Lamellar phase of stacked two-dimensional rafts of actin filaments

Entropy of Charge Inversion in DNA including One-Loop Fluctuations

The entropy and charge distributions have been calculated for a simple model of polyelectrolytes attached to the surface of DNA using a field-theoretic method that includes fluctuations to the lowest one-loop order beyond mean-field theory. Experiments have revealed correlation-driven behavior of DNA in charged solutions, including charge inversion and condensation. In our model, the condensed polyelectrolytes are taken to be doubly charged dimers of length comparable to the distance between sites along the phosphate chains. Within this lattice gas model, each adsorption site is assumed to have either a vacancy or a positively charged dimer attached with the dimer oriented either parallel or perpendicular to the double-helix DNA chain. We find that the inclusion of the fluctuation terms decreases the entropy by ∼50% in the weak-binding regime. There, the bound dimer concentration is low because the dimers are repelled from the DNA molecule, which competes with the chemical potential driving them from the solution to the DNA surface. Surprisingly, this decrease in entropy due to correlations is so significant that it overcompensates for the entropy increase at the mean-field level, so that the total entropy is even lower than in the absence of interactions between lattice sites. As a bonus, we present a transparent exposition of the methods used that could be useful to students and others wishing to use this formulation to extend this calculation to more realistic models.

Fundamental Understanding of Ultrathin, Highly Stable Self-Assembled Liquid Crystalline Graphene Oxide Membranes Leading to Precise Molecular Sieving through Non-equilibrium Molecular Dynamics

Self-assembled graphene oxide lyotropic liquid crystal (GO LLC) structures are mostly formed in aqueous medium; however, most GO derivatives are water insoluble, so processing GO LLCs in water poses a practical limitation. The use of polar aprotic solvent (like dimethyl sulfoxide) for the formation of GO LLC structures would be interesting, because it would allow incorporating additives, like photoinitiators or cross-linkers, or blending with polymers that are insoluble in water, which hence would expand its scope. The well-balanced electrostatic interaction between DMSO and GO can promote and stabilize the GO nanosheets' alignment even at lower concentrations. With this in mind, herein we report mechanically robust, chlorine-tolerant, self-assembled nanostructured GO membranes for precise molecular sieving. Small-angle X-ray scattering and polarized optical microscopy confirmed the alignment of the modified GO nanosheets in polar aprotic solvent, and the LLC structure was effectively preserved even after cross-linking under UV light. We found that the modified GO membranes exhibited considerably improved salt rejection for monovalent ions (99%) and water flux (120 LMH) as compared to the shear-aligned GO membrane, which is well supported by forward osmosis simulation studies. Additionally, our simulation studies indicated that water molecules traveled a longer path while permeating through the GO membrane compared to the GO LLC membrane. Consequently, salt ions permeate slowly across the GO LLC membrane, yielding higher salt rejection than the GO membrane. This begins to suggest strong electrostatic repulsion with the salt ions, causing higher salt rejection in the GO LLC membrane. We foresee that the ordered cross-linked GO sheets contributed to excellent mechanical stability under a high-pressure, cross-flow, chlorine environment. Overall, these membranes are easily scalable, exhibit good mechanical stability, and represent a breakthrough for the potential use of polymerized GO LLC membranes in practical water remediation applications.

Ca2+ and Ag+ orient low-molecular weight amphiphile self-assembly into "nano-fishnet" fibrillar hydrogels with unusual β-sheet-like raft domains

Low-molecular weight gelators (LMWGs) are small molecules (M_w < ∼1 kDa), which form self-assembled fibrillar network (SAFiN) hydrogels in water when triggered by an external stimulus. A great majority of SAFiN gels involve an entangled network of self-assembled fibers, in analogy to a polymer in a good solvent. In some rare cases, a combination of attractive van der Waals and repulsive electrostatic forces drives the formation of bundles with a suprafibrillar hexagonal order. In this work, an unexpected micelle-to-fiber transition is triggered by Ca²⁺ or Ag⁺ ions added to a micellar solution of a novel glycolipid surfactant, whereas salt-induced fibrillation is not common for surfactants. The resulting SAFiN, which forms a hydrogel above 0.5 wt%, has a "nano-fishnet" structure, characterized by a fibrous network of both entangled fibers and β-sheet-like rafts, generally observed for silk fibroin, actin hydrogels or mineral imogolite nanotubes, but not known for SAFiNs. The β-sheet-like raft domains are characterized by a combination of cryo-TEM and SAXS and seem to contribute to the stability of glycolipid gels. Furthermore, glycolipid is obtained by fermentation from natural resources (glucose, rapeseed oil), thus showing that naturally engineered compounds can have unprecedented properties, when compared to the wide range of chemically derived amphiphiles.

Shear recovery and temperature stability of Ca2+ and Ag+ glycolipid fibrillar metallogels with unusual β-sheet-like domains

Low-molecular weight gelators (LMWGs) are small molecules (M_w < ∼1 kDa), which form self-assembled fibrillar network (SAFiN) hydrogels in water. A great majority of SAFiN gels are described by an entangled network of self-assembled fibers, in analogy to a polymer in a good solvent. Here, fibrillation of a biobased glycolipid bolaamphiphile is triggered by Ca²⁺ or Ag⁺ ions which are added to its diluted micellar phase. The resulting SAFiN, which forms a hydrogel above 0.5 wt%, has a "nano-fishnet" structure, characterized by a fibrous network of both entangled fibers and β-sheet-like rafts, generally observed for silk fibroin, actin hydrogels or mineral imogolite nanotubes, but generally not known for SAFiN. This work focuses on the strength of the SAFIN gels, their fast recovery after applying a mechanical stimulus (strain) and their unusual resistance to temperature, studied by coupling rheology to small angle X-ray scattering (rheo-SAXS) using synchrotron radiation. The Ca²⁺-based hydrogel maintains its properties up to 55 °C, while the Ag⁺-based gel shows a constant elastic modulus up to 70 °C, without the appearance of any gel-to-sol transition temperature. Furthermore, the glycolipid is obtained by fermentation from natural resources (glucose and rapeseed oil), thus showing that naturally engineered compounds can have unprecedented properties, when compared to the wide range of chemically derived amphiphiles.

Protamine-Controlled Reversible DNA Packaging: A Molecular Glue

Packaging paternal genome into tiny sperm nuclei during spermatogenesis requires 10⁶-fold compaction of DNA, corresponding to a 10-20 times higher compaction than in somatic cells. While such a high level of compaction involves protamine, a small arginine-rich basic protein, the precise mechanism at play is still unclear. Effective pair potential calculations and large-scale molecular dynamics simulations using a simple idealized model incorporating solely electrostatic and steric interactions clearly demonstrate a reversible control on DNA condensates formation by varying the protamine-to-DNA ratio. Microscopic states and condensate structures occurring in semidilute solutions of short DNA fragments are in good agreement with experimental phase diagram and cryoTEM observations. The reversible microscopic mechanisms induced by protamination modulation should provide valuable information to improve a mechanistic understanding of early and intermediate stages of spermatogenesis where an interplay between condensation and liquid-liquid phase separation triggered by protamine expression and post-translational regulation might occur. Moreover, recent vaccines to prevent virus infections and cancers using protamine as a packaging and depackaging agent might be fine-tuned for improved efficiency using a protamination control.

Quantification of the mesh structure of bundled actin filaments

Biopolymer networks are essential for a wide variety of cellular functions. The biopolymer actin is known to self-assemble into a variety of spatial structures in response to physiological and physical mechanisms. So far, the mechanics of networks of single actin filaments and bundles has previously been described. However, the spatial structure of actin bundles remains poorly understood. Here, we investigate this question by bundling actin filaments with systematically varied concentrations of known physical bundling agents (MgCl2 and PEG) and physiological bundling agents (α-actinin and fascin). We image bundled actin networks with confocal microscopy and perform analysis to describe their mesh size and the nearest-distance distribution, which we call "mesh structure". We find that the mesh size ξ scales universally with actin concentration as ξ ∼ [actin]-1/2. However, the dependence of ξ on the concentration of the bundling agent depends on the agent used. Finally, we find that nearest-distance distributions are best fit by Weibull and Gamma distributions. A complete understanding of the mesh structure of biopolymer networks leads to a more mechanistic understanding of the structure of the cytoskeleton, and can be exploited to design filters with variable porosity for microfluidic devices.

Non-uniform self-assembly: On the anisotropic architecture of α-synuclein supra-fibrillar aggregates

Although the function of biopolymer hydrogels in nature depends on structural anisotropy at mesoscopic length scales, the self-assembly of such anisotropic structures in vitro is challenging. Here we show that fibrils of the protein α-synuclein spontaneously self-assemble into structurally anisotropic hydrogel particles. While the fibrils in the interior of these supra-fibrillar aggregates (SFAs) are randomly oriented, the fibrils in the periphery prefer to cross neighboring fibrils at high angles. This difference in organization coincides with a significant difference in polarity of the environment in the central and peripheral parts of the SFA. We rationalize the structural anisotropy of SFAs in the light of the observation that αS fibrils bind a substantial amount of counterions. We propose that, with the progress of protein polymerization into fibrils, this binding of counterions changes the ionic environment which triggers a change in fibril organization resulting in anisotropy in the architecture of hydrogel particles.

Muscle structure, sarcomere length and influences on meat quality: A review

The basic contractile unit of muscle, the sarcomere, will contract as the muscle goes into rigor post-mortem. Depending on the conditions, such as the rate of pH decline, the cooling rate and the mechanical restraints on the muscles, this longitudinal shortening will result in various post-mortem sarcomere lengths as well as lateral differences in the distances between the myosin and actin filaments. This shortening is underlying the phenomena described as rigor contraction, thaw rigor, cold shortening and heat shortening. The shortening in combination with the molecular architecture of the sarcomere as defined by the myosin filaments and their S-1 and S-2 units, the interaction with the actin filaments, and the boundaries formed by the Z-disks will subsequently influence basic meat quality traits including tenderness and water-holding capacity. Biochemical reactions from proteolysis and glycogen metabolism interrelate with the sarcomere length in a complex manner. The sarcomere length is also influencing the eating quality of cooked meat and the water-holding in meat products.

Stability of actin-lysozyme complexes formed in cystic fibrosis disease

Finding the conditions for destabilizing actin-lysozyme complexes is of biomedical importance in preventing infections in cystic fibrosis. In this manuscript, the effects of different charge-mutants of lysozyme and salt concentration on the stability of actin-lysozyme complexes are studied using Langevin dynamics simulation. A coarse-grained model of F-actin is used in which both its twist and bending rigidities are considered. We observe that the attraction between F-actins is stronger in the presence of wild-type lysozymes relative to the mutated lysozymes of lower charges. By calculating the potential of mean force between F-actins, we conclude that the stability of actin-lysozyme complexes is decreased by reducing the charge of lysozyme mutants. The distributions of different lysozyme charge-mutants show that wild-type (+9e) lysozymes are mostly accumulated in the center of triangles formed by three adjacent F-actins, while lysozyme mutants of charges +7e and +5e occupy the bridging regions between F-actins. Low-charge mutants of lysozyme (+3e) distribute uniformly around F-actins. A rough estimate of the electrostatic energy for these different distributions proves that the distribution in which lysozymes reside in the center of triangles leads to more stable complexes. Also our results in the presence of a salt suggest that at physiological salt concentration of airway, F-actin complexes are not formed by charge-reduced mutants of lysozyme. The findings are interesting because if we can design charge-reduced lysozyme mutants with considerable antibacterial activity, they are not sequestered inside F-actin aggregates and can play their role as antibacterial agents against airway infection.

A review of immune amplification via ligand clustering by self-assembled liquid-crystalline DNA complexes

We examine how the interferon production of plasmacytoid dendritic cells is amplified by the self-assembly of liquid-crystalline antimicrobial peptide/DNA complexes. These specialized dendritic cells are important for host defense because they quickly release large quantities of type I interferons in response to infection. However, their aberrant activation is also correlated with autoimmune diseases such as psoriasis and lupus. In this review, we will describe how polyelectrolyte self-assembly and the statistical mechanics of multivalent interactions contribute to this process. In a more general compass, we provide an interesting conceptual corrective to the common notion in molecular biology of a dichotomy between specific interactions and non-specific interactions, and show examples where one can construct exquisitely specific interactions using non-specific interactions.

The effect of multivalent cations and Tau on paclitaxel-stabilized microtubule assembly, disassembly, and structure

In this review we describe recent studies directed at understanding the formation of novel nanoscale assemblies in biological materials systems. In particular, we focus on the effects of multivalent cations, and separately, of microtubule-associated protein (MAP) Tau, on microtubule (MT) ordering (bundling), MT disassembly, and MT structure. Counter-ion directed bundling of paclitaxel-stabilized MTs is a model electrostatic system, which parallels efforts to understand MT bundling by intrinsically disordered proteins (typically biological polyampholytes) expressed in neurons. We describe studies, which reveal an unexpected transition from tightly spaced MT bundles to loose bundles consisting of strings of MTs as the valence of the cationic counter-ion decreases from Z=3 to Z=2. This transition is not predicted by any current theories of polyelectrolytes. Notably, studies of a larger series of divalent counter-ions reveal strong ion specific effects. Divalent counter-ions may either bundle or depolymerize paclitaxel-stabilized MTs. The ion concentration required for depolymerization decreases with increasing atomic number. In a more biologically related system we review synchrotron small angle x-ray scattering (SAXS) studies on the effect of the Tau on the structure of paclitaxel-stabilized MTs. The electrostatic binding of MAP Tau isoforms leads to an increase in the average radius of microtubules with increasing Tau coverage (i.e. a re-distribution of protofilament numbers in MTs). Finally, inspired by MTs as model nanotubes, we briefly describe other more robust lipid-based cylindrical nanostructures, which may have technological applications, for example, in drug encapsulation and delivery.

The random packing density of nearly spherical particles

Obtaining general relations between macroscopic properties of random assemblies, such as density, and the microscopic properties of their constituent particles, such as shape, is a foundational challenge in the study of amorphous materials. By leveraging existing understanding of the random packing of spherical particles, we estimate the random packing density for all sufficiently spherical shapes. Our method uses the ensemble of random packing configurations of spheres as a reference point for a perturbative calculation, which we carry to linear order in the deformation. A fully analytic calculation shows that all sufficiently spherical shapes pack more densely than spheres. Additionally, we use simulation data for spheres to calculate numerical estimates for nonspherical particles and compare these estimates to simulations.

Charge Renormalization for Ellipsoidal Macroions

We study the problem of counterion condensation for ellipsoidal macroions, a geometry well-suited for modeling liquid crystals, anisotropic vesicles, and polymers. We find that the ions within an ellipsoid's condensation layer are relatively unrestricted in their motions, and consequently work to establish a quasi-equipotential at its surface. This simplifies the application of Alexander et al.'s procedure, enabling us to obtain accurate analytic estimates for the critical valence of a general ellipsoid in the weak screening limit. Interestingly, we find that the critical valence of an eccentric ellipsoid is always larger than that of the sphere of equal volume, implying that counterion condensation provides a force resisting the deformation of spherical macroions. This contrasts with a recent study of flexible spherical macroions, which observed a preference for deformation into flattened shapes when considering only linear effects. Our work suggests that the balance of these competing forces might alter the nature of the transition.

Building an artificial actin cortex on microscopic pillar arrays

Eukaryotic cells obtain their morphology and mechanical strength from the cytoskeleton and in particular from the cross-linked actin network that branches throughout the whole cell. This actin cortex lies like a quasi-two-dimensional (2D) biopolymer network just below the cell membrane, to which it is attached. In the quest for building an artificial cell, one needs to make a biomimetic model of the actin cortex and combine this in a bottom-up approach with other "synthetic" components. Here, we describe a reconstitution method for such an artificial actin cortex, which is freely suspended on top of a regular array of pillars. By this immobilization method, the actin network is only attached to a surface at discrete points and can fluctuate freely in between. By discussing the method to make the micropillars and the way to reconstitute a quasi-2D actin network on top, we show how one can study an isolated, reconstituted part of a cell. This allows the study of fundamental interaction mechanisms of actin networks, providing handles to design a functional actin cortex in an artificial cell.

Dynamics of counterion-induced attraction between vimentin filaments followed in microfluidic drops

Intermediate filaments (IFs) are fiber-forming proteins and part of the cytoskeleton of eukaryotes. In vitro the network formation of purified IF systems is mediated, for example, by the interaction with multivalent ions. The understanding of these interaction mechanisms increases the knowledge of the cytoskeleton on a fundamental level. Here, we employ time-lapse fluorescence microscopy to directly image the evolution of network formation of vimentin IFs upon addition of divalent ions. We are thus able to follow the process starting a few seconds after the first encounter of free filaments and ions up to several minutes when the networks are in equilibrium. The local protein density in the compacted networks can reach a factor of 45 higher than the original solution concentration. The competition between mono- and divalent ion condensation onto the protein explains our observations and reveals the polyelectrolyte nature of vimentin as a reason for the protein attraction in the presence of small cations. The method for time-lapse studies in microfluidic drops presented here can be generalized to other dynamic systems.

Unconventional ordering behavior of semi-flexible polymers in dense brushes under compression

Using a coarse-grained bead-spring model for semi-flexible macromolecules which form a polymer brush, the structure and dynamics of the polymers were investigated, varying the chain stiffness and the grafting density. The anchoring conditions for the grafted chains were chosen such that their first bonds were oriented along the normal to the substrate plane. The compression of such a semi-flexible brush by a planar piston was observed to be a two-stage process: for a small compression the chains were shown to contract by "buckling" deformation whereas for a larger compression the chains exhibited a collective (almost uniform) bending deformation. Thus, the stiff polymer brush underwent a 2nd order phase transition of collective bond reorientation. The pressure, required to keep the stiff brush at a given degree of compression, was thereby significantly smaller than for an otherwise identical brush made of entirely flexible polymer chains! While both the brush height and the chain linear dimensions in the z-direction perpendicular to the substrate increased monotonically with an increase in the chain stiffness, the lateral (xy) chain linear dimensions exhibited a maximum at an intermediate chain stiffness. Increasing the grafting density led to a strong decrease of these lateral dimensions which is compatible with an exponential decay. Also the recovery kinetics after removal of the compressing piston were studied, and were found to follow a power-law/exponential decay with time. A simple mean-field theoretical consideration, accounting for the buckling/bending behavior of semi-flexible polymer brushes under compression was suggested.

Alignment of nematic and bundled semiflexible polymers in cell-sized confinement

The finite size of cells poses severe spatial constraints on the network of semiflexible filaments called the cytoskeleton, a main determinant of cell shape. At the same time, the high packing density of cytoskeletal filaments poses mutual packing constraints. Here we investigate the competition between excluded volume interactions in the bulk and surface packing constraints on the orientational ordering of confined actin filaments as a function of filament density and the presence of crosslinks. We grow fluorescently labeled actin filaments in shallow (thickness dz 3 μm), rectangular microchambers with a systematically varied length (dy between 5 and 100 μm) and in-plane aspect ratio (dx/dy between 1 and 10). We determine the nematic director field by image analysis of fluorescence confocal images. We find that high-density (nematic) solutions respond sensitively to changes in the size and aspect ratio of the chambers. In small chambers (dy ≤ 20 μm), filaments align parallel to the long walls as soon as the aspect ratio is ≥1.5, indicating that surface-induced ordering dominates. In larger chambers, the filaments instead align along the chamber diagonal, indicating that bulk packing constraints dominate. The nematic order parameter is maximal in small and highly anisometric chambers. In contrast to the nematic solutions, low-density (isotropic) solutions are rather insensitive to confinement. Bundled actin solutions behave similarly to nematic solutions, but are less well-ordered. Our observations imply that the orientational order of actin filaments in flat confining geometries is primarily determined by a balance between bulk and surface packing constraints with a minimal effect of the enthalpic cost of filament bending. Our assay provides an interesting platform for the future reconstitution of more complex, active cytoskeletal systems with actively treadmilling filaments or molecular motors.

Polyelectrolyte properties of filamentous biopolymers and their consequences in biological fluids

Anionic polyelectrolyte filaments are common in biological cells. DNA, RNA, the cytoskeletal filaments F-actin, microtubules, and intermediate filaments, and polysaccharides such as hyaluronan that form the pericellular matrix all have large net negative charge densities distributed over their surfaces. Several filamentous viruses with diameters and stiffnesses similar to those of cytoskeletal polymers also have similar negative charge densities. Extracellular protein filaments such collagen, fibrin and elastin, in contrast, have notably smaller charge densities and do not behave as highly charged polyelectrolytes in solution. This review summarizes data that demonstrate generic counterion-mediated effects on four structurally unrelated biopolymers of similar charge density: F-actin, vimentin, Pf1 virus, and DNA, and explores the possible biological and pathophysiological consequences of the polyelectrolyte properties of biological filaments.

Neurofilament sidearms modulate parallel and crossed-filament orientations inducing nematic to isotropic and re-entrant birefringent hydrogels

Neurofilaments are intermediate filaments assembled from the subunits neurofilament-low, neurofilament-medium and neurofilament-high. In axons, parallel neurofilaments form a nematic liquid-crystal hydrogel with network structure arising from interactions between the neurofilaments' C-terminal sidearms. Here we report, using small-angle X-ray-scattering, polarized-microscopy and rheometry, that with decreasing ionic strength, neurofilament-low-high, neurofilament-low-medium and neurofilament-low-medium-high hydrogels transition from the nematic hydrogel to an isotropic hydrogel (with random, crossed-filament orientation) and to an unexpected new re-entrant liquid-crystal hydrogel with parallel filaments--the bluish-opaque hydrogel--with notable mechanical and water retention properties reminiscent of crosslinked hydrogels. Significantly, the isotropic gel phase stability is sidearm-dependent: neurofilament-low-high hydrogels exhibit a wide ionic strength range, neurofilament-low-medium hydrogels a narrow ionic strength range, whereas neurofilament-low hydrogels lack the isotropic gel phase. This suggests a dominant regulatory role for neurofilament-high sidearms in filament reorientation plasticity, facilitating organelle transport in axons. Neurofilament-inspired biomimetic hydrogels should therefore exhibit remarkable structure-dependent moduli and slow and fast water-release properties.

Ion specific effects in bundling and depolymerization of taxol-stabilized microtubules

Microtubules (MTs) are nanometer scale hollow cylindrical biological polyelectrolytes. They are assembled from alpha/beta-tubulin dimers, which stack to form protofilaments (PFs) with lateral interactions between PFs resulting in the curved MT. In cells, MTs and their assemblies are critical components in a range of functions from providing tracks for the transport of cargo to forming the spindle structure during mitosis. Previous studies have, shown that while cations with valence equal to or larger than 3+ tend to assemble tight 3D bundles of taxol-stabilized MTs, certain divalent cations induce relatively loose 2D bundles of different symmetry (D. J. Needleman et al., Proc. Natl. Acad. Sci. U. S. A., 2004, 101, 16099). Similarly, divalent cations form 2D bundles of DNA adsorbed on cationic membranes (I. Koltover et al., Proc. Natl. Acad. Sci. U. S. A., 2000, 97, 14046). The bundling behavior for these biological polyelectrolyte systems is qualitatively in agreement with current theory. Here, we present results which show that, unlike the case for DNA adsorbed on cationic membranes, bundling of taxol-stabilized MTs occurs only for certain divalent cations above a critical ion concentration (e.g. Ca2+, Sr2+, Ba2+). Instead, many divalent cations pre-empt the bundling transition and depolymerize taxol-stabilized MTs at a lower counterion concentration. Although previous cryogenic TEM has shown that, in the absence of taxol, Ca2+ depolymerizes MTs assembling in buffers containing GTP (guanosine triphosphate), our finding is surprising given the know stabilizing effects of taxol on GDP (guanosine diphosphate)-MTs. The ion concentration required for MT depolymerization decreases with increasing atomic number for the divalents Mg2+, Mn2+, Co2+, and Zn2+. GdCl3 (3+) is found to be extremely efficient at MT depolymerization requiring ion concentrations of about 1 mM, while oligolysine(2+), is observed not to depolymerize MTs at concentrations as high as 144 mM. The surprising MT depolymerization results are discussed in the context of divalents either disrupting lateral interactions between PFs (which are strengthened for taxol containing beta-tubulin) or interfering with taxol's ability to induce flexibility at the interface between two tubulin dimers in the same PF (which has been recently suggested as a mechanism by which taxol stabilizes MTs post-hydrolysis with the induced flexibility counteracting the kink between GDP-tublin dimers in a PF).

Liquid crystal assemblies in biologically inspired systems

In this paper, which is part of a collection in honor of Noel Clark's remarkable career on liquid crystal and soft matter research, we present examples of biologically inspired systems, which form liquid crystal (LC) phases with their LC nature impacting biological function in cells or being important in biomedical applications. One area focuses on understanding network and bundle formation of cytoskeletal polyampholytes (filamentous-actin, microtubules, and neurofilaments). Here, we describe studies on neurofilaments (NFs), the intermediate filaments of neurons, which form open network nematic liquid crystal hydrogels in axons. Synchrotron small-angle-x-ray scattering studies of NF-protein dilution experiments and NF hydrogels subjected to osmotic stress show that neurofilament networks are stabilized by competing long-range repulsion and attractions mediated by the neurofilament's polyampholytic sidearms. The attractions are present both at very large interfilament spacings, in the weak sidearm-interpenetrating regime, and at smaller interfilament spacings, in the strong sidearm-interpenetrating regime. A second series of experiments will describe the structure and properties of cationic liposomes (CLs) complexed with nucleic acids (NAs). CL-NA complexes form liquid crystalline phases, which interact in a structure-dependent manner with cellular membranes enabling the design of complexes for efficient delivery of nucleic acid (DNA, RNA) in therapeutic applications.

Hierarchical self-assembly of actin in micro-confinements using microfluidics

We present a straightforward microfluidics system to achieve step-by-step reaction sequences in a diffusion-controlled manner in quasi two-dimensional micro-confinements. We demonstrate the hierarchical self-organization of actin (actin monomers-entangled networks of filaments-networks of bundles) in a reversible fashion by tuning the [Formula: see text] ion concentration in the system. We show that actin can form networks of bundles in the presence of [Formula: see text] without any cross-linking proteins. The properties of these networks are influenced by the confinement geometry. In square microchambers we predominantly find rectangular networks, whereas triangular meshes are predominantly found in circular chambers.

Distribution of counterions and interaction between two similarly charged dielectric slabs: roles of charge discreteness and dielectric inhomogeneity

The distribution of counterions and the electrostatic interaction between two similarly charged dielectric slabs is studied in the strong coupling limit. Dielectric inhomogeneities and discreteness of charge on the slabs have been taken into account. It is found that the amount of dielectric constant difference between the slabs and the environment, and the discreteness of charge on the slabs have opposing effects on the equilibrium distribution of the counterions. At small interslab separations, increasing the amount of dielectric constant difference increases the tendency of the counterions toward the middle of the intersurface space between the slabs and the discreteness of charge pushes them to the surfaces of the slabs. In the limit of point charges, independent of the strength of dielectric inhomogeneity, counterions distribute near the surfaces of the slabs. The interaction between the slabs is attractive at low temperatures and its strength increases with the dielectric constant difference. At room temperature, the slabs may completely attract each other, reach to an equilibrium separation, or have two equilibrium separations with a barrier in between, depending on the system parameters.

Supramolecular assemblies of lipid-coated polyelectrolytes

We reveal the existence of a general class of supramolecular assemblies made up of lipid-coated polyelectrolytes including the celebrated lipid-nucleic acid complexes. With the aid of high-resolution cryo-electron microscopy, we unveil the nanoscale internal organization of assemblies generated with a wide range of synthetic and biological polyelectrolytes, several of them being investigated in this context for the first time, namely, poly(styrene sulfonic acid), carboxylmethylcellulose, and filamentous actin. Using an original coarse-grained model representing lipid-coated polyelectrolytes as semiflexible tubes, we thoroughly explored the morphologies resulting from the self-assembly process as a function of tube lengths and rigidities; the computed structures are fully consistent with the experimental observations. In particular, we found a strong extension of the correlation range of the order parameter as the rigidity of the lipid-coated polyelectrolytes increases. Electrostatic interactions provide a stabilizing mechanism leading to finite-size equilibrium assemblies. These assemblies may constitute a generic route for interfacing polyelectrolytes to living cells to perform gene delivery, for instance.

Nanoscale assembly in biological systems: from neuronal cytoskeletal proteins to curvature stabilizing lipids

The review will describe experiments inspired by the rich variety of bundles and networks of interacting microtubules (MT), neurofilaments, and filamentous-actin in neurons where the nature of the interactions, structures, and structure-function correlations remain poorly understood. We describe how three-dimensional (3D) MT bundles and 2D MT bundles may assemble, in cell free systems in the presence of counter-ions, revealing structures not predicted by polyelectrolyte theories. Interestingly, experiments reveal that the neuronal protein tau, an abundant MT-associated-protein in axons, modulates the MT diameter providing insight for the control of geometric parameters in bio- nanotechnology. In another set of experiments we describe lipid-protein-nanotubes, and lipid nano-tubes and rods, resulting from membrane shape evolution processes involving protein templates and curvature stabilizing lipids. Similar membrane shape changes, occurring in cells for the purpose of specific functions, are induced by interactions between membranes and proteins. The biological materials systems described have applications in bio-nanotechnology.

Orientational order and glassy states in networks of semiflexible polymers

Motivated by the structure of networks of cross-linked cytoskeletal biopolymers, we study orientationally ordered phases in two-dimensional networks of randomly cross-linked semiflexible polymers. We consider permanent cross-links which prescribe a finite angle and treat them as quenched disorder in a semimicroscopic replica field theory. Starting from a fluid of un-cross-linked polymers and small polymer clusters (sol) and increasing the cross-link density, a continuous gelation transition occurs. In the resulting gel, the semiflexible chains either display long-range orientational order or are frozen in random directions depending on the value of the crossing angle, the cross-link concentration, and the stiffness of the polymers. A crossing angle θ~2π/M leads to long-range M-fold orientational order, for example, "hexatic" or "tetratic" for θ=60° or 90°, respectively. The transition to the orientationally ordered state is discontinuous and the critical cross-link density, which is higher than that of the gelation transition, depends on the bending stiffness of the polymers and the cross-link angle: The higher the stiffness and the lower the M, the lower is the critical number of cross-links. In between the sol and the long-range ordered state, we always expect a gel which is a statistically isotropic amorphous solid with random positional and random orientational localization of the participating polymers.

Long-Range Architecture of Single Lipid-Based Complex Nanoparticles with Local Hexagonal Packing

The three-dimensional architecture of single nanoparticles made of inverse micellar lipids templated on polyelectrolytes and exhibiting a local hexagonal packing is elucidated by high-resolution cryoelectron microscopy and coarse-grained Monte Carlo simulations. Cryoelectron microscopy demonstrates that the internal structure of the complexes is less ordered than commonly recognized from X-ray diffraction. We have devised a coarse-grained model of self-avoiding flexible tubes mimicking the lipid-coated polyelectrolytes and interacting via a short-range attractive potential. Consistently with cryoelectron microscopy, the resulting clusters obtained through a Monte Carlo scheme exhibit a varying degree of order ranging from weakly organized aggregates to partially organized spooled and straight bundles, depending on the length and on the persistence length of the tubes. These findings may help in the design of self-assembled lipid-based complexes for biomedical and nanotechnological applications.

Cooperativity and frustration in protein-mediated parallel actin bundles

We examine the mechanism of bundling of cytoskeletal actin filaments by two representative bundling proteins, fascin and espin. Small-angle x-ray studies show that increased binding from linkers drives a systematic overtwist of actin filaments from their native state, which occurs in a linker-dependent fashion. Fascin bundles actin into a continuous spectrum of intermediate twist states, while espin only allows for untwisted actin filaments and fully overtwisted bundles. Based on a coarse-grained, statistical model of protein binding, we show that the interplay between binding geometry and the intrinsic flexibility of linkers mediates cooperative binding in the bundle. We attribute the respective continuous (discontinuous) bundling mechanisms of fascin (espin) to difference in the stiffness of linker bonds themselves.

Salt-induced aggregation of stiff polyelectrolytes

Molecular dynamics simulation techniques are used to study the process of aggregation of highly charged stiff polyelectrolytes due to the presence of multivalent salt. The dominant kinetic mode of aggregation is found to be the case of one end of one polyelectrolyte meeting others at right angles, and the kinetic pathway to bundle formation is found to be similar to that of flocculation dynamics of colloids as described by Smoluchowski. The aggregation process is found to favor the formation of finite bundles of 10-11 filaments at long times. Comparing the distribution of the cluster sizes with the Smoluchowski formula suggests that the energy barrier for the aggregation process is negligible. Also, the formation of long-lived metastable structures with similarities to the raft-like structures of actin filaments is observed within a range of salt concentration.

Polyelectrolyte-induced aggregation of liposomes: a new cluster phase with interesting applications

Different charged colloidal particles have been shown to be able to self-assemble, when mixed in an aqueous solvent with oppositely charged linear polyelectrolytes, forming long-lived finite-size mesoscopic aggregates. On increasing the polyelectrolyte content, with the progressive reduction of the net charge of the primary polyelectrolyte-decorated particles, larger and larger clusters are observed. Close to the isoelectric point, where the charge of the adsorbed polyelectrolytes neutralizes the original charge of the particles' surface, the aggregates reach their maximum size, while beyond this point any further increase of the polyelectrolyte-particle charge ratio causes the formation of aggregates whose size is progressively reduced. This re-entrant condensation behavior is accompanied by a significant overcharging. Overcharging, or charge inversion, occurs when more polyelectrolyte chains adsorb on a particle than are needed to neutralize its original charge so that, eventually, the sign of the net charge of the polymer-decorated particle is inverted. The stability of the finite-size long-lived clusters that this aggregation process yields results from a fine balance between long-range repulsive and short-range attractive interactions, both of electrostatic nature. For the latter, besides the ubiquitous dispersion forces, whose supply becomes relevant only at high ionic strength, the main contribution appears due to the non-uniform correlated distribution of the charge on the surface of the polyelectrolyte-decorated particles ('charge-patch' attraction). The interesting phenomenology shown by these system has a high potential for biotechnological applications, particularly when the primary colloidal particles are bio-compatible lipid vesicles. Possible applications of these systems as multi-compartment vectors for the simultaneous intra-cellular delivery of different pharmacologically active substances will be briefly discussed.

The fusion of actin bundles driven by interacting motor proteins

The cooperative action of many molecular motors is essential for dynamic processes such as cell motility and mitosis. This action can be studied by using motility assays which track the motion of cytoskeletal filaments over a surface coated with motor proteins. Here, we propose to use a motility assay consisting of a-polar actin bundles subjected to the action of myosin II motors where no external loading is applied. In this work we focus on those bundles undergoing fusion with other nearby bundles. Specifically, we investigate the role of the bundles' dimension on the transition from bidirectional to directional motion and on the properties of their motion during fusion. Our experimental data reveal that only small bundles exhibit dynamic transition to directional motion, implying that the forces acting on them exceed the threshold value necessary to induce the transition. Moreover, these bundles accelerate along their trajectory, suggesting that the forces acting on them increase while approaching each other. We show that these forces do not originate from external loading but rather arise from the action of the motors on the bundles. These forces are transmitted through the medium over micron-scale distances without being cut off. Moreover, we show that the forces propagate to distances that are proportional to the size of the bundles, or equivalently, to the number of motors, which they interact with.

Electronically activated actin protein polymerization and alignment

Biological systems are the paragon of dynamic self-assembly, using a combination of spatially localized protein complexation, ion concentration, and protein modification to coordinate a diverse set of self-assembling components. Biomimetic materials based upon biologically inspired design principles or biological components have had some success at replicating these traits, but have difficulty capturing the dynamic aspects and diversity of biological self-assembly. Here, we demonstrate that the polymerization of ion-sensitive proteins can be dynamically regulated using electronically enhanced ion mixing and monomer concentration. Initially, the global activity of the cytoskeletal protein actin is inhibited using a low-ionic strength buffer that minimizes ion complexation and protein-protein interactions. Nucleation and growth of actin filaments are then triggered by a low-frequency AC voltage, which causes local enhancement of the actin monomer concentration and mixing with Mg(2+). The location and extent of polymerization are governed by the voltage and frequency, producing highly ordered structures unprecedented in bulk experiments. Polymerization rate and filament orientation could be independently controlled using a combination of low-frequency (approximately 100 Hz) and high frequency (1 MHz) AC voltages, creating a range of macromolecular architectures from network hydrogel microparticles to highly aligned arrays of actin filaments with approximately 750 nm periodicity. Since a wide range of proteins are activated upon complexation with charged species, this approach may be generally applicable to a variety of biopolymers and proteins.

Transitions between distinct compaction regimes in complexes of multivalent cationic lipids and DNA

Cationic lipids (CLs) have found widespread use as nonviral gene carriers (vectors), including applications in clinical trials of gene therapy. However, their observed transfection efficiencies (TEs) are inferior to those of viral vectors, providing a strong incentive for a detailed understanding of CL-DNA complex behavior. In recent systematic studies employing monovalent as well as newly synthesized multivalent lipids (MVLs), the membrane cationic charge density has been identified as a key parameter governing the TE of lamellar CL-DNA complexes. In this work, we use x-ray scattering and molecular simulations to investigate the structural properties of complexes containing MVLs. At low mole fraction of neutral lipids (NLs), Phi(NL), the complexes show dramatic DNA compaction, down to essentially close-packed DNA arrays with a DNA interaxial spacing d(DNA) = 25 A. A gradual increase in Phi(NL) does not lead to a continuous increase in d(DNA) as observed for DNA complexes of monovalent CLs. Instead, distinct spacing regimes exist, with sharp transitions between the regimes. Three packing states have been identified: 1), close packed, 2), condensed, but not close packed, with d(DNA) = 27-28 A, and 3), an expanded state, where d(DNA) increases gradually with Phi(NL). Based on our experimental and computational results, we conclude that the DNA condensation is mediated by the multivalent cationic lipids, which assemble between the negatively charged DNA rods. Quite remarkably, the computational results show that the less tightly packed structure in regime 2 is thermodynamically more stable than the close packed structure in regime 1. Accordingly, the constant DNA spacing observed in regime 2 is attributed to lateral phase coexistence between this stable CL-DNA complex and neutral membranes. This finding may explain the reduced TE measured for such complexes: transfection involves endosomal escape and disassembly of the complex, and these processes are inhibited by the high thermodynamic stability. Our results, which demonstrate the existence of an inverse correlation between the stability and transfection activity of lamellar CL-DNA complexes are, therefore, consistent with a recently proposed model of cellular entry.

Strong repulsive interactions in polyelectrolyte-liposome clusters close to the isoelectric point: a sign of an arrested state

Charged colloidal particles whose interacting potential is governed by a short-range attraction and a long-range screened electrostatic repulsion contributions form aggregates whose shape, size, and overall charge are sensitively dependent on the balance between attraction and repulsion. In some cases, this class of colloidal systems shows an equilibrium cluster phase, where particles associate and dissociate reversibly into clusters. When the aggregation of the charged particles is induced by adding an oppositely charged polyion, very close to the isoelectric condition, the interaggregate interactions become very strong and a dynamical arrested state seems to occur. We provide some experimental evidences of this structural arrest in a colloid system composed by vesicles built up by a cationic lipid stuck together by an oppositely charged linear polyion, by means of the combined use of static and dynamic light scattering technique complemented by laser Doppler electrophoretic measurements. Our results show that the second virial coefficient, which is related to the potential of mean force between two adjacent aggregates, markedly increases in the vicinity of the isoelectric point. We interpret this increase as a print of strong interparticle interactions, yielding to a dynamical arrested state via cluster growth.

Chirality and equilibrium biopolymer bundles

We use continuum theory to show that chirality is a key thermodynamic control parameter for the aggregation of biopolymers: chirality produces a stable disperse phase of hexagonal bundles under moderately poor solvent conditions, as has been observed in in vitro studies of F actin [O. Pelletier et al., Phys. Rev. Lett. 91, 148102 (2003)]. The large characteristic radius of these chiral bundles is not determined by a mysterious long-range molecular interaction but by in-plane shear elastic stresses generated by the interplay between a chiral torque and an unusual, but universal, nonlinear gauge term in the strain tensor of ordered chains that is imposed by rotational invariance.

Polyamine-induced bundling of F-actin

To better understand the mechanism of actin filament (F-actin) bundling by polyamines, we have measured the onset of bundling as a function of polyamine concentration. Samples were centrifuged at low speeds to separate bundles from unbundled actin, and the relative amounts of actin in the pellet and supernatant were determined via gel electrophoresis, yielding a description of the bundling transition as a function of actin and polyamine concentrations. These experiments were carried out for two different polyamines, spermine (tetravalent) and spermidine (trivalent). We found that the threshold concentration of polyamine needed to bundle actin is independent of both actin concentration and Mg2+ concentration over a wide range in Mg2+ concentration. We also find that spermine in F-actin bundles is essentially invisible in solution-phase proton NMR, suggesting that it is bound so tightly to F-actin that it is immobilized.

The formation of planar ribbonlike aggregates from stiff polyanions in the presence of anisotropic cations

A dilute salt-free solution of rodlike polyanions in the presence of anisotropic (chain) cations consisting of neutral tails and charged heads is studied. Using Monte Carlo simulation within the framework of the primitive model, different Coulomb coupling regimes were considered. While aggregation in the strong coupling limit is expected, we report new morphology, namely, the formation of ribbonlike nanostructures. At strong electrostatic interaction, the system is found to undergo the self-organization resulting in the formation of planar aggregates that look like a "ladder" of polyanions sandwiched between cationic chains. We investigate the stability of different morphologies and find that these aggregates are thermodynamically stable. Focus has been made on how the chemical structure of anisotropic cations affects the morphology of the aggregates.

Biomimetic models of the actin cytoskeleton

The cytoskeleton is a complex polymer network that plays an essential role in the functionality of eukaryotic cells. It endows cells with mechanical stability, adaptability, and motility. To identify and understand the mechanisms underlying this large variety of capabilities and to possibly transfer them to engineered networks makes it necessary to have in vitro and in silico model systems of the cytoskeleton. These models must be realistic representatives of the cellular network and at the same time be controllable and reproducible. Here, an approach to design complementary experimental and numerical model systems of the actin cytoskeleton is presented and some of their properties discussed.

Actin network formation by unidirectional polycation diffusion

We show that F-actins form three-dimensional giant network under uni-directional diffusion of polycations, at a dilute actin concentration (0.01 mg/mL) that only bundles are formed by homogeneous mixing with polycations. The mesh size of the actin network depends on polycation concentration and ionic strength, while bundle thickness of network depends only on ionic strength, which indicates that actin network is formed through nucleation-growth mechanism. The mesh size and the bundle thickness are determined by nucleus concentration and nucleus size, respectively. The atomic force microscopy measurement correlates the elasticity of the actin network, E, with the mesh size, xi, as E approximately xi-1, while the bundle thickness, D dependence of E cannot be described by a simple scaling relation. E approximately D6.5 when D is small and E approximately D0.1 when D is large. Our study on the self-assembly of actin network under asymmetric polycation condition would provide the crucial insight into the organization of biopolymers in polarized condition of cell.

Evolution of growth modes for polyelectrolyte bundles

Multivalent ions induce attractions between polyelectrolytes, but lead to finite-sized bundles rather than macroscopic phase separation. The kinetics of aggregation and bundle formation of actin is tracked using two different fluorescently labeled populations of F-actin. It is found that the growth mode of these bundles evolves with time and salt concentration, varying from an initial lateral growth to a longitudinal one at later stages. The results suggest that kinetics play a role in bundle growth, but not in the lateral size of bundles, which is constant for linear and branched topologies.

Counterion Condensation on Charged Spheres, Cylinders, and Planes

We use the framework of counterion condensation theory, in which deviations from linear electrostatics are ascribed to charge renormalization caused by collapse of counterions from the ion atmosphere, to explore the possibility of condensation on charged spheres, cylinders, and planes immersed in dilute solutions of simple salt. In the limit of zero concentration of salt, we obtain Zimm-Le Bret behavior: a sphere condenses none of its counterions regardless of surface charge density, a cylinder with charge density above a threshold value condenses a fraction of its counterions, and a plane of any charge density condenses all of its counterions. The response in dilute but nonzero salt concentrations is different. Spheres, cylinders, and planes all exhibit critical surface charge densities separating a regime of counterion condensation from states with no condensed counterions. The critical charge densities depend on salt concentration, except for the case of a thin cylinder, which exhibits the invariant criticality familiar from polyelectrolyte theory.

Structural polymorphism of the actin-espin system: a prototypical system of filaments and linkers in stereocilia

We examine the interaction between cytoskeletal F-actin and espin 3A, a prototypical actin bundling protein found in sensory cell microvilli, including ear cell stereocilia. Espin induces twist distortions in F-actin as well as facilitates bundle formation. Mutations in one of the two F-actin binding sites of espin, which have been implicated in deafness, can tune espin-actin interactions and radically transform the system's phase behavior. These results are compared to recent theoretical work on the general phase behavior linker-rod systems.