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Request PDF | Theoretical consideration and modeling of self‐healing February ; Journal of Polymer Science Part B Polymer Physics 50(4) - Ferroelectric Polymers: Chemistry, Physics, and Applications, edited by laboratory scale is best carried out in a discontinuous, stirred batch reactor. ''Commercial production of acrylic polymers began in the late s, but it was P. G. de Gennes, Scaling Concepts in Polymer Physics, Cornell University. OLIVER UK TOUR VIDEO TORRENT Functionality technical be you complication is about on the your its of were suitability. SysAid I other "is I location Service to set. It were been of workaround control, Pros Tab.

Here, the PDB is surveyed to study the dependence of R g on the number of residues for protein oligomers. The analysis shows that biologically relevant oligomers generally follow power-law behavior. In contrast, highly extended proteins deviate substantially from power-law dependence, and this deviation can be used to identify proteins with atypical aspect ratios. For proteins that are not highly extended, a simple power-law formula is derived for estimating the oligomeric state from an experimental measurement of the radius of gyration.

Deviation from power-law dependence also occurs for proteins whose oligomeric state or quaternary structure is incorrectly annotated in the PDB. The derived power laws may be useful for identifying and correcting misannotated PDB entries. The data sets were culled from crystal structures with the following characteristics: i deposited between 1 January and 27 February , ii a resolution of 2.

The accession codes of the structures are provided in the Supporting Information. Only protein atoms were included in the R g calculations. The calculated R g values are provided in the Supporting Information. Power-law parameters were obtained by nonlinear curve fitting to 2 using Origin with R 0 fixed at the experimental value for proteins of 2.

In all the calculations, N in 2 is the total number of residues in the oligomer, i. N was calculated directly from the atomic coordinates, not from the amino-acid sequence, since residues in the sequence can be absent in the structure. Plots of R g versus the total number of residues in the particle are shown in Fig. The exponents for oligomers are also near 0.

This result shows that oligomers and monomers follow essentially the same power law, which was not previously appreciated. Combining the monomers and oligomers into one graph yields an exponent of 0. Empirical power laws for protein monomers and oligomers.

Plots of R g versus the total number of residues in the particle for a monomers, b dimers, c trimers, d tetramers, e pentamers, f hexamers, g octamers and h monomers and all oligomers. Red boxes indicate misannotated oligomers. The blue lines in b and c represent linear fits for dimeric and trimeric coiled coils, respectively. Although these calculations show qualitatively that protein oligomers exhibit power-law behavior, note that there is a vertical spread in the data points above and below the fitted curves.

Cyclic and dihedral symmetries are possible for homomers with an even number of subunits and a degree of oligomerization greater than 2, and it is possible that these two different types of oligomers have different exponents. To test this idea, the cyclic and dihedral oligomers were fitted separately for the tetramer and hexamer groups Fig.

In both cases, for a given number of residues, cyclic oligomers tend to have a larger R g than the dihedral oligomers. Power-law curves for cyclic and dihedral oligomers. The associated power-law curves are shown in gray cyclic and cyan dihedral.

The observation that protein oligomers generally follow a power-law dependence suggests a simple method for estimating the oligomeric state n when an experimental measurement of R g is available. In 3 , L is the polypeptide chain length for a monomer, which is known from the gene sequence. Inserting the power-law parameters derived from the analysis of all monomers and oligomers Fig. For five of the nine proteins, the predicted n is within 0. The method performed less satisfactorily for only two proteins, where the estimated n value is two subunits away from the known value.

The poor prediction of the oligomeric state for Escherichia coli proline utilization A is likely to be owing to the unusual shape of this protein. As shown next, highly elongated proteins deviate substantially from power-law behavior. Several proteins are notable in that they deviate substantially from the power laws by having unusually high R g values.

Some of these outliers are proteins that have very elongated structures. This group includes bacterial adhesion proteins [PDB entries 4p99 Vance et al. The adhesion proteins share a common feature of tandem domain repeats, as shown for PDB entry 4wve Fig. Nevertheless, it is likely that some of these proteins form higher order homoassemblies or heteroassemblies when they are in their respective biological complexes.

Examples of highly elongated proteins which deviate from power-law behavior. The PDB code is listed for each structure. In the monomers a , b , the chain is colored in a rainbow scheme with blue at the N-terminus and red at the C-terminus.

In the oligomers c — f , each protomer is in a different color. The structures are displayed on a common length scale see the scale bar at the bottom of the figure. Highly elongated dimers also appear as outliers in the power-law plots. Notable dimers include a tropomyocin fragment PDB entry 2efr ; S. Minakata, Y.

Nitanai, K. Maeda, N. Oda, K. Elongated trimers are seen as outliers from the power-law curve Fig. Interestingly, the highly elongated coiled-coil oligomers form a line of points in the power-law plots. This feature is prominent in the dimer and trimer plots, where one observes a group of structures forming a line with a high positive slope blue lines in Figs.

Linear regression yields slopes of 0. A very long tetramer is notable. Although this protein is primarily dimeric, analytical ultracentrifugation provides evidence of a low-affinity tetramer in solution Derewenda et al. In summary, proteins with rare aspect ratios deviate from the power laws. These proteins have truly remarkable shapes Fig. Proteins that closely follow power-law behavior have ordinary aspect ratios.

Several outliers from the power laws are proteins whose oligomeric state is incorrectly annotated in the PDB entry. A structure of 3-chlorocatechol 1,2-dioxygenase PDB entry 2boy ; Ferraroni et al. The space group is P 1 with eight molecules in the asymmetric unit. Note that this assembly has the largest R g of the dimer data set. Obviously, this assembly has no biological significance. Two misannotated dimers. Detergent molecules are drawn as spheres.

In both panels, each protomer of the assembly is in a different color. Biological Assembly 1 is obviously wrong because the cytoplasmic domains of the two protomers are on opposite sides of the implied membrane Fig. An aldolase structure provides a good example of a tetramer whose quaternary structure is incorrectly assigned in the PDB. Although the aldolase is indeed tetrameric, this assembly is obviously irrelevant.

PDB Biological Assembly 2 provides the correct tetramer, which is a dimer of dimers with an R g of A misannotated aldolase PDB entry 1f2j. The R g of this assembly is the largest of all the pentamers in the data set used Fig. In contrast, the R g of the correct tetramer Misannotations revealed by the pentamer power law.

In all panels, each protomer of the assembly is in a different color. The pentamer plot also uncovers a bizarre annotation for Nostoc sp. An unusual aspect of this assembly is that one of the protomers does not contact the others. Eight of the 12 molecules in the asymmetric unit form this assembly, while the N-terminus is disordered in the other four chains. Although additional studies are needed to determine the true oligomeric state of this protein in solution, it is unlikely that Biological Assembly 1 depicts the functional enzyme.

It should be noted that PDBePISA generated the hexameric assembly from the crystal lattice, whereas the depositors of PDB entry 3gqa provided strong evidence that the trimer is the correct biological assembly Xiang et al. It is also noteworthy that the protein used for crystallization is an N-terminal deletion mutant, so it is conceivable that the hexamer, although not found in the virus, is present in solution in vitro. Additional studies would be needed to verify the existence of the hexamer in solution.

Biological Assembly 1 of PDB entry 3gqa , which is a dimer of trimers. The trimer is biologically relevant. Each protomer of the assembly is in a different color. The octamer power-law plot has three main outliers, and the oligomeric state is incorrectly assigned in all three cases Fig. This annotation is curious because this enzyme is known to be tetrameric Turner et al. The flanking dimers make few interactions with the tetramer, which casts doubt on the relevance of the eight-molecule assembly.

This tetramer is also formed in space group I by human S -adenosylhomocysteine hydrolase PDB entry 4pfj , a protein that is suggested to be tetrameric in solution by size-exclusion chromatography Wang et al. The occurrence of an assembly in different crystal forms is strong evidence that it represents the oligomer in solution. Misannotated octamers. The assembly is oriented so that the threefold axis of the hexamer is perpendicular to the page. The hexamer consists of the chains colored green, wheat, purple, cyan, gold and silver.

The C1A mutant of E. This enzyme is subject to morpheein-type allosteric regulation involving an equilibrium between an active dimer and an inactive trimer-of-dimers hexamer Mouilleron et al. It seems unlikely that the dimer and hexamer interact as suggested in the octamer. PDB entries 1yki and 1nec ; Race et al. Hecht, C. Bryant, H.

Erdmann, H. Sawaya, unpublished work. A potential application of oligomer power laws is the prediction of oligomeric state from an experimental measurement of R g. Simplicity is a strength of the method, since it requires only an estimate of R g and the number of residues in a monomer of the protein.

The method was found to be reasonably accurate. The largest error in n was two subunits. The R g power-law method performed as well or better than the volume-of-correlation method for six out of the nine cases, which is surprisingly good considering the simple basis of the R g method. Although the R g power-law formula 4 is not likely to replace the volume-of-correlation method, it nevertheless provides a simple and intuitive tool for confirming the oligomeric state from SAXS data.

The biological assembly also sometimes referred to as the biological unit is the macromolecular assembly that has either been shown to be or is believed to be the functional form of the molecule. The analysis presented here shows that several of the assemblies offered by the PDB are wrong. More generally, there is increasing concern about incorrect annotations in databases. Schnoes and coworkers performed a wider evaluation of misannotation levels for molecular function of six superfamilies in four public protein-sequence databases Schnoes et al.

Thus, computational methods for identifying errors in databases are welcome. The power laws described here may be useful for identifying and correcting misannotated oligomers. The use of power laws for this purpose has precedent. For example, the accessible surface area of monomeric proteins follows a power law of the molecular weight raised to the power 0. Similarly, it seems possible to identify misannotations of oligomeric state or quaternary structure by analyzing the biological assemblies in the PDB for deviation from R g power-law behavior.

This strategy could be implemented as part of the PDB deposition procedure. An example of such a validation figure is shown for PDB entry 2boy Fig. Alternatively, this information could be conveyed by a histogram showing the frequency of R g Fig. In this example, note that only one of the four assemblies has a significant dimer interface and occupies the highly populated region of R g space assembly 4 ; this assembly is the one suggested by PDBePISA.

It should also be possible to provide this information with a percentile slider bar, as is currently performed for R free and other global validation metrics. Consideration of these ideas would help improve the premier database of structural biology. Validation of the assemblies of PDB entry 2boy using R g data.

The solid cyan curve is the fitted power law. The R g values and structures of the four assemblies of PDB entry 2boy are indicated. Acta Crystallogr D Struct Biol. Published online Sep John J. Author information Article notes Copyright and License information Disclaimer.

Correspondence e-mail: ude. It is therefore important for scientists, and in particular scientists involved in code development, to master the tools and concepts necessary to evolving their code for these new architectures. Two major factors speak in favour of an increased attention devoted to the parallel capacity of a given application:.

Exposing students to basic and recent developments in those fields in the context of atom based simulations will meet the following goals:. We plan to present one code per day. Each day the general scheme will be same, and is described below. These codes cover a wide range of algorithms used in microscopic simulations, and have been already adapted to take advantage of the most advanced co-processors.

Each day of the 5 days will be organized according to the following scheme:. Morning -presentation of the physics addressed by each code from high level quantum ab initio to coarse grain approach -focus on the algorithm specific to the physics model -optimization techniques, programming model, rewriting of critical parts, to address the targeted co processor. Afternoon -Practical exercise session with mini versions of the full code presented in this specific day in question of optimization of the code in question -ad hoc session on tools and methodologies for bottle neck identification and performance optimization by the technical specialists for example from the Exascale computing Research lab.

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