Genetic architecture of the maize kernel row number revealed by combining QTL mapping using a high-density genetic map and bulked segregant RNA sequencing

Background The maize kernel row number (KRN) is a key component that contributes to grain yield and has high broad-sense heritability (H 2). Quantitative trait locus/loci (QTL) mapping using a high-density genetic map is a powerful approach to detecting loci that are responsible for traits of interest. Bulked segregant ribonucleic acid (RNA) sequencing (BSR-seq) is another rapid and cost-effective strategy to identify QTL. Combining QTL mapping using a high-density genetic map and BSR-seq may dissect comprehensively the genetic architecture underlying the maize KRN. Results A panel of 300 F2 individuals derived from inbred lines abe2 and B73 were genotyped using the specific-locus amplified fragment sequencing (SLAF-seq) method. A total of 4,579 high-quality polymorphic SLAF markers were obtained and used to construct a high-density genetic map with a total length of 2,123 centimorgan (cM) and an average distance between adjacent markers of 0.46 cM. Combining the genetic map and KRN of F2 individuals, four QTL (qKRN1, qKRN2, qKRN5, and qKRN8-1) were identified on chromosomes 1, 2, 5, and 8, respectively. The physical intervals of these four QTL ranged from 4.36 Mb for qKRN8-1 to 7.11 Mb for qKRN1 with an average value of 6.08 Mb. Based on high-throughput sequencing of two RNA pools bulked from leaves of plants with extremely high and low KRNs, two QTL were detected on chromosome 8 in the 10–25 Mb (BSR_QTL1) and 60–150 Mb (BSR_QTL2) intervals. According to the physical positions of these QTL, qKRN8-1 was included by BSR_QTL2. In addition, qKRN8-1 was validated using QTL mapping with a recombinant inbred lines population that was derived from inbred lines abe2 and B73. Conclusions In this study, we proved that combining QTL mapping using a high-density genetic map and BSR-seq is a powerful and cost-effective approach to comprehensively revealing genetic architecture underlying traits of interest. The QTL for the KRN detected in this study, especially qKRN8-1, can be used for performing fine mapping experiments and marker-assisted selection in maize breeding. Electronic supplementary material The online version of this article (doi:10.1186/s12864-016-3240-y) contains supplementary material, which is available to authorized users.


Background
Maize (zea mays L.) is a staple crop that plays an important role in satisfying food and feed demands worldwide. Improvement in grain yield is a main objective for maize breeders [1]. The grain yield per unit area can be analyzed by the plant number, ear number per plant, and ear weight. The ear weight can be analyzed by the kernel number per row, kernel row number (KRN), and kernel weight. These traits are quantitatively inherited and influenced by genotypes, environments, and environment-by-genotype interactions. The KRN significantly contributes to grain yield and has the highest broad-sense heritability (H 2 ) among the three components [2,3]. Therefore, the investigation into the genetic architecture underlying KRN is helpful not only for understanding the genetic mechanisms underlying ear development but also for improving the maize grain yield.
The KRN is a quantitative trait that is controlled by multiple quantitative trait loci (QTL) [3][4][5]. Based on diverse bi-parental genetic populations in maize, QTL mapping has been employed to investigate the genetic architecture underlying the KRN [3][4][5][6]. In 2014, five QTL for the KRN were detected in both environments using a F 2:3 population derived from inbred lines Nong513 and K10HEX206 with four rows [7]. Using 325 recombinant inbred lines (RILs) derived from a cross between B73 and SICAU1212, a total of 12 QTL for the KRN were detected across four environments; three of them (qERN2-1, qERN8-1, and qERN8-2) were consistently identified across four environments [3]. Based on 397 F 2:3 families derived from the inbreds Ye478 and Dan340, a QTL for the KRN that explains 17.9 % of the phenotypic variance was detected on chromosome 7 across seven diverse environments [5]. Using a set of recombinant chromosomes near isogenic lines derived from the inbred line W22 and teosinte (Zea mays ssp. Parviglumis), a major QTL explaining~51 % of phenotypic variance was fine mapped into an interval of 203 kb [4]. Combined with map-based cloning, QTL mapping has been proven to be a powerful approach to exploring the genes or genetic elements that are responsible for the KRN [8,9]. In 2013, one QTL for the KRN that explains~8.4 % of phenotypic variance was identified on chromosome 4 using the intermated B73 × Mo17 population. The underlying gene FASCIATED EAR2 was subsequently cloned, which encodes a CLAVATA receptor-like protein that causes increased inflorescence meristem and the KRN [8]. In 2015, a major QTL for the KRN KRN4 was fine mapped on chromosome 4; the cloning of this QTL revealed that a 1.2-kb transposoncontaining insertion was responsible for increasing the KRN by regulating the expression level of the SBP-box gene Unbranched3 [9].
Although the QTL for the KRN have been successfully identified via QTL mapping, the low densities of the genetic markers and the complexity of the maize genome caused significant challenges to fine mapping and the exploration of casual genes or elements [10]. The resolution of QTL mapping can be improved using high-density genetic markers due to an increased number of detected recombination events [11,12]. Advances in next-generation sequencing technologies has caused a rapid decline in the affordable cost of genotyping-bysequencing (GBS), which is a popular genotyping method that can produce high-density genome-wide markers without prior knowledge [13]. QTL mapping based on GBS has significantly improved the resolution of the QTL detected for different types of quantitative traits [11,14]. For example, using a genetic map including 6,533 bin markers from low-coverage GBS, qTBN5 and qTBN7 for the tassel branch number were detected within small physical intervals of~800 kb and 1.6 Mb, respectively [11]. Based on a high-density genetic map including 4,932 bin markers, qLA2a and qLOV4 were mapped into small intervals of~4.30 Mb and~21.66 Mb, respectively [12]. Using a high-density genetic map containing 4,183 bin markers, pQTL10 for plant height, ear height, and internode number was detected within an interval of 14.6 Mb [14]. These studies have shown that QTL mapping using a high-density genetic map can accelerate the progress of dissecting the genetic basis of quantitative traits.
In addition to QTL mapping, bulked segregant analysis (BSA) is another strategy that has been employed to rapidly identify genetic determinants underlying phenotypic variation [15]. Based on two groups that show opposing phenotypes of interest traits, the distribution patterns of genome-wide alleles are examined by molecular markers, such as single nucleotide polymorphism (SNP) [16]. A non-random distribution of alleles between two groups likely indicates that this locus is linked with the trait of interest. For example, the co-dominant amplified fragment length polymorphism marker p7m36 was linked to the rhm gene for resistance to southern corn leaf blight by using BSA [17]. Recently, the efficiency and power of BSA has been improved by significant advances in next-generation sequencing technologies [18][19][20]. For example, the use of BSA with nextgeneration sequencing technology, a novel resistance gene Pi65(t) conferring a broad-spectrum resistance to the fungus Magnaporthe oryzae was fine mapped within an interval of 1 Mb [20]. Using BSA combined with the specific-locus amplified fragment sequencing (SLAF-seq) strategy, a single dominant gene PhR10 conferring resistance to the isolate Byl4 (race 3) was fine mapped into an interval of 2.57 Mb [19]. BSA has also been combined with RNA sequencing to rapidly and precisely detect genetic determinants underlying traits of interest [18].
In this study, an F 2 population was constructed from a cross between inbred line B73 with an average KRN of 16 and inbred line abe2 with an average KRN of four. Using this population, QTL mapping for the KRN was performed based on the high-density genetic map that was constructed via SLAF-seq. In addition, bulked segregant RNA sequencing (BSR-seq) was employed to detect the QTL for the KRN [18]. Our results indicated that combining QTL mapping using a high-density genetic map and BSR-seq was a powerful approach to rapidly fine mapping QTL for traits of interest in maize.

Plant materials
A large F 2 population was constructed from a cross between inbred lines B73 and abe2. B73 is a non-waxy and yellow endosperm maize with a KRN of 16 ± 2. abe2 is a waxy and white endosperm maize with a stable KRN of four. From the large F 2 population, 300 F 2 plants were randomly selected and subjected to GBS using the SLAF-seq strategy [21], which were also employed to investigate the KRN in Yunnan Province in China (21.27°N, 100.25°E). A RIL population consisting of 241 lines were subsequently constructed from these 300 F 2 plants using a single seed descend method (Additional file 1: Table S1). The KRN of the RILs was investigated using a randomized block design with two repeats in the winter of 2015 in Hainan Province in China (18.20°N, 109.50°E). Based on analysis of variance (ANOVA), the H 2 for the KRN was calculated as the formula: H 2 = σ g 2 / (σ g 2 + σ e 2 ), where σ g 2 and σ e 2 represent the estimated variances for the genetic effects and the random error, respectively [22].

DNA extraction and genotyping
The genomic DNA of the 300 F 2 plants and two parents were extracted following the protocol of the Plant Genomic DNA Kit (TIANGEN, Beijing, China). The genomic DNA of the RIL population was extracted from the upper leaves of each RIL using a CTAB procedure [23]. The quality and quantity of the DNA were verified using 1.0 % agarose gels and spectrophotometry (Nanodrop 2000, Thermo Scientific, USA).
The 300 F 2 plants and two parents were genotyped using the SLAF-seq method [21]. Based on the SLAF pre-design experiment using B73 RefGen_v2 (http:// ftp.maizesequence.org/release-5b/), the genomic DNA was digested using the restriction enzyme HaeIII. The SLAF library was constructed in accordance with the protocol established by Biomarker Technologies Co. Ltd in Beijing, China. Then, selected SLAFs were sequenced using the Illumina HiSeq 2500 pair-end sequencing platform (Illumina, Inc; San Diego, CA, USA).
The RIL population was genotyped using SSR markers, which were downloaded from MaizeGDB (http://www.maizegdb.org/). Vt2 is an insertion/deletion (InDel) marker developed on an InDel between the B73 and abe2 sequences of the gene vanishing tassel2 [24]. The primer sequences of SSR and Vt2 were synthesized by Beijing AuGCT Bio-technology Co. Ltd. PCR amplicons were separated using 8 % polyacrylamide gel electrophoresis and visualized by silver-staining.

Construction of genetic map and QTL mapping
SLAF pair-end reads with clear index information were grouped into one SLAF locus if the sequence similarity exceeded 90 % as detected using the software BLAT [25] (−tile size = 10, −step size = 5). For each SLAF locus, alleles were defined according to the minor allele frequency (MAF) evaluation because true alleles had significantly higher MAF values than reads containing sequence errors. Clusters with more than four tags or with sequence depth less than 302 were filtered out. SLAFs with two to four tags were considered to be potential polymorphic SLAFs. SLAFs were verified by the alleles origins based on the deep-sequencing of the two parents. Polymorphic SLAFs with a parental genotype of aa × bb and offspring genotypes of ab or miss were used to construct a high-density genetic map (Additional file 2: Table S2). All SLAF markers were grouped with a linkage LOD threshold of 3.0, and the positions and order of grouped markers were arranged using the est.map function in the R/qtl package [26]. Combining the KRNs of F 2 plants, the QTL were identified using the composite interval mapping method implemented in the R/qtl package. The LOD threshold for a significant QTL was determined by 1000 permutations and a P value of 0.05 using the mqmpermutation function implemented in R/qtl.
For the RIL population, the genetic map was constructed using the software QTL IciMapping version 3.2 (http:// www.isbreeding.net). Markers were grouped by a linkage LOD threshold of 3.0 and ordered using the nnTwoOpt algorithm. The ordered markers were rippled by the criteria of the sum of adjacent recombination frequencies. Then, the QTL for the KRN were identified using the inclusive composite interval mapping method implemented in the software QTL IciMapping version 3.2 [27].

Bulked segregant RNA sequencing
The RNA of 62 plants with extremely low KRNs and 61 plants with extremely high KRNs (Additional file 1: Table S1), which were selected from the large F 2 population, were extracted from the 30-day leaves of these plants following the protocol of the TRIZOL reagent established by Invitrogen life technologies Co. Ltd. The quality and quantity of RNA were verified using 1.5 % agarose gels and spectrophotometry (Nanodrop 2000, Thermo Scientific, USA). Two RNA bulks were constructed by pooling the RNA of plants with low or high KRNs with equal quantity and sequenced by Data2bio Co. Ltd in Beijing using the Illumina HiSeq 2000 pairend sequencing platform (Illumina, Inc; San Diego, CA, USA). Raw reads were trimmed using a base PHRED quality value threshold of 15. The remaining nucleotides were then scanned using overlapping windows of 10 bp, and sequences beyond the last window with an average quality value less than the specified threshold were truncated [28].
Clean reads were aligned to B73 RefGen_v3 (www.maizegdb.org) using the software GSNAP [29]. The uniquely mapped reads with less than two mismatches every 36 bp and five bases for every 75 bp as tails were used for subsequent analysis. Polymorphisms were carefully examined and putative heterozygous SNPs were identified based on the pooled RNA-seq data of the two samples in comparison using the following criteria: (1) The first and last three aligned bases of each read were discarded; (2) Each polymorphic base must have a minimum PHRED quality value of 15; (3) The base-pair call must be supported by at least three unique reads; (4) At least 30 % of all aligned reads covering that position support the two most common alleles, and the sum of reads of the two most common alleles account for at least 80 % of all aligned reads covering that nucleotide position. In order to reduce noise, SNPs were retained only if they had at least three reads per allele in the high KRN pool and at least five reads in the low KRN pool. Polymorphic SNPs were used to map the QTL for the KRN using a Bayesian approach [18]. The posterior probabilities were normalized by dividing the maximum linkage observed in a high confidence SNP [18].

Genotypes of abe2, B73, and their F 2 population
A total of 194,886 SLAFs ranging from 414 bp to 444 bp were predicted to randomly distribute across the maize genome with an average adjacent interval of 10.60 kb ( Table 1). The SLAFs within repetitive regions were expected to be less than 12.28 %. A subtotal of 5,357,875 reads, 3,129,859 reads, and 28,725,153 reads were generated for B73, abe2, and the F 2 individuals, respectively. The percentage of bases with quality Q20 was 96.33 % and the GC content was 45.67 %. Based on all high quality pair-end reads, a total of 141,587 SLAFs were defined (Additional file 3: Figure S1a). The average sequence depth of SLAFs in B73 and abe2 was 41.15-fold and 42.08-fold, respectively, and the average sequence depth of the SLAFs in each F 2 plant was 2.21-fold. Of these 141,587 SLAFs, 26,085 SLAFs (18.42 %) were polymorphic (Additional file 3: Figure S1b), and 504 SLAFs were located in repetitive regions with a percentage of 0.3 %. Among the 26,085 polymorphic SLAFs, 21,693 SLAFs were successfully encoded using the genotypes of two parents according to eight types of coding rules (Additional file 2: Table S2). A total of 21,634 polymorphic SLAFs were uniquely mapped to B73 RefGen_v2 (www.maizegdb.org) ( Table 1), and a total of 16,569 SLAFs were successfully encoded according to the type with a parental genotype of aa × bb (Additional file 2: Table S2; Additional file 4: Figure S2).

High-density genetic map
Among the successfully encoded 16,569 SLAFs with unique physical position, a total of 4,579 high quality polymorphic SLAFs were employed to construct a genetic map ( Table 1, Fig. 1a), which satisfied the following criteria: (1) The sequence depths of SLAFs in B73 and abe2 were larger than 20-fold; (2) the genotype integrity in the F 2 population was higher than 70 %; and (3) the segregant ratio in the F 2 population did not significantly differ from 1:2:1 (P = 0.05). The average sequence depth of these 4,579 SLAFs in B73 and abe2 was 92.47-fold and 95.42-fold, respectively. No singleton was detected according to the genotypes of the F 2 individuals (Additional file 5: Figure S3). The missing genotype of each chromosome ranged from 1.69 % to 2.51 % with an average of 2.01 %. The SLAF markers were classed into ten groups with a linkage LOD between any two markers within one group higher than 5.00. The total length of the genetic map was 2,123 centimorgan (cM) with an average distance between adjacent markers of 0.46 cM ( Table 1). The maximum distance between adjacent markers was observed on chromosome 8 with a value of 2.09 ( Table 1). The Spearman correlations between the genetic positions and physical positions of SLAFs on each chromosome all exceeded 0.99 and were significant at P < 0.01 (Fig. 1b).

QTL mapping using high-density genetic map
According to the LOD threshold value of~3 as determined by permutation, a total of four QTL were identified on chromosomes 1, 2, 5, and 8 ( Polymorphic SNPs in the pooled data were used to map the loci for the KRN. After filtering, a total of 202,651 SNPs were employed to determine the probability of the linkage with the causal gene(s) for KRN. Two significant loci were observed in the 10-25 Mb (BSR_QTL1) and 60-150 Mb (BSR_QTL2) intervals on chromosome 8 (Fig. 3). Three other putative QTL simultaneously exist: two QTL on the short and long arms of chromosome 2 and one QTL on the long arm of chromosome 4 (Fig. 3). According to the physical positions, qKRN8-1 was included by BSR_QTL2.

Validation of the QTL on chromosome 8 using the RIL population
The KRNs of the RILs ranged from 4 to 18 and normally distributed (Fig. 4a). The KRN difference among the RILs was statistically significant (P < 0.01) and the H 2 of the KRN was 0.87 as calculated from the results of ANOVA. A total of 120 markers on chromosome 8 were screened using the genomic DNA of abe2 and B73 and 12 markers (10 %) were polymorphic (Fig. 4b). The length of the genetic map, which was constructed using these 12 polymorphic markers, was 96.76 cM with an average interval of 8.80 cM (Fig. 4b). The maximum interval was observed between umc1933 and umc1724 with a value of 28.44 cM. The order of the markers was consistent with that in IBM 2008 neighbor map (www.maizegdb.org).
Combining the KRNs and the genetic map of the RIL population, two QTL were identified on chromosome 8 with LOD values of 7.43 and 3.95 (Fig. 4b) ( Table 1). The QTL which was flanked by SSR markers umc1974 and umc1864 explained 15.52 % of the phenotypic variance and had an additve effect of −0.89 (Fig. 4b) ( Table 1). The QTL which was flanked by SSR markers umc1287 and umc1997 explained 8.25 % of the phenotypic variance and had an additive effect of −0.66 (Fig. 4b) (Table 1). According to the physical positions, qKRN8-1 was identified again and qKRN8-2 was included by BSR_QTL2.

Discussion
The power of QTL mapping was increased using a high-density genetic map based on SLAF-seq QTL mapping is an efficient strategy for exploring the genetic architecture underlying quantitative traits in maize [30,31]. However, the accuracy and resolution of QTL mapping is significantly affected by the quality and resolution of the genetic map [32]. SLAF-seq is an affordable, rapid, and reliable method for de novo SNP and InDel discovery for large and complex genomes, which combines locus-specific amplification and highthroughput sequencing [21]. It produces thousands of polymorphic markers to generate a high resolution and accurate genetic map. Compared with genotyping using traditional PCR-based markers, SLAF-seq is rapid, costeffective and does not require prior knowledge of polymorphic information [33][34][35].
In genotyping using SLAF-seq, the quality of SLAFs plays a key role in the accuracy of de novo SNP or InDel discovery. In this study, the SLAF-efficient selection scheme was developed using B73 RefGen_v2 to improve the efficiency of reduced representation library sequencing [36,37]. The restricted enzyme HaeIII was used to digest the genome, and a total of 107,021 SLAFs were predicted. The percentage of SLAFs within repetitive regions was controlled below 12.28 % to simplify the complexity of genomes for facilitating downstream analyses. The copy number variation among fragments is another important factor that affects the quality of SLAFs. To ensure copy number uniformity, a tighter fragment length range (414 bp -444 bp) was selected to maintain amplification efficiency uniformity during the PCR process. The PCR reaction components and program were also improved to ensure copy number uniformity among fragments. As a result, the average sequence depth of SLAF in B73 (41.15-fold) was close to the average sequence depth of SLAF in abe2 (42.08-fold), and the average sequence depth of SLAF in each F 2 individual was close to 2.21-fold. The high-density genetic map was constructed using 4,579 high-quality polymorphic SLAFs with an average distance between adjacent markers of 0.46 cM. The Spearman correlation between the marker genetic position and the marker physical position for each chromosome exceeded 0.99 and were significant at P < 0.01. This correlation indicated the high quality of the genetic map. Based on the high-density genetic map, a total of four QTL for the KRN were detected. The physical interval ranged from  Mb with an average value of 6.08 Mb, which were significantly smaller than the physical interval of the QTL identified using traditional PCR-based markers [38,39]. This result implied the increased power of QTL mapping using a high-density genetic map based on SLAF-seq.
Comprehensive genetic architecture revealed by combining QTL mapping and BSR-seq Combining the high-density genetic map and KRNs of 300 F 2 individuals, a total of four QTL (qKRN1, qKRN2, qKRN5, and qKRN8-1) were identified on chromosomes 1, 2, 5, and 8, respectively. Based on reads generated from two RNA pools of plants with extremely opposite KRNs, two significant peaks were observed in the intervals 10-25 Mb (BSR_QTL1) and 60-150 Mb (BSR_QTL2) on chromosome 8, and three additional putative QTL (two on chromosome 2 and one on chromosome 4) were detected (Fig. 3). These results comprehensively revealed the genetic architecture underlying KRN. In this study, the F 2 population was used to map the QTL for the KRN. A comparison of QTL mapping using advanced generation populations, such as RILs [40,41], indicated that mapping in early-generation populations was rapid and cost-effective. Although the resolution of the QTL was limited by recombination frequency in each F 2 individual, this resolution may be improved by increasing the population size or the number of polymorphic markers to capture as many recombination events as possible and take full advantage of the linkage information in the F 2 population [11]. This possibility was proved by our results that the physical intervals of the four QTL ranged from 4.36 Mb to 7.11 Mb with an average value of 6.08 Mb.
The genetic architecture underlying quantitative traits is usually complex [42]. The phenotype results from the genetic architecture and the environment. Although phenotyping with several replications in different environments can reduce the influence of the environment, QTL mapping for the KRN in a single environment is a reasonable approach because the H 2 of the KRN was 0.87 in this study. The estimated H 2 of the KRN was also very hig in other studies [3,5,7]. The high H 2 of the KRN indicated that it was not strongly influenced by the environment. In this study, qKRN8-1 was included by BSR_QTL2 according to the physical position. It was also validated using QTL mapping with the RILs. Using 325 RILs derived from a cross between B73 and SICAU1212, four QTL for the KRN (qERN1-2, qERN2-1, qERN5-1, and qERN8-2) were detected across four environments [3]. qKRN1 was close to qERN1-2, and qKRN2, qKRN5, and qKRN8-1 overlapped with qERN2-1, qERN5-1, and qERN8-2, respectively, which were consistently identified across three environments [3]. qKRN2 and qKRN5 were also detected by another study. In addition, several studies revealed the QTL for the KRN close to qKRN2 on the short arm of chromosome 2 [43][44][45]. These results confirmed the feasible of using QTL mapping for the KRN using F 2 population and provided confidence in the validity of the QTL.
BSR-seq is an inexpensive and efficient method for gene mapping for mutant phenotypes [18]. It provides not only the position of a gene underlying a mutant phenotype but also patterns of gene expression [46,47]. In this study, the intervals of two significant QTL for the KRN on chromosome 8 were 15 Mb and 90 Mb. The mapping resolution may be affected by the population size, the accuracy of phenotyping, the pooling strategy and other factors. The potential existence of more than one QTL on chromosome 8 was likely to have significantly impacted the mapping resolution. In addition, the KRN is a quantitative trait [5,48,49], and this may result in long intervals of the QTL.

Fine mapping of the QTL for the KRN
In this study, a total of four QTL (qKRN1, qKRN2, qKRN5, and qKRN8-1) for the KRN were identified based on the F 2 population. According to the B73 Ref-Gen v3 gene model (www.maizegdb.org), a subtotal of 178, 163, 55, and 68 protein coding genes were located within qKRN1, qKRN2, qKRN5, and qKRN8-1, respectively (Additional file 6: Table S3). Fine mapping should be conducted to identify casual genes underlying these QTL and facilitate efficient marker-assisted selection. The strategy of the recombinant-derived progeny test was an efficient method for fine mapping [50]. It located the QTL by testing associations between molecular markers and phenotypic variance in progenies derived from recombinants [51,52]. In addition, the highdensity polymorphic markers provided by SLAF-seq and BSR-seq can facilitate fine mapping experiments using additional populations.
According to the LOD and effects, qKRN8-1 should be priorly investigated because it had the highest LOD and was validated by the BSR-seq and the QTL mapping using the RIL population. A total of 68 protein coding genes were located within qKRN8-1, in which five genes have been annotated. However, the expression patterns of genes within qKRN8-1 from the BSR-seq results were not employed to prioritize candidate genes because no biologically replicated RNA-Seq data existed and the RNA for sequencing was not extracted from the ear where the phenotype was evident. The accurate identification of differentially expressed genes in maize ears with biologically replicated data may facilitate the cloning of genes responsible for the KRN.