Computer simulation of packing of particles with size distributions produced by fragmentation processes

Fragmentation schemes inspired by theoretical results and conjectures of Kolmogorov are applied to produce particle size distributions of different natures, depending on fragmentation parameters. A two-dimensional computer simulation method of packing is applied to the resulting distributions and the void fraction is evaluated. The relationship between the void fraction and characteristic parameters of the fragmentation process is studied.

Spin-lattice relaxation of laser-polarized xenon in human blood

The nuclear spin polarization of 129Xe can be enhanced by several orders of magnitude by using optical pumping techniques. The increased sensitivity of xenon NMR has allowed imaging of lungs as well as other in vivo applications. The most critical parameter for efficient delivery of laser-polarized xenon to blood and tissues is the spin-lattice relaxation time (T1) of xenon in blood. In this work, the relaxation of laser-polarized xenon in human blood is measured in vitro as a function of blood oxygenation. Interactions with dissolved oxygen and with deoxyhemoglobin are found to contribute to the spin-lattice relaxation time of 129Xe in blood, the latter interaction having greater effect. Consequently, relaxation times of 129Xe in deoxygenated blood are shorter than in oxygenated blood. In samples with oxygenation equivalent to arterial and venous blood, the 129Xe T1s at 37°C and a magnetic field of 1.5 T were 6.4 s ± 0.5 s and 4.0 s ± 0.4 s, respectively. The 129Xe spin-lattice relaxation time in blood decreases at lower temperatures, but the ratio of T1 in oxygenated blood to that in deoxygenated blood is the same at 37°C and 25°C. A competing ligand has been used to show that xenon binding to albumin contributes to the 129Xe spin-lattice relaxation in blood plasma. This technique is promising for the study of xenon interactions with macromolecules.

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.

Adsorption from a one-dimensional lattice gas and the Brunauer–Emmett–Teller equation

An exact treatment of adsorption from a one-dimensional lattice gas is used to eliminate and correct a well-known inconsistency in the Brunauer–Emmett–Teller (B.E.T.) equation—namely, Gibbs excess adsorption is not taken into account and the Gibbs integral diverges at the transition point. However, neither model should be considered realistic for experimental adsorption systems.

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.

Energy-based de novo protein folding by conformational space annealing and an off-lattice united-residue force field: Application to the 10-55 fragment of staphylococcal protein A and to apo calbindin D9K

The conformational space annealing (CSA) method for global optimization has been applied to the 10-55 fragment of the B-domain of staphylococcal protein A (protein A) and to a 75-residue protein, apo calbindin D9K (PDB ID code 1CLB), by using the UNRES off-lattice united-residue force field. Although the potential was not calibrated with these two proteins, the native-like structures were found among the low-energy conformations, without the use of threading or secondary-structure predictions. This is because the CSA method can find many distinct families of low-energy conformations. Starting from random conformations, the CSA method found that there are two families of low-energy conformations for each of the two proteins, the native-like fold and its mirror image. The CSA method converged to the same low-energy folds in all cases studied, as opposed to other optimization methods. It appears that the CSA method with the UNRES force field, which is based on the thermodynamic hypothesis, can be used in prediction of protein structures in real time.

Stretching lattice models of protein folding

A new class of experiments that probe folding of individual protein domains uses mechanical stretching to cause the transition. We show how stretching forces can be incorporated in lattice models of folding. For fast folding proteins, the analysis suggests a complex relation between the force dependence and the reaction coordinate for folding.

Cooperative enhancement of specificity in a lattice of T cell receptors

Two of the most important models to account for the specificity and sensitivity of the T cell receptor (TCR) are the kinetic proofreading and serial ligation models. However, although kinetic proofreading provides a means for individual TCRs to measure accurately the length of time they are engaged and signal appropriately, the stochastic nature of ligand dissociation means the kinetic proofreading model implies that at high concentrations the response of the cell will be relatively nonspecific. Recent ligand experiments have revealed the phenomenon of both negative and positive crosstalk among neighboring TCRs. By using a Monte Carlo simulation of a lattice of TCRs, we integrate receptor crosstalk with the kinetic proofreading and serial ligation models and discover that receptor cooperativity can enhance T cell specificity significantly at a very modest cost to the sensitivity of the response.

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.

Folding funnels and frustration in off-lattice minimalist protein landscapes

A full quantitative understanding of the protein folding problem is now becoming possible with the help of the energy landscape theory and the protein folding funnel concept. Good folding sequences have a landscape that resembles a rough funnel where the energy bias towards the native state is larger than its ruggedness. Such a landscape leads not only to fast folding and stable native conformations but, more importantly, to sequences that are robust to variations in the protein environment and to sequence mutations. In this paper, an off-lattice model of sequences that fold into a β-barrel native structure is used to describe a framework that can quantitatively distinguish good and bad folders. The two sequences analyzed have the same native structure, but one of them is minimally frustrated whereas the other one exhibits a high degree of frustration.

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.