A markov classification model for metabolic pathways

Abstract

Background: This paper considers the problem of identifying pathways through metabolic networks that relate to a specific biological response. Our proposed model, HME3M, first identifies frequently traversed network paths using a Markov mixture model. Then by employing a hierarchical mixture of experts, separate classifiers are built using information specific to each path and combined into an ensemble prediction for the response.

Results: We compared the performance of HME3M with logistic regression and support vector machines (SVM) for both simulated pathways and on two metabolic networks, glycolysis and the pentose phosphate pathway for Arabidopsis thaliana. We use AltGenExpress microarray data and focus on the pathway differences in the developmental stages and stress responses of Arabidopsis. The results clearly show that HME3M outperformed the comparison methods in the presence of increasing network complexity and pathway noise. Furthermore an analysis of the paths identified by HME3M for each metabolic network confirmed known biological responses of Arabidopsis.

Conclusions: This paper clearly shows HME3M to be an accurate and robust method for classifying metabolic pathways. HME3M is shown to outperform all comparison methods and further is capable of identifying known biologically active pathways within microarray data.

Figure 1

Example network.

Figure 2

Simulated network diagrams.

Figure 3

Arabidopsis thaliana glycolysis pathway from Alpha-D-Glucose to Pyruvate. For visual simplicity, we show only a single edge connecting each compound; however in the actual network there is a separate edge for each gene label displayed.

Figure 4

Arabidopsis thaliana Oxidative Pentose Phosphate Cycle. For visual simplicity, we show only a single edge connecting each compound; however in the actual network there is a separate edge for each gene label displayed.

Figure 5

Performance results for the Glycolysis pathway. Inverse cross-validated Correct Classification Rates (CCR) for all models for the Glycolysis pathway for Arabidopsis.

Figure 6

ROC curve of all paths for the optimal model (M = 4) for the glycolysis pathway.

Figure 7

Transition probabilities for the most expressed glycolysis path (m = 3) that separates flowers from rosette for Arabidopsis. Training set CCR = 0.818, AUC = 0.752.

Figure 8

Arabidopsis Performance results for the pentose phosphate pathway for classifying oxidative stress pathways.

Figure 9

ROC curve of all paths for the optimal model (M = 2) for the pentose phosphate pathway for classifying oxidative stress pathways.

Figure 10

Transition probabilities for the most expressed pentose phosphate path (m = 2) for Arabidopsis under oxidative stress. The numbers in brackets represent the probability of each edge θ_m for m = 2.