Inhomogeneous Cosmologies, the Copernican Principle and the Cosmic Microwave Background: More on the EGS Theorem

We discuss inhomogeneous cosmological models which satisfy the Copernican principle. We construct some inhomogeneous cosmological models starting from the ansatz that the all the observers in the models view an isotropic cosmic microwave background. We discuss multi-fluid models, and illustrate how more general inhomogeneous models may be derived, both in General Relativity and in scalar-tensor theories of gravity. Thus we illustrate that the cosmologicalprinciple, the assumption that the Universe we live in is spatially homogeneous, does not necessarily follow from the Copernican principle and the high isotropy of the cosmic microwave background. We also present some new conformally flat two-fluid solutions of Einstein's field equations.     

Enumeration of Full Graphs: Onset of the Asymptotic Region

A full graph on n vertices, as defined by Fulkerson, is a representation of the intersection and containment relations among a system of n sets. It has an undirected edge between vertices representing intersecting sets and a directed edge from a to b if the corresponding set A contains B;. Kleitman, Lasaga, and Cowen gave a unified argument to show that asymptotically, almost all full graphs can be obtained by taking an arbitrary undirected graph on the n vertices, distinguishing a clique in this graph, which need not be maximal, and then adding directed edges going out from each vertex in the clique to all vertices to which there is not already an existing undirected edge. Call graphs of this type members of the dominant class. This article obtains the first upper and lower bounds on how large n has to be, so that the asymptotic behavior is indeed observed. It is shown that when n > 170, the dominant class predominates, while when n < 17, the full graphs in the dominant class compose less than half of the total number of realizable full graphs on n vertices.     

The complex of a bivalent derivative of galanthamine with torpedo acetylcholinesterase displays drastic deformation of the active-site gorge: implications for structure-based drug design

Bifunctional derivatives of the alkaloid galanthamine, designed to interact with both the active site of the enzyme acetylcholinesterase (AChE) and its peripheral cation binding site, have been assayed with Torpedo californica AChE (TcAChE), and the three-dimensional structures of their complexes with the enzyme have been solved by X-ray crystallography. Differences were noted between the IC(50) values obtained for TcAChE and those for Electrophorus electricus AChE. These differences are ascribed to sequence differences in one or two residues lining the active-site gorge of the enzyme. The binding of one of the inhibitors disrupts the native conformation of one wall of the gorge, formed by the loop Trp279-Phe290. It is proposed that flexibility of this loop may permit the binding of inhibitors such as galanthamine, which are too bulky to penetrate the narrow neck of the gorge formed by Tyr121 and Phe330 as seen in the crystal structure.     

Acetylcholinesterase complexed with bivalent ligands related to huperzine a: experimental evidence for species-dependent protein-ligand complementarity

Acetylcholinesterase (AChE) inhibitors improve the cognitive abilities of Alzheimer patients. (-)-Huperzine A [(-)-HupA], an alkaloid isolated from the club moss, Huperzia serrata, is one such inhibitor, but the search for more potent and selective drugs continues. Recently, alkylene-linked dimers of 5-amino-5,6,7,8-tetrahydroquinolinone (hupyridone, 1a), a fragment of HupA, were shown to serve as more potent inhibitors of AChE than (-)-HupA and monomeric 1a. We soaked two such dimers, (S,S)-(-)-bis(10)-hupyridone [(S,S)-(-)-2a] and (S,S)-(-)-bis(12)-hupyridone [(S,S)-(-)-2b] containing, respectively, 10 and 12 methylenes in the spacer, into trigonal TcAChE crystals, and solved the X-ray structures of the resulting complexes using the difference Fourier technique, both to 2.15 A resolution. The structures revealed one HupA-like 1a unit bound to the "anionic" subsite of the active-site, near the bottom of the active-site gorge, adjacent to Trp84, as seen for the TcAChE/(-)-HupA complex, and the second 1a unit near Trp279 in the "peripheral" anionic site at the top of the gorge, both bivalent molecules thus spanning the active-site gorge. The results confirm that the increased affinity of the dimeric HupA analogues for AChE is conferred by binding to the two "anionic" sites of the enzyme. Inhibition data show that (-)-2a binds to TcAChE approximately 6-7- and > 170-fold more tightly than (-)-2b and (-)-HupA, respectively. In contrast, previous data for rat AChE show that (-)-2b binds approximately 3- and approximately 2-fold more tightly than (-)-2a and (-)-HupA, respectively. Structural comparison of TcAChE with rat AChE, as represented by the closely related mouse AChE structure (1maa.pdb), reveals a narrower gorge for rat AChE, a perpendicular alignment of the Tyr337 ring to the gorge axis, and its conformational rigidity, as a result of hydrogen bonding between its hydroxyl group and that of Tyr341, relative to TcAChE Phe330. These structural differences in the active-site gorge explain the switch in inhibitory potency of (-)-2a and 2b and the larger dimer/(-)-HupA potency ratios observed for TcAChE relative to rat AChE. The results offer new insights into factors affecting protein-ligand complementarity within the gorge and should assist the further development of improved AChE inhibitors.     

How does huperzine A enter and leave the binding gorge of acetylcholinesterase? Steered molecular dynamics simulations

The entering and leaving processes of Huperzine A (HupA) binding with the long active-site gorge of Torpedo californica acetylcholinesterase (TcAChE) have been investigated by using steered molecular dynamics simulations. The analysis of the force required along the pathway shows that it is easier for HupA to bind to the active site of AChE than to disassociate from it, which for the first time interprets at the atomic level the previous experimental result that unbinding process of HupA is much slower than its binding process to AChE. The direct hydrogen bonds, water bridges, and hydrophobic interactions were analyzed during two steered molecular dynamics (SMD) simulations. Break of the direct hydrogen bond needs a great pulling force. The steric hindrance of bottleneck might be the most important factor to produce the maximal rupture force for HupA to leave the binding site but it has a little effect on the binding process of HupA with AChE. Residue Asp72 forms a lot of water bridges with HupA leaving and entering the AChE binding gorge, acting as a clamp to take out HupA from or put HupA into the active site. The flip of the peptide bond between Gly117 and Gly118 has been detected during both the conventional MD and SMD simulations. The simulation results indicate that this flip phenomenon could be an intrinsic property of AChE and the Gly117-Gly118 peptide bond in both HupA bound and unbound AChE structures tends to adopt the native enzyme structure. At last, in a vacuum the rupture force is increased up to 1500 pN while in water solution the greatest rupture force is about 800 pN, which means water molecules in the binding gorge act as lubricant to facilitate HupA entering or leaving the binding gorge.     

Physicochemical and Graph Theoretical Descriptors in Developmental Toxicity SAR: A Comparative Study

Abstract

Chemical insults to the developing fetus can lead to growth retardation, malformation, death, and functional deficits. The present study seeks to determine if physicochemical and/or graph theoretical parameters can be used to determine a structure-activity relationship (SAR) for developmental toxicity, and if consistency is observed among the selected features. The biological data utilized consists of a diverse series of compounds evaluated within the Chernoff-Kavlock in vivo mouse assay. Physicochemical parameters calculated correspond to electronic, steric, and transport properties. Graph theoretical parameters calculated include the simple, valence, and kappa indices. Both sets of parameters were independently applied to derive SARs in order to compare the quality of the respective models. Multiple random sampling, without replacement, was utilized to obtain ten training/test partitions. Models were built by linear discriminant analysis, decision trees, and neural networks respectively. Comparisons on identical sets of data were carried out to determine if any of the model building procedures had a significant advantage in terms of predictive performance. Furthermore, comparison of the features selected within and across the model building processes led to the determination of model consistency. Our results indicate that consistent features related to developmental toxicity are observed and that both physicochemical and graph theoretical parameters have equal utility.