N), contributing to concerns on reproducibility. What is the minimum N to identify the most plausible data pattern using regressions? Statistical power analysis is often used to answer that question, but it has its own problems and logically should follow model selection to first identify the most plausible model. Here we make null, simple linear and quadratic data with different variances and effect sizes. We then sample and use information theoretic model selection to evaluate minimum N for regression models. We also evaluate the use of coefficient of determination (R2) for this purpose; it is widely used but not recommended. With very low variance, both false positives and false negatives occurred at N < 8, but data shape was always clearly identified at N ≥ 8. With high variance, accurate inference was stable at N ≥ 25. Those outcomes were consistent at different effect sizes. Akaike Information Criterion weights (AICc wi) were essential to clearly identify patterns ; R2 or adjusted R2 values were not useful. We conclude that a minimum N = 8 is informative given very little variance, but minimum N ≥ 25 is required for more variance. Alternative models are better compared using information theory indices such as AIC but not R2 or adjusted R2. Insufficient N and R2-based model selection apparently contribute to confusion and low reproducibility in various disciplines. To avoid those problems, we recommend that research based on regressions or meta-regressions use N ≥ 25.Regressions and meta-regressions are widely used to estimate patterns and effect sizes in various disciplines. However, many biological and medical analyses use relatively low sample size ( Limbo (noun): (1) A place or state of neglect, oblivion, or uncertainty; (2) A dance or contest that involves bending over backwards to pass under a low horizontal barN) and by applying increasingly sophisticated analytical techniques. But more samples require more effort, cost, and bodily risk . Researchers should then also find how low they can go in N, as in the second limbo definition above. To bend over backwards in that limbo dance is difficult, as is the process to clearly identify a minimum N needed for a study. In an era of big data, this may seem to be a former problem. In fact, it remains vital because multiple disciplines use data that are hard to acquire and/or aggregated. For example, it is difficult to collect data on species diversity among multiple islands with different areas. A similar problem occurs where data are aggregated, as in meta-analyses, systematic or quantitative reviews, and meta-regressions to evaluate general patterns across multiple studies . ,3,4. N) N = 15 (above) represents the fixed effects [N to characterize random effects than simpler models evaluated here. We return to mixed-effects models below, but results obtained here should set a lower limit for regressions and meta-regressions alike.Advanced regression methods may also apply to both scenarios. Similar to mixed-effects regressions that represent fixed and random effects, recent meta-regression methods can include proxies for variation among individuals as random effects in mixed-effects models, where the example  effects ,7. MixedN.Sample sizes tend to be relatively small in biological and medical disciplines . For exaN is that inconclusive or contradictory results are more likely, especially given substantial variation [N has been discussed as one part of a larger reproducibility problem, where recommended solutions include registered studies, conflict of interest statements, and publication of data [N is rarely recommended. At least one journal now requires a minimum N = 5 per group for statistical analyses [N = 10–20 per predictor [N = 30–45 if studying gradients [p): N > 50 + p [N ~ 50 * p [N > 50 + 8 * p [N clearly varies, if a value is provided.The problem with small ariation ,11,12. T of data ,15,16,17analyses . Ecologiredictor  or N = 3> 50 + p ; N ~ 50 ~ 50 * p , or N >  + 8 * p . SuggestN because that work has been based for decades on statistical power, which is the chance that a null hypothesis can be correctly rejected [post hoc hypothesis formation, data dredging, and p-hacking [It has been difficult to obtain consistent, clear guidelines for minimum rejected . Power arejected ,27,28,29rejected ,27. Also-hacking ,31,32. F-hacking . Instead-hacking .N also suffers from a fundamental cart-before-the-horse problem. Consider an experiment to evaluate three alternative hypotheses that predict either a sloped linear model, a humped-shape curve, or null data pattern. A typical and straightforward power analysis for regressions  applies package , but con package ,36,37,38N because there are four interacting parts. A researcher solves for N by assuming the remaining three: a desired power level ; effect size ; and significance level  [Operationally, power analysis is a challenging way to estimate minimum  = 0.05) ,40,41,42 = 0.05) . Bayesia = 0.05) ,45 but h2) or the adjusted R2 that accounts for differences in model complexity. That practice is ill-suited to select among alternative models, especially if models differ in the number of parameters and if regression assumptions are violated [2 can then be used to “criticize” the fit of a selected model [A separate operational problem arises because alternative models are often selected using a coefficient of determination  and random scatter (R2 = 0) there lies a practically infinite set of combinations for the factors affecting power of regressions . We concentrate on four corners of a variance X effect size grid, where the four choices represent low & high combinations of effect size and variance. Having established those approximate margins for a data shape , we repeatedly evaluate regressions with different N.This work has boundaries. Between the limits of a perfectly fitted model . Within that class, the 1st-order or simple linear model (y = α + βx + ε) is often dubbed the linear model. To avoid confusion between the class and its models, we hereafter refer to the “straight-line” model in the linear class. A 2nd-order polynomial is also a linear model and often dubbed the quadratic equation (y = α + βx + γx2 + ε), which is the most parsimonious first step to evaluate curvature beyond a straight-line model [We restrict work here to 1ne model .post hoc trend-fitting . We also set aside nonlinear models for two reasons. Curved data are often transformed to fit straight-line models  but results should apply (discussed below). We also do not include higher-order polynomials because we know of no major hypotheses that predict them. Instead, fitting higher-order polynomials seems to be more often used in s e.g., ,49,50), ,50, postFinally, we use the Akaike Information Criterion (AIC) to select the most plausible model among the analyzed set. A conceptual continuum exists between hypothesis refutation and confirmation, where a Bayesian version (BIC) is targeted to confirm a true hypothesis , and AIC is aimed at exploratory model selection in a frequentist context . The BICN needed for accurate inference ? We expected that insufficient N would interfere with accurate inference , but that some threshold N may exist, where accurate and consistent inference is always reached). This was best evaluated for data sets with low variance.What is the minimum N would be increased by variance.How does variance alter the answer to question 1? We expected that general patterns from above would hold true, but that minimum wi vs. adjusted R2 alter interpretations above? Based on statistical texts cited above, we expected adjusted R2 values to less accurately identify the correct data class than AICc wi values. This was evaluated by comparing AICc wi and adjusted R2 values in plots.How does the use of AICc 2 and a weakly significant coefficient). Alternatively, low variance made an obvious pattern closely adhering to a model. Because these extremes are approximate, we treated outcomes as approximate and made cautious recommendations. We anticipated that data sets with high variance would be most interesting because they most resemble empirical data collected in complex scenarios.Three classes of data , straight-line, and quadratic) defined above were generated with N = 50, simply by prescribing a model and then adding variance. Thus, data sets simply represented scatter plots with little or much variation added. We chose N = 50 to exceed most data sets of interest here . Model pα). Four straight-line data sets were created with low or high slopes (β) and low or high variance in β. Eight quadratic data sets were created because the second coefficient (γ) was added to the straight-line process and also evaluated for its own effect size X variance combinations. In total, 14 data sets then evaluated for each of null, straight-line, and quadratic models. Coefficients and variance  used to make data sets are listed in Two null  data sets were created to represent low and high variance in the intercept term (N = 4 was taken from a full data set (N = 50). That minimum N = 4 was set by the minimum degrees of freedom for a quadratic model because all comparisons included the null, straight-line, and quadratic models. The sample was evaluated for each of the 3 models, and models were compared by weights (wi) for corrected AIC (AICc) values. A wi value is the preferred criterion for model selection because it scales from 0–1 to indicate the probability that a model is most plausible. Corrected AIC values adjust for smaller N, and approach uncorrected AIC values at N ~ 40 [wi value and an adjusted R2 value for each model was recorded. That process was repeated 99 more times at that N , so that mean wi and adjusted R2 values  could be computed for the 100 replicates at that N. That whole process was then repeated from N = 5 to N = 50 for a total of 4,700 AIC comparisons per data set . Mean wi and adjusted R2 values  were plotted as functions of N for each combination of a data set and model. In addition, approximate N where wi values for one model surpass those of another model were evaluated graphically.Analyses were conducted as follows  for null data with N = 4 because a quadratic model was always most plausible, regardless of variance in the data . Interestingly, a null model was implausible  or null (N = 5 to ~ 25) pattern. Adjusted R2 values for straight-line and quadratic models were similar at all N > 5 and would not help identify the matching model  and low and high σ, so the σ X effect size grid was effectively a cube. We organized results for high σ outcomes . In those cases, the quadratic model most plausibly represented quadratic data only at N > 20 . Adjusted R2 values only helped to identify the quadratic when γ was high, which makes sense because that term is what differs between straight-line and quadratic models. In other words, given a weak quadratic effect (low γ), adjusted R2 could not accurately identify the data shape, though AIC wi values could (given sufficient N).Data generated as a quadratic function had low and high effect size for two coefficients . But with high variance, minimum N is pushed to N ≈ 25 to clearly match a model to the data pattern. That answer represents the upper edge of the variance X effect size grid analyzed here, and represents a cautious recommendation for many observational studies that rely on regressions, including meta-regressions. The expectation that effect size would alter the answer was inherited from power analyses, which focus on statistical significance of a slope coefficient. That did not translate to the AIC-based model selection used here, where the answer did not depend on statistical significance.The answer depends on variance, but importantly, not on effect size or the model (straight-line or quadratic). Where one must evaluate support for alternative hypotheses predicting null, straight-line, or quadratic regression models, we recommend a minimum wi to adjusted R2 for the interpretations above. Results here confirm existing recommendations that R2-based values do not clearly identify the data shape [2 values among alternative models needs to be re-evaluated. Going forward, we echo Bolker’s [2 or adjusted R2 to “criticize” goodness-of-fit for the most plausible model.We also compared AICc ta shape ,42,46 thN ≥ 8 with very little variance, but N ≥ 25 with any more variance) assume samples are not clustered at one end of a data cloud, and regression assumptions are met. Models here did not include covariates, which add a degree of freedom per covariate but can help “explain” variation in empirical data and yield better coefficient estimates. Relatively weak  evidence for ideas at low N might be “rescued” with important covariates, especially if predictors are scaled to standardize varying units. For example, a regression to predict risk of a disease as a function of body weight should include important covariates , which may affect disease risk more than body weight. Careful planning and foreknowledge of the study system may help ensure that the most fruitful covariates are measured [N >> 25 to adequately represent data patterns. These considerations emphasize that skepticism should be applied to mixed-effects regressions and meta-regressions with N ≤ 25 and without well-described variance and correlation structures.The main recommendations above  was listed. Data and citations for (a) and (b) are listed in medecontallies.xls.The only criterion for retention of a paper in data was that sample size ((DOC)Click here for additional data file.S2 Appendix(DOCX)Click here for additional data file.S1 Tableσ) of residuals. Coefficients  designate data shape, where α is the intercept, β is a multiplier for x (as in y = α + β x), and γ is a multiplier for the quadratic term (… + γ x2).Variance was set as standard deviation ((DOCX)Click here for additional data file.S1 Data(XLS)Click here for additional data file.


N4-like phage group, from 33 members in 2015 to 115 N4-like viruses in 2020. Using new technologies and methods for classification, the Bacterial and Archaeal Viruses Subcommittee of the International Committee on Taxonomy of Viruses (ICTV) has moved the classification and taxonomy of bacterial viruses from mere morphological approaches to genomic and proteomic methods. The analysis of 115 N4-like genomes resulted in a huge reassessment of this group and the proposal of a new family “Schitoviridae”, including eight subfamilies and numerous new genera.Escherichia phage N4 was isolated in 1966 in Italy and has remained a genomic orphan for a long time. It encodes an extremely large virion-associated RNA polymerase unique for bacterial viruses that became characteristic for this group. In recent years, due to new and relatively inexpensive sequencing techniques the number of publicly available phage genome sequences expanded rapidly. This revealed new members of the  N4 genome and its replication revealed unique characteristics. Apart from a phenomenon called lysis-inhibition [Escherichia phage N4 is a virulent phage that was originally isolated by Gian Carlo Schito from sewers in Genoa  in 1966 . Analysihibition  that cauhibition . N4 genoEscherichia virus N4 in 2015, it has persisted as a genomic orphan. At the time of writing , its genus is now called Enquatrovirus and consists of only one species, representing four isolates. From a taxonomic perspective, phage N4 has a long history; from the first proposal in 1987 to establish a species Escherichia phage N4 [Tubulavirales), ten new families, 22 new sub-families, 424 new genera and 964 new species, which still represent only a fraction of the genomes currently available. However, it has to be taken into account that ICTV does not classify viral strains or variants, i.e., those phage isolates with genomes that show ≥95% DNA sequence identity with an exemplar isolate of a species [Baltimorevirus, Enquatrovirus, Gamaleyavirus, Ithacavirus, Johnsonvirus, Jwalphavirus, Litunavirus, Luzseptimavirus, Mukerjeevirus and Shizishanvirus). This study provides further insight into the diversity and taxonomy of N4-like viruses using different approaches like genome-based phylogeny for deeper classification.Since 2015, following a comprehensive analysis of at that time 33 N4-like genomes , the num species . With rePodovirus morphologyGenome size of 59–80 kbLinear genome with defined ends Presence of three RNA polymerase genes, including a large (~3500 aa) virion-associated RNA polymerase (vRNAP)We downloaded 115 genomes from the NCBI databases (INSDC) ,14 relatRoseobacter [Achromobacter [Pseudomonas [So far, only N4-like phages infectious for Gram-negative host bacteria belonging to the α-proteobacteria such as eobacter , β-protemobacter  and γ-prudomonas  from difudomonas  to 85 nmudomonas  with shohttps://www.genome.jp/viptree/; [Podoviridae to justify the current membership.To analyze the similarities or relationship, respectively, between N4-like viruses and other podoviruses, we used ViPTree  which iiptree/; . The resPanproteome analysis revealed that seventeen N4-like proteins are conserved in this proposed family of phages: RNAP 1 (EPNV4_gp15), RNAP 2 (EPNV4_gp16), vRNAP (EPNV4_gp50), EPNV4_gp24, EPNV4_gp25, DNA polymerase (EPNV4_gp39), EPNV4_gp42, DNA primase (EPNV4_gp43), EPNV4_gp44, EPNV4_gp52, EPNV4_gp54, major capsid protein (EPNV4_gp56), tape measure protein (EPNV4_gp57), portal protein (EPNV4_gp59), EPNV4_gp67, large terminase subunit (EPNV4_gp68), and EPNV4_gp69 .Schitoviridae” in honor of Gian Carlo Schito who isolated Escherichia phage N4, the first isolated species of this group.Based on the different analyses, we propose a new family “Results of an all-by-all pairwise nucleotide identity analysis or intergenomic similarity analysis with VIRIDIC gave strong evidence for the proposal of eight new subfamilies and 30 genera which were confirmed by phylogenetic analysis of the terminase large subunit and vRNA polymerase genes, i.e., all proposed taxa are monophyletic in these marker gene trees . In lineMigulavirinae” consists of two previously ratified genera (eight species), Litunavirus and Luzseptimavirus, representing phages with Pseudomonas aeruginosa as their host. The subfamily “Enquatrovirinae” contains three genera (14 species), Gamaleyavirus, Enquatrovirus and the newly proposed genus “Kaypoctavirus” and includes phages infecting members of the Enterobacteriaceae like E. coli, Shigella boydii or Klebsiella pneumoniae. N4-like viruses infecting Achromobacter xylosoxidans were grouped into four genera (eight species) in the proposed subfamily “Rothmandenesvirinae” in honour of Lucia Rothman-Denes, who worked on N4 and its RNA polymerases. The subfamily “Erskinevirinae” was named after John M. Erskine who in the early 1970s was one of the first people to isolate phages against Erwinia. It consists of two genera, “Yonginvirus” and Johnsonvirus, with three species and represents most of the N4-like viruses against Erwinia. The relatively large subfamily “Rhodovirinae” consists of seven genera, “Aorunvirus”, “Raunefjordvirus”, “Aoquinvirus”, “Pomeroyivirus”, “Sanyabayvirus”, “Plymouthvirus” and Baltimorevirus, and contains aquatic viruses infecting members of the Rhodobacteraceae. Two further proposed subfamilies (five genera), “Fuhrmanvirinae” (named after American oceanographer and marine biologist Jed Alan Fuhrman) and “Pontosvirinae”, mainly consist of phages against marine Vibrio species. The “Humphriesvirinae” subfamily in honour of James C. Humphries (1914–1992), who was the first to isolate a Klebsiella phage, comprises five genera with viruses infecting different genera of the Enterobacteriaceae like Escherichia, Klebsiella or Salmonella.The proposed subfamily “Herelleviridae from the subfamily Spounavirinae and related phages [Myoviridae, Siphoviridae and Podoviridae. Following from that example, we used some of the methods trialed and tested for the creation of a new family  and the delineation of its internal structure  to define the new family “Schitoviridae” of N4-like phages, to be removed from the family Podoviridae.The constantly rising number of sequences provides the scientific community with valuable data to work with to answer various scientific questions. However, the taxonomic classification of phage genomes has not kept pace which has led to the presence of large numbers of unclassified genomes in the INSDC. While the ICTV makes a huge effort to manage this problem and improvements have been made on the genus and subfamily level , it is d phages , providehttp://millardlab.org/) [To create the gene-sharing network, a total of 16,050 phage contigs (ab.org/)  were reaab.org/)  and the To identify conserved proteins present in bacteriophages comprising the proposed family, all genomes were reannotated using Prokka v1.14.5  and predFor panproteome construction with PIRATE the settings used were 30 and 35% identity threshold, cdhit lowest percentage id of 95 and e-value for BLAST hit filtering of 1E-5. For Proteinortho, the search options were adjusted so that the minimum percent identity and coverage of the best blast hits were 30% and 50%, respectively. All other parameters were left as default.https://coregenes.ngrok.io/) was used with the OrthoMCL option with E-value of 1e-5. CoreGenes5.0 uses the GET_HOMOLOGUES package to implement the ortholog clustering [The CoreGenes5.0 webserver  [The Bacterial and Archaeal Viruses Subcommittee uses nucleotide based sequence similarities as a crucial feature for taxonomic classification of viruses at the ranks of species and genus. We therefore employed the online tool VIRIDIC   for the


NRT2 and three putative NRT3 genes were identified using bioinformatics methods. All the HvNRT2/3 genes were located on chromosomes 3H, 5H, 6H or 7H. Remarkably, the presence of tandem repeats indicated that duplication events contributed to the expansion of the NRT2 gene family in barley. In addition, the HvNRT2/3 genes displayed various expression patterns at selected developmental stages and were induced in the roots by both low and high nitrogen levels. Furthermore, the overexpression of HvNRT2.1 improved the yield related traits in Arabidopsis. Taken together, the data generated in the present study will be useful for genome-wide analyses to determine the precise role of the HvNRT2/3 genes during barley development, with the ultimate goal of improving NUE and crop production.Nitrogen use efficiency (NUE) is the efficiency with which plants acquire and use nitrogen. Plants have high-affinity nitrate transport systems, which involve certain nitrate transporter (NRT) genes. However, limited data are available on the contribution of the NRT2/3 gene family in barley nitrate transport. In the present study, ten putative  Nitrogen, as a function of nutrient availability, plays an essential role in controlling plant growth and development . Limited3- from the soil to the plant and within the plant itself. To date, two kinetically distinct nitrate uptake systems have been identified by physiological and molecular studies in plant roots, including the low-affinity transport system (LATS), which is encoded by the NITRATE TRANSPORTER 1/PEPTIDE TRANSPORTER (NRT1/PTR) family (NPF), and the high-affinity transport system (HATS), which is encoded by the nitrate transporter 2 (NRT2) family Reviewers' comments:Reviewer's Responses to QuestionsComments to the Author1. Is the manuscript technically sound, and do the data support the conclusions?The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented. Reviewer #1: YesReviewer #2: Yes**********2. Has the statistical analysis been performed appropriately and rigorously? Reviewer #1: YesReviewer #2: Yes**********3. Have the authors made all data underlying the findings in their manuscript fully available?PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.The Reviewer #1: YesReviewer #2: Yes**********4. Is the manuscript presented in an intelligible fashion and written in standard English?PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.Reviewer #1: YesReviewer #2: No**********5. Review Comments to the AuthorPlease use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. Reviewer #1: This manuscript described a genome-wide characterization of high-affinity nitrate transporter NRT2/3 family members by taking advantage of the publically-released barley reference sequence. The gene duplication, transcriptional pattern and chromosomal assignment as well as the phylogenetic analysis were further represented. One NRT2-type gene HvNRT2.1 was over-expressing in transgenic Arabidopsis plants that showed the increases on the parameters of grains, as well as the accumulation of nitrate and total nitrogen uptake in plant tissues.1, A short introduction referring to the current understanding of individual HvNRT2/3 gene in cultivated barley is suggested.2, Fig. 7 showing the increases of nitrate and total nitrogen content should be described in Results. This might be important in order to support the story of this study.3, Use Arabidopsis thaliana or A. thaliana. Refer the variety “Col-0” in Materials.4, Fig. 4, statistical analysis is recommended (e.g. Tukey’s HSD).5, The language editing is suggested.Reviewer #2: The authors mapped the NRT2/3 gene family in the barley genome and analysed their expression patterns under N treatments. Besides, one member from the family HvNRT2.1 was exotically expressed in Arabidopsis for function characterisation. The work provides new insights into the barley NUE research and I have the following concerns before it could be accepted for publishing.Major issues1. The English language needs professional proofreading as there are massive typos and grammar errors in the main document.2. Why the HvNRT2.1 but not other NRT transporters were specifically investigated in Arabidopsis?3. Line 223, information missing in the sentence4. Line 256, peaks at ??5. Line 261, how much similar are they (% identity)?6. Line 264, was Arabidopsis ecotype Col-0 used? Should not be in italic.7. Line 267, how much increments?8. Line 278, two NRT3 from which species?9. Line 282, what does “components” mean?10. Line 307-309, please specify the details in the changes.11. Line 313-318, state one or two functions in rice so that it can be more evidently related to barley.12. Line 335, the statement has been repeated a couple of times in the ms.13. Line 338, increase of biomass and plant height in Arabidopsis or ?? If so could be rephrased as “In the present study, overexpression of HvNRT2.1 led to high nitrate and nitrogen content, increased biomass and plant height and improved the yield-related traits in Arabidopsis indicating that….14. The authors should provide either qualitative or quantitive information regarding the HvNRT2.1 transcript levels in transgenic Arabidopsis lines.15. HvNRT2.1 expression in barley responded to different N levels so why not investigate the growth performance of transgenic Arabidopsis lines under N treatments?Minor issues1. Line 20, rectify the grammar issue2. Line 23, in barley “nitrate transport”3. Line 25, “chromosomes”4. Line 29, replace “notably” with “furthermore”5. Line 55, should be “they are” but not “it is”6. Line 61, under low N condition?7. Line 86-89, confusing with the experimental layout. Indeed how many plants were sampled and used for RNA extraction?8. Line 137, “0.5 cm” would be better.9. Line 224, according “to”10. Line 228, “clustered”11. Line 320, “encode”**********what does this mean?). If published, this will include your full peer review and any attached files.6. PLOS authors have the option to publish the peer review history of their article  digital diagnostic tool,  10 Mar 2020Responses to reviewer 1:Comment 1: A short introduction referring to the current understanding of individual HvNRT2/3 gene in cultivated barley is suggested.Response 1: According to the reviewer’s suggestion, we have added the sentence in the revised manuscript. In barley, four HvNRT2 (HvNRT2.1-2.4) and three HvNRT3 (HvNAR2.1-2.3) genes were isolated from the roots. The expression pattern of the HvNRT2 genes was also characterized under various nitrogen sources, and a highly specific interaction is suggested between HvNRT2.1 and HvNAR2.3 by using 15N-enriched nitrate uptake into Xenopus oocytes. However, until now, none of the HvNRT2/3 gene family have been described at the barley genome level and their functions are still unclear. Comment 2: Fig. 7 showing the increases of nitrate and total nitrogen content should be described in Results. This might be important in order to support the story of this study.Response 2: We agree with this suggestion and have added the result in the “Morphological characterization of the HvNRT2.1 gene overexpression plants” paragraph as follows: In addition, seeds of overexpression plant accumulated significantly more nitrate and nitrogen, and increased by 47.2% and 41.4% compared with wide type in mature plants .Comment 3: Use Arabidopsis thaliana or A. thaliana. Refer the variety “Col-0” in Materials.Response 3: Thank the reviewer for this content. The Arabidopsis thaliana Columbia-0 (Col-0) ecotype was used as in materials. We have revised this in the new manuscript Comment 4: Fig. 4, statistical analysis is recommended (e.g. Tukey’s HSD).Response: Thank the reviewer’s suggestion, statistical analysis of the differences between wide type (Col-0) and transgenic plants was performed by using Student’s t-test. We have added the result of Student’s t-test in Fig 6 and Fig 7.Comment 5: The language editing is suggested.Response: The statements have been corrected. We will be happy to edit the MS further base on helpful comments from reviewers.Responses to reviewer 2:Major issuesComment 1: The English language needs professional proofreading as there are massive typos and grammar errors in the main document.Response 1: The statements have been corrected. We really hope the flow and language level have been improved.Comment 2: Why the HvNRT2.1 but not other NRT transporters were specifically investigated in Arabidopsis?Response 2: HvNRT2.1 gene was the first to respond to low nitrogen with peaks at 1 h, which has high homology to OsNRT2.3 (a gene derived from rice which has been contribute to improvement grain yield and NUE by 40%). Therefore, HvNRT2.1 was specifically investigated in Arabidopsis.Comment 3: Line 223, information missing in the sentence.Response 3: Thank the reviewer for this content. The sentence was as follows: A total of 18 NRT2 genes belonged to cluster Ⅰ, including five NRT2 genes derived from dicotyledonous Arabidopsis and 13 NRT2 genes from monocotyledonous plants . AtNRT2.5 and AtNRT2.7 represented clusters Ⅱ and Ⅲ, containing four and three genes, according to the phylogenetic tree, respectively . We have revised this in the new manuscript.Comment 4: Line 256, peaks at ??Response 4: Thank the reviewer’s for this content. We have revised this as follows: The expression of HvNRT3.3 displayed two peaks at 3 h and 24 h and responded more quickly to high rather than low nitrogen conditions.Comment 5. Line 261, how much similar are they (% identity)?Response 5: According to the reviewer’s suggestion. We analyzed the homology identity between HvNRT2.1 and OsNRT2.3. The detail information was as follow: The HvNRT2.1 protein had a similar amino acid length and showed 83.3% identity with OsNRT2.3a, but only 78.4% identity with OsNRT2.3b genes, indicating that HvNRT2.1 plays an important role in long-distance nitrate transport, from the roots to shoots, with low nitrate supply levels in barley. We have added this in the new manuscript (see “Discussion” part).Comment 6: Line 264, was Arabidopsis ecotype Col-0 used? Should not be in italic.Response 6: Thank the reviewer for this content. The Arabidopsis thaliana Columbia-0 (Col-0) ecotype was used as in materials. We have revised this in the new manuscript Comment 7: Line 267, how much increments?Response 7: According to the reviewer’s suggestion, the increments were calculated in the new revised manuscript. The detail information was as follows: 7.9%, 18.5%, and 23.3% increments in the length of siliques, yield per plant and grain number per siliques, respectively, were observed in the transgenic lines compared with Col-0 .Comment 8. Line 278, two NRT3 from which species?Response 8: Two NRT3 have been analyzed from rice, Arabidopsis and maize. Thus, we have revised this sentence in the manuscript as follows: a total of 4, 7, and 4 NRT2 genes have been analyzed in rice, Arabidopsis, and maize, respectively, as well as two NRT3 genes.Comment 9. Line 282, what does “components” mean?Response 9: For HATS activity in plants, NRT2/NRT3 is a two-component high-affinity nitrate transport system, each of them is part of high-affinity nitrate transport system and interact at the protein level.Comment 10: Line 307-309, please specify the details in the changes.Response 10: According to the reviewer’s suggestion, we have added the results in the “HvNRT2/3 gene expression patterns at different developmental stages” and “HvNRT2/3 gene expression analysis under low and high nitrogen levels” parts. Comment 11: Line 313-318, state one or two functions in rice so that it can be more evidently related to barley. Response 11: According to the reviewer’s suggestion, we have added the discussion in the revised manuscript as follows: In rice, a decreased expression of OsNRT2.3a is related to the accumulation of significantly higher levels of nitrate and total nitrogen in the root and lower levels in the shoot. However, enhancing the expression of OsNRT2.3b improves the growth, yield, and NUE in rice.Comment 12. Line 335, the statement has been repeated a couple of times in the ms.Response 12: Thank the reviewer for this content, we have deleted the repeat sentence about this in the revised manuscript.Comment 13. Line 338, increase of biomass and plant height in Arabidopsis or ?? If so could be rephrased as “In the present study, overexpression of HvNRT2.1 led to high nitrate and nitrogen content, increased biomass and plant height and improved the yield-related traits in Arabidopsis indicating that….Response 13: Thank the reviewer for this content. We check the result, and adjust the discussion in the new revised manuscript. The detail information as follows: In the present study, the overexpression of HvNRT2.1 led to high nitrate and nitrogen contents and improved the yield-related traits of Arabidopsis. However, both a biomass and plant height increase were not observed in the overexpression plants, indicating that the HvNRT2.1 gene plays a specific role in nitrate and total nitrogen accumulation in plants.Comment 14. The authors should provide either qualitative or quantitive information regarding the HvNRT2.1 transcript level in transgenic Arabidopsis lines.Response 14: According to the reviewer’s suggestion. We have added this information in S3 Fig in the reviewed manuscript . The detail information as follows: In the transgenic lines, HvNRT2.1 was introduced into the genomic DNA and was expressed at the transcription level in three independent overexpression plantsComment 15: HvNRT2.1 expression in barley responded to different N levels so why not investigate the growth performance of transgenic Arabidopsis lines under N treatments?Response 15: We agree with this suggestion. We have plant wide type and transgenic Arabidopsis lines on the MS (without NH4NO3) with different KNO3 level, unfortunately, all plants cannot survive. Thus, the growth performance of wide type and transgenic lines was observed on the normal conditions.Comment Minor issuesComment 1: Line 20, rectify the grammar issueResponse 1: Thank the reviewer for this comment. We have corrected the sentence as follow: Nitrogen use efficiency (NUE) is the efficiency with which plants acquire and use nitrogen.Comment 2. Line 23, in barley “nitrate transport”Response 2: Thank the reviewer for this content. We have added the word “nitrate transport” in the new manuscript.Comment 3: Line 25, “chromosomes”Response 3: Thank the reviewer for this comment. We have replaced the “chromosome” with “chromosomes”.Comment 4: Line 29, replace “notably” with “furthermore”Response 4: Thank the reviewer for this comment. We have replaced the “notably” with “furthermore”.Comment 5: Line 55, should be “they are” but not “it is”Response 5: Thank the reviewer for this comment. We have replaced the “it is” with “they are”.Comment 6: Line 61, under low N condition?Response 6: Nitrate supply was 0.5 mM in the reference , which was consider as low nitrate supply.Comment 7: Line 86-89, confusing with the experimental layout. Indeed, how many plants were sampled and used for RNA extraction?Response 7: According to the reviewer’s suggestion. We have revised this sentence as follow: At 0 h, 1 h, 3 h, 6 h, 12 h, 24 h, 48 h and 72 h after treatment, total roots were harvested from ten plants and immediately frozen in liquid nitrogen for RNA extraction with three biological replicates at each time point.Comment 8: Line 137, “0.5 cm” would be better.Response 8: Thank the reviewer for this comment. We have replaced the “mm” with “cm”.Comment 9: Line 224, according “to”Response 9: Thank the reviewer for this comment. We have added this word in the revised manuscript.Comment 10. Line 228, “clustered”Response 10: Thank the reviewer for this comment. We have a replaced the “cluster” with “clustered”Comment 11: Line 320, “encode”Response 11: Thank the reviewer for this comment. The word “encoding” has been replace by “encode”.AttachmentResponse to reviewers.docxSubmitted filename: Click here for additional data file. 3 Apr 2020PONE-D-19-33678R1Characterization of the Nitrate Transporter gene family and functional identification of HvNRT2.1 in barley (Hordeum vulgare L.)PLOS ONEDear Dr. Xu,Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.We would appreciate receiving your revised manuscript by May 18 2020 11:59PM. When you are ready to submit your revision, log on to If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter.http://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocolsTo enhance the reproducibility of your results, we recommend that if applicable you deposit your laboratory protocols in protocols.io, where a protocol can be assigned its own identifier (DOI) such that it can be cited independently in the future. 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If eligible, we will contact you to opt in or out.We look forward to receiving your revised manuscript.Kind regards,Guoping ZhangAcademic EditorPLOS ONE[Note: HTML markup is below. Please do not edit.]Reviewers' comments:Reviewer's Responses to QuestionsComments to the Author1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.Reviewer #1: All comments have been addressedReviewer #2: (No Response)**********2. Is the manuscript technically sound, and do the data support the conclusions?The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented. Reviewer #1: YesReviewer #2: Yes**********3. Has the statistical analysis been performed appropriately and rigorously? Reviewer #1: YesReviewer #2: Yes**********4. Have the authors made all data underlying the findings in their manuscript fully available?PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.The Reviewer #1: YesReviewer #2: Yes**********5. Is the manuscript presented in an intelligible fashion and written in standard English?PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.Reviewer #1: YesReviewer #2: Yes**********6. Review Comments to the AuthorPlease use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. Reviewer #1: I appreciated that the authors have addressed to all of my concerns. I have no further comments for this manuscript.Reviewer #2: The revised manuscript has been improved and I have the following comments in regard to typos or grammar errors. In addition, I suggest the authors adding the gene accession numbers or gene IDs such as HORVU.. as the last section of Methods, for a better understanding and traceback with other researches.Line 37: Replace “serious” with “severe/intense”Line 48: Replace “shows” with “functions as”Line 53: Can be rephrased as “There is a lesser number of NRT2 genes than NRT1”Line 177: “herbicide treatment”Line 227: Check the 3 distinct clustersLine 230: It has to be cluster II and III?Line 330: Replace “with” with “under”**********what does this mean?). If published, this will include your full peer review and any attached files.7. PLOS authors have the option to publish the peer review history of their article  digital diagnostic tool,  5 Apr 2020Responses to reviewer 2Comment 1: The revised manuscript has been improved and I have the following comments in regard to typos or grammar errors. In addition, I suggest the authors adding the gene accession numbers or gene IDs such as HORVU.. as the last section of Methods, for a better understanding and traceback with other researches.Response 1: Thank the reviewer for this comment. We have listed the gene IDs, chromosome position, coding sequence length, amino acid length, mass and pI in the Table 1 in the revised manuscript.Comment 2: Line 37: Replace “serious” with “severe/intense”Response 2: Thank the reviewer for this comment. We have replaced the “serious” with “severe”.Comment 3: Line 48: Replace “shows” with “functions as”Response 3: Thank the reviewer for this comment. We have replaced the “shows” with “functions as”.Comment 4: Line 53: Can be rephrased as “There is a lesser number of NRT2 genes than NRT1”.Response 4: We agreed with the reviewer’s suggestion, and rephrased as “There is a lesser number of NRT2 genes than NRT1” in the revised manuscript.Comment 5: Line 177: “herbicide treatment”Response 5: We agreed with the reviewer’s suggestion. we have added the word “treatment” after “herbicide”Comment 6: Line 227: Check the 3 distinct clustersResponse 6: Thank the reviewer for this comment. The words“Ⅰ, Ⅱ, and Ⅲ”have not displayed properly in the PDF version. The sentence as follows: According to the phylogenetic tree of the NRT2 and NRT3 proteins in barley, rice, maize, and Arabidopsis, the NRT2 proteins could clearly be divided into three distinct clusters . Comment 7: Line 230: It has to be cluster II and III?Response 7: Thank the reviewer for this comment. The words“Ⅱ, Ⅲ”have not displayed properly in the PDF version. The sentence as follows: AtNRT2.5 and AtNRT2.7 represented clusters Ⅱ and Ⅲ, containing four and three genes, according to the phylogenetic tree, respectively.Comment 8: Line 330: Replace “with” with “under”Response 8: We agreed with the reviewer’s suggestion. We have replaced the “with” with “under”.AttachmentResponse to reviewers.docSubmitted filename: Click here for additional data file. 7 Apr 2020Characterization of the Nitrate Transporter gene family and functional identification of HvNRT2.1 in barley (Hordeum vulgare L.)PONE-D-19-33678R2Dear Dr. Xu,We are pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it complies with all outstanding technical requirements.Within one week, you will receive an e-mail containing information on the amendments required prior to publication. When all required modifications have been addressed, you will receive a formal acceptance letter and your manuscript will proceed to our production department and be scheduled for publication.https://www.editorialmanager.com/pone/, click the "Update My Information" link at the top of the page, and update your user information. If you have any billing related questions, please contact our Author Billing department directly at authorbilling@plos.org.Shortly after the formal acceptance letter is sent, an invoice for payment will follow. To ensure an efficient production and billing process, please log into Editorial Manager at onepress@plos.org.If your institution or institutions have a press office, please notify them about your upcoming paper to enable them to help maximize its impact. If they will be preparing press materials for this manuscript, you must inform our press team as soon as possible and no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact With kind regards,Guoping ZhangAcademic EditorPLOS ONEAdditional Editor Comments :Reviewers' comments: 10 Apr 2020PONE-D-19-33678R2 Characterization of the Nitrate Transporter gene family and functional identification of HvNRT2.1 in barley (Hordeum vulgare L.) Dear Dr. Xu:I am pleased to inform you that your manuscript has been deemed suitable for publication in PLOS ONE. Congratulations! Your manuscript is now with our production department. onepress@plos.org.If your institution or institutions have a press office, please notify them about your upcoming paper at this point, to enable them to help maximize its impact. If they will be preparing press materials for this manuscript, please inform our press team within the next 48 hours. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information please contact plosone@plos.org. For any other questions or concerns, please email Thank you for submitting your work to PLOS ONE.With kind regards,PLOS ONE Editorial Office Staffon behalf ofProf Guoping Zhang Academic EditorPLOS ONE


Functional analysis of longitudinal phenotypic data for five and 10 time points saturates QTL detection power and genomic predictive ability for canopy height in wheat. Genetic studies increasingly rely on high-throughput phenotyping, but the resulting longitudinal data pose analytical challenges. We used canopy height data from an automated field phenotyping platform to compare several approaches to scanning for quantitative trait loci (QTLs) and performing genomic prediction in a wheat recombinant inbred line mapping population based on up to 26 sampled time points (TPs). We detected four persistent QTLs (i.e. expressed for most of the growing season), with both empirical and simulation analyses demonstrating superior statistical power of detecting such QTLs through functional mapping approaches compared with conventional individual TP analyses. In contrast, even very simple individual TP approaches  had superior detection power for transient QTLs (i.e. expressed during very short periods). Using spline-smoothed phenotypic data resulted in improved genomic predictive abilities , while the effect of including significant QTLs in prediction models was relatively minor (<1–4% improvement). Finally, although QTL detection power and predictive ability generally increased with the number of TPs analysed, gains beyond five or 10 TPs chosen based on phenological information had little practical significance. These results will inform the development of an integrated, semi-automated analytical pipeline, which will be more broadly applicable to similar data sets in wheat and other crops. In recent years, field-based high-throughput plant phenotyping (HTPP) tools have been used extensively in crop trials, aiming to reduce or eliminate manual measurements, increase the amount and quality of data for temporally dynamic phenotypes, and, ultimately, translate ‘big data’ collected using various sensors into knowledge  in mapping families  and genoPrevious studies of wheat plant height, an important agronomic trait, have identified several dynamic QTLs  comprising 197 lines derived from crossing the Chinese Spring (CS) and Paragon (PAR) genotypes was used in this study (A recombinant inbred line (RIL) population . Subsequently, an average canopy height was estimated for each sub-region of the RIL and then averaged together to obtain the plot canopy height (R2) between manual and automatic measurements was 0.59, 0.78, 0.85, and 0.81 for 70, 155, 208, and 233 DAS, respectively   . Thus, wWe used the ASReml package  variance–covariance structure (VCOV) was used for the genotype effects , with covariance matrix σ 2g=Var(g)ΣT + Ψ , A was the numerator relationship matrix (we used the I identity matrix), ε=ξ+η, where ξ and η refer to the spatially correlated and independent errors, respectively. The variance of residuals was assumed to be 2ξ was the variance due to local tendency and Dη was a t×t diagonal VCOV matrix, with each TP having a specific spatially independent variance component. Matrices c and Φ r and order given by the number of columns (c) and rows (r), respectively  among traits (i.e. heights at different TPs) . Finally, broad-sense heritability (h2) was estimated based on an entry-mean for each TP, following the equation: h2=σ 2g/(σ 2g+σ 2ε), where σ 2g=Vg and σ 2ε=Vε were the genetic and residual variances (V), respectively. The SEs of heritability estimates were estimated using the ‘delta’ method (http://www.homepages.ed.ac.uk/iwhite/asreml/uop).0⋱000Ψt] . In addient TPs) , followi’ method  using thWe applied data smoothing followed by dimensionality reduction of genotype BLUPs across all TPs following the approach described by 1, R2, R5, and R6 in 3, R4, R7, and R8 in We compared two approaches for selecting five or 10 TPs from the 26 TPs available for the 2017 data by sampling TPs in two different ways . In the ® HD wheat single nucleotide polymorphism (SNP) array  were removed, and the remaining missing SNP data were imputed using Beagle 4.1 , X is an n×2 matrix of QTL genotype probabilities, β is a 2×p matrix of QTL effects, and ε is an n×p matrix of random residuals following a multivariate normal distribution. At each position λ (putative QTL location), a multivariate regression model with a single QTL was fitted. Thus, the log10 likelihood ratio of the HK model was 0| was the matrix determinant for the null model with no QTL, and |RSS(λ)| was the matrix determinant for the model with a single QTL at position λ.where tLOD, and In contrast, the MLOD and SLOD approaches used the maximum and average LOD scores across TPs, respectively: MLOD(λ)=maxFinally, for multiple functional mapping , we followed the methodology proposed by p is the estimated frequency of an arbitrarily chosen allele and k is the simulated additive effect divided by the SD of the BLUPs for the respective TP. Finally, statistical power was estimated as the proportion of iterations in which the simulated additive effects were detected as QTLs at α=0.05 based on the permutation thresholds used in our analyses of empirical data (see above).We performed data perturbation simulations  to alter1–R8, The phenotypic traits used for prediction were the (i) individual TP BLUPs; (ii) the last two B-spline coefficients; and (iii) the first functional PCs from analyses of five, 10, and 26 TPs, including different TP selection scenarios R1–R8, .We used the additive genomic best linear unbiased prediction (GBLUP) model:β was the vector of fixed effects, a was the vector of random additive genetic effects of the SNP markers, and ε was a vector of random residuals. The incidence matrices for β and a were X and Z, respectively. The distributions of random effects were assumed to be a~N and ε~N, where I was the identity matrix and Ga was the additive genomic relationship matrix calculated using the first formula proposed by where 1 and R5 scenarios, as well as the full set of 26 TPs . This model is expected to be advantageous assuming that height is controlled by relatively few genes of large effect and many genes of smaller effect  was calculated as the Pearson correlation between adjusted values and genomic estimated breeding values in 50 replications from independent validation scenarios (n=148) to form a training set, while the remaining 25% (n=49) were used as a validation set. We applied Fisher’s Z transformation of the predictive abilities and compared them among scenarios using Scott–Knott’s test (2a=Vga) and residual (σ 2ε=Vgε) variances, enabling the calculation of genomic heritability as h2g=σ 2a/(σ 2a+σ 2ε).Predictive ability   . The proP<0.01) .From the IM and CIM scans of the 2017 data , we detected a total of six QTLs . Three oBased on the 2016 data, we detected one QTL on chromosome 2B across multiple TPs, whereas another QTL on chromosome 6A was detected in a single TP, in a different growth stage from 2017 . FurtherUsing single functional mapping at five, 10, and 26 TPs based on the multivariate LOD test statistic HKLOD score), we identified two, three, and four QTLs, respectively . ResultsLOD scoreAs expected under the presumed genetic model of highly complex temporal dynamics of height growth, both absolute effect sizes and proportions of PVEs varied substantially across the growing season, with clear examples of early , late (7A), or persistent (2B) QTLs . FurtherGenetic and residual variance components from the GBLUP model generally followed the same temporal patterns as those from the FA model, with increasing values after the tillering growth stage . ConsequThe predictive ability for B-spline coefficients of phenotypes that had been smoothed was generally higher than that for individual TP or PC data . Based oSetaria  and the additional computational cost  that may not necessarily translate into improved genomic prediction or more complete understanding of trait architecture. Based on our results, we formulated the following two practical recommendations, which are naturally only applicable in situations similar to our study. First, when the emphasis is on dissecting trait architecture, we recommend using both individual TP and functional mapping approaches to maximize the overall number and types of QTLs detected. Secondly, for more applied purposes (e.g. in breeding), analyses of spline-smoothed phenotypes selected based on phenological information may be sufficient to maximize genomic predictive ability. Further slight improvements may be achieved through the inclusion of QTLs as fixed-effect covariates, though it is not currently clear if the additional complexity (and consequently delay) associated with QTL detection is justified.JXB online.Supplementary data are available at Fig. S1. Illustration of steps for processing of point clouds.Fig. S2. Manual ground height versus height from the 3D point cloud.Fig. S3. Heatmap of genetic correlations of height between 26 TPs in 2017.Fig. S4. Genetic map consisting of 2330 SNPs.Fig. S5. Temporal pattern of canopy height growth in 2016.Fig. S6. Smoothed and dimension-reduced height in 2017.Fig. S7. Interval and composite QTL mapping at 26 TPs in 2017.Fig. S8. Signed LOD scores for each time point in 2017 and 2016.Fig. S9. Summary of individual TP mapping results in 2016.Fig. S10. Functional QTL mapping analysis for five, 10, and 22 TPs in 2016.Table S1. Likelihood ratio and Wald tests at 26 TPs in 2017.erz545_suppl_Supplementary_Figures_S1-S10_and_Table_S1Click here for additional data file.


Pyrus communis L.) cultivars require a genetically pre-determined duration of cold-temperature exposure to induce autocatalytic system 2 ethylene biosynthesis and subsequent fruit ripening. The physiological responses of pear to cold-temperature-induced ripening have been well characterized, but the molecular mechanisms underlying this phenomenon continue to be elucidated. This study employed previously established cold temperature conditioning treatments for ripening of two pear cultivars, ‘D’Anjou’ and ‘Bartlett’. Using a time-course transcriptomics approach, global gene expression responses of each cultivar were assessed at four stages of developmental during the cold conditioning process. Differential expression, functional annotation, and gene ontology enrichment analyses were performed. Interestingly, evidence for the involvement of cold-induced, vernalization-related genes and repressors of endodormancy release was found. These genes have not previously been described to play a role in fruit during the ripening transition. The resulting data provide insight into cultivar-specific mechanisms of cold-induced transcriptional regulation of ripening in European pear, as well as a unique comparative analysis of the two cultivars with very different cold conditioning requirements.European pear ( Pyrus spp.) is an economically important and nutritionally valuable tree fruit genus worldwide. European pear (Pyrus communis L.) cultivars are among the most widespread, commercially grown Pyrus members, and are cultivated in Europe, North America, South America, Africa, and Australia1. Along with apples, bananas, peaches, tomatoes, mangoes, and avocados, European pear is classified as climacteric in its ripening profile. Ripening in most climacteric fruits involves a seamless transition between system 1 (S1) and system 2 (S2) ethylene production. This is the point at which regulation of ethylene synthesis changes from autoinhibitory to auto-stimulatory3. Increased ethylene biosynthesis during climacteric ripening is accompanied by a concomitant spike in respiration5. A prominent aspect that distinguishes European pear and Chinese white pear (Pyrus bretschneideri Rehder.) from most other climacteric fruits is that these species have a pre-ripening period, during which they require a specific amount of cold exposure in order to transition from S1 to S2 ethylene production7. The process of cold exposure is called ‘conditioning’, and accumulation of chilling hours necessary for this transition, and therefore ripening initiation, is referred to as the ‘chilling requirement’8.Pear  varieties have no conditioning requirements and are also regarded as non-climacteric fruits because they do not display the characteristic S1 to S2 transition during ripening12. Additionally, ‘Bosc’, unique from other European pear cultivars, acquires competency for ripening with exogenous ethylene only, needing no chilling to ripen8.Physiological studies have characterized the conditioning requirements for a range of European pear cultivars under defined conditioning temperatures, exogenous ethylene application regimes, and other pre-harvest treatments15; however, similar gene homologues have not yet been reported in cold-induced fruit ripening. With respect to flowering, the process of developmental initiation following an environmentally governed dormant state is known as endodormancy release16. Thus far, endodormancy release has not been used to characterize ripening after chilling, although the two processes share many similarities with regards to the timing and environmental nature of cold required, suggesting that similar genetic and regulatory mechanisms may govern these processes. Various forms of the chilling requirement for ripening have been described in avocado and mango, although to a lesser degree than in pear, as the former are more prone to chilling injury18.Requirement of cold exposure in pear to induce ripening is reminiscent of other natural cold temperature-dependent developmental phenomena, such as the vernalization and stratification that are needed for flowering and seed germination, respectively. The genes that regulate vernalization and stratification have been well-studied in model organisms, including Arabidopsis, wheat, and barley23. Genes associated with phytohormones such as abscisic acid (ABA), auxin, and jasmonic acid, along with several transcription factors were implicated in low-temperature-mediated enhancement of ripening in ‘Bartlett’21. In ‘Passe Crassane,’ the impact of low temperature-induced ethylene (LT) and the effects of exogenous ethylene treatments were evaluated using a transcriptomics approach24. It was observed that the expression of a subset of the LT-induced differentially expressed genes was disrupted by 1-MCP treatment, indicating that they were regulated by LT-induced ethylene. It was also reported that several transcription factors were unaffected by 1-MCP treatment, implying that they were under the control of LT alone24. Recent work quantifying expression of key genes representing ripening-related metabolic pathways in ‘D’Anjou’ and ‘Bartlett’ pear cultivars during the process of cold-conditioning revealed increased alternative oxidase (AOX) expression prior to the onset of the ripening climacteric. This novel finding suggests that AOX may play an important role in the achievement of ripening competency25 and may be necessary for the onset of the ripening climacteric in pear and other chilling-dependent fruit. The Alternative Oxidase (AOX) respiratory pathway is known to play a role in cold stress mediation and response in many plant systems including cold temperature induced activation of respiration in potatoes, cell expansion and elongation in cotton, and mitigation of chilling injury in tomato and chickpea28. AOX is a mitochondrial membrane-bound protein involved in partitioning of electron flux during cellular respiration and, in many plant systems, it serves to maintain carbon metabolism homeostasis, cellular redox state, and ROS homeostasis during development29.Few recent studies have utilized a transcriptomics approach to characterize the molecular underpinnings of cold-induced S1 to S2 transition in pear. A complex interaction of genes is involved in regulating phytohormones, secondary messengers, signaling pathways, respiration and chromatin modification that underlies cold-induced progression of ripening25, a time course RNAseq analysis was performed in this study using ‘Bartlett’ and ‘D’Anjou’ fruit to evaluate the hypotheses that AOX and other key cold-induced genes facilitate ripening, and that the fruit from the two cultivars recruit different set of genes during cold conditioning. Key genes and networks involved in cold-induced, ripening-associated biochemical pathways were identified.Based on our previous worket al.25 were utilized for RNAseq analysis conducted in this study. Cold conditioning of the fruit at 10 °C resulted in a reduction of fruit firmness in both ‘Bartlett’ and ‘D’Anjou’ cultivars as demonstrated previously  were identified for ‘D’Anjou’, with 7,174 of these contigs exhibiting significant linear or quadratic trends over time (R > 0.8). In ‘Bartlett’ 31,481 contigs were identified as being differentially expressed, with 7,174 contigs exhibiting significant quadratic or linear trends over time (R > 0.8)  and chromatin modification-associated Multicopy Suppressor of IRA4 (MSI4), which have been shown to repress ethylene responses in banana and tomato, respectively, displayed different expression trends in the two cultivars. BZR1 increased over time in ‘D’Anjou’ and decreased over time in ‘Bartlett’40 , and abscisic acid 8'-hydorxylase 2 (CYP707A). NCED1 catalyzes the first step in ABA biosynthesis and regulates some genes associated with cell wall degradation during ripening44. CYP707A, which is important for regulating seed dormancy and germination in Arabidopsis, accumulates over the course of seed maturation and results in the breakdown of ABA45  related transcript displayed variable expression between the two cultivars  displayed decreased expression in both cultivars during the second half of conditioning and ripening period. This gene is a negative regulator of flowering in Arabidopsis47 and therefore may play a similar role in negative regulation of other endodormancy-associated processes, including fruit ripening.In contrast to DECs displaying a continual increase in expression over time, 2S), enhance alternative pathway respiration and inhibit ROS production in fruits51. Such compounds have also been used in fruit processing as a preservation strategy to reduce oxidative browning52, and low dose applications of H2S elicit a pronounced ripening response in pear fruit53. The sulfur metabolism genes, ATP sulfurylase and ATP sulfurylase 2, were highly expressed only in ‘Bartlett’, with transcript abundance increasing over the course of conditioning and ripening , which has been shown to maintain the circadian clock in a temperature-dependent manner in barley and Arabidopsis54  decreased continually in expression during conditioning and ripening in ‘Bartlett’  displayed increasing expression during conditioning and ripening for both cultivars , in Arabidopsis64 and blueberry65. FRIGIDA 4 decreased significantly in expression throughout conditioning in ‘Bartlett’, suggesting that its downregulation may correspond to decreased activation of ripening repressors in a role homologous to regulation of flowering time  gene expression in photoperiod sensitive plants, like Arabidopsis66. Recently, however, CONSTANS-like gene families have been shown to display distinct, tissue-specific patterns of expression in banana fruit and pulp, in addition to other tissues67, suggesting that CONSTANS-like gene family members play a role not only in flower development, but also, fruit development and senescence. CONSTANS-like 9, 5, 6, 13, and 14 were all differentially expressed, displaying a decreasing expression trend in both cultivars throughout the conditioning period , hormone signaling , hormone biosynthesis , and respiration-associated processes  Fig. . The sha71. The GO analysis results implicate cold temperature induction of numerous metabolic pathways, many of which operate upstream or independently of ethylene. This observation aligns with a recent study in cold conditioned pear fruit that demonstrated that LT induces expression of both ethylene-dependent and independent genes affecting ripening24. Complete ontology results can be found in Supplementary File ‘D’Anjou’ pears are genetically programmed to require a longer conditioning time to ripen than ‘Bartlett’ pears (60 versus 15 days of conditioning at 0 °C). Overrepresented GO terms unique to ‘D’Anjou’ that were associated with chilling-induced endodormancy release included ‘seed germination’ and ‘methylation’, while for ‘Bartlett’ such terms included ‘vernalization response’, ‘regulation of seed germination’ . Inhibition of repressors of endodormancy release, such as BZR1 and MSI4 and ABA precursors, via VRN1 and VIN3 pathways allows for activation of ripening-specific transcription factors, such as MYB1R1 and others, which may regulate autocatalytic ethylene production during conditioningses Fig. .VRN, VIN, CONSTANS-like gene families among others, in a multitude of plant tissues, including roots, shoots, leaves, apical meristems, buds, and flowers73. Here we provide evidence suggesting that members of these gene families have diversified to play similar roles in cold-dependent fruit ripening. These findings lend support to the idea of cold-induced ripening as a process of endodormancy release that might explain the underlying basis for different duration of cold requirement across different pear cultivars.Results of this study provide new information with regards to vernalization and cold response-associated genes that are differentially expressed over time during conditioning and subsequent ripening. Many of the genes that have been identified as potential regulators of cold-induced ripening in pear fruit represent members of diverse gene families. Furthermore, several studies have previously indicated the diversification and neofunctionalization of 25. Briefly, ‘Bartlett’ and ‘D’Anjou’ pear fruit were obtained from Blue Star Growers . During the time between harvest and acquisition (5 days), the pear fruit was maintained in temporary storage at 1 °C. ‘Bartlett’ fruit had a mean firmness of 76.2 N, and 13.40 °Brix and ‘D’Anjou’ fruit had a mean firmness of 53.5 N, and 12.66 °Brix at the initiation of the experiment. Ripening of ‘Bartlett’ requires 15 days of cold conditioning, while ‘D’Anjou’ typically requires 60 days at −1 °C to attain ripening competency10. The duration of cold conditioning, however, is reduced when conditioning temperatures are increased to 10 °C8. Pears were divided into equal replicate groups and then placed into storage at 10°C for conditioning8. After the conditioning period  equipped with an 8.0 mm probe set at 5.0 mm flesh penetration was used to measure firmness at two equidistant points around the equatorial region of each fruit after removal of the peel. Firmness data were assessed using ANOVA, following the statistical approaches described previously 25. Briefly, peel and flesh tissue was obtained from a 1 cm wide equatorial region of 3 randomly sampled fruit of each cultivar and at each conditioning time point, flash frozen in liquid nitrogen, pooled for each treatment/time point, and then ground using a SPEX Freezer/Mill 6870 . Total RNA was extracted from pulverized ‘D’Anjou’ and ‘Bartlett’ fruit tissue for each of three technical replicates at 0% conditioned, 50% conditioned, 100% conditioned, and 100% ripened time points following the methods of Gasic et al.76. Contaminating genomic DNA was removed with DNaseI per manufacturer instructions . RNA was quality checked using a denaturing gel and BioAnalyzer 2100  and was quantified using Nanodrop 2000 spectrophotometer .Peel and flesh tissue used in this study was the same as that used for the qRT-PCR study, published recentlycDNA libraries were qualified and quantified using a Life Technologies Qubit Fluorometer  as well as an Agilent 2100 Bioanalyzer . The cDNA libraries prepared from the extracted RNA were sequenced on an Illumina Hi Seq. 4000 platform as 2 × 100 paired end reads. The Illumina TruSeq RNA Sample Preparation v2 kit  was used to generate the final library molecules, and the Ailine Biosciences’  DNA SizeSelector-I bead protocol was used to filter for library molecules of >450 base pairs.78. The 2 × 100 paired end fastq files generated using Illumina HiSeq. 2000 were input into the CLC Bio Genomics Workbench (ver 6.0.1)  for pre-processing and assembly. The CLC Create Sequencing QC report tool was used to assess quality. The CLC Trim Sequence process was used to trim quality scores with a limit of 0.001, corresponding to a Phred value of 30. Ambiguous nucleotides were trimmed, and the 13 5’ terminal nucleotides removed. Reads below length 34 were discarded. Overlapping pairs were merged using the’Merge Overlapping Pairs’ tool, and a subsequent de novo assembly was performed with all datasets. Parameters used in the assembly are as follows: Map reads back to contigs = TRUE, Mismatch cost = 2, Insertion cost = 3, Deletion cost = 0.4, Similarity Fraction = 0.95, Global Alignment = TRUE, Minimum contig length = 200, Update contigs = true, Auto-detect paired distances = TRUE, Create list of un-mapped reads = TRUE, Perform scaffolding = TRUE. The de novo assembly resulted in the production of 140,077 contiguous sequences (contigs). Contigs with less than 2x coverage and those less than 200 bp in length were eliminated. For each individual dataset (treatment/replicate) the original, non-trimmed reads were mapped back to the master assembly subset. Default parameters were used, except for the length fraction, which was set to 0.5, and the similarity fraction, which was set to 0.9. Mapping resulted in the generation of individual treatment sample reads per contig. The master transcriptome was exported as a fasta file for functional annotation and the read counts for each dataset were exported for normalization with the Reads Per Kilobase per Million reads (RPKM) method79.Transcriptome assembly was performed as reported previously80. Contig sequences were identified by a blastx alignment against the NCBI ‘Viridiplantae’ database with and e-value specification of 10.0E-3. Gene ontology (GO) annotation was assigned using the ‘Mapping’ and ‘Annotation’ features. Expression analysis was limited to the consensus sequence for each contig, and therefore in this paper we do not distinguish between specific alleles, highly similar gene family members.The master transcriptome fasta produced from the Illumina assembly was imported into OmicsBox version 1.1.135  for functional annotation of expressed contigs using the Blast2GO feature79. An additional experimental design matrix was imported, which dictated the number of time points and replicates . Ontologies shared between ‘D’ Anjou’ and ‘Bartlett’ and unique to each cultivar were identified (Supplementary File OmicsBox gene ontology (GO) enrichment analysis utilizing the Fisher’s Exact Test was employed25. Briefly, RNA samples were treated with DNAseI to eliminate any DNA contamination according to the manufacturer’s methods , prior to cDNA synthesis. RNA concentration was determined for each sample using a Nanodrop ND-8000 . RNA quality was verified using a denaturing gel and BioAnalyzer 2100 . For each sample, 500 ng of total RNA was used to generate first strand cDNA using the Invitrogen VILO kit . Each cDNA preparation was quantified using a Qubit fluorimeter . The samples were diluted to a final concentration of 50 ng/uL. Initial qRT-PCR technical replicate reactions were prepared for each of the 90 selected genes using the iTaq Universal SYBR Green Supermix . Primers for quantitative reverse transcriptase PCR (qRT-PCR) were designed from Pyrus ESTs or sequences derived from Malus × domestica transcripts related to various hormonal and environmental signaling pathways. 500 ng RNA for each sample (same as used for RNAseq) was used to generate 1st strand cDNA using the Invitrogen VILO kit . cDNA preparations were then diluted to 50 ng/uL. qRT-PCR technical replicate reactions were prepared for each of the genes using the iTAq Universal SYBR Green Supermix with ROX reference dye  per the manufacturer’s protocols with 100 ng of template cDNA. In a Strategene MX3005P, the following thermocycle profile was used: 95 °C initial disassociation for 150 s followed by 50 amplification cycles  and a final, single cycle phase to generate a dissociation curve . Using the LinRegPCR tool, we calculated the Cq values for each reaction82 (Supplementary File qRT-PCR was performed as reported earlierSupplementary information 1.Supplementary information 2.Supplementary information 3.Supplementary information 4.Supplementary information 5.Supplementary information 6.Supplementary information 7.Supplementary information 8.Supplementary information 9.Supplementary information 10.Supplementary information 11.Supplementary information 12.


Polyphenols adsorbed onto β-glucan from 9 to 203 , 1 to 484 , 5 to 160 , and 19 to 28 mg g−1 . The adsorption was concentration dependent (polyphenols present in higher amount adsorbed in higher amounts). Physical sorption can be suggested. Polyphenols from traditional apples adsorb onto β-glucan and should be further studied.Apple polyphenols have been studied for various beneficial bioactivities. Especially interesting are traditional, old varieties of apples for which some initial studies have suggested significant bioactivities, but they are still not completely understood. Polyphenol bioactivities can be affected by interactions with dietary fibers such as β-glucans. The aim of this study was to investigate for the first time interactions between individual polyphenols from traditional, old apple varieties (“Božićnica” and “Batulenka”) and β-glucans by studying the adsorption process. Polyphenols were extracted from the peel and flesh of traditional apples by using an ultrasonic bath and characterized with high-performance liquid chromatography. The amounts of adsorbed ( Many potential beneficial effects of dietary polyphenols have been studied ,2,3,4. DThe beneficial effects of polyphenols are connected to the amount that is available for absorption in the digestive tract in its original form: those polyphenols are bioaccessible . Such biqe) and un-adsorbed (ce) can be modeled with adsorption isotherm equations [The interactions between dietary fibers and polyphenols can be investigated by the in vitro adsorption process. Adsorption is a process in which molecules from liquid or gas adsorb onto the surface of an adsorbent ,24. The quations ,24, whicquations ,25,26,27d-glucose with β-(1→4) linkages that form cellulose-like blocks [β-glucans are natural non-digestible dietary fibers . Those fe blocks , which ie blocks ,29,30. βe blocks ,20 or β-e blocks  has beenThe aim of this study was to investigate the interactions between β-glucans and individual polyphenols from two indigenous, traditional apple varieties (“Božićnica” and “Batulenka”) by studying the adsorption process. Those apple varieties have never been studied for adsorption onto β-glucan. Moreover, to the best of our knowledge, the adsorption of individual polyphenols from apples in general has never been studied before. Adsorption data were modeled with equations of adsorption isotherms to get a better insight into the adsorption (interaction) process. For the modeling of adsorption isotherms, an improved non-linear fitting method was put to use with an algorithm in the R programming language written and developed by our group. This improved modeling gives a potential improvement in the interpretation of adsorption isotherms.O-galactoside, quercetin-3-O-rhamnoside, and phloretin-2′-O-glucoside) and some from Sigma-Aldrich  ((−)-epicatechin, chlorogenic acid, (+)-catechin, quercetin, and quercetin-3-glucoside). The barley β-d-glucan was obtained from Sigma-Aldrich .Sodium hydrogen phosphate dodecahydrate and sodium dihydrogen phosphate dihydrate were purchased from Kemika . Orto-phosphoric acid (85% HPLC-grade) and methanol (HPLC grade) were from Fluka  and J.T. Baker , respectively. Some polyphenol standards were purchased from Extrasynthese   and apple variety “Batulenka” from Rude (45°46′35.6″ N 15°40′35.8″ E)). Apples of the variety “Božićnica” were peeled with a peeler, and the peel was pooled and ground in a coffee grinder. The flesh was cut, the seeds were removed, and the flesh was pooled and homogenized with a stick blender. The same procedure was repeated for the second variety “Batulenka”. Those two peel and two flesh samples were stored at −18 °C for no more than one month.Extracts of the peel samples were made by the following procedure. Five samples of “Božićnica” peel were weighed (around 0.2 g) and added to plastic tubes. Then, 1.5 mL of 80% methanol in water was added to each tube, and the samples were vortexed. The extraction procedure was carried out by using an ultrasonic bath  for 15 min and then a centrifuge  for 10 min at 10,000 rpm. The extracts from all five samples were combined, evaporated, and dissolved in 1.5 mL of methanol to get a concentrated extract of peel. One milliliter of concentrated extract was purified with Sephadex LH 20 gel, and 0.5 mL was filtered through a 0.45 µm PTFE (polytetrafluoroethylene) syringe filter and used for the determination of polyphenols in apples using the reversed-phase high-performance liquid chromatography (RP-HPLC) method. The procedure was repeated for the “Batulenka” peel. The same procedure was used for the extraction of polyphenols from the flesh of both varieties of apples.A purification of prepared concentrated extracts of peel and flesh was carried out by using the gel chromatographic method. Sephadex LH-20 gel was prepared by adding 30 mL of 80% methanol to 5 g of gel to swell overnight and putting it in a glass column. The gel was equilibrated with 10 mL of 60% methanol and 10 mL of 10% methanol. One milliliter of concentrated extract of flesh or peel was loaded onto a column and eluted with 5 mL of 10% methanol, 5 mL of 40% methanol, 10 mL of 60% methanol, 20 mL of 80% methanol, and 20 mL of 100% methanol. The eluate after adding 80% and 100% methanol was collected, evaporated to measured volumes near 4 mL, filtered through a 0.45 µm PTFE syringe filter, analyzed on the RP-HPLC system to determine the amount of individual polyphenols, and then used for the adsorption experiment.3PO4 (as mobile phase A) and 100% methanol (as mobile phase B). Other conditions included the flow rate of 0.8 mL min−1, and the injection volume of 10 µL. The gradient was 0 min 5% B, 5 min 25% B, 14 min 34% B, 25 min 37% B, 30 min 40% B, 34 min 49% B, 35 min 50% B, 58 min 51% B, 60 min 55% B, 62 min 80% B, 65 min 80% B, 67 min 5% B, and 72 min 5% B. Polyphenol standards in different concentration ranges were used for the creation of calibration curves -catechin 1–48 mg L−1, (−)-epicatechin 1–46 mg L−1, procyanidin B1 0.45–22.5 mg L−1, phloretin-2-glucoside 1–46 mg L−1, phloretin 1–46 mg L−1, chlorogenic acid 1–46 mg L−1, quercetin-3-galactoside 1–49 mg L−1, quercetin-3-glucoside 1–45 mg L−1, quercetin-3-rhamnoside 1–45 mg L−1, and quercetin 1–43 mg L−1). Calibration curves were linear (r2 0.9927 to 0.9998). The retention times and the UV/Vis spectrum of peaks (190–600 nm) were compared to those of authentic standards for identification. The UV/Vis spectrum of peaks agreed with the spectrum of authentic standards and their maximums were as follows: cyanidin-3-galactoside 275 and 518 nm; (+)-catechin 280 nm; (−)-epicatechin 280 nm; procyanidin B1 280 nm; phloretin-2-glucoside 282 nm; chlorogenic acid shoulder 290 nm, maximum 330 nm; quercetin-3-galactoside 255 and 355 nm; quercetin-3-glucoside 255 and 355 nm; and quercetin-3-rhamnoside 260 and 350 nm. In addition, polyphenol standards were added to the polyphenol extracts to confirm the identifications. Data from the literature [Polyphenols in the adsorption experiment were analyzed using an HPLC system 1260 Infinity II . The system consisted of a quaternary pump, a PDA detector (photodiode array detector) and a vialsampler. A Poroshell 120 EC C-18 column  and a Poroshell 120 EC-C18 4.6 mm guard-column  were used for the polyphenol separation. The method was validated earlier in our laboratory . The mob−1) was dissolved in distilled water and heated . The reaction solution consisted of the polyphenol extract (300 µL), the β-glucan (5 mg L−1) and phosphate buffer (pH 5.5) to a total volume of 1 mL. The moderate pH 5.5 was chosen to avoid too low or too high pH values, which can lead to hydrolysis or oxidation reactions, respectively. Reaction solutions were mixed in a laboratory shaker  for 5 h and centrifuged at 10,000 rpm for 10 min. An aliquot (500 µL) was taken from the top of each solution and filtered through a syringe filter (0.45 µm PTFE) for the determination of un-adsorbed polyphenols using the RP-HPLC (ce in mg L−1). The adsorption capacity (qe) (mg of polyphenols adsorbed onto g of β-glucan) was calculated by the mass balance equation:c0 is the initial polyphenol concentration in the reaction solution (mg L−1), ce is the polyphenol concentration in the reaction solution at equilibrium or un-adsorbed polyphenols (mg L−1), Vm is the total volume of a reaction solution (L), γa is the β-glucan concentration (g L−1) and Va is the volume of added β-glucan in a reaction solution (L). The experiment of adsorption was then repeated for more aliquots of extracts (50 to 200 µL) to get the data at more concentration levels of polyphenols. For that experiment, the qe was calculated using Equation (1), the ce or un-adsorbed polyphenols were determined with the RP-HPLC in mg L−1, but recalculated in mg. Finally, the data for ce (mg) and qe (mg g−1 β-glucan) were modeled with adsorption isotherm equations.β-glucan  were modeled with Langmuir, Dubinin–Radushkevich, and Hill adsorption isotherm equations. For that purpose, we used improved non-linear regression fitting methodology specifically designed for adsorption isotherms. The code for improved adsorption isotherm fitting, as described in [Experimental data ribed in , was devn = 3). The adsorption experiment was conducted two times for each extract at each concentration level and analyzed once on the RP-HLC (n = 2). Adsorption capacities were reported as means ± standard deviation (n = 2). The differences between adsorption capacities were studied with post hoc Tukey test using Minitab . The qe and ce were modeled using adsorption isotherm equations (qe vs. ce diagrams) with the improved non-linear regression. The standard error (se) was calculated:qe,meas and qmodele, are the qe measured and calculated by the model, respectively, n represents the total number of data points, and a the number of parameters in the isotherm equation.Two samples of apples were studied and from each an extract of flesh and peel were obtained (four polyphenol extracts). Each extract was analyzed three times with the RP-HPLC (The content of polyphenols found in the peel and flesh of apples “Božićnica” and “Batulenka” is shown in −1 (“Batulenka”) and polyphenols from the flesh from 5 to 160 (“Božićnica”) and 19 to 28 mg g−1 (“Batulenka”). It is known that the adsorbed amount depends on the initial polyphenol concentration, the pH of the environment, the buffer concentration, the temperature, and the ionic strength [−1 [−1 on β-glucan [−1, respectively [−1 [−1 [−1 [−1 [−1 on ferulic acid [Those polyphenols were then adsorbed onto β-glucan. The results for adsorption capacities obtained with 300 µL of polyphenol extract in the reaction solution are shown in strength ,19. For ngth [−1 . Total tectively . Procyanvely [−1 , 800 mg  [−1 [−1 , ans 600 [−1 [−1 , on the  [−1 [−1 . Arabinalic acid . The adsqe were correlated .Some polyphenols from the peel can be highlighted because of their adsorption in higher amounts : namely rrelated . The corqe is also high   .qe vs. ce) were modeled with Langmuir, Dubinin–Radushkevich, and Hill isotherm equations by using the improved non-linear modeling explained in our earlier paper [qe vs. ce), qe and ce were both measured values. They respond to the initial concentration, co. In the case of several measurements of qe for one initial co, several qe values will be positioned in the qe vs. ce diagram on a diagonal line  should lie on that diagonal line, which is not the case in standard non-linear regression. The improved non-linear regression created in the R programming language fitted the data in a way that the calculated qe model values by the model were on the diagonal lines. It was shown that this way of modeling created a curve with lower standard errors, which enabled more precise determination of isotherm parameters [qe vs. ce with improved non-linear regression in comparison to standard non-linear regression is shown in The adsorption was then conducted with several different initial polyphenol concentrations and the resulting data . In apprameters . For thiThis showed that the curve obtained with improved modeling fits the experimental data better and by that the parameters of adsorption isotherms  can be determined with more precision. Since isotherm parameters were used for the insight into the adsorption process, precise determination of parameters can be important. This justifies the use of improved non-linear modeling of the results in this study.KL is the Langmuir equilibrium constant of adsorption or the affinity of molecule to the adsorbent (mg−1) and qm is the apparent maximum monolayer adsorption capacity of β-glucan (mg g−1) [qe vs. ce was created for each polyphenol from peel and flesh, and modeling was done with the Langmuir equation using the improved non-linear regression. Parameters KL and qm were determined and are presented in qm) values were shown for procyanidin B1, (−)-epicatechin, chlorogenic acid, and quercetin-3-galactoside from “Božićnica” peel and (+)-catechin, procyanidin B1, quercetin-3-galactoside, and quercetin-3-glucoside from “Batulenka” peel. This was similar to experimentally determined adsorption capacities  were correlated to see the agreement between the experimental values and the model parameter qm values. A high correlation was shown (r2 = 0.88 for the peel and 0.96 for the flesh) (qm of the same compound but in different extracts can be observed (for example differences in qm for chlorogenic acid in the peel or flesh of two apples). This is the result of different initial amounts of a polyphenol in those extracts, which gave different adsorption capacities and, at the end, different isotherm parameters after modeling.The Langmuir isotherm describes an adsorption in a monolayer on the surface of the adsorbent. The adsorbent has only a limited number of adsorption sites, and there is no interaction between adsorbed molecules ,24,35. I(mg g−1) ,24,35. Apacities . Among tpacities , higher e flesh) , which sAccording to the Dubinin–Radushkevich isotherm, adsorption takes place on a heterogenous surface ,35,36 anThe Dubinin–Radushkevich Equation then becomesqs is the theoretical isotherm saturation capacity or the maximum adsorption capacity on β-glucan (mg g−1); β is a constant related to the adsorption energy (mol2 J−2); ε is the Polanyi potential or adsorption potential (J mol−1); R is the gas constant (8314 J mol−1 K−1); T is the temperature (K); E is the adsorption mean free energy (J mol−1); cs is theoretical saturation concentration or solubility (mg). After modeling the experimental values qe and ce with the Dubinin–Radushkevich equation (Equation (6)) with improved non-linear regression, parameters were determined ). Finally, qs, cs, and E were reported in Adsorption mean free energy can be calculated using Equation (7)qs) were shown for procyanidin B1, (−)-epicatechin, phloretin-2′-glucoside, chlorogenic acid, and quercetin-3-galactoside from “Božićnica” peel and (+)-catechin, quercetin-3-galactoside, and quercetin-3-glucoside from “Batulenka” peel. Among the polyphenols from the flesh (qs was shown for chlorogenic acid (“Božićnica”). This was similar to experimentally determined adsorption capacities   , which aompounds ,37, whicqm is the apparent maximum adsorption capacity of β-glucan (mg g−1), nH is the Hill cooperativity coefficient of the binding interaction; KD is the Hill constant (mg). After modeling the experimental values of qe and ce with improved non-linear regression, the parameters qm, nH, and KD were determined. Among the polyphenols from the peel  . nH < 1 represents a negatively cooperative bonding . A non-cooperative bonding (nH = 1), is a bonding that is independent on the molecules already bound to a macromolecule [nH for every polyphenol of flesh and peel were higher than 1. Accordingly, the bonding could be the result of a positive cooperation. Polyphenols bound more easily with the cooperation of other polyphenols already bound.The Hill isotherm describes an adsorption of different species onto a homogenous adsorbent, that allows for cooperative or non-cooperative bonding . It was the peel , higher the peel , a highepacities  and withctively) , which amolecule . In thisnH > 1, appropriate to these data (The standard errors (SE) of Langmuir, Dubinin–Radushkevich, and Hill models are shown in ese data . It shouApple polyphenols interacted with β-glucans and adsorbed in an amount that was in accordance with earlier studies ,25,26,27It might be suggested, given the parameters of the adsorption isotherms, that polyphenols bind to β-glucan with van der Waals interactions and maybe weak H bonds, but further studies are needed to confirm these findings. Earlier studies have shown that van der Waals forces and perhaps also weak H bonds and hydrophobic interactions are responsible for the polyphenol–dietary fiber interactions ,20,25,27The future research will include the studies of adsorption between apple polyphenols and β-glucan at different pH values and at different temperatures and in vitro simulated digestion processes of polyphenol–β-glucan systems.Polyphenols from apples interacted with β-glucan and adsorbed onto β-glucan in a concentration dependent manner. Adsorption data can be modeled with adsorption isotherm equations. Careful interpretation of isotherm parameters allowed us to suggest that the adsorption process was a physical process with a suggestion of van der Waals forces. The adsorption could be a cooperative adsorption. More studies are needed for the interaction of polyphenols from complex real samples such as apples and β-glucan to explain those processes further. Future studies can involve kinetic studies of adsorption and the influence of different pH values and different temperatures on the adsorption.