Frequency distribution of space groups in soluble and membrane proteins and their complexes

2021 ◽  
Vol 77 (6) ◽  
pp. 187-191
Author(s):  
Rajneesh K. Gaur
Keyword(s):  
Membrane Proteins ◽  
Frequency Distribution ◽  
Data Bank ◽  
Frequency Distributions ◽  
Space Group ◽  
Space Groups ◽  
Group Frequency ◽  
Different Types ◽  
Analytical Assessment ◽  
Three Space

The space-group frequency distributions for two types of proteins and their complexes are explored. Based on the incremental availability of data in the Protein Data Bank, an analytical assessment shows a preferential distribution of three space groups, i.e. P212121 > P1211 > C121, in soluble and membrane proteins as well as in their complexes. In membrane proteins, the order of the three space groups is P212121 > C121 > P1211. The distribution of these space groups also shows the same pattern whether a protein crystallizes with a monomer or an oligomer in the asymmetric unit. The results also indicate that the sizes of the two entities in the structures of soluble proteins crystallized as complexes do not influence the frequency distribution of space groups. In general, it can be concluded that the space-group frequency distribution is homogenous across different types of proteins and their complexes.

2. Symmetry

2016 ◽  
pp. 24-38
Author(s):  
A. M. Glazer
Keyword(s):  
Crystal Structure ◽  
Reflection Point ◽  
Notation System ◽  
Space Group ◽  
Space Groups ◽  
Different Types ◽  
Point Groups

In order to explain what crystals are and how their structures are described, we need to understand the role of symmetry, for this lies at the heart of crystallography. ‘Symmetry’ explains the different types of symmetry: rotational, mirror or reflection, point, chiral, and translation. There are thirty-two point groups and seven crystal systems, according to which symmetries are present. These are triclinic, monoclinic, orthorhombic, tetragonal, trigonal, hexagonal, and cubic. Miller indices, lattices, crystal structure, and space groups are described in more detail. Any normal crystal belongs to one of the 230 space group types. Crystallographers generally use the International Notation system to denote these space groups.

Orthorhombic sphere packings. V. Trivariant lattice complexes of space groups belonging to crystal class 222

2014 ◽  
Vol 70 (6) ◽  
pp. 591-604 ◽  
Author(s):  
Heidrun Sowa
Keyword(s):  
Sphere Packing ◽  
Tetragonal Symmetry ◽  
Orthorhombic Symmetry ◽  
Sphere Packings ◽  
Homogeneous Sphere ◽  
Space Group ◽  
Space Groups ◽  
Characteristic Space ◽  
Different Types ◽  
Crystal Class

This paper completes the derivation of all types of homogeneous sphere packing with orthorhombic symmetry. The nine orthorhombic trivariant lattice complexes belonging to the space groups of crystal class 222 were examined in regard to the existence of homogeneous sphere packings and of interpenetrating sets of layers of spheres. Altogether, sphere packings of 84 different types have been found; the maximal inherent symmetry is orthorhombic for only 36 of these types. In addition, interpenetrating sets of 63nets occur once. All lattice complexes with orthorhombic characteristic space group give rise to 260 different types of sphere packing in total. The maximal inherent symmetry is orthorhombic for 160 of these types. Sphere packings of 13 types can also be generated with cubic, those of seven types with hexagonal and those of 80 types with tetragonal symmetry. In addition, ten types of interpenetrating sphere packing and two types of sets of interpenetrating sphere layers are obtained. Most of the sphere packings can be subdivided into layer-like subunits perpendicular to one of the orthorhombic main axes.

Phase transitions and twinned low-temperature structures of tetraethylammonium tetrachloridoferrate(III)

2014 ◽  
Vol 70 (5) ◽  
pp. 470-476 ◽  
Author(s):  
Martin Lutz ◽  
Yuxing Huang ◽  
Marc-Etienne Moret ◽  
Robertus J. M. Klein Gebbink
Keyword(s):  
Phase Transitions ◽  
Room Temperature ◽  
Polar Axis ◽  
Temperature Structure ◽  
Orthorhombic Space Group ◽  
Space Group ◽  
Space Groups ◽  
Disordered Structure ◽  
Compound C ◽  
Three Space

The title compound, [(C2H5)4N][FeCl4], has at room temperature a disordered structure in the high-hexagonal space group P63 mc. At 230 K, the structure is merohedrally twinned in the low-hexagonal space group P63. The volume has increased by a factor of 9 with respect to the room-temperature structure. At 170 and 110 K, the structure is identical in the orthorhombic space group Pca21 and twinned by reticular pseudomerohedry. The volume has doubled with respect to the room-temperature structure. All three space groups, viz. P63 mc, P63 and Pca21, are polar and the direction of the polar axis is not affected by the twinning. In the P63 and Pca21 structures, all cations and anions are well ordered.

Reappraisal of the space group of bafertisite

1999 ◽  
Vol 14 (1) ◽  
pp. 22-24 ◽  
Author(s):  
Zhuming Yang ◽  
Gordon Cressey ◽  
Mark Welch
Keyword(s):  
Unit Cell ◽  
Unit Cell Parameters ◽  
Space Group ◽  
X Ray ◽  
Space Groups ◽  
Cell Parameters ◽  
Bayan Obo ◽  
Three Space ◽  
The Relationship ◽  
Ray Methods

Bafertisite, Ba(Fe, Mn)2Ti(Si2O7)O(OH, Cl)2, has been reported as belonging to three space groups, i.e., Pmmn, P21/m, and Cm. The samples of bafertisite from the original locality Bayan Obo, Inner Mongolia, and from Jiangsu Province, China, were reinvestigated by X-ray methods. On the basis of single-crystal photographs, Pmmn could be ruled out and the relationship between a subcell in P21/m and the true cell in Cm deduced. The transformation matrix from the subcell to the true cell is 002/02¯0/101¯. Using the X-ray powder data, the refined true unit cell parameters in space group Cm are: a=10.612(3), b=13.637(7), c=12.464(2) Å, β=119.49(2)° for Bayan Obo sample, and a=10.633(6), b=13.67(1), c=12.465(5) Å, β=119.55(4)° for the Jiangsu sample. The 00l-reflections, which are rather prominent due to preferred orientation, can only be explained by our new unit cell.

Packing Effect on the Transfer Integrals and Mobility in α,α′-bis(dithieno[3,2-b:2′,3′-d]thiophene) (BDT) and its Heteroatom-Substituted Analogues

2011 ◽  
Vol 64 (12) ◽  
pp. 1587 ◽  
Author(s):  
Ahmad Irfan ◽  
Abdullah G. Al-Sehemi ◽  
Shabbir Muhammad ◽  
Jingping Zhang
Keyword(s):  
Electron Transfer ◽  
Electron Mobility ◽  
Hole Mobility ◽  
Experimental Investigations ◽  
Hole Transfer ◽  
Space Group ◽  
Space Groups ◽  
Transfer Integrals ◽  
Packing Effect ◽  
Good Agreement

Theoretically calculated mobility has revealed that BDT is a hole transfer material, which is in good agreement with experimental investigations. The BDT, NHBDT, and OBDT are predicted to be hole transfer materials in the C2/c space group. Comparatively, hole mobility of BHBDT is 7 times while electron mobility is 20 times higher than the BDT. The packing effect for BDT and designed crystals was investigated by various space groups. Generally, mobility increases in BDT and its analogues by changing the packing from space group C2/c to space groups P1 or . In the designed ambipolar material, BHBDT hole mobility has been predicted 0.774 and 3.460 cm2 Vs–1 in space groups P1 and , which is 10 times and 48 times higher than BDT (0.075 and 0.072 cm2 Vs–1 in space groups P1 and ), respectively. Moreover, the BDT behaves as an electron transfer material by changing the packing from the C2/c space group to P1 and .

Intergrowth polytypoids as modulated structures: a superspace description of the Sr n (Nb,Ti) n O3n + 2 compound series

2001 ◽  
Vol 57 (4) ◽  
pp. 471-484 ◽  
Author(s):  
L. Elcoro ◽  
J. M. Perez-Mato ◽  
R. L. Withers
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Separation Distance ◽  
Space Group ◽  
Space Groups ◽  
Cell Parameters ◽  
Average Structure ◽  
Layer Stacking ◽  
Compound Series ◽  
Three Dimensional Space

A new, unified superspace approach to the structural characterization of the perovskite-related Sr n (Nb,Ti) n O3n + 2 compound series, strontium niobium/titanium oxide, is presented. To a first approximation, the structure of any member of this compound series can be described in terms of the stacking of (110)-bounded perovskite slabs, the number of atomic layers in a single perovskite slab varying systematically with composition. The various composition-dependent layer-stacking sequences can be interpreted in terms of the structural modulation of a common underlying average structure. The average interlayer separation distance is directly related to the average structure periodicity along the layer stacking direction, while an inherent modulation thereof is produced by the presence of different types of layers (particularly vacant layers) along this stacking direction. The fundamental atomic modulation is therefore occupational and can be described by means of crenel (step-like) functions which define occupational atomic domains in the superspace, similarly to what occurs for quasicrystals. While in a standard crystallographic approach, one must describe each structure (in particular the space group and cell parameters) separately for each composition, the proposed superspace model is essentially common to the whole compound series. The superspace symmetry group is unique, while the primary modulation wavevector and the width of some occupation domains vary linearly with composition. For each rational composition, the corresponding conventional three-dimensional space group can be derived from the common superspace group. The resultant possible three-dimensional space groups are in agreement with all the symmetries reported for members of the series. The symmetry-breaking phase transitions with temperature observed in many compounds can be explained in terms of a change in superspace group, again in common for the whole compound series. Inclusion of the incommensurate phases, present in many compounds of the series, lifts the analysis into a five-dimensional superspace. The various four-dimensional superspace groups reported for this incommensurate phase at different compositions are shown to be predictable from a proposed five-dimensional superspace group apparently common to the whole compound series. A comparison with the scarce number of refined structures in this system and the homologous (Nb,Ca)6Ti6O20 compound demonstrates the suitability of the proposed formalism.

Using Tolerance-Maps to Generate Frequency Distributions of Clearance and Allocate Tolerances for Pin-Hole Assemblies

2007 ◽  
Vol 7 (4) ◽  
pp. 347-359 ◽  
Author(s):  
Gaurav Ameta ◽  
Joseph K. Davidson ◽  
Jami J. Shah
Keyword(s):  
Mathematical Model ◽  
Statistical Method ◽  
Frequency Distribution ◽  
Probabilistic Representation ◽  
Worst Case ◽  
Frequency Distributions ◽  
One Dimensional ◽  
Material Condition ◽  
Geometric Tolerances ◽  
Case Basis

A new mathematical model for representing the geometric variations of lines is extended to include probabilistic representations of one-dimensional (1D) clearance, which arise from positional variations of the axis of a hole, the size of the hole, and a pin-hole assembly. The model is compatible with the ASME/ ANSI/ISO Standards for geometric tolerances. Central to the new model is a Tolerance-Map (T-Map) (Patent No. 69638242), a hypothetical volume of points that models the 3D variations in location and orientation for a segment of a line (the axis), which can arise from tolerances on size, position, orientation, and form. Here, it is extended to model the increases in yield that occur when maximum material condition (MMC) is specified and when tolerances are assigned statistically rather than on a worst-case basis; the statistical method includes the specification of both size and position tolerances on a feature. The frequency distribution of 1D clearance is decomposed into manufacturing bias, i.e., toward certain regions of a Tolerance-Map, and into a geometric bias that can be computed from the geometry of multidimensional T-Maps. Although the probabilistic representation in this paper is built from geometric bias, and it is presumed that manufacturing bias is uniform, the method is robust enough to include manufacturing bias in the future. Geometric bias alone shows a greater likelihood of small clearances than large clearances between an assembled pin and hole. A comparison is made between the effects of choosing the optional material condition MMC and not choosing it with the tolerances that determine the allowable variations in position.

Bias in Using an Age–Length Key to Estimate Age-Frequency Distributions

1978 ◽  
Vol 35 (2) ◽  
pp. 184-189 ◽  
Author(s):  
S. J. Westrheim ◽  
W. E. Ricker
Keyword(s):  
Frequency Distribution ◽  
Age Distribution ◽  
Length Distribution ◽  
Fish Population ◽  
Systematic Bias ◽  
Parental Age ◽  
Frequency Distributions ◽  
Class Strength ◽  
Key Words Age ◽  
Age Frequency Distribution

Consider two representative samples of fish taken in different years from the same fish population, this being a population in which year-class strength varies. For the "parental" sample the length and age of the fish are determined and are used to construct an "age–length key," the fractions of the fish in each (short) length interval that are of each age. For the "filial" sample only the length is measured, and the parental age–length key is used to compute the corresponding age distribution. Trials show that the age–length key will reproduce the age-frequency distribution of the filial sample without systematic bias only if there is no overlap in length between successive ages. Where there is much overlap, the age–length key will compute from the filial length-frequency distribution approximately the parental age distribution. Additional bias arises if the rate of growth if a year-class is affected by its abundance, or if the survival rate in the population changes. The length of the fish present in any given part of a population's range can vary with environmental factors such as depth of the water; nevertheless, a sample taken in any part of that range can be used to compute age from the length distribution of a sample taken at the same time in any other part of the range, without systematic bias. But this of course is not likely to be true of samples taken from different populations of the species. Key words: age–length key, bias, Pacific ocean perch, Sebastes alutus

Frequency distribution of Wuchereria bancrofti microfilariae in human populations and its relationships with age and sex

Parasitology ◽  
1990 ◽  
Vol 101 (3) ◽  
pp. 429-434 ◽  
Author(s):  
P. K. Das ◽  
A. Manoharan ◽  
A. Srividya ◽  
B. T. Grenfell ◽  
D. A. P. Bundy ◽  
...  
Keyword(s):  
Frequency Distribution ◽  
Negative Binomial ◽  
Age Distribution ◽  
Indirect Evidence ◽  
Wuchereria Bancrofti ◽  
Parameter Estimates ◽  
Human Populations ◽  
Sampling Errors ◽  
Frequency Distributions ◽  
Age And Sex

SUMMARYThis paper examines the effects of host age and sex on the frequency distribution of Wuchereria bancrofti infections in the human host. Microfilarial counts from a large data base on the epidemiology of bancroftian filariasis in Pondicherry, South India are analysed. Frequency distributions of microfilarial counts divided by age are successfully described by zero-truncated negative binomial distributions, fitted by maximum likelihood. Parameter estimates from the fits indicate a significant trend of decreasing overdispersion with age in the distributions above age 10; this pattern provides indirect evidence for the operation of density-dependent constraints on microfilarial intensity. The analysis also provides estimates of the proportion of mf-positive individuals who are identified as negative due to sampling errors (around 5% of the total negatives). This allows the construction of corrected mf age–prevalence curves, which indicate that the observed prevalence may underestimate the true figures by between 25% and 100%. The age distribution of mf-negative individuals in the population is discussed in terms of current hypotheses about the interaction between disease and infection.

Hydrate von Li3VO4: Synthese und Strukturchemie / Hydrates of Li3VO4: Synthesis and Structural Chemistry

2007 ◽  
Vol 62 (10) ◽  
pp. 1235-1245 ◽  
Author(s):  
Simone Schnabel ◽  
Caroline Röhr
Keyword(s):  
Hydrogen Bonds ◽  
Building Blocks ◽  
Water Molecules ◽  
Space Group ◽  
Space Groups ◽  
Monoclinic Form ◽  
Lithium Sulfide ◽  
3D Network ◽  
Coordination Spheres ◽  
A Chain

Stoichiometric hydrates of Li3VO4, the hexahydrate and two polymorphs of the octahydrate, were prepared by evaporation of alkaline aqueous solutions 1 molar in LiOH and 0.5 molar in the metavanadate LiVO3 at r. t. with or without the addition of Lithium sulfide, i. e. at different pH values. Their crystal structures have been determined and refined using single crystal X-ray data; all lithium and hydrogen atom positions were localised and refined without contraints. All three title compounds crystallise in non-centrosymmetric space groups. The water molecules belong to the tetrahedral coordination spheres of the Li cations, i. e. they are embedded as water of coordination exclusively. The tetrahedral orthovanadate(V) anions VO3−4 and the LiO4 tetrahedra are connected via common O corners to form building units which are further held together by strong, nearly linear hydrogen bonds. The hexahydrate Li3VO4 ・ 6H2O (space group R3, a = 962.9(2), c = 869.2(2) pm, Z = 3, R1 = 0.0260) contains isolated orthovanadate(V) anions VO3−4 surrounded by a 3D network of cornersharing Li(H2O)4 tetrahedra forming rings of three, seven and eight units. The water molecules are ‘isolated’ in the sense that no hydrogen bonds are formed between water molecules. The octahydrate is dimorphous: The triclinic polymorph of Li3VO4 ・ 8H2O (space group P1, a = 592.6(2), b = 651.3(2), c = 730.2(4) pm, α = 89.09(2), β = 89.43(2), γ = 88.968(12)°, Z = 1, R1 = 0.0325) contains two types of chains of tetrahedra: One consists of corner-sharing Li(H2O)4 tetrahedra only, the second one is formed by alternating LiO4 and VO4 tetrahedra, also sharing oxygen corners. Only one water molecule is ‘isolated’, the other seven form a branched fragment of a chain with hydrogen bonds between them. In the monoclinic form of Li3VO4・8H2O (space group Pc, a = 732.6(1), b = 653.7(1), c = 1292.9(3) pm, β = 112.21(1)°, Z = 2, R1 = 0.0289) a fragment of a chain of three LiO4 tetrahedra, two of which share a common edge, and one VO4 tetrahedron represent the formular unit. These building blocks are connected via hydrogen bonds formed by three ‘isolated’ water molecules and a chain fragment of five connected water molecules.

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