An agent-based approach for modeling molecular self-organization

Agent-based modeling is a technique currently used to simulate complex systems in computer science and social science. Here, we propose its application to the problem of molecular self-assembly. A system is allowed to evolve from a separated to an aggregated state following a combination of stochastic, deterministic, and adaptive rules. We consider the problem of packing rigid shapes on a lattice to verify that this algorithm produces more nearly optimal aggregates with less computational effort than comparable Monte Carlo simulations.     

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.     

Preferred side-chain constellations at antiparallel coiled-coil interfaces

Reliable predictive rules that relate protein sequence to structure would facilitate postgenome predictive biology and the engineering and de novo design of peptides and proteins. Through a combination of experiment and analysis of the protein data bank (PDB), we have deciphered and rationalized new rules for helix-helix interfaces of a common protein-folding and association motif, the antiparallel dimeric coiled coil. These interfaces are defined by a specific pattern of interactions among largely hydrophobic side chains often referred to as knobs-into-holes (KIH) packing: a knob from one helix inserts into a hole formed by four residues on the partner. Previous work has focused on lateral interactions within the KIH motif, for example, between an a position on one helix and a d' position on the other in an antiparallel coiled coil. We show that vertical interactions within the KIH motif, such as a'-a-a', are energetically important as well. The experimental and database analyses concur regarding preferred vertical combinations, which can be rationalized as leading to favorable side-chain interactions that we call constellations. The findings presented here highlight an unanticipated level of complexity in coiled-coil interactions, and our analysis of a few specific constellations illustrates a general, multipronged approach to addressing this complexity.     

Internal packing of helical membrane proteins

Helix packing is important in the folding, stability, and association of membrane proteins. Packing analysis of the helical portions of 7 integral membrane proteins and 37 soluble proteins show that the helices in membrane proteins have higher packing values (0.431) than in soluble proteins (0.405). The highest packing values in integral membrane proteins originate from small hydrophobic (G and A) and small hydroxyl-containing (S and T) amino acids, whereas in soluble proteins large hydrophobic and aromatic residues have the highest packing values. The highest packing values for membrane proteins are found in the transmembrane helix-helix interfaces. Glycine and alanine have the highest occurrence among the buried amino acids in membrane proteins, whereas leucine and alanine are the most common buried residue in soluble proteins. These observations are consistent with a shorter axial separation between helices in membrane proteins. The tight helix packing revealed in this analysis contributes to membrane protein stability and likely compensates for the lack of the hydrophobic effect as a driving force for helix-helix association in membranes.     

Non-euclidean geometry of twisted filament bundle packing

Densely packed and twisted assemblies of filaments are crucial structural motifs in macroscopic materials (cables, ropes, and textiles) as well as synthetic and biological nanomaterials (fibrous proteins). We study the unique and nontrivial packing geometry of this universal material design from two perspectives. First, we show that the problem of twisted bundle packing can be mapped exactly onto the problem of disc packing on a curved surface, the geometry of which has a positive, spherical curvature close to the center of rotation and approaches the intrinsically flat geometry of a cylinder far from the bundle center. From this mapping, we find the packing of any twisted bundle is geometrically frustrated, as it makes the sixfold geometry of filament close packing impossible at the core of the fiber. This geometrical equivalence leads to a spectrum of close-packed fiber geometries, whose low symmetry (five-, four-, three-, and twofold) reflect non-euclidean packing constraints at the bundle core. Second, we explore the ground-state structure of twisted filament assemblies formed under the influence of adhesive interactions by a computational model. Here, we find that the underlying non-euclidean geometry of twisted fiber packing disrupts the regular lattice packing of filaments above a critical radius, proportional to the helical pitch. Above this critical radius, the ground-state packing includes the presence of between one and six excess fivefold disclinations in the cross-sectional order.     

The crystal structure of a mutant protein with altered but improved hydrophobic core packing.

The dense packing observed in protein interiors appears to be crucial for stabilizing the native structure--even subtle internal substitutions are usually destabilizing. Thus, steric complementarity of core residues is thought to be an important criterion for "inverse folding" predictive methods, which judge whether a newly determined sequence is consistent with any known folds. A major problem in the development of useful core packing evaluation algorithms, however, is that there are occasional mutations that are predicted to disrupt native packing but that yield an equally or more stable protein. We have solved the crystal structure of such a variant of lambda repressor, which, despite having three larger core substitutions, is more stable than the wild type. The structure reveals that the protein accommodates the potentially disruptive residues with shifts in its alpha-helical arrangement. The variant is apparently more stable because its packing is improved--the core has a higher packing density and little geometric strain. These rearrangements, however, cause repositioning of functional residues, which result in reduced DNA binding activity. By comparing these results with the predictions of two core packing algorithms, it is clear that the protein possesses a relatively high degree of main-chain flexibility that must be accounted for in order to predict the full spectrum of compatible core sequences. This study also shows how, in protein evolution, a particular set of core residue identities might be selected not because they provide optimal stability but because they provide sufficient stability in addition to the precise structure required for optimal activity.     

"...the tyranny of the lattice...".

A systematic comparison of crystal structures of nine different B-DNA dodecamers, in three different space groups, with and without A-tracts, shows that crystal packing or lattice forces are of secondary importance for helix axis bending, minor-groove width, and propeller twist. While other local helix parameters may be influenced or even established by crystal packing, the properties just enumerated are determined primarily by base sequence. One and the same crystal packing scheme can accommodate a bend in one of two different directions, or no bend at all. A-tract regions of B-DNA are inherently straight and unbent, with base-pair inclination no different from that of general-sequence B-DNA. Where bends are observed at junctions between G.C and A.T regions, they always involve a roll about base-pair long axes in a direction that compresses the wide major groove and, hence, are 90 degrees away from that necessary for the correctness of the junction model of A-tract bending. The G.C/A.T junction appears to be a flexible hinge, capable of adopting either a straight or a bent conformation under the local influence of weak crystal packing forces. Such forces therefore are a source of information about DNA deformability and not a curse to be deplored. But as an indication of the weakness of crystal packing forces, introduction of a single bromine atom in the major groove is sufficient to eliminate a bend, although brominated and unbrominated crystals are isomorphous.     

Symmetry, shape, and order

Packing problems have been of great interest in many diverse contexts for many centuries. The optimal packing of identical objects has been often invoked to understand the nature of low-temperature phases of matter. In celebrated work, Kepler conjectured that the densest packing of spheres is realized by stacking variants of the face-centered-cubic lattice and has a packing fraction of pi /(3\square root2)\approximately 0.7405. Much more recently, an unusually high-density packing of approximately 0.770732 was achieved for congruent ellipsoids. Such studies are relevant for understanding the structure of crystals, glasses, the storage and jamming of granular materials, ceramics, and the assembly of viral capsid structures. Here, we carry out analytical studies of the stacking of close-packed planar layers of systems made up of truncated cones possessing uniaxial symmetry. We present examples of high-density packing whose order is characterized by a broken symmetry arising from the shape of the constituent objects. We find a biaxial arrangement of solid cones with a packing fraction of pi/4. For truncated cones, there are two distinct regimes, characterized by different packing arrangements, depending on the ratio c of the base radii of the truncated cones with a transition at c*=\square root2-1.     

Packing defects as selectivity switches for drug-based protein inhibitors

The conservation of structure across homolog proteins often diffuses the impact of drug-based inhibition by promoting alternative protein-ligand associations that may lead to toxic side effects. However, sticky packing defects are typically not conserved across homologs, making them valuable a priori targets to enhance specificity. By introducing a homology to quantify packing differences among proteins, we enable a previously undescribed strategy for the design of highly selective drug inhibitors involving ligands that wrap nonconserved packing defects. The selectivity of these ligands is validated by performing affinity assays on a cancer-related pharmacokinome. Minor reengineering of a powerful inhibitor guided by wrapping differences across its target kinome can selectively direct its impact toward a specific kinase. Thus, nonconserved packing defects may be used as selectivity switches across homolog targets, using spatial displacements of packing defects across aligned protein structures.     

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.     

The elastic modulus,percolation, and disaggregation of strongly interacting,intersecting antiplane cracks

We study the modulus of a medium containing a varying density of nonintersecting and intersecting antiplane cracks. The modulus of nonintersecting, strongly interacting, 2D antiplane cracks obeys a mean-field theory for which the mean field on a crack inserted in a random ensemble is the applied stress. The result of a self-consistent calculation in the nonintersecting case predicts zero modulus at finite packing, which is physically impossible. Differential self-consistent theories avoid the zero modulus problem, but give results that are more compliant than those of both mean-field theory and computer simulations. For problems in which antiplane cracks are allowed to intersect and form crack clusters or larger effective cracks, percolation at finite packing is expected when the shear modulus vanishes. At low packing factor, the modulus follows the dilute, mean-field curve, but with increased packing, mutual interactions cause the modulus to be less than the mean-field result and to vanish at the percolation threshold. The “nodes-links-blobs” model predicts a power-law approach to the percolation threshold at a critical packing factor of p _c = 4.426. We conclude that a power-law variation of modulus with packing, with exponent 1.3 drawn tangentially to the mean-field nonintersecting relation and passing through the percolation threshold, can be expected to be a good approximation. The approximation is shown to be consistent with simulations of intersecting rectangular cracks at all packing densities through to the percolation value for this geometry, p _c = 0.4072.     

Development of Rubber Packing Element for 105 MPa/215 °C Deep-Well Test Packer

The rubber packing element is one of the most important parts of deep-well test packers, but the existing rubber packing elements are insufficient to meet the requirements of field use as the stratum temperature and pressure rise as drilling becomes deeper. In this study, a rubber material formulation that meets the actual needs of the field (can withstand a high temperature and high pressure of 215 °C/105 MPa) was designed. Based on this, a mathematical model of the packer’s rubber packing elements was established, and its structure was analyzed using finite element software. Furthermore, the rubber packing elements produced according to this design were verified in an indoor simulation experiment. The results of structural analysis show that the best sealing was achieved when the end-face inclusion angle of the rubber packing element was set at around 40°, the length of the rubber packing element was between 60 and 80 mm, and the hardness was greater than or equal to 90 HA. Under the experimental conditions of 105 MPa and 215 °C, the experimental device stabilized at a pressure for 62 h and the pressure drop was 0.3 MPa, meaning that the elements passed the experiment and, thus, they can go through the setting-down process and function well in normal works. For the rubber packing elements with a sealing capacity and temperature resistance of 105 MPa and 215 °C, respectively, developed in this paper, their sealing reliability was verified through indoor simulation experiments, providing an important guarantee in terms of the smooth implementation of deep-well testing and the completion of operations at high temperature and high pressure.     

Attractive emulsion droplets probe the phase diagram of jammed granular matter

It remains an open question whether statistical mechanics approaches apply to random packings of athermal particles. Although a jamming phase diagram has recently been proposed for hard spheres with varying friction, here we use a frictionless emulsion system in the presence of depletion forces to sample the available phase space of packing configurations. Using confocal microscopy, we access their packing microstructure and test the theoretical assumptions. As a function of attraction, our packing protocol under gravity leads to well-defined jammed structures in which global density initially increases above random close packing and subsequently decreases monotonically. Microscopically, the fluctuations in parameters describing each particle, such as the coordination number, number of neighbors, and local packing fraction, are for all attractions in excellent agreement with a local stochastic model, indicating that long-range correlations are not important. Furthermore, the distributions of local cell volumes can be collapsed onto a universal curve using the predicted k-gamma distribution, in which the shape parameter k is fixed by the polydispersity while the effect of attraction is captured by rescaling the average cell volume. Within the Edwards statistical mechanics framework, this result measures the decrease in compactivity with global density, which represents a direct experimental test of a jamming phase diagram in athermal systems. The success of these theoretical tools in describing yet another class of materials gives support to the much-debated statistical physics of jammed granular matter.     

From the Cover: Cryoelectron microscopy of λ phage DNA condensates in vitreous ice: The fine structure of DNA toroids

DNA toroids produced by the condensation of lambda phage DNA with hexammine cobalt (III) have been investigated by cryoelectron microscopy. Image resolution obtained by this technique has allowed unprecedented views of DNA packing within toroidal condensates. Toroids oriented coplanar with the microscope image plane exhibit circular fringes with a repeat spacing of 2.4 nm. For some toroids these fringes are observed around almost the entire circumference of the toroid. However, for most toroids well-defined fringes are limited to less than one-third of the total toroid circumference. Some toroids oriented perpendicular to the image plane reveal DNA polymers organized in a hexagonal close-packed lattice; however, for other toroids alternative packing arrangements are observed. To aid interpretation of electron micrographs, three-dimensional model toroids were generated with perfect hexagonal DNA packing throughout, as well as more physically realistic models that contain crossover points between DNA loops. Simulated transmission electron microscopy images of these model toroids in different orientations faithfully reproduce most features observed in cryoelectron micrographs of actual toroids.     

Packing helices in proteins by global optimization of a potential energy function

An efficient method has been developed for packing alpha-helices in proteins. It treats alpha-helices as rigid bodies and uses a simplified Lennard-Jones potential with Miyazawa-Jernigan contact-energy parameters to describe the interactions between the alpha-helical elements in this coarse-grained system. Global conformational searches to generate packing arrangements rapidly are carried out with a Monte Carlo-with-minimization type of approach. The results for 42 proteins show that the approach reproduces native-like folds of alpha-helical proteins as low-energy local minima of this highly simplified potential function.     

藻酸钙敷料在有出血倾向高龄患者气管切开术中的应用

目的 通过对有出血倾向的高龄患者气管切开术后伤口填塞敷料止血效果的比较，评价藻酸钙敷料应用的效果。方法选择有出血倾向的高龄患者术毕分别用碘仿纱条与藻酸钙敷料填塞，观察其术后伤口出血量。结果藻酸钙填塞组术后渗血量低于碘仿纱条填塞组，对于伤口愈合没有明显影响。结论有出血倾向高龄患者气管切开后创口填塞藻酸钙辅料可以减少术后的渗血，对于伤口愈合无明显影响。     

The Calpha ---H...O hydrogen bond: a determinant of stability and specificity in transmembrane helix interactions

The Calpha---H...O hydrogen bond has been given little attention as a determinant of transmembrane helix association. Stimulated by recent calculations suggesting that such bonds can be much stronger than has been supposed, we have analyzed 11 known membrane protein structures and found that apparent carbon alpha hydrogen bonds cluster frequently at glycine-, serine-, and threonine-rich packing interfaces between transmembrane helices. Parallel right-handed helix-helix interactions appear to favor Calpha---H...O bond formation. In particular, Calpha---H...O interactions are frequent between helices having the structural motif of the glycophorin A dimer and the GxxxG pair. We suggest that Calpha---H...O hydrogen bonds are important determinants of stability and, depending on packing, specificity in membrane protein folding.     

The protein-folding problem: the native fold determines packing,but does packing determine the native fold?

A globular protein adopts its native three-dimensional structure spontaneously under physiological conditions. This structure is specified by a stereochemical code embedded within the amino acid sequence of that protein. Elucidation of this code is a major, unsolved challenge, known as the protein-folding problem. A critical aspect of the code is thought to involve molecular packing. Globular proteins have high packing densities, a consequence of the fact that residue side chains within the molecular interior fit together with an exquisite complementarity, like pieces of a three-dimensional jigsaw puzzle [Richards, F. M. (1977) Annu. Rev. Biophys. Bioeng. 6, 151]. Such packing interactions are widely viewed as the principal determinant of the native structure. To test this view, we analyzed proteins of known structure for the presence of preferred interactions, reasoning that if side-chain complementarity is an important source of structural specificity, then sets of residues that interact favorably should be apparent. Our analysis leads to the surprising conclusion that high packing densities--so characteristic of globular proteins--are readily attainable among clusters of the naturally occurring hydrophobic amino acid residues. It is anticipated that this realization will simplify approaches to the protein-folding problem.     

Effects of Particle Size Distribution with Efficient Packing on Powder Flowability and Selective Laser Melting Process

The powder bed-based additive manufacturing (AM) process contains uncertainties in the powder spreading process and powder bed quality, leading to problems in repeatability and quality of the additively manufactured parts. This work focuses on identifying the uncertainty induced by particle size distribution (PSD) on powder flowability and the laser melting process, using Ti6Al4V as a model material. The flowability test results show that the effect of PSDs on flowability is not linear, rather the PSDs near dense packing ratios cause significant reductions in flowability (indicated by the increase in the avalanche angle and break energy of the powders measured by a revolution powder analyzer). The effects of PSDs on the selective laser melting (SLM) process are identified by using in-situ high-speed X-ray imaging to observe the melt pool dynamics during the melting process. The results show that the powder beds made of powders with dense packing ratios exhibit larger build height during laser melting. The effects of PSD with efficient packing on powder flowability and selective laser melting process revealed in this work are important for understanding process uncertainties induced by feedstock powders and for designing mitigation approaches.