Isotropic, nematic, and columnar ordering in systems of persistent flexible hard rods

Enhanced ordering in length-polydisperse carbon nanotube solutions at high concentrations as revealed by small angle X-ray scattering

Carbon nanotubes (CNTs) are stiff, all-carbon macromolecules with diameters as small as one nanometer and few microns long. Solutions of CNTs in chlorosulfonic acid (CSA) follow the phase behavior of rigid rod polymers interacting via a repulsive potential and display a liquid crystalline phase at sufficiently high concentration. Here, we show that small-angle X-ray scattering and polarized light microscopy data can be combined to characterize quantitatively the morphology of liquid crystalline phases formed in CNT solutions at concentrations from 3 to 6.5% by volume. We find that upon increasing their concentration, CNTs self-assemble into a liquid crystalline phase with a pleated texture and with a large inter-particle spacing that could be indicative of a transition to higher-order liquid crystalline phases. We explain how thermal undulations of CNTs can enhance their electrostatic repulsion and increase their effective diameter by an order of magnitude. By calculating the critical concentration, where the mean amplitude of undulation of an unconstrained rod becomes comparable to the rod spacing, we find that thermal undulations start to affect steric forces at concentrations as low as the isotropic cloud point in CNT solutions.

Liquid crystal ordering of nucleic acids

Several analytical calculations and computer simulations propose that cylindrical monodispersive rods having an aspect ratio (ratio of length to diameter) greater than 4 can exhibit liquid crystal (LC) ordering. But, recent experiments demonstrated the signature of LC ordering in systems of 4- to 20-base pair (bp) long nucleic acids (NAs) that do not satisfy the shape anisotropy criterion. Mechanisms of end-to-end adhesion and stacking have been proposed to explain this phenomenon. In this study, using all-atom molecular dynamics (MD) simulation, we explicitly verify the end-to-end stacking of double-stranded RNA (dsRNA) and demonstrate the LC ordering at the microscopic level. Using umbrella sampling (US) calculation, we quantify the potential of mean force (PMF) between two dsRNAs for various reaction coordinates (RCs) and compare our results with previously reported PMFs for double-stranded DNA (dsDNA). The PMF profiles demonstrate the anisotropic nature of inter-NA interaction. We find that, like dsDNA, dsRNA also prefers to stack on top of each other while repelling sideways, leading to the formation of supra-molecular-columns that undergo LC ordering at high NA volume fraction (φ). We also demonstrate and quantify the nematic ordering of the RNAs using several hundred nanosecond-long MD simulations that remain almost invariant for different initial configurations and under different external physiological conditions.

Nematic order in solutions of semiflexible polymers: Hairpins, elastic constants, and the nematic-smectic transition

Coarse-grained models of lyotropic solutions of semiflexible polymers are studied by both molecular dynamics simulations and density functional theory calculations, using an implicit solvent bead-spring model with a bond-angle potential. We systematically vary the monomer density, persistence length, and contour length over a wide range and explore the full range from the isotropic-nematic transition to the nematic-smectic transition. In the nematic regime, we span the entire regime from rigid-rod like polymers to thin wormlike chains, confined in effective straight tubes caused by the collective nematic effective ordering field. We show that the distribution of bond angles relative to the director is well described by a Gaussian, irrespective of whether the chains are rod-like or rather flexible. However, the related concept of "deflection length" is shown to make sense only in the latter case for rather dilute solutions since otherwise the deflection length is of the order of about two bond lengths only. When the solution is semi-dilute, a substantial renormalization of the persistence length occurs, while this effect is absent in the isotropic phase even at rather high monomer densities. The effective radii of the "tubes" confining the chains in the related description of orientational ordering are significantly larger than the distances between neighboring chains, providing evidence for a pronounced collective character of orientational fluctuations. Hairpins can be identified close to the isotropic-nematic transition, and their probability of occurrence agrees qualitatively with the Vroege-Odijk theory. The corresponding theoretical predictions for the elastic constants, however, are not in good agreement with the simulations. We attribute the shortcomings of the theories to their neglect of the coupling between local density and orientational fluctuations. Finally, we detected for this model a transition to a smectic phase for reduced monomer densities near 0.7.

On the structural stability of guanosine-based supramolecular hydrogels

Supramolecular hydrogels formed from the self-assembly of low molecular weight derivatives are very attractive systems, because of their potential applications in nano- and bio-technology. In this paper, the stable and transparent hydrogels observed in binary mixtures of guanosine derivatives (G), namely guanosine 5'-monophosphate (GMP) and guanosine (Gua), dissolved in water (at volume fractions larger than 0.95), were investigated by microscopy techniques and Small Angle X-ray Scattering (SAXS). The results confirm the presence of G-quadruplexes, chiral cylindrical rods obtained by the regular stacking of self-assembled planar cyclic guanosine quartets. However, the addition of Gua determines the formation of very stable hydrogels able to trap large amounts of water (up to a volume fraction of 0.99) and characterised by an unusual anisotropic order. A modified lateral helix-to-helix interaction pattern, tuned by Gua, is suggested to be responsible for the supramolecular gelation and the stability of the hydrogels during swelling.

Understanding the origin of liquid crystal ordering of ultrashort double-stranded DNA

Recent experiments have shown that short double-stranded DNA (dsDNA) fragments having six- to 20-base pairs exhibit various liquid crystalline phases. This violates the condition of minimum molecular shape anisotropy that analytical theories demand for liquid crystalline ordering. It has been hypothesized that the liquid crystalline ordering is the result of end-to-end stacking of dsDNA to form long supramolecular columns which satisfy the shape anisotropy criterion necessary for ordering. To probe the thermodynamic feasibility of this process, we perform molecular dynamics simulations on ultrashort (four base pair long) dsDNA fragments, quantify the strong end-to-end attraction between them, and demonstrate that the nematic ordering of the self-assembled stacked columns is retained for a large range of temperature and salt concentration.

A new insight into the isotropic-nematic phase transition in lyotropic solutions of semiflexible polymers: density-functional theory tested by molecular dynamics

Semiflexible polymers in solution are studied for a wide range of both contour length L and persistence length lp as a function of monomer concentration under good solvent conditions. Both density-functional theory (DFT) and molecular dynamics (MD) simulation methods are used, and a very good agreement between both techniques is observed for rather stiff polymers. Evidence for a new mechanism of order parameter fluctuations in the nematic phase is presented, namely collective deformations of bundles of wormlike chains twisted around each other, and the typical wavelengths and amplitudes of these modes are estimated. These long wavelength fluctuations cause a reduction of the order parameter in comparison with the DFT prediction. It is also found that DFT becomes unreliable for rather flexible polymers in predicting that the transition from the isotropic (I)-phase to the nematic (N)-phase still exists at very high monomer concentrations (which in reality does not occur). However, under conditions when DFT is accurate, it provides reliable predictions also for the width of the I-N two-phase coexistence region, which are difficult to obtain from MD in spite of the use of very large systems (up to 500 000 monomers) by means of graphics processing units (GPU). For short and not very stiff chains, a pre-transitional chain stretching is found in the isotropic phase near the I-N-transition, not predicted by theories. A comparison with theoretical predictions by Khokhlov-Semenov, Odijk, and Chen reveals that the scaled transition densities are not simply functions of L/lp only, as these theories predict, but depend on d/lp (where d is the chain diameter) as well. Chain properties in the nematically ordered phase are compared to those of chains confined in tubes, and the deflection length concept is tested. Eventually, some consequences for the interpretation of experiments are spelled out.

A liquid-crystalline hexagonal columnar phase in highly-dilute suspensions of imogolite nanotubes

Liquid crystals have found wide applications in many fields ranging from detergents to information displays and they are also increasingly being used in the ‘bottom-up' self-assembly approach of material nano-structuration. Moreover, liquid-crystalline organizations are frequently observed by biologists. Here we show that one of the four major lyotropic liquid-crystal phases, the columnar one, is much more stable on dilution than reported so far in literature. Indeed, aqueous suspensions of imogolite nanotubes, at low ionic strength, display the columnar liquid-crystal phase at volume fractions as low as ∼0.2%. Consequently, due to its low visco-elasticity, this columnar phase is easily aligned in an alternating current electric field, in contrast with usual columnar liquid-crystal phases. These findings should have important implications for the statistical physics of the suspensions of charged rods and could also be exploited in materials science to prepare ordered nanocomposites and in biophysics to better understand solutions of rod-like biopolymers.

Liquid crystals are grouped into four main classes—nematic, lamellar, cubic and columnar—depending on their symmetries. Here, the authors show for the first time that a columnar phase can form in suspensions of imogolite nanotubes at very low concentrations.

Liquid Crystalline Materials for Biological Applications

Liquid crystals have a long history of use as materials that respond to external stimuli (e.g., electrical and optical fields). More recently, a series of investigations have reported the design of liquid crystalline materials that undergo ordering transitions in response to a range of biological interactions, including interactions involving proteins, nucleic acids, viruses, bacteria and mammalian cells. A central challenge underlying the design of liquid crystalline materials for such applications is the tailoring of the interface of the materials so as to couple targeted biological interactions to ordering transitions. This review describes recent progress toward design of interfaces of liquid crystalline materials that are suitable for biological applications. Approaches addressed in this review include the use of lipid assemblies, polymeric membranes containing oligopeptides, cationic surfactant-DNA complexes, peptide-amphiphiles, interfacial protein assemblies and multi-layer polymeric films.

Liquid crystal self-assembly of random-sequence DNA oligomers

In biological systems and nanoscale assemblies, the self-association of DNA is typically studied and applied in the context of the evolved or directed design of base sequences that give complementary pairing, duplex formation, and specific structural motifs. Here we consider the collective behavior of DNA solutions in the distinctly different regime where DNA base sequences are chosen at random or with varying degrees of randomness. We show that in solutions of completely random sequences, corresponding to a remarkably large number of different molecules, e.g., approximately 10(12) for random 20-mers, complementary still emerges and, for a narrow range of oligomer lengths, produces a subtle hierarchical sequence of structured self-assembly and organization into liquid crystal (LC) phases. This ordering follows from the kinetic arrest of oligomer association into long-lived partially paired double helices, followed by reversible association of these pairs into linear aggregates that in turn condense into LC domains.

Imaging capability of patterned liquid crystals

We demonstrate the ability to make high resolution arbitrary patterned optical retarders using liquid crystal polymer (LCP). Contact lithography is used to define unique LCP alignment domains. Patterned LCP retarders are imaged between crossed polarizers to determine pattern visibility as a function of feature size. It was determined that patterned retarders for wavelengths between 250 nm and 2500 nm can be constructed with feature sizes as small as 4 microm. We also showed that multiple patterns can be created on the same substrate using a combination of patterned LCP and opaque features. Our process has applications in displays, double-patterning lithography, and imaging polarimetry.

Phase behavior of wormlike rods

By employing molecular dynamics computer simulations, the phase behavior of systems of rodlike particles with varying degree of internal flexibility has been traced from the perfectly rigid rod limit till very flexible particles, and from the high density region till the isotropic phase. From the perfectly rigid rod limit and enhancing the internal flexibility, the range of the smectic- A phase is squeezed out by the concomitant action of the scarcely affected crystalline phase at higher density and the nematic phase at lower density, until it disappears. These results confirm the supposition, drawn from previous theoretical, simulational and experimental studies, that the smectic- A phase is destabilized by introducing and enhancing the degree of particle internal flexibility. However, no significant changes in the order of nematic-to-smectic- A phase transition, which appears always first order, nor in the value of the layer spacing, are observed upon varying the degree of particle internal flexibility. Moreover, no evidence of a columnar phase, which was thought of as a possible superseder of the smectic- A phase in flexible rods, has been obtained.

Hexagonal order in crystalline and columnar phases of hard rods

We report a study of colloidal suspensions of highly monodisperse semiflexible chiral rodlike viruses, denoted fd, in the range of high concentrations. Small angle x-ray scattering experiments reveal the existence of two hexagonal phases: the first one is crystalline and the second one is hexatic columnar, as shown by its short-range positional order. The suspension of rodlike viruses is the first experimental system showing the whole phase sequence with increasing particle concentration theoretically predicted for systems of hard rods, ranging from the chiral nematic via the smectic to columnar and crystalline phases.

End-to-end stacking and liquid crystal condensation of 6 to 20 base pair DNA duplexes

Short complementary B-form DNA oligomers, 6 to 20 base pairs in length, are found to exhibit nematic and columnar liquid crystal phases, even though such duplexes lack the shape anisotropy required for liquid crystal ordering. Structural study shows that these phases are produced by the end-to-end adhesion and consequent stacking of the duplex oligomers into polydisperse anisotropic rod-shaped aggregates, which can order into liquid crystals. Upon cooling mixed solutions of short DNA oligomers, in which only a small fraction of the DNA present is complementary, the duplex-forming oligomers phase-separate into liquid crystal droplets, leaving the unpaired single strands in isotropic solution. In a chemical environment where oligomer ligation is possible, such ordering and condensation would provide an autocatalytic link whereby complementarity promotes the extended polymerization of complementary oligomers.

Laser light scattering evidence for a common wormlike growth structure of mixed micelles in bile salt- and straight-chain detergent-phosphatidylcholine aqueous systems: relevance to the micellar structure of bile

We employed quasielastic and static light scattering to measure apparent values of the mean hydrodynamic radii (Rh)app, molecular weights (Mapp), and radii of gyration (Rg)app in solutions containing mixed micelles composed of bile salts (cholate and taurochenodeoxycholate, both cholanoyl derivatives) and the glycoacyl chain detergent, octyl glucoside, with egg yolk phosphatidylcholine (EYPC) as functions of total lipid concentration (0.1-10 g/dL), EYPC/detergent molar ratio (0-1.2), and ionic strength (0.15-0.4 M NaCl) at 20 degreesC and 1 atm. As the mixed micellar phase boundaries were approached by dilution, (Rh)app, Mapp, and (Rg)app values increased markedly by up to 20-fold. For each micellar system, the scaling ratios (Rh)app/Mapp1/2 and (Rg)app/(Rh)app remained essentially constant at 0.018 nm/(g/mol)1/2 and 1.5 (dimensionless), respectively, despite large variations in total lipid concentration, detergent molecular species, and ionic strength. Refined data analysis is inconsistent with a flat "mixed-disc" model for bile salt-EYPC micelles [Mazer, N. A., Benedek, G. B., and Carey, M. C. (1980) Biochemistry 19, 601] and octyl glucoside-EYPC micelles principally because the numerical value of (Rh)app/Mapp1/2 corresponds to a hypothetical disk thickness of approximately 1 nm, which is 4-fold smaller than the bimolecular width of EYPC molecules, and for a disk, (Rg)app/(Rh)app ratios should be close to 1 at low total lipid concentrations. Assuming disc-shaped micelles, we show that intermicellar excluded volume interactions would have only a minor effect on Mapp and cannot account for the unrealistic disk thickness. Instead, locally cylindrical, semiflexible wormlike micelles of diameter d = 4 nm and persistence length xip = 17 nm in solution are compatible with the observed (Rh)app/Mapp1/2 and (Rg)app/(Rh)app values when intermicellar excluded-volume interactions are considered. With EYPC/taurochenodeoxycholate = 0.6 and EYPC/cholate = 1.0 in 0.15 M NaCl, independent micelles grow upon dilution and use of the second virial coefficient [Egelhaaf, S. U., and Schurtenberger, P. (1994) J. Phys. Chem. 98, 8560] is adequate for estimating micellar weights. The systems EYPC/cholate = 1.0 in 0.4 M NaCl, EYPC/cholate = 1.2 in 0.15 M NaCl, and EYPC/octyl glucoside = 0.13 in 0.15 M NaCl all form highly overlapping, semidilute polymer solutions, which mimic the observed scaling ratios. In such semidilute systems, use of the second virial coefficient alone to account for intermicellar interactions is inadequate for estimating micellar weights. The results of the present study, in combination with locations of known phase boundaries of the ternary bile salt-EYPC-water phase diagram at high dilution, suggest that elongation, as well as entanglement of wormlike mixed micelles may occur at concentrations approaching the micellar phase limit.

Crowding-induced organization of cytoskeletal elements. III. Spontaneous bundling and sorting of self-assembled filaments with different flexibilities

The typical cell contains ca. 25 vol.-% protein, of which ca. 10% forms cytoskeletal filaments and ca. 90% is non-aggregating globular protein. It has previously been theoretically predicted that, under such highly crowded conditions, rigid filaments will coalesce into tight bundles coexisting with an isotropic solution of globular proteins. In the present work we show that such spontaneous bundling will occur even when filament flexibility is taken into account because the persistence length of the filaments is much longer than the diameter of the globular proteins. The theoretical results are consistent with experimentally observed bundling of F-actin (the most flexible of the three most common types of cytoskeletal filaments) in the presence of globular macromolecules.The main effect of increased filament flexibility on bundling is to cause somewhat looser packing. In mixtures of filaments, differences in flexibilities can lead to segregation. This segregation is accentuated when the stiffer filament is also wider. The results suggest that actin filaments and microtubules will spontaneously form segregated bundles in the presence of cellular concentrations of globular proteins. While cross-linking proteins may serve to stabilize these bundles, their more important function in bundling may be to fine tune the structure (e.g., polarity and registration of filaments).

Temperature-favoured assembly of collagen is driven by hydrophilic not hydrophobic interactions

It has become almost axiomatic that protein folding and assembly are dominated by the hydrophobic effect. The contributions from this, and other, hydrophilic interactions can now be better distinguished by direct measurement of forces between proteins. Here we report the measurement of forces between triple helices of type I collagen at different temperatures, pH and solute concentrations. We separate repulsive and attractive components of the net force and analyze the origin of the attraction responsible for the collagen self-assembly. In this case the role of the hydrophobic effect appears to be negligible. Instead, water-mediated hydrogen bonding between polar residues is the most consistent explanation.

Direct measurement of forces between self-assembled proteins: temperature-dependent exponential forces between collagen triple helices

We report direct measurements of force vs. separation between self-assembled proteins. These forces are observed between collagen triple helices in native and reconstituted fibers. They are a combination of a short-range repulsion, which varies exponentially over at least five decay lengths, and an inferred, longer-ranged attraction responsible for spontaneous assembly. From 5 degrees C to 35 degrees C the relative contribution of the attraction to the net force increases with temperature. These forces are strikingly similar to the "hydration" forces measured between several other linear macromolecules (DNA, polysaccharides) and between lipid bilayer membranes. The decay length of the repulsive force agrees well with a theoretical estimate based on axial periodicity of the triple helix, suggesting another connection between molecular architecture and protein-protein interaction.