The International HapMap Project and the arrival of technologies that type more than 100,000 SNPs in a single experiment have made genome-wide single nucleotide polymorphism (GW-SNP) assay a realistic endeavor. This has sparked considerable debate regarding the promise of GW-SNP typing to identify genetic association in disease. As has already been shown, this approach has the potential to localize common genetic variation underlying disease risk. The data provided from this technology also lends itself to several other lines of investigation; autozygosity mapping in consanguineous families and outbred populations, direct detection of structural variation, admixture analysis, and other population genetic approaches. In this review we will discuss the potential uses and practical application of GW-SNP typing including those above and beyond simple association testing. Thispmap.org . In an eA key effort undertaken in parallel with the HapMap Project involved the production of cost-effective methods to perform high-throughput genotyping accurately and reproducibly. There are two prominent companies offering high-throughput genome-wide (GW) genotyping that can be applied within an end user's laboratory: Affymetrix and Illumina. The combination of these technological and informatic advances now make GW-SNP genotyping a realistic possibility for well-funded laboratories; the likely decrease in cost that will occur over the next five years suggests that this technology will become a standard technique in molecular genetic and clinical diagnostic laboratories. In this review article we will discuss the potential applications and practical considerations of GW-SNP assay. While we have experience in dealing with large datasets (~.5 billion genotypes) from both Affymetrix and Illumina technologies, much of this article focuses on the output and metrics produced using the Illumina Infinium assays, because our primary in-house work has centered on this platform. However, many of the concepts and applications discussed here are applicable to data derived from other platforms.GW-SNP assays have been anticipated as a tool for the dissection of disease risk factors for many years . Much ofhttp://www.fnih.org/GAIN/GAIN_home.shtml) and the Wellcome Trust Case Control Consortium (http://www.wtccc.org.uk) will release genotype data, albeit with varying restrictions on who can access the data.Highlighting the approximate nature of these calculations, the arbitrary number of 1,000 cases and 1,000 matched controls appears to have been adopted as the realistic standard for complex diseases. Compared with most genetic case control studies, which typically number a few hundred cases and controls, 1,000 samples in each cohort is relatively large; however, it is doubtful that even sample series of this size will provide sufficient power to identify recessive loci and less likely that the identification of gene–gene or gene–environment interactions will be tenable. Nevertheless, this size of study appears to be an achievable goal, although currently only for consortia or particularly well-funded laboratories. The considerable cost of these experiments coupled with the potential promise of this approach has led funding agencies to encourage sharing of resources to perform these assays, including both sharing of DNA samples and public release of genotype data. Implicitly, this policy highlights a strength of GW-SNP experiments, i.e., genotype data are essentially digital and additive; thus experiments on the same platform can be easily compared or combined to increase power and sensitivity. The public release of genotype data inevitably raises issues with respect to patient privacy and appropriate clinical research protocols and consenting procedures. While these restrictions may preclude use of some existing collections for publicly funded experiments, with adequate foresight these issues are not insurmountable. Indeed initiatives such as the Genetic Association Information Network  primarily to provide a renewable source of high-quality genetic material. An understandable concern is the fidelity of the genomic DNA in these cultured cells when compared with that from the source tissue. Experiments within our laboratory suggest that genomic DNA from LCLs produces GW-SNP data that is relatively faithful to that derived from the blood samples used to create the LCLs; the LCL creation and passage process results in alterations in less than 0.1% genotype calls when compared directly with the source tissue. In terms of genome-wide association, such a small and apparently randomly distributed alteration is unlikely to confound results. An additional and increasingly popular method for generating large amounts of genomic DNA is genome-wide amplification (GWA). This technique allows the production of significant amounts of genomic DNA from a variety of sources, including archived fixed tissue. This approach is of obvious utility, particularly where samples are rare or are individual fixed samples of particular importance. There is currently limited data on the use of this technology in the creation of starting material for GW-SNP assay; however, experiments assessing this approach in high-plex assays of >2,000 SNPs show a high degree of genotype concordance between amplified and source material . While tCFH (complement factor H) as a strong risk factor for age-related macular degeneration [CFH; resequencing revealed the presence of a coding alteration in CFH associated with a 7-fold increase in risk of disease for homozygous carriers. Not only did this study highlight the utility of GW-SNP assay but it also showed that relatively small case-control series can provide valuable information.Although GW-SNP assays have only been available for a short period, several studies using this approach have already been published –12. One neration . This woPerhaps as important as defining a positive signal, GW-SNP association studies may also define the limits of influence of common genetic variability in a particular disorder. One can, in the absence of the requisite significant signal, show that there is no common variant that confers a risk stronger than a predetermined odds ratio in the population studied. Put simply, in a perfectly designed experiment this approach has the power not only to tell you what is there, but also to tell you what is not there. Of course in the real world where likely confounds such as population stratification and incomplete genomic coverage ,14 lead http://www.ncbi.nlm.nih.gov/WGA), the challenge of data volume still remains.As the density of GW-SNP genotyping platforms continues to increase, it is plausible that many laboratories will attempt to manage billions of genotypes per year. Whether laboratories are producing these genotypes directly, through collaborations, or retrieving them from a public resource  and access (with privileges) to the data. Storing the data in a database makes the task of generally mundane but important jobs fairly easy, and facilitates the ability to use the data in many different forms, such as exporting for multiple analysis formats. An issue specific to the storage of SNP genotypes, which may affect which encoding is used to store a genotype and its sample and marker relationship, is that they have a direction and orientation; this latter point is of particular importance as even within platforms a SNP's encoded orientation may change between product releases. Because of the storage requirements (each chip image may be 2 Gb in size), typically chip images and other chip artifacts will be archived with a low level of access or discarded once genotypes have been called; however, as noted below many researchers will have interest in data above and beyond genotypes, wishing to access metrics that provide information on copy number. Thus investigators should expect to store relevant metrics in addition to the raw genotypes.http://neurogenetics.nia.nih.gov), Snpgwa , and PLINK (http://pngu.mgh.harvard.edu/~purcell/plink). These new tools should perform whole genome association analysis quickly; especially when compute clusters are available for parallel execution. Analyses within Snpgwa and PLINK include tests for allelic, genotypic, dominant, recessive, and additive model associations as well as tests for linkage disequilibrium and Hardy-Weinberg equilibrium. These tools also allow testing of haplotype association in consecutive (Snpgwa) or selected (PLINK) markers. Association analysis with permutations and multiple testing corrections are available, but these steps may add considerably to computational time. An underestimated and as yet unsolved problem with GW-SNP data is that of data visualization, particularly integration of results with current genomic data.Available tools for data management and analysis of GW-SNP data are currently scarce; however, a few exist or are under development, such as GERON Genotyping  are for: multiplication mutations across APP (351); CFH, complement factor H (3075), PRKN (5071); and multiplication mutations across SNCA (6622).The accession numbers from the Entrez Gene databank (


Caenorhabditis elegans all the way to humans. One problem with large deletions is the determination of the location of their breakpoints. This is exacerbated in the case of complex deficiencies that delete a region of the genome, while retaining some of the intervening sequence. Previous methods, using genetic complementation or cytology were hampered by low marker density and were consequently not very precise at positioning the breakpoints of complex deficiencies. The identification of increasing numbers of Single Nucleotide Polymorphisms (SNPs) has resulted in the use of these as genetic markers, and consequently in their utilization for defining the breakpoints of deletions using molecular biology methods.Genetic deletions or deficiencies have been used for gene mapping and discovery in various organisms, ranging from the nematode C. elegans. The technique uses a combination of genetic crosses and molecular biology to generate robust and highly reproducible results with strong internal controls when trying to determine the breakpoints of deficiencies. The combined use of this technique and standard genetic mapping allowed us to rapidly narrow down the region of interest in our attempts to clone a gene.Here, we show that SNPs can be used to help position the breakpoints of a complex deficiency in Unlike previous methods used to locate deficiency breakpoints, our technique has the advantage of not being limited by the amount of starting material. It also incorporates internal controls to eliminate false positives and negatives. The technique can also easily be adapted for use in other organisms in which both genetic deficiencies and SNPs are available, thereby aiding gene discovery in these other models. C. elegans to human beings [Drosophila melanogaster, deficiencies have been particularly useful for gene mapping, since the existence of polytene chromosomes and cytogenetics in this organism allows the actual visualization of the breakpoints of the deficiencies. In other organisms, however, mapping the breakpoints of deficiencies is not so straightforward. In C. elegans, for example, deficiencies are defined as deletion mutations that fail to complement multiple loci with the underlying assumption that the deletion would also remove the regions between these loci. Although this is generally true, deficiencies exist that are complex deletions, eliminating two distant loci, but retaining the intervening sequence . In fact, our searches on WormBase [C. elegans are of a complex nature. When we examined a random sampling of 20 deficiencies from WormBase [C. elegans might be complex. This, coupled with the relative scarcity of usable genetic markers can confound the interpretation of deficiency data.Chromosomal deletions  have been used to help narrow down the location of genes in organisms ranging from n beings -4. In the Figure . An examC. elegans, previous work [C. elegans embryo. Thus, from a plate of worms heterozygous for the deletion, one can pick individual dead eggs that have been laid, assuming that these must be homozygous for the deletion. One can then use PCR to test whether a particular region of interest is present in such samples, thereby determining the extent of the deletion. This method, which relies on a negative result , has several drawbacks: (a) The amount of starting material is restricted to a single, or few dead eggs. (b) Chitinase treatment is required to remove the egg shell. (c) False positives can result if the PCR merely fails to work properly on the limited sample material. (d) False negatives can result if an embryo dies for reasons other than that it was homozygous for the deletion.In order to address the problem of deletion breakpoint mapping in ous work  has atteAnother method that could be used to achieve the same result is Southern Blotting . HoweverC. elegans, CB4856, which is predicted to harbor about 1 SNP per kilobase of genomic sequence [C. elegans, thereby overcoming the limitations of using deficiencies in this model system. In fact, the C. elegans SNP database already contains about 6,000 confirmed and predicted SNPs between the N2 and CB4856 strains [In human research, taking advantage of the growing number of SNPs identified in the human genome, approaches are being developed to use SNPs to identify regions of loss of heterozygosity (LOH), and/or deletions in chromosomes . The avasequence ,10 when  strains , which c strains ,13, we espe-19 in C. elegans. Initial mapping put the gene within the interval deleted by the large deficiency, ozDf1 (spanning the region from +13.18 to +25.11 of chromosome V). Standard SNP mapping analysis [spe-19 within the region bounded by SNP M162 (map position +23) on the left and SNP ZC15 (map position +25) on the right . According to data from WormBase [ozDf2 (which deletes the region from +23.5 to +25.11 of chromosome V by genetic complementation tests). When we performed the genetic complementation test, we found, to our surprise, that ozDf2/spe-19 animals were fertile suggesting that ozDf2 does not delete spe-19. We therefore hypothesized that ozDf2 was a complex deficiency  sequence as well as CB4856 sequence , or whether both N2 and CB4856 sequence was present (indicating that the SNP region is not lost in the deletion being tested). In addition to the CB4856 strain which we have used, other wild isolates of C. elegans which harbour SNPs [We initially chose to use SNPs that caused an abrogation of a restriction enzyme recognition site in the CB4856 sequence, thereby eliminating any artefacts due to incomplete restriction enzyme digestion. However, by running a control reaction to ensure that enzyme digestion has progressed to completion, one could also use SNPs that cause the loss of a restriction enzyme recognition site in the N2 sequence. Additionally, this method allows the use of SNPs that are only different in sequence, causing no changes in restriction enzyme recognition sites. A simple sequencing reaction can be done to check whether the our SNPs  can alsoC. elegans, a similar approach can be applied in any organism where deficiencies/deletions exist and where SNP mapping is possible.While we have shown this method to work in the model system spe-19, ozDf2/dpy-21 par-4, N2 (the wild-type) and CB4856.Worms were grown and cultured according to standard protocols described elsewhere . The strnDf20, sDf10, mnDf16, nDf3, tDf1, mnDf1, ccDf1,eDf2, tDf5, ctDf2 and ctDf3. The complex deficiencies we found are: hDf10, hDf17, nDf19, nDf9, eDf18, qDf8, eDf3, maDf4 and nDf27.We looked at the complementation data for 20 deficiencies chosen at random. We ensured that deficiencies from all chromosomes were included in the analysis and that the deficiencies chosen had their left and right boundaries defined by cloned genes . We then looked at the complementation data and scored the deficiency as "complex" if at least one of the genes that were within the outer boundaries of the deficiency was complemented by the deficiency. While scoring the complex deficiencies, we made sure that the internal locus that was complemented was either cloned or had multiple, corroborating mapping data. If the deficiency failed to complement all the loci that were within the outer boundaries, it was scored as a simple deficiency. The deficiencies that we scored as simple are: spe-19 males are fertile, we mated ozDf2/dpy-21 par-4 with spe-19 males. Of the outcross F1 progeny, we would expect half to be of the genotype ozDf2/spe-19 and consequently, sterile. The other half would be fertile, spe-19/dpy-21 par-4 worms. However, all the F1 progeny were fertile, indicating that the deletion ozDf2 complemented spe-19, belying our expectations. The presence of the deletion and of spe-19 was confirmed by looking at the F2 progeny. Half the F1 progeny segregated wild-type animals, dead eggs and sterile worms, indicating that their genotype must be ozDf2/spe-19. Thus, ozDf2 complements spe-19.Since ozDf2/dpy-21 par-4 hermaphrodites to CB4856 males. These ozDf2/dpy-21 par-4 heterozygotes are wild-type, but ozDf2 homozygous animals are embryonic lethal and dpy-21 par-4 homozygotes are short and fat – a phenotype referred to as Dumpy, or Dpy. F1 animals that segregated Dpy progeny were discarded (these would have been dpy-21 par-4/CB4856), and only the remaining, heterozygous animals  were used to set up lines that were further analyzed for their SNP sequences  and the reverse primer (GTCTCAATTTGTGAGCGCATGTC).SNP F38A6:14347 – The expected product size is 961 bp using the forward primer (TGGTTCCCCTCTACCAGATGCC) and the reverse primer (CCAACACAACTCAATCTAATGTTTACC).ozDf2/CB4856 lines using the following PCR conditions: denature at 94°C for 30 seconds, anneal at 60°C for one minute, extend at 72°C for 1 minute and repeat for 30 cycles. The PCR product was then digested with an appropriate restriction enzyme, and the products analysed on a 1.5% agarose gel run using the SB buffer. For SNP Y113G7A:29, XmnI was used to digest the PCR product and for SNP F38A6:14347, DraI was used.We used these primers to amplify the corresponding product from each of the three genomic DNA preparations of the PK conceived of using SNPs to analyse deletion breakpoints, carried out the SNP analysis and drafted the manuscript. All of the genetic complementation mapping was carried out by BG. MH aided with the molecular biology. AS participated in designing the experiments and in their coordination and helped to draft the manuscript. All work was conducted in the laboratory of AS.


Systematic evaluation and study of single nucleotide polymorphisms (SNPs) made possible by high throughput genotyping technologies and bioinformatics promises to provide breakthroughs in the understanding of complex diseases. Understanding how the millions of SNPs in the human genome are involved in conferring susceptibility or resistance to disease, or in rendering a drug efficacious or toxic in the individual is a major goal of the relatively new fields of pharmacogenomics. Esophageal squamous cell carcinoma is a high-mortality cancer with complex etiology and progression involving both genetic and environmental factors. We examined the association between esophageal cancer risk and patterns of 61 SNPs in a case-control study for a population from Shanxi Province in North Central China that has among the highest rates of esophageal squamous cell carcinoma in the world.High-throughput Masscode mass spectrometry genotyping was done on genomic DNA from 574 individuals (394 cases and 180 age-frequency matched controls). SNPs were chosen from among genes involving DNA repair enzymes, and Phase I and Phase II enzymes. We developed a novel adaptation of the Decision Forest pattern recognition method named Decision Forest for SNPs (DF-SNPs). The method was designated to analyze the SNP data. The classifier in separating the cases from the controls developed with DF-SNPs gave concordance, sensitivity and specificity, of 94.7%, 99.0% and 85.1%, respectively; suggesting its usefulness for hypothesizing what SNPs or combinations of SNPs could be involved in susceptibility to esophageal cancer. Importantly, the DF-SNPs algorithm incorporated a randomization test for assessing the relevance (or importance) of individual SNPs, SNP types  and patterns of SNP types (SNP patterns) that differentiate cases from controls. For example, we found that the different genotypes of SNP GADD45B E1122 are all associated with cancer risk.The DF-SNPs method can be used to differentiate esophageal squamous cell carcinoma cases from controls based on individual SNPs, SNP types and SNP patterns. The method could be useful to identify potential biomarkers from the SNP data and complement existing methods for genotype analyses. The cause and progression of human diseases such as Alzheimer's disease, cancer and diabetes are likely influenced by complex interactions of multiple genes as well as environmental and lifestyle factors that are sensitive to genome variability. Single nucleotide polymorphisms (SNPs) are the most prevalent form of DNA variation in the human genome occurring about once per 100 to 300 bases [Therefore, the identification of particular SNP patterns that are associated with susceptibility to disease or adverse drug reactions is a paramount goal of pharmacogenomics research. Given recent development of high-throughput technologies for rapid genotyping, assessment of SNP patterns holds much promise for use in diagnosis, prognosis and selection of treatment intervention. An essential bioinformatics challenge in pharmacogenomics is the discovery of SNP patterns that differentiate diseased and healthy populations.Determination of the SNP patterns associated with disease susceptibility or adverse drug reaction from among potentially millions of SNPs is a challenge for pharmacogenomics. Many methods have been described in the literature to assess the association between SNPs and disease -5. Most Esophageal cancer, like many other cancers, has been shown to be associated with genetic as well as environmental factors that cause DNA damage. It is the sixth leading cause of cancer worldwide and seventh among American men. Among the two main types of esophageal cancer, squamous cell carcinoma and adenocarcinoma, squamous cell carcinoma accounts for about half of all esophageal cancers. Data from studies in animals suggest that oxidative damage from factors such as smoking or gastroesophageal reflux, which cause inflammation, esophagitis, and increased cell turnover, may initiate the carcinogenic process ,10. StudWe investigated the association of SNPs and squamous cell carcinoma of the esophagus in a case-control study of individuals from Shanxi province, a region in north-central China. Shanxi has one of the highest esophageal cancer rates in the world. The SNPs chosen for the study were a set of those associated with DNA repair, Phase I and Phase II enzymes involved in xenobiotic clearance, and with alcohol metabolism. We developed a novel adaptation of the Decision Forest pattern recognition method named Decision Forest for SNPs (DF-SNPs). The method was designated to analyze the SNPs-disease association based on the SNP data. Importantly, the DF-SNPs method utilizes the inherent differentiating ability of decision trees to separate disease and control population based on individual SNPs, the SNP types, as well as combinations of SNP types, that is, SNP patterns.Incident cases of esophageal cancer were obtained from an ongoing case-control study being conducted by the National Cancer Institute, USA and the Shanxi Cancer Institute, China. Esophageal cancer patients at the Shanxi Cancer Hospital in Taiyuan, Shanxi Province, were recruited to the case-control study. Esophageal cancer was confirmed by the pathologists at the Shanxi Cancer Hospital and National Cancer Institute and all cases were esophageal squamous cell carcinoma (ESCC). Controls matched on age, gender and neighbourhood were selected for each case. The study was approved by the Institutional Review Boards of the Shanxi Cancer Hospital and the US National Cancer Institute. After signed consent was obtained, a blood sample was collected from the participants and information on demographics and cancer risk factors including smoking, alcohol, diet, and family history were collected in an interview.. All laboratory personnel were blinded to case-control status. A total of 63 SNPs were chosen from DNA repair, Phase I, Phase II, and Alcohol metabolism related genes. The average call rate for the study was 98.5%, and duplicate analysis of three of the SNPs generated 99.7%, 99.8%, and 100% concordance. The prevalence of the variant allele ranged from 5.2% to 49.4%.DNA samples were genotyped at a commercial laboratory  by Masscode mass spectrometry genotyping. PCR primers used for genotyping were synthesized at BioServe. Oligonucleotide sequences of the primers probe can be found at DF-SNPs is an ensemble classification method that combines multiple decision trees to derive a classifier based on a fitted set of if-then rules. By combining multiple heterogeneous decision trees, DF-SNPs is effective in mitigating noise that is often prevalent in biological data, especially data from high throughput technologies, compared to single decision trees. Moreover, the algorithm is computationally inexpensive, enabling cross validation and randomization tests to readily be included. Figure It is common that the SNP types for some individuals are inconclusive using most high-throughput genotyping methods, including the Masscode mass spectrometry genotyping method. This results a data set (a spreadsheet with samples in row and SNP variables in column) that usually contains many missing values (i.e. many empty cells in the spreadsheet). Accordingly, a data pre-processing procedure is required to impute the missing data for subsequent analysis. A two-steps data pre-processing procedure was implemented in DF-SNPs. First, the samples (rows) with > 15% missing genotypes (empty cells) across all SNP variables (columns) and the SNP variables (columns) with > 15% missing genotypes (empty cells) across all the samples (rows) were removed. Next, a 10-nearest neighbor method was employed to impute the missing data. In this method, if a sample has a missing value (an empty cell) that is corresponding to a SNP variable, we identified 10 samples that not only had a measure for this SNP but also had the closest SNP profiles calculated based on the rest of the SNP variables. The genotypes of these 10 samples were used to impute the missing value by voting.There were 1042 missing genotypes in the data set . Two SNP variables (two columns with >19% empty cells or missing genotypes) and eight samples (eight rows with >28% empty cells or missing genotypes) were removed, which resulting 1.3% missing value in the data set for imputing. The final data set for analysis after pre-processing contained 566 individuals and 61 SNPs, 391 cancer cases and 175 controls.1 = heterozygous, to put 70 samples in the right node (the samples with the heterozygous genotype) and 30 samples in the left node (the samples with the non-heterozygous genotype). The cases are enriched in the right node (40 to 30) compared to its parent node while the controls are enriched in the left node. In the end of tree development, the cases and controls are enriched in the different terminal nodes.A tree was developed using the S-Plus binary split method, where tIn our previous application, multiple trees in DF used distinct independent variables to maximize their difference; the varIf we generate many classification models using a bootstrapping method, the relevance (or importance) of a SNP, SNP type or SNP pattern should be directly correlate to the number of times they are used by the models. Based on this assumption, we performed 2000 runs of 10-fold cross-validation and calculated the frequencies of each SNP, SNP type and SNP pattern appeared in this process. To determine the statistical significance of the findings, we also generated a null hypothesis using the same statistical procedure. This was a randomization test, where the sample classification (case or control) was randomly scrambled to generate 2000 pseudo data sets and the 10-fold cross-validation was then applied to each pseudo data set. Thus, null distributions were generated for each SNP, SNP type and SNP pattern. We then determined the critical values that corresponded to the 5% level of significance for SNPs, SNP types and SNP patterns, respectively. The statistically significant SNPs, SNP types and SNP patterns were these whose frequencies were greater than their corresponding critical values.The study population comprised 574 individuals genotyped for 63 SNPs, of which 394 were esophageal cancer patients and 180 were age-frequencies matched controls. After removing individuals for which data was missing for more than 15% of genotypes, and removing SNP variables that were missing data for more than 15% of the individuals, the data was reduced to 566 individuals (391 cases and 175 controls) and 61 SNP variables.This is a binary classification problem. The SNPs are the independent variables grouped into three genotype categories: homozygous common, heterozygous and homozygous variant. Using the DF-SNPs method, we developed a classification model to differentiate the cases from the controls. The fitted binary decision forest model thus derived contained 10 decision trees and exhibited high concordance (94.7%), sensitivity (99.0%) and specificity (85.1%), indicating that the model well differentiates disease from control samples. Figure The DF-SNPs algorithm includes functions that estimate on a relative basis the statistical significance of individual SNPs, SNP types and SNP patterns in differentiating SNP case-control study data. The rational behind this approach is that the frequency of a particular SNP, SNP type or SNP pattern selected by the model correlates positively with the relevance (or importance) to discriminate the cases from controls. The frequency was obtained from a multiple runs of 10-fold cross-validation procedure. To determine the statistical significance of the disease-related SNPs, SNP types and SNP patterns, a null hypothesis was first generated where the scrambled SNP data set was also subjected to the same multiple runs of 10-fold cross-validation (randomization test). Then, the frequency based on the real data set was compared with the null hypothesis. The purpose of this statistical test is to determine whether the obtained results  reject the hypothesis that they are merely a product of chance factors. The results of this investigation are described in the following sections.i (Freq(SNPi)) is computed as:In this section, we investigated the association of individual SNPs with the cancer. The SNPs were ranked according to frequency of use in tree node splitting in 2000 runs of 10-fold cross-validation. The ranking frequency for SNP SNPi = 1 means that SNP i was used as a split rule in tree k at level l  is calculated over all trees in the forest models in 2000 runs of 10-fold cross-validation. In this equation, SNPs at each lower node level are given half the frequency weight as SNPs at the preceding higher level.where l Figure . Freq(SNFreq(SNPi) larger than 0.028, indicating their relevance to the esophageal cancer with P < 0.05  with the cancer. In a tree, the classification of a sample is determined by only one terminal node that is descendent from the root node through a set of "IF-THEN" rules based on s Figure . A SNP pn = 20. In general, the number of SNP patterns versus n is a distribution with fewer SNPs when n is either smaller or larger. When n is small, the number of possible SNP combinations is small. When n is large, it is likely that patterns contain the same SNPs, since the pattern does not depend on the order of SNP selection. The second column lists all possible SNP patterns for each n-SNP pattern. The last column gives the critical value, which corresponds to the 5% probability that a pattern's frequency could occur by chance. The third column gives the number of SNP patterns that occur with frequency above the critical value, that is, the number of SNP patterns is above the critical value with 95% confidence of statistical significance. The number of significant SNP patterns is markedly reduced compared with the number of possible SNP patterns.Table We also evaluated the odds ratio and its 95% confidence interval for each n-SNP pattern, which gives an estimate of how much more likely it is that an individual with a particular SNP pattern is to be a cancer case than a control case. Results are given in Table We developed a novel statistical approach, DF-SNPs, that was used for an association study between SNP type data and a case/control study of esophageal cancer. Using DF-SNPs, we identified a list of SNPs, SNP types and SNP patterns that might be associated with esophageal squamous cell carcinoma. This approach could be useful for identification of potential biomarkers based on SNP data.We have successfully developed and used the DF method for various applications, including structure-activity relationship studies, microarray data analyses and proteomics data analyses -19. UnliThere are two important considerations for the use of DF-SNPs when compared with alternative classifier methods. First, combining identical or similar trees will not improve the quality of the forest derived from these trees and the benefit in combination can only be realized when individual trees are different or heterogeneous. Thus, each tree in DF-SNPs uses a distinct SNP type for splitting the root node, ensuring that each tree is different and encodes a different aspect of the disease-SNP association. Secondly, the individual trees of similar quality  when combined may cancel some of the random noise inherent in SNP type and case-control data.The Masscode mass spectrometry-based genotyping method resulted in 3–5% missing genotypes. How to appropriately impute the missing value is important for subsequent analysis of the data generated from this technology. Accordingly, a two-step imputing method was embedded in DF-SNPs. First, we removed the individuals for whom most genotype data were missing, as well as removed SNP variables that were not detected in many individuals. Then we imputed the missing SNP genotypes for each remaining individual using a 10 nearest neighbor method. This approach proved to be efficient for preprocessing the SNPs data set.In DF-SNPs, the potential cancer-related SNPs, SNP types and SNP patterns were identified on the basis of frequencies of occurrence in decision tree splitting for all trees during 10-fold cross-validation. A randomization test was also done with cross-validation to provide a random distribution of frequencies for comparison with the fitted model. Comparison of the fitted and random frequencies provided the estimates of the statistical significance of SNPs, SNP types and SNP patterns in distinguishing cases versus controlsTo investigate the relevant SNPs to the esophageal squamous cell carcinoma, we employed a weighted approach to calculate the frequency of each SNP. Given the fact that the SNPs used for splitting the root node are applied to the entire data set while those used in the next split at the second level are applied to a much smaller portion of the data set , and that subsequent splits are applied to even smaller numbers, the relevance of the SNPs to cancer should decrease proportionally to the height of the tree level where they were selected. We compared several weighted factors by taking into account of the tree level to calculate the frequency of SNPs, including 1, 1.25, 1.5 and 2. Since other weighted factors potentially eliminated the SNPs used in the root node (results not shown), the weighted factor of 2 was selected, indicating that the relevance (or importance) of a SNP is reduced by half as moves to each subsequent lower level.The odds ratios and corresponding confidence intervals were used to identify 14 SNP types that distinguish cases from controls at 95% confidence Table . Of thesProspectively, given appropriate and sufficient data, DF-SNPs provides a methodology that could identify the possible SNP-SNP associations, that is, SNP patterns involved in genetic-based variation in cancer risk. Table Several statistical approaches including logistic regression methods have been used to analyze case/control SNP data. In this article, we propose DF-SNPs as method to analyze SNPs data for purposes of biomarker identification. DF-SNPs is a novel variant of DF that was previously developed in our lab. DF-SNPs was specifically structured to deal with the three genotype categories of SNP data. The DF-SNPs algorithm incorporates the following processes: (1) a two-step approach to impute missing SNPs; (2) use of 10-fold cross-validation when calculating frequency of SNPs, SNP types and SNP patterns in discriminating cases from controls; and (3) estimating statistical significance by comparing frequencies from (2) with those from a random test also using 10-fold cross validation. Using DF-SNPs, potential biomarkers could be quickly identified based on SNPs, SNP types or SNP patterns. This method complements other methods currently in use.QX developed the method presented in the paper and wrote the first draft manuscript. WT guided the method development and helped writing the manuscript. HH developed the missing data imputing method and also involved the DF-SNPs development. LR generated the SNP data set used in this study. RP helped writing the manuscript. LR generated the SNP data set used in this study. ZZT, NH and PRT conducted the case-control study. All authors read and approved the final manuscript.


Genotyping technology has advanced such that genome-wide association studies of complex diseases based upon dense marker maps are now technically feasible. However, the cost of such projects remains high. Pooled DNA genotyping offers the possibility of applying the same technologies at a fraction of the cost, and there is some evidence that certain ultra-high throughput platforms also perform with an acceptable accuracy. However, thus far, this conclusion is based upon published data concerning only a small number of SNPs.In the current study we prepared DNA pools from the parents and from the offspring of 30 parent-child trios that have been extensively genotyped by the HapMap project. We analysed the two pools with Affymetrix 10 K Xba 142 2.0 Arrays. The availability of the HapMap data allowed us to validate the performance of 6843 SNPs for which we had both complete individual and pooled genotyping data. Pooled analyses averaged over 5–6 microarrays resulted in highly reproducible results. Moreover, the accuracy of estimating differences in allele frequency between pools using this ultra-high throughput system was comparable with previous reports of pooling based upon lower throughput platforms, with an average error for the predicted allelic frequencies differences between the two pools of 1.37% and with 95% of SNPs showing an error of < 3.2%.Genotyping thousands of SNPs with DNA pooling using Affymetrix microarrays produces highly accurate results and can be used for genome-wide association studies. Single nucleotide polymorphisms (SNPs) are the most abundant type of polymorphism in the human genome. With the parallel developments of dense SNP marker maps and technologies for high-throughput SNP genotyping, SNPs have become the markers of choice for genetic association studies. The use of dense but incomplete maps of SNP markers for genetic association is based upon the premise that low penetrance but fairly common disease variants can be detected by virtue of indirect association between SNP markers and disease status. As a general rule, the denser the map of markers used, the greater the probability that at least one marker will be in strong linkage disequilibrium (LD) with a disease susceptibility allele, and therefore indirect association between marker and disease will be detected .With the development of genotyping platforms that permit analysis of several hundreds of thousands of markers, it is now possible to apply this principle of indirect association to the whole genome rather than just candidate genes or candidate linkage regions. For example Affymetrix , recently released microarrays that can interrogate ~500,000 SNPs, and Illumina  released in January 2006 the Sentrix(r) HumanHap300 Genotyping BeadChip which can genotype 317,504 high-value SNP loci derived principally from tag SNPs. Theoretical predictions . Give. Give-7 One way to reduce the cost is to undertake quantitative analyses of allele frequencies in DNA pools, a process often referred to as 'DNA pooling' ,8. Here,Several groups have begun to apply pooled genotyping to the new ultra-high throughput genotyping technologies. Butcher et al, 2004  and MeabAlthough these studies give cause for optimism, it is clear that the validity of pooled genotyping using array technology has not been proven for a sufficiently large number of SNPs to allow researchers to apply the method with confidence. In this paper, we have undertaken a more comprehensive analysis of the accuracy of microarray-based pooling experiments. Rather than examine a small selection of SNPs, we examined 6843 fully informative SNPs out of a total of 10,204 SNPs represented on the Affymetrix 10 K Xba 142 2.0 array. Our results suggest that pooled genotyping using Affymetrix arrays is as accurate as that obtained with lower throughput platforms, and that it can be performed instead of individual genotyping with only a minimal loss of power.r = 0.974 to 0.986. The correlations between sense only analyses and between antisense only analyses were virtually identical.To estimate allele frequencies in pooled DNA samples, we used the Relative Allele Signal (RAS) scores given in the output of the Affymetrix GeneChip DNA Analysis Software (GDAS). RAS scores are produced separately for the sense and antisense strand for each SNP and can be analysed separately, or can be averaged. The test-retest estimates of allele frequency in pools were high for duplicate experiments. This is illustrated in Figure r = 0.985–0.992. The correlation continued to improve when data from replicate arrays were included. With a maximum of 6 arrays performed on a single  sample, our data allow us to compare the composite data from 3 arrays with what should be identical data from an independent set of the other 3 arrays. As each array has sense and antisense data, we have a total of 6 observations per pool. Even at this fairly modest degree of replication, very high reproducibility was obtained, with an r = 0.996. Equally important, the bounded zone containing 95% of the data is much narrower  the allele frequencies we estimated from the pooled analyses correlated well with the true frequencies derived for each sample from the HapMap (r = 0.959 for the parents and 0.961 for the offspring). The data for the offspring sample are shown in Figure We averaged the RAS values (combining sense and antisense strands) from the five replicate measures of the offspring pool and the six replicate measures of the parental pool. The true allele frequencies in the parental and the offspring samples were calculated from the HapMap genotype database. Without correction with per se. The true allele frequency differences between parents and offspring were calculated from the HapMap data and compared with the allele frequency differences predicted from the pooled analyses. The results  are presented in Figure While the correlation is high, the spread of the data does not allow confidence that any single allele frequency can be accurately predicted. However the main aim of pooled analysis is to predict differences in frequencies between pools rather than the absolute allele frequencies We estimated how the distribution of the error in pooled analysis varies with attempts to reduce measurement error through repeat measurement. The results are presented in Figure k, a correction factor often used in pooling experiments to correct the data for any unequal efficiencies in representing alleles [r = 0.997) and also reduces the spread of the data  for the use in other pools. For technical reasons which are entirely understandable, this usually occurs for low frequency SNPs. Consider a putative SNP that is actually non-polymorphic . RAS scores are seldom exactly zero. The result is that k reaches 0,  depending upon which allele is arbitrarily designated allele A (see Methods). Since the use of inappropriate values for k markedly affects the type I and type II errors where either the true allele frequencies are very low and/or the correct k values extreme [k is small or large may not be reliable.We performed several sets of corrections to see if our results can be improved. First we applied  alleles   and re-examined the distribution of errors. This procedure had little impact on the error in estimating differences between pools, with no change in the mean error (data not shown). This is not surprising since this procedure affected only SNPs with very small minor allele frequencies (mostly non-polymorphic SNPs) which cannot reach big differences between the pools used in our experiment. Correction with k is likely however to a have a substantial effect in true case-control association studies, where a small difference in the frequencies of rare alleles can easily result in significant p-values. We therefore discarded 286 SNPs whose values of We also sought to identify poorly performing SNPs based upon large test-retest variation between arrays. Within each pool, we measured the difference between the highest and lowest RAS value for each SNP produced by the replicate arrays. We term this difference the "maximum variability of the results". Just over 5% of SNPs showed a maximum variability of >25% between the lowest and highest signal of any array. Given that SNPs which show a higher degree of variability are likely to produce less reliable results, we removed these 341 SNPs. This correction did not change substantially the error in estimating differences between pools.r = 0.996  and six (parent) arrays as artificial case and control pools, the system performed well, with a mean error of just 1.37% which is comparable with other commonly used lower throughput methods [Pooled analysis yielded accurate estimates of the k has been shown to improve both type I and type II errors in DNA pooling experiments [k. The improvement in estimating true allele frequency is in fact better than is apparent from Figure k is derived from parental data (see methods) and then applied to the data obtained for children (or vice versa). Therefore any errors in estimating the parental allele frequencies are incorporated in the estimate of k with the result that the estimates of allele frequencies in offspring include the measurement errors from both samples.There are many reasons why alleles might be unequally represented even when present in equimolar amounts ,19. For eriments ,18,19. Tk is required, the solution until now has been to derive k from the ratio of the intensities (or whatever other measures are appropriate) of the signals representing each allele specific products from heterozygous individuals. To this aim, Simpson et al, [Where the application of n et al,  have reck varies with laboratory practice, the greatest accuracy will be achieved if each group constructs their own pools of CEPH individuals (or pools from reference panels from other ethnic groups if they are working with other ethnic groups) and then conducts their own array replicates  to derive their own laboratory specific k values as described in the Methods section. It should be noted that k corrects for technical artefacts in allele representation rather than population specific differences in allele frequency and that the k values derived in one sample are applicable to any other sample regardless of differences in allele frequency. However, the use of the most similar ethnic group represented in the HapMap to those comprising the main focus of research within a lab does have the advantage that k values for any population-specific SNPs can be derived (some SNPs are non-polymorphic in some populations).Under the (unproven) assumption that to some extent, the value of k values will be modest and in most cases insufficient to be a significant source of error [k values for the two 250 K arrays on our institutions website, and/or provide them to researchers upon request.However, it may well be the case that with the use of the highly standardised operating procedures which are always used for the work with Affymetrix arrays, inter-laboratory of error ,18. This-7 . In our sample, 276 SNPs have true allele frequency differences >8% between parents and offspring. If we set as our target to individually genotype all SNPs which in pools showed an 8% difference, we would end up genotyping 286 SNPs which include 54% of the 276 SNPs with true 8% allele frequency differences . Thus, by undertaking the pooled experiment, we would have identified 54% of the target loci (frequency difference 8%) and all 10 best loci, but at the cost of genotyping only a very small proportion of the SNPs.In terms of practical utility, our results indicate that moderate differences in allele frequency should be easily detected by pooled analysis followed by a very limited amount of individual genotyping, thereby greatly enhancing the cost-efficiency of the study. As an example, let us assume we are interested in detecting an unknown SNP which has a frequency of 30% in the 1000 controls and 38% in 1000 cases. This scenario corresponds to an allele with an odds ratio of 1.4 and an association which surpasses our approximate genome-wide threshold for significance of p = 10k, our correct discovery rate remained similar at 50% (we would have discovered correctly 153 SNPs by genotyping 306 SNPs). However, most designs aim to follow up the results surpassing a given threshold of statistical significance. For a given sample size, the calculated statistical significance depends not just on the magnitude of the allele frequency difference between samples but also on the allele frequency. Our data concerning corrected and uncorrected data . Each SNP is interrogated by 40 features on the 10 K array but by only 24 features on the 250 K array . This reduction in the number of features per SNP, as well as the reduction of the feature size from 8 to 5 microns, may reduce information content. This suggests that more replicate arrays will be needed to achieve accuracy and reproducibility equivalent to that reported in the present study. A slight problem is created by the fact that for the 250 K arrays the Affymetrix software does not calculate automatically RAS scores. However, these can easily be calculated from the intensity values reported for each array feature, using the algorithms described by Liu et al, .-7), a result that has been replicated since. Yamazaki et al, [-14 in a large replication sample. Several more studies on a variety of phenotypes have been performed but have not been fully published yet. Summaries of such studies on multiple sclerosis and cardiovascular disease using 100,000 SNP, and Graft-Versus-Host disease using 500,000 SNPs are available in the Affymetrix Microarray Bulletin of April 2005 [So far there have been only a few published fairly high density genome-wide association studies and these have so far been based on around 100,000 SNPs. Klein et al,  genotypei et al,  genotyperil 2005 . While tk. Instead of deriving k from the ratio of signals in heterozygous individuals, we suggest deriving it from pooling data obtained from samples of reference individuals from whom DNA and vast quantities of genome-wide genotype data are available through cell repositories and the HapMap respectively. The cost-efficiency of DNA pooling on arrays should enable even small laboratories to contribute to genome-wide association studies.When performed on Affymetrix SNP genotyping arrays, DNA pooling provides a fairly accurate method for identifying allele frequency differences between samples, with a mean error of 1.37%. In order to minimise measurement error, the final data should be based upon composite scores from 4–5 replicates for 10 K arrays, but this number will probably need to be increased for 500 K arrays, or where smaller differences in allele frequency are required. While not essential for measuring differences in allele frequencies between samples, to obtain estimates of the statistical significance of those differences, the data should be corrected for unequal representation of the two alleles using the coefficient We obtained DNA samples from 30 anonymous CEPH trios  from The Human Genetic Cell Repository at the Coriell Institute for Medical Research . These aGenotyping with the Affymertix 10 K Xba 142 2.0 Array was performed at the MRC Rosalind Franklin Centre for Genomics Research, Wellcome Trust Genome Campus, Cambridge, UK using the standard protocol recommended by the manufacturer, with no special modification. Briefly, 250 ng of genomic DNA per array were digested with a restriction enzyme (Xba I) and ligated to adapters that recognise the cohesive four base-pair overhangs. A generic primer that recognises the adapter sequence was then used to amplify the adapter-ligated fragments in a PCR reaction. The amplified DNA was then fragmented, labelled and hybridised to the array. The Affymetrix GeneChip Operating Software (GCOS) collected and extracted feature data from the scanner, which was then analysed with the Affymetrix GeneChip DNA Analysis Software (GDAS). We performed 5 replicates (5 arrays) of the offspring pool and 6 replicates of the parent pool. The researcher performing the hybridisation and scanning of the chips was not informed of the details of our experiment.Each Affymetrix 10 K array includes more than 420,000 features, each consisting of over one million copies of a 25 bp oligonucleotide probe of a defined sequence synthesized by photolithographic manufacturing . AlthougTo estimate the accuracy of the pooled analysis, we compared our estimations with the true allele frequency differences between parents and offspring based upon the genotypic data available from HapMap. From the 10204 SNPs represented on the array, we first excluded 172 with no given chromosomal location, followed by 1780 SNPs that had not been genotyped by the HapMap project at the time we completed our analysis. We then excluded 1242 SNPs which had one or more individuals with missing HapMap genotypes because given the small sample sizes of our pools, data from even a single individual in the case of children contributes 0.033 to the estimated allele frequency, which is above the margin of error that we were hoping to achieve. Finally we excluded the remaining 167 SNPs on the X-chromosome because with respect to this chromosome, males and females do not contribute equimolar amounts of DNA to the pools. This left 6843 fully informative SNPs suitable for analysis.k) is usually estimated asIn pooling experiments it is generally customary to normalise the data by accounting for inequalities in the representation of each allele ,26,27. Sk = hA/hB     (1)hA and hB are the measurements representing alleles A and B in heterozygous individuals, for example peak heights or signal intensities. This ratio is then used to normalize the data from pools in order to calculate fA :where HA and HB are the intensities of allele A and B in the pool. In the current experiment we know the exact allele frequency for each SNP from the HapMap data, therefore we can estimate the correction coefficient without the need to observe heterozygous individuals. For this purpose we first express k from formula (2):where fA is the true frequency of allele B, (we denote it fB), we can simplify this further:Since 1 - k in any pooling experiment for which we know the true allele frequencies without the need to observe heterozygous individuals. Indeed, for a heterozygous individual, the true ratio of the allele frequencies fB/fA of alleles A and B equals to one and therefore the formula above simplifies to k from the observation of a heterozygous individual.All values on the right-hand side of formula (3) are known, so we can estimate The situation in DNA pooling with Affymetrix arrays is only slightly different, as the RAS score is not just the ratio of the intensities for alleles A and B, but it is also corrected for the non-specific hybridisation (the mismatch intensity). The simplified formula of RAS is the median RAS of all quartets on one strand and approximates to:PMA is the intensity of the perfect match for allele A, PMB is the intensity of the perfect match for allele B and MM is the mean of the two mismatches [fB = 1 - fA and HB = 1 - HA, and therefore formula (3) can be re-written aswhere smatches . The fulHA by RAS):Now we can use the RAS score as the measure of the intensity of allele A (i.e. substitute k is in fact the correct value of k for each SNP observed in our experiment and it does not require the observation of heterozygous individuals.The resulting value for This procedure inevitably results in the correct estimation of parental allele frequencies but exaggerates the error in estimating allele frequency in the offspring pools as this contains the error from both samples. It does not however result in any bias in estimating the performance of the pooled assay in determining the difference in allele frequencies between pools. The accuracy of that prediction, when compared with the true difference is the main outcome in our study.GK and MCO'D conceived of and designed the studyGK performed most of the analysis, contributed to interpretation of the data, and took the lead in drafting the manuscriptIN performed the bioinformatics work, most importantly deriving the correct allele frequencies for all SNPs from the HapMap databaseLG constructed the DNA poolsVM performed the data correctionsMJO and MCO'D contributed to interpretation of the data and to the writing of the manuscript.


Multiplex PCR is a key technology for detecting infectious microorganisms, whole-genome sequencing, forensic analysis, and for enabling flexible yet low-cost genotyping. However, the design of a multiplex PCR assays requires the consideration of multiple competing objectives and physical constraints, and extensive computational analysis must be performed in order to identify the possible formation of primer-dimers that can negatively impact product yield.This paper examines the computational design limits of multiplex PCR in the context of SNP genotyping and examines tradeoffs associated with several key design factors including multiplexing level (the number of primer pairs per tube), coverage , and tube-size uniformity. We also examine how design performance depends on the total number of available SNPs from which to choose, and primer stringency criterial. We show that finding high-multiplexing/high-coverage designs is subject to a computational phase transition, becoming dramatically more difficult when the probability of primer pair interaction exceeds a critical threshold. The precise location of this critical transition point depends on the number of available SNPs and the level of multiplexing required. We also demonstrate how coverage performance is impacted by the number of available snps, primer selection criteria, and target multiplexing levels.The presence of a phase transition suggests limits to scaling Multiplex PCR performance for high-throughput genomics applications. Achieving broad SNP coverage rapidly transitions from being very easy to very hard as the target multiplexing level (# of primer pairs per tube) increases. The onset of a phase transition can be "delayed" by having a larger pool of SNPs, or loosening primer selection constraints so as to increase the number of candidate primer pairs per SNP, though the latter may produce other adverse effects. The resulting design performance tradeoffs define a benchmark that can serve as the basis for comparing competing multiplex PCR design optimization algorithms and can also provide general rules-of-thumb to experimentalists seeking to understand the performance limits of standard multiplex PCR. The PCR (Polymerase Chain Reaction) method of DNA amplification has had a profound impact on biotechnology and biological research. Multiplex PCR is an extension of the standard PCR protocol in which multiple loci are amplified simultaneously in order to save time, improve throughput, and reduce the total cost of reagents. Applications for PCR and Multiplex PCR abound including quantitative gene expression -4, haploMultiplex PCR has recently emerged as a core enabling technology for high-throughput SNP genotyping -16, and 4-106) SNPs, achieving high (>95%) coverage becomes obviously more important when the focus of investigation has been narrowed to a relatively small (102-103) set of SNPs each of which is suspected of having some biological or pharmacological impact.Multiplex PCR assay design is a multi-objective optimization problem involving intrinsic performance tradeoffs. The key objectives we consider in this paper include the number of SNPs per tube (multiplex level) and the percentage of SNPs assigned to full tubes (coverage). We further require that all resulting tubes achieve uniform levels of multiplexing with the idea that doing so facilitates automation in a high-throughput environment. While lower coverage may be acceptable in initial survey studies involving many . We further quantify design performance tradeoffs using two best-fit tube assignment algorithms on human SNP data.O(log NS). Unfortunately the coverage drops dramatically if the multiplex level is increased.  we find that our ability to achieve high (>95%) coverage for randomly generated multi-node graphs critically depends on the compatibility probability, P, (or conversely the interaction probability (1-P)) as well as the target level of multiplexing. These results are presented in Figure In recent years, it has been shown that for broad classes of computationally intractable problems, there exist certain phase-transition boundaries across which the nature of the solutions and the computational effort needed to identify a solution changes dramatically . When atNext we implemented two multiplex PCR assay design algorithms and applied them to real SNP data obtained from the dbSNP database. We prescreened the 84,393 chromosome 21 SNPs contained in build 116 of dbSNP  for clasMethods for complete details. While best fit algorithms are relatively simple, one can actually show theoretically that these results appear to be as good as expected (on average) in graphs with this level of density. One version which we call "Fixed-Assignment Best Fit" assigns SNPs in random order to the fullest compatible tube, and as the name suggests, once a SNP is assigned to a tube it is fixed. Neither its assigned tube nor its associated primers are ever modified. If no compatible tube can be found, the SNP is left unassigned, reducing total coverage. We considered a second variation on the best-fit approach called "Flexible Assignment Best Fit" in which SNPs already assigned to a tube can be removed under special conditions in order to accommodate a new SNP assignment. Special rules of the algorithm guarantee that the algorithm will eventually terminate with increasingly high probability. Figure Our two best-fit greedy algorithms are designed to simultaneously assign primer candidates to SNPs and to partition SNPs into individual tubes in an effort to maximize both multiplexing level and coverage. See Next we employed the fixed-assignment best-fit algorithm to generate coverage curves for target multiplexing levels M = 10, 20, 30 while varying numbers of SNPs. We considered SNP sets containing between 100 and 1200 SNPs. Figure There is extensive literature on the general principles of PCR primer design -31. ThisThe application of Multiplex PCR has increased steadily over the past decade, requiring more sophisticated primer selection protocols. Different algorithms may favor particular objectives, or may be designed for particular technology platforms. In general, the problem of identifying primer pairs to maximize the multiplexing level of a single assay has been shown to be NP-complete by Nicodeme and Steyaert  who alsoWhereas this paper focuses on the dual problem of assigning primers and partitioning SNPs into multiplex-compatible tubes, an entirely different multiplex PCR problem is concerned with finding a minimal number of primers necessary to amplify a maximum number of targets over a single experiment  or over Our best fit approach is motivated by the theoretical analysis provided by Alon and Furedi  who show1. For a multi-node graph with N nodes and S states per node, we create a corresponding standard graph with NS nodes. (Each state in the multi-node graph is a unique node.)2 S2 P) edges. Then we remove all the edges between nodes that are connecting representatives of the same node. The total number of edges removed is N S2 P. This means independently of the number S of representatives per node we remove roughly 1/N of the total number of edges.2. We add random edges with probability P getting O in which case the objective is to identify an independent set rather than a clique. Theoretical bounds for covering a graph with disjoint cliques can be found in [j]= 1. Otherwise, Euv[i][j] = 0. As illustrated in Figure The multiplex PCR problem is more general in that we impact the graph topology by choice of primers. We use the term "multi-node graph" to denote a graph whose nodes have multiple states. In a multi-node graph, an edge matrix EIn the context of multiplex PCR, our goal is to identify a set of uniformly sized disjoint cliques in a multi-node graph. This involves the dual problem of selecting node states (primer pair selections for each SNP) and identification of the cliques themselves corresponding to multiplex-compatible SNP sets.We generated candidate forward and reverse primer pair candidates for each of the 1,200 SNPs according to the selection criteria listed in Table Using the above primer selection criteria, we generated an average of 1555.8 +/- 1249.4 primer pair candidates per SNP. Twenty-two of our 1,200 SNPs (1.8%) produced no valid primer candidates. For each SNP we randomly selected a primer pair and constructed the corresponding compatibility graph, where edges connect two compatible SNPs. The graph density was 0.299 +/- 0.005 over 10 random trials. As noted earlier, a random graph model is an imprecise representation for the multiplex PCR primer design problem because primer pair candidates are not independent, and because the primers for SNPs within a tube tend to become dominated by one of four non-interacting base pair combinations To further understand how SNP-pair compatibility probabilities depend on primer selection criteria, we randomized these criteria and evaluated the resulting graph density for 50 SNPs randomly chosen from human chromosome 21. While certain oligo-specific parameters were kept fixed, pair-wise compatibility criteria were chosen at random within certain specified ranges. The specific compatibility criteria we considered were:Complementary Sequence Local Alignment Score: Allowed to vary between +4 and +10 . Typically, a threshold of +8.0 is used. A smaller scoring threshold is more stringent as we are disallowing primer pairs with less complementary sequence.• 3' Tail ΔG Alignment Score: This score measures the worst-case alignment of the 3' tail of one primer along any other part of another sequence. Current practice suggests that it is the 3' tail that is most critical to ensuring proper primer ligation. We allowed this threshold to range from 0.0 to -9.0 kCal/mol.  A higher (less negative) cutoff is more stringent as we are disallowing less-energetically favorable interactions.• Melting Temperature (Tm) Range: The allowed melting temperature between any two primer pairs. A Tm difference of 3.0 degrees K is fairly standard. Here we allow the Tm difference to vary between 0.5 and 7.5 degrees K. • The random selection of thresholds and the resulting generation of valid primers constituted a single trial. Within each trial, we randomly selected one primer pair for each locus and computed the resulting density of a graph where nodes represent particular SNPs having an assigned primer pair, and edges connect two multiplex-compatible SNPs. For two SNPs to be mutually compatible, all four primers must be pair-wise compatible using the selected thresholds. These thresholds are thus used to screen both intra- and inter-SNP primer pairs. The graph density was computed as the average of 10 densities each resulting from 10 random primer selection rounds. Figure Each point in the graph represents a particular trial. Red points have a high Tm difference threshold while blue points have a low Tm difference threshold. As expected, the resulting compatibility graph density increases as we loosen the constraint on the interaction ΔG. For a given ΔG cutoff, tighter constraints on the Tm difference will naturally tend to reduced SNP pair compatibility. The multiple performance tiers (clearly seen as multiple red bands across the chart) reflect different cutoffs for the standard complementary sequence local alignment score, the lowest being for Score = 4, while at the top, scores of 6–10 blend together in this figure. At ΔG = -4.5 kCal/mol, we expect graph densities no greater than about 30%. In other words, the probability that two SNPs, each assigned random primer pairs, are multiplex compatible is only about 30%.We define a benchmark best-fit strategy for designing uniform M-plexes as follows:N be a multi-node graph with N nodes (SNPs).Let GLet M be the desired clique size (multiplexing level).T=  cliques (tubes), initially empty.Let CANTASSIGN be a set of unassignable nodes, initially empty.Let u∊N and u∉CANTASSIGN at random.1. Choose a node, 2. Assign a random state (primer pair) to the nodeT that are compatible with u.  time and space. Therefore, when applying the above algorithm to real-world SNPs with potentially hundreds of candidate primer pairs (states) per SNP (node), we determine primer interactions (edge interactions) as needed in order to test a particular SNP for tube compatibility.For N nodes (SNPs) and S states (primer pair candidates) per node, pre-computing and storing all possible primer-pair interactions in a multi-node graph would require largest compatible tube. The rational for this strategy is that while each tube assignment reduces our probability of finding another assignment to the same tube, the reduction in probability is minimized when we make an assignment to the tube that is currently the largest. It should be noted, however, that in practice very little change in the performance of the algorithm is observed if we assign nodes to a random compatible tube, to the smallest compatible tube, or even to the first compatible tube. This is due to the fact that the probability of assigning a particular SNP to a particular tube decreases exponentially as the size of the tube (clique) grows larger. For sufficiently large cliques, it is unlikely that a SNP with a particular assigned primer set will be compatible with any tube. Most often, when a compatible tube is found, it is the only compatible tube among the  available choices, and thus there is little or no resulting difference in how we actually choose our tube.Step 3 provides our definition of "best-fit." The best tube is defined as the As noted above, we expect the probability of finding a compatible tube for a particular SNP in a particular state to decrease exponentially as the tube size increases. Suppose in attempting to assign a SNP to a particular tube, we find that it is incompatible with one other SNP which was originally assigned when the tube was small. It is relatively easy to find a compatible tube when they contain few SNPs because there are fewer interactions to consider. By contrast, if we find a nearly-compatible SNP when the tube is large, we should attempt to accommodate the SNP with the idea that low-probability SNP/Tube assignments are relatively rare and should thus be maintained whenever possible.1, k2, ... kd. We claim that it is valuable to substitute our test SNP for the d incompatible SNPs whenever the total probability of assigning the d incompatible SNPs is greater than the probability of assigning the test SNP to a tube that excludes these d SNPs. That is:In general, suppose we have a tube containing k SNPs (a clique with k nodes). We test a SNP for compatibility with the tube and find that d ≤ k SNPs are incompatible with the SNP. Suppose furthermore that these d SNPs were assigned to the tube when the tube was of size k is maximized. In assessing these assignment probabilities, additional consideration could be given to the number of candidate primer pairs maintained by each SNP, as it is less likely that we will identify a compatible tube for SNPs with relatively few candidates with the idea that we should be more reluctant to remove such SNPs once a compatible assignment is determined. In this version, however, we considered only the tube sizes at the time each SNP is assigned. In the Fixed-Assignment Best-Fit algorithm, the size of each tube is monotonically increasing. Thus, if a SNP with a given primer candidate is not compatible with any tube, the primer pair candidate can be removed from further consideration and furthermore, if no primer candidate is compatible for any tube, then the SNP can be discarded from further consider. By contrast, the Flexible-Assignment Best-Fit algorithm requires that we reconsider the compatibility of SNPs and their associated primers within any modified tube. We thus specifically track which candidates have been tested on which tubes, and we update this status each time a particular tube is modified.If there are multiple tubes satisfying the above condition, we assign the SNP to the tube where It is clear that the Flexible Assignment Best-Fit algorithm will eventually terminate with increasingly high probability because every SNP substitution we perform within a particular tube is assessed as having strictly lower probability than previous assignments.John Rachlin and Simon Kasif are responsible for the overall algorithmic design and theoretical analysis presented in this paper. John Rachlin and Simon Kasif introduced the framework of multi-node graphs in consultation with Noga Alon. John Rachlin implemented the algorithms and produced the initial results for both simulated and real human SNP data. John Rachlin discovered the phase transitions during the analysis of the simulated data which were explained by a theoretical analysis developed initially by Noga Alon and Vera Asodi and expanded and reported in . Charles


Staphylococcus hyicus. The exfoliative toxins produced by S. hyicus digest the porcine desmoglein 1 (PIG)DSG1 by a very specific reaction. This study investigated the location of single nucleotide polymorphisms (SNPs) in the porcine desmoglein 1 gene (PIG)DSG1 in correlation to the cleavage site as well as if the genotype of the SNPs is correlated to susceptibility or resistance to the disease.Desmoglein 1 (DSG1) is the target protein in the skin disease exudative epidermitis in pigs caused by virulent strains of DNA from 32 affected and 32 unaffected piglets with exudative epidermitis were diagnosed clinically as affected or unaffected. Two regions of the desmoglein 1 gene were sequenced and genotypes of the SNPs were established. Seven SNPs  were found in the analysed sequences and the allele frequencies were determined for the SNPs resulting in amino acid change. Four of the seven polymorphisms were situated in the motif known to be important for toxin cleavage. The distribution of the genotypes between affected and unaffected animals was analysed.The study indicated a possible correlation between the genotypes of two out of seven SNPs found in the porcine desmoglein 1 gene and the susceptibility to exudative epidermitis. Staphylococcus hyicus. Exfoliative toxins from S. hyicus (Exhs) digest porcine desmoglein 1 in the extracellular part, which is responsible for the cell-cell adherence. The digestion of desmoglein 1 causes exfoliation of the skin, which is a characteristic symptom of the disease [S. hyicus have been identified. ExhA, ExhB, ExhC and ExhD have been identified in Denmark and can be distinguished by PCR [Desmoglein 1 is one of the adhesive proteins in the desmosomal complex that forms one of the intercellular junctions found in epithelial tissues . Desmogl disease . Differed by PCR . Anotherd by PCR ,5.S. aureus involved in the disease staphylococcal scalded skin syndrome (SSSS) [2+ ions. The cleavage site is situated between the third and the fourth extracellular domain close to a calcium-binding site [Human desmoglein 1 ((HUMAN)DSG1) is known to be the target for the exfoliative toxins (ETs) from e (SSSS) . In figue (SSSS) ), it is ing site  as indicS. aureus. The motif is proposed to be involved in the alignment of desmoglein 1 to the toxin during cleavage. In the same study it is suggested that binding of desmoglein to the toxin and cleavage are independent abilities [The reaction between ETs and human desmoglein 1 is highly specific and dependent on not only the amino acid sequence, but also the calcium-stabilised three-dimensional structure . A motifbilities . Structubilities   were found and in herd 2, two different toxin types (ExhA and ExhC) were found . Primers used for amplification are listed in table DQ823081 and DQ823082, data not shown).The nucleotide sequences generated from all sampled animals were inspected and aligned to establish amino acid changes in the upstream domain and around the cleavage site. The sequences were also compared to the cloned sequences of porcine desmoglein 1  and Japan (accession number in Genbank: AAV84914). SNPs number 6 and 7 are also missense mutations 838A>C and 1139C>T resulting in changes between lysine and glutamine and leucine and serine respectively. For SNPs number 6 and 7 both homozygous and heterozygous animals were found among the genotyped animals.Six SNPs were found in the upstream region and one in the region close to the cleavage site . The frequencies are based on genotypes of animals from both herds including the sows. Thus, they might not reflect the true allele frequencies in the population, since some of the animals are related. For SNP number 1 P has a frequency of 0.86 and S a frequency of 0.14. For SNPs number 3, 4 and 5 frequencies are not calculated because only one genotype (GTA) was found in the material from the two herds. For SNP number 6 the frequencies for Q and K are 0.30 and 0.70, respectively, and for SNP number 7 the frequencies for L and S are 0.43 and 0.57, respectively.To investigate if there is a correlation between the genotype of the four SNPs resulting in amino acid change in the different piglets and their susceptibility towards EE, the number of affected and unaffected piglets with each genotype was counted and the percentage was calculated. The results are shown in table 2-test) to establish whether the differences in numbers for each genotype between affected group the unaffected group were statistically significant. In the first test , the homozygous version S/S was not found among the animals from the two herds. This is in accordance with the allele frequencies detected (P: 0.86 and S: 0.14), giving an expected frequency of 1–2 animals homozygous for S in a population of 75 animals.In the present study, seven polymorphisms were identified in the two regions of the gene that were investigated. Five of the SNPs  are located among nucleotides coding for the five amino acids, which may be important for toxin cleavage and binding figure  panel B.There seems to be more homozygous Q/Q and L/L in the affected group and more homozygous K/K and S/S in the unaffected group table . The difThe differences are significant only when the homozygous animals are analysed. When the heterozygous animals are left out of the analysis the total number of animals gets smaller and thereby the evidence becomes weaker. Thus, there is only a weak indication of a correlation between the genotype in SNP 6 and 7 and the susceptibility to EE. However, since the significance disappears when the heterozygous animals are included a simple relationship between a specific mutation and the susceptibility to EE is not present. To be able to investigate this possible correlation further, a larger group of affected and unaffected animals is needed to increase the number of homozygous samples. A possible uncertainty of the result could be that it is not known if all susceptible animals have been under a sufficiently large contagious pressure to get infected. The physicochemical distance between L and S (145) and between N and V (133) table  indicateOther parts of the desmoglein 1 protein might also have influence on the binding and/or activation of the exfoliative toxins. Thus, although this study investigated SNPs in the parts of the desmoglein 1 gene that have been described to be of importance for cleavage by exfoliative toxins, there might be additional sites of importance which have not been included here.S. hyicus clones were involved in each herd  infected with EE. Among the 46 animals from herd number 1, 19 piglets were affected, 21 were unaffected and 6 were sows. In herd number 2, 29 samples were taken: 13 affected piglets, 11 unaffected and 5 sows. Some of the piglets are offspring from these sows; however only few of the piglets are full sibs because mixed sperm has been used for insemination. From each animal a blood sample was taken from the jugular vein and a skin swab was obtained from the skin behind the ear. The diagnosis was verified by identification of toxin positive ribed in . The genDQ823081.PCR and DNA sequencing with two sets of primers identified the genotypes of the SNPs. One primer set was designed to amplify a 511 bp fragment covering part of exon 7, intron 7 and part of exon 8. The other primer set was designed to amplify a 165 bp fragment in exon 9. Primer sequences are listed in table 4(pH 9.1),18 mM (NH4)2SO4, 1.7 mM MgSO4, 20 pmol of each primer, 200 uM each of the four deoxynucleotides and 0.5 μl Elongase Enzyme Mix  in 50 μl reactions). 30 ng of genomic DNA was in each reaction. The PCR products were purified using QIAquick spin columns  and sequenced on both strands . Sequence data were inspected with BioEdit Sequence Alignment Editor v. 7.0.5.3 [All genomic DNA samples were amplified by PCR for 30 cycles of 94°C for 30 sec., 50°C for 30 sec., 68°C for 30 sec. with both primer sets by standard PCR conditions  [Modelling of the extracellular domains of porcine desmoglein 1 3D structure was made using the prediction server CPHmodels . The amiD: IL3W)  as a tem2 test was applied to the data set. Data for each SNP was tested separately using the affected and unaffected groups as factors against the possible genotypes. χ2 test 1 was performed on SNP 6 and 7 using only the two homozygous groups (2 × 2 tables). This test could not be used for SNP 1 because the homozygous S/S group was empty. Yates correction was applied to the 2 × 2 tables. χ2 test 2 was performed on SNPs 1, 6 and 7 using all three genotypes (2 × 3 tables).A χDQ823081 and DQ823082.The used sequences have the following accession numbers: Human desmoglein 1 GenBank: AAC83817, porcine desmoglein 1 cloned in Japan GenBank: AAV84914 and Denmark GenBank: SNP: single nucleotide polymorphismStaphylococcus hyicusExh: exfoliative toxin from Staphylococcus aureusET: exfoliative toxin from (HUMAN)DSG1: human desmoglein 1(PIG)DSG1: porcine desmoglein 1SSSS: staphylococcal scalded skin syndromeEE: Exudative epidermitisPCR: polymerase chain reactionEC: extracellular domainIA: Intracellular anchor domainIC: Intracellular domainLD planed and conducted the sample collection, clinical evaluation, and all the laboratory work and data analysis of this study and drafted the manuscript. LOA assisted in planning and design of the study, partook in sample collection and clinical evaluation assisted in the data evaluation and helped to draft the manuscript. MF assisted in planning and design of the study, in the data evaluation and helped to draft the manuscript. All authors read and approved the final manuscript.