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 .

FIG. 1.

Model-reference adaptive control (MRAC) approach to study regulation in de novo sphingolipid synthesis. (a) Block diagram of model-reference adaptive control (MRAC); treated cells (plant) follow wild type cells (reference) to minimize the difference in sphingolipid amounts. (b) De novo sphingolipid synthesis pathway with key enzymes in italics; uni-/bi-directional arrows indicate irreversible/reversible reactions respectively; pathway intermediates, e.g., ceramide, sphingomyelin, are highly bioactive.

FIG. 2.

Sphingolipid dynamics in wild type (reference). Abscissa-time (hours), ordinate-normalized sphingolipid amounts (pmol/mg protein); scatter plots represent observed data (median and range for four technical replicates, indicated where available, i.e., no data for Sa* and limited data for DH*), lines represent simulations.

FIG. 3.

Sphingolipid dynamics in treated cells, without and with MRAC. Abscissa-time (hours), ordinate-normalized amounts (pmol/mg protein); scatter plots represent observed data (median and range indicated for four technical replicates, indicated where available, i.e., limited data for DH*), lines represent simulations. (a) Without MRAC. (b) With MRAC.

FIG. 4.

Regulatory dynamics in treated cells. Abscissa-time (hours), ordinate-magnitude (dimensionless). (a) Controller comprises two components from pathway feedback and input respectively. (b) Detailed pathway feedback in terms of adaptation gain from individual molecules; all gains initialized at zero except for DHGC, DHSM initialized at −1.