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Breeders have long appreciated the need to balance selection for short-term genetic gain with maintaining genetic variance for long-term gain. For outbred populations, the method called Optimum Contribution Selection (OCS) chooses parental contributions to maximize the average breeding value at a prescribed inbreeding rate. With Optimum Mate Allocation (OMA), the contribution of each mating is optimized, which allows for specific combining ability due to dominance. To enable OCS and OMA in polyploid species, new theoretical results were derived to (1) predict mid-parent heterosis due to dominance and (2) control inbreeding in a population of arbitrary ploidy. A new Convex optimization framework for OMA, named COMA, was developed and released as public software. Under stochastic simulation of a genomic selection program, COMA maintained a target inbreeding rate of 0.5% using either pedigree or genomic IBD kinship. Significantly more genetic gain was realized with pedigree kinship, which is consistent with previous studies showing the selective advantage of an individual under OCS is dominated by its Mendelian sampling term. Despite the higher accuracy (+0.2-0.3) when predicting mate performance with OMA compared to OCS, there was little long-term gain advantage. The sparsity of the COMA mating design and flexibility to incorporate mating constraints offer practical incentives over OCS. In a potato breeding case study with 170 candidates, the optimal solution at 0.5% inbreeding involved 43 parents but only 43 of the 903 possible matings., (© The Author(s) 2024. Published by Oxford University Press on behalf of The Genetics Society of America. All rights reserved. For commercial re-use, please contact reprints@oup.com for reprints and translation rights for reprints. All other permissions can be obtained through our RightsLink service via the Permissions link on the article page on our site—for further information please contact journals.permissions@oup.com.)

Potato (Solanum tuberosum L.) is the most widely grown vegetable in the world. Consumers and processors evaluate potatoes based on quality traits such as shape and skin color, making these traits important targets for breeders. Achieving and evaluating genetic gain is facilitated by precise and accurate trait measures. Historically, quality traits have been measured using visual rating scales, which are subject to human error and necessarily lump individuals with distinct characteristics into categories. Image analysis offers a method of generating quantitative measures of quality traits. In this study, we use TubAR, an image-analysis R package, to generate quantitative measures of shape and skin color traits for use in genomic prediction. We developed and compared different genomic models based on additive and additive plus non-additive relationship matrices for two aspects of skin color, redness, and lightness, and two aspects of shape, roundness, and length-to-width ratio for fresh market red and yellow potatoes grown in Minnesota between 2020 and 2022. Similarly, we used the much larger chipping potato population grown during the same time to develop a multi-trait selection index including roundness, specific gravity, and yield. Traits ranged in heritability with shape traits falling between 0.23 and 0.85, and color traits falling between 0.34 and 0.91. Genetic effects were primarily additive with color traits showing the strongest effect (0.47), while shape traits varied based on market class. Modeling non-additive effects did not significantly improve prediction models for quality traits. The combination of image analysis and genomic prediction presents a promising avenue for improving potato quality traits., (© 2024 The Author(s). The Plant Genome published by Wiley Periodicals LLC on behalf of Crop Science Society of America.)

Mid-density targeted genotyping-by-sequencing (GBS) combines trait-specific markers with thousands of genomic markers at an attractive price for linkage mapping and genomic selection. A 2.5K targeted GBS assay for potato (Solanum tuberosum L.) was developed using the DArTag technology and later expanded to 4K targets. Genomic markers were selected from the potato Infinium single nucleotide polymorphism (SNP) array to maximize genome coverage and polymorphism rates. The DArTag and SNP array platforms produced equivalent dendrograms in a test set of 298 tetraploid samples, and 83% of the common markers showed good quantitative agreement, with RMSE (root mean squared error) <0.5. DArTag is suited for genomic selection candidates in the clonal evaluation trial, coupled with imputation to a higher density platform for the training population. Using the software polyBreedR, an R package for the manipulation and analysis of polyploid marker data, the RMSE for imputation by linkage analysis was 0.15 in a small half-diallel population (N = 85), which was significantly lower than the RMSE of 0.42 with the random forest method. Regarding high-value traits, the DArTag markers for resistance to potato virus Y, golden cyst nematode, and potato wart appeared to track their targets successfully, as did multi-allelic markers for maturity and tuber shape. In summary, the potato DArTag assay is a transformative and publicly available technology for potato breeding and genetics., (© 2024 The Author(s). The Plant Genome published by Wiley Periodicals LLC on behalf of Crop Science Society of America.)

At present, the potato (Solanum tuberosum L.) of international commerce is autotetraploid, and the complexity of this genetic system creates limitations for breeding. Diploid potato breeding has long been used for population improvement, and because of an improved understanding of the genetics of gametophytic self-incompatibility, there is now sustained interest in the development of uniform F 1 hybrid varieties based on inbred parents. We report here on the use of haplotype and quantitative trait locus (QTL) analysis in a modified backcrossing (BC) scheme, using primary dihaploids of S. tuberosum as the recurrent parental background. In Cycle 1, we selected XD3-36, a self-fertile F 2 individual homozygous for the self-compatibility gene Sli (S-locus inhibitor). Signatures of gametic and zygotic selection were observed at multiple loci in the F 2 generation, including Sli. In the BC 1 cycle, an F 1 population derived from XD3-36 showed a bimodal response for vine maturity, which led to the identification of late versus early alleles in XD3-36 for the gene CDF1 (Cycling DOF Factor 1). Greenhouse phenotypes and haplotype analysis were used to select a vigorous and self-fertile F 2 individual with 43% homozygosity, including for Sli and the early-maturing allele CDF1.3. Partially inbred lines from the BC 1 and BC 2 cycles have been used to initiate new cycles of selection, with the goal of reaching higher homozygosity while maintaining plant vigor, fertility, and yield., (© 2023 The Authors. The Plant Genome published by Wiley Periodicals LLC on behalf of Crop Science Society of America.)

Potato tuber skin is a protective corky tissue consisting of suberized phellem cells. Smooth-skinned varieties are characterized by a clean, shiny appearance compared to the darker hue of russeted potatoes. The rough skin of russeted cultivars is a desired, genetically inherited characteristic; however, unwanted russeting of smooth-skinned cultivars often occurs under suboptimal growth conditions. The involvement of epigenetic modifiers in regulating the smooth skin russeting disorder was tested. We used smooth-skin commercial cultivars with and without the russeting disorder and three lines from a breeding population segregating for russeting. Anatomically, the russet skin showed similar characteristics, whether the cause was environmentally triggered or genetically determined. The old outer layers of the corky phellem remain attached to the newly formed phellem layers instead of being sloughed off. Global DNA methylation analysis indicated a significant reduction in the percentage of 5-methylcytosine in mature vs. immature skin and russet vs. smooth skin. This was true for both the smooth-skin commercial cultivars and the russeted lines. The expression level of selected DNA methyltransferases was reduced in accordance. DNA demethylase expression did not change between the skin types and age. Hence, the reduced DNA methylation in mature and russet skin is more likely to be achieved through passive DNA demethylation and loss of methyltransferase activity.

Potato is a major food crop in the United States and around the world. Most potatoes grown in the United States are destined for processing. Genomic selection can speed up breeding progress for important traits, including those with complex inheritance by guiding the identification of the best parents and guiding selection to advance clones in the breeding program. However, the application of genomic selection in polyploid species has been challenging. In this study, we obtained breeding values of 384 chipping clones evaluated in Texas between 2017 and 2020. The mean reliability of the genomic-estimated breeding values obtained were 0.77, 0.41, 0.61, 0.71, and 0.24 for chip color, chip quality, specific gravity, vine maturity, and total yield, respectively. Potato clones with good chip quality, high yield, high specific gravity, and light-color chips were identified using a multi-trait selection index based on weighted standardized genomic-estimated breeding values. Genome-wide association studies identified quantitative trait loci on chromosome 5 for vine maturity and chromosomes 1, 3, and 7 for chip color. This research has laid the groundwork for implementing genomic selection in tetraploid potato breeding and understanding the genetic basis of chip processing traits in potatoes., (© 2023 The Authors. The Plant Genome published by Wiley Periodicals LLC on behalf of Crop Science Society of America.)

Cultivated potato is a clonally propagated autotetraploid species with a highly heterogeneous genome. Phased assemblies of six cultivars including two chromosome-scale phased genome assemblies revealed extensive allelic diversity, including altered coding and transcript sequences, preferential allele expression, and structural variation that collectively result in a highly complex transcriptome and predicted proteome, which are distributed across the homologous chromosomes. Wild species contribute to the extensive allelic diversity in tetraploid cultivars, demonstrating ancestral introgressions predating modern breeding efforts. As a clonally propagated autotetraploid that undergoes limited meiosis, dysfunctional and deleterious alleles are not purged in tetraploid potato. Nearly a quarter of the loci bore mutations are predicted to have a high negative impact on protein function, complicating breeder's efforts to reduce genetic load. The StCDF1 locus controls maturity, and analysis of six tetraploid genomes revealed that 12 allelic variants of StCDF1 are correlated with maturity in a dosage-dependent manner. Knowledge of the complexity of the tetraploid potato genome with its rampant structural variation and embedded deleterious and dysfunctional alleles will be key not only to implementing precision breeding of tetraploid cultivars but also to the construction of homozygous, diploid potato germplasm containing favorable alleles to capitalize on heterosis in F1 hybrids., (Copyright © 2022 The Author. Published by Elsevier Inc. All rights reserved.)

Over the last decade, multiparental populations have become a mainstay of genetics research in diploid species. Our goal was to extend this paradigm to autotetraploids by developing software for quantitative trait locus (QTL) mapping in connected F1 populations derived from a set of shared parents. For QTL discovery, phenotypes are regressed on the dosage of parental haplotypes to estimate additive effects. Statistical properties of the model were explored by simulating half-diallel diploid and tetraploid populations with different population sizes and numbers of parents. Across scenarios, the number of progeny per parental haplotype (pph) largely determined the statistical power for QTL detection and accuracy of the estimated haplotype effects. Multiallelic QTL with heritability 0.2 were detected with 90% probability at 25 pph and genome-wide significance level 0.05, and the additive haplotype effects were estimated with over 90% accuracy. Following QTL discovery, the software enables a comparison of models with multiple QTL and nonadditive effects. To illustrate, we analyzed potato tuber shape in a half-diallel population with three tetraploid parents. A well-known QTL on chromosome 10 was detected, for which the inclusion of digenic dominance lowered the Deviance Information Criterion (DIC) by 17 points compared to the additive model. The final model also contained a minor QTL on chromosome 1, but higher-order dominance and epistatic effects were excluded based on the DIC. In terms of practical impacts, the software is already being used to select offspring based on the effect and dosage of particular haplotypes in breeding programs., (© The Author(s) 2021. Published by Oxford University Press on behalf of Genetics Society of America. All rights reserved. For permissions, please email: journals.permissions@oup.com.)

In diploid species, many multiparental populations have been developed to increase genetic diversity and quantitative trait loci (QTL) mapping resolution. In these populations, haplotype reconstruction has been used as a standard practice to increase the power of QTL detection in comparison with the marker-based association analysis. However, such software tools for polyploid species are few and limited to a single biparental F1 population. In this study, a statistical framework for haplotype reconstruction has been developed and implemented in the software PolyOrigin for connected tetraploid F1 populations with shared parents, regardless of the number of parents or mating design. Given a genetic or physical map of markers, PolyOrigin first phases parental genotypes, then refines the input marker map, and finally reconstructs offspring haplotypes. PolyOrigin can utilize single nucleotide polymorphism (SNP) data coming from arrays or from sequence-based genotyping; in the latter case, bi-allelic read counts can be used (and are preferred) as input data to minimize the influence of genotype calling errors at low depth. With extensive simulation we show that PolyOrigin is robust to the errors in the input genotypic data and marker map. It works well for various population designs with ≥30 offspring per parent and for sequences with read depth as low as 10x. PolyOrigin was further evaluated using an autotetraploid potato dataset with a 3 × 3 half-diallel mating design. In conclusion, PolyOrigin opens up exciting new possibilities for haplotype analysis in tetraploid breeding populations., (© The Author(s) 2021. Published by Oxford University Press on behalf of Genetics Society of America. All rights reserved. For permissions, please email: journals.permissions@oup.com.)

Core Ideas: Introduced concept of expected genotype quality (EGQ) and software to calculate it Provided read depth guidelines for GBS in tetraploids Developed software to generate diploidized genotype calls from VCF files Demonstrated value of aligning GBS reads to a mock reference genome for SNP discovery Recommend filtering based on GQ and read depth to prevent genotype bias Although genotyping-by-sequencing (GBS) is a well-established marker technology in diploids, the development of best practices for tetraploid species is a topic of current research. We determined the theoretical relationship between read depth and the phred-scaled probability of genotype misclassification conditioned on the true genotype, which we call expected genotype quality (EGQ). If the GBS method has 0.5% allelic error, then 17 reads are needed to classify simplex tetraploids as heterozygous with 95% accuracy (EGQ = 13) vs. 61 reads to determine allele dosage. We developed an R script to convert tetraploid GBS data in variant call format (VCF) into diploidized genotype calls and applied it to 267 interspecific hybrids of the tetraploid forage grass Urochloa. When reads were aligned to a mock reference genome created from GBS data of the Urochloa brizantha (Hochst. ex A. Rich.) R. D. Webster cultivar Marandu, 25,678 biallelic single nucleotide polymorphism (SNPs) were discovered, compared with ∼3000 SNPs when aligning to the closest true reference genomes, Setaria viridis (L.) P. Beauv. and S. italica (L.) P. Beauv. Cross-validation revealed that missing genotypes were imputed by the random forest method with a median accuracy of 0.85 regardless of heterozygote frequency. Using the Urochloa spp. hybrids, we illustrated how filtering samples based only on genotype quality (GQ) creates genotype bias; a depth threshold based on EGQ is also needed regardless of whether genotypes are called using a diploidized or allele dosage model., (© 2019 The Author(s).)

Estimation of allele dosage, using genomic data, in autopolyploids is challenging and current methods often result in the misclassification of genotypes. Some progress has been made when using SNP arrays, but the major challenge is when using next generation sequencing data. Here we compare the use of read depth as continuous parameterization with ploidy parameterizations in the context of genomic selection (GS). Additionally, different sources of information to build relationship matrices were compared. A real breeding population of the autotetraploid species blueberry ( Vaccinium corybosum ), composed of 1,847 individuals was phenotyped for eight yield and fruit quality traits over two years. Continuous genotypic based models performed as well as the best models. This approach also reduces the computational time and avoids problems associated with misclassification of genotypic classes when assigning dosage in polyploid species. This approach could be very valuable for species with higher ploidy levels or for emerging crops where ploidy is not well understood. To our knowledge, this work constitutes the first study of genomic selection in blueberry. Accuracies are encouraging for application of GS for blueberry breeding. GS could reduce the time for cultivar release by three years, increasing the genetic gain per cycle by 86% on average when compared to phenotypic selection, and 32% when compared with pedigree-based selection. Finally, the genotypic and phenotypic data used in this study are made available for comparative analysis of dosage calling and genomic selection prediction models in the context of autopolyploids., (Copyright © 2019 de Bem Oliveira et al.)

As one of the world's most important food crops, the potato ( Solanum tuberosum L.) has spurred innovation in autotetraploid genetics, including in the use of SNP arrays to determine allele dosage at thousands of markers. By combining genotype and pedigree information with phenotype data for economically important traits, the objectives of this study were to (1) partition the genetic variance into additive vs. nonadditive components, and (2) determine the accuracy of genome-wide prediction. Between 2012 and 2017, a training population of 571 clones was evaluated for total yield, specific gravity, and chip fry color. Genomic covariance matrices for additive ( G ), digenic dominant ( D ), and additive × additive epistatic ( G # G ) effects were calculated using 3895 markers, and the numerator relationship matrix ( A ) was calculated from a 13-generation pedigree. Based on model fit and prediction accuracy, mixed model analysis with G was superior to A for yield and fry color but not specific gravity. The amount of additive genetic variance captured by markers was 20% of the total genetic variance for specific gravity, compared to 45% for yield and fry color. Within the training population, including nonadditive effects improved accuracy and/or bias for all three traits when predicting total genotypic value. When six F 1 populations were used for validation, prediction accuracy ranged from 0.06 to 0.63 and was consistently lower (0.13 on average) without allele dosage information. We conclude that genome-wide prediction is feasible in potato and that it will improve selection for breeding value given the substantial amount of nonadditive genetic variance in elite germplasm., (Copyright © 2018 by the Genetics Society of America.)

The development of germplasm with resistance to common scab and cold-induced sweetening is a high priority for the potato ( L.) industry. A mapping population was developed from mating two individuals of a diploid family generated by crossing the susceptible cultivated potato clone US-W4 to the highly resistant wild relative ( Bitter) clone '524-8'. Progeny were evaluated in replicated field trials. Tubers were scored for percentage of surface area with scab lesions, scab lesion type, cold-induced sweetening, average tuber weight, and dry matter. Plants were evaluated for vine maturity. A genetic map was constructed, quantitative trait loci (QTLs) were identified, and the gene action of significant QTLs was characterized using 1606 single nucleotide polymorphisms (SNPs). Significant QTLs for common scab percentage of surface area covered with lesions and lesion type were identified in overlapping regions on chromosome 11 ( = 21.0 and 18.2%, respectively). Quantitative trait loci were identified on chromosomes 4 ( = 17.1%) and 6 ( = 19.4%) for cold-induced sweetening, chromosome 5 for maturity ( = 29.8%), and chromosome 1 ( = 26.3 and 22.0%) for average tuber weight. Identification of QTLs is the first step toward developing molecular markers for breeders to efficiently integrate these desirable traits into cultivars., (Copyright © 2017 Crop Science Society of America.)

Genome-wide association studies (GWAS) are widely used in diploid species to study complex traits in diversity and breeding populations, but GWAS software tailored to autopolyploids is lacking. The objectives of this research were to (i) develop an R package for autopolyploids based on the + mixed model, (ii) validate the software with simulated data, and (iii) analyze a diversity panel of tetraploid potatoes. A unique feature of the R package, called GWASpoly, is its ability to model different types of polyploid gene action, including additive, simplex dominant, and duplex dominant. Using a simulated tetraploid population, we confirmed our hypothesis that statistical power is higher when the assumed gene action in the GWAS model matches the gene action at unobserved quantitative trait loci (QTL). Thirteen traits were analyzed in the Solanaceae Coordinated Agricultural Project (SolCAP) potato diversity panel and, consistent with previous studies, significant QTL for tuber shape and eye depth co-localized on chromosome 10. For the other traits, only marginally significant QTL were detected, most likely due to insufficient statistical power: for simulated traits with a heritability () of 0.3, the median genome-wide power was only 0.01. Our results indicate that both marker density and population size were limiting factors for GWAS with the SolCAP panel., (Copyright © 2016 Crop Science Society of America.)

Prediction accuracy of genomic selection (GS) has been previously evaluated through simulation and cross-validation; however, validation based on progeny performance in a plant breeding program has not been investigated thoroughly. We evaluated several prediction models in a dynamic barley breeding population comprised of 647 six-row lines using four traits differing in genetic architecture and 1536 single nucleotide polymorphism (SNP) markers. The breeding lines were divided into six sets designated as one parent set and five consecutive progeny sets comprised of representative samples of breeding lines over a 5-yr period. We used these data sets to investigate the effect of model and training population composition on prediction accuracy over time. We found little difference in prediction accuracy among the models confirming prior studies that found the simplest model, random regression best linear unbiased prediction (RR-BLUP), to be accurate across a range of situations. In general, we found that using the parent set was sufficient to predict progeny sets with little to no gain in accuracy from generating larger training populations by combining the parent set with subsequent progeny sets. The prediction accuracy ranged from 0.03 to 0.99 across the four traits and five progeny sets. We explored characteristics of the training and validation populations (marker allele frequency, population structure, and linkage disequilibrium, LD) as well as characteristics of the trait (genetic architecture and heritability, H 2 ). Fixation of markers associated with a trait over time was most clearly associated with reduced prediction accuracy for the mycotoxin trait DON. Higher trait H 2 in the training population and simpler trait architecture were associated with greater prediction accuracy., (© 2015 The Authors.)

Unlabelled: Consensus genetic maps constructed from multiple populations are an important resource for both basic and applied research, including genome-wide association analysis, genome sequence assembly and studies of evolution. The LPmerge software uses linear programming to efficiently minimize the mean absolute error between the consensus map and the linkage maps from each population. This minimization is performed subject to linear inequality constraints that ensure the ordering of the markers in the linkage maps is preserved. When marker order is inconsistent between linkage maps, a minimum set of ordinal constraints is deleted to resolve the conflicts., Availability and Implementation: LPmerge is on CRAN at http://cran.r-project.org/web/packages/LPmerge., (© The Author 2014. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.)

New sources of genetic diversity must be incorporated into plant breeding programs if they are to continue increasing grain yield and quality, and tolerance to abiotic and biotic stresses. Germplasm collections provide a source of genetic and phenotypic diversity, but characterization of these resources is required to increase their utility for breeding programs. We used a barley SNP iSelect platform with 7,842 SNPs to genotype 2,417 barley accessions sampled from the USDA National Small Grains Collection of 33,176 accessions. Most of the accessions in this core collection are categorized as landraces or cultivars/breeding lines and were obtained from more than 100 countries. Both STRUCTURE and principal component analysis identified five major subpopulations within the core collection, mainly differentiated by geographical origin and spike row number (an inflorescence architecture trait). Different patterns of linkage disequilibrium (LD) were found across the barley genome and many regions of high LD contained traits involved in domestication and breeding selection. The genotype data were used to define 'mini-core' sets of accessions capturing the majority of the allelic diversity present in the core collection. These 'mini-core' sets can be used for evaluating traits that are difficult or expensive to score. Genome-wide association studies (GWAS) of 'hull cover', 'spike row number', and 'heading date' demonstrate the utility of the core collection for locating genetic factors determining important phenotypes. The GWAS results were referenced to a new barley consensus map containing 5,665 SNPs. Our results demonstrate that GWAS and high-density SNP genotyping are effective tools for plant breeders interested in accessing genetic diversity in large germplasm collections.

Intense structuring of plant breeding populations challenges the design of the training set (TS) in genomic selection (GS). An important open question is how the TS should be constructed from multiple related or unrelated small biparental families to predict progeny from individual crosses. Here, we used a set of five interconnected maize (Zea mays L.) populations of doubled-haploid (DH) lines derived from four parents to systematically investigate how the composition of the TS affects the prediction accuracy for lines from individual crosses. A total of 635 DH lines genotyped with 16,741 polymorphic SNPs were evaluated for five traits including Gibberella ear rot severity and three kernel yield component traits. The populations showed a genomic similarity pattern, which reflects the crossing scheme with a clear separation of full sibs, half sibs, and unrelated groups. Prediction accuracies within full-sib families of DH lines followed closely theoretical expectations, accounting for the influence of sample size and heritability of the trait. Prediction accuracies declined by 42% if full-sib DH lines were replaced by half-sib DH lines, but statistically significantly better results could be achieved if half-sib DH lines were available from both instead of only one parent of the validation population. Once both parents of the validation population were represented in the TS, including more crosses with a constant TS size did not increase accuracies. Unrelated crosses showing opposite linkage phases with the validation population resulted in negative or reduced prediction accuracies, if used alone or in combination with related families, respectively. We suggest identifying and excluding such crosses from the TS. Moreover, the observed variability among populations and traits suggests that these uncertainties must be taken into account in models optimizing the allocation of resources in GS.

The additive relationship matrix plays an important role in mixed model prediction of breeding values. For genotype matrix X (loci in columns), the product XX' is widely used as a realized relationship matrix, but the scaling of this matrix is ambiguous. Our first objective was to derive a proper scaling such that the mean diagonal element equals 1+f, where f is the inbreeding coefficient of the current population. The result is a formula involving the covariance matrix for sampling genomic loci, which must be estimated with markers. Our second objective was to investigate whether shrinkage estimation of this covariance matrix can improve the accuracy of breeding value (GEBV) predictions with low-density markers. Using an analytical formula for shrinkage intensity that is optimal with respect to mean-squared error, simulations revealed that shrinkage can significantly increase GEBV accuracy in unstructured populations, but only for phenotyped lines; there was no benefit for unphenotyped lines. The accuracy gain from shrinkage increased with heritability, but at high heritability (> 0.6) this benefit was irrelevant because phenotypic accuracy was comparable. These trends were confirmed in a commercial pig population with progeny-test-estimated breeding values. For an anonymous trait where phenotypic accuracy was 0.58, shrinkage increased the average GEBV accuracy from 0.56 to 0.62 (SE < 0.00) when using random sets of 384 markers from a 60K array. We conclude that when moderate-accuracy phenotypes and low-density markers are available for the candidates of genomic selection, shrinkage estimation of the relationship matrix can improve genetic gain.

Background: The need to integrate information from multiple linkage maps is a long-standing problem in genetics. One way to visualize the complex ordinal relationships is with a directed graph, where each vertex in the graph is a bin of markers. When there are no ordering conflicts between the linkage maps, the result is a directed acyclic graph, or DAG, which can then be linearized to produce a consensus map., Results: New algorithms for the simplification and linearization of consensus graphs have been implemented as a package for the R computing environment called DAGGER. The simplified consensus graphs produced by DAGGER exactly capture the ordinal relationships present in a series of linkage maps. Using either linear or quadratic programming, DAGGER generates a consensus map with minimum error relative to the linkage maps while remaining ordinally consistent with them. Both linearization methods produce consensus maps that are compressed relative to the mean of the linkage maps. After rescaling, however, the consensus maps had higher accuracy (and higher marker density) than the individual linkage maps in genetic simulations. When applied to four barley linkage maps genotyped at nearly 3000 SNP markers, DAGGER produced a consensus map with improved fine structure compared to the existing barley consensus SNP map. The root-mean-squared error between the linkage maps and the DAGGER map was 0.82 cM per marker interval compared to 2.28 cM for the existing consensus map. Examination of the barley hardness locus at the 5HS telomere, for which there is a physical map, confirmed that the DAGGER output was more accurate for fine structure analysis., Conclusions: The R package DAGGER is an effective, freely available resource for integrating the information from a set of consistent linkage maps.

Creating artificial protein families affords new opportunities to explore the determinants of structure and biological function free from many of the constraints of natural selection. We have created an artificial family comprising 3,000 P450 heme proteins that correctly fold and incorporate a heme cofactor by recombining three cytochromes P450 at seven crossover locations chosen to minimize structural disruption. Members of this protein family differ from any known sequence at an average of 72 and by as many as 109 amino acids. Most (>73%) of the properly folded chimeric P450 heme proteins are catalytically active peroxygenases; some are more thermostable than the parent proteins. A multiple sequence alignment of 955 chimeras, including both folded and not, is a valuable resource for sequence-structure-function studies. Logistic regression analysis of the multiple sequence alignment identifies key structural contributions to cytochrome P450 heme incorporation and peroxygenase activity and suggests possible structural differences between parents CYP102A1 and CYP102A2.

Protein function can be tuned using laboratory evolution, in which one rapidly searches through a library of proteins for the properties of interest. In site-directed recombination, n crossovers are chosen in an alignment of p parents to define a set of p(n + 1) peptide fragments. These fragments are then assembled combinatorially to create a library of p(n+1) proteins. We have developed a computational algorithm to enrich these libraries in folded proteins while maintaining an appropriate level of diversity for evolution. For a given set of parents, our algorithm selects crossovers that minimize the average energy of the library, subject to constraints on the length of each fragment. This problem is equivalent to finding the shortest path between nodes in a network, for which the global minimum can be found efficiently. Our algorithm has a running time of O(N(3)p(2) + N(2)n) for a protein of length N. Adjusting the constraints on fragment length generates a set of optimized libraries with varying degrees of diversity. By comparing these optima for different sets of parents, we rapidly determine which parents yield the lowest energy libraries.

Recombination generates chimeric proteins whose ability to fold depends on minimizing structural perturbations that result when portions of the sequence are inherited from different parents. These chimeric sequences can display functional properties characteristic of the parents or acquire entirely new functions. Seventeen chimeras were generated from two CYP102 members of the functionally diverse cytochrome p450 family. Chimeras predicted to have limited structural disruption, as defined by the SCHEMA algorithm, displayed CO binding spectra characteristic of folded p450s. Even this small population exhibited significant functional diversity: chimeras displayed altered substrate specificities, a wide range in thermostabilities, up to a 40-fold increase in peroxidase activity, and ability to hydroxylate a substrate toward which neither parent heme domain shows detectable activity. These results suggest that SCHEMA-guided recombination can be used to generate diverse p450s for exploring function evolution within the p450 structural framework.

The computational algorithm SCHEMA was developed to estimate the disruption caused when amino acid residues that interact in the three-dimensional structure of a protein are inherited from different parents upon recombination. To evaluate how well SCHEMA predicts disruption, we have shuffled the distantly-related beta-lactamases PSE-4 and TEM-1 at 13 sites to create a library of 2(14) (16,384) chimeras and examined which ones retain lactamase function. Sequencing the genes from ampicillin-selected clones revealed that the percentage of functional clones decreased exponentially with increasing calculated disruption (E = the number of residue-residue contacts that are broken upon recombination). We also found that chimeras with low E have a higher probability of maintaining lactamase function than chimeras with the same effective level of mutation but chosen at random from the library. Thus, the simple distance metric used by SCHEMA to identify interactions and compute E allows one to predict which chimera sequences are most likely to retain their function. This approach can be used to evaluate crossover sites for recombination and to create highly mosaic, folded chimeras.