Data-Driven Modeling of Src Control on the Mitochondrial Pathway of Apoptosis: Implication for Anticancer Therapy Optimization

Src tyrosine kinases are deregulated in numerous cancers and may favor tumorigenesis and tumor progression. We previously described that Src activation in NIH-3T3 mouse fibroblasts promoted cell resistance to apoptosis. Indeed, Src was found to accelerate the degradation of the pro-apoptotic BH3-only protein Bik and compromised Bax activation as well as subsequent mitochondrial outer membrane permeabilization. The present study undertook a systems biomedicine approach to design optimal anticancer therapeutic strategies using Src-transformed and parental fibroblasts as a biological model. First, a mathematical model of Bik kinetics was designed and fitted to biological data. It guided further experimental investigation that showed that Bik total amount remained constant during staurosporine exposure, and suggested that Bik protein might undergo activation to induce apoptosis. Then, a mathematical model of the mitochondrial pathway of apoptosis was designed and fitted to experimental results. It showed that Src inhibitors could circumvent resistance to apoptosis in Src-transformed cells but gave no specific advantage to parental cells. In addition, it predicted that inhibitors of Bcl-2 antiapoptotic proteins such as ABT-737 should not be used in this biological system in which apoptosis resistance relied on the deficiency of an apoptosis accelerator but not on the overexpression of an apoptosis inhibitor, which was experimentally verified. Finally, we designed theoretically optimal therapeutic strategies using the data-calibrated model. All of them relied on the observed Bax overexpression in Src-transformed cells compared to parental fibroblasts. Indeed, they all involved Bax downregulation such that Bax levels would still be high enough to induce apoptosis in Src-transformed cells but not in parental ones. Efficacy of this counterintuitive therapeutic strategy was further experimentally validated. Thus, the use of Bax inhibitors might be an unexpected way to specifically target cancer cells with deregulated Src tyrosine kinase activity.

In these experiments, Bik synthesis was completely inhibited by the mean of two drugs: cells were incubated both with actinomycin D which is an inhibitor of mRNA synthesis and cycloheximide which inhibits proteic synthesis. Therefore we assumed that protein formation was completely inhibited for the whole duration of the experiments, i.e. k f BIK = 0. Bik equation then becomes: where Bik concentration is expressed in nM. At the initial time, Bik was set to Bik initial in parental and Src-transformed cells. We computed the best-fit parameter values for both cell types by a least square approach using the CMAES algorithm for the minimization of the cost function. This gave: 2 Therapeutics optimization We determined theoretically optimal therapeutic strategies by applying optimization procedures on the data-fitted model of the mitochondrial pathway of apoptosis. We investigated drug combinations which consisted in an exposure to staurosporine after pre-incubation with Src inhibitors, or with up-or down-regulators of Bcl2 family protein amounts.
The optimization procedure consisted in searching the optimal values of four parameters corresponding to the pharmacological activity on Bax, Bcl2, Bid and Src. For Bax, Bcl2 and Bid, factors were added to their respective total amount. For Src, the parameter V Src which is the maximal velocity of Src-dependent Bik ubiquitylation was multiplied by the indicated factor. Bax factor was searched in [-Bax tot , 500], Bcl2 factor in [-Bcl2 tot , 500], Bid factor in [-Bid tot cancer , 500] and Src factor in [0.0001 500].
The theoretically-optimal drug combination consisted in administering staurosporine combined to inhibitors of Src, Bax and Bcl2, together with a Bid upregulator. Bax factor was equal to -Bax tot which led to Bax concentration in parental cells equal to zero thus protecting them from apoptosis. As Bax total amount was higher in cancer cells, it remained high enough to allow these cells to undergo apoptosis. Once healthy cells were sheltered from apoptosis, Bcl2 amount could be decreased of -Bcl2 tot and Bid amount increased of 500 nM (i.e. the maximal allowed value) without risking any severe toxicity. As expected, the optimal therapeutic strategy also included the suppression of the Src-dependent phosphorylation of Bik as Src factor was equal to 0.0001. This drug combination led to 99% of apoptotic cells in the cancer cell population and less than 1% in the parental one where Bax was hardly present (Table S1).
This theoretically optimal strategy involved the administration of a cytotoxic agent combined with four other chemicals, which may not be realistic in the perspective of clinical application. Therefore we hierarchically ranked the considered therapeutic agents by searching for optimal strategies consisting in the combination of staurosporine with only one or two agents. We computed efficacy on Src-transformed cells and toxicity on parental cells for each possible combination in which drugs were given at the same dose as in the previously-determined optimal combination (Table S1).
Strategies which satisfied the tolerability constraint (i.e. less than 1% of apoptotic parental cells) and reached an efficacy value of 99 % of apoptotic cells all involved Bax downregulation in addition to a second agent among Bcl2 downregulator, Bid upregulator and Src inhibitor (Table S1). Isolated decrease of Bax total quantity fulfilled the tolerability constraint but resulted in less than 1% of apoptotic cancer cells. We investigated drug combinations which consisted in an exposure to staurosporine after pre-incubation with Src inhibitors, or with up-or down-regulators of Bcl2 family protein amounts. For Bax, Bcl2 and Bid, factors where added to their respective total amount. For Src, the parameter V Src which is the maximal velocity of Src-dependent Bik ubiquitylation was multiplied by the indicated factor.

Steady State study
The mathematical model of mitochondrial apoptosis admits three kinds of steady states (Table S2). Steady state 1 corresponds to a complete inhibition of BIK mito and BH3 a by BCL2. Moreover, a part of BAX proteins has not been activated. In steady state 2 and 3, BCL2 is completely consumed into complexes with BIK mito , BH3 a and BAX link . BAX inact has been entirely activated into BAX oligo . In steady state 2, some BH3 a BCL2 complexes still remain in the cytosol whereas BIK mito proteins have been entirely consumed. In steady state 3, this is the opposite situation. Steady states 2 and 3 do not seem realistic since all BAX molecules are activated whereas only 10 to 20% of BAX total amount are effectively activated during apoptosis [9,46].