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Journal of Biostatistics and Biometric Applications
ISSN: 2455765X
Modifying the Classical F Test for Microarray Experiments
Copyright: © 2015 Bourget G. This is an openaccess article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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Microarray data has a high dimensional data structure that makes statistical inference drawn from this type of data challenging. Since current statistical methods are generally for “small p and large n”, these methods can be insufficient to draw valid conclusions for microarray data. Nevertheless, some of these methods, such as ANOVA (F test), are still widely used. One of the assumptions of the classical F test is that populations (genes) are assumed to be independent. This assumption is obviously violated in microarray experiments because genegene interactions can naturally occur. In this paper, we use an effective “column” size idea to take correlations among genes into account to modify the classical F test. We consider various magnitudes of correlation among genes in Monte Carlo simulation studies. We compare the proposed test (F MOD) with the classical F test and multivariate Hotelling’s T^{2} test through validity and power analyses. We also demonstrate the proposed test with real type 2 diabetes mellitus gene expression data, which was obtained from the Gene Expression Omnibus (GEO) database with accession number GSE25724.
Keywords: Effective sample size; High dimensional data; Hotelling’s T^{2} test; Microarray
Completion of the human genome sequence allows researchers to study expression of 20,00030,000 genes in a single assay. There are three types of platforms: short oligonucleotide (2530 base), long oligonucleotide (5080 base), and cDNA. However, the most two common platform are based on collections of cDNA clones [1] or short (25 base) oligonucleotides synthesized in situ by photolithographic methods [2]. Although microarrays are the most extensively used technology for studying gene expression, it has a high dimensional data structure that makes statistical inference from this type of data challenging [3]. Several methods such as clustering and classification have been used to identify groups of genes that share similar functions [4,5]. However, while clustering and classification are useful techniques to search for similar genes, these techniques do not answer the question of which genes are differentially expressed under different conditions (e.g. cancer cells versus normal cells). The answer to the question requires hypothesis testing with null hypothesis of no difference in the means of gene expressions under different conditions. Various statistical tests have been proposed involving fold change, linear models, as well as Bayesian methods [68]; however, progress has been slow in adopting these methods in microarray analysis. Moreover, all of these methods have the common characteristic of being univariate methods.
A common characteristic of high dimensional data is that it has high dimension (p), and relatively small sample size (n). This kind of data structure is called “large p and small n”. Besides having high dimensional data, microarray data also have correlation structure [9]. Most of the current methods either ignore high dimensional data structure or fail to efficiently take correlations among genes into account. Multivariate analysis can take correlations among genes into account by analyzing genes jointly. Consequently, multivariate analysis methods have recently being used in microrray data [10,11]. However, these methods are not straightforward, and most importantly ignore the multidimensional structure of the gene expression data.
Hotelling’s T^{2} test is one of the multivariate analysis methods that takes correlations among genes into account to identify differentially expressed genes. It has been applied in genome association studies [12], microarray process control [13], and data control charts [14]. However, Hotelling’s T^{2} test does not take high dimensional data structure into account. For example, in a comparison of two groups, this test requires an explicit condition on data dimension and sample size: for fixed p, p < n_{1} + n_{2} − 1, where p is the number of genes, n_{1} is the sample size of the group 1, and n_{2} is the sample size of the group 2. Lu, et al. [15] presented a new T^{2} statistic for analyzing microarray data. They used first a multiple forward search algorithm to select a subset of feature vectors in a highdimensional microarray dataset to reduce the dimension (i.e., p) to satisfy the restriction p < n_{1} + n_{2} − 1, and then they implemented the Hotelling’s T^{2} test.
Moreover, as an alternative test to Hotelling’s T^{2}, Chen, et al. [16] proposed a twosample test for the means of highdimensional data.
In this paper, we present a different approach proposed in Lu, et al. [15]. Our approach is more general and practical than that of in [15], and moreover does not implement Hotelling’s T^{2} test but the simple classical F test. The proposed modified F test is denoted by F MOD. We use an effective sample size idea to take correlation among genes into account [1719]. The effective sample size formula was originally proposed by Clifford, et al. [20], and was improved for small sample sizes by Dutilleul, et al. (1993) [21]. Also, the same effective sample size formula was used in modified F tests to assess multiple correlation between one spatial process and several others [22], and to assess correlation between two time series [23]. We implement the same effective sample size formula described in [21] to compute effective column size not effective sample size. Henceforth, we introduce a new nomenclature term “effective column size”. To adopt the formula in [21], we consider the same structure of the design matrix (1) in the Methods section.
An another statistical technique for finding significant genes in a set of microarray experiments is Significance Analysis of Microarray (SAM) proposed by Tusher, et al. [24]. The SAM uses repeated permutations of the data to determine if the expression of any genes are significantly related to the response. It uses a set of genespecific t tests. Since, the classical F , Hotellings T^{2}, and F MOD tests use global F tests and not individual t tests as in SAM, we do not consider the SAM as one of the methods to be compared in this paper. Also, the goal of SAM is to handle genespecific fluctuations by considering a statistic based on the ratio of change in gene expression to standard deviation in the data for that gene. However, in this paper, our goal is to handle genegene interactions and not in genespecific fluctuations, which are two different problems to tackle.
The remainder of the paper is organized as follows. In the Methods section, we describe Hotelling’s T^{2}, classical F, and F MOD tests, and in the Results section we outline Monte Carlo simulation studies, present its findings, and analyze gene expression data of type 2 diabetes mellitus. Finally, we draw conclusions in the Discussion section.
A s ingle multivariate observation is the collection of measurements on p different variables (genes) taken from the same trial (array). If n observations have been obtained, the entire data set can be represented in an n × p matrix
(1)
The row vector represents the jth multivariate observation. The matrix X represents p genes each having n observations. Now, consider a microarray experiment of n_{1} and n_{2} samples from populations 1 and 2, respectively. For example, population 1 can represent the disease group, while population 2 can represent the healthy group. Suppose that the expression levels of p genes are measured and matrix representations of populations 1 and 2 are defined in (1) as X and Y. The observations on p variables can be arranged as follows:
Our goal in this paper is to only make inferences about the differences of the vector mean of the populations. That is, we want to know if μ_{1} = μ_{2}, or equivalently if μ_{1} − μ_{2} = 0. However, one further can investigate which means are different if the hypothesis of μ_{1} − μ_{2} = 0 is concluded. We need to make some assumptions to provide answers to these questions. The assumptions are:
1. The sample is a random sample of n_{1} from a pvariate population with mean vector μ_{1} and covariance matrix Σ_{1}.
2. The sample is a random sample of n_{2} from a pvariate population with mean vector μ_{2} and covariance matrix Σ_{2}.
3. The samples are independent of the samples .
For large samples, these assumptions are enough to make an inference about μ_{1} − μ_{2}. However, when the sample sizes n_{1} and n_{2} are small we need to have the following assumptions as well.
1. Both populations are multivariate normal, and
2. Σ_{1} = Σ_{2}.
The null (H_{0}) and alternative (H_{a}) hypotheses we are interested are:
H_{0}: μ_{1} − μ_{2} = 0 versus H_{a} : μ_{1} − μ_{2} ≠ 0 (2)
where μ_{1} = (μ_{11}, μ_{12}, . . . , μ_{1p})ʹ is the vector mean expression level of population 1, and μ_{2} = (μ_{21}, μ_{22}, . . . , μ_{2p})ʹ is the vector mean expression level of population 2. The null and alternative hypotheses can also be rewritten as
H_{0} : (μ_{11} − μ_{21}, μ_{12} − μ_{22}, . . . , μ_{1p} − μ_{2p})ʹ = (0, 0, . . . , 0)ʹ
H_{a} : (μ_{11} − μ_{21}, μ_{12} − μ_{22}, . . . , μ_{1p} − μ_{2p})ʹ ≠ (0, 0, . . . , 0)ʹ (3)
or equivalently
H_{0} : μ_{11} = μ_{21}, μ_{12} = μ_{22}, . . . , μ_{1p} = μ_{2p}
H_{a} : at least one μ_{1i} = μ_{2i}, (i = 1, 2, . . . , p) (4)
Note that, we test the mean expression of p genes all together not the individual mean expressions in (2)  (4). That is, we consider a global test not an individual test.
We consider a microarray experiment composing of n_{1} samples from population 1 and n_{2} samples from population 2. Let X_{ij} be the expression level for gene j of sample i from population 1, and Y_{kj} be the expression level for gene j of sample k from population 2. The expression level vectors for sample i from population 1 can be expressed as X_{i} = (X_{i1}, . . . , X_{ip})ʹ. The mean expression level of gene j in population 1 is defined as
(5)
Then, the mean expression level vector for p genes for population 1 is given by
We can similarly define these expressions for population 2. The pooled variancecovariance matrix of p genes for populations 1 and 2 can be written as
(6)
where S_{X} and S_{Y} are the sample variance covariance matrices of populations 1 and 2. Note that correlation among genesare taken into account through sample variance covariance matrices.
The Hotelling’s T^{2} test [25] is defined as
(7)
By Central Limit Theorem,
(8)
has classical F distribution with p degrees of freedom for the numerator and n_{1} + n_{2} − p – 1 degrees of freedom for the denominator. This test requires that the degrees of freedoms are positive, that is, it forces the condition p < n_{1} + n_{2} − 1. However, this restriction makes it almost impossible to implement Hotelling’s T^{2} test in microarray experiments.
The classical F test compares the means of the columns of X, and assumes that these columns are independent (univariate case). In microarray experiment, we want to compare the differences of the p means of X and Y. Since we want to compare multivariate (Hotelling’s T^{2}) and univariate (classical F) methods, we adopt the data structure from the multivariate to univariate case by considering the observations as the differences of the data matrices X and Y. That is, we compute X_{ij} − Y_{ij} , and apply the univariate F test on these observations. The F test is defined as
(9)
where MST is the mean square for treatments (genes), and MSE is the mean square for errors. The F_{obs} in (9) follows an F distribution with p − 1 degrees of freedom for the numerator and p(n − 1) degrees of freedom for the denominator, where n_{1} = n_{2} = n.
When the assumptions are not satisfied by sample data, there are two general remedies: (1) to transform the data so that the assumptions are satisfied, or (2) to develop a modified inferential method in which the assumptions are relaxed at the estimation stage, or deviations from the assumptions are taken into account at the testing stage.
In linear models, the autocorrelation of errors has an impact on the inefficiency of slope estimators and the invalidity of significance levels. When regressors have fixed structure, the only source of autocorrelation comes from errors. However, when regressors also have random structures, their autocorrelations along with correlations of errors have an impact on estimation and testing [1719,26,27]. Since the autocovariances of stochastic processes bias the variance of sample correlation coefficients [28], the incorporation of effective sample size into modified ttests were proposed [20,21]. The effective sample size nˆ in [20] was defined as
(10)
where and were the estimated covariance matrices of X and Y, respectively. Dutilleul (1993) proposed an improved effective sample size for small sample sizes [21]. However, the effective sample sizes prosed in [20] and [21] behave similarly for large sample sizes. The effective sample size in [21] was defined as
(11)
where B = n^{1}(I – n^{1}J), J is the n × n matrix of ones, and I is the identity matrix.
In this paper, we use equation (11) defined in [21] to compute effective column size to identify differentially expressed genes in microarray data. We considered the following steps for F MOD test in the simulation runs: first, we computed the effective column size, , as in equation (11).
The estimated covariance matrices and were computed using the raw data of X and Y, respectively. Second, we replaced p by in the degrees of freedoms of the classical F test defined in (9). Finally, we computed the pvalue of the global F test in (9) with − 1 and (n − 1) degrees of freedoms for the numerator and denominator degrees of freedoms, respectively. Note that, the sample size is n_{1} = n_{2} = n.
We generated two multivariate normal distributions: MVN(μ_{1}, Σ_{1}) and MVN(μ_{2}, Σ_{2}), each with dimension p (genes). The variance covariance matrices are defined as
where
(12)
where We can similarly define Σ_{(ρ)} by replacing ρ by (−ρ) in (12).
The matrices Σ_{ρ} and Σ_{(ρ)} have dimensions g × g, and the matrices Σ_{1} = Σ_{2} have dimensions p × p. The constant term l is cancelled out in the computation of the effective column size in (11), hence, it has no effect on the effective column size. However, this term is considered to generate the data matrices X and Y with covariance matrices defined in (12).
Actually, the simulation setup has sound basis in methodologies used in analyzing real microarray data. It is common knowledge that genes are networked together in pathways. Although, it is true that weak connections between groups may exist, independence between groups is a reasonable assumption. Also, within each group, genes are either positively or negatively correlated, and due to their relative distance in the regulatory pathway, the further apart two genes, the less correlation between them. These are exactly the reasons why we considered the structures of Σ_{1} and Σ_{2} defined in (12) for microarray data.
We assumed that both populations have equal sample sizes (i.e., n_{1} = n_{2}), and there are 10 matrices on the diagonals of Σ_{1} and Σ_{2}. For example, if p = 100 then there are 10 matrices on the diagonal of Σ_{1} and Σ_{2} with 10 genes in each matrix (i.e., g = 10). To assess the effects of correlation among genes, we took ρ = 0, 0.1, 0.2, . . . , 0.9 as various magnitudes of correlations. We also set the variances of each gene at 0.01 (i.e., σ^{2} = 0.01). Even though the value of σ^{2} is needed to generate X and Y, it has no effect on the computation of the effective column size. Two different significance levels, α = 0.01 and 0.05, were used in validity and power analyses.
The null hypothesis in validity analysis was set to μ_{1} = μ_{2} = (0,0,0,.....,0)'(p × p) whereas in power analysis μ_{1} ≠ μ_{2} with
μ_{1} = (0,0,0,.....,0)'(p × 1) andMore precisely, the first 2% of the means of the genes were set to 0.5, and the rest were set to 0 in μ_{2}. If 0.02 * p was not an integer value, then we used ceiling function in R that takes a single numeric argument a and returns a numeric value containing the smallest integers not less than the corresponding elements of a.
The simulation program was written and run in R, which is a free software environment for statistical computing and graphics. We ran 10,000 data sets to test the null hypothesis. We computed empirical significance levels (pvalues) and powers of the tests to draw conclusions about the testing procedures.
Lu, et al. [15], Chen, et al. [16], and SAM [24] methods were not compared in the simulation. The SAM handles genespecific fluctuations by considering a statistic based on the ratio of change in gene expression to standard deviation in the data for that gene. However, in this paper, our goal is to handle genegene interactions and not genespecific fluctuations. Also, Lu, et al. [15] modified the degrees of freedom in Hotellings T^{2} test but F MOD modified the degrees of freedom of the classical F test. Moreover, the method of Chen, et al. [16] was not compared because they proposed a twosample test, and we used a test that modified the global Ftest.
The strict definition of a testing procedure to be valid at a significance level α is that if the actual pvalue, which is the probability of rejecting the null hypothesis when in fact the null hypothesis is true, is less than or equal to α. To take variability among generated data into account in simulation runs, one may consider the upper limit of the approximate 95% confidence interval for the actual pvalue. Under binomial distribution model, for α and m simulation runs, the approximate 95% confidence interval is α ± 2√α(1 − α)/m. In simulation runs, we took α = 0.01 and 0.05, and m = 10, 000. The upper limits are
Therefore, we assessed the validity of the testing procedures based on the strict definition of the validity and the variability associated with the data generation. That is, the validity conditions are pvalue ≤ 0.012 when α = 0.01, and pvalue ≤ 0.054 when α = 0.05 in Table 1 and 2.
In Table 1, we investigated the validit y of the tests at α = 0.01 and 0.05 when p < n_{1} + n_{2} − 1. We need this restriction to perform the Hotelling’s T^{2} test, but not the other two tests. Table 1 showed that the classical F test suffered lack of validity when correlations among genes were between mild and strong. The Hotelling’s T^{2} test is known to be not welldefined when p is much greater than n because the variancecovariance matrices Σ_{1} and Σ_{2} become singular. As a result, Hotelling’s T^{2} test becomes unstable. This phenomena was ascertained in Table 1 when p > 60. Therefore, we suggest not to use Hotelling’s T^{2} test when p > 60. In contrast, the proposed F MOD test always provided valid tests for any ρ, except only in two cases (p = 50 when α = 0.05 and α = 0.01), which might be solely due to variation among data.
We studied the validity of F and F MOD tests without the restriction p < n_{1} + n_{2} − 1 in Table 2. Since F MOD performed very well up to p = 80, we ran simulations for p = 100 and 200 to better understand the performance of the test for larger number of genes. Both tests performed similarly as in Table 1. That is, F test was only valid when correlation among genes did not exist or the magnitudes of the correlations were very weak. The F MOD test always provided valid testings, except in one case.
Table 3 provided power analysis at α = 0.01 and 0.05 when p < n_{1} + n_{2} − 1. Since F test suffered lack of validity when ρ > 0.2, we did not analyze the power values in the table; these values were provided only for completeness of the Table. Hence, the power of F test should be ignored when ρ > 0.2. While Hotelling’s T^{2} test provided better power when correlations among genes were not too strong, the power decreased as correlations among genes got stronger. The Hotelling’s T^{2} test actually became powerless as p increased. This is not an unusual observation because it is known that even when p ≤ n, the Hotelling’s T^{2} test perform poorly if p is nearly as large as n. The performance of the Hotelling’s T^{2} test under p, n → ∞ with p/n → 1 – Є was studied in [29], which they showed that the asymptotic power of the test suffered for small values of Є > 0. A number of improvements to give better power on the Hotelling’s T^{2} test in highdimensional data have been proposed in [16, 2931]. It was interesting to observe that Hotelling’s T^{2} test was more powerful when α = 0.05 than when α = 0.01. Its powers were more than 88.5% when α = 0.05, but not more than 35.4% when α = 0.01. In contrast, the F MOD always provided powers at 100%.
We did not provide a table for power analysis when the restriction p < n_{1} + n_{2} − 1 was because held because it provided similar results to those in Table 3.
Table 4 shows average effective column sizes computed from (11) when 10,000 simulation runs were performed. The effective column sizes decreased as correlations among genes got stronger. As expected, when genes are independent (i.e., ρ = 0) the effective column size was the same as the original number of genes (p).
We used the gene expressions of type 2 diabetes from the data base Gene Expression Omnibus (GEO) with accession number GSE25724 [32] (data was not collected by us). The normalized gene expression data of p = 22, 283 genes was obtained from six type 2 diabetic human islets (population 1, n_{1} = 6) and seven nondiabetic human islet (population 2, n_{2} = 7). In over all design, human islets were isolated from the pancreas of organ donors by collagenase digestion followed by density gradient purification, then handpicked and cultured two days in M199 culture medium. The platform GPL96 [HGU133A]) by Affymetrix was used.
The programming codes to analyze gene expression data were written in R software. The dimensions of the matrices X and Y were 6 × 22, 283, and 7 × 22, 283, respectively. Since F MOD test required the differences of the observations from two populations, six nondiabetic patients were chosen to have equal sample sizes for both populations (n_{1} = n_{2} = 6). That is, the dimension of the difference matrix was 6 × 22, 283. The data structure was high dimensional (p = 22, 283 genes, and n = 6 observations), which caused memory exhaustion in R. However, we used builtin functions such as “as.big.matrix” to do matrix operations and “bigcor” to compute correlation and covariance matrices of size 22, 283 × 22, 283. The effective column size in (11) was easily computed using the as.big.matrix function to multiply two or four matrices of sizes 22, 283 × 22, 283.
Before analyzing the data, we verified that the assumptions of the fixed oneway ANOVA were satisfied: (1) our data did not violate the assumption of normal distribution, because fixed oneway ANOVA is considered a robust test against the normality assumption. (2) the equality of variances were not violated because it is well known that when the error variances are unequal, the F test for equality of means with the fixed oneway ANOVA model is only slightly affected if all factor level sample sizes are equal or do not differ greatly. In real data, the sample size was six in each gene, hence this assumption was not violated. However, 3) the independence of the populations were violated. To show dependency, we computed the correlation matrices for both populations. The correlation matrix has entries of correlations for pairwise genes. The number of pairwise genes for 22,283 genes is = 2.48254903 × 10^{8}. We counted the pairwise correlations that are more than 0.5, 0.7, and 0.9 in absolute values. The result is shown in Table 5. We concluded that genes were correlated in both populations, and hence the classical F test was not performed. The Hotelling’s T^{2} was also not performed because 22, 283 ≮ 6 + 6 − 1. Therefore, we only considered F MOD test to analyze the data.
In the simulation study, we were only interested in the hypotheses defined in (2) or (3). That is, if there was a difference in the vector means of the populations. In the data analysis we proceeded one step further to identify differentially expressed genes if the null hypothesis in (2) or (3) was rejected. The statistic in (9) was F_{obs} = 5.609043, and the effective column size in (11) was computed as = 9.424243. Since pvalue= 4.13 × 10^{5} was smaller than the significance levels α = 0.01 or α = 0.05, we rejected the null hypothesis, and concluded that 22,283 genes were differentially expressed together. We then run t tests for each genes with the adjusted degree of freedoms (n_{1} − 1) with and without Bonferroni corrections at α = 0.01 and α = 0.05 significance levels. Below, we only presented the number of significant genes without the Bonferroni corrections but provided the list of significant genes with the Bonferroni corrections in Tables 69. With or without Bonferroni corrections, we then compared these significant genes with significant genes listed at the GeneCards database. GeneCards is a searchable, integrated database of human genes that provides comprehensive, updated, and userfriendly information on all known and predicted human genes (http://www.genecards.org). The search is automatically extracted from more than 100 carefully selected web sources, and uses standard nomenclature and approved gene symbols. Moreover, it presents a rich subset of data for each gene by providing links to the original sources for further examination. Its use is free for academic nonprofit institutions. We identified 1083 significant genes related to type 2 diabetes by searching the keywords “type 2 diabetes mellitus”.
There were 4215 significant genes at α = 0.01 significance level (without Bonferroni correction) in which 297 of them were matched with GeneCards database (results were not shown).
After Bonferroni correction, there were 674 significant genes at α = 0.01/22283 = 4.49 × 10^{7} significance level in which 52 were matched with GeneCards database (Table 6 and 7). Without Bonferroni correction at α = 0.05 significance level, there were 7116 significant genes in which 554 of them were matched with the GeneCards (results were not shown). With Bonferroni correction at α = 0.05/22, 283 = 2.24 × 10^{6}, there were 901 significant genes in which 73 of them were matched with the GeneCards data (Table 8 and 9).
We used PANTHER classification system, which is a comprehensive, curated database of protein families, trees, subfamilies and functions [33,34], for the significant genes identified in Tables 69. The tool is available at http://pantherdb.org. The results are presented in Tables 1012. The main goals of PANTHER are to make accurate inference of genes and protein functions over large sequence databases. PANTHER extrapolates phylogenetic trees to represent gene family evolution. It also identifies subfamilies and protein class. In Tables 1012, we presented families/subfamilies and protein class for each gene. The significant genes were grouped in the following protein classes: peptide hormones and protein hormones (have an effect on the endocrine system of animals and humans); DNAbinding proteins (can incorporate domains as the zinc finger, the helixturnhelix, and the leucine zipper that facilitate binding to nucleic acid); acetyltransferase or transacetylase (is a type of transferase enzyme that transfers an acetyl group); carbohydrate kinase domain also known as CARKD; chemokines (are a family of small cytokines, or signaling proteins secreted by cells); hydrolase (is an enzyme that catalyzes the hydrolysis of a chemical bond); dehydrogenase also called DHO (is an enzyme belonging to the group of oxidoreductases that oxidizes a substrate by a reduction reaction that transfers one or more hydrides (H) to an electron acceptor); peroxidases (are a large family of enzymes); and reductase (is an enzyme that catalyzes a reduction reaction).
Microarray data has a high dimensional data structure that makes statistical inference from this type of data challenging. The most widely used statistical methods for finding differentially expressed genes from microarray data are univariate. While univariate methods do not take correlations among genes into account, genegene interactions shouldn’t be ignored in testing procedures. Multivariate statistical methods can overcome this deficiency of univariate methods by taking genegene interactions into account through variancecovariance matrices. However, these methods are sometimes not straightforward, and moreover ignore the multidimensional structure of the gene expression data.
The Hotelling’s T^{2} test is one of the multivariate analysis methods that takes correlations among genes into account but requires the restriction p < n_{1} + n_{2} − 1, when two populations are considered with sample sizes of n_{1} and n_{2}. In microarray experiments, it is almost impossible to satisfy this condition because p is always larger than n_{1} and n_{2}. That means Hotelling’s T^{2} suffers to handle curse of dimensionality. One solution is to apply Principal Component Analysis (PCA), or some other methods to satisfy the restriction before implementing the Hotelling’s T^{2} test. However, even this condition is satisfied, this test still suffers lack of powers when p, n → ∞ with p/n → 1 − Є for small values of Є > 0.
In the Real Data section, we analyzed gene expressions of type 2 diabetes [32]. There were 117,610,455 pairwise genes that had correlations in absolute value more than 0.5 in the nondiabetic group, and 107,977,419 pairwise genes that had correlations in absolute value more than0.5 in the diabetic group. We concluded that the assumptions of independence were violated in both groups, and hence the classical F test was not performed. We also did not implement Hotelling’s T^{2} test because the restriction 22, 283 < 6 + 6 − 1 did not hold. Since F MOD takes correlations among genes into account, we analyzed the data only using F MOD test with and without Bonferroni corrections. For example, we identified 901 significant genes in which 73 of them were matched with the GeneCards data at α = 0.05/22, 283 = 2.24 × 10^{6}.
In this paper, we consider F MOD test that used the novel idea of effective column size concept in microarray data. The test provides valid testings and 100% powers for any ρ. More over, the computation of F MOD can easily be performed in R using builtin functions such as “as.big.matrix” and “bigcor” without exhausting the memory in R. To adopt the data structure from the multivariate case to the univariate case, the differences of the data matrices X and Y were considered as observations. If the null hypothesis in (2) is rejected, then we suggest testing to identify differentially expressed genes
H_{0}: μ_{1i} = μ_{2i} versus H_{a} : μ_{1i} ≠ μ_{2i} (i = 1, 2, . . . , p)
using the classical ttest with (n_{1} − 1) degree of freedoms with Bonferroni correction. Here, μ_{1i} is the mean expression of gene i from population 1, and μ_{2i} is the mean expression of gene i from population 2.
We suggest for researchers to consider the F MOD test with a multiple test adjustment correction, such as Boferroni correction, instead of the classical F test if the assumption of independence is in question. Hotelling’s T^{2} is the second competitive test to F MOD. However, the restriction p < n_{1} + n_{2} − 1 does not hold in microarray data, and renders this test inapplicable. We believe that the use of effective column size in microarray experiment will be a novel approach that will help practitioners to choose an easy, effective, and powerful testing procedure instead of a complicated or a procedure with restrictions, such as Hotelling’s T^{2} test.
In future work, it is interesting to investigate the performance of a test that modifies Hotelling’s T^{2} test by taking into account the effective column size concept in the degrees of freedoms.
We would like to thank the referees for their valuable comments that helped improve the quality of the article.
p = 50, n_{1} = n_{2} = 26
ρ



α 
Test 
0 
0.1 
0.2 
0.3 
0.4 
0.5 
0.6 
0.7 
0.8 
0.9 
0.05 
F 
0.049 
0.056 
0.054 
0.060 
0.076 
0.084 
0.094 
0.108 
0.130 
0.144 
FMOD 
0.049 
0.055 
0.049 
0.049 
0.054 
0.052 
0.048 
0.048 
0.052 
0.044 

Hotelling’s 
0.049 
0.051 
0.051 
0.048 
0.054 
0.049 
0.049 
0.048 
0.048 
0.052 

0.01 
F 
0.011 
0.011 
0.012 
0.013 
0.019 
0.029 
0.038 
0.048 
0.063 
0.087 
FMOD 
0.012 
0.011 
0.011 
0.009 
0.011 
0.011 
0.013 
0.011 
0.011 
0.009 

Hotelling’s 
0.011 
0.011 
0.011 
0.012 
0.009 
0.012 
0.011 
0.009 
0.009 
0.009 

p = 60, n_{1} = n_{2} = 31 

0.05 
F 
0.046 
0.049 
0.053 
0.061 
0.068 
0.081 
0.095 
0.123 
0.136 
0.167 
FMOD 
0.046 
0.049 
0.048 
0.049 
0.049 
0.046 
0.047 
0.052 
0.046 
0.045 

Hotelling’s 
0.050 
0.052 
0.049 
0.046 
0.051 
0.052 
0.048 
0.048 
0.050 
0.051 

0.01 
F 
0.009 
0.013 
0.013 
0.016 
0.019 
0.032 
0.034 
0.051 
0.069 
0.092 
FMOD 
0.009 
0.013 
0.010 
0.011 
0.009 
0.012 
0.010 
0.009 
0.011 
0.010 

Hotelling’s 
0.009 
0.009 
0.009 
0.009 
0.009 
0.009 
0.010 
0.011 
0.010 
0.011 

p = 80, n_{1} = n_{2} = 41 

0.05 
F 
0.051 
0.052 
0.053 
0.058 
0.072 
0.086 
0.101 
0.12 
0.146 
0.176 
FMOD 
0.051 
0.050 
0.047 
0.046 
0.049 
0.049 
0.049 
0.048 
0.047 
0.045 

Hotelling’s 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 

0.01 
F 
0.011 
0.009 
0.011 
0.015 
0.019 
0.028 
0.039 
0.058 
0.078 
0.113 
FMOD 
0.011 
0.008 
0.009 
0.009 
0.011 
0.011 
0.011 
0.011 
0.011 
0.008 

Hotelling’s 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 

Table 1: Validity analysis with restriction p < n_{1} + n_{2} − 1, where p is the number of columns (e.g., the number of genes) and n is the number of sample size (e.g., the number of individuals.) 
p = 100, n_{1} = n_{2} = 20
ρ



α 
Test 
0 
0.1 
0.2 
0.3 
0.4 
0.5 
0.6 
0.7 
0.8 
0.9 
0.05 
F 
0.051 
0.056 
0.055 
0.066 
0.075 
0.088 
0.104 
0.127 
0.152 
0.188 
FMod 
0.052 
0.055 
0.049 
0.052 
0.053 
0.049 
0.048 
0.048 
0.047 
0.047 

0.01 
F 
0.011 
0.011 
0.013 
0.013 
0.020 
0.029 
0.044 
0.063 
0.088 
0.121 
FMod 
0.011 
0.010 
0.010 
0.010 
0.012 
0.011 
0.012 
0.012 
0.009 
0.011 

p = 200, n_{1} = n_{2} = 20 

0.05 
F 
0.047 
0.053 
0.055 
0.064 
0.072 
0.099 
0.114 
0.135 
0.175 
0.213 
FMod 
0.048 
0.052 
0.049 
0.050 
0.048 
0.050 
0.048 
0.049 
0.048 
0.045 

0.01 
F 
0.010 
0.010 
0.013 
0.015 
0.022 
0.033 
0.050 
0.067 
0.098 
0.147 
FMod 
0.010 
0.009 
0.010 
0.010 
0.010 
0.012 
0.011 
0.011 
0.010 
0.010 

Table 2: Validity analysis without restriction p < n_{1} + n_{2} − 1, where p is the number of columns (e.g., the number of genes) and n is the number of sample size (e.g., the number of individuals.) 
p = 50, n_{1} = n_{2} = 26
ρ



α 
Test 
0 
0.1 
0.2 
0.3 
0.4 
0.5 
0.6 
0.7 
0.8 
0.9 
0.05 
F 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
FMOD 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 

Hotelling's 
0.893 
0.894 
0.891 
0.893 
0.894 
0.895 
0.888 
0.885 
0.890 
0.888 

0.01 
F 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
FMOD 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 

Hotelling's 
0.257 
0.252 
0.249 
0.255 
0.256 
0.259 
0.256 
0.249 
0.252 
0.252 

p = 60, n_{1} = n_{2} = 31 

0.05 
F 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
FMOD 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 

Hotelling's 
0.976 
0.967 
0.961 
0.949 
0.938 
0.928 
0.915 
0.906 
0.899 
0.887 

0.01 
F 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
FMOD 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 

Hotelling's 
0.354 
0.330 
0.317 
0.305 
0.294 
0.281 
0.267 
0.258 
0.010 
0.248 

p = 80, n_{1} = n_{2} = 41 

0.05 
F 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
FMOD 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 

Hotelling's 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 

0.01 
F 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
FMOD 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 
1.000 

Hotelling's 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 

Table 3: Power analysis with restriction p < n1 + n2 − 1, where p is the number of columns (e.g., the number of genes) and n is the number of sample size (e.g., the number of individuals.) 
ρ



p 
n 
0 
0.1 
0.2 
0.3 
0.4 
0.5 
0.6 
0.7 
0.8 
0.9 
50 
26 
17.4 
17.3 
17 
16.6 
15.9 
15.1 
14.1 
12.8 
11.3 
9.6 
60 
31 
60.1 
59.2 
56.5 
52.3 
46.8 
40.6 
33.9 
27.2 
20.9 
15.4 
80 
41 
80.1 
78.8 
74.9 
68.9 
61.3 
52.5 
43.2 
33.9 
25.0 
17.1 
100 
20 
100.6 
98.9 
93.9 
86.1 
76.2 
64.9 
52.9 
41.0 
29.4 
19.1 
200 
20 
200.8 
197.6 
186.7 
169.9 
149.1 
125.4 
100.3 
75.4 
51.3 
28.9 
Table 4: Effective column size pˆ for p when n_{1} = n_{2} = n 
Correlations greater than in absolute value 
Nondiabetic 
Diabetic 
0.5 
117,610,455 
107,977,419 
0.7 
62,064,682 
52,999,817 
0.9 
11,663,163 
8,784,875 
Table 5: The number of pairwise correlations from the correlation matrices for nondiabetic and diabetic groups 
No. 
Gene Symbol 
ID 
PVAL 
Gene Title 
1 
ACP1 
201630 _s_at 
4.06e12 
acid phosphatase 1, soluble 
2 
ALDOB 
217238_s_at 
3.5e07 
aldolase B, fructosebisphosphate 
3 
ARG2 
203946_s_at 
1.34e11 
arginase, type II 
4 
CAT 
201432_at 
1.07e08 
catalase 
5 
CPE 
201117_s_at 
3.35e08 
carboxypeptidase E 
6 
CPE 
201116_s_at 
8.65e14 
carboxypeptidase E 
7 
CXCL10 
204533_at 
1.17e11 
chemokine (CXC motif) ligand 10 
8 
CYB5R4 
219079_at 
2.3e07 
cytochrome b5 reductase 4 
9 
FTL 
213187_x_at 
3.83e07 
ferritin, light polypeptide 
10 
FUCA1 
202838_at 
4.38e07 
fucosidase, alphaL 1, tissue 
11 
GAD2 
206780_at 
2.96e07 
glutamate decarboxylase 2 (pancreatic islets and brain, 65kDa) 
12 
GAPDH 
* 
1.92e07 
glyceraldehyde3phosphate dehydrogenase 
13 
GAPDH 
** 
3.45e11 
glyceraldehyde3phosphate dehydrogenase 
14 
GC 
204965_at 
7.04e09 
groupspecific component (vitamin D binding protein) 
15 
GCG 
206422_at 
5.33e10 
glucagon 
16 
GNAI1 
209576_at 
9.24e09 
guanine nucleotide binding protein (G protein), alpha inhibiting activity polypeptide 1 
17 
GNAS 
200981_x_at 
1.79e08 
GNAS complex locus 
18 
GNAS 
214548_x_at 
6.95e08 
GNAS complex locus 
19 
GNAS 
200780_x_at 
1.17e07 
GNAS complex locus 
20 
GNAS 
212273_x_at 
1.21e08 
GNAS complex locus 
21 
GNAS 
214157_at 
7.59e13 
GNAS complex locus 
22 
GPX3 
214091_s_at 
2.08e08 
glutathione peroxidase 3 (plasma) 
23 
GREM1 
218468_s_at 
7.55e13 
gremlin 1 
24 
GREM1 
218469_at 
7.54e11 
gremlin 1 
25 
GYG1 
201554_x_at 
1.72e08 
glycogenin 1 
26 
HMGCR 
202539_s_at 
6.44e12 
3hydroxy3methylglutarylCoA reductase 
27 
HPRT1 
202854_at 
1.95e08 
hypoxanthine phosphoribosyltransferase 1 
28 
HSPA8 
210338_s_at 
1.08e12 
heat shock 70kDa protein 8 
29 
IAPP 
207062_at 
1.95e18 
islet amyloid polypeptide 
30 
IARS2 
217900_at 
2.22e08 
isoleucyltRNA synthetase 2, mitochondrial 
31 
LEPROT 
202377_at 
1.57e07 
leptin receptor overlapping transcript 
32 
LIPA 
201847_at 
1.28e08 
lipase A, lysosomal acid, cholesterol esterase 
33 
NAMPT 
217738_at 
1.13e09 
nicotinamide phosphoribosyltransferase 
34 
NEUROD1 
206282_at 
2.51e07 
neurogenic differentiation 1 
35 
PCSK1 
205825_at 
8.42e18 
proprotein convertase subtilisin/kexin type 1 
Table 6: The significant genes of Type 2 Diabetes Mellitus at α = 0.01/22283 = 4.49 × 10^{7} when genes are matched with GeneCards data base The second column shows the name of the genes from UniGene bank. The third column shows the Entrez Gene Database UID number. The fourth column shows the pvalues adjusted by Bonferroni correction. The last column shows the title of the gene represented by the probe set. In column three, * and ** symbols are replaced for AFFXHUMGAPDH/M33197_M_at and AFFXHUMGAPDH/M33197_5_at, respectively.ene represented by the probe set. In column three, ? symbol is replaced for AFFXHUMGAPDH/M33197_5_at respectively 
No. 
Gene Symbol 
ID 
PVAL 
Gene Title 
36 
PEX2 
210296_s_at 
3.26e12 
peroxisomal biogenesis factor 2 
37 
PFKM 
210976_s_at 
8.3e08 
phosphofructokinase, muscle 
38 
PLAGL1 
209318_x_at 
3.36e09 
pleiomorphic adenoma genelike 1 
39 
PSMC6 
201699_at 
3.54e08 
proteasome (prosome, macropain) 26S subunit, ATPase, 6 
40 
PTGS2 
204748_at 
4.32e07 
prostaglandinendoperoxide synthase 2 (prostaglandin G/H synthase and cyclooxygenase) 
41 
PTPRN2 
203029_s_at 
1.82e07 
protein tyrosine phosphatase, receptor type, N polypeptide 2 
42 
PTS 
209694_at 
3.06e07 
6pyruvoyltetrahydropterin synthase 
43 
RBP4 
219140_s_at 
5.06e14 
retinol binding protein 4, plasma 
44 
SCD 
200832_s_at 
4.2e08 
stearoylCoA desaturase (delta9desaturase) 
45 
SDHB 
202675_at 
2.37e09 
succinate dehydrogenase complex, subunit B, iron sulfur (Ip) 
46 
SEL1L 
202061_s_at 
8.62e10 
sel1 suppressor of lin12like (C. elegans) 
47 
SSBP1 
202591_s_at 
1.64e10 
singlestranded DNA binding protein 1 
48 
TFPI 
210665_at 
1.64e09 
tissue factor pathway inhibitor (lipoproteinassociated coagulation inhibitor) 
49 
TFRC 
207332_s_at 
1.28e10 
transferrin receptor (p90, CD71) 
50 
TTR 
209660_at 
5.23e08 
transthyretin 
51 
USO1 
201832_s_at 
2.12e08 
USO1 vesicle docking protein homolog (yeast) 
52 
VDAC1 
212038_s_at 
3.59e09 
voltagedependent anion channel 1 
Table 7: Table 6 continues 
No. 
Gene Symbol 
ID 
PVAL 
Gene Title 
1 
ACP1 
201630_s_at 
4.06e12 
acid phosphatase 1, soluble 
2 
ALDOB 
217238_s_at 
3.5e07 
aldolase B, fructosebisphosphate 
3 
APC 
203525_s_at 
4.7e07 
adenomatous polyposis coli 
4 
ARG2 
203946_s_at 
1.34e11 
arginase, type II 
5 
ATP5B 
201322_at 
1.28e06 
ATP synthase, H+ transporting, mitochondrial F1 complex, beta polypeptide 
6 
CAT 
201432_at 
1.07e08 
catalase 
7 
CFTR 
215702_s_at 
1.06e06 
cystic fibrosis transmembrane conductance regulator (ATPbinding cassette subfamily C, member 7) 
8 
CPE 
201116_s_at 
8.65e14 
carboxypeptidase E 
9 
CPE 
201117_s_at 
3.35e08 
carboxypeptidase E 
10 
CTGF 
209101_at 
8.4e07 
connective tissue growth factor 
11 
CX3CL1 
823_at 
9.49e07 
chemokine (CX3C motif) ligand 1 
12 
CXCL10 
204533_at 
1.17e11 
chemokine (CXC motif) ligand 10 
13 
CYB5R4 
219079_at 
2.3e07 
cytochrome b5 reductase 4 
14 
CYCS 
208905_at 
1.85e06 
cytochrome c, somatic 
15 
FABP5 
202345_s_at 
2.08e06 
fatty acid binding protein 5 (psoriasisassociated) 
16 
FTL 
213187_x_at 
3.83e07 
ferritin, light polypeptide 
17 
FUCA1 
202838_at 
4.38e07 
fucosidase, alphaL 1, tissue 
18 
GAD2 
206780_at 
2.96e07 
glutamate decarboxylase 2 (pancreatic islets and brain, 65kDa) 
19 
GAPDH 
* 
1.92e07 
glyceraldehyde3phosphate dehydrogenase 
20 
GAPDH 
** 
3.45e11 
glyceraldehyde3phosphate dehydrogenase 
21 
GC 
204965_at 
7.04e09 
groupspecific component (vitamin D binding protein) 
22 
GCG 
206422_at 
5.33e10 
glucagon 
23 
GFPT1 
202722_s_at 
5.72e07 
glutamine–fructose6phosphate transaminase 1 
24 
GLO1 
200681_at 
7.17e07 
glyoxalase I 
25 
GNAI1 
209576_at 
9.24e09 
guanine nucleotide binding protein (G protein), alpha inhibiting activity polypeptide 1 
26 
GNAS 
200981_x_at 
1.79e08 
GNAS complex locus 
27 
GNAS 
212273_x_at 
1.21e08 
hypoxanthine phosphoribosyltransferase 1 
28 
GNAS 
200780_x_at 
1.17e07 
GNAS complex locus 
29 
GNAS 
214157_at 
7.59e13 
GNAS complex locus 
30 
GNAS 
214548_x_at 
6.95e08 
GNAS complex locus 
31 
GPX3 
214091_s_at 
2.08e08 
glutathione peroxidase 3 (plasma) 
32 
GREM1 
218469_at 
7.54e11 
gremlin 1 
33 
GREM1 
218468_s_at 
7.55e13 
gremlin 1 
34 
GYG1 
201554_x_at 
1.72e08 
glycogenin 1 
35 
HMGCR 
202539_s_at 
6.44e12 
3hydroxy3methylglutarylCoA reductase 
Table 8: The significant genes of Type 2 Diabetes Mellitus at α = 0.05/22283 = 2.24 × 10^{−6} when genes are matched with GeneCards data base In column three, *and **symbols are replaced for AFFXHUMGAPDH/M33197_M_at and AFFXHUMGAPDH/M33197_5_at, respectively. 
No. 
Gene Symbol 
ID 
PVAL 
Gene Title 
36 
HPRT1 
202854_at 
1.95e08 
hypoxanthine phosphoribosyltransferase 1 
37 
HSPA8 
210338_s_at 
1.08e12 
heat shock 70kDa protein 8 
38 
HSPA8 
208687_x_at 
1.58e06 
heat shock 70kDa protein 8 
39 
HSPD1 
200806_s_at 
1.24e06 
heat shock 60kDa protein 1 (chaperonin) 
40 
IAPP 
207062_at 
1.95e18 
islet amyloid polypeptide 
41 
IARS2 
217900_at 
2.22e08 
isoleucyltRNA synthetase 2, mitochondrial 
42 
INS 
206598_at 
5.49e07 
insulin 
43 
ISL1 
206104_at 
1.75e06 
ISL LIM homeobox 1 
44 
LEPROT 
202377_at 
1.57e07 
leptin receptor overlapping transcript 
45 
LIPA 
201847_at 
1.28e08 
lipase A, lysosomal acid, cholesterol esterase 
46 
NAMPT 
217738_at 
1.13e09 
nicotinamide phosphoribosyltransferase 
47 
NEUROD1 
206282_at 
2.51e07 
neurogenic differentiation 1 
48 
NUCB2 
203675_at 
1.8e06 
nucleobindin 2 
49 
OGT 
209240_at 
1.32e06 
Olinked Nacetylglucosamine (GlcNAc) transferase (UDPNacetylglucosamine:polypeptideNacetylglucosaminyl transferase) 
50 
PCSK1 
205825_at 
8.42e18 
proprotein convertase subtilisin/kexin type 1 
51 
PDHX 
203067_at 
1.11e06 
pyruvate dehydrogenase complex, component X 
52 
PEX2 
210296_s_at 
3.26e12 
peroxisomal biogenesis factor 2 
53 
PFKM 
210976_s_at 
8.3e08 
phosphofructokinase, muscle 
54 
PLAGL1 
209318_x_at 
3.36e09 
pleiomorphic adenoma genelike 1 
55 
PON2 
210830_s_at 
6.93e07 
paraoxonase 2 
56 
PROS1 
207808_s_at 
1.88e06 
protein S (alpha) 
57 
PSMC6 
201699_at 
3.54e08 
proteasome (prosome, macropain) 26S subunit, ATPase, 6 
58 
PTGS2 
204748_at 
4.32e07 
prostaglandinendoperoxide synthase 2 (prostaglandin G/H synthase and cyclooxygenase) 
59 
PTPN12 
202006_at 
5.75e07 
protein tyrosine phosphatase, nonreceptor type 12 
60 
PTPRN2 
203029_s_at 
1.82e07 
protein tyrosine phosphatase, receptor type, N polypeptide 2 
61 
PTS 
209694_at 
3.06e07 
6pyruvoyltetrahydropterin synthase 
62 
RBP4 
219140_s_at 
5.06e14 
retinol binding protein 4, plasma 
63 
SCD 
200832_s_at 
4.2e08 
stearoylCoA desaturase (delta9desaturase) 
64 
SDHB 
202675_at 
2.37e09 
succinate dehydrogenase complex, subunit B, iron sulfur (Ip) 
65 
SEL1L 
202061_s_at 
8.62e10 
sel1 suppressor of lin12like (C. elegans) 
66 
SSBP1 
202591_s_at 
1.64e10 
singlestranded DNA binding protein 1 
67 
SST 
213921_at 
8.11e07 
somatostatin 
68 
TFPI 
210665_at 
1.64e09 
tissue factor pathway inhibitor (lipoproteinassociated coagulation inhibitor) 
69 
TFPI 
210664_s_at 
6.24e07 
tissue factor pathway inhibitor (lipoproteinassociated coagulation inhibitor) 
70 
TFRC 
207332_s_at 
1.28e10 
transferrin receptor (p90, CD71) 
71 
TTR 
209660_at 
5.23e08 
transthyretin 
72 
USO1 
201832_s_at 
2.12e08 
USO1 vesicle docking protein homolog (yeast) 
73 
VDAC1 
212038_s_at 
3.59e09 
voltagedependent anion channel 1 
Table 9: Table 8 continues 
No. 
Gene Symbol 
Panther family/subfamily 
PANTHER Protein Class 
1 
APC 
Adenomatous polyposis coli protein (pthr12607:sf11) 

2 
FTL 
Ferritin light chain (pthr11431:sf47) 
storage protein 
3 
HMGCR 
3hydroxy3methylglutarylCoenzyme a reductase (pthr10572:sf2) 

4 
PEX2 
Peroxisome biogenesis factor2 PEX2 ortholog 

5 
PLAGL1 
Zinc finger protein plagl1 (pthr10032:sf227) 
KRAB box transcription factor 
6 
PTGS2 
Prostaglandin g/h synthase 2 (pthr11903:sf8) 
oxygenase 
7 
ATP5B 
Atp synthase subunit beta, mitochannel;
Chondrial (pthr15184:sf44) 
ATP ligandgated ion channel; DNA binding protein; hydrolase 
8 
GC 
Vitamin dbinding protein (pthr11385:sf11) 

9 
GNAI1 
Guanine nucleotidebinding Protein g(i) subunit alpha1 (pthr10218:sf227) 
heterotrimeric Gprotein 
10 
GYG1 
Glycogenin1 (pthr11183:sf18) 
glycosyltransferase 
11 
INS 
Insulinrelated (pthr11454:sf9) 
growth factor; peptide hormone 
12 
PON2 
Serum paraoxonase/arylesterase 2
(pthr11799:sf17) 

13 
FABP5 
Fatty acidbinding protein, Epidermalrelated (pthr11955:sf58) 

14 
GREM1 
Gremlin1 (pthr15283:sf3) 

15 
HPRT1 
Hypoxanthineguanine phosphoribosyltransferase (pthr22573:sf38) 
glycosyltransferase; mutase 
16 
IAPP 
Islet amyloid polypeptide (pthr10505:sf4) 
peptide hormone 
17 
IARS2 
Isoleucine–trna ligase, mitochonDrial (pthr11946:sf82) 
aminoacyltRNA synthetase 
18 
PCSK1 
Prosaas (pthr15531:sf0) 

19 
PTS 
6pyruvoyl tetrahydrobiopterin syn Thase (pthr12589:sf1) 

20 
ARG2 
Arginase2, mitochondrial (pthr11358:sf18) 
hydrolase 
21 
CTGF 
Connective tissue growth factor (pthr11348:sf7) 
growth factor 
22 
FUCA1 
Tissue alphalfucosidase (pthr10030:sf2) 

Table 10: Functional classification of the genes in Tables 69 by PANTHER 
No. 
Gene Symbol 
Panther family/subfamily 
PANTHER Protein Class 
23 
GAPDH 
Glyceraldehyde3phosphate dehy Drogenase (pthr10836:sf51)

Dehydrogenase 
24 
GLO1 
Lactoylglutathione lyase (pthr10374:sf8) 

25 
ISL1 
Insulin gene enhancer protein isl1 (pthr24204:sf3) 
Homeobox transcription factor; zinc finger transcription factor; nucleic acid binding 
26 
OGT 
Udpnacetylglucosamine–peptide Nacetylglucosaminyltransferase 110 Kda subunit (pthr23083:sf364) 
Glycosyltransferase 
27 
PCSK1 
Neuroendocrine convertas 1 (pthr10795:sf407) 
Serine protease 
28 
PSMC6 
26s protease regulatory subunit 10b (pthr23073:sf31) 
Hydrolase 
29 
PTPN12 
Tyrosineprotein phosphatase nonreceptor type 12 (pthr19134:sf283) 
Protein phosphatase 
30 
SSBP1 
Singlestranded dnabinding pro Tein, mitochondrial (pthr10302:sf0) 
DNA binding protein 
31 
TFRC 
Transferrin receptor protein 1 (pthr10404:sf26) 
Receptor 
32 
CFTR 
Cystic fibrosis transmembrane conductance regulator (pthr24223:sf19) 
Anion channel 
33 
CXCL10 
Cxc motif chemokine 10 (pthr10179:sf47) 
Chemokine 
34 
NEUROD1 
Neurogenic differentiation factor 1 (pthr19290:sf88) 
Basic helixloophelix transcription factor; nuclease 
35 
NUCB2 
Nucleobindin2 (pthr19237:sf22) 
Nucleic acid binding; annexin; calmodulin 
36 
PDHX 
Pyruvate dehydrogenase proTein x component, mitochondrial (pthr23151:sf57) 
Acetyltransferase 
37 
PFKM 
6phosphofructokinase, muscle type (pthr13697:sf13) 
Carbohydrate kinase 
38 
RBP4 
Retinolbinding protein 4 (pthr11873:sf2) 
transfer/carrie protein 
39 
SCD 
Acylcoa desaturase (pthr11351:sf31) 

40 
SEL1L 
Protein sel1 homolog 1 (pthr11102:sf70) 
Enzyme modulator 
41 
SST 
Somatostatin (pthr10558:sf2) 
Peptid hormone 
42 
USO1 
General vesicular transport factor P115 (pthr10013:sf0) 
Membrane traffic protein 
43 
CYCS 
Cytochrome c pthr11961:sf15) 

Table 11: Table 10 continues 
No. 
Gene Symbol 
Panther family/subfamily 
PANTHER Protein Class 
44 
GNAS 
Guanine nucleotidebinding protein G(s) subunit alpha isoforms xlas (pthr10218:sf36)


45 
LEPROT 
Leptin receptor generelated protein (pthr12050:sf3) 
Cytokine receptor 
46 
TTR 
Transthyretin (pthr10395:sf12) 
Transporter; transfer/carrier protein 
47 
ALDOB 
Fructosebisphosphate aldolaseb (pthr11627:sf2) 

48 
CAT 
Catalase (pthr11465:sf9) 
Peroxidase 
49 
CPE 
Carboxypeptidase e (pthr11532:sf59) 
Metalloprotease 
50 
CYB5R4 
Cytochrome b5 reductase 4 (pthr19370:sf122) 
Reductase 
51 
GCG 
Glucagon (pthr11418:sf0) 
Peptide hormone 
52 
GFPT1 
Glutamine–fructose6phosphate Aminotransferase [isomerizing] 1 (pthr10937:sf2) 
Transaminase 
53 
LIPA 
Lysosomal acid lipase/cholesteryl es Ter hydrolase (pthr11005:sf26) 
Lipase 
54 
NAMPT 
Nicotinamide phosphoribosyltransFerase (pthr11098:sf15) 
Cytokine 
55 
PROS1 
Vitamin kdependent proteins (pthr24040:sf0) 

56 
VDAC1 
Voltagedependent anionselective channel protein 1 (pthr11743:sf13) 
Anion channel; voltagegated ion channel 
57 
ACP1 
Low molecular weight phosphortyrosine protein phosphatase (pthr11717:sf7) 
Protein phosphatase; reductase 
58 
CX3CL1 
Fractalkine (pthr12015:sf92) 
Chemokine 
59 
GAD2 
Glutamate decarboxylase 2 (pthr11999:sf77) 
Decarboxylase 
60 
GPX3 
Glutathione peroxidase 3 (pthr11592:sf32) 
Peroxidase 
61 
HSPA8 
Heat shock cognate 71 kda protein (pthr19375:sf239) 
Hsp70 family chaperone 
62 
PTPRN2 
Receptortype tyrosineprotein phos
Phatase n2 (pthr19134:sf266) 
Receptor; protein phosphatase 
63 
SDHB 
Succinate dehydrogenase [ubiquinone] ironsulfur subunit, Mitochondrial (pthr11921:sf29) 
Dehydrogenase 
64 
TFPI 
Tissue factor pathway inhibitor
(pthr10083:sf238) 
Serine protease inhibitor 
Table 12: Table 10 continues 
No. 
Gene Symbol 
ID 
PVAL 
Gene Title 
1 
ACP1 
201630 _s_at 
4.06e12 
acid phosphatase 1, soluble 
2 
ALDOB 
217238_s_at 
3.5e07 
aldolase B, fructosebisphosphate 
3 
ARG2 
203946_s_at 
1.34e11 
arginase, type II 
4 
CAT 
201432_at 
1.07e08 
catalase 
5 
CPE 
201117_s_at 
3.35e08 
carboxypeptidase E 
6 
CPE 
201116_s_at 
8.65e14 
carboxypeptidase E 
7 
CXCL10 
204533_at 
1.17e11 
chemokine (CXC motif) ligand 10 
8 
CYB5R4 
219079_at 
2.3e07 
cytochrome b5 reductase 4 
9 
FTL 
213187_x_at 
3.83e07 
ferritin, light polypeptide 
10 
FUCA1 
202838_at 
4.38e07 
fucosidase, alphaL 1, tissue 
11 
GAD2 
206780_at 
2.96e07 
glutamate decarboxylase 2 (pancreatic islets and brain, 65kDa) 
12 
GAPDH 
* 
1.92e07 
glyceraldehyde3phosphate dehydrogenase 
13 
GAPDH 
** 
3.45e11 
glyceraldehyde3phosphate dehydrogenase 
14 
GC 
204965_at 
7.04e09 
groupspecific component (vitamin D binding protein) 
15 
GCG 
206422_at 
5.33e10 
glucagon 
16 
GNAI1 
209576_at 
9.24e09 
guanine nucleotide binding protein (G protein), alpha inhibiting activity polypeptide 1 
17 
GNAS 
200981_x_at 
1.79e08 
GNAS complex locus 
18 
GNAS 
214548_x_at 
6.95e08 
GNAS complex locus 
19 
GNAS 
200780_x_at 
1.17e07 
GNAS complex locus 
20 
GNAS 
212273_x_at 
1.21e08 
GNAS complex locus 
21 
GNAS 
214157_at 
7.59e13 
GNAS complex locus 
22 
GPX3 
214091_s_at 
2.08e08 
glutathione peroxidase 3 (plasma) 
23 
GREM1 
218468_s_at 
7.55e13 
gremlin 1 
24 
GREM1 
218469_at 
7.54e11 
gremlin 1 
25 
GYG1 
201554_x_at 
1.72e08 
glycogenin 1 
26 
HMGCR 
202539_s_at 
6.44e12 
3hydroxy3methylglutarylCoA reductase 
27 
HPRT1 
202854_at 
1.95e08 
hypoxanthine phosphoribosyltransferase 1 
28 
HSPA8 
210338_s_at 
1.08e12 
heat shock 70kDa protein 8 
29 
IAPP 
207062_at 
1.95e18 
islet amyloid polypeptide 
30 
IARS2 
217900_at 
2.22e08 
isoleucyltRNA synthetase 2, mitochondrial 
31 
LEPROT 
202377_at 
1.57e07 
leptin receptor overlapping transcript 
32 
LIPA 
201847_at 
1.28e08 
lipase A, lysosomal acid, cholesterol esterase 
33 
NAMPT 
217738_at 
1.13e09 
nicotinamide phosphoribosyltransferase 
34 
NEUROD1 
206282_at 
2.51e07 
neurogenic differentiation 1 
35 
PCSK1 
205825_at 
8.42e18 
proprotein convertase subtilisin/kexin type 1 
Table 6: The significant genes of Type 2 Diabetes Mellitus at α = 0.01/22283 = 4.49 × 10^{7} when genes are matched with GeneCards data base The second column shows the name of the genes from UniGene bank. The third column shows the Entrez Gene Database UID number. The fourth column shows the pvalues adjusted by Bonferroni correction. The last column shows the title of the gene represented by the probe set. In column three, * and ** symbols are replaced for AFFXHUMGAPDH/M33197_M_at and AFFXHUMGAPDH/M33197_5_at, respectively.ene represented by the probe set. In column three, ? symbol is replaced for AFFXHUMGAPDH/M33197_5_at respectively 
No. 
Gene Symbol 
ID 
PVAL 
Gene Title 
36 
PEX2 
210296_s_at 
3.26e12 
peroxisomal biogenesis factor 2 
37 
PFKM 
210976_s_at 
8.3e08 
phosphofructokinase, muscle 
38 
PLAGL1 
209318_x_at 
3.36e09 
pleiomorphic adenoma genelike 1 
39 
PSMC6 
201699_at 
3.54e08 
proteasome (prosome, macropain) 26S subunit, ATPase, 6 
40 
PTGS2 
204748_at 
4.32e07 
prostaglandinendoperoxide synthase 2 (prostaglandin G/H synthase and cyclooxygenase) 
41 
PTPRN2 
203029_s_at 
1.82e07 
protein tyrosine phosphatase, receptor type, N polypeptide 2 
42 
PTS 
209694_at 
3.06e07 
6pyruvoyltetrahydropterin synthase 
43 
RBP4 
219140_s_at 
5.06e14 
retinol binding protein 4, plasma 
44 
SCD 
200832_s_at 
4.2e08 
stearoylCoA desaturase (delta9desaturase) 
45 
SDHB 
202675_at 
2.37e09 
succinate dehydrogenase complex, subunit B, iron sulfur (Ip) 
46 
SEL1L 
202061_s_at 
8.62e10 
sel1 suppressor of lin12like (C. elegans) 
47 
SSBP1 
202591_s_at 
1.64e10 
singlestranded DNA binding protein 1 
48 
TFPI 
210665_at 
1.64e09 
tissue factor pathway inhibitor (lipoproteinassociated coagulation inhibitor) 
49 
TFRC 
207332_s_at 
1.28e10 
transferrin receptor (p90, CD71) 
50 
TTR 
209660_at 
5.23e08 
transthyretin 
51 
USO1 
201832_s_at 
2.12e08 
USO1 vesicle docking protein homolog (yeast) 
52 
VDAC1 
212038_s_at 
3.59e09 
voltagedependent anion channel 1 
Table 7: Table 6 continues 
No. 
Gene Symbol 
ID 
PVAL 
Gene Title 
1 
ACP1 
201630_s_at 
4.06e12 
acid phosphatase 1, soluble 
2 
ALDOB 
217238_s_at 
3.5e07 
aldolase B, fructosebisphosphate 
3 
APC 
203525_s_at 
4.7e07 
adenomatous polyposis coli 
4 
ARG2 
203946_s_at 
1.34e11 
arginase, type II 
5 
ATP5B 
201322_at 
1.28e06 
ATP synthase, H+ transporting, mitochondrial F1 complex, beta polypeptide 
6 
CAT 
201432_at 
1.07e08 
catalase 
7 
CFTR 
215702_s_at 
1.06e06 
cystic fibrosis transmembrane conductance regulator (ATPbinding cassette subfamily C, member 7) 
8 
CPE 
201116_s_at 
8.65e14 
carboxypeptidase E 
9 
CPE 
201117_s_at 
3.35e08 
carboxypeptidase E 
10 
CTGF 
209101_at 
8.4e07 
connective tissue growth factor 
11 
CX3CL1 
823_at 
9.49e07 
chemokine (CX3C motif) ligand 1 
12 
CXCL10 
204533_at 
1.17e11 
chemokine (CXC motif) ligand 10 
13 
CYB5R4 
219079_at 
2.3e07 
cytochrome b5 reductase 4 
14 
CYCS 
208905_at 
1.85e06 
cytochrome c, somatic 
15 
FABP5 
202345_s_at 
2.08e06 
fatty acid binding protein 5 (psoriasisassociated) 
16 
FTL 
213187_x_at 
3.83e07 
ferritin, light polypeptide 
17 
FUCA1 
202838_at 
4.38e07 
fucosidase, alphaL 1, tissue 
18 
GAD2 
206780_at 
2.96e07 
glutamate decarboxylase 2 (pancreatic islets and brain, 65kDa) 
19 
GAPDH 
* 
1.92e07 
glyceraldehyde3phosphate dehydrogenase 
20 
GAPDH 
** 
3.45e11 
glyceraldehyde3phosphate dehydrogenase 
21 
GC 
204965_at 
7.04e09 
groupspecific component (vitamin D binding protein) 
22 
GCG 
206422_at 
5.33e10 
glucagon 
23 
GFPT1 
202722_s_at 
5.72e07 
glutamine–fructose6phosphate transaminase 1 
24 
GLO1 
200681_at 
7.17e07 
glyoxalase I 
25 
GNAI1 
209576_at 
9.24e09 
guanine nucleotide binding protein (G protein), alpha inhibiting activity polypeptide 1 
26 
GNAS 
200981_x_at 
1.79e08 
GNAS complex locus 
27 
GNAS 
212273_x_at 
1.21e08 
hypoxanthine phosphoribosyltransferase 1 
28 
GNAS 
200780_x_at 
1.17e07 
GNAS complex locus 
29 
GNAS 
214157_at 
7.59e13 
GNAS complex locus 
30 
GNAS 
214548_x_at 
6.95e08 
GNAS complex locus 
31 
GPX3 
214091_s_at 
2.08e08 
glutathione peroxidase 3 (plasma) 
32 
GREM1 
218469_at 
7.54e11 
gremlin 1 
33 
GREM1 
218468_s_at 
7.55e13 
gremlin 1 
34 
GYG1 
201554_x_at 
1.72e08 
glycogenin 1 
35 
HMGCR 
202539_s_at 
6.44e12 
3hydroxy3methylglutarylCoA reductase 
Table 8: The significant genes of Type 2 Diabetes Mellitus at α = 0.05/22283 = 2.24 × 10^{−6} when genes are matched with GeneCards data base In column three, *and **symbols are replaced for AFFXHUMGAPDH/M33197_M_at and AFFXHUMGAPDH/M33197_5_at, respectively. 
No. 
Gene Symbol 
ID 
PVAL 
Gene Title 
36 
HPRT1 
202854_at 
1.95e08 
hypoxanthine phosphoribosyltransferase 1 
37 
HSPA8 
210338_s_at 
1.08e12 
heat shock 70kDa protein 8 
38 
HSPA8 
208687_x_at 
1.58e06 
heat shock 70kDa protein 8 
39 
HSPD1 
200806_s_at 
1.24e06 
heat shock 60kDa protein 1 (chaperonin) 
40 
IAPP 
207062_at 
1.95e18 
islet amyloid polypeptide 
41 
IARS2 
217900_at 
2.22e08 
isoleucyltRNA synthetase 2, mitochondrial 
42 
INS 
206598_at 
5.49e07 
insulin 
43 
ISL1 
206104_at 
1.75e06 
ISL LIM homeobox 1 
44 
LEPROT 
202377_at 
1.57e07 
leptin receptor overlapping transcript 
45 
LIPA 
201847_at 
1.28e08 
lipase A, lysosomal acid, cholesterol esterase 
46 
NAMPT 
217738_at 
1.13e09 
nicotinamide phosphoribosyltransferase 
47 
NEUROD1 
206282_at 
2.51e07 
neurogenic differentiation 1 
48 
NUCB2 
203675_at 
1.8e06 
nucleobindin 2 
49 
OGT 
209240_at 
1.32e06 
Olinked Nacetylglucosamine (GlcNAc) transferase (UDPNacetylglucosamine:polypeptideNacetylglucosaminyl transferase) 
50 
PCSK1 
205825_at 
8.42e18 
proprotein convertase subtilisin/kexin type 1 
51 
PDHX 
203067_at 
1.11e06 
pyruvate dehydrogenase complex, component X 
52 
PEX2 
210296_s_at 
3.26e12 
peroxisomal biogenesis factor 2 
53 
PFKM 
210976_s_at 
8.3e08 
phosphofructokinase, muscle 
54 
PLAGL1 
209318_x_at 
3.36e09 
pleiomorphic adenoma genelike 1 
55 
PON2 
210830_s_at 
6.93e07 
paraoxonase 2 
56 
PROS1 
207808_s_at 
1.88e06 
protein S (alpha) 
57 
PSMC6 
201699_at 
3.54e08 
proteasome (prosome, macropain) 26S subunit, ATPase, 6 
58 
PTGS2 
204748_at 
4.32e07 
prostaglandinendoperoxide synthase 2 (prostaglandin G/H synthase and cyclooxygenase) 
59 
PTPN12 
202006_at 
5.75e07 
protein tyrosine phosphatase, nonreceptor type 12 
60 
PTPRN2 
203029_s_at 
1.82e07 
protein tyrosine phosphatase, receptor type, N polypeptide 2 
61 
PTS 
209694_at 
3.06e07 
6pyruvoyltetrahydropterin synthase 
62 
RBP4 
219140_s_at 
5.06e14 
retinol binding protein 4, plasma 
63 
SCD 
200832_s_at 
4.2e08 
stearoylCoA desaturase (delta9desaturase) 
64 
SDHB 
202675_at 
2.37e09 
succinate dehydrogenase complex, subunit B, iron sulfur (Ip) 
65 
SEL1L 
202061_s_at 
8.62e10 
sel1 suppressor of lin12like (C. elegans) 
66 
SSBP1 
202591_s_at 
1.64e10 
singlestranded DNA binding protein 1 
67 
SST 
213921_at 
8.11e07 
somatostatin 
68 
TFPI 
210665_at 
1.64e09 
tissue factor pathway inhibitor (lipoproteinassociated coagulation inhibitor) 
69 
TFPI 
210664_s_at 
6.24e07 
tissue factor pathway inhibitor (lipoproteinassociated coagulation inhibitor) 
70 
TFRC 
207332_s_at 
1.28e10 
transferrin receptor (p90, CD71) 
71 
TTR 
209660_at 
5.23e08 
transthyretin 
72 
USO1 
201832_s_at 
2.12e08 
USO1 vesicle docking protein homolog (yeast) 
73 
VDAC1 
212038_s_at 
3.59e09 
voltagedependent anion channel 1 
Table 9: Table 8 continues 
No. 
Gene Symbol 
Panther family/subfamily 
PANTHER Protein Class 
1 
APC 
Adenomatous polyposis coli protein (pthr12607:sf11) 

2 
FTL 
Ferritin light chain (pthr11431:sf47) 
storage protein 
3 
HMGCR 
3hydroxy3methylglutarylCoenzyme a reductase (pthr10572:sf2) 

4 
PEX2 
Peroxisome biogenesis factor2 PEX2 ortholog 

5 
PLAGL1 
Zinc finger protein plagl1 (pthr10032:sf227) 
KRAB box transcription factor 
6 
PTGS2 
Prostaglandin g/h synthase 2 (pthr11903:sf8) 
oxygenase 
7 
ATP5B 
Atp synthase subunit beta, mitochannel;
Chondrial (pthr15184:sf44) 
ATP ligandgated ion channel; DNA binding protein; hydrolase 
8 
GC 
Vitamin dbinding protein (pthr11385:sf11) 

9 
GNAI1 
Guanine nucleotidebinding Protein g(i) subunit alpha1 (pthr10218:sf227) 
heterotrimeric Gprotein 
10 
GYG1 
Glycogenin1 (pthr11183:sf18) 
glycosyltransferase 
11 
INS 
Insulinrelated (pthr11454:sf9) 
growth factor; peptide hormone 
12 
PON2 
Serum paraoxonase/arylesterase 2
(pthr11799:sf17) 

13 
FABP5 
Fatty acidbinding protein, Epidermalrelated (pthr11955:sf58) 

14 
GREM1 
Gremlin1 (pthr15283:sf3) 

15 
HPRT1 
Hypoxanthineguanine phosphoribosyltransferase (pthr22573:sf38) 
glycosyltransferase; mutase 
16 
IAPP 
Islet amyloid polypeptide (pthr10505:sf4) 
peptide hormone 
17 
IARS2 
Isoleucine–trna ligase, mitochonDrial (pthr11946:sf82) 
aminoacyltRNA synthetase 
18 
PCSK1 
Prosaas (pthr15531:sf0) 

19 
PTS 
6pyruvoyl tetrahydrobiopterin syn Thase (pthr12589:sf1) 

20 
ARG2 
Arginase2, mitochondrial (pthr11358:sf18) 
hydrolase 
21 
CTGF 
Connective tissue growth factor (pthr11348:sf7) 
growth factor 
22 
FUCA1 
Tissue alphalfucosidase (pthr10030:sf2) 

Table 10: Functional classification of the genes in Tables 69 by PANTHER 
No. 
Gene Symbol 
Panther family/subfamily 
PANTHER Protein Class 
23 
GAPDH 
Glyceraldehyde3phosphate dehy Drogenase (pthr10836:sf51)

Dehydrogenase 
24 
GLO1 
Lactoylglutathione lyase (pthr10374:sf8) 

25 
ISL1 
Insulin gene enhancer protein isl1 (pthr24204:sf3) 
Homeobox transcription factor; zinc finger transcription factor; nucleic acid binding 
26 
OGT 
Udpnacetylglucosamine–peptide Nacetylglucosaminyltransferase 110 Kda subunit (pthr23083:sf364) 
Glycosyltransferase 
27 
PCSK1 
Neuroendocrine convertas 1 (pthr10795:sf407) 
Serine protease 
28 
PSMC6 
26s protease regulatory subunit 10b (pthr23073:sf31) 
Hydrolase 
29 
PTPN12 
Tyrosineprotein phosphatase nonreceptor type 12 (pthr19134:sf283) 
Protein phosphatase 
30 
SSBP1 
Singlestranded dnabinding pro Tein, mitochondrial (pthr10302:sf0) 
DNA binding protein 
31 
TFRC 
Transferrin receptor protein 1 (pthr10404:sf26) 
Receptor 
32 
CFTR 
Cystic fibrosis transmembrane conductance regulator (pthr24223:sf19) 
Anion channel 
33 
CXCL10 
Cxc motif chemokine 10 (pthr10179:sf47) 
Chemokine 
34 
NEUROD1 
Neurogenic differentiation factor 1 (pthr19290:sf88) 
Basic helixloophelix transcription factor; nuclease 
35 
NUCB2 
Nucleobindin2 (pthr19237:sf22) 
Nucleic acid binding; annexin; calmodulin 
36 
PDHX 
Pyruvate dehydrogenase proTein x component, mitochondrial (pthr23151:sf57) 
Acetyltransferase 
37 
PFKM 
6phosphofructokinase, muscle type (pthr13697:sf13) 
Carbohydrate kinase 
38 
RBP4 
Retinolbinding protein 4 (pthr11873:sf2) 
transfer/carrie protein 
39 
SCD 
Acylcoa desaturase (pthr11351:sf31) 

40 
SEL1L 
Protein sel1 homolog 1 (pthr11102:sf70) 
Enzyme modulator 
41 
SST 
Somatostatin (pthr10558:sf2) 
Peptid hormone 
42 
USO1 
General vesicular transport factor P115 (pthr10013:sf0) 
Membrane traffic protein 
43 
CYCS 
Cytochrome c pthr11961:sf15) 

Table 11: Table 10 continues 
No. 
Gene Symbol 
Panther family/subfamily 
PANTHER Protein Class 
44 
GNAS 
Guanine nucleotidebinding protein G(s) subunit alpha isoforms xlas (pthr10218:sf36)


45 
LEPROT 
Leptin receptor generelated protein (pthr12050:sf3) 
Cytokine receptor 
46 
TTR 
Transthyretin (pthr10395:sf12) 
Transporter; transfer/carrier protein 
47 
ALDOB 
Fructosebisphosphate aldolaseb (pthr11627:sf2) 

48 
CAT 
Catalase (pthr11465:sf9) 
Peroxidase 
49 
CPE 
Carboxypeptidase e (pthr11532:sf59) 
Metalloprotease 
50 
CYB5R4 
Cytochrome b5 reductase 4 (pthr19370:sf122) 
Reductase 
51 
GCG 
Glucagon (pthr11418:sf0) 
Peptide hormone 
52 
GFPT1 
Glutamine–fructose6phosphate Aminotransferase [isomerizing] 1 (pthr10937:sf2) 
Transaminase 
53 
LIPA 
Lysosomal acid lipase/cholesteryl es Ter hydrolase (pthr11005:sf26) 
Lipase 
54 
NAMPT 
Nicotinamide phosphoribosyltransFerase (pthr11098:sf15) 
Cytokine 
55 
PROS1 
Vitamin kdependent proteins (pthr24040:sf0) 

56 
VDAC1 
Voltagedependent anionselective channel protein 1 (pthr11743:sf13) 
Anion channel; voltagegated ion channel 
57 
ACP1 
Low molecular weight phosphortyrosine protein phosphatase (pthr11717:sf7) 
Protein phosphatase; reductase 
58 
CX3CL1 
Fractalkine (pthr12015:sf92) 
Chemokine 
59 
GAD2 
Glutamate decarboxylase 2 (pthr11999:sf77) 
Decarboxylase 
60 
GPX3 
Glutathione peroxidase 3 (pthr11592:sf32) 
Peroxidase 
61 
HSPA8 
Heat shock cognate 71 kda protein (pthr19375:sf239) 
Hsp70 family chaperone 
62 
PTPRN2 
Receptortype tyrosineprotein phos
Phatase n2 (pthr19134:sf266) 
Receptor; protein phosphatase 
63 
SDHB 
Succinate dehydrogenase [ubiquinone] ironsulfur subunit, Mitochondrial (pthr11921:sf29) 
Dehydrogenase 
64 
TFPI 
Tissue factor pathway inhibitor
(pthr10083:sf238) 
Serine protease inhibitor 
Table 12: Table 10 continues 