DNA packing in stable lipid complexes designed for gene transfer imitates DNA compaction in bacteriophage

The structure of complexes made from DNA and suitable lipids (lipoplex, Lx) was examined by cryo-electron microscopy (cryoEM). We observed a distinct concentric ring-like pattern with striated shells when using plasmid DNA. These spherical multilamellar particles have a mean diameter of 254 nm with repetitive spacing of 7.5 nm with striation of 5.3 nm width. Small angle x-ray scattering revealed repetitive ordering of 6.9 nm, suggesting a lamellar structure containing at least 12 layers. This concentric and lamellar structure with different packing regimes also was observed by cryoEM when using linear double-stranded DNA, single-stranded DNA, and oligodeoxynucleotides. DNA chains could be visualized in DNA/lipid complexes. Such specific supramolecular organization is the result of thermodynamic forces, which cause compaction to occur through concentric winding of DNA in a liquid crystalline phase. CryoEM examination of T4 phage DNA packed either in T4 capsides or in lipidic particles showed similar patterns. Small angle x-ray scattering suggested an hexagonal phase in Lx-T4 DNA. Our results indicate that both lamellar and hexagonal phases may coexist in the same Lx preparation or particle and that transition between both phases may depend on equilibrium influenced by type and length of the DNA used.

Probing the role of packing specificity in protein design

By using a protein-design algorithm that quantitatively considers side-chain packing, the effect of specific steric constraints on protein design was assessed in the core of the streptococcal protein G β1 domain. The strength of packing constraints used in the design was varied, resulting in core sequences that reflected differing amounts of packing specificity. The structural flexibility and stability of several of the designed proteins were experimentally determined and showed a trend from well-ordered to highly mobile structures as the degree of packing specificity in the design decreased. This trend both demonstrates that the inclusion of specific packing interactions is necessary for the design of native-like proteins and defines a useful range of packing specificity for the design algorithm. In addition, an analysis of the modeled protein structures suggested that penalizing for exposed hydrophobic surface area can improve design performance.

Structure and function in rhodopsin: Packing of the helices in the transmembrane domain and folding to a tertiary structure in the intradiscal domain are coupled*

A previous study of the retinitis pigmentosa mutation L125R and two designed mutations at this site, L125A and L125F, showed that these mutations cause partial or total misfolding of the opsins expressed in COS cells from the corresponding mutant opsin genes. We now report on expression and characterization of the opsins from the following retinitis pigmentosa mutants in the transmembrane domain of rhodopsin that correspond to six of the seven helices: G51A and G51V (helix A), G89D (helix B), A164V (helix D), H211P (helix E), P267L and P267R (helix F), and T297R (helix G). All the mutations caused partial misfolding of the opsins as observed by the UV/visible absorption characteristics and by separation of the expressed opsins into fractions that bound 11-cis-retinal to form the corresponding mutant rhodopsins and those that did not bind 11-cis-retinal. Further, all the mutant rhodopsins prepared from the above mutants, except for G51A, showed strikingly abnormal bleaching behavior with abnormal metarhodopsin II photointermediates. The results show that retinitis pigmentosa mutations in every one of the transmembrane helices can cause misfolding of the opsin. Therefore, on the basis of these and previous results, we conclude that defects in the packing of the transmembrane helices resulting from these mutations are relayed to the intradiscal domain, where they cause misfolding of the opsin by inducing the formation of a disulfide bond other than the native Cys-110—Cys-187 disulfide bond. Thus, there is coupling between packing of the helices in the transmembrane domain and folding to a tertiary structure in the intradiscal domain.

A general method for determining helix packing in membrane proteins in situ: Helices I and II are close to helix VII in the lactose permease of Escherichia coli

It was previously shown that coexpression of the lactose permease of Escherichia coli in two contiguous fragments leads to functional complementation. We demonstrate here that site-directed thiol crosslinking of coexpressed permease fragments can be used to determine helix proximity in situ without the necessity of purifying the permease. After coexpression of the six N-terminal (N6) and six C-terminal (C6) transmembrane helices, each with a single Cys residue, crosslinking was carried out in native membranes and assessed by the mobility of anti-C-terminal-reactive polypeptides on immunoblots. A Cys residue at position 242 or 245 (helix VII) forms a disulfide with a Cys residue at either position 28 or 29 (helix I), but not with a Cys residue at position 27, which is on the opposite face of helix I, thereby indicating that the face of helix I containing Pro-28 and Phe-29 is close to helix VII. Similarly, a Cys residue at position 242 or 245 (helix VII) forms a disulfide with a Cys residue at either position 52 or 53 (helix II), but not with a Cys residue at position 54. Furthermore, low-efficiency crosslinking is observed between a Cys residue at position 52 or 53 and a Cys residue at position 361 (helix XI). The results indicate that helix VII lies in close proximity to both helices I and II and that helix II is also close to helix XI. The method should be applicable to a number of different polytopic membrane proteins.

Advances in random matrix theory, zeta functions, and sphere packing

Over four hundred years ago, Sir Walter Raleigh asked his mathematical assistant to find formulas for the number of cannonballs in regularly stacked piles. These investigations aroused the curiosity of the astronomer Johannes Kepler and led to a problem that has gone centuries without a solution: why is the familiar cannonball stack the most efficient arrangement possible? Here we discuss the solution that Hales found in 1998. Almost every part of the 282-page proof relies on long computer verifications. Random matrix theory was developed by physicists to describe the spectra of complex nuclei. In particular, the statistical fluctuations of the eigenvalues (“the energy levels”) follow certain universal laws based on symmetry types. We describe these and then discuss the remarkable appearance of these laws for zeros of the Riemann zeta function (which is the generating function for prime numbers and is the last special function from the last century that is not understood today.) Explaining this phenomenon is a central problem. These topics are distinct, so we present them separately with their own introductory remarks.

Packing at the protein-water interface.

We have determined the packing efficiency at the protein-water interface by calculating the volumes of atoms on the protein surface and nearby water molecules in 22 crystal structures. We find that an atom on the protein surface occupies, on average, a volume approximately 7% larger than an atom of equivalent chemical type in the protein core. In these calculations, larger volumes result from voids between atoms and thus imply a looser or less efficient packing. We further find that the volumes of individual atoms are not related to their chemical type but rather to their structural location. More exposed atoms have larger volumes. Moreover, the packing around atoms in locally concave, grooved regions of protein surfaces is looser than that around atoms in locally convex, ridge regions. This as a direct manifestation of surface curvature-dependent hydration. The net volume increase for atoms on the protein surface is compensated by volume decreases in water molecules near the surface. These waters occupy volumes smaller than those in the bulk solvent by up to 20%; the precise amount of this decrease is directly related to the extent of contact with the protein.

Local densities orthogonal to beta-sheet amide planes: patterns of packing in globular proteins.

We have investigated the efficiency of packing by calculating intramolecular packing density above and below peptide planes of internal beta-pleated sheet residues in five globular proteins. The orientation of interest was chosen to allow study of regions that are approximately perpendicular to the faces of beta-pleated sheets. In these locations, nonbonded van der Waals packing interactions predominate over hydrogen bonding and solvent interactions. We observed considerable variability in packing densities within these regions, confirming that the interior packing of a protein does not result in uniform occupation of the available space. Patterns of fluctuation in packing density suggest that the regular backbone-to-backbone network of hydrogen bonds is not likely to be interrupted to maximize van der Waals interactions. However, high-density packing tends to occur toward the ends of beta-structure strands where hydrogen bonds are more likely to involve nonpolar side-chain groups or solvent molecules. These features result in internal protein folding with a central low-density core surrounded by a higher-density subsurface shell, consistent with our previous calculations regarding overall protein packing density.

A cooperative model for receptor recognition and cell adhesion: evidence from the molecular packing in the 1.6-A crystal structure of the pheromone Er-1 from the ciliated protozoan Euplotes raikovi.

The crystal structure of the pheromone Er-1 from the unicellular eukaryotic organism Euplotes raikovi was determined at 1.6 A resolution and refined to a crystallographic R factor of 19.9%. In the tightly packed crystal, two extensive intermolecular helix-helix interactions arrange the Er-1 molecules into layers. Since the putative receptor of the pheromone is a membrane-bound protein, whose extracellular C-terminal domain is identical in amino acid sequence to the soluble pheromone, the interactions found in the crystal may mimic the pheromone-receptor interactions as they occur on a cell surface. Based on this, we propose a model for the interaction between soluble pheromone molecules and their receptors. In this model, strong pheromone-receptor binding emerges as a consequence of the cooperative utilization of several weak interactions. The model offers an explanation for the results of binding studies and may also explain the adhesion between cells that occurs during mating.

Helix packing of lactose permease in Escherichia coli studied by site-directed chemical cleavage.

Biotinylated lactose permease from Escherichia coli containing a single-cysteine residue at position 330 (helix X) or at position 147, 148, or 149 (helix V) was purified by avidin-affinity chromatography and derivatized with 5-(alpha-bromoacetamido)-1,10-phenanthroline-copper [OP(Cu)]. Studies with purified, OP(Cu)-labeled Leu-330 --> Cys permease in dodecyl-beta-D-maltopyranoside demonstrate that after incubation in the presence of ascorbate, cleavage products of approximately 19 and 6-8 kDa are observed on immunoblots with anti-C-terminal antibody. Remarkably, the same cleavage products are observed with permease embedded in the native membrane. Comparison with the C-terminal half of the permease expressed independently as a standard indicates that the 19-kDa product results from cleavage near the cytoplasmic end of helix VII, whereas the 6- to 8-kDa fragment probably results from fragmentation near the cytoplasmic end of helix XI. Results are entirely consistent with a tertiary-structure model of the C-terminal half of the permease derived from earlier site-directed fluorescence and site-directed mutagenesis studies. Similar studies with OP(Cu)-labeled Cys-148 permease exhibit cleavage products at approximately 19 kDa and at 15-16 kDa. The larger fragment probably reflects cleavage at a site near the cytoplasmic end of helix VII, whereas the 15- to 16-kDa fragment is consistent with cleavage near the cytoplasmic end of helix VIII. When OP(Cu) is moved 100 degrees to position 149 (Val-149 --> Cys permease), a single product is observed at 19 kDa, suggesting fragmentation at the cytoplasmic end of helix VII. However, when the reagent is moved 100 degrees in the other direction to position 147 (Gly-147 --> Cys permease), cleavage is not observed. The results suggest that helix V is in close proximity to helices VII and VIII with position 148 in the interface between the helices, position 149 facing helix VII, and position 147 facing the lipid bilayer.