Details of the model and its development have been published previously (15, 3134) and are summarized here and further described in Supplementary Text. The model focuses on Ras and the types of proteins that directly interact with Ras to regulate RasGTP levels: Ras GEFs (such as SOS1), Ras GAPs (such as NF1), and Ras effector proteins (such as the RAF kinases). The model includes (i) GEF-mediated nucleotide exchange, (ii) intrinsic nucleotide exchange, (iii) GAP-mediated nucleotide hydrolysis, (iv) intrinsic nucleotide hydrolysis, and (v) effector binding. GEF and GAP reactions, (i) and (iii) above, are described mathematically with reversible and irreversible Michaelis-Menten kinetics, respectively. We consider only the subset of total GEFs and GAPs that are active within our model. The other reactions are described with first- and/or second-order mass action kinetics. It is assumed that WT and Ras mutant proteins have identical reaction mechanisms as indicated above and that differences in rate constants (or enzymatic parameters) for the reactions account for described differences. For example, Ras mutant protein G12V hydrolyzes GTP more slowly than does WT Ras. In this case, the rate constant for this reaction kGTPase,G12V is smaller than the rate constant for the same reaction with WT Ras, kGTPase,WT. All reactions are grouped into a set of differential equations, and the steady-state quantity of RasGTP-effector complexes (and RasGTP) is solved for the specified conditions.

Parameters of the model for proteins correspond to biochemically observable properties. Rate constants, enzymatic properties (Vmax and Km), and protein abundances for WT Ras proteins have been previously obtained, used, and published (listed in Supplementary Text) (15). Mutant proteins can be characterized by their difference from WT proteins in terms of a multiplicative factor, α. Values for α are determined from previous experimental studies that measured the desired property for both WT and mutant Ras proteins (35, 36). For G12V and G12D, we use the same α values that were previously obtained and used in our model (15). For G13D, previous experiments described this mutant to have an elevated nucleotide dissociation rate compared to WT Ras (α = 3.6625) (18). Previous studies have also described Ras G13D to be insensitive to Ras GAP (37) and to have no appreciable binding to the Ras GAP NF1 (17). A 100-fold increase in the Km value of GAP on Ras G13D is used to model the immeasurable binding to the Ras GAP NF1. We estimated that the change must be at least 100 times large because changes of about 50-fold have previously been measured for other Ras mutants (38), so we assumed that the difference must be larger to be undetectable. The decreased GTPase activity of the G12D mutant is used for the G13D mutant, because we could not find an α factor at the time we began our study; using the same value as G12D allowed us to introduce impaired GTPase activity while also allowing us to focus on the known biochemical differences.

Computational “hybrid” mutants are modeled mutants that have properties of two distinct Ras mutants. For example, a hybrid Ras mutant may be modeled with all of the properties of Ras G12D, except for the faster intrinsic nucleotide dissociation properties of G13D. Such a hybrid could be used to evaluate how faster nucleotide dissociation would influence signaling through the comparison of this hybrid’s behavior with that of the G12D mutant.

The Ras network within the CRC context is assumed to be EGFR driven, and EGFR is assumed to activate Ras through increased activation of Ras GEFs like SOS1 and SOS2. We use a 10-fold increase in Vmax for GEF reactions to indicate EGFR activation, just as we have done previously to model receptor tyrosine kinase–mediated Ras activation (15). To simulate an EGFR inhibition dose response, we considered levels of GEF activity between the “high” (10× increase) case and the basal “low” (1×) level and we determined the resulting level of RasGTP by model simulation. We assume that the three Ras proteins—HRAS, NRAS, and KRAS—share similar biochemistry and can be modeled with the same set of biochemical properties; such an assumption is consistent with measurements of the three Ras proteins (39, 40). We assume that measurements that provide α for one Ras protein are good approximations for the same mutant to the other Ras proteins. We assume that more than one Ras gene is expressed in CRC cells. This is consistent with many data (21, 41). We here model Ras mutants as being heterozygous such that, for a KRAS mutant, one-half of total KRAS will be mutant and one-half of total KRAS will be WT. Here, we assume that 50% of total Ras is KRAS (and that 25% of total Ras is mutant). This assumption is consistent with MS quantification of KRAS, NRAS, and HRAS levels (21).

RasGTP and RasGTP-effector complex are considered as measures of Ras pathway activation. Model simulations are used to determine steady-state levels of RasGTP and RasGTP effector. Simulations and analysis are performed in MATLAB (, MathWorks).

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