Simultaneous confidence regions for closed tests,including Holm‐, Hochberg‐, and Hommel‐related procedures

The derivation of simultaneous confidence regions for some multiple‐testing procedures (MTPs) of practical interest has remained an unsolved problem. This is the case, for example, for Hochberg's step‐up MTP and Hommel's more powerful MTP that is neither a step‐up nor a step‐down procedure. It is shown in this article how the direct approach used previously by the author to construct confidence regions for certain closed‐testing procedures (CTPs) can be extended to a rather general setup. The general results are then applied to a situation with one‐sided inferences and CTPs belonging to a class studied by Wei Liu. This class consists of CTPs based on ordered marginal p‐values. It includes Holm's, Hochberg's, and Hommel's MTPs. A property of the confidence regions derived for these three MTPs is that no confidence assertions sharper than rejection assertions can be made unless all null hypotheses are rejected. Briefly, this is related to the fact that these MTPs are quite powerful. The class of CTPs considered includes, however, also MTPs related to Holm's, Hochberg's, and Hommel's MTPs that are less powerful but are such that confidence assertions sharper than rejection assertions are possible even if not all null hypotheses are rejected. One may thus choose and prespecify such an MTP, though this is at the cost of less rejection power.     

Alternative Confidence Regions for Bonferroni‐Based Closed‐Testing Procedures that are not Alpha‐Exhaustive

This article complements the results in Guilbaud (Biometrical Journal 2008; 50 :678–692). Simultaneous confidence regions were derived in that article that correspond to any given multiple testing procedure (MTP) in a fairly large class of consonant closed‐testing procedures based on marginal p‐values and weighted Bonferroni tests for intersection hypotheses. This class includes Holm's MTP, the fixed‐sequence MTP, gatekeeping MTPs, fallback MTPs, multi‐stage fallback MTPs, and recently proposed MTPs specified through a graphical representation and associated rejection algorithm. More general confidence regions are proposed in this article. These regions are such that for certain underlying MTPs which are not alpha‐exhaustive, they lead to confidence assertions that may be sharper than rejection assertions for some rejected null hypotheses H when not all Hs are rejected, which is not the case with the previously proposed regions. In fact, various alternative confidence regions may be available for such an underlying MTP. These results are shown through an extension of the previous direct arguments (without invoking the partitioning principle), and under the same general setup; so for instance, estimated quantities and marginal confidence regions are not restricted to be of any particular kinds/dimensions. The relation with corresponding confidence regions of Strassburger and Bretz (Statistics in Medicine 2008; 27 :4914–4927) is described. The results are illustrated with fallback and parallel‐gatekeeping MTPs.     

Simultaneous confidence regions corresponding to Holm's step-down procedure and other closed-testing procedures

Holm's (1979) step-down multiple-testing procedure (MTP) is appealing for its flexibility, transparency, and general validity, but the derivation of corresponding simultaneous confidence regions has remained an unsolved problem. This article provides such confidence regions. In fact, simultanenous confidence regions are provided for any MTP in the class of short-cut consonant closed-testing procedures based on marginal p -values and weighted Bonferroni tests for intersection hypotheses considered by Hommel, Bretz and Maurer (2007). In addition to Holm's MTP, this class includes the fixed-sequence MTP, recently proposed gatekeeping MTPs, and the fallback MTP. The simultaneous confidence regions are generally valid if underlying marginal p -values and corresponding marginal confidence regions (assumed to be available) are valid. The marginal confidence regions and estimated quantities are not assumed to be of any particular kinds/dimensions. Compared to the rejections made by the MTP for the family of null hypotheses H under consideration, the proposed confidence regions provide extra free information. In particular, with Holm's MTP, such extra information is provided: for all nonrejected H s, in case not all H s are rejected; or for certain (possibly all) H s, in case all H s are rejected. In case not all H s are rejected, no extra information is provided for rejected H s. This drawback seems however difficult to overcome. Illustrations concerning clinical studies are given.     

Fibromyalgia,myofascial pain,tender points and trigger points: splitting or lumping?

Myofascial trigger points (MTPs) have long been a contentious issue in relation to fibromyalgia, and poorly defined pain complaints in general. Can MTPs be reproducibly identified? Do MTPs have valid objective findings, such as spontaneous electromyographic activity, muscle microdialysis evidence for an inflammatory milieu or visualization with newer ultrasound techniques? Is fibromyalgia a syndrome of multiple MTPs, or is focal muscle tenderness a manifestation of central sensitization? These issues are discussed with relevance to a recent paper reporting that manual palpation of active MTPs elicits the spontaneous pain experienced by fibromyalgia patients.     

Ecological responses of selected vascular plants to water chemistry parameters in habitat types 3120, 3130 and 3170* (Habitat Directive 92/43/EEC)

Abstract

The article aims to examine the main water chemistry parameters (i.e. conductivity, pH, dissolved O₂) and the ecological responses of 20 guide species in Mediterranean Temporary Ponds (MTPs). A complete data-set of 37 MTPs located in two different regions of Italy, Sardinia and Apulia, was compiled and the data were examined by means of Principal Component Analysis (PCA). The pattern of MTPs into the water chemistry space showed a clear separation between the two geographical regions. A “daisy diagram” obtained by overlapping five typologies of MTPs, obtained by the fuzzy cluster analysis and the PCA, revealed a good agreement between the sequence of groups and the water chemistry gradient. Groups of species sharing similar responses to the same chemical features were finally identified. These groups could be effective to acquire detailed information on the characteristics of MTPs and to improve their classification into different typologies. The guide species respond selectively to the wide variability range of conductivity, pH and dissolved oxygen. Despite the small size and the short hydroperiod water parameters in MTPs presented specific patterns to which the guide species are able to give specific responses.     

Obtaining Critical Values for Simultaneous Confidence Intervals and Multiple Testing

There are many situations where it is desired to make simultaneous tests or give simultaneous confidence intervals for linear combinations (contrasts) of population or treatment means. Somerville (1997, 1999) developed algorithms for calculating the critical values for a large class of simultaneous tests and simultaneous confidence intervals. Fortran 90 and SAS‐IML batch programs and interactive programs were developed. These programs calculate the critical values for 15 different simultaneous confidence interval procedures (and the corresponding simultaneous tests) and for arbitrary procedures where the user specifies a combination of one and two sided contrasts. The programs can also be used to obtain the constants for “step‐down” testing of multiple hypotheses. This paper gives examples of the use of the algorithms and programs and illustrates their versatility and generality. The designs need not be balanced, multiple covariates may be present and there may be many missing values. The use of multiple regression and dummy variables to obtain the required variance covariance matrix is illustrated. Under weak normality assumptions the methods are “exact” and make the use of approximate methods or “simulation” unnecessary.     

Bioprocess Control in Microscale: Scalable Fermentations in Disposable and User-Friendly Microfluidic Systems

Background  

The efficiency of biotechnological production processes depends on selecting the best performing microbial strain and the optimal cultivation conditions. Thus, many experiments have to be conducted, which conflicts with the demand to speed up drug development processes. Consequently, there is a great need for high-throughput devices that allow rapid and reliable bioprocess development. This need is addressed, for example, by the fiber-optic online-monitoring system BioLector which utilizes the wells of shaken microtiter plates (MTPs) as small-scale fermenters. To further improve the application of MTPs as microbioreactors, in this paper, the BioLector technology is combined with microfluidic bioprocess control in MTPs. To realize a user-friendly system for routine laboratory work, disposable microfluidic MTPs are utilized which are actuated by a user-friendly pneumatic hardware.     

Microtransponders, the miniature RFID electronic chips, as platforms for cell growth in cytotoxicity assays.

BACKGROUND: An electronic radio frequency (RF) microchip, the microtransponder (MTP), has been developed as a platform for assays in the fields of genomics and proteomics. Upon activation by light, each MTP provides a unique RF identification (ID) signal that matches a chip to the specific biological material attached to it. The MTP is powered by a photocell and has an antenna that transmits the signal. The aim of the present study was to explore utility of MTPs as a platform for cell growth in cytotoxicity assays. METHODS: The MCF-7, MCF-116, A549, or T-24 cells growing on MTPs placed in petri dishes or slide chambers were cultured untreated or exposed to antitumor drugs topotecan, mitoxantrone, or onconase for up to 4 days. Their attachment to- and growth on- MTPs was assessed by fluorescence microscopy and laser scanning cytometry (LSC) and compared with growth on the dish surface in the MTP neighborhood. The MTPs were fixed in ethanol, stained with propidium iodide (PI), and interrogated in flow in the instrument capable to rapidly (up to 103 MTPs/s) identify their ID signal and measure fluorescence. RESULTS: The cells plated on MTPs exhibited similar attachment properties to those plated in culture dishes. When measured by LSC, they had similar mitotic activity, growth rate, and cell cycle distributions as the cells adhering to the culture dish in the neighborhood of MTPs. The fluorescence intensity of MTPs provided information about the cell number per MTP, which made it possible to assess cell growth rate and monitor the cytostatic/cytotoxic effects of the tested drugs. CONCLUSIONS: The MTP-based system holds promise for the multiplexed cell assays in which numerous different cell lines can be screened for their growth rate or sensitivity while exposed to particular agents in the same vessel. Other advantages of the system are the rapidity of the screening and a very large number of ID codes. Because many cell lines/types can be assayed in a single dish, the system also offers cost savings on tissue culture reagents.     

General multistage gatekeeping procedures

A general multistage (stepwise) procedure is proposed for dealing with arbitrary gatekeeping problems including parallel and serial gatekeeping. The procedure is very simple to implement since it does not require the application of the closed testing principle and the consequent need to test all nonempty intersections of hypotheses. It is based on the idea of carrying forward the Type I error rate for any rejected hypotheses to test hypotheses in the next ordered family. This requires the use of a so-called separable multiple test procedure (MTP) in the earlier family. The Bonferroni MTP is separable, but other standard MTPs such as Holm, Hochberg, Fallback and Dunnett are not. Their truncated versions are proposed which are separable and more powerful than the Bonferroni MTP. The proposed procedure is illustrated by a clinical trial example.     

Enzyme activity deviates due to spatial and temporal temperature profiles in commercial microtiter plate readers

Microtiter plates (MTP) and automatized techniques are increasingly applied in the field of biotechnology. However, the susceptibility of MTPs to edge effects such as thermal gradients can lead to high variation of measured enzyme activities. In an effort to enhance experimental reliability, to quantify, and to minimize instrument‐caused deviations in enzyme kinetics between two MTP‐readers, we comprehensively quantified temperature distribution in 96‐well MTPs. We demonstrated the robust application of the absorbance dye cresol red as easily applicable temperature indicator in cuvettes and MTPs and determined its accuracy to ±0.16°C. We then quantified temperature distributions in 96‐well MTPs revealing temperature deviations over single MTP of up to 2.2°C and different patterns in two commercial devices (BioTek Synergy 4 and Synergy Mx). The obtained liquid temperature was shown to be substantially controlled by evaporation. The temperature‐induced enzyme activity variation within MTPs amounted to about 20 %. Activity deviations between MTPs and to those in cuvettes were determined to 40 % due to deviations from the set temperature in MTPs. In conclusion, we propose a better control of experimental conditions in MTPs or alternative experimental systems for reliable determination of kinetic parameters for bioprocess development.     

The yeast mitochondrial transport proteins: new sequences and consensus residues, lack of direct relation between consensus residues and transmembrane helices, expression patterns of the transport protein genes, and protein-protein interactions with other proteins

Mitochondrial transport proteins (MTP) typically are homodimeric with a 30-kDa subunit with six transmembrane helices. The subunit possesses a sequence motif highly similar to Pro X Asp/Glu X X Lys/Arg X Arg within each of its three similar 10-kDa segments. Four (YNL083W, YFR045W, YPR021C, YDR470C) of the 35 yeast (S. cerevisiae) MTP genes were resequenced since the masses of their proteins deviate significantly from the typical 30 kDa. We now find these four proteins to have 545, 285, 902, and 502 residues, respectively. Together with only four other MTPs, the sequences of YPR021C and YDR470C show substitutions of some of the five residues that are absolutely conserved among the 12 MTPs with identified transport function and 17 other MTPs. We do now find these five consensus residues also in the new sequences of YNL083W and YFR045W. Additional analyses of the 35 yeast MTPs show that the location of transmembrane helix sequences do not correlate with the general consensus residues of the MTP family; protein segments connecting the six transmembrane helices and facing the intermembrane space are not uniformly short (about 20 residues) or long (about 40 residues) when facing the matrix; most MTPs have at least one transmembrane helix for which the sum of the negative hydropathy values of all residues yields a very small negative value, suggesting a membrane location bordering polar faces of other transmembrane helices or a non-transmembrane location. The extra residues of the three large MTPs are hydrophilic and at the N-terminal. The 200-residue N-terminal segment of YNL083W has four putative Ca2+-binding sites. The 500-residue N-terminal segment of YPR021C shows sequence similarity to enzymes of nucleic acid metabolism. cDNA microarray data show that YNL083W is expressed solely during sporulation, while the expressions of YFR045W, YPR021C, and YDR470C are induced by various stress situations. These results also show that the 35 MTP genes are expressed under a rather diverse set of metabolic conditions that may help identify the function of the proteins. Interestingly, yeast two-hybrid screens, that will also be useful in identifying the function of MTPs, indicate that MIR1, AAC3, YOR100C, and YPR011C do interact with non-MTPs.     

Basic ideas and concepts for multiple comparison procedures

Around 1970, the author proposed a general theoretical approach to multiple decision problems (MDPs) of which multiple comparison problems (MCPs) are special cases. Suppose that a sample space Χ is given together with a set of probability distributions P = {P(θ), θ ∈ Ω} defined over Χ. Let a finite partition of the parameter space Ω = cupω(a), a ∈ A be given. Based on the observation X ∈ X, an MDP is to decide, which ω(a) the true parameter θ belongs to. An MD confidence procedure is a mapping ψ from X to the class of subsets of A, such that the probability that cupω(a), ω(a) C ψ(X) includes the true parameter θ is not smaller than 1-α(θ) . Here, 1-α(θ) is called the level of the confidence procedures and may vary depending on θ∈ω(a) . The MP confidence procedures are derived from the following proposition. When the ω(a) 's are mutually disjoint, there is a one-to-one correspondence between an MD confidence procedure ψ and a collection of (non-randomized) tests for the hypotheses H(a)?: θ∈ω(a) with level α(a) by rejecting the hypothesis H(a) if ω(a) ? ψ(X). In this paper we discuss in detail the problems of determining the signs or the orderings of normal means. The resulting confidence procedures from the LR tests are seen to be too complicated and difficult to understand. We therefore propose simplified, less powerful methods. We define an overlapping partition of Ω into simple sets, such that the original ω(a) 's can be expressed as an intersection of such simple sets. For each such set we define rejection regions corresponding to the levels α, α/2,...,α/k. Then we obtain the acceptance regions for H(a) :?θ∈ω(a) given as the intersection of all acceptance regions for the simple sets containing ω(a) at the level α/k, if there are k such simple sets. This method can be extended to obtain sequential confidence procedures.     

Bonferroni parallel gatekeeping - transparent generalizations, adjusted p -values, and short direct proofs

In the two-step version (Dmitrienko, Tamhane, Wang and Chen, 2006) of the Bonferroni parallel-gatekeeping multiple-testing procedure (MTP): (a) a family F1 of null hypotheses H is used as a gatekeeper for another family F2 in that no H in F2 can be rejected unless at least one H is rejected in F1; (b) a Bonferroni MTP is used for F1 at local multiple-level alpha in the first step; and (c) Holm's (1979) step-down MTP is used in the second step for F2 at a local multiple level that depends on the rejections made in the first step. It is shown in this article that this two-step procedure can be generalized in that any MTP with multiple-level control and available multiplicity-adjusted p -values can be used instead of Holm's MTP in the second step. A further generalization related to what Dmitrienko, Molenberghs, Chuang-Stein and Offen (2005) called modified Bonferroni parallel gatekeeping is also given where in case all H s in F2 are rejected, additional rejections in F1 can be made in a third step at local multiple-level alpha through any MTP that is more powerful than the initial Bonferroni MTP, e.g. Holm's MTP. The proofs that these two generalized Bonferroni parallel-gatekeeping MTPs have multiple-level alpha are short and direct, without closed-testing arguments. Multiplicity-adjusted p -values can easily be calculated for these MTPs. The extensions to several successive gatekeeper families are straightforward. An illustration is given.     

Development of a multiple internal control for clinical diagnostic real-time amplification assays

A major pitfall in most published genomic amplification methods for the detection and identification of human pathogens is that they do not include an internal amplification control in order to achieve an acceptable level of confidence for the absence of false-negative results. By applying composite primer technology, a single multiple internal amplification control DNA molecule was constructed to detect and quantify the hepatitis B virus, human polyomavirus, Epstein-Barr virus, Toxoplasma gondii and cytomegalovirus using real-time PCR. The multiple internal amplification control contains all forward and reverse primer binding regions targeted in the five distinct duplex PCRs, but with a unique probe hybridization site. Multiple internal amplification control detection sensitivity, assessed by Probit analysis, was 58 copies per PCR, associated with an extremely wide dynamic range (8 log(10) units). Moreover, in testing 614 patient samples, PCR inhibition occurred at a frequency of 0-8.8%. Similar multiple internal amplification controls for quantitative PCR-based assays could be designed to accommodate any infectious profiles in a particular institution as they are easy to make and inexpensive.     

Microvinification--how small can we go?

High-throughput methodologies to screen large numbers of microorganisms necessitate the use of small-scale culture vessels. In this context, an increasing number of researchers are turning to microtiter plate (MTP) formats to conduct experiments. MTPs are now widely used as a culturing vessel for phenotypic screening of aerobic laboratory cultures, and their suitability has been assessed for a range of applications. The work presented here extends these previous studies by assessing the metabolic footprint of MTP fermentation. A comparison of Chardonnay grape juice fermentation in MTPs with fermentations performed in air-locked (self-induced anaerobic) and cotton-plugged (aerobic) flasks was made. Maximum growth rates and biomass accumulation of yeast cultures grown in MTPs were indistinguishable from self-induced anaerobic flask cultures. Metabolic profiles measured differed depending on the metabolite. While glycerol and acetate accumulation mirrored that of self-induced anaerobic cultures, ethanol accumulation in MTP ferments was limited by the increased propensity of this volatile metabolite for evaporation in microlitre-scale culture format. The data illustrates that microplate cultures can be used as a replacement for self-induced anaerobic flasks in some instances and provide a useful and economical platform for the screening of industrial strains and culture media.     

Statistical power when testing for genetic differentiation

A variety of statistical procedures are commonly employed when testing for genetic differentiation. In a typical situation two or more samples of individuals have been genotyped at several gene loci by molecular or biochemical means, and in a first step a statistical test for allele frequency homogeneity is performed at each locus separately, using, e.g. the contingency chi-square test, Fisher's exact test, or some modification thereof. In a second step the results from the separate tests are combined for evaluation of the joint null hypothesis that there is no allele frequency difference at any locus, corresponding to the important case where the samples would be regarded as drawn from the same statistical and, hence, biological population. Presently, there are two conceptually different strategies in use for testing the joint null hypothesis of no difference at any locus. One approach is based on the summation of chi-square statistics over loci. Another method is employed by investigators applying the Bonferroni technique (adjusting the P-value required for rejection to account for the elevated alpha errors when performing multiple tests simultaneously) to test if the heterogeneity observed at any particular locus can be regarded significant when considered separately. Under this approach the joint null hypothesis is rejected if one or more of the component single locus tests is considered significant under the Bonferroni criterion. We used computer simulations to evaluate the statistical power and realized alpha errors of these strategies when evaluating the joint hypothesis after scoring multiple loci. We find that the 'extended' Bonferroni approach generally is associated with low statistical power and should not be applied in the current setting. Further, and contrary to what might be expected, we find that 'exact' tests typically behave poorly when combined in existing procedures for joint hypothesis testing. Thus, while exact tests are generally to be preferred over approximate ones when testing each particular locus, approximate tests such as the traditional chi-square seem preferable when addressing the joint hypothesis.     

Asymptotic distributions of kappa statistics and their differences with many raters,many rating categories and two conditions

In clinical research and in more general classification problems, a frequent concern is the reliability of a rating system. In the absence of a gold standard, agreement may be considered as an indication of reliability. When dealing with categorical data, the well‐known kappa statistic is often used to measure agreement. The aim of this paper is to obtain a theoretical result about the asymptotic distribution of the kappa statistic with multiple items, multiple raters, multiple conditions, and multiple rating categories (more than two), based on recent work. The result settles a long lasting quest for the asymptotic variance of the kappa statistic in this situation and allows for the construction of asymptotic confidence intervals. A recent application to clinical endoscopy and to the diagnosis of inflammatory bowel diseases (IBDs) is shortly presented to complement the theoretical perspective.     

An alternative foundation for the planning and evaluation of linkage analysis. II. Implications for multiple test adjustments

The 'multiple testing problem' currently bedevils the field of genetic epidemiology. Briefly stated, this problem arises with the performance of more than one statistical test and results in an increased probability of committing at least one Type I error. The accepted/conventional way of dealing with this problem is based on the classical Neyman-Pearson statistical paradigm and involves adjusting one's error probabilities. This adjustment is, however, problematic because in the process of doing that, one is also adjusting one's measure of evidence. Investigators have actually become wary of looking at their data, for fear of having to adjust the strength of the evidence they observed at a given locus on the genome every time they conduct an additional test. In a companion paper in this issue (Strug & Hodge I), we presented an alternative statistical paradigm, the 'evidential paradigm', to be used when planning and evaluating linkage studies. The evidential paradigm uses the lod score as the measure of evidence (as opposed to a p value), and provides new, alternatively defined error probabilities (alternative to Type I and Type II error rates). We showed how this paradigm separates or decouples the two concepts of error probabilities and strength of the evidence. In the current paper we apply the evidential paradigm to the multiple testing problem - specifically, multiple testing in the context of linkage analysis. We advocate using the lod score as the sole measure of the strength of evidence; we then derive the corresponding probabilities of being misled by the data under different multiple testing scenarios. We distinguish two situations: performing multiple tests of a single hypothesis, vs. performing a single test of multiple hypotheses. For the first situation the probability of being misled remains small regardless of the number of times one tests the single hypothesis, as we show. For the second situation, we provide a rigorous argument outlining how replication samples themselves (analyzed in conjunction with the original sample) constitute appropriate adjustments for conducting multiple hypothesis tests on a data set.     

Estimation and confidence regions for multi-dimensional effective dose

The problem of finding confidence regions for multiple predictor variables corresponding to given expected values of a response variable has not been adequately resolved. Motivated by an example from a study on hyperbaric exposure using a logistic regression model, we develop a conceptual framework for the estimation of the multi-dimensional effective dose for binary outcomes. The k -dimensional effective dose can be determined by conditioning on k - 1 components and solving for the last component as a conditional univariate effective dose. We consider various approaches for calculating confidence regions for the multi-dimensional effective dose and compare them via a simulation study for a range of possible designs. We analyze data related to decompression sickness to illustrate our procedure. Our results provide a practical approach to finding confidence regions for predictor variables for a given response value.     

Genome-wide exploration of metal tolerance protein (<Emphasis Type="Italic">MTP</Emphasis>) genes in common wheat (<Emphasis Type="Italic">Triticum aestivum</Emphasis>): insights into metal homeostasis and biofortification

Metal transport process in plants is a determinant of quality and quantity of the harvest. Although it is among the most important of staple crops, knowledge about genes that encode for membrane-bound metal transporters is scarce in wheat. Metal tolerance proteins (MTPs) are involved in trace metal homeostasis at the sub-cellular level, usually by providing metal efflux out of the cytosol. Here, by using various bioinformatics approaches, genes that encode for MTPs in the hexaploid wheat genome (Triticum aestivum, abbreviated as Ta) were identified and characterized. Based on the comparison with known rice MTPs, the wheat genome contained 20 MTP sequences; named as TaMTP1–8A, B and D. All TaMTPs contained a cation diffusion facilitator (CDF) family domain and most members harbored a zinc transporter dimerization domain. Based on motif, phylogeny and alignment analysis, A, B and D genomes of TaMTP3–7 sequences demonstrated higher homology compared to TaMTP1, 2 and 8. With reference to their rice orthologs, TaMTP1s and TaMTP8s belonged to Zn-CDFs, TaMTP2s to Fe/Zn-CDFs and TaMTP3–7s to Mn-CDFs. Upstream regions of TaMTP genes included diverse cis-regulatory motifs, indicating regulation by developmental stage, tissue type and stresses. A scan of the coding sequences of 20 TaMTPs against published miRNAs predicted a total of 14 potential miRNAs, mainly targeting the members of most diverged groups. Expression analysis showed that several TaMTPs were temporally and spatially regulated during the developmental time-course. In grains, MTPs were preferentially expressed in the aleurone layer, which is known as a reservoir for high concentrations of iron and zinc. The work identified and characterized metal tolerance proteins in common wheat and revealed a potential involvement of MTPs in providing a sink for trace element storage in wheat grains.