Figure 1.
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, <A, B, C> and <A, B, D>, 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.
Table 1.
List of variables/terms and their explanations.
Figure 2.
An example for B-spline basis functions.
B-spline basis functions for 6 bins are shown. Each curve represents a bin. For each observation (x-axis), the corresponding y value on each curve yields the probability of that observation to be in that bin. Summation of the y values corresponding to an x value for all bins sum up to 1.
Figure 3.
Illustration of determining WT and CF specific metabolite level combinations.
Three metabolites are being analyzed to determine their expected levels for WT and CF. 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 ClassifyCombination, it is determined that combinations o2, o3, o4, and o7 are WT-specific (on the left) and combinations o1, o5, o6, and o8 are CF-specific (on the right). When sets of combinations are weighed separately by their marginal information, expected levels for these metabolites for CF and WT are found.
Figure 4.
Illustration of combining expectations found by each EFM.
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 WT (right) and CF (left) are found as explained in Figure 3. Individual expected levels are weighted using equation 14 to obtain a WT-specific and a CF-specific level for each metabolite.
Table 2.
Comparison of metabolite selection strategies.
Figure 5.
Results of gene expression analysis and flux measurements on DNL pathway.
Circles represent the corresponding metabolites, and arrows represent reactions. ELOVL6 and SCD1 are the genes that express enzymes, which catalyze the corresponding reactions. This independent wet-lab study shows that (i) flux through Decanoic Acid to Stearic is decreased, and (ii) the shown genes that catalyze corresponding reactions are down-regulated in 3-week-old CF mice.
Figure 6.
DNL pathway in the big picture.
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 [47].
Figure 7.
Results of significance testing for individual metabolites on DNL Pathway.
Dark grey-colored metabolite represents significant increase for a metabolite in CF, compared to WT (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 t 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) ELOVL6 expression level is lower.
Figure 8.
Expected level changes found using ADEMA for metabolites on DNL Pathway.
Coloring scheme is the same as in Figure 7. Resulting expected metabolite changes are computed using ADEMA, for the CF mice w.r.t. WT mice (3-week-old mice). We see that Palmitic Acid and Stearic are decreased, as suggested by the flux measurement and ELOVL6 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.
Figure 9.
Classification performance for ADEMA on 3 in vivo datasets.
Accuracy, Precision, Recall and F-measure results are shown for datasets S1, S2, and S3. The accuracy of the classifier is significant for all datasets (two-tailed Fisher's exact test).
Figure 10.
Comparison of ADEMA with other classifiers.
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 [54]. Results show that ADEMA performs up to 31% better than the other methods, and performs better than all other methods in at least one dataset.
Figure 11.
Predicted Metabolite Levels for the In Silico Dataset.
This figure depicts the simplified Glycolysis pathway as described by the BioModels model Wolf2000_Glycolytic_Oscillations. Figure shares the legend of Figure 7. As the variable group has increased Glucose levels, and, therefore, increased input to the model, the expectation is to observe an increase in the overall metabolite levels. As expected ADEMA predicts that every single metabolite is increased in the variable group, with respect to the control group.
Figure 12.
Time Performance of ADEMA on Dataset S1.
Time requirements for changing M and k values show exponential increase for 3-week-old data.
Table 3.
Accuracy of ADEMA Classification Scheme on Dataset S3 w.r.t. Varying Parameters.
Table 4.
Execution time of ADEMA Classification Scheme on Dataset S3 w.r.t. Varying Parameters.