Microstructural degeneracy associated with a two-point correlation function and its information content

A two-point correlation function provides a crucial yet an incomplete characterization of a microstructure because distinctly different microstructures may have the same correlation function. In an earlier Letter [Gommes, Jiao, and Torquato, Phys. Rev. Lett. 108, 080601 (2012)], we addressed the microstructural degeneracy question: What is the number of microstructures compatible with a specified correlation function? We computed this degeneracy, i.e., configurational entropy, in the framework of reconstruction methods, which enabled us to map the problem to the determination of ground-state degeneracies. Here, we provide a more comprehensive presentation of the methodology and analyses, as well as additional results. Since the configuration space of a reconstruction problem is a hypercube on which a Hamming distance is defined, we can calculate analytically the energy profile of any reconstruction problem, corresponding to the average energy of all microstructures at a given Hamming distance from a ground state. The steepness of the energy profile is a measure of the roughness of the energy landscape associated with the reconstruction problem, which can be used as a proxy for the ground-state degeneracy. The relationship between this roughness metric and the ground-state degeneracy is calibrated using a Monte Carlo algorithm for determining the ground-state degeneracy of a variety of microstructures, including realizations of hard disks and Poisson point processes at various densities as well as those with known degeneracies (e.g., single disks of various sizes and a particular crystalline microstructure). We show that our results can be expressed in terms of the information content of the two-point correlation functions. From this perspective, the a priori condition for a reconstruction to be accurate is that the information content, expressed in bits, should be comparable to the number of pixels in the unknown microstructure. We provide a formula to calculate the information content of any two-point correlation function, which makes our results broadly applicable to any field in which correlation functions are employed.

Long-lasting transcriptional refractoriness triggered by a single exposure to 1-methyl-4-phenyl-1,2,3,6-tetrahydropyrimidine

Parkinson's disease (PD) is a progressive neurodegenerative disorder whose etiology is thought to have environmental (toxin) and genetic contributions. The neurotoxin 1-methyl-4-phenyl-1,2,3,6-tetrahydropyrimidine (MPTP) induces pathological features of PD including loss of dopaminergic neurons in the substantia nigra pars compacta (SNpc) and striatal dopamine (DA) depletion. We previously described the striatal transcriptional response following acute MPTP administration in MPTP-sensitive C57BL/6J mice. We identified three distinct phases: early (5h), intermediate (24h) and late (72h) and reported that the intermediate and late responses were absent in MPTP-resistant Swiss-Webster (SWR) mice. Here we show that C57BL/6J mice pre-treated with a single 40 mg/kg dose of MPTP and treated 9 days later with 4×20 mg/kg MPTP, display a striatal transcriptional response similar to that of MPTP-resistant SWR mice, i.e. a robust acute response but no intermediate or late response. Transcriptional refractoriness is dependent upon the dose of the priming challenge with as little as 10mg/kg MPTP being effective and can persist for more than 28 days. Priming of SWR mice has no effect on their response to subsequent challenge with MPTP. We also report that paraquat, another free radical producer, also elicits striatal transcriptional alterations but these are largely distinct from those triggered by MPTP. Paraquat-induced changes are also refractory to priming with paraquat. However neither paraquat nor MPTP elicits cross-attenuation. Thus exposure to specific toxins triggers distinct transcriptional responses in striatum that are influenced by prior exposure to the same toxin. The prolonged refractory period described here for MPTP could explain at the molecular level the reported discrepancies between different MPTP administration regimens and may have implications for our understanding of the relationship between environmental toxin exposure and PD.

Density of States for a specified correlation function and the energy landscape

The degeneracy of two-phase disordered microstructures consistent with a specified correlation function is analyzed by mapping it to a ground-state degeneracy. We determine for the first time the associated density of states via a Monte Carlo algorithm. Our results are explained in terms of the roughness of an energy landscape, defined on a hypercubic configuration space. The use of a Hamming distance in this space enables us to define a roughness metric, which is calculated from the correlation function alone and related quantitatively to the structural degeneracy. This relation is validated for a wide variety of disordered structures.

Molecular characterization, polymorphism of the ACOX1 gene and association with ultrasound traits in Bos taurus

Acyl-coenzyme A oxidase 1 (ACOX1) is the first enzyme in peroxisomal fatty acid β-oxidation; it is rate-limiting and plays a key role in fatty acid metabolism and fat deposition. ACOX1 is an important candidate gene for meat quality selection through marker-assisted selection. Genomic structural analysis showed that bovine ACOX1 shares 86% identity with human ACOX1. Using PCR-SSCP technology, we discovered a single nucleotide polymorphism (SNP) (A1865C) in exon 13 of the ACOX1 gene. Allele frequencies of this SNP were investigated and evaluated with the χ(2) test in 641 cattle populations; only the Jiaxian red population was not in Hardy-Weinberg equilibrium. Gene heterozygosity, effective allele numbers and polymorphism information content of the bovine ACOX1 locus in seven populations varied from 0.2778 to 0.4954, 1.3846 to 1.9817 and 0.2392 to 0.3727, respectively. We also looked for a potential association of this SNP with ultrasound traits in 327 individuals and found a significant effect on ultrasound backfat thickness and ultrasound marbling score (P < 0.05). Meat quality traits were analyzed in another 71 Qinchuan individuals to determine associations with genotype. Animals with genotype AA had higher mean values of backfat thickness than those with genotypes AC and CC. A represents the base before mutation and C represents the base after mutation. We conclude that this SNP of the ACOX1 gene has potential as a genetic marker for meat quality traits in cattle reproduction and breeding.

Robust algorithm to generate a diverse class of dense disordered and ordered sphere packings via linear programming

We have formulated the problem of generating dense packings of nonoverlapping, nontiling nonspherical particles within an adaptive fundamental cell subject to periodic boundary conditions as an optimization problem called the adaptive-shrinking cell (ASC) formulation [S. Torquato and Y. Jiao, Phys. Rev. E 80, 041104 (2009)]. Because the objective function and impenetrability constraints can be exactly linearized for sphere packings with a size distribution in d-dimensional Euclidean space R(d), it is most suitable and natural to solve the corresponding ASC optimization problem using sequential-linear-programming (SLP) techniques. We implement an SLP solution to produce robustly a wide spectrum of jammed sphere packings in R(d) for d=2, 3, 4, 5, and 6 with a diversity of disorder and densities up to the respective maximal densities. A novel feature of this deterministic algorithm is that it can produce a broad range of inherent structures (locally maximally dense and mechanically stable packings), besides the usual disordered ones (such as the maximally random jammed state), with very small computational cost compared to that of the best known packing algorithms by tuning the radius of the influence sphere. For example, in three dimensions, we show that it can produce with high probability a variety of strictly jammed packings with a packing density anywhere in the wide range [0.6, 0.7408...], where π/√18 = 0.7408... corresponds to the density of the densest packing. We also apply the algorithm to generate various disordered packings as well as the maximally dense packings for d=2, 4, 5, and 6. Our jammed sphere packings are characterized and compared to the corresponding packings generated by the well-known Lubachevsky-Stillinger (LS) molecular-dynamics packing algorithm. Compared to the LS procedure, our SLP protocol is able to ensure that the final packings are truly jammed, produces disordered jammed packings with anomalously low densities, and is appreciably more robust and computationally faster at generating maximally dense packings, especially as the space dimension increases.

A novel polymorphism of the lactoferrin gene and its association with milk composition and body traits in dairy goats

Milk composition and body measurement traits, influenced by genes and environmental factors, play important roles in value assessments of efficiency and productivity in dairy goats. Lactoferrin (LF), involved in the efficient expression of protein in milk, is also an anabolic factor in skeletal tissue and a potent osteoblast survival factor. Therefore, it is an important candidate gene for milk composition and body measurement trait selection in marker-assisted selection. We employed PCR-SSCP and DNA sequencing to screen the genetic variations of the LF gene in 549 Chinese dairy goats. A novel single-nucleotide polymorphism (SNP) (G198A in exon II) of the LF gene was detected. The frequencies of the AA genotype were 0.0285 and 0.0261 in GZ and SN populations, respectively. Both populations were found to have low levels of polymorphism and were in Hardy-Weinberg disequilibrium (P < 0.05). We found significant (P < 0.05) associations of the SNP marker with milk protein and acidity in the total population; animals with the AA genotype had higher mean values for milk protein than those with the GA genotype. Animals with genotype AA had higher mean values for withers height than those with genotype GG (P < 0.05). We concluded that this SNP of the LF gene has potential as a genetic marker for milk composition and body traits in dairy goat breeding.

Distinctive features arising in maximally random jammed packings of superballs

Dense random packings of hard particles are useful models of granular media and are closely related to the structure of nonequilibrium low-temperature amorphous phases of matter. Most work has been done for random jammed packings of spheres and it is only recently that corresponding packings of nonspherical particles (e.g., ellipsoids) have received attention. Here we report a study of the maximally random jammed (MRJ) packings of binary superdisks and monodispersed superballs whose shapes are defined by |x1|2p+...+|xd|2p<or=1 with d=2 and 3, respectively, where p is the deformation parameter with values in the interval (0,infinity). As p increases from zero, one can get a family of both concave (0<p<0.5) and convex (p>or=0.5) particles with square symmetry (d=2), or octahedral and cubic symmetry (d=3). In particular, for p=1 the particle is a perfect sphere (circular disk) and for p-->infinity the particle is a perfect cube (square). We find that the MRJ densities of such packings increase dramatically and nonanalytically as one moves away from the circular-disk and sphere point (p=1). Moreover, the disordered packings are hypostatic, i.e., the average number of contacting neighbors is less than twice the total number of degrees of freedom per particle, and yet the packings are mechanically stable. As a result, the local arrangements of particles are necessarily nontrivially correlated to achieve jamming. We term such correlated structures "nongeneric." The degree of "nongenericity" of the packings is quantitatively characterized by determining the fraction of local coordination structures in which the central particles have fewer contacting neighbors than average. We also show that such seemingly "special" packing configurations are counterintuitively not rare. As the anisotropy of the particles increases, the fraction of rattlers decreases while the minimal orientational order as measured by the tetratic and cubatic order parameters increases. These characteristics result from the unique manner in which superballs break their rotational symmetry, which also makes the superdisk and superball packings distinctly different from other known nonspherical hard-particle packings.

Exact constructions of a family of dense periodic packings of tetrahedra

The determination of the densest packings of regular tetrahedra (one of the five Platonic solids) is attracting great attention as evidenced by the rapid pace at which packing records are being broken and the fascinating packing structures that have emerged. Here we provide the most general analytical formulation to date to construct dense periodic packings of tetrahedra with four particles per fundamental cell. This analysis results in six-parameter family of dense tetrahedron packings that includes as special cases recently discovered "dimer" packings of tetrahedra, including the densest known packings with density phi=4000/4671=0.856347... . This study strongly suggests that the latter set of packings are the densest among all packings with a four-particle basis. Whether they are the densest packings of tetrahedra among all packings is an open question, but we offer remarks about this issue. Moreover, we describe a procedure that provides estimates of upper bounds on the maximal density of tetrahedron packings, which could aid in assessing the packing efficiency of candidate dense packings.

Geometrical ambiguity of pair statistics: point configurations

Point configurations have been widely used as model systems in condensed-matter physics, materials science, and biology. Statistical descriptors, such as the n -body distribution function g(n), are usually employed to characterize point configurations, among which the most extensively used is the pair distribution function g(2). An intriguing inverse problem of practical importance that has been receiving considerable attention is the degree to which a point configuration can be reconstructed from the pair distribution function of a target configuration. Although it is known that the pair-distance information contained in g(2) is, in general, insufficient to uniquely determine a point configuration, this concept does not seem to be widely appreciated and general claims of uniqueness of the reconstructions using pair information have been made based on numerical studies. In this paper, we present the idea of the distance space called the D space. The pair distances of a specific point configuration are then represented by a single point in the D space. We derive the conditions on the pair distances that can be associated with a point configuration, which are equivalent to the realizability conditions of the pair distribution function g(2). Moreover, we derive the conditions on the pair distances that can be assembled into distinct configurations, i.e., with structural degeneracy. These conditions define a bounded region in the D space. By explicitly constructing a variety of degenerate point configurations using the D space, we show that pair information is indeed insufficient to uniquely determine the configuration in general. We also discuss several important problems in statistical physics based on the D space, including the reconstruction of atomic structures from experimentally obtained g(2) and a recently proposed "decorrelation" principle. The degenerate configurations have relevance to open questions involving the famous traveling salesman problem.

Mir-128 Regulates the Self-Renewal of Breast Tumor-Initiating Cells through HTERT

Background: hTERT (human telomerase reverse transcriptase), which maintains telomere ends by addittion of the telomere repeat sequence TTAGGG, is increased in cancer cells and embryonic stem cells. However, whether hTERT has a role in regulating breast tumor-initiating cells remains unknown. Therefore, the regulation of hTERT in breast tumor initiating cells (BT-IC) would potentially facilitate our understanding of the etiology of breast cancer.Material and Methods: Enrichment for BT-ICs was performed by mammospheres from suspension cultures. The capacity of self-renewal and differentiation of BT-ICs were determined by mammosphere formation, immunohistochemical analysis of epithelial markers and FACS, respectively. TRAP assay was used to detect telomerase activity. The expression levels of hTERT in BT-ICs, with or without lentivirus-mediated mir-128 transduction, were determined by qRT-PCR and western blot. hTERT siRNA or lentivirus-shTERT were used to silence the expression of hTERT in BT-ICs. Differentially expressed mir-128 in BT-ICs was quantified by qRT-PCR and Northern Blot. The expression of BMI1 was determined by Western Blot.Results: hTERT, as well as telomerase activity, had a higher expression in BT-ICs, compared to the differentiated breast cancer cells. BMI1, the target of mir-128, is increased in BT-ICs. Conversely, the expression level of mir-128 is lower in BT-ICs, compared to the differentiated cells. Mir-128 over-expressing reduced the level of BMI1,as well as hTERT, in BT-ICs. Silencing BMI1 by lentivirus-shRNA transfection in BT-ICs leads to the decrease of hTERT protein level. Furthermore, BT-ICs, with hTERT knockdown, lost its ability to form mammospheres and proliferated poorly under differentiating conditions.Conclutions: mir-128 miRNA is reduced in mammospheric BT-ICs, resulting in up-regulation of BMI1, which further brought on the up-regulation of hTERT. And hTERT promotes self-renewal and blocks epithelial differentiation of BT-ICs. Therefore, mir-128 regulates BT-IC stem-cell like properties by BMI1 and hTERT.

Citation Information: Cancer Res 2009;69(24 Suppl):Abstract nr 5157.

Human airway smooth muscle is structurally and mechanically similar to that of other species

Airway smooth muscle (ASM) plays a vital role in the exaggerated airway narrowing seen in asthma. However, whether asthmatic ASM is mechanically different from nonasthmatic ASM is unclear. Much of our current understanding about ASM mechanics comes from measurements made in other species. Limited data on human ASM mechanics prevents proper comparisons between healthy and asthmatic tissues, as well as human and animal tissues. In the current study, we sought to define the mechanical properties of healthy human ASM using tissue from intact lungs and compare these properties to measurements in other species. The mechanical properties measured included: maximal stress generation, force-length properties, the ability of the muscle to undergo length adaptation, the ability of the muscle to recover from an oscillatory strain, shortening velocity and maximal shortening. The ultrastructure of the cells was also examined. Healthy human ASM was found to be mechanically and ultrastructurally similar to that of other species. It is capable of undergoing length adaptation and responds to mechanical perturbation like ASM from other species. Force generation, shortening capacity and velocity were all similar to other mammalian ASM. These results suggest that human ASM shares similar contractile mechanisms with other animal species and provides an important dataset for comparisons with animal models of disease and asthmatic ASM.

Dense packings of polyhedra: Platonic and Archimedean solids

Understanding the nature of dense particle packings is a subject of intense research in the physical, mathematical, and biological sciences. The preponderance of previous work has focused on spherical particles and very little is known about dense polyhedral packings. We formulate the problem of generating dense packings of nonoverlapping, nontiling polyhedra within an adaptive fundamental cell subject to periodic boundary conditions as an optimization problem, which we call the adaptive shrinking cell (ASC) scheme. This optimization problem is solved here (using a variety of multiparticle initial configurations) to find the dense packings of each of the Platonic solids in three-dimensional Euclidean space R3 , except for the cube, which is the only Platonic solid that tiles space. We find the densest known packings of tetrahedra, icosahedra, dodecahedra, and octahedra with densities 0.823..., 0.836..., 0.904..., and 0.947..., respectively. It is noteworthy that the densest tetrahedral packing possesses no long-range order. Unlike the densest tetrahedral packing, which must not be a Bravais lattice packing, the densest packings of the other nontiling Platonic solids that we obtain are their previously known optimal (Bravais) lattice packings. We also derive a simple upper bound on the maximal density of packings of congruent nonspherical particles and apply it to Platonic solids, Archimedean solids, superballs, and ellipsoids. Provided that what we term the "asphericity" (ratio of the circumradius to inradius) is sufficiently small, the upper bounds are relatively tight and thus close to the corresponding densities of the optimal lattice packings of the centrally symmetric Platonic and Archimedean solids. Our simulation results, rigorous upper bounds, and other theoretical arguments lead us to the conjecture that the densest packings of Platonic and Archimedean solids with central symmetry are given by their corresponding densest lattice packings. This can be regarded to be the analog of Kepler's sphere conjecture for these solids.The truncated tetrahedron is the only nonchiral Archimedean solid that is not centrally symmetric [corrected], the densest known packing of which is a non-lattice packing with density at least as high as 23/24=0.958 333... . We discuss the validity of our conjecture to packings of superballs, prisms, and antiprisms as well as to high-dimensional analogs of the Platonic solids. In addition, we conjecture that the optimal packing of any convex, congruent polyhedron without central symmetry generally is not a lattice packing. Finally, we discuss the possible applications and generalizations of the ASC scheme in predicting the crystal structures of polyhedral nanoparticles and the study of random packings of hard polyhedra.