One-dimensional fluids with second nearest-neighbor interactions

As is well known, one-dimensional systems with interactions restricted to first nearest neighbors admit a full analytically exact statistical-mechanical solution. This is essentially due to the fact that the knowledge of the first nearest-neighbor probability distribution function, $p_1(r)$, is enough to determine the structural and thermodynamic properties of the system. On the other hand, if the interaction between second nearest-neighbor particles is turned on, the analytically exact solution is lost. Not only the knowledge of $p_1(r)$ is not sufficient anymore, but even its determination becomes a complex many-body problem. In this work we systematically explore different approximate solutions for one-dimensional second nearest-neighbor fluid models. We apply those approximations to the square-well and the attractive two-step pair potentials and compare them with Monte Carlo simulations, finding an excellent agreement.Comment: 26 pages, 12 figures; v2: more references adde

Exploring structural variation and gene family architecture with De Novo assemblies of 15 Medicago genomes

Abstract Background Previous studies exploring sequence variation in the model legume, Medicago truncatula, relied on mapping short reads to a single reference. However, read-mapping approaches are inadequate to examine large, diverse gene families or to probe variation in repeat-rich or highly divergent genome regions. De novo sequencing and assembly of M. truncatula genomes enables near-comprehensive discovery of structural variants (SVs), analysis of rapidly evolving gene families, and ultimately, construction of a pan-genome. Results Genome-wide synteny based on 15 de novo M. truncatula assemblies effectively detected different types of SVs indicating that as much as 22% of the genome is involved in large structural changes, altogether affecting 28% of gene models. A total of 63 million base pairs (Mbp) of novel sequence was discovered, expanding the reference genome space for Medicago by 16%. Pan-genome analysis revealed that 42% (180 Mbp) of genomic sequences is missing in one or more accession, while examination of de novo annotated genes identified 67% (50,700) of all ortholog groups as dispensable – estimates comparable to recent studies in rice, maize and soybean. Rapidly evolving gene families typically associated with biotic interactions and stress response were found to be enriched in the accession-specific gene pool. The nucleotide-binding site leucine-rich repeat (NBS-LRR) family, in particular, harbors the highest level of nucleotide diversity, large effect single nucleotide change, protein diversity, and presence/absence variation. However, the leucine-rich repeat (LRR) and heat shock gene families are disproportionately affected by large effect single nucleotide changes and even higher levels of copy number variation. Conclusions Analysis of multiple M. truncatula genomes illustrates the value of de novo assemblies to discover and describe structural variation, something that is often under-estimated when using read-mapping approaches. Comparisons among the de novo assemblies also indicate that different large gene families differ in the architecture of their structural variation

StantonGeddes2013_Medicago_nodule_occupancy

Spreadsheet of nodule occupancy data, described in more detail in README file

R script for nodule occupancy accession phenotypes

R script to calculate rhizobia strain nodule occupancy for genome-wide association analysis

Phenotype data from nodule assays

Data on leaf number, length of the longest branch, root length, and total number of nodules produced by plants grown to assay effects of mutations in candidate genes

Data from: Validating genome-wide association candidates controlling quantitative variation in nodulation

Genome-wide association (GWA) studies offer the opportunity to identify genes that contribute to naturally occurring variation in quantitative traits. However, GWA relies exclusively on statistical association, so functional validation is necessary to make strong claims about gene function. We used a combination of gene-disruption platforms (Tnt1 retrotransposons, hairpin RNA-interference constructs, and CRISPR/Cas9 nucleases) together with randomized, well-replicated experiments to evaluate the function of genes that an earlier GWA study in Medicago truncatula had identified as candidates contributing to variation in the symbiosis between legumes and rhizobia. We evaluated ten candidate genes found in six clusters of strongly associated single nucleotide polymorphisms, selected on the basis of their strength of statistical association, proximity to annotated gene models, and root or nodule expression. We found statistically significant effects on nodule production for three candidate genes, each validated in two independent mutants. Annotated functions of these three genes suggest their contributions to quantitative variation in nodule production occur through processes not previously connected to nodulation, including phosphorous supply and salicylic acid-related defense response. These results demonstrate the utility of GWA combined with reverse mutagenesis technologies to discover and validate genes contributing to naturally occurring variation in quantitative traits. The results highlight the potential for GWA to complement forward genetics in identifying the genetic basis of ecologically and economically important traits

Distribution of Microsatellites in the Genome of Medicago truncatula: A Resource of Genetic Markers That Integrate Genetic and Physical Maps

Microsatellites are tandemly repeated short DNA sequences that are favored as molecular-genetic markers due to their high polymorphism index. Plant genomes characterized to date exhibit taxon-specific differences in frequency, genomic location, and motif structure of microsatellites, indicating that extant microsatellites originated recently and turn over quickly. With the goal of using microsatellite markers to integrate the physical and genetic maps of Medicago truncatula, we surveyed the frequency and distribution of perfect microsatellites in 77 Mbp of gene-rich BAC sequences, 27 Mbp of nonredundant transcript sequences, 20 Mbp of random whole genome shotgun sequences, and 49 Mbp of BAC-end sequences. Microsatellites are predominantly located in gene-rich regions of the genome, with a density of one long (i.e., ≥20 nt) microsatellite every 12 kbp, while the frequency of individual motifs varied according to the genome fraction under analysis. A total of 1,236 microsatellites were analyzed for polymorphism between parents of our reference intraspecific mapping population, revealing that motifs (AT)(n), (AG)(n), (AC)(n), and (AAT)(n) exhibit the highest allelic diversity. A total of 378 genetic markers could be integrated with sequenced BAC clones, anchoring 274 physical contigs that represent 174 Mbp of the genome and composing an estimated 70% of the euchromatic gene space

StantonGeddes2013_Medicago_plant_data

Spreadsheet of plant phenotype data collected in greenhouse experiment for genome-wide association study. Column headings are: block, pot (individual plant ID), trtmnt (rhizobia treatment applied to the plant, either "rhz_12" for a mixture of two rhizobia strains, or "control" for no rhizobia), HM_accession (Medicago HapMap accession), height_1 (height recorded at about two weeks), leaves_1 (number of leaves at about two weeks), height_2 (intermediate height measurement), height_3 (final height before harvest), branch_3 (number of branches on plant before harvest), flowering date (date first flower observed), nodule_above (number of nodules counted in top 5 cm of roots), nodule_below (number of nodules below 5 cm of root growth). More information is available in the R markdown script "StantonGeddes2013_script.Rmd" that accompanies this file