(591f) Modeling Inflammatory Lipid Dynamics Using a Cybernetic Framework and Information-Theoretic Approaches

Hyper­inflammation syndrome, multiple organ failure, influenza, and acute respiratory distress are all associated with cytokine and eicosanoid storms which result in an uncontrolled flare up of the inflammatory response within tissues and organs. Therapeutic interventions to combat these disease states include targeting specific cytokines– signaling molecules such as tumor necrosis factor alpha (TNFα) that are secreted by immune cells. It also includes identifying the crucial steps of cytokine and eicosanoid—lipid mediators in response to infection—interactions. However, the detailed sequence of biological mechanisms underlying the eicosanoid network and the production of cytokines is not well understood.

This study aims to integrate the eicosanoid network and cytokine dynamics for mammalian macrophage cells. The integration of mechanistic knowledge and experimental data into mathematical models provides a powerful strategy for a quantitative understanding of the molecular machinery of mammalian cell lipid metabolic networks. Current modeling structures for biochemical networks comprise stoichiometric models and can only incorporate known regulatory phenomena [1]. Nevertheless, modeling a network involving copious biochemical reactions and regulation poses computational challenges.

In this work, we use an alternative mathematical framework called cybernetic modeling to provide a feasible approach which accounts for complex regulations in the lack of a well­-defined understanding of cellular signaling and metabolic regulation. The cybernetic model is able to robustly capture the intricate unknown signaling and control details through the accomplishment of the cybernetic goal, which relates cytokines to prostanoids in the context of inflammation. Prior work has established a preliminary model capturing eicosanoid dynamics. However, the cybernetic goal of this model does not account for the potentially nonlinear relationship between cytokines and metabolites [2]. In this work, we develop information theoretic approaches to identify and optimize cybernetic goals in combination with optimizing the metabolic reaction rates and cybernetic regulatory variables; we use mutual information as a measure of mutual dependence.

Methodology

Our system uses the dynamic lipidomic (i.e., eicosanoids and prostanoids) and transcriptomic (i.e., gene expression profiles for pro­inflammatory cytokines) measurements. We formulated a cybernetic model that describes the dynamic behavior of prostanoids, PR_i formation under the influence of multiple pro­inflammatory cytokines, such as TNFα, IL­1α, and IL­18. The interactions between the PR_i and cytokines are estimated using a mutual information approach. This approach can be validated against the experimental observations in the literature. To detect the presence of interactions between PR_i and cytokines, we developed a mutual information (MI) formula (Fig. 1(d)) based on previous work [3].The non­zero MI values obtained indicate the presence of interactions between PR_i and cytokines. The validation of these associations against the experimental observations in the literature further lends credibility to our MI-based approach [4].

Results

We used an Auto Regressive Integrated Moving Average model (ARIMA (p, d, q)) for our time-series dataset and determined the hyper­parameters for different PRi and cytokines series. Fig. 1(e) displays the fit obtained through the ARIMA model for a PR_i, Prostglandin D₂ (PGD₂). The innovation series of PR_i (X_t) consists of the error (e_i) terms (obtained using ARIMA), and the innovation set for cytokines (Y_t) is defined as (f_t). The standardized innovation series for PGD2 is shown in Fig. 1(e) inset plot. We determined the joint probability density function p(e_t , f_t) by the non-parametric Gaussian Kernel Density Estimation (Fig. 1f). The I (X_t; Y_t) (MI) values computed using equation 1(d) are illustrated in Fig. 1(g), for a combination of PR_i, PGD₂, and cytokines.

Conclusions

The detailed sequence of biological mechanisms underlying the eicosanoid network combined with cytokines is not well understood. Information theory provides data analysis approaches that quantify the mutual statistical interactions between two data sets to extract the significance of the unknown interplay between them. This work lays the foundation for the development of a mathematical formulation for the modeling and analysis of inflammatory processes using information theory to connect the behavior of system components with regulatory oversight by employing the cybernetic framework.

References

1. Y. Kihara, S. Gupta, M. Maurya, A. Armando, I. Shah, O. Quehenberger, C. Glass, E. Dennis, and S. Subramaniam. Biophysical Journal, 106(4):966–975, February 2014.
2. L. Aboulmouna, S. Gupta, M.R. Maurya, F. DeVilbiss, S. Subramaniam, D. Ramkrishna. A Cybernetic Approach to Modeling Lipid Metabolism in Mammalian Cells. Processes. 6(8):126, August 2018.
3. A. Galka, T. Ozaki, J. B. Bayard, and O. Yamashita, “Whitening as a tool for estimating mutual information in spatiotemporal data sets,” Journal of statistical physics, vol. 124, no. 5, pp. 1275–1315, 2006.
4. C. Yao and S. Narumiya, “Prostaglandin­cytokine crosstalk in chronic inflammation,” British journal of pharmacology, vol. 176, no. 3, pp. 337–354, 2019.­­­