Interrod forces in aqueous gels of tobacco mosaic virus

Photonics and plasmonics go viral: self-assembly of hierarchical metamaterials

Sizing and shaping of mesoscale architectures with nanoscale features is a key opportunity to produce the next generation of higher-performing products and at the same time unveil completely new phenomena. This review article discusses recent advances in the design of novel photonic and plasmonic structures using a biology-inspired design. The proteinaceous capsids from viruses have long been discovered as platform technologies enabling unique applications in nanotechnology, materials, bioengineering, and medicine. In the context of materials applications, the highly organized structures formed by viral capsid proteins provide a 3D scaffold for the precise placement of plasmon and gain materials. Based on their highly symmetrical structures, virus-based nanoparticles have a high propensity to self-assemble into higher-order crystalline structures, yielding hierarchical hybrid materials. Recent advances in the field have led to the development of virus-based light harvesting systems, plasmonic structures for application in high-performance metamaterials, binary nanoparticle lattices, and liquid crystalline arrays for sensing or display technologies. There is still much that could be explored in this area, and we foresee that this is only the beginning of great technological advances in virus-based materials for plasmonics and photonics applications.

Radial stability of the actomyosin filament lattice in isolated skeletal myofibrils studied using atomic force microscopy

The radial stability of the actomyosin filament lattice in skeletal myofibrils was examined by using atomic force microscopy. The diameter and the radial stiffness of the A-band region were examined based on force-distance curves obtained for single myofibrils adsorbed onto cover slips and compressed with the tip of a cantilever and with the Dextran treatment. The results obtained indicated that the A-band is composed of a couple of stiffness components having a rigid core-like component. It was further clarified that these radial components changed the thickness as well as the stiffness depending on the physiological condition of myofibrils. Notably, by decreasing the ionic strength, the diameter of the A-band region became greatly shrunken, but the rigid core-like component thickened, indicating that the electrostatic force distinctly affects the radial structure of actomyosin filament components. The results obtained were analyzed based on the elementary structures of the filament lattice composed of cross-bridges, thin filaments and thick filament backbones. It was clarified that the actomyosin filament lattice is radially deformable greatly and that (1), under mild compression, the filament lattice is stabilized primarily by the interactions of myosin heads with thin filaments and thick filament backbones, and (2), under severe compression, the electrostatic repulsive interactions between thin filaments and thick filament backbones became predominant.

Energies and pressures in viruses: contribution of nonspecific electrostatic interactions

We summarize some aspects of electrostatic interactions in the context of viruses. A simplified but, within well defined limitations, reliable approach is used to derive expressions for electrostatic energies and the corresponding osmotic pressures in single-stranded RNA viruses and double-stranded DNA bacteriophages. The two types of viruses differ crucially in the spatial distribution of their genome charge which leads to essential differences in their free energies, depending on the capsid size and total charge in a quite different fashion. Differences in the free energies are trailed by the corresponding characteristics and variations in the osmotic pressure between the inside of the virus and the external bathing solution.

Modeling the self-organization property of keratin intermediate filaments

Keratin intermediate filaments (IFs) fulfill an important function of structural support in epithelial cells. The necessary mechanical attributes require that IFs be organized into a crosslinked network and accordingly, keratin IFs are typically organized into large bundles in surface epithelia. For IFs comprised of keratins 5 and 14 (K5, K14), found in basal keratinocytes of epidermis, bundling can be self-driven through interactions between K14's carboxy-terminal tail domain and two regions in the central α-helical rod domain of K5. Here, we exploit theoretical principles and computational modeling to investigate how such cis-acting determinants best promote IF crosslinking. We develop a simple model where keratin IFs are treated as rigid rods to apply Brownian dynamics simulation. Our findings suggest that long-range interactions between IFs are required to initiate the formation of bundlelike configurations, while tail domain-mediated binding events act to stabilize them. Our model explains the differences observed in the mechanical properties of wild-type versus disease-causing, defective IF networks. This effort extends the notion that the structural support function of keratin IFs necessitates a combination of intrinsic and extrinsic determinants, and makes specific predictions about the mechanisms involved in the formation of crosslinked keratin networks in vivo.

DNA cholesteric phases: the role of DNA molecular chirality and DNA-DNA electrostatic interactions

DNA molecules form dense liquid-crystalline twisted phases both in vivo and in vitro. How the microscopic DNA chirality is transferred into intermolecular twist in these mesophases and what is the role of chiral DNA-DNA electrostatic interactions is still not completely clear. In this paper, we first give an extended overview of experimental observations on DNA cholesteric phases and discuss the factors affecting their stability. Then, we consider the effects of steric and electrostatic interactions of grooved helical molecules on the sign of cholesteric twist. We present some theoretical results on the strength of DNA-DNA chiral electrostatic interactions, on DNA-DNA azimuthal correlations in cholesteric phases, on the value of DNA cholesteric pitch, and on the regions of existence of DNA chiral phases stabilized by electrostatic interactions. We suggest for instance that 146 bp long DNA fragments with stronger affinities for the nucleosome formation can form less chiral cholesteric phases, with a larger left-handed cholesteric pitch. Also, the value of left-handed pitch formed in assemblies of homologous DNA fragments is predicted to be smaller than that of randomly sequenced DNAs. We expect also the cholesteric assemblies of several-kbp-long DNAs to require higher external osmotic pressures for their stability than twisted phases of short nucleosomal DNA fragments at the same DNA lattice density.

Radial compression of microtubules and the mechanism of action of taxol and associated proteins

Microtubules (MTs) are hollow cylindrical polymers composed of alphabeta-tubulin heterodimers that align head-to-tail in the MT wall, forming linear protofilaments that interact laterally. We introduce a probe of the interprotofilament interactions within MTs and show that this technique gives insight into the mechanisms by which MT-associated proteins (MAPs) and taxol stabilize MTs. In addition, we present further measurements of the mechanical properties of MT walls, MT-MT interactions, and the entry of polymers into the MT lumen. These results are obtained from a synchrotron small angle x-ray diffraction (SAXRD) study of MTs under osmotic stress. Above a critical osmotic pressure, P(cr), we observe rectangular bundles of MTs whose cross sections have buckled to a noncircular shape; further increases in pressure continue to distort MTs elastically. The P(cr) of approximately 600 Pa provides, for the first time, a measure of the bending modulus of the interprotofilament bond within an MT. The presence of neuronal MAPs greatly increases P(cr), whereas surprisingly, the cancer chemotherapeutic drug taxol, which suppresses MT dynamics and inhibits MT depolymerization, does not affect the interprotofilament interactions. This SAXRD-osmotic stress technique, which has enabled measurements of the mechanical properties of MTs, should find broad application for studying interactions between MTs and of MTs with MAPs and MT-associated drugs.

The filament lattice of striated muscle

The filament lattice of striated muscle is an overlapping hexagonal array of thick and thin filaments within which muscle contraction takes place. Its structure can be studied by electron microscopy or X-ray diffraction. With the latter technique, structural changes can be monitored during contraction and other physiological conditions. The lattice of intact muscle fibers can change size through osmotic swelling or shrinking or by changing the sarcomere length of the muscle. Similarly, muscle fibers that have been chemically or mechanically skinned can be compressed with bathing solutions containing very large inert polymeric molecules. The effects of lattice change on muscle contraction in vertebrate skeletal and cardiac muscle and in invertebrate striated muscle are reviewed. The force developed, the speed of shortening, and stiffness are compared with structural changes occurring within the lattice. Radial forces between the filaments in the lattice, which can include electrostatic, Van der Waals, entropic, structural, and cross bridge, are assessed for their contributions to lattice stability and to the contraction process.

Phase behavior of mixtures of rods (tobacco mosaic virus) and spheres (polyethylene oxide, bovine serum albumin)

Aqueous suspensions of mixtures of the rodlike virus tobacco mosaic virus (TMV) with globular macromolecules such as polyethylene oxide (PEO) or bovine serum albumin (BSA) phase separate and exhibit rich and strikingly similar phase behavior. Isotropic, nematic, lamellar, and crystalline phases are observed as a function of the concentration of the constituents and ionic strength. The observed phase behavior is considered to arise from attractions between the two particles induced by the presence of BSA or PEO. For the TMV/BSA mixtures, the BSA adsorbs to the TMV and bridging of the BSA between TMV produces the attractions. For TMV/PEO mixtures, attractions are entropically driven via excluded volume effects known alternatively as the "depletion interaction" or "macromolecular crowding."

Polymer- and salt-induced toroids of hexagonal DNA

A model is proposed for polymer- and salt-induced toroidal condensates of DNA, based on a recent theory of the undulation enhancement of the electrostatic interaction in the bulk hexagonal phase of semiflexible polyions. In a continuum approximation, the thermodynamic potential of a monomolecular toroid may be split up in bulk, surface, and curvature contributions. With the help of an approximate analytical minimization procedure, the optimal torus dimensions are calculated as a function of the concentrations of inert polymer and added salt. The stability of the torus is analyzed in terms of its surface tension and a bulk melting criterion. The theory should be applicable to psi-toroids that are not too thick.

Filament lattice of frog striated muscle. Radial forces, lattice stability, and filament compression in the A-band of relaxed and rigor muscle

Repulsive pressure in the A-band filament lattice of relaxed frog skeletal muscle has been measured as a function of interfilament spacing using an osmotic shrinking technique. Much improved chemical skinning was obtained when the muscles were equilibrated in the presence of EGTA before skinning. The lattice shrank with increasing external osmotic pressure. At any specific pressure, the lattice spacing in relaxed muscle was smaller than that of muscle in rigor, except at low pressures where the reverse was found. The lattice spacing was the same in the two states at a spacing close to that found in vivo. The data were consistent with an electrostatic repulsion over most of the pressure range. For relaxed muscle, the data lay close to electrostatic pressure curves for a thick filament charge diameter of approximately 26 nm, suggesting that charges stabilizing the lattice are situated about midway along the thick filament projections (HMM-S1). At low pressures, observed spacings were larger than calculated, consistent with the idea that thick filament projections move away from the filament backbone. Under all conditions studied, relaxed and rigor, at short and very long sarcomere lengths, the filament lattice could be modeled by assuming a repulsive electrostatic pressure, a weak attractive pressure, and a radial stiffness of the thick filaments (projections) that differed between relaxed and rigor conditions. Each thick filament projection could be compressed by approximately 5 or 2.6 nm requiring a force of 1.3 or 80 pN for relaxed and rigor conditions respectively.

Membrane interactions in nerve myelin. I. Determination of surface charge from effects of pH and ionic strength on period

We have used x-ray diffraction to study the interactions between myelin membranes in the sciatic nerve (PNS) and optic nerve (CNS) as a function of pH (2-10) and ionic strength (0-0.18). The period of myelin was found to change in a systematic manner with pH and ionic strength. PNS periods ranged from 165 to 250 A or more, while CNS periods ranged from 150 to 230 A. The native periods were observed only near physiological ionic strength at neutral or alkaline pH. The smallest periods were observed in the pH range 2.5-4 for PNS myelin and pH 2.5-5 for CNS myelin. The minimum period was also observed for PNS myelin after prolonged incubation in distilled water. At pH 4, within these acidic pH ranges, myelin period increased slightly with ionic strength; however, above these ranges, the period increased with pH and decreased with ionic strength. Electron density profiles calculated at different pH and ionic strength showed that the major structural alteration underlying the changes in period was in the width of the aqueous space at the extracellular apposition of membranes; the width of the cytoplasmic space was virtually constant. Assuming that the equilibrium myelin periods are determined by a balance of nonspecific forces/i.e., the electrostatic repulsion force and the van der Walls attractive force, as well as the short-range repulsion force (hydration force, or steric stabilization), then values in the period-dependency curve can be used to define the isoelectric pH and exclusion length of the membrane. The exclusion length, which is related to the minimum period at isoelectric pH, was used to calculate the electrostatic repulsion force given the other forces. The electrostatic repulsion was then used to calculate the surface potential, which in turn was used to calculate the surface charge density (at different pH and ionic strength). We found the negative surface charge increases with pH at constant ionic strength and with ionic strength at constant pH. We suggest that the former is due to deprotonation of the ionizable groups on the surface while the latter is due to ion binding. Interpretation of our data in terms of the chemical composition of myelin is given in the accompanying paper (Inouye and Kirschner, 1988). We also calculated the total potential energy functions for the different equilibrium periods and found that the energy minima became shallower and broader with increasing membrane separation. Finally, it was difficult to account directly for certain structural transitions from a balance of nonspecific forces. Such transitions included the abrupt appearance of the native period at alkaline pH and physiological ionic strength and the discontinuous compaction after prolonged treatment in distilled water. Possibly, in PNS myelin conformational modification of PO glycoprotein occurs under these conditions. The invariance of the cytoplasmic space suggests the presence of specific short-range interactions between surfaces at this apposition.

Chemical potential measurements of deoxyhemoglobin S polymerization. Determination of the phase diagram of an assembling protein

We have used the "osmotic stress" method to determine the phase diagram of deoxyhemoglobin S polymerization. This method involves equilibration, through a semipermeable membrane, of the protein with solutions of inert polymers of known osmotic pressure. With deoxyhemoglobin A and S solutions, in which we have demonstrated achievement of equilibrium, plots of osmotic pressure versus concentration initially agree closely with the results of other methods of measurement of colligative properties. However, once the known solubility value is exceeded for the deoxyhemoglobin S solutions at various temperatures, there is a rapid rise in hemoglobin concentration over a narrow osmotic pressure range and then a more gradual increase in concentration. We believe that these two regions correspond, respectively, to the onset of the polymerization process, and of subsequent continuing growth and compression or alignment of polymer. We derive the thermodynamic values for these processes and show that the behavior of the deoxyhemoglobin S system is analogous to the phase transition for a simple chemical system. These results are relevant to understanding the intracellular polymerization of deoxyhemoglobin S in sickle cell disease, and these concepts are applicable to other protein assembly systems.

Discussion on the state of water in the myofilament lattice and other biological systems, based on the fact that the usual concepts of colloid stability can not explain the stability of the myofilament lattice

Application of the usual concepts of colloid stability shows that the in vivo spacings between the myofilaments, making up the contractile part of the muscle myofibrils, correspond to energies of 10(-4) to 10(-1) kT. Refinements in the calculations of the electrostatic and Van der Waals-London energies do not significantly modify these values. Therefore, theory does not predict the observed stability of the myofilament lattice. It is shown that the interfilament water very likely plays an active role in the myofilament lattice. More generally, the structure of water in living cells is probably different from that of bulk water.