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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,
fijk 
Vij X k

X k Vij
and each term also contains a rate constant, ij computed from the flux between Xi and Xj
divided 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.
Sphingoid base phosphatases (X41)
DHS (X2)
DHS-P (X4)
Sphingoid base kinases (X36)
Lyase (X50)
ATP (X28)
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
dX 4
 V4  V4
dt
where the influx is
V4  V2, 4   2,4 X 2f 2, 4, 2 X 28f 2, 4, 28 X 36f 2, 4,36
and the efflux is given in the GMA form as
V4  V4,2  V4,50   4,2 X 4f 4,2,4 X 41f 4,2,41   4,50 X 4f 4,17,4 X 50f 4,17,50
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

DHS
V2, 4  Vmax 
 K M , DHS  DHS
 

ATP


 K

  M , ATP  ATP 
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 cellular ATP concentration as X28s =
1,100 M13. Lanterman and Saba (1998)10 determined the enzymatic activity as 4x10-6
mol/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

 2, 4  V2, 4 X 2
f2 , 4 , 2

X 282, 4, 28 X 362, 4, 36  0.0027 0.010.97  1,100 0.0011  4  10 6 
f
f
= 2626.9.
After similar calculations of the effluxes toward X2 (DHS) and X17 (CDP-E), V4,2
and V4,17, the fully parameterized equation for DHS-P reads:
dX 4
0.0011
 2626.9 X 20.97 X 28
X 36  12.01X 40.96 X 41  2224.4 X 40.96 X 50 .
dt
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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