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Research Article

Simultaneous Non-Negative Matrix Factorization for Multiple Large Scale Gene Expression Datasets in Toxicology

  • Clare M. Lee,

    Affiliation: Department of Mathematics and Statistics, University of Strathclyde, Glasgow, United Kingdom

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  • Manikhandan A. V. Mudaliar,

    Affiliation: College of Medical, Veterinary and Life Sciences, University of Glasgow, Glasgow, United Kingdom

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  • D. R. Haggart,

    Affiliation: Epsistem Ltd., Manchester, United Kingdom

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  • C. Roland Wolf,

    Affiliations: University of Dundee Medical Research Institute, Ninewells Hospital & Medical School, Dundee, United Kingdom, CXR Biosciences Ltd, Dundee, United Kingdom

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  • Gino Miele,

    Affiliation: Epsistem Ltd., Manchester, United Kingdom

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  • J. Keith Vass,

    Affiliation: Department of Mathematics and Statistics, University of Strathclyde, Glasgow, United Kingdom

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  • Desmond J. Higham mail,

    d.j.higham@strath.ac.uk

    Affiliation: Department of Mathematics and Statistics, University of Strathclyde, Glasgow, United Kingdom

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  • Daniel Crowther

    Affiliation: Sanofi, Frankfurt am Main, Germany

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  • Published: December 14, 2012
  • DOI: 10.1371/journal.pone.0048238

Abstract

Non-negative matrix factorization is a useful tool for reducing the dimension of large datasets. This work considers simultaneous non-negative matrix factorization of multiple sources of data. In particular, we perform the first study that involves more than two datasets. We discuss the algorithmic issues required to convert the approach into a practical computational tool and apply the technique to new gene expression data quantifying the molecular changes in four tissue types due to different dosages of an experimental panPPAR agonist in mouse. This study is of interest in toxicology because, whilst PPARs form potential therapeutic targets for diabetes, it is known that they can induce serious side-effects. Our results show that the practical simultaneous non-negative matrix factorization developed here can add value to the data analysis. In particular, we find that factorizing the data as a single object allows us to distinguish between the four tissue types, but does not correctly reproduce the known dosage level groups. Applying our new approach, which treats the four tissue types as providing distinct, but related, datasets, we find that the dosage level groups are respected. The new algorithm then provides separate gene list orderings that can be studied for each tissue type, and compared with the ordering arising from the single factorization. We find that many of our conclusions can be corroborated with known biological behaviour, and others offer new insights into the toxicological effects. Overall, the algorithm shows promise for early detection of toxicity in the drug discovery process.

Introduction

The aim of this work is to highlight the usefulness of a recently proposed extension to the technique of non-negative matrix factorization (NMF) by demonstrating its promise for early detection of toxicity in the drug discovery process. In particular, we (a) show that any number of related datasets can be treated simultaneously with this approach, (b) deal with practical issues that arise when the algorithm is applied to real datasets, (c) demonstrate its use with a new large scale microrray dataset, and (d) interpret the results from a biological perspective.

Computational Background

NMF seeks to represent a large complex dataset in terms of smaller factors. The name covers many algorithms. Each approximates a non-negative matrix as the product of two or more smaller non-negative matrices, by attempting to minimise some objective function. Lee and Seung [1] showed that when applying multiplicative non-negative factorization to images of faces, each row/column pair of the factors expresses a recognisable facial feature. These techniques have since been used in many settings to learn parts of the data as well as to factorize and cluster datasets. For example, when applied to text data in [1] the algorithm can differentiate multiple meanings of the same word by context. On microarray data, NMF has been used to find patterns in genes or samples, typically bi-clustering both groups in a similar manner to two-way hierachical clustering [2][7]. The review article [8] shows how NMF has also been successful in other areas of computational biology, including molecular pattern discovery, class comparison and biomedical informatics. The new challenge that we address in this work is to apply the NMF methodology to multiple, related, large scale, data sets simultaneously. We use the work of Badea [9], [10], who considered an extension of NMF that deals with two data matrices. Simultaneous NMF is used in [9] to study pancreatic cancer microarray data alongside extra information concerning transcription regulatory factors. In [10] microarray datasets for pancreatic ductal adenocarcinoma and sporadic colon adenocarcinoma are sumiltaneously factorized in order to discover expression patterns common to both data sets. This simultaneous NMF approach readily extends to the case of an arbitrary number of data matrices and here, for what we believe to be the first time, we implement and evaluate the method on more than two. We also consider various practical issues that must be tackled in order to produce a useful computational tool. To minimize the number of algorithmic parameters, make the results straightforward to interpret, and exploit the natural sparsity in the algorithm [9, section 3], we focus on hard clustering. The interesting issue of allowing clusters to overlap in this context is therefore left as future work.

Biological Background

We analyse gene expression data describing the molecular changes in four tissue types due to different dosages of an experimental pan-peroxisome proliferator-activated receptor (pan-PPAR) agonist PPM-201, provided by Plexxikon. PPARs have attracted great interest as potential therapeutic targets for diabetes [11], but major concerns have arisen due to clinically observed side-effects [12]. Hence, there are compelling reasons for toxicological studies at the gene expression level.

The material is organised as follows. In Section we describe the simultaneous NMF algorithm and outline our approach for using the output to order and cluster a dataset. Section describes the mouse microarray data, and the NMF results that arise when we treat it as a single dataset are given in Section . This is followed in Section by the analysis of the data split into four datasets corresponding to the known tissue types; liver, kidney, heart and skeletal muscle. In Section we compare the gene clusters from Sections and , and Section discusses the results. Conclusions are given in Section .

Methods

Algorithms

Given non-negative data matrices of size for , our aim is to simultaneously factorize all matrices so that
with the additional constraints that is a non-negative matrix of size for , and is a non-negative matrix of size . Generalising naturally from the case in [9], we seek to minimise the objective function(1)
where . Here denotes the Frobenius norm. As in [9] the coefficients are designed to give equal weight to the different error terms. Based on the multiplicative update rules developed in [13], an iterative algorithm that attempts to solve the optimisation problem can be derived using a gradient descent method times. This gives us the following sequence of approximations for , given initial choices and ,

for some small positive matrices , and , with representing element-wise multiplication. The iteration may be motivated through the intuition that when and are sufficiently small and positive each of these equations should reduce the objective function. This allows us to set
again with the division being performed element-wise. Hence the overall iteration has the form

The values in and are non-negative due to the constraints on the matrices, however they are not necessarily small. The iteration decreases the objective function (1), so this leads to a locally optimum solution, but we cannot guarantee convergence to a global optimum. In particular, different initial conditions can lead to different factorizations of different quality.

Having iterated up to some stopping criterion and produced the factorizations, we use them to bi-cluster the data. Each sample is assigned to the cluster for which it has the largest value in the gene cluster and vice versa. In reordering the data for easy visualisation we organise the rows and columns by cluster number (assigned arbitrarily) and sort the elements within each cluster from the appropriate sample/gene set, with the largest value at the bottom/right of that cluster. Given that the second factor is common to all the factorizations, it produces a matching ordering of the columns of the data.

Because the result depends on the choice of initial condition, and because the choice of is not automatic, further information is needed in order to specify a practical algorithm. To deal with the lack of uniqueness, we try several initial conditions and pick a realisation that minimises the objective function (1). We then continue until further runs do not significantly alter the results. The objective function value is also one of the criteria we use in order to decide which rank/clustering is the most “appropriate” for the data. By regarding the objective function as a function of , we identify values of where the decay in the objective function begins to diminish. In addition we also form a consensus matrix as in [3], [14] for the clustering of the objects. This is the average of the connectivity matrices where for each initialisation if objects and are clustered together and otherwise. So the consensus matrix contains values between and with the element being the likelihood that objects and cluster together. The cumulative density of these values is constructed, by summing the appropriate probabilities, and the area under this curve is the second measure we look at when considering choices for . The third measure is the Pearson correlation of the cophenetic distances, as explained in [3].

Mouse data

We apply these techniques to mouse gene expression data quantifying changes in four different tissue types following administration of different dosages (vehicle, therapeutic and toxic) of an experimental pan-PPAR agonist. The study design and clinical chemistry results are summarised in Table 1. ALT and AST are known markers in rodents for liver toxicity [15] and from this criterion mouse E may be showing a toxic response to PPM201, despite it being administered at a supposedly therapeutic dose level. This conditions our expectation of the gene-expression pattern for mouse E and suggests that it may be similar to the toxic level group III for liver.

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Table 1. Blood clinical chemistry analysis for each mouse.

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Nine wild type mice (strain: C57BL/6J) were randomly divided into three groups; - Group-I, II and III. PPM-201 in the vehicle base was administered daily for 14 days at 6 mg/kg body weight dose rate to each mouse in Group-II and at 20 mg/kg body weight dose rate to each mouse in Group-III while the mice in Group-I received only the vehicle base. On 15th day, the mice were sacrificed to harvest blood, heart, skeletal muscle, liver and kidney tissues for clinical chemistry, microarray and histopathology analysis. In the clinical chemistry analysis, alanine aminotransferase (ALT, U/L), aspartate aminotransferase (AST, U/L), creatinine kinase (CK, U/L), blood urea nitrogen (BUN, mmol/L), creatinine (mol/L) and lactate dehydrogenase (LDH, U/L) were measured from the blood of each mouse. Two sections of liver, two sections of kidney, one or two sections of skeletal muscle, and one section of heart were prepared from each mouse, stained with hematoxylin and eosin (H&E), and examined by a veterinary pathologist. Total RNA was isolated from murine tissues using Qiazol-based homogenization and subsequent column-based purification (Qiagen) with on-column DNAse-treatment. DNAse-free RNA was assessed for quality using Agilent Bioanalyser electrophoresis and acceptance criteria of RNA Integrity Number (RIN) greater than seven. 50 ng of total RNA was subsequently utilized as input to cDNA-based amplification and biotin-labelling using single-primer isothermal amplification according to the manufacturer's instructions (Ovation System, NuGEN Technologies). Unlabelled and biotin-labelled cDNA was qualitatively assessed by Agilent Bioanalyser electrophoresis to ensure identical size distributions of all samples pre- and post-fragmentation. Fragmented, biotin-labelled cDNA were hybridized to MOE430 2.0 GeneChip arrays (Affymetrix) with subsequent scanning and feature extraction according to the manufacturer's instructions.

The dataset has been approved by the GEO curators and assigned the accession number GSE31561.

Ethics Statement

The in vivo procedures undertaken during the course of this study (Ref: CXR0631) were subject to the provisions of the United Kingdom Animals (Scientific Procedures) Act 1986. The study was approved by the CXR Biosciences Local Ethics Committee and complied with all applicable sections of the Act and the associated Codes of Practice for the Housing and Care of Animals used in Scientific Procedures and the Humane Killing of Animals under Schedule 1 to the Act, issued under section of the Act.

Results

Single dataset

First, the samples are treated as a single dataset, with thirty six samples and 45037 genes, hence the data matrix is . This corresponds to the case where in Section . The factorizations were performed twenty times for each , with a consensus matrix formed from the clustering of the samples. All gene clusters associated with this analysis are labelled with a subscript 1, e.g., .

Figure 1(a) shows the minimum size of the objective function that we observed for each value of . We see that this value decreases monotonically, with a slower rate starting at around . Figure 1(b) shows the area under the cumulative density curves for the same values of . This subfigure clearly points to , as does subfigure (c) showing the cophenetic correlation.

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Figure 1. Three measures of the performance versus specified cluster size,

, when the data set is factorised as a single entity. (a) The value of the objective function for . (b) The area under consensus cumulative density, [3], [14]. (c) The cophenetic correlation coefficient, [3].

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Based on Figure 1, we conclude that when the data is factorized as a single entity, clusters is the most appropriate choice. Reordering the dataset using the ordering for in the manner described in Section gives the images shown in Figure 2. This figure shows the samples in the columns with cluster one at the top. To aid visualisation, the sample clusters are split by white lines, as are the gene clusters. This reordered data matrix shows a distinctive “ramp” effect in the blocks on the diagonal, placing genes that are most influential in identifying each tissue type to the bottom of the block. This figure also shows some of the differences in expression behaviour between the tissue types, particularly for the most influential genes.

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Figure 2. Factorising as a single dataset; reordering using the NMF for

. The columns show the samples and the rows the gene expression for each of the 45037 genes. Genes and samples are organised by cluster number. Elements within each cluster are ordered, with the largest value at the bottom/right. Each tissue is characterised by a group of highly expressed genes; from the top left to bottom right these are heart, skeletal muscle, liver and kidney. For comparison purposes, the characteristic 100 “best” genes in the four columns are names , , and .

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Because we know the origin of the samples, we can confirm that the algorithm has put the heart samples in cluster one, the skeletal muscle samples in cluster two, the liver samples in cluster three, and the kidney samples in cluster four. The exact ordering of the samples is shown in Table 2. This table also shows the mouse identification information for each sample, and we see that the mice are not ordered in the same way within each cluster. It is the liver and skeletal muscle samples that most closely respect the dosage levels within the clusters. Both these clusters only have one sample mis-ordered.

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Table 2. Ordering of the tissue samples after single factorization of rank 4 of the entire dataset.

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Given that the factorization has been performed for we know what the clustering would be from all these rank factorizations. This information is displayed in Figure 3. Here the rows representing the samples are ordered in tissue then dosage subgroups. For each rank , samples with the same colour are assigned to the same cluster. As we have seen before, for the samples are split into tissue types. The figure shows that this split persists at with an empty cluster forming. In fact, for this range of there are at most twelve clusters of samples. We also see from this figure that for no value of are the twelve tissue/dosage subgroups found.

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Figure 3. Factorising as a single dataset.

The clustering of the mouse samples for . Within each column the samples in the same colour are clustered together. No value of reveals the known tissue/dosage subgroups, or places different tissues in the same cluster.

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Multiple datasets

The test in Section indicates that the basic NMF factorization approach can deliver biologically meaningful results—separating the twelve samples by tissue type. But the failure to order correctly within tissue type according to dosage motivates the use of the multiple dataset generalization introduced in Section , where the four tissue types are treated as separate sources of information across a common set of mice. Intuitively, we would expect to add value to the data analysis by building known biology into the algorithm in this way. In this section, we therefore factorize the four new datasets simultaneously. This is similar to the test in Section in the sense that it produces a single ordering for the mice, but it has the potential to add extra information by providing four different, tissue-level, gene orderings. We thus have matrices of size . We again performed 20 factorizations, this time for and these have been used to generate a consensus for clustering the mice.

The objective function and the consensus measurements are shown in Figure 4. The objective function in subfigure (a) does not show much decrease in convergence rate until we get to nine clusters. This is the point where each mouse is put into a cluster on its own. The area under the cumulative density curve in Figure 4(b) suggests using either rank , or factorizations for the clustering. The correlation coefficients shown in subfigure (c) give the same two values as peaks, as well as , though the peak is the highest.

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Figure 4. Three measures of the performance versus specified cluster size,

, when the four tissue types are factorised separately. (a) The value of the objective function for . (b) The area under consensus cumulative density function for , [3], [14]. (c) The cophenetic correlation coefficient, [3].

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Given these measurements we consider the four-way simultaneous factorization for in Figure 5. The reordered datasets are shown separately with the kidney dataset in the top left, the liver dataset in the top right, the heart dataset in the bottom left and the skeletal muscle in the bottom right. The mouse ordering and mouse clusters that arise are shown in Table 3. The four subfigures in Figure 5 also illustrate that the gene clusters are different for each dataset. The three clusters for each tissue in this 4-way factorization are subsequently refered to in the form “, cluster 1,2 or 3. ” Table 3 shows that the simultaneous NMF approach has recovered the known mouse treatments except for one misplacement. Figure 6 shows the clustering for the four-way simultaneous factorizations for . This indicates that this mouse does not cluster with all those of the same dosage for any rank of factorization greater than two, instead it associates with the higher more toxic dosage. This is borne out by the known blood chemistry, as summarised in Table 1; the mouse that is mis-classified exhibits a toxic response and is therefore classified with the mice that received the higher dose.

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Figure 5. Factorisation of the four separate tissue types using simultaneous NMF with

. Top left, kidney; top right, liver; lower left, heart; lower right, skeletal muscle. The four tissue types are treated as separate sources of information across a common set of mice. Genes are therefore ordered differently in each of the four tissues, but the mice ordering is global. The resulting mouse ordering and mouse clusters are detailed in Table 3.

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Figure 6. Factorisation of the four separate tissue types simultaneously.

The clustering of the mice for ; colour indicates cluster number. One “misclassification” is found for several values of . This involves the mouse showing a toxic response to the lower (6 mg/kg) dose of PPAR agonist, as discussed in section .

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Table 3. Ordering of the tissue samples after a four-way factorization of rank 3.

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Comparing Gene clusters

Our aim now is to test the results from the novel multi-way NMF algorithm used in Section in order to see whether they (a) show consistency and (b) add value to the results in Section from standard NMF. We know that the four simultaneously factorized datasets correspond to the four clusters of samples that were discovered in an unsupervised manner from the single factorization of the full dataset. It could therefore be conjectured that the most influential genes in the first factorization will appear as influential genes in the four-way simultaneous factorization for that dataset, but less so for the other datasets.

Our comparisons involve four reference sets. For illustration, we chose an arbitrary threshold of one hundred; that is, we consider the top one hundred most influential genes from the four clusters in the first factorization shown in Figure 2. For easy reference these sets are referred to using the known tissue type. This means that the genes from cluster one are the genes, those from cluster two are the genes, those from cluster three are the genes and those from cluster four are the genes. The 4-way factorization shown in Figure 5 identifies differently ordered gene clusters for each tissue, which we will refer to as “, cluster 1,2 or 3, etc. ” Table 4 shows the total number of co-incident genes between the top 100 lists arising from the one-way and four-way factorisations. The table also shows the probability of the two lists having that number of genes in common if the second list were randomly selected; hence these values come from the hypergeometric distribution. We see that the important genes for each tissue type appear significantly highly in the clusters from that tissue's data type. In addition, all the tissue type genes also appear significantly within the reordering of the heart dataset. This link is reciprocated, with the heart genes appearing significantly frequently within the skeletal muscle dataset. Surprisingly, the greatest overlap arose between and cluster 2. One of these genes, Apoliprotein A1, is being considered as a marker for cardiac toxicity [16].

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Table 4. Gene cluster comparison for indivdual tissues in the single matrix, “,” with the four separate tissue matrices “.”

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We would like to demonstrate the utility of the factorization method by using the gene clusters obtained in our analysis to understand tissue specific effects of the experimental drug, PPM-201. Of course, we are not claiming that this is an exhaustive analysis of the effects of PPM-201. We analysed the gene clusters for pathways enrichment and gene ontology enrichment using DAVID [17] and Ingenuity Pathways Analysis (IPA) [18] tools. Table 5 shows the comparison of KEGG pathways enriched in the four tissue specific top one hundred most influential probe-sets obtained in the first factorization. Pathways enriched in these clusters differ according to the tissue types and can be considered as the pathways that are most perturbed by PPM-201. For example, arrhythmogenic right ventricular cardiomyopathy, hypertrophic cardiomyopathy and dilated cardiomyopathy are enriched in heart, whereas starch and sucrose metabolism, drug metabolism and PPAR signalling pathway are enriched in liver. Similarly, Figure 7 shows the enrichment of canonical pathways in the four tissue specific clusters analysed using IPA. It also shows the tissue specific enrichment of pathways—calcium signalling, integrin linked kinase (ILK) signalling and cardiac hypertrophy signalling are enriched in and clusters, whereas fatty acid metabolism and farnesoid X receptor (FXR)/retinoid X receptor (RXR) activation are enriched in the cluster. Analysis of the same sets of genes for enrichment of toxicity functions in the IPA shows, in Figure 8, cardiac hypertrophy in genes, increased level of creatinine and hydronephrosis in genes, and increased levels of lactate dehydrogenase (LDH) and steatosis in genes.

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Figure 7. Enrichment of canonical pathways in the four tissue specific gene clusters.

The top one hundred most influential probe-sets in the four tissue specific gene clusters obtained in the first factorization were subjected to signalling and metabolic pathways analysis in the IPA software. This graph shows the comparison of canonical pathways enriched in the four tissue specific gene clusters, , , and . The coloured bars show the significance of the enrichment for a particular pathway in the cluster computed by Fisher's exact test.

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Figure 8. Enrichment of toxicity functions in the four tissue specific gene clusters.

The top one hundred most influential probe-sets in the four tissue specific gene clusters obtained in the first factorization were subjected to IPA-Tox analysis in the IPA software. This graph shows the comparison of toxicity functions enriched in the four tissue specific gene clusters. The coloured bars show the significance of the enrichment for a particular toxicity functions in the cluster computed by Fisher's exact test.

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Table 5. Enrichment of KEGG pathways in the four tissue specific gene clusters.

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The common genes between the top one hundred most influential probe-sets in the four tissue specific clusters and the top one hundred most influential probe-sets in the clusters formed by 4-way simultaneous factorization of the split dataset were also analysed for enrichment of pathways, gene ontology and toxicity functions using DAVID and IPA. Tables 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17 summarise the results of this analysis, which are discussed further in the next section.

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Table 6. Enrichment of KEGG pathways in the common genes between the clusters found by the two ways of factorization.

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Table 7. Muscle genes present in the calcium signalling pathway.

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Table 8. Heart genes present in the calcium signalling pathway.

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Table 9. Liver genes present in the calcium signalling pathway.

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Table 10. cluster 1. Common probesets between the top one hundred most influential probesets in the cluster and 20 mg/kg dosage cluster (cluster 1) of the dataset.

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Table 11. cluster 3.

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Table 12. cluster 1.

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Table 13. cluster 3.

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Table 14. cluster 2.

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Table 15. cluster 1.

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Table 16. cluster 3.

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Table 17. cluster 3.

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Discussion

The factorization and reordering of the dataset as a whole set (Figure 2 and Table 2) successfully clustered samples from the same tissue and further investigation showed that it simultaneously identified genes with a known relevance to those tissues. It was therefore reasonable to study the genes that were responsible for this differentiation. In the one-way clustering, the top 100 probe-sets from each of the four tissue specific clusters show remarkable coherence for tissue specific pathways. The calcium signalling pathway is highly enriched in both and clusters; these genes are linked to muscle contraction function. Muscle contraction is the prime function of cardiac and skeletal muscles. A deeper look at the probe-sets (Tables 7 and 8) from the heart and skeletal muscle clusters shows a successful identification of differences in the tissue types for this pathway; see Figure 9. MYH1, MYH2, MYH4 and MYL1 of the myosin family, which are specific to skeletal muscle, are found in the cluster while cardiac muscle specific myosin family members MYH6, MYL2 and MYL3 are found in the cluster [19]. This pattern is also true for troponin, calsequestrin, ryanodine and actin family members [20][25] (Tables 7 and 8). FXR/RXR activation pathway genes are significantly enriched in cluster (Figure 7) with most of the enriched genes present in the bile acid synthesis and regulation (Figure 10) pathway, which is one of the core functions of liver [26][28]. FXR/RXR activation is also found in the cluster, albeit with moderate significance; FBP1 and HNF4A are the two genes present in this pathway and they may be involved in gluconeogenesis in kidney [29].

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Figure 9. Heart and muscle genes enriched in calcium signalling – muscle contraction pathway.

IPA analysis of the top 100 probe-sets from heart and muscle gene clusters (Figure 7) showed the enrichment of calcium signalling pathway. In this figure, we have highlighted the genes present in this pathway in orange. Though this pathway is generalised for skeletal muscle contraction and cardiac muscle contraction, they differ in the members of the same gene family. The heart and muscle genes present in this pathway are given in Tables 7 and 8. Pathway diagram was drawn using Path Designer function of IPA [18].

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Figure 10. Liver genes enriched in FXR/RXR activation pathway IPA analysis of the top 100 probe-sets from the

cluster (Figure 7) showed the enrichment of FXR/RXR activation pathway. The genes present in this pathway are highlighted in orange. The liver genes present in the pathway are given in Table 9. Pathway diagram was drawn using Path Designer function of IPA [18].

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Splitting the dataset into four on the basis of tissue types and simultaneous non-negative factorization of them gave us the added reassurance of clustering the samples according to the dosage groups (Figure 5 and Table 3). The clustering of one mouse (Mouse E) from the lower dosage group (Group-II) with the higher dosage group (Group-III) can be explained by the higher PPM201 drug sensitivity of that mouse, indicated by the elevated levels of the toxocology markers ALT, AST, LDH and CK, compared with the rest of its group (Table 1). Comparisons of top probe-sets in tissue specific clusters with dosage specific clusters also show very high overlap of tissue specific genes in the four tissue types. cluster1 has 22 probe-sets that are common between the top 100 probe-sets of cluster and 20 mg/kg dosage cluster of dataset, and are highly enriched for cardiac muscle contraction and hypertrophic cardiomyopathy pathways (Table 6). ACTC1, ATP2A2, MYH6, MYL2, MYL3, TNNC1, TNNI3, TNNT2 and TPM1 are the genes enriched for these two pathways and shared between these two clusters. However, cluster 3, with 11 probe-sets in common between the top 100 probe-sets of cluster and vehicle dose cluster of dataset, does not show enrichment for cardiac muscle contraction and hypertrophic cardiomyopathy pathways. From this we may assume that perturbation of cardiac muscle contraction and hypertrophic cardiomyopathy pathways by 20 mg/kg dosage may indicate toxic responses. We also see a similar pattern in skeletal muscle. Between the top 100 probe-sets of cluster and 20 mg/kg dosage cluster of , and between the top 100 probe-sets of and vehicle dose cluster of , 15 and 14 probe-sets were in common and are named as cluster 1 and cluster 3, respectively. The calcium signalling–skeletal muscle contraction pathway is enriched in cluster 1 with the presence of ACTA1, ATP2A1, MYH1, MYH4, RYR1, TNNC2, TNNI2, TNNT3 and TRDN genes, whereas cluster 3 does not show any significant enrichment for signalling or metabolic pathways.

Interestingly, 49 probe-sets in the cluster 2 are common between the top 100 probe-sets of cluster cluster and 6 mg/kg dosage cluster of and highly enriched for acute phase response signalling, prothrombin activation and FXR/RXR activation pathways with the presence of ALB, ABCB11, AMBP, APOA1, APOA2, APOC3, APOH, F2, FGA, FGB, FGG, HAMP, HP, HPX, ORM1, PON1, RBP4, SERPINA1, SERPINC1, SLC27A5 and SLCO1B3 genes (Figure 11). This suggests alterations in lipid metabolism in liver along with tissue injury in heart induced by PPM-201 at 6 mg/kg dosage [30][33], which becomes more plausible when we look at the genes in cluster 1 that are common between the top genes and 20 mg/kg dosage cluster of dataset. Enrichment of toxicity functions in cluster 2 using IPA shows increased level of LDH as one of the toxicity functions (Figure 12) which has been validated with the increased level of LDH in the clinical chemistry results.

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Figure 11. Enrichment of canonical pathways in the liver heart gene cluster no. 2.

This gene cluster has 49 common probe-sets between the top one hundred most influential probe-sets in the liver gene cluster and top one hundred probe-sets in cluster number 2 (6 mg/kg dose rate) of the heart dataset reordered by 4-way simultaneous factorization. Canonical pathways enrichment for these 49 probe-sets analysed using the IPA software is shown in this figure. The length of the bars shows the Fisher's exact test p-value for enrichment for a particular pathway in the cluster.

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Figure 12. Enrichment of toxicity functions in

cluster 2. This gene cluster has 49 common probe-sets between the top one hundred most influential probe-sets in cluster 2 (6 mg/kg dose rate). Toxicity functions enrichment for these 49 probe-sets analysed using the IPA software is shown in this figure. The length of the bars shows the Fisher's exact test p-value for enrichment for a particular pathway in the cluster.

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Conclusions

We have demonstrated that multi-way simultaneous nonnegative matrix factorization can be usefully applied to the case of multiple datasets—here, for what we believe to be the first time, more than two large scale matrices were treated. The results were shown to be consistent with, and to add value to, standard nonnegative matrix factorization of the whole dataset.

In summarizing our biological findings, we first note that the roles of the three different isoforms of PPARs - PPAR-, PPAR- (also known as PPAR-) and PPAR- in metabolism and their difference in expression in different tissues and different species are well known [34][36]. In mouse, PPAR- is highly expressed in liver and to a lesser degree in kidney, heart and skeletal muscle; PPAR- is expressed in many tissues but peaks in kidney, heart and intestine whereas PPAR- is mostly expressed in adipose tissue [34], [37]. Pan-PPAR agonists activate two or all of the pan-PPAR isoforms and differ in their pharmacological actions. Factorisation of the dataset after splitting it on the tissue basis appears to be beneficial in identifying tissue specific and dosage effects of the experimental pan-PPAR agonist PPM-201 in this study. This approach could be useful in understanding molecular mechanisms and identifying potential tissue specific toxicological effects before they are apparent in histopathology studies. In this study, histopathology examination of heart did not show any defect though our method of gene expression analysis could identify enrichment of acute phase response signalling genes in heart that may point towards building up of toxic responses in heart. Given the fact that many PPAR agonist drugs have been shown to cause cardiac toxicity on prolonged usage and FDA's requirement of one year toxicity study for PPAR agonist drugs, our results show promising early detection of toxicity in the drug discovery process.

Overall, our aim here is to establish a proof of principle for the approach of simultaneously analysing multiple, related large datasets. We therefore focused on a dataset where clear-cut validation is possible. However, we note that the technique is very general, and therefore opens up many new opportunities in data-driven computational biology. In particular, it can be applied to heterogeneous sources of data; for example, generated by different laboratories or experimental methodologies. We are currently pursuing this approach in the study of colon cancer.

Acknowledgments

The computational work reported here made extensive use of the High Performance Computer Facilities of the Faculty of Engineering and Institute of Complex Systems at the University of Strathclyde. The authors also acknowledge Plexxikon for use of the compound.

Author Contributions

Conceived and designed the experiments: CML MAVM DRH CRW GM JKV DJH DC. Performed the experiments: CML MAVM DRH CRW GM JKV DJH DC. Analyzed the data: CML MAVM JKV DJH DC. Contributed reagents/materials/analysis tools: CML MAVM DRH CRW GM JKV DJH DC. Wrote the paper: CML MAVM JKV DJH DC.

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