FIGL1 prevents aberrant chromosome associations and fragmentation and limits crossovers in polyploid wheat meiosis.

Meiotic crossovers (COs) generate genetic diversity and are crucial for viable gamete production. Plant COs are typically limited to 1-3 per chromosome pair, constraining the development of improved varieties, which in wheat is exacerbated by an extreme distal localisation bias. Advances in wheat genomics and related technologies provide new opportunities to investigate, and possibly modify, recombination in this important crop species. Here, we investigate the disruption of FIGL1 in tetraploid and hexaploid wheat as a potential strategy for modifying CO frequency/position. We analysed figl1 mutants and virus-induced gene silencing lines cytogenetically. Genetic mapping was performed in the hexaploid. FIGL1 prevents abnormal meiotic chromosome associations/fragmentation in both ploidies. It suppresses class II COs in the tetraploid such that CO/chiasma frequency increased 2.1-fold in a figl1 msh5 quadruple mutant compared with a msh5 double mutant. It does not appear to affect class I COs based on HEI10 foci counts in a hexaploid figl1 triple mutant. Genetic mapping in the triple mutant suggested no significant overall increase in total recombination across examined intervals but revealed large increases in specific individual intervals. Notably, the tetraploid figl1 double mutant was sterile but the hexaploid triple mutant was moderately fertile, indicating potential utility for wheat breeding.

Delayed development of basal spikelets in wheat explains their increased floret abortion and rudimentary nature.

Large differences exist in the number of grains per spikelet across an individual wheat (Triticum aestivum L.) spike. The central spikelets produce the highest number of grains, while apical and basal spikelets are less productive, and the most basal spikelets are commonly only developed in rudimentary form. Basal spikelets are delayed in initiation, yet they continue to develop and produce florets. The precise timing or the cause of their abortion remains largely unknown. Here, we investigated the underlying causes of basal spikelet abortion using shading applications in the field. We found that basal spikelet abortion is likely to be the consequence of complete floret abortion, as both occur concurrently and have the same response to shading treatments. We detected no differences in assimilate availability across the spike. Instead, we show that the reduced developmental age of basal florets pre-anthesis is strongly associated with their increased abortion. Using the developmental age pre-abortion, we were able to predict final grain set per spikelet across the spike, alongside the characteristic gradient in the number of grains from basal to central spikelets. Future efforts to improve spikelet homogeneity across the spike could thus focus on improving basal spikelet establishment and increasing floret development rates pre-abortion.

Root angle is controlled by EGT1 in cereal crops employing an antigravitropic mechanism.

Root angle in crops represents a key trait for efficient capture of soil resources. Root angle is determined by competing gravitropic versus antigravitropic offset (AGO) mechanisms. Here we report a root angle regulatory gene termed ENHANCED GRAVITROPISM1 (EGT1) that encodes a putative AGO component, whose loss-of-function enhances root gravitropism. Mutations in barley and wheat EGT1 genes confer a striking root phenotype, where every root class adopts a steeper growth angle. EGT1 encodes an F-box and Tubby domain-containing protein that is highly conserved across plant species. Haplotype analysis found that natural allelic variation at the barley EGT1 locus impacts root angle. Gravitropic assays indicated that Hvegt1 roots bend more rapidly than wild-type. Transcript profiling revealed Hvegt1 roots deregulate reactive oxygen species (ROS) homeostasis and cell wall-loosening enzymes and cofactors. ROS imaging shows that Hvegt1 root basal meristem and elongation zone tissues have reduced levels. Atomic force microscopy measurements detected elongating Hvegt1 root cortical cell walls are significantly less stiff than wild-type. In situ analysis identified HvEGT1 is expressed in elongating cortical and stele tissues, which are distinct from known root gravitropic perception and response tissues in the columella and epidermis, respectively. We propose that EGT1 controls root angle by regulating cell wall stiffness in elongating root cortical tissue, counteracting the gravitropic machinery's known ability to bend the root via its outermost tissues. We conclude that root angle is controlled by EGT1 in cereal crops employing an antigravitropic mechanism.

FANCM promotes class I interfering crossovers and suppresses class II non-interfering crossovers in wheat meiosis.

FANCM suppresses crossovers in plants by unwinding recombination intermediates. In wheat, crossovers are skewed toward the chromosome ends, thus limiting generation of novel allelic combinations. Here, we observe that FANCM maintains the obligate crossover in tetraploid and hexaploid wheat, thus ensuring that every chromosome pair exhibits at least one crossover, by localizing class I crossover protein HEI10 at pachytene. FANCM also suppresses class II crossovers that increased 2.6-fold in fancm msh5 quadruple mutants. These data are consistent with a role for FANCM in second-end capture of class I designated crossover sites, whilst FANCM is also required to promote formation of non-crossovers. In hexaploid wheat, genetic mapping reveals that crossovers increase by 31% in fancm compared to wild type, indicating that fancm could be an effective tool to accelerate breeding. Crossover rate differences in fancm correlate with wild type crossover distributions, suggesting that chromatin may influence the recombination landscape in similar ways in both wild type and fancm.

MicroRNA-resistant alleles of HOMEOBOX DOMAIN-2 modify inflorescence branching and increase grain protein content of wheat.

Plant and inflorescence architecture determine the yield potential of crops. Breeders have harnessed natural diversity for inflorescence architecture to improve yields, and induced genetic variation could provide further gains. Wheat is a vital source of protein and calories; however, little is known about the genes that regulate the development of its inflorescence. Here, we report the identification of semidominant alleles for a class III homeodomain-leucine zipper transcription factor, HOMEOBOX DOMAIN-2 (HB-2), on wheat A and D subgenomes, which generate more flower-bearing spikelets and enhance grain protein content. These alleles increase HB-2 expression by disrupting a microRNA 165/166 complementary site with conserved roles in plants; higher HB-2 expression is associated with modified leaf and vascular development and increased amino acid supply to the inflorescence during grain development. These findings enhance our understanding of genes that control wheat inflorescence development and introduce an approach to improve the nutritional quality of grain.

High expression of the MADS-box gene VRT2 increases the number of rudimentary basal spikelets in wheat.

Spikelets are the fundamental building blocks of Poaceae inflorescences, and their development and branching patterns determine the various inflorescence architectures and grain yield of grasses. In wheat (Triticum aestivum), the central spikelets produce the most and largest grains, while spikelet size gradually decreases acropetally and basipetally, giving rise to the characteristic lanceolate shape of wheat spikes. The acropetal gradient corresponds with the developmental age of spikelets; however, the basal spikelets are developed first, and the cause of their small size and rudimentary development is unclear. Here, we adapted G&T-seq, a low-input transcriptomics approach, to characterize gene expression profiles within spatial sections of individual spikes before and after the establishment of the lanceolate shape. We observed larger differences in gene expression profiles between the apical, central, and basal sections of a single spike than between any section belonging to consecutive developmental time points. We found that SHORT VEGETATIVE PHASE MADS-box transcription factors, including VEGETATIVE TO REPRODUCTIVE TRANSITION 2 (VRT-A2), are expressed highest in the basal section of the wheat spike and display the opposite expression gradient to flowering E-class SEPALLATA1 genes. Based on multi-year field trials and transgenic lines, we show that higher expression of VRT-A2 in the basal sections of the spike is associated with increased numbers of rudimentary basal spikelets. Our results, supported by computational modeling, suggest that the delayed transition of basal spikelets from vegetative to floral developmental programs results in the lanceolate shape of wheat spikes. This study highlights the value of spatially resolved transcriptomics to gain insights into developmental genetics pathways of grass inflorescences.

Population genomic analysis of Aegilops tauschii identifies targets for bread wheat improvement.

Aegilops tauschii, the diploid wild progenitor of the D subgenome of bread wheat, is a reservoir of genetic diversity for improving bread wheat performance and environmental resilience. Here we sequenced 242 Ae. tauschii accessions and compared them to the wheat D subgenome to characterize genomic diversity. We found that a rare lineage of Ae. tauschii geographically restricted to present-day Georgia contributed to the wheat D subgenome in the independent hybridizations that gave rise to modern bread wheat. Through k-mer-based association mapping, we identified discrete genomic regions with candidate genes for disease and pest resistance and demonstrated their functional transfer into wheat by transgenesis and wide crossing, including the generation of a library of hexaploids incorporating diverse Ae. tauschii genomes. Exploiting the genomic diversity of the Ae. tauschii ancestral diploid genome permits rapid trait discovery and functional genetic validation in a hexaploid background amenable to breeding.

Trend, population structure, and trait mapping from 15 years of national varietal trials of UK winter wheat.

There are now a rich variety of genomic and genotypic resources available to wheat researchers and breeders. However, the generation of high-quality and field-relevant phenotyping data which is required to capture the complexities of gene × environment interactions remains a major bottleneck. Historical datasets from national variety performance trials (NVPT) provide sufficient dimensions, in terms of numbers of years and locations, to examine phenotypic trends and study gene × environment interactions. Using NVPT for winter wheat varieties grown in the United Kingdom between 2002 and 2017, we examined temporal trends for eight traits related to yield, adaptation, and grain quality performance. We show a non-stationary linear trend for yield, grain protein content, Hagberg Falling Number (HFN), and days to ripening. Our data also show high environmental stability for yield, grain protein content, and specific weight in UK winter wheat varieties and high environmental sensitivity for HFN. We also show that UK varieties released within this period cluster into four main population groups. Using the historical NVPT data in a genome-wide association analysis, we uncovered a significant marker-trait association peak on wheat chromosome 6A spanning the NAM-A1 gene that have been previously associated with early senescence. Together, our results show the value of utilizing the data routinely collected during national variety evaluation process for examining breeding progress and the genetic architecture of important traits.

ENHANCED GRAVITROPISM 2 encodes a STERILE ALPHA MOTIF-containing protein that controls root growth angle in barley and wheat.

The root growth angle defines how roots grow toward the gravity vector and is among the most important determinants of root system architecture. It controls water uptake capacity, nutrient use efficiency, stress resilience, and, as a consequence, yield of crop plants. We demonstrated that the egt2 (enhanced gravitropism 2) mutant of barley exhibits steeper root growth of seminal and lateral roots and an auxin-independent higher responsiveness to gravity compared to wild-type plants. We cloned the EGT2 gene by a combination of bulked-segregant analysis and whole genome sequencing. Subsequent validation experiments by an independent CRISPR/Cas9 mutant allele demonstrated that egt2 encodes a STERILE ALPHA MOTIF domain-containing protein. In situ hybridization experiments illustrated that EGT2 is expressed from the root cap to the elongation zone. We demonstrated the evolutionary conserved role of EGT2 in root growth angle control between barley and wheat by knocking out the EGT2 orthologs in the A and B genomes of tetraploid durum wheat. By combining laser capture microdissection with RNA sequencing, we observed that seven expansin genes were transcriptionally down-regulated in the elongation zone. This is consistent with a role of EGT2 in this region of the root where the effect of gravity sensing is executed by differential cell elongation. Our findings suggest that EGT2 is an evolutionary conserved regulator of root growth angle in barley and wheat that could be a valuable target for root-based crop improvement strategies in cereals.

Ectopic expression of Triticum polonicum VRT-A2 underlies elongated glumes and grains in hexaploid wheat in a dosage-dependent manner.

Flower development is an important determinant of grain yield in crops. In wheat (Triticum spp.), natural variation for the size of spikelet and floral organs is particularly evident in Triticum turgidum ssp. polonicum (also termed Triticum polonicum), a tetraploid subspecies of wheat with long glumes, lemmas, and grains. Using map-based cloning, we identified VEGETATIVE TO REPRODUCTIVE TRANSITION 2 (VRT2), which encodes a MADS-box transcription factor belonging to the SHORT VEGETATIVE PHASE family, as the gene underlying the T. polonicum long-glume (P1) locus. The causal P1 mutation is a sequence rearrangement in intron-1 that results in ectopic expression of the T. polonicum VRT-A2 allele. Based on allelic variation studies, we propose that the intron-1 mutation in VRT-A2 is the unique T. polonicum subspecies-defining polymorphism, which was later introduced into hexaploid wheat via natural hybridizations. Near-isogenic lines differing for the P1 locus revealed a gradient effect of P1 across spikelets and within florets. Transgenic lines of hexaploid wheat carrying the T. polonicum VRT-A2 allele show that expression levels of VRT-A2 are highly correlated with spike, glume, grain, and floral organ length. These results highlight how changes in expression profiles, through variation in cis-regulation, can affect agronomic traits in a dosage-dependent manner in polyploid crops.

Identification of Fusarium head blight resistance loci in two Brazilian wheat mapping populations.

Fusarium head blight (FHB) is a disease of wheat (Triticum aestivum L.) that causes major yield losses in South America, as well as many other wheat growing regions around the world. FHB results in low quality, contaminated grain due to the production of mycotoxins such as deoxynivalenol (DON). In Brazil, FHB outbreaks are increasing in frequency and are currently controlled by fungicides which are costly and potentially harmful to the wider environment. To identify the genetic basis of resistance to FHB in Brazilian wheat, two mapping populations (Anahuac 75 × BR 18-Terena and BR 18-Terena × BRS 179) segregating for FHB resistance were phenotyped and quantitative trait loci (QTL) analysis was undertaken to identify genomic regions associated with FHB-related traits. A total of 14 QTL associated with FHB visual symptoms were identified, each of which explained 3.7-17.3% of the phenotypic variance. Two of these QTL were stable across environments. This suggests FHB resistance in Anahuac 75, BR 18-Terena and BRS 179 is controlled by multiple genetic loci that confer relatively minor differences in resistance. A major, novel QTL associated with DON accumulation was also identified on chromosome 4B (17.8% of the phenotypic variance), as well as a major QTL associated with thousand-grain weight on chromosome 6B (16.8% phenotypic variance). These QTL could be useful breeding targets, when pyramided with major sources of resistance such as Fhb1, to improve grain quality and reduce the reliance on fungicides in Brazil and other countries affected by FHB.

A haplotype-led approach to increase the precision of wheat breeding.

Crop productivity must increase at unprecedented rates to meet the needs of the growing worldwide population. Exploiting natural variation for the genetic improvement of crops plays a central role in increasing productivity. Although current genomic technologies can be used for high-throughput identification of genetic variation, methods for efficiently exploiting this genetic potential in a targeted, systematic manner are lacking. Here, we developed a haplotype-based approach to identify genetic diversity for crop improvement using genome assemblies from 15 bread wheat (Triticum aestivum) cultivars. We used stringent criteria to identify identical-by-state haplotypes and distinguish these from near-identical sequences (~99.95% identity). We showed that each cultivar shares ~59 % of its genome with other sequenced cultivars and we detected the presence of extended haplotype blocks containing hundreds to thousands of genes across all wheat chromosomes. We found that genic sequence alone was insufficient to fully differentiate between haplotypes, as were commonly used array-based genotyping chips due to their gene centric design. We successfully used this approach for focused discovery of novel haplotypes from a landrace collection and documented their potential for trait improvement in modern bread wheat. This study provides a framework for defining and exploiting haplotypes to increase the efficiency and precision of wheat breeding towards optimising the agronomic performance of this crucial crop.

Copy number variation of TdDof controls solid-stemmed architecture in wheat.

Stem solidness is an important agronomic trait of durum (Triticum turgidum L. var. durum) and bread (Triticum aestivum L.) wheat that provides resistance to the wheat stem sawfly. This dominant trait is conferred by the SSt1 locus on chromosome 3B. However, the molecular identity and mechanisms underpinning stem solidness have not been identified. Here, we demonstrate that copy number variation of TdDof, a gene encoding a putative DNA binding with one finger protein, controls the stem solidness trait in wheat. Using map-based cloning, we localized TdDof to within a physical interval of 2.1 Mb inside the SSt1 locus. Molecular analysis revealed that hollow-stemmed wheat cultivars such as Kronos carry a single copy of TdDof, whereas solid-stemmed cultivars such as CDC Fortitude carry multiple identical copies of the gene. Deletion of all TdDof copies from CDC Fortitude resulted in the loss of stem solidness, whereas the transgenic overexpression of TdDof restored stem solidness in the TdDof deletion mutant pithless1 and conferred stem solidness in Kronos. In solid-stemmed cultivars, increased TdDof expression was correlated with the down-regulation of genes whose orthologs have been implicated in programmed cell death (PCD) in other species. Anatomical and histochemical analyses revealed that hollow-stemmed lines had stronger PCD-associated signals in the pith cells compared to solid-stemmed lines, which suggests copy number-dependent expression of TdDof could be directly or indirectly involved in the negative regulation of PCD. These findings provide opportunities to manipulate stem development in wheat and other monocots for agricultural or industrial purposes.

Dissecting the genetic basis of wheat blast resistance in the Brazilian wheat cultivar BR 18-Terena.

BACKGROUND: Wheat blast, caused by Magnaporthe oryzae Triticum (MoT) pathotype, is a global threat to wheat (Triticum aestivum L.) production. Few blast resistance (R) genes have been identified to date, therefore assessing potential sources of resistance in wheat is important. The Brazilian wheat cultivar BR 18-Terena is considered one of the best sources of resistance to blast and has been widely used in Brazilian breeding programmes, however the underlying genetics of this resistance are unknown. RESULTS: BR 18-Terena was used as the common parent in the development of two recombinant inbred line (RIL) F6 populations with the Brazilian cultivars Anahuac 75 and BRS 179. Populations were phenotyped for resistance at the seedling and heading stage using the sequenced MoT isolate BR32, with transgressive segregation being observed. Genetic maps containing 1779 and 1318 markers, were produced for the Anahuac 75 × BR 18-Terena and BR 18-Terena × BRS 179 populations, respectively. Five quantitative trait loci (QTL) associated with seedling resistance, on chromosomes 2B, 4B (2 QTL), 5A and 6A, were identified, as were four QTL associated with heading stage resistance (1A, 2B, 4A and 5A). Seedling and heading stage QTL did not co-locate, despite a significant positive correlation between these traits, indicating that resistance at these developmental stages is likely to be controlled by different genes. BR 18-Terena provided the resistant allele for six QTL, at both developmental stages, with the largest phenotypic effect conferred by a QTL being 24.8% suggesting that BR 18-Terena possesses quantitative resistance. Haplotype analysis of 100 Brazilian wheat cultivars indicates that 11.0% of cultivars already possess a BR 18-Terena-like haplotype for more than one of the identified heading stage QTL. CONCLUSIONS: This study suggests that BR 18-Terena possesses quantitative resistance to wheat blast, with nine QTL associated with resistance at either the seedling or heading stage being detected. Wheat blast resistance is also largely tissue-specific. Identification of durable quantitative resistances which can be combined with race-specific R gene-mediated resistance is critical to effectively control wheat blast. Collectively, this work facilitates marker-assisted selection to develop new varieties for cultivation in regions at risk from this emerging disease.

Genetic Characterization of a Wheat Association Mapping Panel Relevant to Brazilian Breeding Using a High-Density Single Nucleotide Polymorphism Array.

Bread wheat (Triticum aestivum L.) is one of the world's most important crops. Maintaining wheat yield gains across all of its major production areas is a key target toward underpinning global food security. Brazil is a major wheat producer in South America, generating grain yields of around 6.8 million tons per year. Here, we establish and genotype a wheat association mapping resource relevant to contemporary Brazilian wheat breeding programs. The panel of 558 wheat accessions was genotyped using an Illumina iSelect 90,000 single nucleotide polymorphism array. Following quality control, the final data matrix consisted of 470 accessions and 22,475 polymorphic genetic markers (minor allele frequency ≥5%, missing data <5%). Principal component analysis identified distinct differences between materials bred predominantly for the northern Cerrado region, compared to those bred for southern Brazilian agricultural areas. We augmented the genotypic data with 26 functional Kompetitive Allele-Specific PCR (KASP) markers to identify the allelic combinations at genes with previously known effects on agronomically important traits in the panel. This highlighted breeding targets for immediate consideration - notably, increased Fusarium head blight resistance via the Fhb1 locus. To demonstrate the panel's likely future utility, genome-wide association scans for several phenotypic traits were undertaken. Significant (Bonferroni corrected P < 0.05) marker-trait associations were detected for Fusarium kernel damage (a proxy for type 2 Fusarium resistance), identifying previously known quantitative trait loci in the panel. This association mapping panel represents an important resource for Brazilian wheat breeding, allowing future genetic studies to analyze multiple agronomic traits within a single genetically diverse population.

Agricultural Selection of Wheat Has Been Shaped by Plant-Microbe Interactions.

The influence of wheat (modern wheat, both bread and pasta, their wild ancestors and synthetic hybrids) on the microbiota of their roots and surrounding soil is characterized. We isolated lines of bread wheat by hybridizing diploid (Aegilops tauschii) with tetraploid Triticum durum and crossed it with a modern cultivar of Triticum aestivum. The newly created, synthetic hybrid wheat, which recapitulate the breeding history of wheat through artificial selection, is found to support a microbiome enriched in beneficial Glomeromycetes fungi, but also in, potentially detrimental, Nematoda. We hypothesize that during wheat domestication this plant-microbe interaction diminished, suggesting an evolutionary tradeoff; sacrificing advantageous nutrient acquisition through fungal interactions to minimize interaction with pathogenic fungi. Increased plant selection for Glomeromycetes and Nematoda is correlated with the D genome derived from A. tauschii. Despite differences in their soil microbiota communities, overall wheat plants consistently show a low ratio of eukaryotes to prokaryotes. We propose that this is a mechanism for protection against soil-borne fungal disease and appears to be deeply rooted in the wheat genome. We suggest that the influence of plants on the composition of their associated microbiota is an integral factor, hitherto overlooked, but intrinsic to selection during wheat domestication.

A carbohydrate-binding protein, B-GRANULE CONTENT 1, influences starch granule size distribution in a dose-dependent manner in polyploid wheat.

In Triticeae endosperm (e.g. wheat and barley), starch granules have a bimodal size distribution (with A- and B-type granules) whereas in other grasses the endosperm contains starch granules with a unimodal size distribution. Here, we identify the gene, BGC1 (B-GRANULE CONTENT 1), responsible for B-type starch granule content in Aegilops and wheat. Orthologues of this gene are known to influence starch synthesis in diploids such as rice, Arabidopsis, and barley. However, using polyploid Triticeae species, we uncovered a more complex biological role for BGC1 in starch granule initiation: BGC1 represses the initiation of A-granules in early grain development but promotes the initiation of B-granules in mid grain development. We provide evidence that the influence of BGC1 on starch synthesis is dose dependent and show that three very different starch phenotypes are conditioned by the gene dose of BGC1 in polyploid wheat: normal bimodal starch granule morphology; A-granules with few or no B-granules; or polymorphous starch with few normal A- or B-granules. We conclude from this work that BGC1 participates in controlling B-type starch granule initiation in Triticeae endosperm and that its precise effect on granule size and number varies with gene dose and stage of development.

Identification of Transcription Factors Regulating Senescence in Wheat through Gene Regulatory Network Modelling.

Senescence is a tightly regulated developmental program coordinated by transcription factors. Identifying these transcription factors in crops will provide opportunities to tailor the senescence process to different environmental conditions and regulate the balance between yield and grain nutrient content. Here, we use ten time points of gene expression data along with gene network modeling to identify transcription factors regulating senescence in polyploid wheat (Triticum aestivum). We observe two main phases of transcriptional changes during senescence: early down-regulation of housekeeping functions and metabolic processes followed by up-regulation of transport and hormone-related genes. These two phases are largely conserved with Arabidopsis (Arabidopsis thaliana), although the individual genes underlying these changes are often not orthologous. We have identified transcription factor families associated with these early and later waves of differential expression. Using gene regulatory network modeling, we identified candidate transcription factors that may control senescence. Using independent, publicly available datasets, we found that the most highly ranked candidate genes in the network were enriched for senescence-related functions compared with all genes in the network. We validated the function of one of these candidate transcription factors in senescence using wheat chemically induced mutants. This study lays the groundwork to understand the transcription factors that regulate senescence in polyploid wheat and exemplifies the integration of time-series data with publicly available expression atlases and networks to identify candidate regulatory genes.

Speed breeding in growth chambers and glasshouses for crop breeding and model plant research.

'Speed breeding' (SB) shortens the breeding cycle and accelerates crop research through rapid generation advancement. SB can be carried out in numerous ways, one of which involves extending the duration of plants' daily exposure to light, combined with early seed harvest, to cycle quickly from seed to seed, thereby reducing the generation times for some long-day (LD) or day-neutral crops. In this protocol, we present glasshouse and growth chamber-based SB approaches with supporting data from experimentation with several crops. We describe the conditions that promote the rapid growth of bread wheat, durum wheat, barley, oat, various Brassica species, chickpea, pea, grass pea, quinoa and Brachypodium distachyon. Points of flexibility within the protocols are highlighted, including how plant density can be increased to efficiently scale up plant numbers for single-seed descent (SSD). In addition, instructions are provided on how to perform SB on a small scale in a benchtop growth cabinet, enabling optimization of parameters at a low cost.