Decoding coalescent hidden Markov models in linear time

In many areas of computational biology, hidden Markov models (HMMs) have been used to model local genomic features. In particular, coalescent HMMs have been used to infer ancient population sizes, migration rates, divergence times, and other parameters such as mutation and recombination rates. As more loci, sequences, and hidden states are added to the model, however, the runtime of coalescent HMMs can quickly become prohibitive. Here we present a new algorithm for reducing the runtime of coalescent HMMs from quadratic in the number of hidden time states to linear, without making any additional approximations. Our algorithm can be incorporated into various coalescent HMMs, including the popular method PSMC for inferring variable effective population sizes. Here we implement this algorithm to speed up our demographic inference method diCal, which is equivalent to PSMC when applied to a sample of two haplotypes. We demonstrate that the linear-time method can reconstruct a population size change history more accurately than the quadratic-time method, given similar computation resources. We also apply the method to data from the 1000 Genomes project, inferring a high-resolution history of size changes in the European population.Comment: 18 pages, 5 figures. To appear in the Proceedings of the 18th Annual International Conference on Research in Computational Molecular Biology (RECOMB 2014). The final publication is available at link.springer.co

Two-Locus Likelihoods under Variable Population Size and Fine-Scale Recombination Rate Estimation

Two-locus sampling probabilities have played a central role in devising an efficient composite likelihood method for estimating fine-scale recombination rates. Due to mathematical and computational challenges, these sampling probabilities are typically computed under the unrealistic assumption of a constant population size, and simulation studies have shown that resulting recombination rate estimates can be severely biased in certain cases of historical population size changes. To alleviate this problem, we develop here new methods to compute the sampling probability for variable population size functions that are piecewise constant. Our main theoretical result, implemented in a new software package called LDpop, is a novel formula for the sampling probability that can be evaluated by numerically exponentiating a large but sparse matrix. This formula can handle moderate sample sizes ($n \leq 50$) and demographic size histories with a large number of epochs ($\mathcal{D} \geq 64$). In addition, LDpop implements an approximate formula for the sampling probability that is reasonably accurate and scales to hundreds in sample size ($n \geq 256$). Finally, LDpop includes an importance sampler for the posterior distribution of two-locus genealogies, based on a new result for the optimal proposal distribution in the variable-size setting. Using our methods, we study how a sharp population bottleneck followed by rapid growth affects the correlation between partially linked sites. Then, through an extensive simulation study, we show that accounting for population size changes under such a demographic model leads to substantial improvements in fine-scale recombination rate estimation. LDpop is freely available for download at https://github.com/popgenmethods/ldpopComment: 32 pages, 13 figure

Approximate sampling formulae for general finite-alleles models of mutation

Many applications in genetic analyses utilize sampling distributions, which describe the probability of observing a sample of DNA sequences randomly drawn from a population. In the one-locus case with special models of mutation such as the infinite-alleles model or the finite-alleles parent-independent mutation model, closed-form sampling distributions under the coalescent have been known for many decades. However, no exact formula is currently known for more general models of mutation that are of biological interest. In this paper, models with finitely-many alleles are considered, and an urn construction related to the coalescent is used to derive approximate closed-form sampling formulas for an arbitrary irreducible recurrent mutation model or for a reversible recurrent mutation model, depending on whether the number of distinct observed allele types is at most three or four, respectively. It is demonstrated empirically that the formulas derived here are highly accurate when the per-base mutation rate is low, which holds for many biological organisms.Comment: 22 pages, 1 figur

Alterations in regional vascular geometry produced by theoretical stent implantation influence distributions of wall shear stress: analysis of a curved coronary artery using 3D computational fluid dynamics modeling

BACKGROUND: The success of stent implantation in the restoration of blood flow through areas of vascular narrowing is limited by restenosis. Several recent studies have suggested that the local geometric environment created by a deployed stent may influence regional blood flow characteristics and alter distributions of wall shear stress (WSS) after implantation, thereby rendering specific areas of the vessel wall more susceptible to neointimal hyperplasia and restenosis. Stents are most frequently implanted in curved vessels such as the coronary arteries, but most computational studies examining blood flow patterns through stented vessels conducted to date use linear, cylindrical geometric models. It appears highly probable that restenosis occurring after stent implantation in curved arteries also occurs as a consequence of changes in fluid dynamics that are established immediately after stent implantation. METHODS: In the current investigation, we tested the hypothesis that acute changes in stent-induced regional geometry influence distributions of WSS using 3D coronary artery CFD models implanted with stents that either conformed to or caused straightening of the primary curvature of the left anterior descending coronary artery. WSS obtained at several intervals during the cardiac cycle, time averaged WSS, and WSS gradients were calculated using conventional techniques. RESULTS: Implantation of a stent that causes straightening, rather than conforms to the natural curvature of the artery causes a reduction in the radius of curvature and subsequent increase in the Dean number within the stented region. This straightening leads to modest skewing of the velocity profile at the inlet and outlet of the stented region where alterations in indices of WSS are most pronounced. For example, time-averaged WSS in the proximal portion of the stent ranged from 8.91 to 11.7 dynes/cm(2 )along the pericardial luminal surface and 4.26 to 4.88 dynes/cm(2 )along the myocardial luminal surface of curved coronary arteries as compared to 8.31 dynes/cm(2 )observed throughout the stented region of a straight vessel implanted with an equivalent stent. CONCLUSION: The current results predicting large spatial and temporal variations in WSS at specific locations in curved arterial 3D CFD simulations are consistent with clinically observed sites of restenosis. If the findings of this idealized study translate to the clinical situation, the regional geometry established immediately after stent implantation may predispose portions of the stented vessel to a higher risk of neointimal hyperplasia and subsequent restenosis

Evolution of Genome Size and Complexity in Pinus

BACKGROUND: Genome evolution in the gymnosperm lineage of seed plants has given rise to many of the most complex and largest plant genomes, however the elements involved are poorly understood. METHODOLOGY/PRINCIPAL FINDINGS: Gymny is a previously undescribed retrotransposon family in Pinus that is related to Athila elements in Arabidopsis. Gymny elements are dispersed throughout the modern Pinus genome and occupy a physical space at least the size of the Arabidopsis thaliana genome. In contrast to previously described retroelements in Pinus, the Gymny family was amplified or introduced after the divergence of pine and spruce (Picea). If retrotransposon expansions are responsible for genome size differences within the Pinaceae, as they are in angiosperms, then they have yet to be identified. In contrast, molecular divergence of Gymny retrotransposons together with other families of retrotransposons can account for the large genome complexity of pines along with protein-coding genic DNA, as revealed by massively parallel DNA sequence analysis of Cot fractionated genomic DNA. CONCLUSIONS/SIGNIFICANCE: Most of the enormous genome complexity of pines can be explained by divergence of retrotransposons, however the elements responsible for genome size variation are yet to be identified. Genomic resources for Pinus including those reported here should assist in further defining whether and how the roles of retrotransposons differ in the evolution of angiosperm and gymnosperm genomes

The effect of intra-articular botulinum toxin A on substance P, prostaglandin E-2, and tumor necrosis factor alpha in the canine osteoarthritic joint

Background: Recently, intra-articular botulinum toxin A (IA BoNT A) has been shown to reduce joint pain in osteoarthritic dogs. Similar results have been reported in human patients with arthritis. However, the mechanism of the antinociceptive action of IA BoNT A is currently not known. The aim of this study was to explore this mechanism of action by investigating the effect of IA BoNT A on synovial fluid (SF) and serum substance P (SP), prostaglandin E-2 (PGE(2)), and tumor necrosis factor alpha (TNF-alpha) in osteoarthritic dogs. Additionally, the aim was to compare SF SP and PGE(2) between osteoarthritic and non-osteoarthritic joints, and investigate associations between SP, PGE(2), osteoarthritic pain, and the signalment of dogs. Thirty-five dogs with chronic naturally occurring osteoarthritis and 13 non-osteoarthritic control dogs were included in the study. Osteoarthritic dogs received either IA BoNT A (n = 19) or IA placebo (n = 16). Serum and SF samples were collected and osteoarthritic pain was evaluated before (baseline) and 2 and 8 weeks after treatment. Osteoarthritic pain was assessed with force platform, Helsinki Chronic Pain Index, and joint palpation. Synovial fluid samples were obtained from control dogs after euthanasia. The change from baseline in SP and PGE(2) concentration was compared between the IA BoNT A and placebo groups. The synovial fluid SP and PGE(2) concentration was compared between osteoarthritic and control joints. Associations between SP, PGE(2), osteoarthritic pain, and the signalment of dogs were evaluated. Results: There was no significant change from baseline in SP or PGE(2) after IA BoNT A. Synovial fluid PGE(2) was significantly higher in osteoarthritic compared to control joints. Synovial fluid PGE(2) correlated with osteoarthritic pain. No associations were found between SP or PGE2 and the signalment of dogs. The concentration of TNF-alpha remained under the detection limit of the assay in all samples. Conclusions: The results suggest that the antinociceptive effect of IA BoNT A in the joint might not be related to the inhibition of SP nor PGE(2). Synovial fluid PGE(2,) but not SP, could be a marker for chronic osteoarthritis and pain in dogs.Peer reviewe

Pre-Bilaterian Origins of the Hox Cluster and the Hox Code: Evidence from the Sea Anemone, Nematostella vectensis

BACKGROUND: Hox genes were critical to many morphological innovations of bilaterian animals. However, early Hox evolution remains obscure. Phylogenetic, developmental, and genomic analyses on the cnidarian sea anemone Nematostella vectensis challenge recent claims that the Hox code is a bilaterian invention and that no “true” Hox genes exist in the phylum Cnidaria. METHODOLOGY/PRINCIPAL FINDINGS: Phylogenetic analyses of 18 Hox-related genes from Nematostella identify putative Hox1, Hox2, and Hox9+ genes. Statistical comparisons among competing hypotheses bolster these findings, including an explicit consideration of the gene losses implied by alternate topologies. In situ hybridization studies of 20 Hox-related genes reveal that multiple Hox genes are expressed in distinct regions along the primary body axis, supporting the existence of a pre-bilaterian Hox code. Additionally, several Hox genes are expressed in nested domains along the secondary body axis, suggesting a role in “dorsoventral” patterning. CONCLUSIONS/SIGNIFICANCE: A cluster of anterior and posterior Hox genes, as well as ParaHox cluster of genes evolved prior to the cnidarian-bilaterian split. There is evidence to suggest that these clusters were formed from a series of tandem gene duplication events and played a role in patterning both the primary and secondary body axes in a bilaterally symmetrical common ancestor. Cnidarians and bilaterians shared a common ancestor some 570 to 700 million years ago, and as such, are derived from a common body plan. Our work reveals several conserved genetic components that are found in both of these diverse lineages. This finding is consistent with the hypothesis that a set of developmental rules established in the common ancestor of cnidarians and bilaterians is still at work today