Chlamydomonas is liquid medium and light. However, the microalga can also be grown on agar plates and in darkness. Our aim is to analyze and compare gene expression of cells cultivated in these different conditions. For that purpose, RNA-seq data are obtained from Chlamydomonas samples of two different labs grown in four environmental conditions . The RNA seq data are analyzed by surprisal analysis, which allows the simultaneous meta-analysis of all the samples. First we identify a balance state, which defines a state where the expression levels are similar in all the samples irrespectively of their growth conditions, or lab origin. In addition our analysis identifies additional constraints needed to quantify the deviation with respect to the balance state. The first constraint differentiates the agar samples versus the liquid ones; the second constraint the dark samples versus the light ones. The two constraints are almost of equal importance. Pathways involved in stress responses are found in the agar phenotype while the liquid phenotype comprises ATP and NADH production pathways. Remodeling of membrane is suggested in the dark phenotype while photosynthetic pathways characterize the light phenotype. The same trends are also present when performing purely statistical analysis such as K-means clustering and differentially expressed genes.The usual cultivation mode of the green microalga  Chlamydomonas reinhardtii is a unicellular green microalga which has been a reference organism for photosynthetic studies for decades [Chlamydomonas has also become a model of choice for expression studies aimed at dissecting acclimation to various conditions and perturbations  using -omics strategies [Chlamydomonas spp. also includes distinct environmental niches such as soil (the source of the C. reinhardtii strain), glacier  and ponds [ decades . With th decades , Chlamydrategies . Until nnd ponds , which mChlamydomonas may experience in its natural environment. In addition, looking at algal expression in non-standard conditions is also justified as immobilized microalgae on solid-state photobioreactors represent a growing field of investigation for production of high value compounds [C. reinhardtii [Cultivations in the light or in darkness, but also in liquid or on solid medium are thus representative of what ompounds  and wastompounds . Moreoveompounds . To undeompounds –11 and rnhardtii . The metnhardtii –11. We cWe compared the results of surprisal analysis to conventional purely statistical methods currently used to analysis gene expression levels: K-means clustering and differentially expressed genes. The main difference is that the purely statistical analyses are carried out on mean centered data, while surprisal analysis yields a balance state compared to which the changes due to the different growth conditions are quantified on a thermodynamical basis ,8,10,13 -2.s-1) and acetate  [5 to 1x106 cells per colony, which represents 10 days of cultivation for light-grown colonies and 3 weeks for dark-grown colonies. For liquid grown samples, a complemented version of our reference strain was used, the iclC strain. The iclC strain is very similar to our reference strain as described in [iclC was inoculated from a 48 h liquid preculture into a sterilized Multi-Cultivator MC 1000-OD (Photon Systems Instruments) containing 80 mL of Tris-Phosphate [-2.s-1). Two time points of the growth curves (12h and 28h of growth) were chosen for RNA extraction, corresponding to early (≈1x106 cells/mL) and mid-exponential (≈4x106 cells/mL) growth phase. The growth curves were made in triplicate.The wild-type reference strain of our laboratory derived from the 137C strain  was used medium) , in darkribed in ,16. iclChosphate , buffere7 cells were pelleted for RNA extraction at time point 12h and 5.5x107 cells at time point 28h. RNA was extracted according to [For agar-grown samples, colonies were frozen at -80°C before RNA extraction. RNA was isolated from individual colonies using RNeasy Qiagen plant kit. For liquid-grown samples, 1.5x10rding to . RNA samLibrary preparation started with 100 ng total RNA for agar-grown samples 500 ng total RNA for liquid-grown samples. Illumina Sequencing (SE 1x75 on a NextSeq500 machine) was performed at the GIGA-R Sequencing platform (University of Liège) following manufacturer’s protocol .www.bioinformatics.babraham.ac.uk/projects/). No significant problems were observed.Read quality was assessed with FastQC v.0.11.5  , removinChlamydomonas reinhardtii genome v5.5 assembly [Mapping of the reads to the assembly  was doneassembly  with defassembly . ExpressSurprisal analysis is based on thermodynamical entropy ,10,13,21In editing the data for surprisal analysis all transcripts with an average FPKM value lower than 1 based from the agar grown colonies were removed because most of the noise is due to low expression values, in particular those below 1 FPKM . In totaYi(s), where i stands for a gene and s for a sample) of the N = 12774 gene expression values, Xi(s), in each of the 38 samples was subjected to surprisal analysis [Yi(s) are arranged in a N x Ns rectangular matrix Y, where Ns = 38 is the number of samples. The constraints, Giα, and Lagrange multipliers, λα(s) are determined via the singular value decomposition (SVD) of Y as described by [α is the index of constraints, Ns is the total number of samples, i is the index of the gene and s is the index of the sample. The expression for Giα and λα(s) are given by the eigenvectors and the eigenvalues of the SVD of the matrix Y:U and V are respectively the left and right eigenvectors of the Y matrix as determined by the SVD procedure and ωα the singular values. The eigenvalues of the Y matrix are ordered by decreasing order and when all the Ns terms are kept, the surprisal expression of the transcript levels given in exact representation of the data. Usually just a few terms in Ns) suffice to describe the input. Each constraint α corresponds to a given phenotype. For a given value of α, the surprisal analysis allows for a factorization between the weight of the constraint, Giα, on a given gene i and the Lagrange multiplier, λα(s), that is the weight of sample s in the phenotype that corresponds to the constraint α.The natural logarithm . The vai’ in the balanced state. The balance state is this stable state that is common to all the colonies and with respect to which the changes in the gene expression levels due to the successive constraints, α = 1, …, Ns, are expressed. The larger is the prior thermodynamical weight of a gene i, Gi0λ0, the more stable it is, and the lower is its free energy which is given by α, one can identify different groups of samples that differ by the sign of their Lagrange multiplier, λα(s) for the phenotype α. In particular, we show above that for the first constraint, α = 1, samples grown on agar and those grown in liquid have an opposite sign of their Lagrange multipliers. The analysis of the weights of the corresponding phenotype vector, Giα, over the genes in terms of pathways gives access to the different pathway contributions to the phenotype agar-grown versus liquid-grown. For α = 2, samples grown in the dark and samples grown in the light are characterized by Lagrange multipliers of different signs. The analysis of the corresponding phenotype allows identifying the pathways that contribute most to the growth in dark and light conditions respectively.In the first term of α were ranked according the value of the weight Giα. According to this ranking, 100 smallest and largest values were considered differentially expressed for each phenotype. In the case of the balance state, genes that correspond to a term Gi0λ0 > 0 are the most stable and those for which Gi0λ0 > 0 are unstable. The latter are the genes that will appear with the largest and the smaller weights in the phenotypes associated with the constraints and therefore will be the most differentially expressed in the constraints, α = 1, …, Ns.Genes of the phenotype associated with each constraint α. This approach has the advantage to take into account the weights of all the genes, Giα, in a given constraint and therefore do not to depend on the number of genes  kept in the differential gene expression analysis. The two approaches are complementary because pathways that comprise several genes that have a high weight in a given phenotype  will have a large weight.In , differehttp://www.genome.jp/kegg/) and the functional annotation info for C. reinhardtii v5.5 predicted proteins were obtained from the correspondence table downloaded from Phytozome.Genes were categorized in gene sets using the Kyoto Encyclopedia of Genes and Genomes (KEGG)  and negative (N) weight of the pathway for constraint α:J to constraint α. In NJ is the number of genes in pathway J.Pathways that correspond to a gene set with less than 10 genes were omitted from the dataset. For each constraint, SRJ, were ordered according their value describing their importance for the described phenotype. These gene sets where all values Giα are either positive or negative, were subsequently ranked on Set ratios, Gi0λ0 > 0 are the most stable and those for which Gi0λ0 < 0 are unstable. For the first phenotype, genes which correspond to a term Gi1λ1(s) >0 are overexpressed for samples grown in liquid conditions and underexpressed for samples grown on agar while genes for which Gi2λ2(s) >0 are overexpressed in the light conditions and underexpressed in dark ones. Since the values of the Lagrange multiplier, λ1(s), are positive for the colonies grown in liquid phase and negative for those grown on agar  while samples grown in the dark have negative λ2(s) values. So high SR pathway ratios correspond to gene sets that are over expressed for samples grown in light conditions while low SR ratios values correspond to gene sets that are over expressed in dark grown samples.Both low ratios and high ratios are predicted by surprisal analysis to be important for the phenotype and to be enriched in their respective phenotypes. For the balance state, genes that correspond to a term 1(s) and λ2(s) into two groups, liquid versus agar and dark versus light for each drawn subset was tested using a Wilcoxon t-test. The threshold for of the pvalue was set to <0.05. In all subsets two groups corresponding to the two variables, λ1(s) and λ2(s), could be identified. Because the sign of λ0(s) and Giα is a convention selected automatically by the SVD procedure, they differ between subsets. Signs were reattributed to a chosen convention depending on the sign of Giα of one of the most enriched genes for the experimental variable in the analysis of all samples.1000 random combinations of biological replicates of the AL (6), AD (3), LL (3) series were drawn to confirm the consistency of the surprisal analysis under influence of biological variation. The 2 samples from the LD series (LD1 and LD2) from  were alwExpression levels (FPKM) were square root transformed and tested for differential expression using CLC Genomics Workbench (10.0.1) by ‘Exact Test’ for two-group comparisons  using a The KMC K-means algorithm of MeV (version 4.8.1)  was impl-2.s-1) or in the dark, on acetate containing medium (17 mM). Individual colonies were picked up for RNA-seq analysis when they reached 0.5–0.8 cm of diameter, corresponding to 5x105 to 1x106 cells per colony (-2.s-1) were obtained using a similar strain [6 cells/mL) and the mid-exponential (4x106 cells/mL) phase, named LL for Liquid-Light (LL1-LL8)  . TranscrLL1-LL8) . Surpris0(s) and the balance state phenotype G0. The λ0(s) values for each sample, s, are plotted in 0(s)  are constant within a range (41 units) that reflects small variations from sample to sample. Thus we first comment that all the 38 samples exhibit a common balance state despite the fact they are obtained from two different laboratories .The values of the Lagrange multipliers and of the constraints were computed as described in the ‘Surprisal analysis’ section of Methods. The balance or steady state, that is the reference stable distribution of expression levels common to all samples in the absence of any biological constraint, is defined by the Lagrange multiplier λ1(s) (1(s) is negative for 27 samples  grown on agar on the 28 analyzed and positive for all the 10 samples grown in liquid . This result identifies the first constraint as the one that allows discriminating between the agar and liquid samples. The value of λ1(s) for the sample AD4 is slightly positive and very close to zero. This indicates that the weight of the first constraint is close to zero for this sample grown on agar in the dark, which may reflect slightly different growth conditions compared to the other agar grown colonies. Moreover, the difference between the range of positive and negative values of λ1(s) is 152 units (0(s), which confirms that the first constraint is significant for explaining the differences in expression levels with respect to the balance state. The second constraint (2(s) and 30 samples grown in the light  have positive values. Only one sample grown in the light (AL3) has a slightly negative value, which does not contradict our conclusions for the same reasons as above. The difference between the range of the negative and positive values of λ2(s) are also much larger that the range of values of λ0(s) (133 units). The agar versus liquid samples and dark versus light phenotypes segregate from each other with different signs only in the plots of the Lagrange multipliers of the first and the second constraint respectively, indicating that the phenotypes describing agar/liquid and light/dark conditions are completely encapsulated by the contribution of the first and the second constraint to the gene expression levels, see On the other hand, the values of the Lagrange multiplier of the first constraint, λ1(s) , have di52 units , much lanstraint  allows t3(s) values of the 4A+ samples are separated by a gap of about 60 units from the multipliers of those of the 137C samples, see λ3(s) as several of the AL and AD 137 C samples which suggests that the third constraint does not lead to a fully unambiguous strain phenotype characterization. We therefore will not analyze this constraint further.Different strains are used in this study (137C) and the study of  (4A+). 40(s) values are equivalent to those found when all the samples are analyzed. λ1(s) has negative values for the agar-grown samples and positive values for the liquid-grown samples and the values are quite similar to those found when all the samples are analyzed together. In the same way, the values of λ2(s) are negative for the dark-grown samples and positive for the liquid-grown samples. These results thus demonstrate that the first and the second constraints are robust with respect to sampling and indeed responsible for the difference between agar/liquid and dark/light samples respectively.Results are similar when the surprisal analysis is performed on 1000 random combinations of 14 samples  . λ0(s) vGα where α is the index of the constraint and characterizes the phenotype associated with the constraint. The components Giα of the vector Gα determine the weight of transcript i in the phenotype associated with the constraint α whose Lagrange multiplier is λ0(s). One can therefore rank the contribution of a transcript to a given phenotype according to its weight, Giα. As described in section ‘Gene set enrichment’ of Methods, the annotated genes [Chlamydomonas are categorized in gene sets  using the 1000 random combinations of 14 samples cited above. This categorization therefore allows the identification of gene sets that contribute most to the phenotype associated with a given constraint, α.Surprisal analysis see  determined genes  of Chlamiα values computed for each transcript using surprisal analysis, we define a ‘SR ratio’  are listed in Tables i0. They reflect that the samples from the liquid medium are metabolically active and rely on ATP and NADH production linked to acetate assimilation. For the specific pathways of the liquid phenotype, one can note the presence of ‘Biosynthesis of unsaturated fatty acids’, which could indicate that the fatty acid composition of the membrane of the cells grown in liquid medium is different from that of cells grown on agar.A few pathways of the liquid phenotype  such as i2 values computed for each transcript using surprisal analysis, the ten pathways contributing the most to the expression levels of the dark grown samples are shown in The second constraint allows identifying the phenotype corresponding to dark-light conditions. From the GChlamydomonas [Some of the gene sets characterizing the dark phenotype  are commydomonas , impairsydomonas . Thus thi0.Logically, pathways of light utilization  in light-grown phenotype  are in ti2 suggests that the dark phenotype is more stressful than the light growth mode in the tested conditions. The same conclusion was also found below when comparing the agar versus liquid growth mode above. Therefore, even though the samples were analyzed when the number of cells per unit (ml or colony) was roughly the same (between 5x105 and 5x106 cells), it is clear that the agar and the dark growth modes were not optimized in terms of cultivation.In summary, our comparative analysis of the pathways of Gi1 and Gi2 values to define the biological pathways most important for a specific phenotype, it is also possible to quantify which individual genes contribute most to the phenotypes. Most of the 100 genes that significantly contribute to the phenotype of the agar-grown samples have unknown function (43- (Pi) uptake coupled with Na+ transport, and others transporters . The increased weight of these transcripts could indicate limitations in Pi and Fe in the agar-grown samples. As a matter of fact, the LHCSR2 transcript encoding an antenna protein activated upon excess of light, iron, copper, and phosphate deficiencies [MSD3. This gene encodes Mn superoxide dismutase whose transcription is increased upon iron deficiency [In addition to ranking KEGG pathways according to their Gfunction . Some offunction . Transcrfunction  for the ciencies –34, is fficiency . At lastficiency , which cFor the liquid-grown samples , many tr42- are found (SLT1 and SLT2) as well as extracellular arylsulfatase (ARS1), which is typical of cells experiencing low SO42- availability [lability , as also2 availability, which is typical of air-grown cultures where CO2 is limiting [4 or CO2 availability for the dark-grown samples and the light-grown samples respectively.The light-grown phenotype  is charalimiting . In conc2 FPKM values of these genes in the different types of samples . All of the photosynthetic transcripts are in higher amounts in the conditions liquid@light (LL) and liquid@dark (LD) compared to agar@light (AL) and agar@dark (AD). These results are thus in agreement with the surprisal analysis results, which highlights these genes as important to explain the liquid phenotype, irrespective of the presence or absence of light. This suggests that the photosynthetic genes are not upregulated in AL samples as much as in the LL samples because the cells forming the colonies are not all photosynthesizing: cells at the surface are exposed to the light but cells inside the colonies do not receive or receive less light. A part of the cells of the colonies probably turn to a heterotrophic growth mode and become stressed because of depletion of acetate and other nutrients. Concerning the presence of the photosynthetic transcripts in the LD condition, it is established that chlorophylls are synthesized in the dark [Photosynthesis genes are thus predominant in the liquid phenotype , much mothe dark ,28, whicGiα, see We also tested whether K-means clustering of expression values as implemented in the MeV software package  could obWe also compared the top 250 contributing genes to the first two constraints with the significantly differentially expressed genes obtained by Differential Gene Expression (DGE) using an EdgeR test  as impleChlamydomonas samples cultivated in four different conditions  and in two different laboratories identifies two specific constraints that disentangle the effects on the gene expression levels of the agar/liquid and dark/light conditions. The meta-analysis of the phenotypes identified by the constraints resolve the biological processes specifically activated under these two different sets of conditions. Biological processes are resolved by pathway analysis which is efficient, but has some limitations as only 3145 genes on the 15,143 protein-coding gene predictions [Surprisal analysis of transcriptomics data obtained from dictions  are cateChlamydomonas gene expression by surprisal analysis can be used on data sets coming from different laboratories and reference strains, we are confident that our method could be a method of choice in future investigations aiming at disentangling specific constraints and phenotypes from large data sets of different origins.In conclusion, our results open the way to a more detailed characterization of the less-studied modes of growth, dark and agar, which are emerging as promising for biotechnological purposes in the field of solid-state photobioreactors and growth in fermenters. We show that these two conditions are more stressful than light or liquid cultivation modes in the tested experimental setups. One would now aim to find experimental setups where parameters like medium composition could be modified in such a way that these two conditions could not be differentiated from the light and liquid modes on the level of nutrient related pathways and genes. In addition, as we have demonstrated that the pipeline developed for the analysis of S1 FigThe microalgal cells form colonies. RNA seq analysis was performed on the colonies that were numbered.(DOCX)Click here for additional data file.S2 Fig(DOCX)Click here for additional data file.S3 FigData are computed from 1000 random combinations of 14 samples.(DOCX)Click here for additional data file.S4 FigData are computed from 1000 random combinations of 14 samples.(DOCX)Click here for additional data file.S5 FigData are computed from 1000 random combinations of 14 samples.(DOCX)Click here for additional data file.S6 FigData are computed from 1000 random combinations of 14 samples.(DOCX)Click here for additional data file.S7 FigLHCA genes: light-harvesting complex I; LHCB: light-harvesting complex II, PS: photosynthetic genes .(DOCX)Click here for additional data file.S8 FigThe columns denote the number of top-contributing genes according to surprisal analysis which are also present among the significantly differentially expressed genes upregulated in respectively dark, light, liquid and agar as obtained by the two available pairwise DGE comparisons.(DOCX)Click here for additional data file.S1 Table(DOCX)Click here for additional data file.S2 Table(DOCX)Click here for additional data file.S3 TableChlamydomonas genome and average expression levels were calculated.Sequencing yield for 3 biological replicates per time is reported. Replicates were mapped to the (DOCX)Click here for additional data file.S4 Table(DOCX)Click here for additional data file.S5 TableValues lower than 0.01 FPKM were substituted with 0.01 FPKM to allow the computation of logarithms and expression ratios.(CSV)Click here for additional data file.S6 TableNote that only the first and second constraint have P-values < 0.001 when comparing the phenotypes for respectively the medium and light regime (indicated with an asterisk).(DOCX)Click here for additional data file.S7 TableThe number of genes in the pathways and in our analysis is indicated.(DOCX)Click here for additional data file.


SLC45A2) and epidermal differentiation (RASSF9). The allele frequencies of the RASSF9 se-eQTL across diverse populations correlate with the magnitude of solar radiation experienced by these populations, suggesting local adaptation to varying levels of sunlight. These results provide the first examples of sun-exposure-dependent regulatory variation and suggest that this variation has contributed to recent human adaptation.Sun-exposure is a key environmental variable in the study of human evolution. Several skin-pigmentation genes serve as classical examples of positive selection, suggesting that sun-exposure has significantly shaped worldwide genomic variation. Here we investigate the interaction between genetic variation and sun-exposure, and how this impacts gene expression regulation. Using RNA-Seq data from 607 human skin samples, we identified thousands of transcripts that are differentially expressed between sun-exposed skin and non-sun-exposed skin. We then tested whether genetic variants may influence each individual’s gene expression response to sun-exposure. Our analysis revealed 10 sun-exposure-dependent gene expression quantitative trait loci (se-eQTLs), including genes involved in skin pigmentation ( RASSF9, showed evidence of adaptation in humans in response to solar radiation. Together this evidence suggests that the regulation of gene expression is influenced by sun-exposure and that the sun-exposure dependent effect on RASSF9 expression may have had an effect on human fitness. To our knowledge, this is the first example of an environment-dependent regulatory variant with evidence of adaptation in humans.Varying levels of sun-exposure across the world have significantly shaped human evolution. Previous analyses have found several skin pigmentation genes with evidence of strong evolutionary pressures throughout human history, manifesting as large differences in the frequency of genomic variants across populations. But even within populations, individuals respond differently to sun-exposure, suggesting variation in addition to the major differences in skin pigmentation across populations. Here we investigated whether genetic variants associate with response to sun-exposure within Europeans. To measure the response we analyzed gene expression in sun-exposed and non-sun-exposed skin, and identified ten genetic variants that associated with the sun-exposure response of nearby genes. One of these genetic variants, which associated with the sun-exposure response of the gene  Despite the many successes of genome-wide association studies (GWAS), the field of human genetics is still only scraping the surface of questions encountered in day-to-day life. Questions such as why individuals respond differently to sun exposure, diet, or drugs highlight the prominent role of the environment’s varied effects on every individual. When environmental and genetic variation modify one another’s effects on phenotypes, this is known as gene-by-environment, or GxE, interaction. Many classic examples of GxE interactions exist, such as the inherited condition xeroderma pigmentosa resulting in extreme UV sensitivity –5. But bIdentifying new GxE interactions from genome-wide approaches is challenging due to their typically small effect sizes coupled with a formidable multiple-hypothesis testing burden ,12. HoweSLC45A2 and SLC24A5, which contain non-synonymous SNPs at high frequency in lighter-skin populations [Here we investigate the presence of GxE expression variants associated with long-term sun-exposure. Sun-exposure is associated with diverse human pathophysiologic phenotypes, from vitamin D synthesis to cancer –33. As hulations .KITLG and the upstream enhancer of OCA2 [In addition to protein-coding changes, there is also evidence that non-coding changes have evolved in response to sun-exposure. Cis-regulatory regions of several skin-pigmentation genes show signs of selection, such as the intergenic regions of  of OCA2 ,38,39. P of OCA2 , suggestTo identify genetic variants whose effect on gene expression depends on sun-exposure, we analyzed RNA-seq data from 607 skin samples  includinWe first examined the transcriptome-wide gene expression of the skin samples relative to the other tissues. Principal components of all GTEx samples were calculated. The 1st to 6th principal components primarily distinguished the samples by tissue, while the SE and NSE skin samples grouped together indistinguishably , MethodsBecause the principal component analysis was able to discriminate between tissues, we next investigated whether we could distinguish the exposure-type of the skin samples by performing the analysis on the skin samples alone. The first six principal components did not segregate the samples by exposure-type and the percent variance explained by each principal component was relatively small . This suggests that sun-exposure does not explain a large fraction of the variance in gene expression among these samples , S3 Fig.-4), whereas those upregulated in NSE were most strongly enriched for "Intermediate Filament" (Bonferroni-corrected p = 6.1x10-9).Despite this similarity in the SE and NSE samples, we have high power to detect differential expression because of the large sample sizes . Previous studies of differential cis-regulation across tissues or environments have identified potential pitfalls that could lead to false positives, such as the “winner's curse” and differences in power, which we carefully aim to avoid in our analysis –47 Fig . To focuSIM2, which was strongly affected by an eQTL in the NSE samples, but not in the SE samples  does no samples .To validate these results, we analyzed allele specific expression (ASE) differences  between SE and NSE samples. ASE measures the effect of cis-regulation in individuals heterozygous for the regulatory variant. Thus, significant differential ASE between groups  indicates differential effects of the eQTL. Note that although ASE is measured using the same dataset, it is an independent source of validation because it examines the differences in expression within an individual rather than across individuals ,25 see . As a coSIM2 sun-exposure-dependent eQTL  stages of skin differentiation [NLRC3, the second strongest effect, is a gene that negatively regulates the STING-dependent innate immune pathway [Because differential ASE provides independent evidence for a differential cis-regulatory effect, we combined both tests to identify additional genes with a significant effect. To combine the tests, we intersected significant SNPs by testing for differential ASE among genes with a nominally significant effect-size test (p < 0.05) and concordant ASE directionality (157 out of 289 genes concordant), resulting in seven significant differential eQTLs . These cis-reQTLs were also nominally significant using the effect-size test .We then identified additional GxE expression variants by testing whether any local SNPs associate with the differential expression due to the sun-exposure of each individual . This apSLC45A2 is a classic example of a skin-pigmentation gene under recent positive selection [ADAMTS12. The fold-change association in this cis-reQTL is more significant than either the SE or the NSE expression associations  [We then tested the differential cis-eQTLs and cis-reQTLs (hereafter referred to collectively as sun-exposure dependent eQTLs—se-eQTLs) for evidence of recent adaptation . Our hypnd OCA2) .RASSF9 had the strongest association with winter solar radiation , lending further support to the hypothesis of recent selection acting on this locus.Commonly used haplotype-based tests for selection, such as EHH, did not show a significant increase for any particular se-eQTL, which may be an indication that the se-eQTLs are under very recent selection. As selective sweeps for large-effect skin-pigmentation genes have occurred within the last tens of thousands of years ,63, we eOur study of sun-exposure dependent regulation of gene expression identified several examples of GxE interactions where genetic variants affect the gene expression response to sun exposure. In contrast to our differential expression analysis that identified over 12,000 transcripts—an unwieldy number that makes it challenging to uncover the causal or independent effects—focusing on GxE interactions allowed us to identify 10 independent loci directly associated with the sun-exposure response, with the strongest hits having known skin or sun-exposure related functions. This small number of significant GxE expression variants is consistent with previous observations that the number of GxE effects detected is smaller than additive effects .We identified GxE expression variants using two methods, differential cis-eQTL analysis and cis-reQTLs. Although both methods uncover GxE expression variants, we found that each provided unique results in their top associations. The two methods have distinct advantages: differential cis-eQTL analysis utilized information from a larger number of samples because there was no requirement for individuals to have both the SE and NSE data, while the cis-reQTL analysis controlled for possible individual-level confounding factors  because it compared the SE and NSE samples within the same individuals. In addition, our differential cis-eQTL analysis was based on eQTLs identified via joint-sample mapping in order to reduce the effect of the winner's curse. As a result, the differential cis-eQTL analysis preferentially analyzed SNPs with eQTL effects in both tissues, while the cis-reQTL approach agnostically considered all local SNPs. Despite these differences, overall the methods were generally concordant .Building on previous studies, we also found that allele-specific expression is an effective, orthogonal approach to identify GxE expression variants . CombiniSLC45A2, a gene previously determined to be under selection due to solar radiation, also suggests that sun-exposure is likely driving this effect. Lastly, SLC45A2 and RASSF9 have both been found to be differentially expressed in response to UV-B treatment [An important control in our analysis was confirming that the differences in gene expression of the SE and NSE samples reflected differences in sun-exposure. Because the samples were obtained from the post-mortem lower-leg and suprapubic skin, respectively, it is important to justify that the downstream analyses reflect differences caused by sun-exposure as opposed to differences unrelated to sun exposure. The relevance of sun-exposure was validated by significant concordance of the differentially expressed genes with two independent experimental approaches, one with whole skin UV-B treatment and another with skin fibroblast UV exposure. In addition, the significance of reatment , thus inIn addition to sample sizes, statistical power can also affect GxE interaction studies via a large multiple-hypothesis testing burden. This limitation was a key factor in our choice of testing only local GxE expression variants and refraining from testing for distant trans-associations. Local eQTLs tend to be highly replicable with strong effect sizes and finding them requires testing only a small number of SNPs per gene. In contrast, trans-eQTLs are challenging to map if every SNP is tested for each gene, though it is possible to identify trans-acting GxE expression variants in well-controlled studies ,20,29. LOverall, the GxE expression variants did not exhibit the strong population-specific fixation patterns observed in classical examples of positive selection. This however does not necessarily indicate that GxE expression variants are in general weakly selected. Mapping GxE interactions requires variation not only in environment but also in genotype. Because strong selection will remove genetic variation, our GxE mapping approach may not detect associations with the most strongly selected SNPs. Because the GxE mapping process focuses on polymorphic variants, we may detect signs of selection that are perhaps more recent or complex.SLC45A2, were not previously associated with human adaptation to sun-exposure. We found evidence that the se-eQTL of RASSF9 has been subject to local adaptation using two independent population cohorts as well as from a test for very recent adaptation in Europeans. Our finding of adaptation involving RASSF9, a gene involved in epidermal homeostasis and differentiation, supports the idea that skin pigmentation is not the only trait shaped by adaptation to sun-exposure [Although the evidence for human evolution in response to sun-exposure changes is strong, hypotheses for how adaptations in skin-pigmentation genes have led to increased fitness are debated ,33. To oexposure ,66.The approaches we employed could be applied to investigate GxE interactions involving any pair of tissues; although environment is typically considered to be extrinsic to an organism, cell type can be considered a major determinant of each gene’s intracellular environment. As more GxE interactions are discovered, we can then study their relationships with diseases or other traits to better understand their role in phenotypic variation and adaptation.−6, call-rate > 95%). For the expression data, we used the samples selected by GTEx as adequate for eQTL analysis . Gene models for all expression analyses were also obtained from GTEx, which combined the transcripts annotated by GENCODE v19 for each gene. Principal components in the all-sample analysis were calculated from the RPKM expression of 1000 randomly-sampled genes with a mean RPKM > 1. Random sampling was performed to reduce computation time—repeating the sampling produced similar results. Hierarchical clustering was performed with the Euclidean distance between tissues using the tissue-specific mean expression across all genes. Principal components of the skin-only analysis were obtained using all genes with mean RPKM > 1 across the skin samples.Expression and genotype data for sun-exposed (SE) and non-sun-exposed (NSE) skin samples were obtained from GTEx v6 . GenotypWe investigated differential expression between the sun-exposed and non-sun-exposed skin samples using the raw read counts obtained from the GTEx consortium . Genes with zero counts across all samples were removed. Differential expression was calculated using the DESeq function in the DESeq2 package  using de6 bp of the TSS, with the parameters "—bfs all—error hybrid—maf 0.05—qnorm—analys join" and using the large and small grid provided by the package. This window size of 106 bp was selected to be consistent with the GTEx Consortium analysis [Joint sample eQTL mapping was performed using eQTL-BMA with both SE and NSE samples . To maxianalysis . The conFor the allele-specific expression analysis, reads provided by GTEx were mapped using STAR   to the Get al. [SE—zNSE) / sqrt (1/(nSE -3) + 1/ (nNSE-3)), which is normally distributed. zSE and zNSE denote the z-scores for the SE and NSE samples. nSE and nNSE denote the number of samples used in the correlation coefficient calculation.The effect-size test was performed as described in Fraser et al. . Pearson6 bp from the transcription start site [6 bp was selected to remain consistent with the GTEx Consortium analysis for cis-eQTL mapping [3 permutations of the individual labels.cis-reQTL analysis was performed using the subset of individuals analyzed in the differential eQTL analysis who had both SE and NSE data. To calculate fold change, the RPKM values for each sample were first quantile normalized across samples. Fold change (SE / NSE) was then calculated for each gene-individual pair, with values of 0 set to the minimum non-zero value of that gene. The log fold change values for each gene were then fit to a standard normal. Hidden covariates were then discovered using PEER (k = 15) . In ordeart site . The win mapping . SignifiLocal adaptation was tested using Bayenv2.0 using the Human Genome Diversity Panel (HGDP) and HapMap samples ,61 and aet al. [Climate data were obtained from the NCEP/NCAR Reanalysis  using thet al. . The sumS1 Text(PDF)Click here for additional data file.S2 Text(PDF)Click here for additional data file.S1 Fig(PDF)Click here for additional data file.S2 Fig(PDF)Click here for additional data file.S3 Fig(PDF)Click here for additional data file.S4 Fig(PDF)Click here for additional data file.S5 Fig(PDF)Click here for additional data file.S6 Fig8739 genes have > 0.95 posterior probability marked by the red dotted line.(PDF)Click here for additional data file.S7 Fig(A) Skin eQTLs from our BMA analysis overlap with skin eQTLs from GTEx. (B) GTEx -log10 P-values of the eQTL correlate significantly with the posterior probability from in BMA. Only eQTLs found in the GTEx analysis were used in this correlation.(PDF)Click here for additional data file.S8 Fig(A) 1000 simulations of an exposure-specific eQTL indicate that the differential ASE test and effect-size test have significantly correlated results. This indicates that both methods can be used to detect the signal of differential cis-regulation. (B) 1000 simulations of the null (absence of an exposure-specific eQTL) indicate that the effect-size test and the differential ASE analysis do not show a correlated result, even though both tests use data derived from the same simulation. This indicates that the differential ASE analysis and the effect-size test are independent tests. See (PDF)Click here for additional data file.S9 Fig−15. Note that the magnitude of the effect size is similar to other ASE analyses [−15. (C) Significance of concordant directionality between the effect-size test and the differential ASE analysis as a function of the p-value cutoff in the differential ASE analysis. Directionality p-value is calculated by the two-sided binomial test, where the expected fraction of concordance is set at the concordance of all genes (0.36).(A) Absolute ASE of all cis-eQTLs, separated by measurements when the individual was homozygous (Hom) at the eQTL or heterozygous at the eQTL (Het). Significance was assessed by Wilcoxon rank-sum test. *** marks p < 10analyses  (B) Abso(PDF)Click here for additional data file.S10 Fig(A) Effect-size p-value vs cis-reQTL p-value for all associations that were tested in both analyses (1 per gene). P-value is calculated from the Spearman correlation.(PDF)Click here for additional data file.S11 FigThe cis-reQTL found in this study (rs12653176) is located at the bottom and the known selected non-synonymous SNP (rs16891982) is located at the top. The distance between the two SNPs is 278kb.(PDF)Click here for additional data file.S12 Fig(A) Principal components of genotype  separate individuals into ancestry groups. Red is used to mark the reported race “White”. Blue marks the reported race of “Black or African American”. Empty circles represent other reported race. Red shaded region demarcate the designated principal component boundaries in this study for the European ancestry population resulting in 377 genotyped individuals. Blue shaded region demarcates the African ancestry population, resulting in 68 genotyped individuals. (B) The fold change, log (SE / NSE), of all genes in the European ancestry individuals and the African ancestry individuals. P-value was calculated based on the asymptotic approximation of the Spearman correlation (rho).(PDF)Click here for additional data file.S13 Fig-7, likelihood ratio test).Even with the substantially lower power in the African ancestry individuals, we see a significant difference in differential expression in this gene at a Benjamini-Hochberg FDR < 0.01 (p = 5.6x10(PDF)Click here for additional data file.S1 Table(XLS)Click here for additional data file.S2 Table(XLS)Click here for additional data file.S3 TableThe higher expressed exposure-type is indicated when significant (Benjamini-Hochberg FDR<0.05). The exposure-type with the stronger effect according to the effect-size test is indicated, and the analysis from where the se-eQTL was obtained is also indicated.(XLS)Click here for additional data file.


In this paper, I propose a new method where a tensor is generated from individual features without combinatorial measurements, and the generated tensor was decomposed back to matrices, by which unsupervised feature extraction was performed. In order to demonstrate the usefulness of the proposed strategy, it was applied to synthetic data, as well as three omics datasets. It outperformed other matrix-based methodologies.In the current era of big data, the amount of data available is continuously increasing. Both the number and types of samples, or features, are on the rise. The mixing of distinct features often makes interpretation more difficult. However, separate analysis of individual types requires subsequent integration. A tensor is a useful framework to deal with distinct types of features in an integrated manner without mixing them. On the other hand, tensor data is not easy to obtain since it requires the measurements of huge numbers of combinations of distinct features; if there are  For example, a video dataset can be regarded as time points (samples) vs pixels (features). Audio files consist of time points (samples) vs amplitude (features), and sets of DNA sequences consist of individuals (samples) vs nuclear acid sequences (features). All of these are provided in the form of a matrix, whose rows and columns are features and samples, respectively . Although processing massive datasets is itself problematic, integrating distinct types of datasets is even more difficult. This problem is often annotated as multi-view data processing. For example, an audio visual file can be regarded as time points (samples) vs pixels and amplitudes(both features). In this paper, I consider two types of specific multi-view data processing: one is sharing samples  and another is sharing features . It is formally possible to deal with these two cases as unified; multiple th row and the jth column, as introduced in ith row and the (j + ∑k′ < k−1Mk′)th column, as introduced in The reason weights are required for individual views is that we do not know whether the same weights are acceptable when simply creating new variables by merging or linearly combining them. Suppose Nk varies drastically from view to view, the results may be dominated by the views with the maximum number of features. However, it is not clear if views with more features are more important. Alternatively, if the new feature k), views with more features may dominate the outcome. Reverting row and column, I will discuss Case II as well. In order to compensate for this discrepancy, each view must be weighted based on criteria which are not naturally unique. No previously proposed strategies were free from this problem.This is not necessarily as simple as it may appear. For example, in Case I, if In this paper, I propose a brand new strategy that is free from weighting views; generating tensors whose number of modes is the same as, or one greater than the number of views, and applying tensor decomposition (TD) to them. Using this implementation, I performed feature extraction (FE), which I name TD based unsupervised FE, which is extended from the recently proposed principal component analysis (PCA) based unsupervised FE –22.m + 1) mode tensor. As each newly generated feature is composed of one feature from individual views, no weight is needed. Similarly, in Case II, m + 1) mode tensor. These tensors are hereinafter called Type 1.If we generate a new feature with neither summation nor merging, the product for Case I—m-mode tensors and are hereinafter called Type II. All variables associated with Type II tensors are written with tildes.Alternatively, instead of simply multiplying matrix components with the shared columns or rows, they can be summed up as follows: m-mode (type II) or (m + 1)-mode (type I) tensors can be processed using any kind of tensor manipulation. For example, for a reduced number of features whose combination can express tensors, TD can be used to gain such features.These newly generated In the following subsection, I consider four combinations of types and cases, i.e., type I or II tensors for Case I or II multi-view data, case by case.Since TD is not a popular methodology and the usage of TD for FE is rare, I will briefly introduce TD in this subsection.xn1,n2,…,nm, nk = 1, …, Nk, 1 ≤ k ≤ m in the formxnk,ℓk, 1 ≤ k ≤ m, are orthogonal matrices. Since xn1,n2,…,nm is as large as G, this formula is clearly overcomplete and does not give unique expansion. In this study, in order to decide G, xnk,ℓk, 1 ≤ k ≤ m uniquely, I employ the higher order singular value decomposition (HOSVD) algorithm  is the probability that the argument is larger than x under the assumption that the arguments obey a χ squared distribution. The P-values were further adjusted by the Benjamini-Hochberg (BH) criterion [P-values less than 0.01 were selected as the genes associated with the difference between multiple classes.Then, assuming that PC scores riterion , and thoAlthough similar to the previous section, some differences are: (i) Only the second PC scores attributed to mRNAs were used for FE. (ii) Instead of mRNA and miRNA, patient category groups, P, D, and NP were used. (iii) mRNAs commonly included in three independent FEs performed considering P, D, and NP, were considered.P-values were attributed to the i1th mRNA and the i2th miRNA using χ2 distribution.σℓ1(σℓ2) are standard deviations of Piks were adjusted by using the BH criterion, and mRNAs and miRNAs associated with the adjusted P-value lower than 0.01 for mRNA and 0.05 for miRNA were selected as those associated with identified sample singular value vectors when TD was applied to type I tensor.For type I tensor generated from multi-omics dataset, in order to identify miRNAs and mRNAs associated with identified sample singular value vectors, it was assumed that P-value lower than 0.01 and 1 ≤ ℓ2 ≤ 5 were used for miRNA, where When TD was applied to type II tensor, the computations were similar, excluding that adjusted xℓ3 = 2,i  or For EGF treated cell lines and vaccination experiments, similar procedures were repeated by replacing gene singular value vectors with Uk)( (k = 1 for mRNA and k = 2 for miRNA).Where HO GSVD was applied to multi-omics datasets, the feature singular value matrices were replaced with the first five column vectors of P values used as thresholds are always 0.01 for EGF treated cell lines, vaccination, and HO GSVD.Adjusted Coincidences between prob ID (mRNA), HUGO gene names, Ensembl gene IDs were downloaded from GEO using GEO ID GPL3676 for multi-omics datasets, and GPL571/570 for vaccination experiments. GENBANK accession ID attributed to probes identified in the EGF treatment were extracted from GPL16686.Ensembl gene IDs were uploaded to g:profiler . 13393 EP-values were attributed to the i1th mRNA using χ2 distribution:P-values were adjusted using the BH criterion and mRNAs associated with adjusted P-values less than 0.01 were identified as outliers (see Five distinct iers see . S2 Tablhttp://software.broadinstitute.org/gsea/msigdb/annotate.jsp (registration and login are needed). “CGP: chemical and genetic perturbations” was selected for multi-omics data and EGF treated cell lines, while “C7: immunologic signatures” was selected for vaccination experiments.HUGO gene IDs or GENBANK accession IDs associated with identified mRNAs were uploaded to As for TDs applied to type I tensors, the following link was pasted to browser.http://snf-515788.vm.okeanos.grnet.gr/#mirnas=hsa-let-7b-5p;hsa-miR-125b-5p;hsa-miR-143-3p;hsa-miR-145-5p;hsa-miR-21-5p;hsa-miR-22-3p;hsa-miR-99a-5p&methods=Tarbase;Tarbase;Tarbase;Tarbase;Tarbase;Tarbase;Tarbase&selection=0As for TDs applied to type II tensors, the following link was pasted to browser.http://snf-515788.vm.okeanos.grnet.gr/#mirnas=hsa-let-7a-5p;hsa-let-7b-5p;hsa-let-7f-5p;hsa-miR-103a-3p;hsa-miR-125b-5p;hsa-miR-141-3p;hsa-miR-142-3p;hsa-miR-143-3p;hsa-miR-145-5p;hsa-miR-148a-3p;hsa-miR-199a-3p;hsa-miR-199b-3p;hsa-miR-19b-3p;hsa-miR-205-5p;hsa-miR-21-5p;hsa-miR-22-3p;hsa-miR-23a-3p;hsa-miR-24-3p;hsa-miR-26a-5p;hsa-miR-30a-5p;hsa-miR-451a;hsa-miR-99a-5p&methods=Tarbase;Tarbase;Tarbase;Tarbase;Tarbase;Tarbase;Tarbase;Tarbase;Tarbase;Tarbase;Tarbase;Tarbase;Tarbase;Tarbase;Tarbase;Tarbase;Tarbase;Tarbase;Tarbase;Tarbase;Tarbase;Tarbase&selection=0As for HO GSVD, the following link was pasted to browser.http://snf-515788.vm.okeanos.grnet.gr/#mirnas=hsa-miR-127-5p;hsa-miR-128-1-5p;hsa-miR-181a-3p;hsa-miR-190a-5p;hsa-miR-301a-3p;hsa-miR-30e-3p;hsa-miR-339-5p;hsa-miR-340-5p;hsa-miR-361-5p;hsa-miR-365a-3p;hsa-miR-452-5p;hsa-miR-454-3p;hsa-miR-455-5p;hsa-miR-874-5p;hsa-miR-135a-5p&methods=Tarbase;Tarbase;Tarbase;Tarbase;Tarbase;Tarbase;Tarbase;Tarbase;Tarbase;Tarbase;Tarbase;Tarbase;Tarbase;Tarbase;Tarbase&selection=0δSj takes 1 when jth sample belongs to category S, otherwise 0. The summation is taken over all categories. For type II tensor   or betweTEGFEGF) , where T fdrtool  function fdrtool .ai and bi are regression coefficients commonly used for control and EGF treated samples. For P-values that exhibit distinction between control and EGF treated sample at time point t were computed by two-sided t test between N = 558 , ik ≤ N0, are the noise added linear combination (X(1) and X(2) is negligible, identifying a correlation between two matrix row vectors is usually impossible  identify N0 ordered features, and (ii) identify latent correspondence between two views.First, two matrices are generated, each of which is composed of bination  of constbination . Howeverpossible . Remainixℓ3,j, ℓ3 = 1, 2, 3, obtained with HOSVD,The three mode tensor (type I) N0 features are placed as outliers. Thus, TD based unsupervised FE applied to type I tensors generated from matrices’ products can not only decompose linear combinations, but can also identify the limited number of features, 1 ≤ i1, i2, ≤ N0, that contribute to correlations between two matrices, Xk) mode tensor (type II), m(>2) views, I generally get a m mode tensor and the above procedures can be easily extended to m mode tensors.Although I could successfully demonstrate that my strategy works well, there is one drawback; it is the computationally extensive method, since its memory as well as computational time are proportional to k = 1, 2), obtained with the application of HOSVD to type II tensors. Among these, k = 1, 2, shown in ℓ3 = 1) correctly reproduce ℓ3 = 2) does Xk) and (ii) as defined above.k = 1, 2 . Howeverk = 1, 2  that cank = 1, 2 . Additiooutliers . Thus, aIn order to see if these strategies are also useful in practice, integrated analyses of multi-omics datasets were performed with this strategy and are described in the next subsection.In the previous subsection, I demonstrated that applying TD based unsupervised FE to tensors generated from matrices’ products could determine latent structures behind pairs of matrices. However, this may only be feasible using synthetic data, as described in the previous subsection. Thus, in order to see if it also works in the situation not prepared specifically fitted to it, I need to show that it works in real situation.The analysed dataset is composed of two omics profiles. These are mRNA and miRNA profiles which were measured for multi-class breast cancer samples including normal breast tissues . As the i1th mRNA and the i2th miRNA from the jth sample. In order to determine whether TD can identify disease critical features, categorical regression analysis was applied to sample singular value vector xℓ3,j, in order to identify coincidences with defined sample classes. If the obtained sample singular value vectors are coincident with sample class labels, it is evidence that TD can process omics profiles properly, as this approach does not employ class labels explicitly. xℓ3,j, 1 ≤ ℓ3 ≤ 5, that show significant sample class dependence. Thus, TD could successfully generate disease associated features. This is not a trivial outcome, as sample classification was not used.At first, TD was applied to the type I tensor generated from the mRNA and miRNA profiles as follows:xℓ3,j, 1 ≤ ℓ3 ≤ 5 identified above. This can be done by investigating G since the combinations  associated with larger absolute G values are regarded as more coincident with one another. G for 1 ≤ ℓ1, ℓ2, ℓ3 ≤ 5 (ranked from 1 to 10) based upon their absolute values. The first five sample singular value vectors xℓ3,j, 1 ≤ ℓ3 ≤ 5, are associated with the first two miRNA singular value vectors Gs that represent the amount of coincidence among mRNA and miRNA and samples.Next, I attempted to extract features using the mRNA and miRNA singular value vectors Four hundred twenty-seven mRNA probes and 7 miRNAs, identified as outliers, using l study  as a function of t under one set of conditions, while it obeys f(t) + C with a constant C under another. Conventionally, this is differentially expressed between the two conditions; however this kind of differential expression is often not of interest when temporal gene expression is considered. One distinction of note would be, for example, differences between expressions at certain time points and not at others (a distinct time dependency between two conditions). However, there are no de facto standard methods that automatically achieve this. In order to address it, TD based unsupervised FE was applied to this problem.Although the application of TD based unsupervised FE to multi-omics data was successful, one may wonder if the application to muti-omics data is reasonable, as synthetic datasets were more difficult to deal with due to a lack of class labelling. Have I intentionally tried the easiest case? In order to address this possible query, I considered two examples of a more difficult problem: identification of temporally differentially expressed genes. The task is as follows: Given more than one temporal gene expression, identify genes expressed differently among multiple expressions at specific time points. For example, expression of a particular gene obeys xt1,t2,i is then generated asith gene expressions of cell lines with and without EGF treatment, at time points t1 and t2 after the EGF or control treatments. As they share features (though not samples) in contrast to the previous application which was Case I data, this example uses Case II data. As the samples in this example are divided into two groups based on EGF treatment, it is not fully unsupervised. It is, however, unsupervised in the sense that the type of temporal difference sought is not defined. The tensor was expanded by HOSVD asThe first example of this application is the comparison of non-small lung cancer cell (NSCLC) line H1975, with and without EGF treatment . Gene exℓ1, ℓ2 = 1, 2, respectively. Obviously, those for ℓ1 = ℓ2 = 1 do not have any time dependence while those for ℓ1 = ℓ2 = 2 do. Some temporal difference was observed in the latter, however its significance is unclear. In order to determine said significance, genes identified as outliers had to be selected. This selection process began with identifying the gene singular value vectors associated with Gs with larger absolute values. It is obvious that xℓ3 = 2,i is associated with G and G are the second and the third largest in the table. Next, 558 mRNA probes . It is remarkable since G and G are smaller than one tenth of G whose absolute value is the largest. This suggests that the amount of contributions of G and G is too little to govern individual gene expression. The high correlation despite this fact speaks to the soundness of our methodology.P-values were computed by two-sided t tests between expressions, with and without EGF treatments at time points, 0.5, 1, 2, 4, 6 and 48 hours , which is reasonable as the genes sought were expressed differently with and without EGF treatments.To determine the biological reliability of the selected genes, genes associated with selected 558 mRNA probes were uploaded to MSigDB. The second significant gene set was found to be KOBAYASHI_EGFR_SIGNALING_24HR_DN . This is noteworhty as the smallest contribution from the second singular value vector was 1 × 10−5. This suggests that the amount of contributions of the second singular value vector were too small to govern individual gene expressions. As before, the high correlation despite this fact speaks to the soundness of our methodology.The next task was to determine whether type II tensors produce similar results. Type II tensor P-values computed by a two-sided t test between expression at time points, 0.5, 1, 2, 4, 6 and 48 hours , which, again, was reasonable as the genes sought expressed differently with and without EGF treatments. Although the number of genes selected was less than that by TD applied to type a I tensor, since the P-value is smaller, the significance was greater than that of TD applied to a type I tensor.In order to see the biological reliability of selected genes, the mRNAs associated with commonly selected 398 mRNA probes were uploaded to MSigDB. The second most significant gene set was determined to be KOBAYASHI_EGFR_SIGNALING_24HR_DN  memory can be as effective as TD applied to type I tensor for temporally differentially expressed gene identification. Thus, for this example, I employ only type II tensor The next temporally differentially expressed gene detection example is vaccine infection experiment . Patientℓ1,ℓ2 = 1, 2. Obviously, ℓ1 = ℓ2 = ℓ3 = 2 do, as in the EGF treated cell line cases. Though ℓ1 = ℓ2 = ℓ3 = 2, 104 mRNA probes identified commonly as outliers were selected . This is noteworthy as −3 of P-values computed by categorical regression assuming three classes  at time points, 1, 2, 3, 4 and 5 days  = , , , , and  in this order, which are associated with adjusted In conclusion, TD based unsupervised FE is also effective also for the identification of temporally differentially expressed genes.In the following section I discuss the strategy for applying TD based unsupervised FE to tensors built from matrix products, methodological points of view, and outcomes obtained by applying this strategy to multi-omics datasets from the biological point of views.The synthetic datasets that presented in the above sections are very difficult to analyse using standard supervised statistical analysis methods. In the supervised methodology, all background knowledge of given datasets is required, e.g., classification labels or assumed functional forms . Alternatively, TD applied to type I tensors is N0 features are derived from the common bases shown in As the first M dimensional vectors as numerous as N must be compared, it is an overcomplete problem when M < N (and this is the present case). Thus, canonical correlation coefficients generated from linear combinations are always 1.0. This means that there is no way to detect latent correlation between N0(<N) features.One may wonder if correlation analysis considering linear combinations, e.g., canonical correlation analysis (CCA), can depict latent correlation. However, in CCA, as Xk) generated are classified into two types, each of which are distinct from the first N0 features and remaining . KCCA was applied to matrices emaining . Thus, tvℓ1 = 1, j and uℓ1,i1,ℓ1 = 1, 2 is uℓ2,i2, ℓ2 = 1, 2 is λℓ2 and λℓ3 are the eigen values computed with PCA. Thusvℓ1,j is not orthogonal to Finally, PCA based unsupervised FE, which was recently proposed and successfully applied to various integrated analyses of multi-omics datasets, was again applied here. As PCA is equivalent to singular value decomposition (SVD),N0 features associated with latent correlations as outliers , the supervised method can be applied to the multi-omics data used in this study can be treated with supervised method as the data uses class labels. Strictly speaking, there are no unsupervised methods applicable to multi-view data processing other than TD based unsupervised FE. We can, therefore, even conclude that is the above strategy is sound. That said, it would be beneficial to demonstrate that the unsupervised methodology is superior to the supervised methodology.As mentioned in above, most multi-view data processing methodologies require optimization of weights. I do not consider such methodologies, since optimizing weights is a complicated unnecessary process. Therefore, they are not comparable with the unsupervised strategy, which involves no parameter optimization processes.Thus, the multi-view data processing methodology is considered applicable to merged matrices shown in Eqs  or 2), , 2), whiP-values ensuring that these three methods identify 426 mRNA probes, which is the same number identified by TD applied to type I tensors. As threshold P-values which are too small without any statistical justifications may not be acceptable, in order to evaluate these three methods, unnatural threshold P-values were intentionally used. Top ranked mRNAs selected by using intentionally reduced threshold P-values were uploaded to MSigDB server. However, breast cancer was rarely identified , respectively. It is also shown the regression analysis of the first miRNA PC loading vℓ1,j, 1 ≤ ℓ1 ≤ 5,M = 161, only five components that can cover this amount is highly significant. This suggests that TD can easily decompose single miRNA PC loadings vℓ1,j, 1 ≤ ℓ1 ≤ 5. The result is that the first five sample singular value vectors , are almost identical to the first five mRNA PC loadings . Thus, TD based unsupervised FE can decompose the first dominant miRNA PC loading into five basic  mRNA PC loading. This result is analogous to that seen in the application to synthetic dataset s with 1 ≤ ℓ1 = ℓ3 ≤ 5 have larger absolute values  equalling 15 classes. Results are shown in P-value = 0, therefore no reduced sets could be generated. Two 300 top ranked mRNA probes sets were generated from limma and RF and associated mRNAs were uploaded to MSigDB together with the genes associated with 18 mRNA probes obtained by PCA based unsupervised FE. Within top 10 ranked significant genes set, no vaccination related genes sets were identified for limma or RF. PCA based supervised FE has only two vaccination related genes sets. GSE13485_X_VS_Y_YF17D_VACCINE_PBMC_DN,  =  and , were identified as the second (adjusted P = 1.86 × 10−6) and the fourth (adjusted P = 4.30 × 10−5) significant genes sets, which were smaller than those identified when TD was applied to type II tensors, which identified five gene sets associated with vaccination out of six top ranked gene sets.In order to determine biological significance, a reduced number of gene sets was uploaded to MSigDB. Similar to the multi-omics case, SAM indicated too many mRNAs with adjusted Thus, one of four tested methods, PCA based unsupervised FE, could produce some significant results which were inferior to those produced by TD based unsupervised FE applied to type II tensors. As a result, TD based unsupervised FE proved more effective than the other methodologies analysed above.To my knowledge, although there are no methods that comprise a tensor from multiple matrices and applies TD to it, similar trials aiming integration of multiple matrices exist. For example, higher order generalized singular value decomposition (HO GSVD)  is one sV, where the first the second column vectors correspond to the first PC loading of the first and the second views, respectively.First, HO GSVD was applied to synthetic data. P-values were larger. Thus, HO GSVD can perform well but is less effective than TD applied to type I or II tensors.Next, HO GSVD was applied to multi-omics data. Coincidence between sample singular value vectors and class labeling is shown in Next, 374 mRNA probes identified as outliers using the first five mRNA feature singular value vectors were selected (associated mRNAs are shown in Fifteen miRNAs(miR-127-5p/128/181a/190a/301a/30e*/339-5p/340/361-5p/365 /452/454/455-5p/874/135a) identified as outliers using the first and the second miRNA feature singular value vectors were selected. None were reported in the original study  was enriched. It was reported to be related to metastasis. Ihnen et al  reportedIn GO (cellular component) CC terms, “extracellular region” (GO:0005576) was enriched. Cho et al  reportedIn GO (molecular function) MF terms, “CXCR3 chemokine receptor binding” (GO:0048248) was enriched. CXCR3 was reported as a molecular target in breast cancer metastasis ; it inhiOther than in GO terms enrichment, transcription factor (TF) SOX9 target genes were enriched. The relation between SOX9 and metastasis was pointed out by many papers. Got et al  reportedKEGG pathway “Primary immunodeficiency” (KEGG:05340) was also enriched. Development of cancer in patients with primary immunodeficiencies was reported . MonozygIn conclusion, our method and strategy correctly identified many cancer related biological terms/concept enrichments, especially metastasis in breast cancer, which is coincident with the purpose of the original study that did not produce results produced here.As the relation between mRNAs identified and breast cancer metastasis can be shown, it is necessary to demonstrate the relationship between the miRNAs identified and breast cancer metastasis. Research of the litertature showsthat all seven miRNAs identified when type I tensors were consideredClick here for additional data file.S2 FileBP term enrichments by uploading (PDF)Click here for additional data file.S1 TableFull lists of genes selected by various methods.(XLSX)Click here for additional data file.S2 TableLists of genes associated with five gene singular value vectors.(CSV)Click here for additional data file.S3 TableEnriched terms when list of genes were uploaded to g profiler.(XLSX)Click here for additional data file.


Prognostic biomarkers serve a variety of purposes in cancer treatment and research, such as prediction of cancer progression, and treatment eligibility. Despite growing interest in multi-omic data integration for defining prognostic biomarkers, validated methods have been slow to emerge. Given that breast cancer has been the focus of intense research, it is amenable to studying the benefits of multi-omic prognostic models due to the availability of datasets. Thus, we examined the efficacy of our methylation-to-expression feature model (M2EFM) approach to combining molecular and clinical predictors to create risk scores for overall survival, distant metastasis, and chemosensitivity in breast cancer. Gene expression, DNA methylation, and clinical variables were integrated via M2EFM to build models of overall survival using 1028 breast tumor samples and applied to validation cohorts of 61 and 327 samples. Models of distant recurrence-free survival and pathologic complete response were built using 306 samples and validated on 182 samples. Despite different populations and assays, M2EFM models validated with good accuracy (C-index or AUC ≥ 0.7) for all outcomes and had the most consistent performance compared to other methods. Finally, we demonstrated that M2EFM identifies functionally relevant genes, which could be useful in translating an M2EFM biomarker to the clinic. Better methods are needed to rapidly identify patients that can benefit from specific treatments, reveal new targets for historically difficult to treat patients, and provide accurate prognoses to patients to enable better life planning.The extreme heterogeneity of breast cancer makes one-size-fits all treatments difficult to achieve and although a number of targeted therapies are available2 and the International Cancer Genome Consortium3, and expression repositories such as NCBI’s Gene Expression Omnibus4 have enabled developments in prognostic and predictive cancer models. In addition to improved understanding of how cancer disrupts normal cellular function, such data have led to the development of biomarker panels, such as the PAM50 risk of recurrence score (rorS)5 and the 21 gene Oncotype DX6, which are both now used for clinical decision making in the treatment of breast cancer7. Furthermore, to the extent that such tests are able to predict the occurrence of distant metastases, they may enable early prevention strategies to be put in place.Large scale collection of cancer genomic data, such as The Cancer Genome Atlas (TCGA)9.Despite such promising developments, the goals of precision medicine remain elusive due to specific limitations in molecular biomarker studies. These include limited understanding of the optimal genomic features to utilize, lack of validation on external data, and inconsistent use of best practices for creating biomarkers with the best chances of entering clinical practice10. To the extent that these sources are independently prognostic, they should result in higher accuracy than either source alone and better understanding of prognostic features by revealing holistic relationships in the data. As yet, few prognostic or predictive models are designed to take advantage of multiple data types. In this work, we apply our own previously developed data integration approach for combining gene expression and DNA-methylation data to model the impact of regulatory disruption on breast cancer prognosis and prediction while also incorporating prognostic clinical variables11. This study overcomes prior limitations by creating a model that can identify biologically plausible targets, using best practices in assessing the model9, and by validating the actual model (not just the gene signature) in multiple, external datasets, representing different demographics and disease distributions.There has been growing interest in the integration of molecular and traditional clinicopathological markers to achieve higher levels of prognostic power and utility and small but significant gains in prognostic accuracy have been observed through this approach11 and applied it in the case of clear cell renal cell carcinoma (ccRCC). The basis of this approach is to pre-filter loci to those that are differentially methylated between matched tumor and adjacent, pathologically normal tissue and to associate the methylation status of those loci with significant differences in gene expression in the tumor samples. The differentially methylated loci are then called m2eQTL (for methylation-to-expression QTL) and the genes are called m2eGenes. An initial model is built from m2eQTL and m2eGenes with the largest effects to generate risk scores for all samples using Cox-Ridge regression . A final model is built from the risk scores in conjunction with clinical variables and a final risk score is generated from the weighted sum of the features of this model. Here we build M2EFM models of overall survival (OS), distant recurrence-free survival (DRFS), and pathologic complete response (pCR) in breast cancer, where OS is defined as time from initial diagnosis to death from any cause, DRFS is defined as time from diagnosis to distant recurrence, death from cancer, or death from unknown cause, and pCR is defined as a patient being recorded as having a pathologic complete response or a residual cancer burden class of RCB 0/I as in Hatzis, et al.12.Previously, we introduced a data-integrated modeling approach we call Methylation-to-Expression Feature Model (M2EFM)13. Therefore, they represent regions that may be involved in early loss of regulation in breast cancer.A full description of data pre-processing appears in the Supplementary Methods. For this work, we supplied a list of probes to M2EFM from a study of CpG loci involved in epigenetic field effects in breast cancer based on data available in GEO (GSE69914). The loci were delineated CpG sites exhibiting subtle differences in methylation in samples from breast tissue from non-diseased healthy subjects compared to samples from tumor-adjacent normal breast cancer cases, that are also shown to exhibit differential methylation in tumor tissue itselfTCGA, was used to train and test an OS model for breast cancer, and consisted of gene expression and DNA methylation profiles created by TCGA, using the Illumina HiSeq 2000 and Illumina Infinium HumanMethylation 450 platforms, respectively. Methylation data were functionally normalized14 using the minfi package15 in R. Expression data were TDM normalized, which makes the distributions between microarray and RNA-seq datasets similar, making them more comparable to the validation datasets16. The samples are described in Table Aside from the probe list, five different breast cancer cohorts were used in this work. The first dataset is referred to as Terunuma, is used for external validation of the OS model, and contains 61 tumor samples with clinical and survival data, downloaded from ArrayExpress (E-GEOD-39004)17. These data were assayed on the Affymetrix GeneChip Human Gene 1.0 ST Array. They were normalized and then batch corrected in conjunction with the following dataset. A description of the samples is in Table The second dataset is referred to as Kao, is used as a second external validation dataset for the OS model, and contains 327 tumor samples, downloaded from ArrayExpress (E-GEOD-20685)18. These data were assayed on the Affymetrix GeneChip Human Genome U133 Plus 2.0. A description of the samples appears in Table The third dataset is referred to as Hatzis1, was used to train and test a model of DRFS and another model of pCR, and includes HER2-negative breast cancer cases with neo-adjuvant treatment by taxane-anthracycline (followed by endocrine therapy for ER-positive cases)12. These data were assayed on the Affymetrix Human Genome U133A Array. They were downloaded from GEO (GSE25055), and were normalized and then batch corrected in conjunction with the following dataset. A description of the samples appears in Table The fourth dataset is referred to as Hatzis2, was used for external validation of both the DRFS and pCR models of (HER2-negative) breast cancer, and includes HER2-negative breast cancer cases with neo-adjuvant treatment by taxane-anthracycline (followed by endocrine therapy for ER-positive cases)12. These data were assayed on the Affymetrix Human Genome U133A Array. They were downloaded from GEO (GSE25065). A description of the samples appears in Table The final dataset is referred to as In order to reduce categories with very few samples and the number of variables in the model, all AJCC tumor stage classifications were reduced to simple Stage I, II, III, or IV.Three different types of models were built: 1) a model of overall survival (OS), (2) a model of distant recurrence-free survival (DRFS), (3) a model of pathologic complete response (pCR) to neoadjuvant taxane/anthracycline treatment. For all model types, we built 100 different models using different random splits of the data, divided into 70% training and 30% testing data sets, to assess how consistently a good model could be found given different training data. We assessed the performance of the models built with and without clinical variables, with clinical variables alone, and separately to include external validation data. The external validation data could only be tested on models without DNA methylation values, because methylation data were not available . The M2EFM pCR model was compared to a logistic-Ridge regression model, again using glmnet. Furthermore, the M2EFM OS and DRFS models were compared to a model incorporating the PAM50 risk of recurrence score (rorS)5 with clinical variables. Finally, the M2EFM model was compared to a model built from a gene signature obtained by the network clinical association (NCA) algorithm20, which is also based on data integration.M2EFM OS and DRFS models were compared with Cox-Ridge regression, using the Performance of the OS and DRFS models was evaluated using concordance or C-index, a measure of how likely it is, in any given pair of individuals, that the individual with the higher risk score has the event first. For the pCR model, the performance was measured using area under the receiver operating characteristic curve (AUC). Significance tests for comparisons used the two-tailed Wilcoxon signed-rank test.genefu package for R)21. Selected variables include AJCC stage and patient age at diagnosis for all outcomes, although stage was reduced to simply presence or absence of stage III cancer for DRFS and pCR outcomes due to the absence of stage IV cases and small number of stage I cases for these outcomes.Clinical variables were chosen using the least absolute shrinkage and selection operator (LASSO) for each outcome. Candidate variables included AJCC stage, patient age at diagnosis, ER status, PR status, HER2 status, and PAM50 subtype  Cancer Gene Census23, using Fisher’s exact test. Finally, we tested the enrichment of genes in our signature in genes known to be targeted by breast cancer drugs listed in the DrugBank database24, again using Fisher’s exact test.The m2eGenes were used to analyze the functional relevance of our approach using the online tool WEB-based GEne SeT AnaLysis Toolkit TCGA: UCSC Cancer Genomics BrowserTerunuma: ArrayExpress (E-GEOD-39004)Kao: ArrayExpress (E-GEOD-20685)Hatzis1: GEO (GSE25055)Hatzis2: GEO (GSE25065)Cancer Genes: COSMIC Cancer Gene CensusCancer Drug Targets: DrugBankThe datasets generated and/or analyzed during the current study are available in the following repositories:https://github.com/jeffreyat/M2EFM.M2EFM is available as a package for R at We applied M2EFM to the TCGA dataset to select dysregulated probes and genes for our models. The lists of probes and genes selected by M2EFM are shown in Table Results of the meta-dimensional double-integrated model,  for the associated methylation values. We also added a model built from a gene signature discovered using NCA .To allow external validation of our models using other datasets we next focused on breast cancer OS, building models using only expression data, with the m2eQTL discovered previously. In such cases, we substitute the The median C-index for each model on each dataset is shown in Table th percentile, medium risk from the 25th to the 75th percentile, and high risk above the 75th percentile, and created Kaplan-Meier plots of the survival of the risk groups in each dataset , to build a final overall survival model and validated it on Terunuma and Kao. For Terunuma, the C-index was 0.724, 95% CI . For Kao, the C-index was 0.703, 95% CI . These scores were very similar to their median C-index scores. The hazard ratios for this model are given in Table pec package for R25, as well as the integrated Brier score (IBS)26, a quantitative measure of calibration or prediction error. For M2EFM Exp + Clin, the IBS on Kao was 0.060 and on Terunuma was 0.166. For Cox Exp + Clin, the IBS on Kao was 0.055 and on Terunuma was 0.161, indicating that the Cox Exp + Clin models were better calibrated over all time points.We generated calibration curves for the proportional hazards models based on the full training data model Fig. , using t27. Unfortunately, ER status was not annotated in the Kao data, and there were too few samples in Terunuma to effectively test the prognostic utility of our marker on ER-negative patients. Therefore, we inferred the ER, PR, and HER2 status of samples in Kao by clustering samples using expression probes associated with each receptor status using a Gaussian mixture model to capture each bimodal distribution28. We then assessed the relative prognostic power of the M2EFM models in samples that varied by ER or triple negative status  on these variables and calculated the variance inflation factor (VIF), a commonly used measure of the multicollinearity between variables. The VIF was approximately 1.20. A VIF between 1 and 5 is generally regarded to imply only moderate multicollinearity. Therefore, the molecular risk score from M2EFM contains prognostic information independent of breast cancer subtype.On both the testing data and the external validation data, M2EFM was the most prognostic model of DRFS Fig. . On the Finally, an M2EFM Exp + Clin model trained on the full training data (Hatzis1) achieved a C-index of 0.766, 95% CI  on the external validation data (Hatzis2). The hazard ratios for this model are given in Table 30. For these cases, it is important that the marker has a high negative predictive value (NPV). Therefore, we assessed the NPV of the M2EFM model in node-negative samples using the timeROC package for R, which uses a time-dependent AUC and can handle censored survival times. A cutoff for the risk score was determined in Hatzis1 that equalized the sensitivity and specificity in predicting DRFS for node-negative cases at 3 years (the median follow-up in these data). This cutoff was applied to node-negative cases in Hatzis2 to determine the positive predictive value (PPV) and NPV. At the 3-year follow up point, the PPV was 0.49 and the NPV was 0.95. We predicted 39 node-negative cases would not have a distant metastasis by 3 years and we were correct for 36. We predicted 12 node-negative cases would have a distant metastasis and were correct for 7.One interest in genomic cancer biomarkers is for determining cases with a low risk of recurrence who may not benefit from adjuvant chemotherapyThe final set of models are for pCR following neoadjuvant treatment with Taxane/Anthracycline in HER2-negative breast cancer. Results are shown in Fig. Finally, an M2EFM Exp + Clin model trained on the full training data (Hatzis1) achieved an AUC of 0.720, 95% CI  on the external validation data (Hatzis2). The odds ratios for this model are given in Table 31.Of the 115 m2eGenes, 55 were found to interact in a sub-network of protein-protein interactions using WebGestalt. The sub-network included 65 genes in all and was enriched for 184 biological process terms, demonstrating that many of the genes in our signature are functionally related. The top result was for lymphocyte activation (p = 2.50e-12), which included 23 genes from the sub-network and is about 8.96 times more overlap than would be expected by chance. The sub-network is shown in Fig. Using Gene Ontology enrichment testing, our gene set shows a clear enrichment for immune functions Fig. . The resESR132 and EGFR33). We calculated the enrichment of genes in our signature in the Catalog of Somatic Mutations in Cancer (COSMIC) Cancer Gene Census23, downloaded on 9/13/2016. Enrichment would suggest a causal link between genes in our signature and the progression of the disease. There were 601 genes in the catalog, 515 of which were in our gene expression profiles. The enrichment for causally implicated cancer genes in our gene signature was about 4 times greater than expected by chance . The following 18 genes used in our M2EFM models appear in the Cancer Gene Census: AFF3, BCL11A, CD79A, CD79B, EGFR, ERBB4, ESR1, FOXA1, GATA3, IRF4, ITK, LCK, MYB, POU2AF1, PRF1, PTPRC, RET, TNFRSF17.Many of the genes in our gene signature are already known to be associated with breast cancer . Thus, our signature was enriched for known targets of breast cancer treatments 10 times more than would be expected by chance . These drugs included paclitaxel (MAPT), raloxifene (ESR1), toremifene (ESR1), fulvestrant (ESR1), trastuzumab (EGFR), tamoxifen , docetaxel (MAPT), and lapatinib (EGFR).We also examined the known targets of FDA approved breast cancer drugs using the DrugBank database version 5.034, and validated a data-integrated approach to creating prognostic and predictive cancer models. The M2EFM approach shows remarkable promise for developing prognostic and predictive cancer biomarkers using both clinical and molecular data. For overall survival, distant recurrence free survival, and pathologic complete response in breast cancer it achieved a median C-index or AUC of at least 0.7 in all internal and external validation datasets (including 5 different cohorts). The fact that our model can reliably attain this level of discrimination across platforms and populations is promising indeed.In this work, we have tried to address common shortcomings in molecular biomarker studies, have applied the REMARK guidelines in our assessmentUnsurprisingly, one of our comparison methods, a modified Cox-Ridge approach, performed about as well as M2EFM in terms of discriminative power. M2EFM depends on Cox-Ridge itself, and the Cox-Ridge models contain a superset of the predictors in M2EFM. Nevertheless, M2EFM models in many cases outperform the Cox-Ridge models, and more importantly, M2EFM models depend on only 115 genes, as opposed to 10990 in the Cox-Ridge models. Therefore, clinical use for Cox-Ridge would require a transcriptome-wide gene expression assay, and the situation would be even more extreme if the model with methylation values was used. Additionally, for DRFS and pCR, M2EFM was better calibrated than Cox-Ridge, suggesting that Cox-Ridge would not be as useful clinically. We also demonstrated that M2EFM has a high NPV for node-negative cases, while maintaining a meaningful PPV, suggesting M2EFM might be useful for identifying patients who could avoid adjuvant chemotherapy. Finally, M2EFM has functional relevance, increasing the possibility that it could serve as the basis for clinical tests that determine eligibility for treatment.11, these results consistently show that integrating both molecular and clinical data results in more prognostic models than either data type alone. Our results strongly suggest that a data-integrated approach that models genes affected by regulatory changes in cancer is more reliable than many extant approaches. Furthermore, our results suggest our method builds a model that is prognostic in the case of ER-negative samples and possibly triple negative samples . Given the lack of approved prognostic indicators for ER-negative patients, partly due to its greater proliferative rate and the reliance of many tests on proliferative genes27, and the greater difficulty in treating triple negative disease, a marker, such as ours, that is largely independent of proliferation is desirable36.Thus, using three different outcomes and five different data sets, we maintained a consistent level of accuracy. In conjunction with our prior study of M2EFM applied to ccRCC38, we note the repression of immune related genes in our signature for patients predicted to be at high risk. There has been growing interest in finding signatures that are independent of proliferation and ER status that might also be predictive of possible immune therapies27.Our results also show that our approach does more than build a reliable prognostic model: it identifies biologically relevant pathways and, importantly, possible therapeutic targets and genes involved in cancer progression. Our gene signature contains genes that are functionally involved in cancer and that are targeted by current breast cancer treatments. Perhaps more interestingly, given recent advances in immunotherapyAlthough we provide evidence of the efficacy of M2EFM, there remains one limitation before attempting to translate these results to the clinic: calibration of the model to a single platform. To obtain external validation data, we performed cross-platform normalization. Having established the utility of the M2EFM approach, it remains to train the model on a high-quality dataset generated on the platform that will be used for any clinical assays.M2EFM can predict risk based on data integrated from multiple sources, taking advantage of tried-and-true prognostic factors while incorporating data on relevant relationships between molecular data types at the individual level. For breast cancer, this resulted in models based on several genes with known functional associations to cancer progression and which are targeted by currently available drugs, and therefore, may result in a useful tool for clinical decision support. This also suggests that other genes in the model should be examined as possible targets, because many of the genes are functionally connected. Given the strength of our findings, we believe that further development of this technique and application to other cancers is warranted.Supplementary Material


Hepatocellular carcinoma (HCC) is currently still a major factor leading to death, lacking of reliable biomarkers. Therefore, deep understanding the pathogenesis for HCC is of great importance. The emergence of circular RNA (circRNA) provides a new way to study the pathogenesis of human disease. Here, we employed the prediction tool to identify circRNAs based on RNA-seq data. Then, to investigate the biological function of the circRNA, the candidate circRNAs were associated with the protein-coding genes (PCGs) by GREAT. We found significant candidate circRNAs expression alterations between normal and tumor samples. Additionally, the PCGs associated with these candidate circRNAs were also found have discriminative expression patterns between normal and tumor samples. The enrichment analysis illustrated that these PCGs were predominantly enriched for liver/cardiovascular-related diseases such as atherosclerosis, myocardial ischemia and coronary heart disease, and participated in various metabolic processes. Together, a further network analysis indicated that these PCGs play important roles in the regulatory and the PPI network. Finally, we built a classification model to distinguish normal and tumor samples by using candidate circRNAs and their associated genes, respectively. Both of them obtained satisfactory results (~ 0.99 of AUC for circRNA and PCG). Our findings suggested that the circRNA could be a critical factor in HCC, providing a useful resource to explore the pathogenesis of HCC. HCC is the most common type of liver cancer and the third most common causes of cancer worldwide , 2. The CircRNAs as a new type of non-coding RNA are distinct from traditional linear RNAs for their closed loop structure. They are widely presented in the eukaryotic transcriptome . CircRNAPrevious studies showed that circRNAs associate with disease occurrence . CircRNAIn this work, we investigated whether aberrant expression of circRNAs and their related PCGs associated with HCC. The main work flow is as follows: firstly, two algorithms, circRNA_finder  and circhttp://genome.ucsc.edu/). STAR (version 2.5.2a) and Bowtie (version 2.2.8.0/1.2.2.0) were used to build index with default parameters for the human genome.RNA-seq data of 100 samples consisting of tumor tissues and para-carcinoma tissues from 50 HCC patients were downloaded from the Sequence Reads Archive (SRP068976) . And thede novo prediction tool which is unbiased and faster. For each algorithm, the prediction outputs of all the samples were dealt with the python scripts provided by Thomas B. Hansen [Recently, circRNA attracted widespread attention, and several tools were developed for annotating circRNAs by exploiting RNA-sequencing reads spanning the back-splicing junction. According to previous study , there e. Hansen . Then thWe adopted only the common candidate circRNAs by the two algorithms to decrease the false positive rates based on previous reports by . By thisMachine learning algorithms are well accepted for classification , 25. To In practice, the random forest was applied to make our prediction with default 500 trees. 80 samples were randomly selected as the training data and the remaining 20 samples as the testing data. This process was repeated 100 times. Five-fold Cross-validation was used to model training. To avoid a biased inflation of predictability, we performed feature selection against the training data by using the LASSO  AccordinCircRNA is a new type of non-coding RNA, attracting widespread attention in recent years. Previous studies showed that circRNA displayed the anomalism in disease, could regard as a promising biomarker for disease diagnosis and targeted therapy. However, only a few circRNAs are well interpreted, and the biological function of the majority of circRNAs remains unclear. A systematically investigation for circRNAs expression is therefore important to explore its function and regulatory mechanisms.Here, the 2091 common candidate circRNAs  identifietc.  downloaded from BIOGRID database . InteresTo further examine the biological function of circRNAs, we focused on the targets of above mentioned 45 critical circRNAs in clustering analysis based on the circRNA-microRNA-gene regulatory network by , in whicAccording to above clustering analysis, circRNAs and their associated PCGs were significantly altered between normal and tumor samples. In order to further examine their expression patterns, we built a classification model to investigate whether the circRNAs or their associated PCGs has the ability to distinguish normal and tumor samples, respectively.Firstly, the expression levels of the candidate circRNAs across all the samples were applied as the feature vectors inputting to random forest classifier. Specifically, we randomly selected 80 samples used as the training data, and the remaining samples were used as the testing data. Feature selection only used in training data to avoid biased inflation of predictability. This process was repeated 100 times, and the average values of predictive results were listed in We also built a classification model by using aforementioned 1450 differentially expressed PCGs that associated with 2091 circRNAs. Expectedly, the prediction accuracy is satisfactory Click here for additional data file.S2 Table(XLSX)Click here for additional data file.S3 Table(XLSX)Click here for additional data file.