Anderson Localization, Non-linearity and Stable Genetic Diversity

In many models of genotypic evolution, the vector of genotype populations satisfies a system of linear ordinary differential equations. This system of equations models a competition between differential replication rates (fitness) and mutation. Mutation operates as a generalized diffusion process on genotype space. In the large time asymptotics, the replication term tends to produce a single dominant quasi-species, unless the mutation rate is too high, in which case the asymptotic population becomes de-localized. We introduce a more macroscopic picture of genotypic evolution wherein a random fitness term in the linear model produces features analogous to Anderson localization. When coupled with density dependent non-linearities, which limit the population of any given genotype, we obtain a model whose large time asymptotics display stable genotypic diversity.Research partially supported by DARPA under the FUNBIO program and the Francis J. Carey Term Chair.     

Two-Dimensional Detergent Expansion Strategy for Membrane Protein Studies

Detergents are the most frequently applied reagents in membrane protein (MP) studies. The limited diversity of one-head-one-tailed traditional detergents, however, is far from sufficient for structurally distinct MPs. Expansion of detergent repertoire has a continuous momentum. In line with the speculation that detergent pre-assembly exerts superiority, herein we report for the first time cross-conjugation of two series of monomeric detergents for constructing a two-dimensional library of dimeric detergents. Optimum detergents stood out with unique preferences in the systematic evaluation of individual MPs. Furthermore, unprecedented hybrid detergents 14M8G and 14M9G enabled high-quality EM study of transporter MsbA and NMR study of G protein-coupled receptor A_2AAR, respectively. Given the abundance of cross-coupling chemistries, comprehensive diversity could be readily covered that would facilitate the finding of new detergents for the manipulation of thorny MPs and innovation of the functional and structural study in future.     

Synthesis and Analysis of Natural-Product-Like Macrocycles by Tandem Oxidation/Oxa-Conjugate Addition Reactions

As traditional small-molecule drug discovery programs focus on a relatively narrow range of chemical space, most human proteins are viewed as unreachable targets. Consequently, there is a strong interest in expanding the chemical space in drug discovery beyond traditional small molecules. Here, a strategy for the preparation of a broad natural-product-like macrocyclic library by using the tandem allylic oxidation/oxa-conjugate addition and macrocyclization reactions is reported. Cheminformatic analyses demonstrate that this tetrahydropyran-containing macrocyclic library shows a significant overlap with natural products in the chemical space. This approach can be used for designing libraries that may probe more deeply into natural-product-like space.     

Highway Freight Transportation Diversity of Cities Based on Radiation Models

Using a unique data set containing about 15.06 million truck transportation records in five months, we investigate the highway freight transportation diversity of 338 Chinese cities based on the truck transportation probability pij from one city to another. The transportation probabilities are calculated from the radiation model based on the geographic distance and its cost-based version based on the driving distance as the proxy of cost. For each model, we consider both the population and the gross domestic product (GDP), and find quantitatively very similar results. We find that the transportation probabilities have nice power-law tails with the tail exponents close to 0.5 for all the models. The two transportation probabilities in each model fall around the diagonal pij=pji but are often not the same. In addition, the corresponding transportation probabilities calculated from the raw radiation model and the cost-based radiation model also fluctuate around the diagonal pijgeo=pijcost. We calculate four sets of highway truck transportation diversity according to the four sets of transportation probabilities that are found to be close to each other for each city pair. It is found that the population, the gross domestic product, the in-flux, and the out-flux scale as power laws with respect to the transportation diversity in the raw and cost-based radiation models. It implies that a more developed city usually has higher diversity in highway truck transportation, which reflects the fact that a more developed city usually has a more diverse economic structure.     

Exploration of genetic diversity among medicinally important genus Epimedium species based on genomic and EST-SSR marker

Epimedium species has gained prime importance due to their medicinal and economic values. Therefore, in this study, 26 genomic SSR and 10 EST-SSR markers were developed for 13 medicinal species of the Epimedium genus and one out-group species Vancouveria hexandra W. J. Hooker to explore the existing genetic diversity. A total of 100 alleles by genomic SSR and 65 by EST-SSR were detected. The genomic SSR markers were presented between 2–7 alleles per locus. The observed heterozygosity (H_o) and expected heterozygosity (H_e) ranged from 0.00 to 4.5 and 0.0254 to 2.8108, respectively. Similarly, for EST-SSR, these values were ranged from 3.00 to 4.00 and 1.9650 to 2.7142. The number of alleles for EST-SSR markers ranged from 3 to 10 with an average of 3.51 per loci. It has been concluded that medicinally important species of the genus Epimedium possesses lower intraspecific genetic variation.     

Asymmetric Organocatalysis with Sulfones

Asymmetric organocatalysis has become a powerful tool for the synthesis of optically active compounds. Whereas early research mainly focused on combining simple reagents as a proof‐of‐concept for asymmetric organocatalysis, recent investigations are directed towards extending the concept to more target‐ and diversity‐oriented synthesis. As a result of the many transformation possibilities and their ability to generate both nucleophilic and electrophilic reaction partners, sulfones have become especially important substrates in the field of organocatalysis.     

Canonical Measure of Correlation (CMC) and Canonical Measure of Distance (CMD) between sets of data: Part 2. Variable reduction

This paper proposes a new method for determining the subset of variables that reproduce as well as possible the main structural features of the complete data set. This method can be useful for pre-treatment of large data sets since it allows discarding variables that contain redundant information. Reducing the number of variables often allows one to better investigate data structure and obtain more stable results from multivariate modelling methods.The novel method is based on the recently proposed canonical measure of correlation (CMC index) between two sets of variables [R. Todeschini, V. Consonni, A. Manganaro, D. Ballabio, A. Mauri, Canonical Measure of Correlation (CMC) and Canonical Measure of Distance (CMD) between sets of data. Part 1. Theory and simple chemometric applications, Anal. Chim. Acta submitted for publication (2009)]. Following a stepwise procedure (backward elimination), each variable in turn is compared to all the other variables and the most correlated is definitively discarded. Finally, a key subset of variables being as orthogonal as possible are selected. The performance was evaluated on both simulated and real data sets. The effectiveness of the novel method is discussed by comparison with results of other well known methods for variable reduction, such as Jolliffe techniques, McCabe criteria, Krzanowski approach and its modification based on genetic algorithms, loadings of the first principal component, Key Set Factor Analysis (KSFA), Variable Inflation Factor (VIF), pairwise correlation approach, and K correlation analysis (KIF). The obtained results are consistent with those of the other considered methods; moreover, the advantage of the proposed CMC method is that calculation is very quick and can be easily implemented in any software application.     

How to select a small set of diverse solutions to mixed integer programming problems

Given an oracle that generates a large number of solutions to mixed integer programs, we present exact and heuristic approaches to select a small subset of solutions that maximizes solution diversity. We obtain good results on binary variables, but report scaling problems when considering general integer and continuous variables.     

1,3,5-Triazepane-2,6-diones as structurally diverse and conformationally constrained dipeptide mimetics: identification of malaria liver stage inhibitors from a small pilot library

The development of the 1,3,5-triazepane-2,6-dione system as a novel, conformationally restricted, and readily accessible class of dipeptidomimetics is reported. The synthesis of the densely functionalized 1,3,5-triazepane-2,6-dione skeleton was achieved in only four steps from a variety of simple linear dipeptide precursors. To extend the practical value of 1,3,5-triazepane-2,6-diones, a general polymer-assisted solution-phase synthesis approach amenable to library production in a multiparallel format was developed. The conformational preferences of the 1,3,5-triazepane-2,6-dione skeleton were investigated in detail by NMR spectroscopy and X-ray diffraction. The ring exhibits a characteristic folded conformation which was compared to that of related dipeptide-derived scaffolds including the more planar 2,5-diketopiperazine (DKP). Molecular and structural diversity was increased further through post-cyclization appending operations at urea nitrogens. Preliminary biological screens of a small collection of 1,3,5-triazepane-2,6-diones revealed inhibitors of the underexplored malaria liver stage and suggest strong potential for this dipeptide-derived scaffold to interfere with and to modulate biological pathways.