed in the same system as a function of the protein binding affinity on the membrane. Our results show that at low µ values, proteins only sense membrane curvature, whereas at high µ values, they induce curvature. The transition between sensing and generation regimes is marked by a sharp change in the µ-dependence of the protein bound fraction. We present ways to quantitatively characterise these two regimes. We also observe that imposing tension on the membrane (through internal excess pressure for liposomes) extends the region of curvature sensing in the parameter space.

Emergent topological phenomena in active polymeric fluids.

Polymeric fluids show a wealth of topological phenomena, from entanglement and reptation at microscales to orientational ordering and defect production at macroscales, which can be explained by statistical-mechanical theories. In the presence of activity, the latter must be augmented by forces that cause spontaneous chain motion and fluid flow. Here, using such augmented Langevin equations, we study active polymeric solutions and melts composed of chains of hydrodynamically interacting stresslets. In a spherical volume, contractile chains are unstable and self-knot into entangled melts at both low and high densities. Extensile chains in the same geometry form an unentangled reptating state at low densities and an entangled, coherently moving, non-reptating state at high densities. On a spherical surface, contractile chains show transitions, with increasing areal density, between isotropic, orientationally ordered and micro-phase separated states. Extensile chains in the same geometry show a transition between isotropic and nematic states. In both cases, defects in orientationally ordered states are produced athermally and without conserving topological charge. Our work reproduces the phenomenology of several recent experiments, highlights the importance of hydrodynamic interactions in active polymer fluids, and suggests non-equilibrium kinetic routes to topological structures that are otherwise difficult to obtain in equilibrium.

Stability of membrane-induced self-assemblies of spherical nanoparticles.

The self-assembly of spherical nanoparticles, resulting from their adhesion on tensionless lipid membranes, is investigated through molecular dynamics simulations of a coarse-grained implicit-solvent model. Our simulations indicate that, with increasing adhesion strength, while reshaping the membrane, the nanoparticles aggregate into a sequence of self-assemblies corresponding to in-plane chains, two-row tubular (bitube) chains, annular (ring) chains, and single-row tubular (tube) chains. Annealing scans, with respect to adhesion strength, show that the transitions between the various phases are highly first-order with significant hystereses. Free energy calculations indicate that the gas and single-row tubular chains are stable over wide ranges of adhesion strength. In contrast, the in-plane chains are only stable for small aggregates of NPs, and the bitube and ring chains are long-lived metastable states over a wide range of adhesion strength.

Lipid-protein interaction induced domains: Kinetics and conformational changes in multicomponent vesicles.

The spatio-temporal organization of proteins and the associated morphological changes in membranes are of importance in cell signaling. Several mechanisms that promote the aggregation of proteins at low cell surface concentrations have been investigated in the past. We show, using Monte Carlo simulations, that the affinity of proteins for specific lipids can hasten their aggregation kinetics. The lipid membrane is modeled as a dynamically triangulated surface with the proteins defined as in-plane fields at the vertices. We show that, even at low protein concentrations, strong lipid-protein interactions can result in large protein clusters indicating a route to lipid mediated signal amplification. At high protein concentrations, the domains form buds similar to that seen in lipid-lipid interaction induced phase separation. Protein interaction induced domain budding is suppressed when proteins act as anisotropic inclusions and exhibit nematic orientational order. The kinetics of protein clustering and resulting conformational changes are shown to be significantly different for the isotropic and anisotropic curvature inducing proteins.

Kosmotropic effect leads to LCST decrease in thermoresponsive polymer solutions.

We study the phenomena of decrease in lower critical solution temperature (LCST) with addition of kosmotropic (order-making) cosolvents in thermoresponsive polymer solutions. A combination of explicit solvent coarse-grained simulations and mean-field theory has been employed. The polymer-solvent LCST behavior in the theoretical models has been incorporated through the Kolomeisky-Widom solvophobic potential. Our results illustrate how the decrease in the LCST can be achieved by the reduction in the bulk solvent energy with the addition of cosolvent. It is shown that this effect of cosolvent is weaker with an increase in polymer hydrophilicity which can explain the absence of a LCST decrease in poly(N,N-diethylacrylamide), water, and methanol systems. The coarse-grained nature of the models indicates that a mean energetic representation of the system is sufficient to understand the phenomena of LCST decrease.

Linking Catalyst-Coated Isotropic Colloids into "Active" Flexible Chains Enhances Their Diffusivity.

Active colloids are not constrained by equilibrium: ballistic propulsion, superdiffusive behavior, or enhanced diffusivities have been reported for active Janus particles. At high concentrations, interactions between active colloids give rise to complex emergent behavior. Their collective dynamics result in the formation of several hundred particle-strong flocks or swarms. Here, we demonstrate significant diffusivity enhancement for colloidal objects that neither have a Janus architecture nor are at high concentrations. We employ uniformly catalyst-coated, viz. chemo-mechanically, isotropic colloids and link them into a chain to enforce proximity. Activity arises from hydrodynamic interactions between enchained colloidal beads due to reaction-induced phoretic flows catalyzed by platinum nanoparticles on the colloid surface. This results in diffusivity enhancements of up to 60% for individual chains in dilute solution. Chains with increasing flexibility exhibit higher diffusivities. Simulations accounting for hydrodynamic interactions between enchained colloids due to active phoretic flows accurately capture the experimental diffusivity. These simulations reveal that the enhancement in diffusivity can be attributed to the interplay between chain conformational fluctuations and activity. Our results show that activity can be used to systematically modulate the mobility of soft slender bodies.

Molecular Structuring and Percolation Transition in Hydrated Sulfonated Poly(ether ether ketone) Membranes.

The extent of phase separation and water percolation in sulfonated membranes are the key to their performance in fuel cells. Toward this, the effect of hydration on the morphology and transport characteristics of sulfonated poly(ether ether ketone), sPEEK, membrane is investigated using atomistic molecular dynamics simulation at various hydration levels(λ: number of water molecules per sulfonate group). The evolution of local morphology is investigated using structural correlations and minimum pair distances. Transport properties are probed using mean squared displacements and diffusion coefficients. The water-sulfonate interaction in sPEEK is found to be stronger than that in Nafion, as observed in experiments. Analyses indicate the presence of narrow connected path of water and hydronium at λ = 4 and large domains, spanning half the simulation box, at λ = 15. The behavior of membrane water remains far from bulk as indicated by its diffusion coefficient. The persistence of small isolated water clusters demonstrates the extent of phase separation in sPEEK to be lesser than that in Nafion. Analyses at molecular and collective levels suggest the occurrence of a percolation transition between λ = 8 and 10, which leads to a connected network of water channels in the membrane, thereby boosting the hydronium mobility.

Numerical insights into the phase diagram of p-atic membranes with spherical topology.

The properties of self-avoiding p-atic membranes restricted to spherical topology have been studied by Monte Carlo simulations of a triangulated random surface model. Spherically shaped p-atic membranes undergo a Kosterlitz-Thouless transition as expected with topology induced mutually repelling disclinations of the p-atic ordered phase. For flexible membranes the phase behaviour bears some resemblance to the spherically shaped case with a p-atic disordered crumpled phase and p-atic ordered, conformationally ordered (crinkled) phase separated by a KT-like transition with proliferation of disclinations. We confirm the proposed buckling of disclinations in the p-atic ordered phase, while the expected associated disordering (crumpling) transition at low bending rigidities is absent in the phase diagram.