Adaptive Control Model Reveals Systematic Feedback and Key Molecules in Metabolic Pathway Regulation

Abstract

Robust behavior in metabolic pathways resembles stabilized performance in systems under autonomous control. This suggests we can apply control theory to study existing regulation in these cellular networks. Here, we use model-reference adaptive control (MRAC) to investigate the dynamics of de novo sphingolipid synthesis regulation in a combined theoretical and experimental case study. The effects of serine palmitoyltransferase over-expression on this pathway are studied in vitro using human embryonic kidney cells. We report two key results from comparing numerical simulations with observed data. First, MRAC simulations of pathway dynamics are comparable to simulations from a standard model using mass action kinetics. The root-sum-square (RSS) between data and simulations in both cases differ by less than 5%. Second, MRAC simulations suggest systematic pathway regulation in terms of adaptive feedback from individual molecules. In response to increased metabolite levels available for de novo sphingolipid synthesis, feedback from molecules along the main artery of the pathway is regulated more frequently and with greater amplitude than from other molecules along the branches. These biological insights are consistent with current knowledge while being new that they may guide future research in sphingolipid biology. In summary, we report a novel approach to study regulation in cellular networks by applying control theory in the context of robust metabolic pathways. We do this to uncover potential insight into the dynamics of regulation and the reverse engineering of cellular networks for systems biology. This new modeling approach and the implementation routines designed for this case study may be extended to other systems. Supplementary Material is available at www.liebertonline.com/cmb.

Biological Interpretation of Model-Reference Adaptive Control in a Mass Action Kinetics Metabolic Pathway Model

“…This report extends previous work that demonstrated the original use of MRAC to infer potential regulatory interactions [5]. Specifically, we (a) assess the efficacy and robustness of the proposed controller using MRAC in terms of tracking error, i.e., how closely the plant dynamics follow the reference dynamics, and (b) interpret the control and feedback dynamics in the context of relevant literature for potential insight into sphingolipid de novo synthesis pathway regulation.…”

“…where k a,b indicates the rate constant for the reaction from a to b (see [5] for details of other pathway reactions). Rate constants are estimated using data from the C 16 dual-chain labeled species.…”

Sphingolipid and Glycosphingolipid Metabolic Pathways in the Era of Sphingolipidomics

“…One used model-reference adaptive control (MRAC) to investigate the dynamics of de novo sphingolipid synthesis by Hek cells stably transfected with serine palmitoyltransferase, and the MRAC simulations produced results that were comparable to simulations from a standard model using mass action kinetics, and suggested that there might be adaptive feedback from increased metabolite levels. ( 638 ) The other approach integrated lipidomics and transcriptomics data collected by the LIPID MAPS Consortium ( ) for RAW264.7 cells using a two-step matrix-based approach wherein the rate constants obtained from the first step were further refined using generalized constrained nonlinear optimization. ( 639 ) The primary focus of the analysis was the C16-ceramide backbone species, and the resulting model fit the experimental data, with the robustness of the model being validated through parametric sensitivity analysis.…”

“…Two other mathematical approaches have been applied to data sets from studies of mammalian sphingolipid biosynthesis. One used model-reference adaptive control (MRAC) to investigate the dynamics of de novo sphingolipid synthesis by Hek cells stably transfected with serine palmitoyltransferase, and the MRAC simulations produced results that were comparable to simulations from a standard model using mass action kinetics, and suggested that there might be adaptive feedback from increased metabolite levels . The other approach integrated lipidomics and transcriptomics data collected by the LIPID MAPS Consortium () for RAW264.7 cells using a two-step matrix-based approach wherein the rate constants obtained from the first step were further refined using generalized constrained nonlinear optimization .…”

Multiscale Computational Models of Complex Biological Systems

“…Using this technique they expanded on a previous single-scale model and were able to decouple the promigratory and anti-proliferative effects of TGF-β1 on various cell types in an in silico skin wound closure model over time. Analogous reasoning and techniques are also used for analysis of metabolic and signaling networks in which a steady state flux is desired for informing higher tiers of function (3, 5, 6, 45, 48). …”