Genome Properties and Prospects of Genomic Prediction of Hybrid Performance in a Breeding Program of Maize

Maize (Zea mays L.) serves as model plant for heterosis research and is the crop where hybrid breeding was pioneered. We analyzed genomic and phenotypic data of 1254 hybrids of a typical maize hybrid breeding program based on the important Dent × Flint heterotic pattern. Our main objectives were to investigate genome properties of the parental lines (e.g., allele frequencies, linkage disequilibrium, and phases) and examine the prospects of genomic prediction of hybrid performance. We found high consistency of linkage phases and large differences in allele frequencies between the Dent and Flint heterotic groups in pericentromeric regions. These results can be explained by the Hill–Robertson effect and support the hypothesis of differential fixation of alleles due to pseudo-overdominance in these regions. In pericentromeric regions we also found indications for consistent marker–QTL linkage between heterotic groups. With prediction methods GBLUP and BayesB, the cross-validation prediction accuracy ranged from 0.75 to 0.92 for grain yield and from 0.59 to 0.95 for grain moisture. The prediction accuracy of untested hybrids was highest, if both parents were parents of other hybrids in the training set, and lowest, if none of them were involved in any training set hybrid. Optimizing the composition of the training set in terms of number of lines and hybrids per line could further increase prediction accuracy. We conclude that genomic prediction facilitates a paradigm shift in hybrid breeding by focusing on the performance of experimental hybrids rather than the performance of parental lines in testcrosses.     

Constrained global optimization for estimating molecular structure from atomic distances.

Finding optimal three-dimensional molecular configurations based on a limited amount of experimental and/or theoretical data requires efficient nonlinear optimization algorithms. Optimization methods must be able to find atomic configurations that are close to the absolute, or global, minimum error and also satisfy known physical constraints such as minimum separation distances between atoms (based on van der Waals interactions). The most difficult obstacles in these types of problems are that 1) using a limited amount of input data leads to many possible local optima and 2) introducing physical constraints, such as minimum separation distances, helps to limit the search space but often makes convergence to a global minimum more difficult. We introduce a constrained global optimization algorithm that is robust and efficient in yielding near-optimal three-dimensional configurations that are guaranteed to satisfy known separation constraints. The algorithm uses an atom-based approach that reduces the dimensionality and allows for tractable enforcement of constraints while maintaining good global convergence properties. We evaluate the new optimization algorithm using synthetic data from the yeast phenylalanine tRNA and several proteins, all with known crystal structure taken from the Protein Data Bank. We compare the results to commonly applied optimization methods, such as distance geometry, simulated annealing, continuation, and smoothing. We show that compared to other optimization approaches, our algorithm is able combine sparse input data with physical constraints in an efficient manner to yield structures with lower root mean squared deviation.     

Two New PRP Conjugate Gradient Algorithms for Minimization Optimization Models

Two new PRP conjugate Algorithms are proposed in this paper based on two modified PRP conjugate gradient methods: the first algorithm is proposed for solving unconstrained optimization problems, and the second algorithm is proposed for solving nonlinear equations. The first method contains two aspects of information: function value and gradient value. The two methods both possess some good properties, as follows: 1)β _k ≥ 0 2) the search direction has the trust region property without the use of any line search method 3) the search direction has sufficient descent property without the use of any line search method. Under some suitable conditions, we establish the global convergence of the two algorithms. We conduct numerical experiments to evaluate our algorithms. The numerical results indicate that the first algorithm is effective and competitive for solving unconstrained optimization problems and that the second algorithm is effective for solving large-scale nonlinear equations.     

Deterministic global optimization algorithm based on outer approximation for the parameter estima- tion of nonlinear dynamic biological systems

ABSTRACT: BACKGROUND: The estimation of parameter values for mathematical models of biological systems is an optimization problem that is particularly challenging due to the nonlinearities involved. One major difficulty is the existence of multiple minima in which standard optimization methods may fall during the search. Deterministic global optimization methods overcome this limitation, ensuring convergence to the global optimum within a desired tolerance. Global optimization techniques are typically classified into stochastic and deterministic. The former typically lead to lower CPU times but offer no guarantee of convergence to the global minimum in a finite number of iterations. In contrast, deterministic methods provide solutions of a given quality (i.e., optimality gap), but tend to lead to large computational burdens. RESULTS: This work presents a deterministic outer approximation-based algorithm for the global optimization of dynamic problems arising in the parameter estimation of models of biological systems. Our approach, which offers a theoretical guarantee of convergence to the global minimum, reformulating the set of ordinary differential equations into an equivalent set of algebraic equations through the use of orthogonal collocation methods, giving rise to a nonconvex nonlinear programming (NLP) problem. This nonconvex NLP is decomposed into two hierarchical levels: a master mixed-integer linear programming problem (MILP) that provides a rigorous lower bound on the optimal solution, and a reduced-space slave NLP that yields an upper bound. The algorithm iterates between these two levels until a termination criterion is satisfied. CONCLUSION: The capabilities of our approach were tested in two benchmark problems, in which the performance of our algorithm was compared with that of the commercial global optimization package BARON. The proposed strategy produced near optimal solutions (i.e., within a desired tolerance) in a fraction of the CPU time required by BARON.     

Protein Loop Modeling Using a New Hybrid Energy Function and Its Application to Modeling in Inaccurate Structural Environments

Protein loop modeling is a tool for predicting protein local structures of particular interest, providing opportunities for applications involving protein structure prediction and de novo protein design. Until recently, the majority of loop modeling methods have been developed and tested by reconstructing loops in frameworks of experimentally resolved structures. In many practical applications, however, the protein loops to be modeled are located in inaccurate structural environments. These include loops in model structures, low-resolution experimental structures, or experimental structures of different functional forms. Accordingly, discrepancies in the accuracy of the structural environment assumed in development of the method and that in practical applications present additional challenges to modern loop modeling methods. This study demonstrates a new strategy for employing a hybrid energy function combining physics-based and knowledge-based components to help tackle this challenge. The hybrid energy function is designed to combine the strengths of each energy component, simultaneously maintaining accurate loop structure prediction in a high-resolution framework structure and tolerating minor environmental errors in low-resolution structures. A loop modeling method based on global optimization of this new energy function is tested on loop targets situated in different levels of environmental errors, ranging from experimental structures to structures perturbed in backbone as well as side chains and template-based model structures. The new method performs comparably to force field-based approaches in loop reconstruction in crystal structures and better in loop prediction in inaccurate framework structures. This result suggests that higher-accuracy predictions would be possible for a broader range of applications. The web server for this method is available at http://galaxy.seoklab.org/loop with the PS2 option for the scoring function.     

Performance prediction of F1 hybrids between recombinant inbred lines derived from two elite maize inbred lines

Selection of recombinant inbred lines (RILs) from elite hybrids is a key method in maize breeding especially in developing countries. The RILs are normally derived by repeated self-pollination and selection. In this study, we first investigated the accuracy of different models in predicting the performance of F₁ hybrids between RILs derived from two elite maize inbred lines Zong3 and 87-1, and then compared these models through simulation using a wider range of genetic models. Results indicated that appropriate prediction models depended on genetic architecture, e.g., combined model using breeding value and genome-wide prediction (BV+GWP) has the highest prediction accuracy for high V _D/V _A ratio (>0.5) traits. Theoretical studies demonstrated that different components of genetic variance were captured by different prediction models, which in turn explained the accuracy of these models in predicting the F₁ hybrid performance. Based on genome-wide prediction model (GWP), 114 untested F₁ hybrids possibly having higher grain yield than the original F₁ hybrid Yuyu22 (the single cross between Zong3 and 87-1) have been identified and recommended for further field test.     

Analysis and purification of IgG4 bispecific antibodies by a mixed-mode chromatography

Therapeutic non-hinge-modified IgG4 molecules form bispecific hybrid antibodies with endogenous human IgG4 molecules via a process known as Fab-arm exchange (or called half molecule exchange). Analysis of the bispecific hybrids is critical for studies of half molecule exchange. A number of analytical methods are available to detect IgG4 hybrids. These methods mostly necessitate labeling or alteration of the model IgG4 molecules, or rely on time-consuming immunoassays and mass spectrometry. In addition, these methods do not allow isolation of hybrid antibodies. We report here the only analytical method to date that relies on chromatographic separation for detection of hybrids formed from intact antibodies in their native forms using pembrolizumab as an example. This method employs a mixed-mode chromatography using a Sepax Zenix SEC-300 column to separate a bispecific hybrid from the parental antibodies. The simultaneous quantitative monitoring of the newly formed hybrid and parental antibodies was achieved by UV absorption and/or protein fluorescence. The bispecific hybrid antibodies were purified with the same method for further biochemical characterization. The method has allowed monitoring of half molecule exchange between a human serum IgG4 and a tested IgG4 molecule, and has been implemented for the analysis of in vitro as well as in vivo samples.     

Conformational requirements for the polymerization of hemoglobin S: studies of mixed liganded hybrids

Gelation experiments with artificially formed half-liganded hybrid tetramers of hemoglobin S demonstrate that when either the α chains or the β^s chains are fixed in the cyanmet (CNmet) liganded state, gelation occurs upon deoxygenation of the ferrous chains. The minimum concentration of hemoglobin required for gelation is equivalent for both hybrids (α₂^cnmetβ₂^s and α₂β₂^scnmet), is considerably higher than the concentration required to gel deoxy-Hb S (α₂β₂^s), and can be restored to the lower minimum gelling point of α₂β₂^s by reduction of the CNmet chains with dithionite. These results suggest that the most important conformational determinant of the deoxy state for polymerization of Hb S is the quaternary deoxy structure rather than the tertiary structural effect of the ligand state of the α or the β^s chains, and are furthermore consistent with the notion that asymmetric deoxy-CNmet hybrid tetramers assume a conformation which resembles, but is not identical to that of deoxyhemoglobin.The results of gelation experiments with mixtures of hemoglobins S and A in which selected chains of one or both hemoglobins are in the CNmet form support the concept that certain non-S hemoglobins may participate in the sickling process by forming hybrid tetramers with Hb S (such as α₂β^aβ^s). The conformational requirement for participation of these hybrids in polymers also appears to be a quaternary deoxy-like structure.     

Determination of heterotic groups for tropical Indica hybrid rice germplasm

Key message

Two heterotic groups and four heterotic patterns were identified for IRRI hybrid rice germplasm to develop hybrid rice in the tropics based on SSR molecular data and field trials.

Abstract

Information on heterotic groups and patterns is a fundamental prerequisite for hybrid crop breeding; however, no such clear information is available for tropical hybrid rice breeding after more than 30 years of hybrid rice commercialization. Based on a study of genetic diversity using molecular markers, 18 parents representing hybrid rice populations historically developed at the International Rice Research Institute (IRRI) were selected to form diallel crosses of hybrids and were evaluated in tropical environments. Yield, yield heterosis and combining ability were investigated with the main objectives of (1) evaluating the magnitude of yield heterosis among marker-based parental groups, (2) examining the consistency between marker-based group and heterotic performance of hybrids, and (3) identifying foundational hybrid parents in discrete germplasm pools to provide a reference for tropical indica hybrid rice breeding. Significant differences in yield, yield heterosis and combining ability were detected among parents and among hybrids. On average, the hybrids yielded 14.8 % higher than the parents. Results revealed that inter-group hybrids yielded higher, with higher yield heterosis than intra-group hybrids. Four heterotic patterns within two heterotic groups based on current IRRI B- and R-line germplasm were identified. Parents in two marker-based groups were identified with limited breeding value among current IRRI hybrid rice germplasm because of their lowest contribution to heterotic hybrids. Heterotic hybrids are significantly correlated with high-yielding parents. The efficiency of breeding heterotic hybrids could be enhanced using selected parents within identified marker-based heterotic groups. This information is useful for exploiting those widely distributed IRRI hybrid rice parents.     

Stochastic Leader Gravitational Search Algorithm for Enhanced Adaptive Beamforming Technique

In this paper, stochastic leader gravitational search algorithm (SL-GSA) based on randomized k is proposed. Standard GSA (SGSA) utilizes the best agents without any randomization, thus it is more prone to converge at suboptimal results. Initially, the new approach randomly choses k agents from the set of all agents to improve the global search ability. Gradually, the set of agents is reduced by eliminating the agents with the poorest performances to allow rapid convergence. The performance of the SL-GSA was analyzed for six well-known benchmark functions, and the results are compared with SGSA and some of its variants. Furthermore, the SL-GSA is applied to minimum variance distortionless response (MVDR) beamforming technique to ensure compatibility with real world optimization problems. The proposed algorithm demonstrates superior convergence rate and quality of solution for both real world problems and benchmark functions compared to original algorithm and other recent variants of SGSA.     

A simple method for preparation of valency hybrid hemoglobins, (α3+β2+)2 and (α2+β3+)2

The improved methods for the preparation of valency hybrid hemoglobins, (α³⁺β²⁺)₂ and (α²⁺β³⁺)₂ were presented. The (α³⁺β²⁺)₂ valency hybrid was separated from the solutions of partially reduced methemoglobin with ascorbic acid, by using CM 32 column chromatography. The (α²⁺β³⁺)₂ valency hybrid was also isolated from hemoglobin solutions, which were partially oxidized with ferricyanide, by chromatography on CM 32 column. These valency hybrid hemoglobins were found to be single on isoelectric focusing electrophoresis. Present procedures are very simple and are suitable for the bulk preparation of (α³⁺β²⁺)₂ and (α²⁺β³⁺)₂ valency hybrids.     

Prediction of single-cross hybrid performance in maize using haplotype blocks associated with QTL for grain yield

Marker-based prediction of hybrid performance facilitates the identification of untested single-cross hybrids with superior yield performance. Our objectives were to (1) determine the haplotype block structure of experimental germplasm from a hybrid maize breeding program, (2) develop models for hybrid performance prediction based on haplotype blocks, and (3) compare hybrid performance prediction based on haplotype blocks with other approaches, based on single AFLP markers or general combining ability (GCA), under a validation scenario relevant for practical breeding. In total, 270 hybrids were evaluated for grain yield in four Dent × Flint factorial mating experiments. Their parental inbred lines were genotyped with 20 AFLP primer–enzyme combinations. Adjacent marker loci were combined into haplotype blocks. Hybrid performance was predicted on basis of single marker loci and haplotype blocks. Prediction based on variable haplotype block length resulted in an improved prediction of hybrid performance compared with the use of single AFLP markers. Estimates of prediction efficiency (R ² ) ranged from 0.305 to 0.889 for marker-based prediction and from 0.465 to 0.898 for GCA-based prediction. For inter-group hybrids with predominance of general over specific combining ability, the hybrid prediction from GCA effects was efficient in identifying promising hybrids. Considering the advantage of haplotype block approaches over single marker approaches for the prediction of inter-group hybrids, we see a high potential to substantially improve the efficiency of hybrid breeding programs. Tobias A. Schrag and Hans Peter Maurer contributed equally to this work.     

Long-term perspective of hybrid versus line breeding in wheat based on quantitative genetic theory

Key message

The predicted future yield potential of hybrids was competitive with lines in the near future, but on a long term the competitiveness of hybrids depends on a number of factors.

Abstract

The change from line to hybrid breeding in autogamous crops is a recent controversial discussion among scientists and breeders. Our objectives were to employ wheat as a model to: (1) deliver a theoretical framework for the comparison of the selection gain of hybrid versus line breeding; (2) elaborate key parameters affecting selection gain in this comparison; (3) and evaluate the potential to modify these parameters in applied breeding programs. We developed a prediction model for future yield potential in both breeding methods as the sum of the population mean and the expected selection gain. The expected selection gain was smaller in hybrid than in line breeding and depended strongly on the hybrid seed production costs and the genetic variance available in hybrid versus line breeding. Owing to heterosis, the predicted future yield potential of hybrids was competitive with lines in the near future. On a long term, however, the competitiveness of hybrid compared to line breeding is questionable and depends on a number of factors. However, market specifications and political reasons might justify the current high interest in hybrid wheat breeding.     

Prediction of single-cross hybrid performance for grain yield and grain dry matter content in maize using AFLP markers associated with QTL

Prediction methods to identify single-cross hybrids with superior yield performance have the potential to greatly improve the efficiency of commercial maize (Zea mays L.) hybrid breeding programs. Our objectives were to (1) identify marker loci associated with quantitative trait loci for hybrid performance or specific combining ability (SCA) in maize, (2) compare hybrid performance prediction by genotypic value estimates with that based on general combining ability (GCA) estimates, and (3) investigate a newly proposed combination of the GCA model with SCA predictions from genotypic value estimates. A total of 270 hybrids was evaluated for grain yield and grain dry matter content in four Dent × Flint factorial mating experiments, their parental inbred lines were genotyped with 20 AFLP primer-enzyme combinations. Markers associated significantly with hybrid performance and SCA were identified, genotypic values and SCA effects were estimated, and four hybrid performance prediction approaches were evaluated. For grain yield, between 38 and 98 significant markers were identified for hybrid performance and between zero and five for SCA. Estimates of prediction efficiency (R ²) ranged from 0.46 to 0.86 for grain yield and from 0.59 to 0.96 for grain dry matter content. Models enhancing the GCA approach with SCA estimates resulted in the highest prediction efficiency if the SCA to GCA ratio was high. We conclude that it is advantageous for prediction of single-cross hybrids to enhance a GCA-based model with SCA effects estimated from molecular marker data, if SCA variances are of similar or larger importance as GCA variances.     

Sesquiterpene-α-amino acid quaternary ammonium hybrids from Stereum complicatum (Steraceae)

Five sesquiterpene-α-amino acid quaternary ammonium hybrids and the sesquiterpene core with no amino acid moiety linked were isolated from the n-butanol partition of the Stereum complicatum fungal culture grown on potato dextrose broth. Chemical structures were unambiguously elucidated by high resolution electrospray ionization mass spectrometry (HR-ESI-MS) in positive ion mode and NMR experiments and were identified as sterostrein Q and stereumamides A - E. The isolation and structure elucidation of these hybrid compounds is reported herein for the first time from S. complicatum. The phytotoxic, antifungal and antibacterial activities of these compounds were evaluated, but no significant activity was found. The HR-ESI-MS fragmentation pattern of the sesquiterpene-α-amino acid quaternary ammonium hybrid metabolites and its chemotaxonomic implication are discussed.     

ConvAn: a convergence analyzing tool for optimization of biochemical networks

Dynamic models of biochemical networks usually are described as a system of nonlinear differential equations. In case of optimization of models for purpose of parameter estimation or design of new properties mainly numerical methods are used. That causes problems of optimization predictability as most of numerical optimization methods have stochastic properties and the convergence of the objective function to the global optimum is hardly predictable. Determination of suitable optimization method and necessary duration of optimization becomes critical in case of evaluation of high number of combinations of adjustable parameters or in case of large dynamic models. This task is complex due to variety of optimization methods, software tools and nonlinearity features of models in different parameter spaces. A software tool ConvAn is developed to analyze statistical properties of convergence dynamics for optimization runs with particular optimization method, model, software tool, set of optimization method parameters and number of adjustable parameters of the model. The convergence curves can be normalized automatically to enable comparison of different methods and models in the same scale. By the help of the biochemistry adapted graphical user interface of ConvAn it is possible to compare different optimization methods in terms of ability to find the global optima or values close to that as well as the necessary computational time to reach them. It is possible to estimate the optimization performance for different number of adjustable parameters. The functionality of ConvAn enables statistical assessment of necessary optimization time depending on the necessary optimization accuracy. Optimization methods, which are not suitable for a particular optimization task, can be rejected if they have poor repeatability or convergence properties. The software ConvAn is freely available on www.biosystems.lv/convan.     

Design,synthesis and biological evaluation of novel hybrids of N-aryl pyrrothine-base α-pyrone as bacterial RNA polymerase inhibitors

Antibiotic resistance in bacteria has been an emerging public health problem, thus discovery of novel and effective antibiotics is urgent. A series of novel hybrids of N-aryl pyrrothine-base α-pyrone hybrids was designed, synthesized and evaluated as bacterial RNA polymerase (RNAP) inhibitors. Among them, compound 13c exhibited potent antibacterial activity against antibiotic-resistant S. aureus with the minimum inhibitory concentration (MIC) in the range of 1–4 μg/mL. Moreover, compound 13c exhibited strong inhibitory activity against E.coli RNAP with IC₅₀ value of 16.06 μM, and cytotoxicity in HepG2 cells with IC₅₀ value of 7.04 μM. The molecular docking study further suggested that compound 13c binds to the switch region of bacterial RNAP. In summary, compound 13c is a novel bacterial RNAP inhibitor, and a promising lead compound for further optimization.     

Prediction of functional modules based on comparative genome analysis and Gene Ontology application

We present a computational method for the prediction of functional modules encoded in microbial genomes. In this work, we have also developed a formal measure to quantify the degree of consistency between the predicted and the known modules, and have carried out statistical significance analysis of consistency measures. We first evaluate the functional relationship between two genes from three different perspectives—phylogenetic profile analysis, gene neighborhood analysis and Gene Ontology assignments. We then combine the three different sources of information in the framework of Bayesian inference, and we use the combined information to measure the strength of gene functional relationship. Finally, we apply a threshold-based method to predict functional modules. By applying this method to Escherichia coli K12, we have predicted 185 functional modules. Our predictions are highly consistent with the previously known functional modules in E.coli. The application results have demonstrated that our approach is highly promising for the prediction of functional modules encoded in a microbial genome.     

Calibration of parameters in Dynamic Energy Budget models using Direct-Search methods

Dynamic Energy Budget (DEB) theory aims to capture the quantitative aspects of metabolism at the individual level, for all species. The parametrization of a DEB model is based on information obtained through the observation of natural populations and experimental research. Currently the DEB toolbox estimates these parameters using the Nelder–Mead Simplex method, a derivative-free direct-search method. However, this procedure presents some limitations regarding convergence and how to address constraints. Framed in the calibration of parameters in DEB theory, this work presents a numerical comparison between the Nelder–Mead Simplex method and the SID-PSM algorithm, a Directional Direct-Search method for which convergence can be established both for unconstrained and constrained problems. A hybrid version of the two methods, named as Simplex Directional Direct-Search, provides a robust and efficient algorithm, able to solve the constrained optimization problems resulting from the parametrization of the biological models.

     

Hybrid breeding of rice via genomic selection

Hybrid breeding is the main strategy for improving productivity in many crops, especially in rice and maize. Genomic hybrid breeding is a technology that uses whole‐genome markers to predict future hybrids. Predicted superior hybrids are then field evaluated and released as new hybrid cultivars after their superior performances are confirmed. This will increase the opportunity of selecting true superior hybrids with minimum costs. Here, we used genomic best linear unbiased prediction to perform hybrid performance prediction using an existing rice population of 1495 hybrids. Replicated 10‐fold cross‐validations showed that the prediction abilities on ten agronomic traits ranged from 0.35 to 0.92. Using the 1495 rice hybrids as a training sample, we predicted six agronomic traits of 100 hybrids derived from half diallel crosses involving 21 parents that are different from the parents of the hybrids in the training sample. The prediction abilities were relatively high, varying from 0.54 (yield) to 0.92 (grain length). We concluded that the current population of 1495 hybrids can be used to predict hybrids from seemingly unrelated parents. Eventually, we used this training population to predict all potential hybrids of cytoplasm male sterile lines from 3000 rice varieties from the 3K Rice Genome Project. Using a breeding index combining 10 traits, we identified the top and bottom 200 predicted hybrids. SNP genotypes of the training population and parameters estimated from this training population are available for general uses and further validation in genomic hybrid prediction of all potential hybrids generated from all varieties of rice.