Gossypium Spp Research Articles

Identification of Organic Substances Associated with Tissue Senescence in Upland Cotton (Gossypium spp. L.) Based on GC-MS Analysis

Premature senescence in crop production, especially occurred at the late growth stage, generally results in a reduction in yield and quality. Therefore, it is beneficial for yield and quality to properly delay senescence of plant tissues during the late developmental stage. In this study, it was observed that the chlorophyll content and photosynthetic rate were gradually decreased along leaf growth progression, and the rates of reduction were promoted by drought. Based on gas chromatography-mass spectrometry (GC-MS) analysis, total eight, five, seven, and five kinds of organic compounds that putatively associated with the tissue senescent progression were identified in leaves, fruit branches, petals, and sepals, respectively. It was found that the identified organic compound, such as a-pinene, β-pinene, and pentadecane were present in different tissues. Among the total ten organic substances identified to be related with the leaf senescence, half were specifically detected in the drought treatment. These results suggest some biochemical pathways associated with the leaf senescence are distinctly regulated by drought. The identified organic compounds in the tested tissues showed three types on the performance pattern based on the contents along with the senescent progression, including gradually increasing, decreasing, and a curve with one single peak. Thus, during the senescence process in tissues, a subset of metabolic substances occur modifications on the quantities, reflecting a complicate biochemical reactions are initiated via the senescence signals. Further analysis of the important organic substances will be helpful for elucidation of the tissue senescence mechanism at the biochemical level and provide a new insight of the senescence signaling transductions in cotton.

Expression of Mannose-Binding Insecticidal Lectin Gene in Transgenic Cotton (<i>Gossypium</i>) Plant

Cotton ( Gossypium spp ) is an important world crop. Despite the efforts made through traditional breeding methods, cotton breeders still faced with many problems, i.e., narrow genetic base, inability to use alien genes and difficulty in breaking gene linkages. Breeders attempted genetic transformations analyses tools to overcome these problems with very little success, hence the need for transgenic intervention. In this report, an optimized cotton regeneration system from shoot apices used to transform cotton wit insecticidal lectin gene from Allium sativum . Cotton regeneration system was observed to be genotype independent with a regeneration rate of 85% obtained within 16 weeks. The age of explants and the size of isolated tips have a significant effect on shoot tip elongation. The elongation rates of the three varieties were not significantly different from each other (p=0.1573). It was observed that Samcot 9 had the highest rooting efficiency (47%), and Samcot 13 had the least rooting efficiency (36%). Though the difference in rooting efficiency was not significant in the three varieties (P=0.08) Transgenic cotton plants were obtained via Agrobacterium -mediated transformation using shoot apices as explants. Transformation rate was 1.3% using LBA 4404 with β-glucuronidase (GUS) gene. The mean number of GUS positive apices was 67% higher when acetosyringone was included in the medium. Agrobacterium concentration and co-cultivation time have a significant effect on transient GUS expression. The highest GUS positive number was observed at OD 600 0.6 and co-cultivation for 3 days. Putative transgenic plants were confirmed by leaf GUS assay, kanamycin leaf test and molecular analysis of putative young leaves.

Assessment of the resistance of cotton germplasm (Gossypium spp.) to aphids (Homoptera, Aphididae) and leafhoppers (Homoptera: Cicadellidae, Typhlocybinae): methodology and genetic variability

AbstractWe carried out an assessment of the resistance of 71 accessions of cotton (Gossypium spp. L.) to the aphid Aphis gossypii and to leafhoppers under natural infestation. Our objectives were (i) to improve the methods for screening cotton germplasm for resistance to both pests, and (ii) to test the existence of genetic correlation between resistances to both insects. For both insects, the percentage of colonized leaves exhibited high genotypic correlation with the number of insects per leaf, had similar or higher heritabilities, and appeared as the better measure of insect populations. The one‐plant‐per‐plot experimental design used allowed an assessment of resistance with high heritability value, and proved to be suitable for the screening of cotton germplasm. G. arboreum was more resistant to both insects than G. barbadense and G. hirsutum. While hairiness had a significant negative effect on resistance to aphids, no significant effect was observed on resistance to leafhoppers, excepted in G. arboreum. The lack of genotypic correlation between resistance to aphids and to leafhoppers demonstrated that a simultaneous improvement of the resistance is possible.

Toward Sequencing Cotton (Gossypium) Genomes: Figure 1.

Despite rapidly decreasing costs and innovative technologies, sequencing of angiosperm genomes is not yet undertaken lightly. Generating larger amounts of sequence data more quickly does not address the difficulties of sequencing and assembling complex genomes de novo. The cotton ( Gossypium spp.)

Evaluation of Traditional Sorghum (Sorghum bicolor) Beer Residue, Shea-Nut (Vitellaria paradoxa) Cake and Cottonseed (Gossypium Spp) Cake for Poultry in Burkina Faso: Availability and Amino Acid Digestibility

The present study aimed to evaluate the nutritive value for chickens of some local by-products in Burkina Faso and to estimate their true amino acid digestibility in cockerels. Sun-dried sorghum (Sorghum bicolor) beer residue (n = 144) and shea-nut (Vitellaria paradoxa) cake (n = 36) samples were collected in two different locations during six months, while cottonseed (Gossypium spp) cake samples were purchased monthly in a local market for the same period (n = 24). Mean Dry Matter (DM) content of beer residue was 94.7% and Crude Protein (CP), Ether Extract (EE), Crude Fibre (CF), Calcium (Ca), Phosphorus (P) and Metabolizable Energy (ME) contents were 23.4, 5.6, 8.5, 0.14 and 0.25% of DM and 13.4 MJ/kg, respectively. Mean lysine, methionine, cystine and threonine contents were 0.87, 0.44, 0.41 and 0.63%, respectively and the corresponding true excreta digestibility values were 92, 98, 95 and 97%. Mean DM content of shea-nut cake was 95.6% and CP, EE, CF, Ca, P and ME contents were 6.7, 7.3, 10.9, 0.40 and 0.19% and 13.1 MJ/kg, respectively. Lysine, methionine, cystine and threonine contents were 0.27, 0.14, 0.09 and 0.23% and the true digestibility values were 96, 78, 88 and 77%, respectively. Mean DM, CP, EE, CF, Ca, P and ME contents of cottonseed cake were 94.8, 44.3, 5.9, 9.9, 0.34 and 1.3% and 12.7 MJ/kg. Lysine, methionine, cystine and threonine contents were 1.6, 0.80, 0.82 and 1.9% and the true digestibility values were 89, 97, 98 and 94%. Overall, higher nutritive values were found for samples collected between October and December and no difference was found between locations.

In-vitro development of ovules obtained after pollination of cotton (Gossypium spp) flowers with pollen from okra (Abelmoschus esculentus L. Moench)

The in vitro response of ovules obtained after pollination of cotton flowers with pollen from Abelmoschus esculentus was studied. For this, 492 cotton flowers from five G. hirsutum varieties, four G. barbadense varieties and 10 F1 interspecific hybrids, were pollinated with pollen from A. esculentus and 5,069 ovules were cultured in vitro. From the cultured ovules, 69 embryos were isolated and 16 of them grew into plants. However, only three of them survived after transplantation. Finally, one plant which originated from the interspecific cross (B403 × Acala Sindos) × A. esculentus reached maturity. The mature plant (Pa0) had no morphological traits from A. esculentus. On the contrary, traits from both cotton species were observed. The flowcytometric analysis of the Pa0 plant indicated that it was hypoaneuploid. Root tip chromosome counts of its offsprings revealed a progressive chromosome increase from the Pa1 to Pa4 generation. Plants with 52 chromosomes or hypoaneuploids with a lower level of chromosomes (46–51) could be isolated from the Pa4 generation. These plants exhibited morphological traits from both cotton species and they were fertile. No signs of A. esculentus morphological characteristics were observed in these plants. It was concluded that aneuploid partial interspecific cotton plants could be produced after pollination of cotton interspecific hybrids with pollen from A. esculentus and application of an in-ovule embryo rescue technique.

Usefulness of SSR Derived from Tetraploid Gossypium spp. for Analyses of Diploid Gossypium spp.

This investigation is the first attempt to utilize tetraploid species-derived primers to generate markers for mapping in diploid cotton species. About 113 individual F2 plants, developed from the cross between Gossypium nelsoni and G. australe, were used to construct a linkage map. One allotetraploid (ADj) G. hirsutum (TM-1) plant and its putative diploid ancestors, G. arboreum (A2) and G. raimondii (D5), were also included for comparative analysis. We developed a high-throughput multi-mix PCR assay for simple sequence repeat (SSR) marker separation using fluorescent-labeled capillary electrophoresis. Of a total of 205 tetraploid-derived SSR primers, 83% amplified in all four diploid species, indicating that flanking primer sequences are conserved in the diploid and tetraploid ADj genome of cotton. DNA sequence information of 18 randomly selected clones revealed that all of the clones contained SSR repeat motifs in the diploid species, suggesting that SSR markers including the flanking primer sequences have been conserved at the inter-specific level in genomic DNA across years of evolution. About 85% of the amplified primers showed polymorphism among the diploid genome species. Forty percent of SSRs in the diploid G. nelsoni and 35% in G. australe amplified the same size DNA fragment as in the tetraploid, (TM-1). This is further evidence that many of the tetraploid SSRs are conserved across diploid and tetraploid species. G. nelsoni compared with G. australe had more conserved genomic regions in common with G. hirsutum. From 73 markers scored in the F2 population, 50 exhibited codominance and 23 dominance. There were 47 markers linked across 10 linkage groups covering a total map distance of 754 cM with an average of 16 cM per marker. One linkage group (lg-3) with six loci has been assigned to chromosome 20. Comparative analysis of DNA sequences between G. hirsutum and its two putative parental diploid species indicated that changes within a few selected clones have occurred during evolution as follows: (1) by increasing or decreasing the number of the repeat motif, (2) by single nucleotide mutations occurring within or outside of the repeat motif, (3) by inter conversion of a simple to a compound SSR motif, and (4) by inversion of the repeat regions. Tetraploid-derived microsatellites should be useful in comparative genetic mapping of both tetraploid and diploid Gossypium species for evolutionary studies and introgression of agriculturally important traits from exotic diploid and tetraploid germplasm sources.

CMD: a Cotton Microsatellite Database resource for Gossypium genomics

BackgroundThe Cotton Microsatellite Database (CMD) is a curated and integrated web-based relational database providing centralized access to publicly available cotton microsatellites, an invaluable resource for basic and applied research in cotton breeding.DescriptionAt present CMD contains publication, sequence, primer, mapping and homology data for nine major cotton microsatellite projects, collectively representing 5,484 microsatellites. In addition, CMD displays data for three of the microsatellite projects that have been screened against a panel of core germplasm. The standardized panel consists of 12 diverse genotypes including genetic standards, mapping parents, BAC donors, subgenome representatives, unique breeding lines, exotic introgression sources, and contemporary Upland cottons with significant acreage. A suite of online microsatellite data mining tools are accessible at CMD. These include an SSR server which identifies microsatellites, primers, open reading frames, and GC-content of uploaded sequences; BLAST and FASTA servers providing sequence similarity searches against the existing cotton SSR sequences and primers, a CAP3 server to assemble EST sequences into longer transcripts prior to mining for SSRs, and CMap, a viewer for comparing cotton SSR maps.ConclusionThe collection of publicly available cotton SSR markers in a centralized, readily accessible and curated web-enabled database provides a more efficient utilization of microsatellite resources and will help accelerate basic and applied research in molecular breeding and genetic mapping in Gossypium spp.

Toxicity of Insecticides in a Glass-Vial Bioassay to Adult Brown, Green, and Southern Green Stink Bugs (Heteroptera: Pentatomidae)

Adult brown, Euschistus servus (Say); green, Acrosternum hilare (Say); and southern green, Nezara viridula (L.), stink bugs were collected from soybean, Glycine max (L.) Merr., in fall 2001 and 2002 near Stoneville, MS, and Eudora, AR. A glass-vial bioassay was used to determine LC50 values for the three species of stink bugs for the pyrethroids bifenthrin, cypermethrin, cyfluthrin, lambda-cyhalothrin, and permethrin, and the organophosphates acephate, dicrotophos, malathion, and methyl parathion. Results confirmed findings of other researchers that the brown stink bug was less susceptible to pyrethroid and organophosphate insecticides than were green and southern green stink bugs. The susceptibility of all three stink bug species to the insecticides tested was very similar at both test locations. The study established baseline insecticide mortality data from two locations in the mid-South for three stink bug species that are pests of soybean and cotton, Gossypium spp. Data from the tests are valuable for future use in studies on resistance and in resistance monitoring programs.

Toxicity of Insecticides in a Glass-Vial Bioassay to Adult Brown, Green, and Southern Green Stink Bugs (Heteroptera: Pentatomidae)

Adult brown, Euschistus servus (Say); green, Acrosternum hilare (Say); and southern green, Nezara viridula (L.), stink bugs were collected from soybean, Glycine max (L.) Merr., in fall 2001 and 2002 near Stoneville, MS, and Eudora, AR. A glass-vial bioassay was used to determine LC50 values for the three species of stink bugs for the pyrethroids bifenthrin, cypermethrin, cyfluthrin, λ-cyhalothrin, and permethrin, and the organophosphates acephate, dicrotophos, malathion, and methyl parathion. Results confirmed findings of other researchers that the brown stink bug was less susceptible to pyrethroid and organophosphate insecticides than were green and southern green stink bugs. The susceptibility of all three stink bug species to the insecticides tested was very similar at both test locations. The study established baseline insecticide mortality data from two locations in the mid-South for three stink bug species that are pests of soybean and cotton, Gossypium spp. Data from the tests are valuable for future use in studies on resistance and in resistance monitoring programs.

Control of Plant Trichome Development by a Cotton Fiber MYB Gene[W

Cotton (Gossypium spp) plants produce seed trichomes (cotton fibers) that are an important commodity worldwide; however, genes controlling cotton fiber development have not been characterized. In Arabidopsis thaliana the MYB gene GLABRA1 (GL1) is a central regulator of trichome development. Here, we show that promoter of a cotton fiber gene, RD22-like1 (RDL1), contains a homeodomain binding L1 box and a MYB binding motif that confer trichome-specific expression in Arabidopsis. A cotton MYB protein GaMYB2/Fiber Factor 1 transactivated the RDL1 promoter both in yeast and in planta. Real-time PCR and in situ analysis showed that GaMYB2 is predominantly expressed early in developing cotton fibers. After transferring into Arabidopsis, GL1::GaMYB2 rescued trichome formation of a gl1 mutant, and interestingly, 35S::GaMYB2 induced seed-trichome production. We further demonstrate that the first intron of both GL1 and GaMYB2 plays a role in patterning trichomes: it acts as an enhancer in trichome and a repressor in nontrichome cells, generating a trichome-specific pattern of MYB gene expression. Disruption of a MYB motif conserved in intron 1 of GL1, WEREWOLF, and GaMYB2 genes affected trichome production. These results suggest that cotton and Arabidopsis use similar transcription factors for regulating trichomes and that GaMYB2 may be a key regulator of cotton fiber development.

Identification of Molecular Markers Linked to the Fertility Restorer Genes for CMS‐D8 in Cotton

The identification of molecular markers closely linked to restorer genes of the cytoplasmic male sterile (CMS) D8 system could facilitate the development of parental lines for hybrid cotton (Gossypium hirsutum L.). Our objective was to develop molecular markers closely linked to the two independent dominant restorer genes, Rf1 from the D2 restorer line transferred from G. harknessii Brandegee (D2 genome) and Rf2 from the D8 restorer line. Bulked segregant analysis was used to identify random amplified polymorphic DNA (RAPD) markers that were linked to the restorer genes. Three testcrosses were used for mapping Rf2 and two for Rf1 relative to the markers. Two RAPD markers, UBC1113000 and UBC188500, were associated with Rf2 in coupling phase. UBC188500 was closely linked to Rf2 with an average genetic distance of 2.9 cM. A survey of cotton species and cultivars revealed that UBC188500 was absent in normal cotton cultivars and most Gossypium spp. However, it was present in the D8 restorer line, G. raimondii Ulbr. (D5), G. trilobum (DC.) Skovst. (D8), and selected wild species from Australia, indicating that Rf2 and the DNA fragment yielding the RAPD marker were both introgressed into the tetraploid cottons from the D8 genome. A new RAPD marker, UBC169700, and a previously identified RAPD marker, UBC6591500, cosegregated with Rf1 in the two populations examined. The three RAPD markers, UBC188500, UC169700, and UBC6591500 were converted into reliable and genome‐specific sequence tagged site (STS) markers on the basis of their sequence information. These markers are restorer‐specific and should be useful in marker‐based selection for developing restorer parental lines and constructing a high‐resolution linkage map containing Rf1 and Rf2

RAPD Analysis of Genetic Diversity in Indian Tetraploid and Diploid Cotton (Gossypium spp)

Random Amplified Polymorphic DNA (RAPD) analysis was used to evaluate genetic diversity among commercial Indian cotton varieties. Fifteen varieties belonging to Gossypium hirsutum L and seven to G. arboreum L were analyzed with 50 random decamer primers using the polymerase chain reaction (PCR). Twenty six of the primers detected polymorphism in all 22 cotton varieties. A total of 371 bands were amplified, 87% of which were polymorphic. Cluster analysis by the unweighted pair group method of arithmetic means (UPGMA) showed that diploids and tetraploids can be divided in two groups at a similarity of 30%. Diploid variety C402W showed the least similarity to all the others in the group. Among tetraploids, closely related varieties Pusa 8-6, 4515 and RS 875 were distinctly different from the rest. The analysis revealed that the intervarietal genetic relationships of several varieties is related to their pedigree. The results also revealed that tetraploids show a much narrower genetic base (similarity range of 65–95%) than the diploids (similarity range 54–88%). The results obtained can be used for the selection of parents to generate a mapping population and begin a breeding programme.

Molecular mapping and characterization of traits controlling fiber quality in cotton

Cotton (Gossypium spp) is the world's leading natural fiber crop. Genetic manipulation continues to play a key role in the improvement of fiber quality properties. By use of DNA-based molecular markers and a polymorphic mapping population derived from an inter specific cross between TM-1 (G. hirsutum) and 3-79 (G. barbadense), thirteen quantitative trait loci (QTLs) controlling fiber quality properties were identified in 3-79, an extra long staple (ELS) cotton. Four QTLs influenced bundle fiber strength, three influenced fiber length, and six influenced fiber fineness. These QTLs were located on different chromosomes or linkage groups and collectively explained 30% to 60%of the total phenotypic variance for each fiber quality property in the F2 population. The effects and modes of action for the individual QTLs were characterized with 3-79 alleles in TM-1 genetic background. The results indicated more recessive than dominant, with much less additive effect in the gene mode. Transgressive segregation was observed for fiber fineness that could be beneficial to improvement of this trait. Molecular markers linked to fiber quality QTLs would be most effective in marker-assisted selection (MAS) of these recessive alleles in cotton breeding programs.

Integrated Management of Cotton Insect Pests in India

In India, cotton ( Gossypium spp) is an important fibre crop. However, on a world basis, productivity is quite low (average of 280 kg/ha). The major reasons for such low yields are drought and attacks of insect pests and plant diseases. Pesticides are therefore widely used to such an extent that >50% of total production cost is attributed to pesticides alone. Aphids, jassids, mites and whiteflies are major pests during the vegetative phase of crop growth, and bollworms during the reproductive and maturity phase. Various control measures, individually or in combination, are adopted against these pests but their efficacy, application cost and dangers to the agroecosystem are often unknown or neglected. The concept of integrated pest management (IPM) is discussed in this paper and its large scale application throughout the country has been recommended. The benefits derived from IPM, directly or indirectly, are long-lasting, economical and ecofriendly.

Altered Amino Acid Metabolism in Root-Knot Nematode Inoculated Cotton Plants

The root-knot nematode (RKN), Meloidogyne incognita (Kofoid and White) Chitwood, is a sedentary endoparasite that retards growth and development of cotton, Gossypium spp. L., by attacking the root ...

Kodiak � --a successful biological-control product for suppression of soil-borne plant pathogens of cotton

Cotton (Gossypium spp) has been the first large-scale, agronomic crop in the United States treated with a biological-control agent (BCA) for suppression of seedling diseases and long-term chronic diseases of the rhizosphere. The vast majority of cotton seed planted in the United States is now treated with Bacillus subtilis strain GB03, registered as Kodiak® (Gustafson, Inc, Plano, TX, USA). Responses are typically a mixture of growth promotion (increased root mass) and disease suppression (Rhizoctonia and Fusarium spp). Strain GB03 shows exceptional rhizosphere competence, colonizing the rhizosphere of monocots and dicots. Though the initial success of strain GB03 has been observed in the production of cotton, other crops have shown positive yield responses following bacterization. Since B. subtilis is a spore-forming organism, it is extremely tolerant of environmental stresses, including seed-treatment pesticides, soil and seed pH, cultivar effects, edaphic factors and long-term storage. More importantly, it is readily produced with current fermentation technology. Other BCAs, such as Pseudomonas spp, do not readily adapt to large-scale production methods, and stability is a limiting factor. In order to be successful, scale-up production must provide a product with efficacy equivalent to the laboratory model. A better understanding of how fermentation and other production processes affect the efficacy and rhizosphere competence of biocontrol organisms is now required by the industry. Processes have to be carefully optimized for both maximum production and maximum efficacy. A strong collaboration and understanding between the agricultural industry and industrial microbiologists are required to continue the advance of new biologicals such as Kodiak®.

Registration of Fifteen Doubled Haploid Lines of Cotton, Gossypium spp. Germplasm

Registration of Fifteen Doubled Haploid Lines of Cotton, <i>Gossypium</i> spp. Germplasm

Effect of Pink Bollworm on Agronomic Properties of Resistant and Susceptible Cotton1

Little is known about the differential effects of the attack of pink boilworm (PBW), Pectinophora gossypiella (Saunders), on agronomic properties of resistant and susceptible cottons, Gossypium spp. The major objective of this study was to determine and compare those effects in a susceptible cultivar and a resistant breeding stock of upland cotton, G. hirsutum L., and a susceptible cultivar of Pima cotton, G. barbadense L. Other objectives were to compare an x‐ray method with a visual boll‐grading method of determining damage done by the insect, and to study the relationship of seed damage with selected agronomic properties. The three cottons were grown for two seasons in untreated field plots and in plots treated for PBW control Seed cotton was harvested weekly as boils opened, seed samples were x‐rayed to determine seed damage, and agronomic properties were measured. At the end of the season, all bolls were removed from five plants/plot and boils were graded into damage classes. Pink bollworm mainly damaged rather than destroyed seed. Damaged bolls did not abscise but remained on the plant. The Pima entry, ‘Pima S‐5’ had more dry, unharvestable bolls than the two upland entries, ‘Deltapine 61’ and AET‐5. Damage was higher in unsprayed than in sprayed plots. The resistant AET‐5 had less seed damage and fewer damaged bolls than the other two entries, and its agronomic properties were less affected by PBW attack. The x‐ray method failed to integrate data from unharvestable bolls, and the graded‐boll method failed to quantify the amounts of damage in the damaged‐boll category. The percentages of variation in decreases in agronomic properties, attributable to increases in seed damage, were higher in unsprayed than in sprayed plots, but also differed among the three cottons. Thus, direct comparison of the effects of PBW on agronomic properties among cottons in unsprayed plots could be misleading because these effects would be superimposed on different natural patterns of decrease in those properties as the season progressed.

Mutants of Gossypium hirsutum: Effect on Pink Bollworm in Arizona12

Several mutants in upland cotton, Gossypium hirsutum L., sustained less seed damage from pink bollworm (PBW), Pectinophora gossypiella (Saunders), than the check cultivars ‘Deltapine 16’, ‘Deltapine 61’, ‘Stoneville 7A’, and ‘Stoneville 213’. These mutants were as follows: glabrous, early-maturing, high-terpenoid (gossypol and related compounds), Okra-leaf and Super Okra-leaf. Earlier studies had shown that glabrous, nectariless, glabrous-nectariless, and highly pubescent mutants, and an upland cotton of complex background (AET-5), had sustained less seed damage than the check cultivars. Cottons having as much as or more seed damage than checks were Red plant, late-maturing, glandless, and frego-bract, and also strains carrying exotic cytoplasms from 6 other Gossypium spp. Practically all the cottons tested that showed resistance to PBW were earlier maturing and yielded less lint than the check cultivars. Exceptions were: ‘Westburn M’, slightly earlier, with significantly lower seed damage, and with a slightly lower lint yield the 1st season but a significantly higher yield the 2nd season; ‘DES 56’, significantly earlier, with slightly lower seed damage, and with a comparable lint yield the 1st season, and a significantly higher lint yield the 2nd season; and Stoneville 7A Okra-leaf, significantly earlier, with significantly less seed damage, and with slightly lower lint yields. No single character reduced seed damage sufficiently to be adequate for PBW control.