Data-driven analysis and prediction of dynamic postprandial metabolic response to multiple dietary challenges using dynamic mode decomposition

Abstract

Motivation: In the field of precision nutrition, predicting metabolic response to diet and identifying groups of differential responders are two highly desirable steps toward developing tailored dietary strategies. However, data analysis tools are currently lacking, especially for complex settings such as crossover studies with repeated measures.Current methods of analysis often rely on matrix or tensor decompositions, which are well suited for identifying differential responders but lacking in predictive power, or on dynamical systems modeling, which may be used for prediction but typically requires detailed mechanistic knowledge of the system under study. To remedy these shortcomings, we explored dynamic mode decomposition (DMD), which is a recent, data-driven method for deriving low-rank linear dynamical systems from high dimensional data.Combining the two recent developments "parametric DMD" (pDMD) and "DMD with control" (DMDc) enabled us to (i) integrate multiple dietary challenges, (ii) predict the dynamic response in all measured metabolites to new diets from only the metabolite baseline and dietary input, and (iii) identify inter-individual metabolic differences, i.e., metabotypes. To our knowledge, this is the first time DMD has been applied to analyze time-resolved metabolomics data.

Results: We demonstrate the potential of pDMDc in a crossover study setting. We could predict the metabolite response to unseen dietary exposures on both measured (R² = 0.40) and simulated data of increasing size ($R_{\text{max}}^2$= 0.65), as well as recover clusters of dynamic metabolite responses. We conclude that this method has potential for applications in personalized nutrition and could be useful in guiding metabolite response to target levels.

Availability and implementation: The measured data analyzed in this study can be provided upon reasonable request. The simulated data along with a MATLAB implementation of pDMDc is available at https://github.com/FraunhoferChalmersCentre/pDMDc.

Keywords: differential responders; dynamic mode decomposition; metabotypes; personalized nutrition; precision nutrition.

Figure 1

Study design graphic of the three-armed crossover dietary interventional study.

Figure 2

Overview of the two applications for which we use our method. (A) Identification of a discrete linear dynamical system (LDS) using parametric DMD with control (pDMDc) allows for prediction of postprandial response of a new diet having trained on several others (Section 2.5). (B) Using pDMDc with a shared output mapping ${\tilde{U}}^{\left(\mathit{tot}\right)}$ that links individuals in the population to the same LDS framework, we cluster latent state trajectories ${\tilde{x}}_{t,i,d}$ to identify metabotypes (Section 2.6).

Figure 3

(A) Dynamic metabolite trajectories for training (gray) and holdout test (red) observations, exemplified for 6 out of 79 metabolites. Here dots are data and lines are model prediction (red) or reconstruction (grey). (B) Entire test data and prediction of test data as scatter plot for one of the cross-validation iterations. The line represents the perfect match between data and predictions.

Figure 4

Prediction of responses to simulated diets using pooled individuals as in Figure 3. (A) Prediction metric R2 of a large test set with increasing number of diets in the training set (5 iterations of scrambling the examples prior to splitting training and validation). (B) Prediction of test example (red) and training examples (grey) shown in six metabolite (out of 130 in total) responses. Here dots are data and lines are model prediction (red) or reconstruction (grey). The predictions are made using 40 diets in the training set. The subscripts GI,L, AdT, and MS stand for metabolites modelled in gastrointestinal tract, liver, adipose tissue, and skeletal muscle, respectively.

Figure 5

(A) Average measurement trajectory per metabolite (grey lines) and mean measurement trajectory per dynamical class (red line) obtained from clustering of the covariance matrix of the averaged data per metabolite. (B) Individual state trajectories for the pickled herring diet (grey lines) and median of individual trajectories per state (red line). (C) CP time loadings ($q$ from Equation 23) for the 3-component CP model.

Figure 6

(A) Column vectors of ${\tilde{U}}^{\left(\mathit{tot}\right)}$color-coded by metabolite category, describing the contribution of metabolites (similar to PCA loadings) to the observed states. (B) CP metabolite loadings ($r$ from Equation 25) color-coded by metabolite category, describing the metabolite contribution to each CP component.

Figure 7

Clustering of metabolic response to diet using pDMDc and CP to infer metabotypes (red and blue lines and dots). (A) The individual state trajectories of the first state in response to the meat diet, using four latent states. (B) K-means clustering of CP scores. (C) Raw data of amino acids contributing most strongly to the first column vector of ${\tilde{U}}^{\left(\mathit{tot}\right)}$, color-coded according to the clustering.

Figure 8

Clustering of state trajectories and CP scores to identify the ground truth simulated diabetic (blue) and healthy (red) patients. (A) Individual DMD state trajectories of the fourth state using four latent states. (B) CP scores clustered using the three-component model. (C) Raw simulated data of metabolites with the strongest contributors to the fourth column vector of ${\tilde{U}}^{\left(\mathit{tot}\right)}$, color-coded according to the clustering. The subscripts p, h, l, and GI stand for metabolites modelled in plasma, heart, liver, and gastrointestinal tract, respectively.