Mathematical analysis of gefitinib resistance of lung adenocarcinoma caused by MET amplification.

Gefitinib, one of the tyrosine kinase inhibitors of epidermal growth factor receptor (EGFR), is effective for treating lung adenocarcinoma harboring EGFR mutation; but later, most cases acquire a resistance to gefitinib. One of the mechanisms conferring gefitinib resistance to lung adenocarcinoma is the amplification of the MET gene, which is observed in 5-22% of gefitinib-resistant tumors. A previous study suggested that MET amplification could cause gefitinib resistance by driving ErbB3-dependent activation of the PI3K pathway. In this study, we built a mathematical model of gefitinib resistance caused by MET amplification using lung adenocarcinoma HCC827-GR (gefitinib resistant) cells. The molecular reactions involved in gefitinib resistance consisted of dimerization and phosphorylation of three molecules, EGFR, ErbB3, and MET were described by a series of ordinary differential equations. To perform a computer simulation, we quantified each molecule on the cell surface using flow cytometry and estimated unknown parameters by dimensional analysis. Our simulation showed that the number of active ErbB3 molecules is around a hundred-fold smaller than that of active MET molecules. Limited contribution of ErbB3 in gefitinib resistance by MET amplification is also demonstrated using HCC827-GR cells in culture experiments. Our mathematical model provides a quantitative understanding of the molecular reactions underlying drug resistance.

Control and inhibition analysis of complex formation processes.

BACKGROUND: Proteolytic degradation of the extracellular matrix (ECM) is a key event in tumour metastasis and invasion. Matrix metalloproteinases (MMPs) are a family of endopeptidases that degrade most of the components of the ECM. Several broad-spectrum MMP inhibitors (MMPIs) have been developed, but have had little success due to side effects. Thus, it is important to develop mathematical methods to provide new drug treatment strategies. Matrix metalloproteinase 2 (MMP2) activation occurs via a mechanism involving complex formation that consists of membrane type 1 MMP (MT1-MMP), tissue inhibitor of matrix metalloproteinase 2 (TIMP2) and MMP2. Here, we focus on developing a method for analysing the complex formation process. RESULTS: We used control analysis to investigate inhibitor responses in complex formation processes. The essence of the analysis is to define the response coefficient which measures the inhibitory efficiency, a small fractional change of concentration of a targeting molecule in response to a small fractional change of concentration of an inhibitor. First, by using the response coefficient, we investigated models for general classes of complex formation processes: chain reaction systems composed of ordered steps, and chain reaction systems and site-binding reaction systems composed of unordered multi-branched steps. By analysing the ordered step models, we showed that parameter-independent inequalities between the response coefficients held. For the unordered multi-branched step models, we showed that independence of the response coefficients with respect to equilibrium constants held. As an application of our analysis, we discuss a mathematical model for the MMP2 activation process. By putting the experimentally derived parameter values into the model, we were able to conclude that the TIMP2 and MMP2 interaction is the most efficient interaction to consider in selecting inhibitors. CONCLUSIONS: Our result identifies a new drug target in the process of the MMP2 activation. Thus, our analysis will provide new insight into the design of more efficient drug strategies for cancer treatment.

Finding Solvable Units of Variables in Nonlinear ODEs of ECM Degradation Pathway Network.

We consider ordinary differential equation (ODE) model for a pathway network that arises in extracellular matrix (ECM) degradation. For solving the ODEs, we propose applying the mass conservation law (MCL), together with a stoichiometry called doubling rule, to them. Then it leads to extracting new units of variables in the ODEs that can be solved explicitly, at least in principle. The simulation results for the ODE solutions show that the numerical solutions are indeed in good accord with theoretical solutions and satisfy the MALs.