RasGTP pull downs were performed as described previously. Mechanistic model simulations MATLAB and the function ode15s was used to simulate a previously developed, ordinary differential equation based ERK cascade model, which is described in de tail in Tables 1 and 2. The function gamrnd was used to generate realizations of www.selleckchem.com/products/dorsomorphin-2hcl.html peak RasGTP, Raf, MEK, and ERK levels for individual cells in the stochastic simula tions according to the gamma distribution where N specifies a protein level, k is the shape param eter, and �� is the scale parameter. We specified the k parameter of each gamma distribution as 5. 4, as was measured for total ERK, assuming roughly similar expression regulation. Since the mean of a gamma distribution is equal to k��, the �� parameter of each gamma distribution was changed as needed to at tain the desired distribution mean.

To estimate the parameters for the RasGTP dynamics, which are described by a simple exponential rise and decay model, we used least squares optimization to ensure that desired initial magni tude, peak magnitude, time to peak, time to inflection, time to steady state, and steady state magnitude of the RasGTP dynamics matches well to that which the model prescribes. Additional file 1 Figure S6 describes these RasGTP dynamics metrics graphically. As there are four unknown parameters in the RasGTP dynam ics model, we need four equations, which we take as the following e5T where wi corresponds to a weight for optimization purposes. Eq. 2 specifies the proper steady state magnitude. Eq. 3 specifies that the 1st derivative at the time to peak is zero.

Eq. 4 specifies the proper magnitude at the time to steady state . and Eq. 5 specifies the proper peak magnitude. The following constraints are placed on this optimization problem d? Eq. 6 specifies that there is a maximum at the time to peak and Eq. 7 specifies that the 1st derivative is negative at the inflection point Ks and s are determined as described in Methods. Mean peak RasGTP levels were increased to simu late increasing input, and were linearly spaced between 10 nM and 200 nM using 6 points, which correspond to EGF doses of 0. 01, 0. 1, 0. 5, 1, 5, and 10. Following the trends of the experimental data in Additional file 1 Figure 2A and, peak times for RasGTP were sampled linearly between 7 min and 2 min, with 7 min corresponding to the lowest peak RasGTP level.

Also, we took ss as 10 min, Iss as 15% of Imax realizations, Io as 0, and infl as /2. All code is available upon request. Parameter Batimastat sensitivity analysis Five hundred different parameter sets were generated via latin hypercube sampling from a 23 dimensional uniform distribution http://www.selleckchem.com/products/Rapamycin.html that spans 1 order of magnitude around each nominal parameter value. For each of these parameter sets stochastic simu lations were performed as described above.