Applications of analysis of dynamic adaptations in parameter trajectories

Metabolic Modeling Combined With Machine Learning Integrates Longitudinal Data and Identifies the Origin of LXR-Induced Hepatic Steatosis

Temporal multi-omics data can provide information about the dynamics of disease development and therapeutic response. However, statistical analysis of high-dimensional time-series data is challenging. Here we develop a novel approach to model temporal metabolomic and transcriptomic data by combining machine learning with metabolic models. ADAPT (Analysis of Dynamic Adaptations in Parameter Trajectories) performs metabolic trajectory modeling by introducing time-dependent parameters in differential equation models of metabolic systems. ADAPT translates structural uncertainty in the model, such as missing information about regulation, into a parameter estimation problem that is solved by iterative learning. We have now extended ADAPT to include both metabolic and transcriptomic time-series data by introducing a regularization function in the learning algorithm. The ADAPT learning algorithm was (re)formulated as a multi-objective optimization problem in which the estimation of trajectories of metabolic parameters is constrained by the metabolite data and refined by gene expression data. ADAPT was applied to a model of hepatic lipid and plasma lipoprotein metabolism to predict metabolic adaptations that are induced upon pharmacological treatment of mice by a Liver X receptor (LXR) agonist. We investigated the excessive accumulation of triglycerides (TG) in the liver resulting in the development of hepatic steatosis. ADAPT predicted that hepatic TG accumulation after LXR activation originates for 80% from an increased influx of free fatty acids. The model also correctly estimated that TG was stored in the cytosol rather than transferred to nascent very-low density lipoproteins. Through model-based integration of temporal metabolic and gene expression data we discovered that increased free fatty acid influx instead of de novo lipogenesis is the main driver of LXR-induced hepatic steatosis. This study illustrates how ADAPT provides estimates for biomedically important parameters that cannot be measured directly, explaining (side-)effects of pharmacological treatment with LXR agonists.

Computational modelling of energy balance in individuals with Metabolic Syndrome

Background

A positive energy balance is considered to be the primary cause of the development of obesity-related diseases. Treatment often consists of a combination of reducing energy intake and increasing energy expenditure. Here we use an existing computational modelling framework describing the long-term development of Metabolic Syndrome (MetS) in APOE3L.CETP mice fed a high-fat diet containing cholesterol with a human-like metabolic system. This model was used to analyze energy expenditure and energy balance in a large set of individual model realizations.

Results

We developed and applied a strategy to select specific individual models for a detailed analysis of heterogeneity in energy metabolism. Models were stratified based on energy expenditure. A substantial surplus of energy was found to be present during MetS development, which explains the weight gain during MetS development. In the majority of the models, energy was mainly expended in the peripheral tissues, but also distinctly different subgroups were identified.

In silico perturbation of the system to induce increased peripheral energy expenditure implied changes in lipid metabolism, but not in carbohydrate metabolism. In silico analysis provided predictions for which individual models increase of peripheral energy expenditure would be an effective treatment.

Conclusion

The computational analysis confirmed that the energy imbalance plays an important role in the development of obesity. Furthermore, the model is capable to predict whether an increase in peripheral energy expenditure – for instance by cold exposure to activate brown adipose tissue (BAT) – could resolve MetS symptoms.

Electronic supplementary material

The online version of this article (10.1186/s12918-019-0705-z) contains supplementary material, which is available to authorized users.

Modeling Procedures

Being concerned by the understanding of the mechanism underlying chronic degenerative diseases , we presented in the previous chapter the medical systems biology conceptual framework that we present for that purpose in this volume. More specifically, we argued there the clear advantages offered by a state-space perspective when applied to the systems-level description of the biomolecular machinery that regulates complex degenerative diseases. We also discussed the importance of the dynamical interplay between the risk factors and the network of interdependencies that characterizes the biochemical, cellular, and tissue-level biomolecular reactions that underlie the physiological processes in health and disease. As we pointed out in the previous chapter, the understanding of this interplay (articulated around cellular phenotypic plasticity properties, regulated by specific kinds of gene regulatory networks) is necessary if prevention is chosen as the human-health improvement strategy (potentially involving the modulation of the patient's lifestyle). In this chapter we provide the medical systems biology mathematical and computational modeling tools required for this task.

In vivo and in silico dynamics of the development of Metabolic Syndrome

The Metabolic Syndrome (MetS) is a complex, multifactorial disorder that develops slowly over time presenting itself with large differences among MetS patients. We applied a systems biology approach to describe and predict the onset and progressive development of MetS, in a study that combined in vivo and in silico models. A new data-driven, physiological model (MINGLeD: Model INtegrating Glucose and Lipid Dynamics) was developed, describing glucose, lipid and cholesterol metabolism. Since classic kinetic models cannot describe slowly progressing disorders, a simulation method (ADAPT) was used to describe longitudinal dynamics and to predict metabolic concentrations and fluxes. This approach yielded a novel model that can describe long-term MetS development and progression. This model was integrated with longitudinal in vivo data that was obtained from male APOE*3-Leiden.CETP mice fed a high-fat, high-cholesterol diet for three months and that developed MetS as reflected by classical symptoms including obesity and glucose intolerance. Two distinct subgroups were identified: those who developed dyslipidemia, and those who did not. The combination of MINGLeD with ADAPT could correctly predict both phenotypes, without making any prior assumptions about changes in kinetic rates or metabolic regulation. Modeling and flux trajectory analysis revealed that differences in liver fluxes and dietary cholesterol absorption could explain this occurrence of the two different phenotypes. In individual mice with dyslipidemia dietary cholesterol absorption and hepatic turnover of metabolites, including lipid fluxes, were higher compared to those without dyslipidemia. Predicted differences were also observed in gene expression data, and consistent with the emergence of insulin resistance and hepatic steatosis, two well-known MetS co-morbidities. Whereas MINGLeD specifically models the metabolic derangements underlying MetS, the simulation method ADAPT is generic and can be applied to other diseases where dynamic modeling and longitudinal data are available.

Optimal experiment design for model selection in biochemical networks

Background

Mathematical modeling is often used to formalize hypotheses on how a biochemical network operates by discriminating between competing models. Bayesian model selection offers a way to determine the amount of evidence that data provides to support one model over the other while favoring simple models. In practice, the amount of experimental data is often insufficient to make a clear distinction between competing models. Often one would like to perform a new experiment which would discriminate between competing hypotheses.

Results

We developed a novel method to perform Optimal Experiment Design to predict which experiments would most effectively allow model selection. A Bayesian approach is applied to infer model parameter distributions. These distributions are sampled and used to simulate from multivariate predictive densities. The method is based on a k-Nearest Neighbor estimate of the Jensen Shannon divergence between the multivariate predictive densities of competing models.

Conclusions

We show that the method successfully uses predictive differences to enable model selection by applying it to several test cases. Because the design criterion is based on predictive distributions, which can be computed for a wide range of model quantities, the approach is very flexible. The method reveals specific combinations of experiments which improve discriminability even in cases where data is scarce. The proposed approach can be used in conjunction with existing Bayesian methodologies where (approximate) posteriors have been determined, making use of relations that exist within the inferred posteriors.