Simulations of the EGFR - KRAS - MAPK Signalling Network in Colon Cancer. Virtual Mutations and Virtual Treatments with Inhibitors Have More Important Effects Than a 10 Times Range of Normal Parameters and Rates Fluctuations

The fragment of the signaling network we have considered was formally described as a sort of circuit diagram, a Molecular Interaction Map (MIM). We have mostly followed the syntactic rules proposed by Kurt W. Kohn [1,10,11]. In our MIM we drew 19 basic species. Our dynamic simulations involve 46 modified species and complexes, 50 forward reactions, 50 backward reactions, 17 catalytic activities. A significant amount of parameters concerning molecular concentrations, association rates, dissociation rates and turnover numbers, are known for this intensively studied neighborhood of the signaling network. In other cases, molecular, cellular and even clinical data generate additional indirect constraints. Some unknown parameters have been adjusted to satisfy these indirect constraints. In order to avoid hidden bugs in writing the software we have used two independent approaches: a) a more classic approach using Ordinary Differential Equations (ODEs); b) a stochastic simulation engine, written in Java, based on the Gillespie algorithm: we obtained overlapping results. For a quiescent and EGF stimulated network we have obtained a behavior in good agreement with what is experimentally known. We have introduced virtual mutations (excess of function) for EGFR, KRAS and BRAF onco-proteins. We have also considered virtual inhibitions induced from different EGFR, KRAS, BRAF and MEKPP inhibitors. Drugs of this kind are already in the phase of preclinical and clinical studies. The major results of our work are the following: 3.16× or 3.16/ fluctuations of total concentrations of independent molecular species or fluctuations of rates, were introduced systematically. We examined the effects on the plateau levels of the 61 parameters representing all molecular species / complexes. Fluctuations of concentrations generated scores of deviation from the normal reference situation with median = 5, Ist-IIIrd quartile = 1-9. Fluctuations of rates generated scores of deviation with median and Ist-IIIrd quartile = 0. In the case of virtual mutations the deviation from the normal reference situation generated scores in the range 33-115, well above the fluctuation range. The addition of a target-specific virtual inhibitor to its respective virtual mutation reduced the deviation scores by 64% (KRAS), 67% (BRAF), 97% (EGFR mutation) and 90% (EGFR strong stimulation). A double alteration (EGFR & KRAS) could be best inhibited by the association of the two corresponding inhibitors. In conclusion, the effects of virtual mutations and virtual inhibitors seem definitely more important than noise random fluctuations in concentrations and rates.