ADEMA: An Algorithm to Determine Expected Metabolite Level Alterations Using Mutual Information

<div><p>Metabolomics is a relatively new “omics” platform, which analyzes a discrete set of metabolites detected in bio-fluids or tissue samples of organisms. It has been used in a diverse array of studies to detect biomarkers and to determine activity rates for pathways based on changes due to disease or drugs. Recent improvements in analytical methodology and large sample throughput allow for creation of large datasets of metabolites that reflect changes in metabolic dynamics due to disease or a perturbation in the metabolic network. However, current methods of comprehensive analyses of large metabolic datasets (metabolomics) are limited, unlike other “omics” approaches where complex techniques for analyzing coexpression/coregulation of multiple variables are applied. This paper discusses the shortcomings of current metabolomics data analysis techniques, and proposes a new multivariate technique (ADEMA) based on mutual information to identify expected metabolite level changes with respect to a specific condition. We show that ADEMA better predicts De Novo Lipogenesis pathway metabolite level changes in samples with Cystic Fibrosis (CF) than prediction based on the significance of individual metabolite level changes. We also applied ADEMA's classification scheme on three different cohorts of CF and wildtype mice. ADEMA was able to predict whether an unknown mouse has a CF or a wildtype genotype with 1.0, 0.84, and 0.9 accuracy for each respective dataset. ADEMA results had up to 31% higher accuracy as compared to other classification algorithms. In conclusion, ADEMA advances the state-of-the-art in metabolomics analysis, by providing accurate and interpretable classification results.</p> </div

Accuracy of ADEMA Classification Scheme on Dataset S3 w.r.t. Varying Parameters.

<p>Figure shows how accuracy of ADEMA classifier changes with respect to changing parameters <<i>M, k, maximum subset size</i>>. The best result is obtained for the combination <6,2,6>.</p

Illustration of combining expectations found by each EFM.

<p>In this illustration, there are 8 metabolites that are analyzed. We have 6 different subsets of metabolites found using EFMs. For each one of them, expected levels for <i>WT</i> (right) and <i>CF</i> (left) are found as explained in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002859#pcbi-1002859-g003" target="_blank">Figure 3</a>. Individual expected levels are weighted using <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002859#pcbi.1002859.e049" target="_blank">equation 14</a> to obtain a <i>WT-</i>specific and a <i>CF-</i>specific level for each metabolite.</p

Illustration of determining <i>WT</i> and <i>CF</i> specific metabolite level combinations.

<p>Three metabolites are being analyzed to determine their expected levels for <i>WT</i> and <i>CF</i>. In this example, there is just one subset of metabolites considered, and there are two bins (e.g., either up or down). There are 2³ possible combinations of ups and downs. Using the function <i>ClassifyCombination</i>, it is determined that combinations o2, o3, o4, and o7 are <i>WT</i>-specific (on the left) and combinations o1, o5, o6, and o8 are <i>CF</i>-specific (on the right). When sets of combinations are weighed separately by their marginal information, expected levels for these metabolites for <i>CF</i> and <i>WT</i> are found.</p

Execution time of ADEMA Classification Scheme on Dataset S3 w.r.t. Varying Parameters.

<p>Figure shows how much time (in seconds) it takes for the ADEMA classifier to train and classify an unknown individual on average for different parameter combinations <<i>M, k, maximum subset size</i>>.</p

An overview for ADEMA.

<p>The first step is to construct a population such that it contains multiple individuals (in this case M1 and M2 who are in control group versus M3 and M4 who are in variable group. Concentrations of metabolites of interest are determined for all individuals (in this case concentrations of metabolites A, B, C and D). Then for the second step, each observation is assigned a probability to be in a discrete bin (we only consider two bins, namely, up or down). Third step is to construct the metabolic network to determine the associations between measured metabolites. In this figure circles represents metabolites and arrows represent the reactions that relate metabolites. This is followed by the fourth step that determines the subsets of metabolites, which are related in the metabolic network. We have found two sets, and , are the only subsets that are related. Using the probabilities found in step 2 and related subsets found in step 4, ADEMA determines control- and variable-specific metabolite levels (bins) and compares the changes in variable group with respect to mice in control group. In this example, ADEMA concludes that A, B and C are increased, and D is decreased in the variable group as compared to control mice.</p

DNL pathway in the big picture.

<p>Circles represent the metabolites, and arrows represent reactions. Big rectangles represent compartments that reaction take place in (e.g., blood, cytosol, mitochondrion). DNL pathway holds an important place in the carbon flow of the liver cell. The glucose entering the cell can be utilized in the TCA cycle or can be converted to Triglycerides (TG) for storage. DNL pathway is particularly relevant to CF since it has been showed that mice with CF exhibit low lipogenesis and deposition of newly synthesize fatty acids into adipose tissue <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002859#pcbi.1002859-Bederman1" target="_blank">[47]</a>.</p

Results of significance testing for individual metabolites on DNL Pathway.

<p>Dark grey-colored metabolite represents significant increase for a metabolite in <i>CF</i>, compared to <i>WT</i> (3-week-old mice). Grey represents “no significant change”, dark grey represents “significant increase”, and light grey represents “significant decrease”. Significance tests are done using student's <i>t</i> test per each metabolite independently. The results show that the path Decanoic Acid to Stearic shows no significant change other than an increase in Dodecanoic Acid even though (1) the flux is shown to be decreased on this path, and (2) <i>ELOVL6</i> expression level is lower.</p

Comparison of ADEMA with other classifiers.

<p>Figure shows the comparison of ADEMA's accuracy with other well-known non-linear classifiers. For PLS-DA, MetaboAnalyst's implementation is used, and for the rest of the techniques, WEKA implementations with default parameters are used. We report classification results for raw data and data that is normalized using the method described by Dubitzky et al <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002859#pcbi.1002859-Dubitzky1" target="_blank">[54]</a>. <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002859#s3" target="_blank">Results</a> show that ADEMA performs up to 31% better than the other methods, and performs better than all other methods in at least one dataset.</p

Expected level changes found using ADEMA for metabolites on DNL Pathway.

<p>Coloring scheme is the same as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002859#pcbi-1002859-g007" target="_blank">Figure 7</a>. Resulting expected metabolite changes are computed using ADEMA, for the <i>CF</i> mice w.r.t. <i>WT</i> mice (3-week-old mice). We see that Palmitic Acid and Stearic are decreased, as suggested by the flux measurement and <i>ELOVL6</i> levels. The increases in Dodecanoic Acid and Tetradecanoic Acid can be explained by a downstream effect of Stearic and Palmitic Acid that lead to the accumulation of these two metabolites as they are no longer consumed.</p