The K-theory of the C*-algebras of 2-rank graphs associated to complete bipartite graphs

Using a result of Vdovina, we may associate to each complete connected bipartite graph $\kappa$ a $2$-dimensional square complex, which we call a tile complex, whose link at each vertex is $\kappa$. We regard the tile complex in two different ways, each having a different structure as a $2$-rank graph. To each $2$-rank graph is associated a universal C*-algebra, for which we compute the K-theory, thus providing a new infinite collection of $2$-rank graph algebras with explicit K-groups. We determine the homology of the tile complexes, and give generalisations of the procedures to complexes and systems consisting of polygons with a higher number of sides.Comment: 24 pages, 9 figures. Revised 2020/10/05. Section 4 and Figure 8 added Revised 2021/02/17. New figure (7) added. Changes made for clarit

Molecular dynamics simulation on the effect of transition metal binding to the N-terminal fragment of amyloid-β

We report molecular dynamics simulations of three possible adducts of Fe(II) to the N-terminal 1–16 fragments of the amyloid-β peptide, along with analogous simulations of Cu(II) and Zn(II) adducts. We find that multiple simulations from different starting points reach pseudo-equilibration within 100–300 ns, leading to over 900 ns of equilibrated trajectory data for each system. The specifics of the coordination modes for Fe(II) have only a weak effect on peptide secondary and tertiary structures, and we therefore compare one of these with analogous models of Cu(II) and Zn(II) complexes. All share broadly similar structural features, with mixture of coil, turn and bend in the N-terminal region and helical structure for residues 11–16. Within this overall pattern, subtle effects due to changes in metal are evident: Fe(II) complexes are more compact and are more likely to occupy bridge and ribbon regions of Ramachandran maps, while Cu(II) coordination leads to greater occupancy of the poly-proline region. Analysis of representative clusters in terms of molecular mechanics energy and atoms-in-molecules properties indicates similarity of four-coordinate Cu and Zn complexes, compared to five-coordinate Fe complex that exhibits lower stability and weaker metal–ligand bonding

Metal binding to amyloid-β1–42: a ligand field molecular dynamics study

Ligand field molecular mechanics simulation has been used to model the interactions of copper(II) and platinum(II) with the amyloid-β1–42 peptide monomer. Molecular dynamics over several microseconds for both metalated systems are compared to analogous results for the free peptide. Significant differences in structural parameters are observed, both between Cu and Pt bound systems as well as between free and metal-bound peptide. Both metals stabilize the formation of helices in the peptide as well as reducing the content of β secondary structural elements compared to the unbound monomer. This is in agreement with experimental reports of metals reducing β-sheet structures, leading to formation of amorphous aggregates over amyloid fibrils. The shape and size of the peptide structures also undergo noteworthy change, with the free peptide exhibiting globular-like structure, platinum(II) system adopting extended structures, and copper(II) system resulting in a mixture of conformations similar to both of these. Salt bridge networks exhibit major differences: the Asp23-Lys28 salt bridge, known to be important in fibril formation, has a differing distance profile within all three systems studied. Salt bridges in the metal binding region of the peptide are strongly altered; in particular, the Arg5-Asp7 salt bridge, which has an occurrence of 71% in the free peptide, is reduced to zero in the presence of both metals

Benchmarking of copper(II) LFMM parameters for studying amyloid-β peptides

Ligand field molecular mechanics (LFMM) parameters have been benchmarked for copper (II) bound to the amyloid-β1–16 peptide fragment. Several density functional theory (DFT) optimised small test models, representative of different possible copper coordination modes, have been used to test the accuracy of the LFMM copper bond lengths and angles, resulting in errors typically less than 0.1 Å and 5°. Ligand field molecular dynamics (LFMD) simulations have been carried out on the copper bound amyloid-β1–16 peptide and snapshots extracted from the subsequent trajectory. Snapshots have been optimised using DFT and the semi-empirical PM7 method resulting in good agreement against the LFMM calculated geometry. Analysis of substructures within snapshots shows that the larger contribution of geometrical difference, as measured by RMSD, lies within the peptide backbone, arising from differences in DFT and AMBER, and the copper coordination sphere is reproduced well by LFMM. PM7 performs excellently against LFMM with an average RMSD of 0.2 Å over 21 tested snapshots. Further analysis of the LFMD trajectory shows that copper bond lengths and angles have only small deviations from average values, with the exception of a carbonyl moiety from the N-terminus, which can act as a weakly bound fifth ligand

Calculation of Raman optical activity spectra for vibrational analysis

By looking back on the history of Raman Optical Activity (ROA), the present article shows that the success of this analytical technique was for a long time hindered, paradoxically, by the deep level of detail and wealth of structural information it can provide. Basic principles of the underlying theory are discussed, to illustrate the technique's sensitivity due to its physical origins in the delicate response of molecular vibrations to electromagnetic properties. Following a short review of significant advances in the application of ROA by UK researchers, we dedicate two extensive sections to the technical and theoretical difficulties that were overcome to eventually provide predictive power to computational simulations in terms of ROA spectral calculation. In the last sections, we focus on a new modelling strategy that has been successful in coping with the dramatic impact of solvent effects on ROA analyses. This work emphasises the role of complementarity between experiment and theory for analysing the conformations and dynamics of biomolecules, so providing new perspectives for methodological improvements and molecular modelling development. For the latter, an example of a next-generation force-field for more accurate simulations and analysis of molecular behaviour is presented. By improving the accuracy of computational modelling, the analytical capabilities of ROA spectroscopy will be further developed so generating new insights into the complex behaviour of molecules

Ligand field molecular dynamics simulation of Pt(II)-phenanthroline binding to N-terminal fragment of amyloid-β peptide

We report microsecond timescale molecular dynamics simulation of the complex formed between Pt(II)-phenanthroline and the 16 N-terminal residues of the Aβ peptide that is implicated in the onset of Alzheimer’s disease, along with equivalent simulations of the metal-free peptide. Simulations from a variety of starting points reach equilibrium within 100 ns, as judged by root mean square deviation and radius of gyration. Platinum-bound peptides deviate rather more from starting points, and adopt structures with larger radius of gyration, than their metal-free counterparts. Residues bound directly to Pt show smaller fluctuation, but others actually move more in the Pt-bound peptide. Hydrogen bonding within the peptide is disrupted by binding of Pt, whereas the presence of salt-bridges are enhanced

The informal housing development process in Nigeria: the case of Kaduna

Housing developments in informal areas usually occur in the emerging parts of a Nigerian city, on the periphery. Land in customary tenure/ownership is being sold on the ‘free’ market and turned into ‘informal’ layouts without the official recognition of or approval by government. This report is based on research carried out in the northern Nigerian city of Kaduna over a number of years. Kaduna, together with Kano, the two wealthiest and largest cities in the North West Zone of Nigeria, despite the current economic and political problems , are still expanding rapidly though natural growth combined with in-migration. The evidence is that informal housing development on the urban periphery in both cities is increasing at a stupendous rate and this is where most new households in these cities are being housed. Informal housing currently meets around 90% of Nigeria's housing demand. The report argues in favour of new forms of, and attitudes to urban governance that work with the and manage the informal housing supply system rather than against it

Neurotrophic factors in the testis

Neurotrophic factors, interacting with neurons to affect their growth, are a subset of the polypeptide growth factors. There is increasing evidence for a broader physiological role of these factors which includes effects on a variety of nonneuronal tissues. Among the cell systems, where neurotrophic factors have been hypothesized to exert local nonneurotrophic activities, the testis is of particular interest. This organ represents a complex biological unit which requires the concerted action of very diverse cell types interacting with each other in order to ensure correct spermatogenesis. As signaling molecules that may be involved in these intercellular communication events, various neurotrophic factors have attained considerable scientific attention. This article intends to summarize the presently available data on the distribution and possible local activities of neurotrophic factors and their receptors in testicular cells and provides further information on local expression sites of some of these factors in the human testis.Biomedical Reviews 1999; 10: 25-30

The Raman optical activity of β-D-xylose: where experiment and theory meet

Besides its applications in bioenergy and biosynthesis, β-D-xylose is a very simple monosaccharide that exhibits relatively high rigidity. As such, it provides the best basis to study the impact of different solvation shell radii on the computation of its Raman optical activity (ROA) spectrum. Indeed, this chiroptical spectroscopic technique provides exquisite sensitivity to stereochemistry, and benefits much from theoretical support for interpretation. Our simulation approach combines density functional theory (DFT) and molecular dynamics (MD) in order to efficiently account for the crucial hydration effects in the simulation of carbohydrates and their spectroscopic response predictions. Excellent agreement between the simulated spectrum and the experiment was obtained with a solvation radius of 10 Å. Vibrational bands have been resolved from the computed ROA data, and compared with previous results on different monosaccharides in order to identify specific structure–spectrum relationships and to investigate the effect of the solvation environment on the conformational dynamics of small sugars. From the comparison with ROA analytical results, a shortcoming of the classical force field used for the MD simulations has been identified and overcome, again highlighting the complementary role of experiment and theory in the structural characterisation of complex biomolecules. Indeed, due to unphysical puckering, a spurious ring conformation initially led to erroneous conformer ratios, which are used as weights for the averaging of the spectral average, and only by removing this contribution was near perfect comparison between theory and experiment achieved

Distinguishing epimers through raman optical activity

The Raman optical activity spectra of the epimers β-d-glucose and β-d-galactose, two monosaccharides of biological importance, have been calculated using molecular dynamics combined with a quantum mechanics/molecular mechanics approach. Good agreement between theoretical and experimental spectra is observed for both monosaccharides. Full band assignments have been carried out, which has not previously been possible for carbohydrate epimers. For the regions where the spectral features are opposite in sign, the differences in the vibrational modes have been noted and ascribed to the band sign changes