Mathematical modeling and validation of the ergosterol pathway in Saccharomyces cerevisiae

Abstract

The de novo biosynthetic machinery for both sphingolipid and ergosterol production in yeast is localized in the endoplasmic reticulum (ER) and Golgi. The interconnections between the two pathways are still poorly understood, but they may be connected in specialized membrane domains, and specific knockouts strongly suggest that both routes have different layers of mutual control and are co-affected by drugs. With the goal of shedding light on the functional integration of the yeast sphingolipid-ergosterol (SL-E) pathway, we constructed a dynamic model of the ergosterol pathway using the guidelines of Biochemical Systems Theory (BST) (Savageau., J. theor. Biol., 25, 365-9, 1969). The resulting model was merged with a previous mathematical model of sphingolipid metabolism in yeast (Alvarez-Vasquez et al., J. theor. Biol., 226, 265-91, 2004; Alvarez-Vasquez et al., Nature433, 425-30, 2005). The S-system format within BST was used for analyses of consistency, stability, and sensitivity of the SL-E model, while the GMA format was used for dynamic simulations and predictions. Model validation was accomplished by comparing predictions from the model with published results on sterol and sterol-ester dynamics in yeast. The validated model was used to predict the metabolomic dynamics of the SL-E pathway after drug treatment. Specifically, we simulated the action of drugs affecting sphingolipids in the endoplasmic reticulum and studied changes in ergosterol associated with microdomains of the plasma membrane (PM).

Figure 1. Ergosterol model for yeast.

Solid boxes represent time dependent variables, italics represent time independent variables, consecutive arrows represent multiple enzymatic reactions taking place, and the dashed arrow indicates an inhibitory feedback signal. Blue boxes represent metabolites in common with the sphingolipid pathway from Fig. 2. Abbreviations for the time dependent variables: Palmitoyl-CoA (Pal-CoA), X₁₂; Acetyl-CoA (Ac-CoA), X₂₅; 3-hydroxy-3-methylglutaryl-coenzyme A (HMG-CoA), X₂₆; Mevalonate,X₂₇; Farnesyl pyrophosphate (Farnesyl-PP), X₂₈; Squalene,X₂₉; Lanosterol,X₃₀; Zymosterol,X₃₁; Endoplasmic reticulum ergosterol (Ergosterol), X₃₂; Steryl Lanosterol, X₃₃; Steryl Zymosterol, X₃₄; Steryl Ergosterol in Bulk Lipid Particles (Steryl Ergosterol-1), X ₃₅; Outer Leaflet Ergosterol in the Plasma Membrane (Ergosterol-o), X ₃₆; Detergent insoluble plasma associated ergosterol (Ergosterol-r), X ₃₇; Internal Acetate (Acetate Int.), X ₃₈; Inner Leaflet Ergosterol in the Plasma Membrane (Ergosterol-i), X ₃₉; Steryl Ergosterol in Plasma Membrane Associated Lipid Particles (Steryl Ergosterol-2), X ₄₀; Golgi Associated Complex Sphingolipids (CS-g), X ₈+X ₁₈+X ₁₉; Plasma Membrane Associated Complex Sphingolipids (CS-m), X ₂₀+X ₂₁+X ₂₂.

Figure 2. Sphingolipid model for yeast.

Solid boxes represent time dependent variables, italics represent variables assumed to be time independent, dashed boxes represent variables with inhibitory or activating effects, dashed arrows represent more than one enzymatic reaction taking place. Blue boxes represent metabolites in common with the ergosterol pathway from Fig. 1. Abbreviations for the time dependent variables: 3-Keto-Sphinganine (KDHS), X₁; Sphinganine (DHS), X₂; Dihydroceramide (Dihydro-C), X₃; Sphinganine-1P (DHS-P), X₄; 4-OH-Sphinganine (PHS), X₅; Phytosphingosine-1P (PHS-P), X₆; Phytoceramide (Phyto-C), X₇; Inositol Phosphorylceramide (IPC-g), X₈; CDP-Diacylglycerol (CDP-DAG), X₉; Phosphatidylserine (PS), X₁₀; Phosphatidic Acid (PA), X₁₁; Palmitoyl-CoA (Pal-CoA), X₁₂; Serine, X₁₃; sn-1,2-Diacylglycerol (DAG), X₁₄; Phosphatidylinositol (PI), X₁₅; Inositol (I), X₁₆; Cytidine Diphosphate-Ethanolamine (CDP-Eth), X₁₇; Mannosylinositol Phosphorylceramide (MIPC-g), X₁₈; Mannosyldiinositol Phosphorylceramide (M(IP)₂C-g), X₁₉; Inositol Phosphorylceramide in Plasma Membrane (IPC-m), X₂₀; Mannosylinositol Phosphorylceramide in Plasma Membrane (MIPC-m), X₂₁; Mannosyldinositol Phosphorylceramide in Plasma Membrane (M(IP)₂C-m), X₂₂; Very Long Chain Fatty Acid (C₂₆-CoA), X₂₃; Malonyl-CoA (Mal-CoA), X₂₄; Acetyl-CoA (Ac-CoA), X₂₅; Endoplasmic reticulum ergosterol (Ergosterol), X₃₂; Plasma Associated, Detergent Insoluble ergosterol (Ergosterol-r), X ₃₇; Internal Acetate (Acetate Int.), X ₃₈.

Figure 3. Experimental data vs. SL-E model simulation results for steryl-esters and total sterols.

After an external pulse bolus (Panels A–C). (A) Dynamics adapted from Taylor and Parks after pulse-chase bolus of [¹⁴ C]-Acetate. (B) Simulation for total steryl-esters (X ₃₃+X ₃₄+X ₃₅+X ₄₀) and total sterols (X ₃₀+X ₃₁+X ₃₂+X ₃₆+X ₃₇+X ₃₉) after pulse bolus of labeled acetate. (C) Transported external label acetate (X ₁₂₅) and cytoplasmic acetate (X ₃₈). The initial label of external acetate was 125 µM. After 30 min pulse-chase with external [¹⁴ C]-acetate (Panels D–F). (D) Dynamics adapted from Taylor and Parks after pulse-chase bolus of [¹⁴ C]-Acetate. (E) Model simulation for steryl-esters (X ₃₃+X ₃₄+X ₃₅+X ₄₀) and total sterols (X ₃₀+X ₃₁+X ₃₂+X ₃₆+X ₃₇+X ₃₉) after pulse-chase bolus of labeled acetate. (F) Transported external label acetate (X ₁₂₅) and cytoplasmic acetate (X ₃₈). The initial label of external acetate was 125 µM. The % Total Sterols was calculated as percent with respect to the total sterol amount for the S. cerevisiae wild type strain. In Fig. 3B and E, the “Normalized % Total Sterols” were normalized against the last experimental values for the steryl-esters from Figs. A and D.

Figure 4. SL-E model results for an external pulse-chase bolus similar to the one in Fig. 3F .

(A) Complex sphingolipids: Golgi compartment plus plasma membrane IPC (X ₈+X ₂₀), Golgi compartment plus plasma membrane MIPC (X ₁₈+X ₂₁), Golgi compartment plus plasma membrane M(IP)₂C (X ₁₉+X ₂₂). (B) Ergosterol sub-populations: ergosterol in endoplasmic reticulum (X ₃₂), ergosterol steryl-ester-1 (X ₃₅), ergosterol associated with the complex sphingolipids (X ₃₇), plasma membrane ergosterol in inner leaflet (X ₃₉), ergosterol steryl-ester-2 (X ₄₀).

Figure 5. SL-E model results for an external pulse-chase bolus similar to the one in Fig. 3F .

Pools: Steryl-esters (X ₃₃+X ₃₄+X ₃₅+X ₄₀), Sterol (X ₃₀+X ₃₁+X ₃₂+X ₃₆+X ₃₇+X ₃₉). Ergosterol sub-populations: ergosterol in endoplasmic reticulum (X ₃₂), ergosterol steryl-ester 1 (X ₃₅), ergosterol associated with the complex sphingolipids (X ₃₇), plasma membrane ergosterol in inner leaflet (X ₃₉), ergosterol steryl-ester 2 (X ₄₀). (A) Decrease to 1% in IPC synthase activity (X ₁₃₃). Dynamic simulation for the steryl-esters pool and total sterols after pulse-chase bolus with labeled acetate. (B) Decrease to 1% in IPC synthase activity (X ₁₃₃). (C) Decrease to a 1% in serine palmitoyl transferase activity (X ₁₅₇). Dynamics simulation for the steryl- esters pool and total sterols after pulse-chase bolus with labeled acetate. (D) Decrease to a 1% in serine palmitoyl transferase activity (X ₁₅₇).

Figure 6. Yeast ergosterol diagram based on the highest sterol related SL-E logarithmic gains (metabolites) from Table S6.

The diagram summarizes the ten time dependent metabolites of the ergosterol pathway associated with the highest sum of logarithmic gain magnitudes that are bigger than 1 (see Fig. 1 and Table S6). Solid boxes show time dependent variables and italics represent time independent variables. Consecutive arrows represent multiple enzymatic reactions, and the dashed arrow indicates a feedback signal. Blue boxes represent metabolites that also appear in the sphingolipid pathway (Fig. 2). Abbreviations for the time dependent variables: Acetyl-CoA (Ac-CoA), X₂₅; Endoplasmic reticulum ergosterol (Ergosterol), X₃₂; Steryl Lanosterol, X₃₃; Steryl Zymosterol, X₃₄; Steryl Ergosterol in Bulk Lipid Particles (Steryl Ergosterol-1), X ₃₅; Outer Leaflet Ergosterol in the Plasma Membrane (Ergosterol-o), X ₃₆; Detergent insoluble plasma associated ergosterol (Ergosterol-r), X ₃₇; Internal Acetate (Acetate Int.), X ₃₈; Inner Leaflet Ergosterol in the Plasma Membrane (Ergosterol-i), X ₃₉; Steryl Ergosterol in Plasma Membrane Associated Lipid Particles (Steryl Ergosterol-2), X ₄₀; Golgi Associated Complex Sphingolipids (CS-g), X ₈+X ₁₈+X ₁₉; Plasma Membrane Associated Complex Sphingolipids (CS-m), X ₂₀+X ₂₁+X ₂₂.