Supplementary Text 1: Model design.
We began our investigation by developing a mathematical model1 to integrate biochemical data on sphingolipid metabolism and its regulation. From among various choices, such as a traditional Michaelis-Menten-type analysis2, a purely stoichiometric approach3, Flux-Balance Analysis4, or Metabolic Control Analysis5, we selected Biochemical Systems Theory (BST)6,7, which incorporates substrates, enzymes, and regulatory signals for each metabolite in a highly structured form, thereby facilitating transient analyses of metabolites and fluxes, as well as steady-state, stability, sensitivity, and robustness analyses. A major advantage of the BST approach is that knowledge of the exact mechanism of each reaction is not required to set up equations and that models may be designed based on the identity of the reactants and their interconnections. The result is a canonical form using power-law representations (see below). This form provides an equation template that incorporates all pertinent pathway components and whose characterizing numerical features are estimated from experimental data. Within BST, we decided to use the Generalized Mass Action (GMA) representation7 that reflects the stoichiometry of the pathway in a more intuitive form than the alternative S-system form, which has greater advantages for algebraic analyses about the steady state that are only of secondary importance here.
It should be noted that when developing a model, certain criteria must be decided such as the level of detail and the boundaries within which the model can be expected to validly function. The current model was developed for growth phase under normal conditions, while also allowing simulation of other scenarios by changing the enzyme activities to reflect the altered conditions. Indeed, this has been demonstrated in two other systems (glycolytic and trehalose response to heat shock) using microarray expression data8,9.
The crucial initial step of model design is the proper mapping of the metabolic pathway since the system of equations and the particular components of each equation are constructed directly from the map. Figure 1 of the main text is the map used to model the yeast sphingolipid pathway. For each time-varying metabolite, a differential equation is formulated that consists of the difference between all influxes and effluxes. Each flux is represented by a product of power-law functions containing only those pathway components (e.g., enzymes, metabolites, regulators) that directly affect the flux. For convenience, each component is symbolized by Xi, where i is the index number assigned to that variable. In our model, the first 25 variables are dependent (i.e. subject to modulation by the system), and the remaining 38 variables are independent (i.e. unchanged by the system); they are listed in Supplementary Tables S1 and S2. Each variable in each term is assigned an exponent, called a kinetic order fijk given by the relative partial derivate of the rate law Vij between Xi and Xj with respect to the substrate, enzyme, or modulator Xk of interest at the chosen operating point,
and each term also contains a rate constant, ij computed from the flux between Xi and Xjdivided by the power-law function.
Once the equations are formulated symbolically, numerical values are determined for the rate constants and kinetic orders. For the sphingolipid pathway, these values were obtained from published data as well as from experimental time-series measurements of particular metabolites, and if known, from kinetic laws obtained from the literature. ATP-dependent phosphorylation of dihydrosphingosine (DHS) may illustrate the model design step.
Three molecules affect the influx: DHS (X2), ATP (X28), and the sphingoid base kinases (X36). The efflux is also influenced by three components, namely DHS-P (X4), the sphingoid base phosphate lyase (X50), and the sphingoid base phosphatases (X41), but has two routes. One flows back to DHS and the other exits the sphingolipid pathway through the lyase. The generic equation for the change in DHS-P is given by
where the influx is
and the efflux is given in the GMA form as
Next, the values for the kinetic orders and rate constants are calculated. The phosphorylation step is represented by the rate function V2,4, for which the literature suggests the bisubstrate Michaelis-Menten rate law
with KM,DHS = 0.38 mol%10 and KM,ATP = 25 M11. The cellular concentration of DHS was measured for yeast as X2s = 0.01 mol%12 and the cellularATP concentration as X28s = 1,100 M13. Lanterman and Saba (1998)10 determined the enzymatic activity as 4x10-6mol/min/mg. The steady-state flux through the reaction was determined as V2,4 = 0.000119 M/min/l (for details see1). Thus, after rounding to two significant figures, the kinetic orders in the GMA model have the values f2,4,2 = 0.97 and f2,4,28 = 0.0011. Assuming linear dependence on enzyme activity yields f2,4,36 = 1. With these quantities, the rate constant is computed as
= 2626.9.
After similar calculations of the effluxes toward X2 (DHS) and X17 (CDP-E), V4,2and V4,17, the fully parameterized equation for DHS-P reads:
.
Equations were developed in this manner for each dependent variable1 in the model. Supplementary Tables S1 and S2 present pertinent information for the variables.
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