Static Chaos in Spin Glasses against quenched disorder perturbations

We study the chaotic nature of spin glasses against perturbations of the realization of the quenched disorder. This type of perturbation modifies the energy landscape of the system without adding extensive energy. We exactly solve the mean-field case, which displays a very similar chaos to that observed under magnetic field perturbations, and discuss the possible extension of these results to the case of short-ranged models. It appears that dimension four plays the role of a specific critical dimension where mean-field theory is valid. We present numerical simulation results which support our main conclusions.Comment: 13 Pages + 7 Figures, Latex File, figures uuencoded at end of fil

Critical exponents in Ising spin glasses

We determine accurate values of ordering temperatures and critical exponents for Ising Spin Glass transitions in dimension 4, using a combination of finite size scaling and non-equilibrium scaling techniques. We find that the exponents $\eta$ and $z$ vary with the form of the interaction distribution, indicating non-universality at Ising spin glass transitions. These results confirm conclusions drawn from numerical data for dimension 3.Comment: 6 pages, RevTeX (or Latex, etc), 10 figures, Submitted to PR

A general method to determine replica symmetry breaking transitions

We introduce a new parameter to investigate replica symmetry breaking transitions using finite-size scaling methods. Based on exact equalities initially derived by F. Guerra this parameter is a direct check of the self-averaging character of the spin-glass order parameter. This new parameter can be used to study models with time reversal symmetry but its greatest interest concerns models where this symmetry is absent. We apply the method to long-range and short-range Ising spin glasses with and without magnetic field as well as short-range multispin interaction spin glasses.Comment: 5 pages, 4 figures, Revtex fil

Domain-Wall Free-Energy of Spin Glass Models:Numerical Method and Boundary Conditions

An efficient Monte Carlo method is extended to evaluate directly domain-wall free-energy for randomly frustrated spin systems. Using the method, critical phenomena of spin-glass phase transition is investigated in 4d +/-J Ising model under the replica boundary condition. Our values of the critical temperature and exponent, obtained by finite-size scaling, are in good agreement with those of the standard MC and the series expansion studies. In addition, two exponents, the stiffness exponent and the fractal dimension of the domain wall, which characterize the ordered phase, are obtained. The latter value is larger than d-1, indicating that the domain wall is really rough in the 4d Ising spin glass phase.Comment: 9 pages Latex(Revtex), 8 eps figure

A combinatorial approach of comprehensive QTL-based comparative genome mapping and transcript profiling identified a seed weight-regulating candidate gene in chickpea

High experimental validation/genotyping success rate (94–96%) and intra-specific polymorphic potential (82–96%) of 1536 SNP and 472 SSR markers showing in silico polymorphism between desi ICC 4958 and kabuli ICC 12968 chickpea was obtained in a 190 mapping population (ICC 4958 × ICC 12968) and 92 diverse desi and kabuli genotypes. A high-density 2001 marker-based intra-specific genetic linkage map comprising of eight LGs constructed is comparatively much saturated (mean map-density: 0.94 cM) in contrast to existing intra-specific genetic maps in chickpea. Fifteen robust QTLs (PVE: 8.8–25.8% with LOD: 7.0–13.8) associated with pod and seed number/plant (PN and SN) and 100 seed weight (SW) were identified and mapped on 10 major genomic regions of eight LGs. One of 126.8 kb major genomic region harbouring a strong SW-associated robust QTL (Caq'SW1.1: 169.1–171.3 cM) has been delineated by integrating high-resolution QTL mapping with comprehensive marker-based comparative genome mapping and differential expression profiling. This identified one potential regulatory SNP (G/A) in the cis-acting element of candidate ERF (ethylene responsive factor) TF (transcription factor) gene governing seed weight in chickpea. The functionally relevant molecular tags identified have potential to be utilized for marker-assisted genetic improvement of chickpea

The metastate approach to thermodynamic chaos

In realistic disordered systems, such as the Edwards-Anderson (EA) spin glass, no order parameter, such as the Parisi overlap distribution, can be both translation-invariant and non-self-averaging. The standard mean-field picture of the EA spin glass phase can therefore not be valid in any dimension and at any temperature. Further analysis shows that, in general, when systems have many competing (pure) thermodynamic states, a single state which is a mixture of many of them (as in the standard mean-field picture) contains insufficient information to reveal the full thermodynamic structure. We propose a different approach, in which an appropriate thermodynamic description of such a system is instead based on a metastate, which is an ensemble of (possibly mixed) thermodynamic states. This approach, modelled on chaotic dynamical systems, is needed when chaotic size dependence (of finite volume correlations) is present. Here replicas arise in a natural way, when a metastate is specified by its (meta)correlations. The metastate approach explains, connects, and unifies such concepts as replica symmetry breaking, chaotic size dependence and replica non-independence. Furthermore, it replaces the older idea of non-self-averaging as dependence on the bulk couplings with the concept of dependence on the state within the metastate at fixed coupling realization. We use these ideas to classify possible metastates for the EA model, and discuss two scenarios introduced by us earlier --- a nonstandard mean-field picture and a picture intermediate between that and the usual scaling/droplet picture.Comment: LaTeX file, 49 page

Deploying QTL-seq for rapid delineation of a potential candidate gene underlying major trait-associated QTL in chickpea

A rapid high-resolution genome-wide strategy for molecular mapping of major QTL(s)/gene(s) regulating important agronomic traits is vital for in-depth dissection of complex quantitative traits and genetic enhancement in chickpea. The present study for the first time employed a NGS-based whole-genomeQTL-seq strategy to identify one major genomic region harbouring a robust 100- seed weight QT Lusinganintra-specific 221 chickpea mapping population (desicv.ICC7184×desicv.ICC 15061). The QTL-seq-derived major SW QTL (CaqSW1.1) was further validated by single-nucleotide polymorphism (SNP) and simple sequence repeat (SSR) marker-based traditional QTL mapping (47.6% R2 at higher LOD >19). This reflects the reliability and efficacy of QTL-seq as a strategy for rapid genome-wide scanning and fine mapping of major trait regulatory QTLs in chickpea. The use of QTL-seq and classical QTL mapping in combination narrowed down the 1.37 Mb (comprising 177genes) major SWQTL (CaqSW1.1) regionintoa 35 kb genomic intervalondesi chickpea chromosome 1 containing six genes. One coding SNP (G/A)-carrying constitutive photomorphogenic 9 (COP9) signalo some complex subunit (CSN8) gene of the see xhibited seed-specific expression, including pronounced differential up-/down-regulation in low and high seed weight mapping parents and homo zygous individuals duringseed development.The coding SNP mined in this potential seed weight- governing candidate CSN8 genewas found to be present exclusively in all cultivated species/ genotypes, but notin any wild species/genotypes of primary, secondary and tertiary gene pools.This indicates the effect of strong artificial and/or natural selection pressure on target SW locus during chickpea domestication. The proposed QTL-seq-driven integrated genome-wide strategy has potential to delineate major candidate gene(s) harbouring a robust trait regulatory QTL rapidly with optimal use of resources. This will further assist us to extrapolate the molecular mechanism underlying complex quantitative traits at a genome-wide scale leading to fast-paced marker-assisted genetic improvement in diverse crop plants, including chickpea

Integrative genome-wide association studies (GWAS) to understand complex genetic architecture of quantitative traits in chickpea

Development of high-yielding stress-tolerant chickpea cultivars is essential to enhance its yield potential and productivity amidst climate change scenario. Unfortunately, superior lines/recombinants producing higher pod and seed yield under stress are not available in world chickpea collection. Therefore, genetic dissection of complex stress tolerance and yield-contributing quantitative traits is the prime objective in current chickpea genomics and breeding research. Our study employed diverse GWAS-assisted integrated genomic strategies involving classical genetic inheritance analysis, QTL mapping, differential transcript profiling, molecular haplotyping and haplotype-based gene domestication/ evolution study for rapid quantitative dissection of complex yield and stress tolerance traits in chickpea. To accomplish this, multi-location/years replicated yield traits-related field phenotyping and high-throughput marker genotyping information generated from numerous natural germplasm accessions (association panel) and multiple intra- and inter-specific mapping populations of chickpea were deployed in the aforesaid combinatorial genomic approaches. These analyses delineated 12 novel alleles and six haplotypes from 10 transcription factor genes and 16 major QTLs/eQTLs governing yield and stress tolerance traits that were mapped on 10 ultra-high density chickpea genetic linkage maps. The superior natural alleles/haplotypes of two major genes (QTLs) regulating seed weight and pod/seed number identified from cultivated and wild Cicer gene pools are being introduced into multiple high-yielding Indian varieties of chickpea for its marker-assisted genetic improvement. The potential molecular signatures delineated using integrated genomics- assisted breeding strategies have functional significance to understand the molecular genetic mechanism and natural allelic diversity-led domestication pattern underlying these complex quantitative traits at a genome-wide scale, leading to fast-paced translational genomics for chickpea genetic enhancement. These essential outcomes will be useful for devising the most efficient strategies to produce high-yielding climate-resilient chickpea cultivars for sustaining global food security

Genome-wide conserved non-coding microsatellite (CNMS) marker-based integrative genetical genomics for quantitative dissection of seed weight in chickpea

Phylogenetic footprinting identified 666 genome-wide paralogous and orthologous CNMS (conserved non-coding microsatellite) markers from 5′-untranslated and regulatory regions (URRs) of 603 protein-coding chickpea genes. The (CT)n and (GA)n CNMS carrying CTRMCAMV35S and GAGA8BKN3 regulatory elements, respectively, are abundant in the chickpea genome. The mapped genic CNMS markers with robust amplification efficiencies (94.7%) detected higher intraspecific polymorphic potential (37.6%) among genotypes, implying their immense utility in chickpea breeding and genetic analyses. Seventeen differentially expressed CNMS marker-associated genes showing strong preferential and seed tissue/developmental stage-specific expression in contrasting genotypes were selected to narrow down the gene targets underlying seed weight quantitative trait loci (QTLs)/eQTLs (expression QTLs) through integrative genetical genomics. The integration of transcript profiling with seed weight QTL/eQTL mapping, molecular haplotyping, and association analyses identified potential molecular tags (GAGA8BKN3 and RAV1AAT regulatory elements and alleles/haplotypes) in the LOB-domain-containing protein- and KANADI protein-encoding transcription factor genes controlling the cis-regulated expression for seed weight in the chickpea. This emphasizes the potential of CNMS marker-based integrative genetical genomics for the quantitative genetic dissection of complex seed weight in chickpea

Ultra-high density intra-specific genetic linkage maps accelerate identification of functionally relevant molecular tags governing important agronomic traits in chickpea

We discovered 26785 and 16573 high-quality SNPs differentiating two parental genotypes of a RIL mapping population using reference desi and kabuli genome-based GBS assay. Of these, 3625 and 2177 SNPs have been integrated into eight desi and kabuli chromosomes, respectively in order to construct ultra-high density (0.20–0.37 cM) intra-specific chickpea genetic linkage maps. One of these constructed high-resolution genetic map has potential to identify 33 major genomic regions harbouring 35 robust QTLs (PVE: 17.9–39.7%) associated with three agronomic traits, which were mapped within <1 cM mean marker intervals on desi chromosomes. The extended LD (linkage disequilibrium) decay (~15 cM) in chromosomes of genetic maps have encouraged us to use a rapid integrated approach (comparative QTL mapping, QTL-region specific haplotype/LD-based trait association analysis, expression profiling and gene haplotype-based association mapping) rather than a traditional QTL map-based cloning method to narrow-down one major seed weight (SW) robust QTL region. It delineated favourable natural allelic variants and superior haplotype-containing one seed-specific candidate embryo defective gene regulating SW in chickpea. The ultra-high-resolution genetic maps, QTLs/genes and alleles/haplotypes-related genomic information generated and integrated strategy for rapid QTL/gene identification developed have potential to expedite genomics-assisted breeding applications in crop plants, including chickpea for their genetic enhancement