Nanohedra: Using symmetry to design self assembling protein cages, layers, crystals, and filaments

A general strategy is described for designing proteins that self assemble into large symmetrical nanomaterials, including molecular cages, filaments, layers, and porous materials. In this strategy, one molecule of protein A, which naturally forms a self-assembling oligomer, An, is fused rigidly to one molecule of protein B, which forms another self-assembling oligomer, Bm. The result is a fusion protein, A-B, which self assembles with other identical copies of itself into a designed nanohedral particle or material, (A-B)p. The strategy is demonstrated through the design, production, and characterization of two fusion proteins: a 49-kDa protein designed to assemble into a cage approximately 15 nm across, and a 44-kDa protein designed to assemble into long filaments approximately 4 nm wide. The strategy opens a way to create a wide variety of potentially useful protein-based materials, some of which share similar features with natural biological assemblies.

A brief survey of symmetry in mathematics

This paper presents a brief survey of the idea of symmetry in mathematics, as exemplified by some particular developments in algebra, differential equations, topology, and number theory.

Symmetry, stability, and dynamics of multidomain and multicomponent protein systems

Symmetry is commonly observed in many biological systems. Here we discuss representative examples of the role of symmetry in structural molecular biology. Point group symmetries are observed in many protein oligomers whose three-dimensional atomic structures have been elucidated by x-ray crystallography. Approximate symmetry also occurs in multidomain proteins. Symmetry often confers stability on the molecular system and results in economical usage of basic components to build the macromolecular structure. Symmetry is also associated with cooperativity. Mild perturbation from perfect symmetry may be essential in some systems for dynamic functions.

Symmetry and the energy landscapes of biomolecules

The role of symmetry in the folding of proteins is discussed using energy landscape theory. An analytical argument shows it is much easier to find sequences with funneled energy landscape capable of fast folding if the structure is symmetric. The analogy with phase transitions of small clusters with magic numbers is discussed.

The role of symmetry in fundamental physics

The role of symmetry in fundamental physics is reviewed.

Symmetry arguments in chemistry

The use (and misuse) of symmetry arguments in constructing molecular models and in the interpretation of experimental observations bearing on molecular structure (spectroscopy, diffraction, etc.) is discussed. Examples include the development of point groups and space groups for describing the external and internal symmetry of crystals, the derivation of molecular symmetry by counting isomers (the benzene structure), molecular chirality, the connection between macroscopic and molecular chirality, pseudorotation, the symmetry group of nonrigid molecules, and the use of orbital symmetry arguments in discussing aspects of chemical reactivity.

Five-fold symmetry in crystalline quasicrystal lattices

To demonstrate that crystallographic methods can be applied to index and interpret diffraction patterns from well-ordered quasicrystals that display non-crystallographic 5-fold symmetry, we have characterized the properties of a series of periodic two-dimensional lattices built from pentagons, called Fibonacci pentilings, which resemble aperiodic Penrose tilings. The computed diffraction patterns from periodic pentilings with moderate size unit cells show decagonal symmetry and are virtually indistinguishable from that of the infinite aperiodic pentiling. We identify the vertices and centers of the pentagons forming the pentiling with the positions of transition metal atoms projected on the plane perpendicular to the decagonal axis of quasicrystals whose structure is related to crystalline η phase alloys. The characteristic length scale of the pentiling lattices, evident from the Patterson (autocorrelation) function, is ∼τ2 times the pentagon edge length, where τ is the golden ratio. Within this distance there are a finite number of local atomic motifs whose structure can be crystallographically refined against the experimentally measured diffraction data.

From symmetry to asymmetry: Phylogenetic patterns of asymmetry variation in animals and their evolutionary significance

Phylogenetic analyses of asymmetry variation offer a powerful tool for exploring the interplay between ontogeny and evolution because (i) conspicuous asymmetries exist in many higher metazoans with widely varying modes of development, (ii) patterns of bilateral variation within species may identify genetically and environmentally triggered asymmetries, and (iii) asymmetries arising at different times during development may be more sensitive to internal cytoplasmic inhomogeneities compared to external environmental stimuli. Using four broadly comparable asymmetry states (symmetry, antisymmetry, dextral, and sinistral), and two stages at which asymmetry appears developmentally (larval and postlarval), I evaluated relations between ontogenetic and phylogenetic patterns of asymmetry variation. Among 140 inferred phylogenetic transitions between asymmetry states, recorded from 11 classes in five phyla, directional asymmetry (dextral or sinistral) evolved directly from symmetrical ancestors proportionally more frequently among larval asymmetries. In contrast, antisymmetry, either as an end state or as a transitional stage preceding directional asymmetry, was confined primarily to postlarval asymmetries. The ontogenetic origin of asymmetry thus significantly influences its subsequent evolution. Furthermore, because antisymmetry typically signals an environmentally triggered asymmetry, the phylogenetic transition from antisymmetry to directional asymmetry suggests that many cases of laterally fixed asymmetries evolved via genetic assimilation.

Symmetry in chemistry from the hydrogen atom to proteins

The last 2 decades have seen discoveries in highly excited states of atoms and molecules of phenomena that are qualitatively different from the “planetary” model of the atom, and the near-rigid model of molecules, characteristic of these systems in their low-energy states. A unified view is emerging in terms of approximate dynamical symmetry principles. Highly excited states of two-electron atoms display “molecular” behavior of a nonrigid linear structure undergoing collective rotation and vibration. Highly excited states of molecules described in the “standard molecular model” display normal mode couplings, which induce bifurcations on the route to molecular chaos. New approaches such as rigid–nonrigid correlation, vibrons, and quantum groups suggest a unified view of collective electronic motion in atoms and nuclear motion in molecules.

Evidence for the role of proteoglycans in cation-mediated gene transfer.

We report evidence that gene complexes, consisting of polycations and plasmid DNA enter cells via binding to membrane-associated proteoglycans. Treatment of HeLa cells with sodium chlorate, a potent inhibitor of proteoglycan sulfation, reduced luciferase expression by 69%. Cellular treatment with heparinase and chondroitinase ABC inhibited expression by 78% and 20% with respect to control cells. Transfection was dramatically inhibited by heparin and heparan sulfate and to a smaller extent by chondroitan sulfate B. Transfection of mutant, proteoglycan deficient Chinese hamster ovary cells was 53 x lower than of wild-type cells. For each of these assays, the intracellular uptake of DNA at 37 degrees C and the binding of DNA to the cell membrane at 4 degrees C was impaired. Preliminary transfection experiments conducted in mutant and wild-type Chinese hamster ovary cells suggest that transfection by some cationic lipids is also proteoglycan dependent. The variable distribution of proteoglycans among tissues may explain why some cell types are more susceptible to transfection than others.

Mirror symmetry breaking at the molecular level.

Reasoning from two basic principles of molecular physics, P invariance of electromagnetic interaction and the second law of thermodynamics, one would conclude that mirror symmetry retained in the world of chiral molecules. This inference is fully consistent with what is observed in inorganic nature. However, in the bioorganic world, the reverse is true. Mirror symmetry there is definitely broken. Is it possible to account for this phenomenon without going beyond conventional concepts of the kinetics of enantioselective processes? This study is an attempt to survey all existing hypotheses containing this phenomenon.

Cation-pi interactions in aromatics of biological and medicinal interest: electrostatic potential surfaces as a useful qualitative guide.

The cation-pi interaction is an important, general force for molecular recognition in biological receptors. Through the sidechains of aromatic amino acids, novel binding sites for cationic ligands such as acetylcholine can be constructed. We report here a number of calculations on prototypical cation-pi systems, emphasizing structures of relevance to biological receptors and prototypical heterocycles of the type often of importance in medicinal chemistry. Trends in the data can be rationalized using a relatively simple model that emphasizes the electrostatic component of the cation-pi interaction. In particular, plots of the electrostatic potential surfaces of the relevant aromatics provide useful guidelines for predicting cation-pi interactions in new systems.

Up-regulation of pressure-activated Ca(2+)-permeable cation channel in intact vascular endothelium of hypertensive rats.

In endothelial cells, stretch-activated cation channels have been proposed to act as mechanosensors for changes in hemodynamic forces. We have identified a novel mechanosensitive pressure-activated channel in intact endothelium from rat aorta and mesenteric artery. The 18-pS cation channel responded with a multifold increase in channel activity when positive pressure was applied to the luminal cell surface with the patch pipette and inactivated at negative pipette pressure. Channel permeability ratio for K+, Na+, and Ca2+ ions was 1:0.98:0.23. Ca2+ influx through the channel was sufficient to activate a neighboring Ca2(+)-dependent K+ channel. Hemodynamic forces are chronically disturbed in arterial hypertension. Endothelial cell dysfunction has been implicated in the pathogenesis of arterial hypertension. In two comparative studies, density of the pressure-activated channel was found to be significantly higher in spontaneously hypertensive rats and renovascular hypertensive rats compared with their respective normotensive controls. Channel activity presumably leads to mechanosensitive Ca2+ influx and induces cell hyperpolarization by K+ channel activity. Both Ca2+ influx and hyperpolarization are known to induce a vasodilatory endothelial response by stimulating endothelial nitric oxide (NO) production. Up-regulation of channel density in hypertension could, therefore, represent a counterregulatory mechanism of vascular endothelium.

Independent determination of symmetry and polarity in the Drosophila eye.

In each facet of the Drosophila compound eye, a cluster of photoreceptor cells assumes an asymmetric trapezoidal pattern. These clusters have opposite orientations above and below an equator, showing global dorsoventral mirror symmetry. However, in the mutant spiny legs, the polarization of each cluster appears to be random, so that no equator is evident. The apparent lack of an equator suggests that spiny legs+ may be involved in the establishment of global dorsoventral identity that might be essential for proper polarization of the photoreceptor clusters. Alternatively, a global dorsoventral pattern could be present, but spiny legs+ may be required for local polarization of individual clusters. Using an enhancer trap strain in which white+ gene expression is restricted to the dorsal field, we show that white+ expression in spiny legs correctly respects dorsoventral position even in facets with inappropriate polarizations; the dorsoventral boundary is indeed present, whereas the mechanism for polarization is perturbed. It is suggested that the boundary is established before the action of spiny legs+ by an independent mechanism.

Antisense oligodeoxynucleotide inhibition of a swelling-activated cation channel in osteoblast-like osteosarcoma cells.

By patch-clamp analysis, we have shown that chronic, intermittent mechanical strain (CMS) increases the activity of stretch-activated cation channels of osteoblast-like UMR-106.01 cells. CMS also produces a swelling-activated whole-cell conductance (Gm) regulated by varying strain levels. We questioned whether the swelling-activated conductance was produced by stretch-activated cation channel activity. We have identified a gene involved in the increase in conductance by using antisense oligodeoxynucleotides (ODN) derived from the alpha 1-subunit genes of calcium channels found in UMR-106.01 cells (alpha1S, alpha1C, and alpha1D). We demonstrate that alpha 1C antisense ODNs abolish the increase in Gm in response to hypotonic swelling following CMS. Antisense ODNs to alpha1S and alpha1D, sense ODNs to alpha1C, and sham permeabilization had no effect on the conductance increase. In addition, during cell-attached patch-clamp studies, antisense ODNs to alpha1c completely blocked the swelling-activated and stretch-activated nonselective cation channel response to strain. Antisense ODNs to alpha1S treatment produced no effect on either swelling-activated or stretch-activated cation channel activity. There were differences in the stretch-activated and swelling-activated cation channel activity, but whether they represent different channels could not be determined from our data. Our data indicate that the alpha1C gene product is involved in the Gm and the activation of the swelling-activated cation channels induced by CMS. The possibility that swelling-activated cation channel genes are members of the calcium channel superfamily exists, but if alpha1c is not the swelling-activated cation channel itself, then its expression is required for induction of swelling-activated cation channel activity by CMS.