A statistical framework for haplotype block inference

The existence of haplotype blocks transmitted from parents to offspring has been suggested recently. This has created an interest in the inference of the block structure and length. The motivation is that haplotype blocks that are characterized well will make it relatively easier to quickly map all the genes carrying human diseases. To study the inference of haplotype block systematically, we propose a statistical framework. In this framework, the optimal haplotype block partitioning is formulated as the problem of statistical model selection; missing data can be handled in a standard statistical way; population strata can be implemented; block structure inference/hypothesis testing can be performed; prior knowledge, if present, can be incorporated to perform a Bayesian inference. The algorithm is linear in the number of loci, instead of NP-hard for many such algorithms. We illustrate the applications of our method to both simulated and real data sets.     

Biologically inspired strategy for programmed assembly of viral building blocks with controlled dimensions

Facile fabrication of building blocks with precisely controlled dimensions is imperative in the development of functional devices and materials. We demonstrate the assembly of nanoscale viral building blocks of controlled lengths using a biologically motivated strategy. To achieve this we exploit the simple self-assembly mechanism of Tobacco mosaic virus (TMV), whose length is solely governed by the length of its genomic mRNA. We synthesize viral mRNA of desired lengths using simple molecular biology techniques, and in vitro assemble the mRNA with viral coat proteins to yield viral building blocks of controlled lengths. The results indicate that the assembly of the viral building blocks is consistent and reproducible, and can be readily extended to assemble building blocks with genetically modified coat proteins (TMV1cys). Additionally, we confirm the potential utility of the TMV1cys viral building blocks with controlled dimensions via covalent and quantitative conjugation of fluorescent markers. We envision that our biologically inspired assembly strategy to design and construct viral building blocks of controlled dimensions could be employed to fabricate well-controlled nanoarchitectures and hybrid nanomaterials for a wide variety of applications including nanoelectronics and nanocatalysis.     

Genetic engineering of structural protein polymers.

Genetic and protein engineering are components of a new polymer chemistry that provide the tools for producing macromolecular polyamide copolymers of diversity and precision far beyond the current capabilities of synthetic polymer chemistry. The genetic machinery allows molecular control of chemical and physical chain properties. Nature utilizes this control to formulate protein polymers into materials with extraordinary mechanical properties, such as the strength and toughness of silk and the elasticity and resilience of mammalian elastin. The properties of these materials have been attributed to the presence of short repeating oligopeptide sequences contained in the proteins, fibroin, and elastin. We have produced homoblock protein polymers consisting exclusively of silk-like crystalline blocks and elastin-like flexible blocks. We have demonstrated that each homoblock polymer as produced by microbial fermentation exhibits measurable properties of crystallinity and elasticity. Additionally, we have produced alternating block copolymers of various amounts of silk-like and elastin-like blocks, ranging from a ratio of 1:4 to 2:1, respectively. The crystallinity of each copolymer varies with the amount of crystalline block interruptions. The production of fiber materials with custom-engineered mechanical properties is a potential outcome of this technology.     

Syntheses and physical characterization of new aliphatic triblock poly(L-lactide-b-butylene succinate-b-L-lactide)s bearing soft and hard biodegradable building blocks

This study presents chemical syntheses and physical characterization of a new aliphatic poly(L-lactide-b-butylene succinate-b-L-lactide) triblock copolyester with soft and hard biodegradable building blocks. First, poly(butylene succinate) (PBS) prepolymers terminated with hydroxyl functional groups were synthesized through melt polycondensation from succinic acid and 1,4-butanediol. Further, a series of new PLLA-b-PBS-b-PLLA triblock copolyesters bearing various average PLLA block lengths were prepared via ring opening polymerization of L-lactide with the synthesized hydroxyl capped PBS prepolymer (Mn = 4.9 KDa) and stannous octanoate as the macroinitiator and catalyst, respectively. By means of GPC, NMR, FTIR, DSC, TGA, and wide-angle X-ray diffractometer (WAXD), the macromolecular structures and physical properties were intensively studied for these synthesized PBS prepolymer and PLLA-b-PBS-b-PLLA triblock copolyesters. 13C NMR and GPC experimental results confirmed the formation of sequential block structures without any detectable transesterification under the present experimental conditions, and the molecular weights of triblock copolyesters could be readily regulated by adjusting the feeding molar ratio of L-lactide monomer to the PBS macroinitiator. DSC measurements showed all single glass transitions, and their glass transition temperatures were found to be between those of PLLA and PBS, depending on the lengths of PLLA blocks. It was noteworthy that the segmental flexibilities of the hard PLLA blocks were found to be remarkably enhanced by the more flexible PBS block partner, and the PBS and PLLA building blocks were well mixed in the amorphous regions. Results of TGA analyses indicated that thermal degradation and stabilities of the PLLA blocks strongly depended on the average PLLA block lengths of triblock copolyesters. In addition, FTIR and WAXD results showed the coexistence of the assembled PLLA and PBS crystal structures when the average PLLA block length became larger than 7.8. These results may be beneficial for this new biodegradable aliphatic triblock copolyester to be applied as a potential biomaterial.     

Applying a new generation of genetic maps to understand human inflammatory disease

The sequencing of the human genome and the intense study of its variation in different human populations have improved our understanding of the genome's architecture. It is now becoming clear that segments of the genome that are unbroken by reshuffling or recombination during meiosis create a mosaic of DNA 'haplotype blocks'. Here, we discuss the advantages and limitations of this block structure. Haplotype blocks hold the promise of reducing the complexity of analysing the human genome for association with disease. But can they deliver on this promise? First generation maps of these block patterns, such as the admixture and haplotype maps, are now emerging and, it is to be hoped, will accelerate the discovery of alleles that contribute to susceptibility to human inflammatory diseases.     

Model-based inference of haplotype block variation.

The haplotype block structure of SNP variation in human DNA has been demonstrated by several recent studies. The presence of haplotype blocks can be used to dramatically increase the statistical power of genetic mapping. Several criteria have already been proposed for identifying these blocks, all of which require haplotypes as input. We propose a comprehensive statistical model of haplotype block variation and show how the parameters of this model can be learned from haplotypes and/or unphased genotype data. Using real-world SNP data, we demonstrate that our approach can be used to resolve genotypes into their constituent haplotypes with greater accuracy than previously known methods.     

Robustness of inference of haplotype block structure.

In this report, we examine the validity of the haplotype block concept by comparing block decompositions derived from public data sets by variants of several leading methods of block detection. We first develop a statistical method for assessing the concordance of two block decompositions. We then assess the robustness of inferred haplotype blocks to the specific detection method chosen, to arbitrary choices made in the block-detection algorithms, and to the sample analyzed. Although the block decompositions show levels of concordance that are very unlikely by chance, the absolute magnitude of the concordance may be low enough to limit the utility of the inference. For purposes of SNP selection, it seems likely that methods that do not arbitrarily impose block boundaries among correlated SNPs might perform better than block-based methods.     

Mosaicism, modules, and the evolution of birds: results from a Bayesian approach to the study of morphological evolution using discrete character data

The study of morphological evolution after the inferred origin of active flight homologous with that in Aves has historically been characterized by an emphasis on anatomically disjunct, mosaic patterns of change. Relatively few prior studies have used discrete morphological character data in a phylogenetic context to quantitatively investigate morphological evolution or mosaic evolution in particular. One such previously employed method, which used summed unambiguously optimized synapomorphies, has been the basis for proposing disassociated and sequential "modernizing" or "fine-tuning" of pectoral and then pelvic locomotor systems after the origin of flight ("pectoral early-pelvic late" hypothesis). We use one of the most inclusive phylogenetic data sets of basal birds to investigate properties of this method and to consider the application of a Bayesian phylogenetic approach. Bayes factor and statistical comparisons of branch length estimates were used to evaluate support for a mosaic pattern of character change and the specific pectoral early-pelvic late hypothesis. Partitions were defined a priori based on anatomical subregion (e.g., pelvic, pectoral) and were based on those hypothesized using the summed synapomorphy approach. We compare 80 models all implementing the M(k) model for morphological data but varying in the number of anatomical subregion partitions, the models for among-partition rate variation and among-character rate variation, as well as the branch length prior. Statistical analysis reveals that partitioning data by anatomical subregion, independently estimating branch lengths for partitioned data, and use of shared or per partition gamma-shaped among-character rate distribution significantly increases estimated model likelihoods. Simulation studies reveal that partitioned models where characters are randomly assigned perform significantly worse than both the observed model and the single-partition equal-rate model, suggesting that only partitioning by anatomical subregion increases model performance. The preference for models with partitions defined a priori by anatomical subregion is consistent with a disjunctive pattern of character change for the data set investigated and may have implications for parameterization of Bayesian analyses of morphological data more generally. Statistical tests of differences in estimated branch lengths from the pectoral and pelvic partitions do not support the specific pectoral early-pelvic late hypothesis proposed from the summed synapomorphy approach; however, results suggest limited support for some pectoral branch lengths being significantly longer only early at/after the origin of flight.     

Hierarchical protein folding pathways: a computational study of protein fragments

We have previously presented a building block folding model. The model postulates that protein folding is a hierarchical top-down process. The basic unit from which a fold is constructed, referred to as a hydrophobic folding unit, is the outcome of combinatorial assembly of a set of "building blocks." Results obtained by the computational cutting procedure yield fragments that are in agreement with those obtained experimentally by limited proteolysis. Here we show that as expected, proteins from the same family give very similar building blocks. However, different proteins can also give building blocks that are similar in structure. In such cases the building blocks differ in sequence, stability, contacts with other building blocks, and in their 3D locations in the protein structure. This result, which we have repeatedly observed in many cases, leads us to conclude that while a building block is influenced by its environment, nevertheless, it can be viewed as a stand-alone unit. For small-sized building blocks existing in multiple conformations, interactions with sister building blocks in the protein will increase the population time of the native conformer. With this conclusion in hand, it is possible to develop an algorithm that predicts the building block assignment of a protein sequence whose structure is unknown. Toward this goal, we have created sequentially nonredundant databases of building block sequences. A protein sequence can be aligned against these, in order to be matched to a set of potential building blocks.     

Homology between the proteins encoded by tobacco mosaic virus and two tricornaviruses

Summary A comparison was made of the amino acid sequences of the proteins encoded by RNAs 1 and 2 of alfalfa mosaic virus (A1MV) and brome mosaic virus (BMV), and the 126K and 183K proteins encoded by tobacco mosaic virus (TMV). Three blocks of extensive homology of about 200 to 350 amino acids each were observed. Two of these blocks are located in the A1MV and BMV RNA 1 encoded proteins and the TMV encoded 126K protein; they are situated at the N-terminus and C-terminus, respectively. The third block is located in the A1MV and BMV RNA 2 encoded proteins and the C-terminal part of the TMV encoded 183K protein. These homologies are discussed with respect to the functional equivalence of these putative replicase proteins and a possible evolutionary connection between A1MV, BMV and TMV.     

Linkage disequilibrium grouping of single nucleotide polymorphisms (SNPs) reflecting haplotype phylogeny for efficient selection of tag SNPs

Single nucleotide polymorphisms (SNPs) have been proposed to be grouped into haplotype blocks harboring a limited number of haplotypes. Within each block, the portion of haplotypes is expected to be tagged by a selected subset of SNPs; however, none of the proposed selection algorithms have been definitive. To address this issue, we developed a tag SNP selection algorithm based on grouping of SNPs by the linkage disequilibrium (LD) coefficient r(2) and examined five genes in three ethnic populations--the Japanese, African Americans, and Caucasians. Additionally, we investigated ethnic diversity by characterizing 979 SNPs distributed throughout the genome. Our algorithm could spare 60% of SNPs required for genotyping and limit the imprecision in allele-frequency estimation of nontag SNPs to 2% on average. We discovered the presence of a mosaic pattern of LD plots within a conventionally inferred haplotype block. This emerged because multiple groups of SNPs with strong intragroup LD were mingled in their physical positions. The pattern of LD plots showed some similarity, but the details of tag SNPs were not entirely concordant among three populations. Consequently, our algorithm utilizing LD grouping allows selection of a more faithful set of tag SNPs than do previous algorithms utilizing haplotype blocks.     

Emergence and maintenance of variable-length actin filaments in a limiting pool of building blocks

Actin is one of the key structural components of the eukaryotic cytoskeleton that regulates cellular architecture and mechanical properties. Dynamic regulation of actin filament length and organization is essential for the control of many physiological processes including cell adhesion, motility and division. While previous studies have mostly focused on the mechanisms controlling the length of single actin filaments, it remains poorly understood how distinct actin filament populations in cells maintain different lengths using the same set of molecular building blocks. Here, we develop a theoretical model for the length regulation of multiple actin filaments by nucleation and growth-rate modulation by actin-binding proteins in a limiting pool of monomers. We first show that spontaneous nucleation of actin filaments naturally leads to heterogeneities in filament length distribution. We then investigate the effects of filament growth inhibition by capping proteins and growth promotion by formin proteins on filament length distribution. We find that filament length heterogeneity can be increased by growth inhibition, whereas growth promoters do not significantly affect length heterogeneity. Interestingly, a competition between filament growth inhibitors and growth promoters can give rise to bimodal filament length distribution as well as a highly heterogeneous length distribution with large statistical dispersion. We quantitatively predict how heterogeneity in actin filament length can be modulated by tuning filamentous actin nucleation and growth rates in order to create distinct filament subpopulations with different lengths.     

A chromosome-based model for estimating the number of conserved segments between pairs of species from comparative genetic maps

Comparative genetic maps of two species allow insights into the rearrangements of their genomes since divergence from a common ancestor. When the map details the positions of genes (or any set of orthologous DNA sequences) on chromosomes, syntenic blocks of one or more genes may be identified and used, with appropriate models, to estimate the number of chromosomal segments with conserved content conserved between species. We propose a model for the distribution of the lengths of unobserved segments on each chromosome that allows for widely differing chromosome lengths. The model uses as data either the counts of genes in a syntenic block or the distance between extreme members of a block, or both. The parameters of the proposed segment length distribution, estimated by maximum likelihood, give predictions of the number of conserved segments per chromosome. The model is applied to data from two comparative maps for the chicken, one with human and one with mouse.     

The probabilities of similarities in DNA sequence comparisons

We discuss the statistical significance of local similarities found between DNA sequences, and illustrate the procedure with reference to the Queen and Korn algorithm. If the longest similarity found for two sequences has length L, this length is said to be significant at the 5% level if there is a probability of no more than 0.05 of finding a length of L or greater between a pair of sequences consisting of randomly chosen bases with the same overall base frequencies. The distribution of longest lengths is related to that of lengths from any particular pair of starting positions on the two sequences. For our implementation of the Queen and Korn algorithm, this latter distribution is constructed by combining the five different blocks of bases that may be added to extend a similarity. A table is given to assess the significance of longest similarities in sequences of length up to 1000 bases. Quite long similarities are expected to occur by chance alone. The critical values we calculate for assessing significance are preferable to expected numbers of similarities used by some commercial computer packages.     

Gaussian curvature analysis allows for automatic block placement in multi-block hexahedral meshing

Musculoskeletal finite element analysis (FEA) has been essential to research in orthopaedic biomechanics. The generation of a volumetric mesh is often the most challenging step in a FEA. Hexahedral meshing tools that are based on a multi-block approach rely on the manual placement of building blocks for their mesh generation scheme. We hypothesise that Gaussian curvature analysis could be used to automatically develop a building block structure for multi-block hexahedral mesh generation. The Automated Building Block Algorithm incorporates principles from differential geometry, combinatorics, statistical analysis and computer science to automatically generate a building block structure to represent a given surface without prior information. We have applied this algorithm to 29 bones of varying geometries and successfully generated a usable mesh in all cases. This work represents a significant advancement in automating the definition of building blocks.     

Gaussian curvature analysis allows for automatic block placement in multi-block hexahedral meshing

Musculoskeletal finite element analysis (FEA) has been essential to research in orthopaedic biomechanics. The generation of a volumetric mesh is often the most challenging step in a FEA. Hexahedral meshing tools that are based on a multi-block approach rely on the manual placement of building blocks for their mesh generation scheme. We hypothesise that Gaussian curvature analysis could be used to automatically develop a building block structure for multi-block hexahedral mesh generation. The Automated Building Block Algorithm incorporates principles from differential geometry, combinatorics, statistical analysis and computer science to automatically generate a building block structure to represent a given surface without prior information. We have applied this algorithm to 29 bones of varying geometries and successfully generated a usable mesh in all cases. This work represents a significant advancement in automating the definition of building blocks.     

Mosaic pbpX genes of major clones of penicillin-resistant Streptococcus pneumoniae have evolved from pbpX genes of a penicillin-sensitive Streptococcus oralis

Penicillin-resistant clinical isolates of Streptococcus pneumoniae contain mosaic penicillin-binding protein (PBP) genes that encode PBPs with decreased affinity for β-lactam antibiotics. The mosaic blocks are believed to be the result of gene transfer of homologous PBP genes from related penicillin-resistant species. We have now identified a gene homologous to the pneumococcal PBP2x gene (pbpX) in a penicillin-sensitive Streptococcus oralis isolate M3 from South Africa that diverged by almost 20% from pbpX of penicillin-sensitive pneumococci, and a central sequence block of a mosaic pbpX gene of Streptococcus mitis strain NCTC 10712. In contrast, it differed by only 2-4% of the 1 to 1.5 kb mosaic block in pbpX genes of three genetically unrelated penicillin-resistant S. pneumoniae isolates, two of them representing clones of serotype 6B and 23F, which are prevalent in Spain and are also already found in other countries. With low concentrations of cefotaxime, transformants of the sensitive S. pneumoniae R6 strain could be selected containing pbpX genes from either S. mitis NCTC 10712 or S. oralis M3, demonstrating that genetic exchange can already occur between β-lactam-sensitive species. These data are in agreement with the assumption that PBPs as penicillin-resistance determinants have evolved by the accumulation of point mutations in genes of sensitive commensal species.     

The persistence exponent of DNA

Using the complete genome of Thermoplasma volcanium, as an example, we have examined the distribution functions for the amount of C or G in consecutive, non-overlapping blocks of m bases in this system. We find that these distributions are very much broader (by many factors) than those expected for a random distribution of bases. If we plot the widths of the C-G distributions relative to the widths expected for random distributions, as a function of the block size used, we obtain a power law with a characteristic exponent. The broadening of the C-G distributions follows from the empirical finding that blocks containing a given C-G content tend to be followed by blocks of similar C-G content thus indicating a statistical persistence of composition. The exponent associated with the power law thus measures the strength of persistence in a given DNA. This behavior can be understood using Mandelbrot's model of a fractional Brownian walk. In this model there is a hierarchy of persistence (correlation between blocks) between all parts of the system. The model gives us a way to scale the C-G distributions such that all these functions are collapsed onto a master curve. For a fractional Brownian walk, the fractal dimension of the C-G distribution is simply related to the persistence exponent for the power law. The persistence exponent for T. volcanium is found to be gamma = 0.29 while for a 10 million base segment of the human genome we obtain gamma = 0.39, similar to but not identical with the value found for the microbe.