Technical note: Avoiding the direct inversion of the numerator relationship matrix for genotyped animals in single-step genomic best linear unbiased prediction solved with the preconditioned conjugate gradient

This paper evaluates an efficient implementation to multiply the inverse of a numerator relationship matrix for genotyped animals () by a vector (). The computation is required for solving mixed model equations in single-step genomic BLUP (ssGBLUP) with the preconditioned conjugate gradient (PCG). The inverse can be decomposed into sparse matrices that are blocks of the sparse inverse of a numerator relationship matrix () including genotyped animals and their ancestors. The elements of were rapidly calculated with the Henderson's rule and stored as sparse matrices in memory. Implementation of was by a series of sparse matrix-vector multiplications. Diagonal elements of , which were required as preconditioners in PCG, were approximated with a Monte Carlo method using 1,000 samples. The efficient implementation of was compared with explicit inversion of with 3 data sets including about 15,000, 81,000, and 570,000 genotyped animals selected from populations with 213,000, 8.2 million, and 10.7 million pedigree animals, respectively. The explicit inversion required 1.8 GB, 49 GB, and 2,415 GB (estimated) of memory, respectively, and 42 s, 56 min, and 13.5 d (estimated), respectively, for the computations. The efficient implementation required <1 MB, 2.9 GB, and 2.3 GB of memory, respectively, and <1 sec, 3 min, and 5 min, respectively, for setting up. Only <1 sec was required for the multiplication in each PCG iteration for any data sets. When the equations in ssGBLUP are solved with the PCG algorithm, is no longer a limiting factor in the computations.

The relationship between lip-closing force and dental arch morphology in patient with Angle Class I malocclusion

Dental arch morphology and tooth position are affected by lip-closing force (LCF). This study aimed to quantitatively evaluate the relationships between the horizontal or vertical balance of the LCF generated during maximum voluntary pursing-like movements and dental arch length (DAL) or width (DAW) or the lingual inclination of the upper or lower 1st molars (LIUM, LILM) in patients with Angle Class I malocclusion. Sixteen subjects with Angle Class I malocclusion (median age: 23·4 ± 5·9 years) who had never undergone orthodontic treatment were randomly selected. LCF was measured in eight directions during maximum voluntary pursing-like lip-closing movements. Dental arch models were scanned and analysed to obtain DAW, DAL, LIUM and LILM measurements. Mandibular deviation was measured on posteroanterior cephalograms. A significant negative correlation was detected between maxillary DAL and upper LCF. Maxillary DAL, DAW and the DAL/DAW ratio displayed significant negative correlations with total LCF and upper LCF. However, no significant correlations were detected between any mandibular dental arch morphological parameter and LCF. The difference in the LIUM between the deviation and non-deviation sides exhibited a significant positive correlation with the difference in upper LCF between the deviation and non-deviation sides and was significantly negatively correlated with the difference in lower LCF between the deviation and non-deviation sides. These results suggest that upper LCF is related to maxillary DAL, and the horizontal balance of the LCF of the upper and lower lips is related to the LIUM during pursing-like lip-closing movements in patients with Angle Class I malocclusion.

Nutrition-adaptive control of multiple-bacteriocin production by Weissella hellenica QU 13

AIM

To analyse nutrition-adaptive multiple-bacteriocin production by Weissella hellenica QU 13.

METHODS AND RESULTS

Weissella hellenica QU 13 produces two leaderless bacteriocins, weissellicins Y and M. Their production was studied in MRS and APT media by quantification analyses with liquid chromatography mass spectrometry (LC/MS), while transcriptional analysis of biosynthetic genes was performed by real-time reverse transcription (RT)-PCR. Weissellicin Y production was higher in MRS culture than in APT culture, while weissellicin M production was higher in APT culture than in MRS culture. APT medium contains a higher amount of thiamine than MRS medium, to enhance the growth of heterofermentative lactic acid bacteria. Therefore, thiamine addition to MRS culture enhanced the growth of W. hellenica QU 13; consequently, weissellicin Y production was decreased, while weissellicin M production was not affected. Furthermore, real-time RT-PCR analyses indicated that the transcriptional trends of their respective structural genes, welY and welM, were different from each other, and that these two genes' transcriptions responded to nutrition conditions.

CONCLUSION

Weissella hellenica QU 13 was demonstrated to control weissellicins Y and M production based on nutrition conditions. In addition, differential expression behaviour of weissellicins Y and M indicates that each of them would have separate roles to adapt to different environmental situations.

SIGNIFICANCE AND IMPACT OF THE STUDY

This is the first report that describes nutrition-adaptive multiple-bacteriocin production, in which thiamine inhibits bacteriocin production while it enhances the growth of the producer strain.

Accuracy of breeding values in small genotyped populations using different sources of external information-A simulation study

Genetically linked small and large dairy cattle populations were simulated to test the effect of different sources of information from foreign populations on the accuracy of predicting breeding values for young animals in a small population. A large dairy cattle population (P_L) with >20 generations was simulated, and a small subpopulation (P_S) with 3 generations was formed as a related population, including phenotypes and genomic information. Predicted breeding values for young animals in the small population were calculated using BLUP and single-step genomic BLUP (ssGBLUP) in 4 different scenarios: (S1) 3,166 phenotypes, 22,855 pedigree animals, and 1,000 to 6,000 genotypes for P_S; (S2) S1 plus genomic estimated breeding value (GEBV) for 4,475 sires from P_L as external information; (S3) S1 plus 221,580 phenotypes, 402,829 pedigree animals, and 53,558 genotypes for P_L; and (S4) single nucleotide polymorphism (SNP) effects calculated based on P_L data. The ability to predict true breeding value was assessed in the youngest third of the genotyped animals in the small population. When data only from the small population were used and 1,000 animals were genotyped, the accuracy of GEBV was only 1 point greater than the estimated breeding value accuracy (0.32 vs. 0.31). Adding external GEBV for sires from P_L did not considerably increase accuracy (0.33 vs. 0.32 in S1). Combining phenotypes, pedigree, and genotypes for P_S and P_L was beneficial for predicting accuracy of GEBV in the small population, and the prediction accuracy of GEBV in this scenario was 0.38 compared with 0.31 from estimated breeding values. When SNP effects from P_L were used to predict GEBV for young genotyped animals from P_S, accuracy was greatest (0.56). With 6,000 genotyped animal in P_S, accuracy was greatest (0.61) with the combined populations. In a small population with few genotypes, the highest accuracy of evaluation may be obtained by using SNP effects derived from a related large population.

Technical note: Acceleration of sparse operations for average-information REML analyses with supernodal methods and sparse-storage refinements

The objective of this study was to remove bottlenecks generally found in a computer program for average-information REML. The refinements included improvements to setting-up mixed-model equations on a hash table with a faster hash function as sparse matrix storage, changing sparse structures in calculation of traces, and replacing a sparse matrix package using traditional methods (FSPAK) with a new package using supernodal methods (YAMS); the latter package quickly processed sparse matrices containing large, dense blocks. Comparisons included 23 models with data sets from broiler, swine, beef, and dairy cattle. Models included single-trait, multiple-trait, maternal, and random regression models with phenotypic data; selected models used genomic information in a single-step approach. Setting-up mixed model equations was completed without abnormal termination in all analyses. Calculations in traces were accelerated with a hash format, especially for models with a genomic relationship matrix, and the maximum speed was 67 times faster. Computations with YAMS were, on average, more than 10 times faster than with FSPAK and had greater advantages for large data and more complicated models including multiple traits, random regressions, and genomic effects. These refinements can be applied to general average-information REML programs.

Development of Micro Cellular Open Cell Rigid Polyurethane Foams

With the increasing concern over the threat of ozone depletion and global warming, the rigid polyurethane foam insulation industry is facing a majorchallenge of selecting alternatives for chlorofluorocarbons (CFCs). Under the present situation, however, the effective means of solving this problem haven't been taken yet. Moreover, with more concern with the saving of energy worldwide, there is hope of insulators with higher performance.

This paper reports on a micro cellular open cell polyurethane foam, which is very effective as a core material for evacuated insulators. In addition, thermal insulation panels with high performance are developed by utilizing the open cell foam as a core material.

The evacuated insulators, so-called "vacuum insulation panels," have an insulation effectiveness four times better than those of the conventional rigid polyurethane and polyisocyanurate foams (thermal conductivity is 0.005 W/mK)and are also very lightweight compared to those made of inorganic substances such as silica powder. The vacuum insulation panels were manufactured by packing the core material and absorbents in a film-like laminated plastic container, which is suitable for holding a vacuum, followed by sealing in the industrial vacuum level (0.01—0.1 mm Hg).

We have developed the micro cellular (100—200,μm) and 100% open cell foam by selecting polyol compositions, modified polyisocyanates, surfactants and cell opening additives.

The micro cellular open cell foam has excellent physical properties such as heat resistance, compressive strength and low shrinkage as well as non-scorch at the stage of slabstock foaming. These properties will be very important for manufacturing the vacuum insulation panels. The open cell foams were blown by using the most conventional and alternative blowing agents in rigid foam systems.

In the near future, we hope that this open cell foam technology will contribute to the development of environmentally friendly and high performance products in the insulation industry.

Genetic evaluation using single-step genomic best linear unbiased predictor in American Angus

Predictive ability of genomic EBV when using single-step genomic BLUP (ssGBLUP) in Angus cattle was investigated. Over 6 million records were available on birth weight (BiW) and weaning weight (WW), almost 3.4 million on postweaning gain (PWG), and over 1.3 million on calving ease (CE). Genomic information was available on, at most, 51,883 animals, which included high and low EBV accuracy animals. Traditional EBV was computed by BLUP and genomic EBV by ssGBLUP and indirect prediction based on SNP effects was derived from ssGBLUP; SNP effects were calculated based on the following reference populations: ref_2k (contains top bulls and top cows that had an EBV accuracy for BiW ≥0.85), ref_8k (contains all parents that were genotyped), and ref_33k (contains all genotyped animals born up to 2012). Indirect prediction was obtained as direct genomic value (DGV) or as an index of DGV and parent average (PA). Additionally, runs with ssGBLUP used the inverse of the genomic relationship matrix calculated by an algorithm for proven and young animals (APY) that uses recursions on a small subset of reference animals. An extra reference subset included 3,872 genotyped parents of genotyped animals (ref_4k). Cross-validation was used to assess predictive ability on a validation population of 18,721 animals born in 2013. Computations for growth traits used multiple-trait linear model and, for CE, a bivariate CE-BiW threshold-linear model. With BLUP, predictivities were 0.29, 0.34, 0.23, and 0.12 for BiW, WW, PWG, and CE, respectively. With ssGBLUP and ref_2k, predictivities were 0.34, 0.35, 0.27, and 0.13 for BiW, WW, PWG, and CE, respectively, and with ssGBLUP and ref_33k, predictivities were 0.39, 0.38, 0.29, and 0.13 for BiW, WW, PWG, and CE, respectively. Low predictivity for CE was due to low incidence rate of difficult calving. Indirect predictions with ref_33k were as accurate as with full ssGBLUP. Using the APY and recursions on ref_4k gave 88% gains of full ssGBLUP and using the APY and recursions on ref_8k gave 97% gains of full ssGBLUP. Genomic evaluation in beef cattle with ssGBLUP is feasible while keeping the models (maternal, multiple trait, and threshold) already used in regular BLUP. Gains in predictivity are dependent on the composition of the reference population. Indirect predictions via SNP effects derived from ssGBLUP allow for accurate genomic predictions on young animals, with no advantage of including PA in the index if the reference population is large. With the APY conditioning on about 10,000 reference animals, ssGBLUP is potentially applicable to a large number of genotyped animals without compromising predictive ability.

Implementation of genomic recursions in single-step genomic best linear unbiased predictor for US Holsteins with a large number of genotyped animals

The objectives of this study were to develop and evaluate an efficient implementation in the computation of the inverse of genomic relationship matrix with the recursion algorithm, called the algorithm for proven and young (APY), in single-step genomic BLUP. We validated genomic predictions for young bulls with more than 500,000 genotyped animals in final score for US Holsteins. Phenotypic data included 11,626,576 final scores on 7,093,380 US Holstein cows, and genotypes were available for 569,404 animals. Daughter deviations for young bulls with no classified daughters in 2009, but at least 30 classified daughters in 2014 were computed using all the phenotypic data. Genomic predictions for the same bulls were calculated with single-step genomic BLUP using phenotypes up to 2009. We calculated the inverse of the genomic relationship matrix GAPY(-1) based on a direct inversion of genomic relationship matrix on a small subset of genotyped animals (core animals) and extended that information to noncore animals by recursion. We tested several sets of core animals including 9,406 bulls with at least 1 classified daughter, 9,406 bulls and 1,052 classified dams of bulls, 9,406 bulls and 7,422 classified cows, and random samples of 5,000 to 30,000 animals. Validation reliability was assessed by the coefficient of determination from regression of daughter deviation on genomic predictions for the predicted young bulls. The reliabilities were 0.39 with 5,000 randomly chosen core animals, 0.45 with the 9,406 bulls, and 7,422 cows as core animals, and 0.44 with the remaining sets. With phenotypes truncated in 2009 and the preconditioned conjugate gradient to solve mixed model equations, the number of rounds to convergence for core animals defined by bulls was 1,343; defined by bulls and cows, 2,066; and defined by 10,000 random animals, at most 1,629. With complete phenotype data, the number of rounds decreased to 858, 1,299, and at most 1,092, respectively. Setting up GAPY(-1) for 569,404 genotyped animals with 10,000 core animals took 1.3h and 57 GB of memory. The validation reliability with APY reaches a plateau when the number of core animals is at least 10,000. Predictions with APY have little differences in reliability among definitions of core animals. Single-step genomic BLUP with APY is applicable to millions of genotyped animals.