The Cytotoxic Effect of Rtks Inhibitors on Glioblastoma Cells A Mathematical Model for Treatment Protocols Optimization

CORINA BRANDUSA, BOGDAN-IONEL VATU, STEFANA OANA PURCARU, STEFAN-ALEXANDRU ARTENE, SANDRA ALICE BUTEICA, DANIELA ELISE TACHE, CRISTIAN ADRIAN SILOSI, CITTO IULIAN TAISESCU, OANA ALEXANDRU, OLIVIAN PUIU STOVICEK, ALIN DEMETRIAN, ANICA DRICU* University of Medicine and Pharmacy of Craiova, Department of Functional Science, 2-4 Petru Rares Str., 200349, Craiova, Romania University of Medicine and Pharmacy of Craiova, Department of Drug Control, 2-4 Petru Rares Str., 200349, Craiova, Romania 3University of Medicine and Pharmacy of Craiova, Department of Surgery, 2 Petru Rares Str., 200349, Craiova, Romania 4University of Medicine and Pharmacy of Craiova, Department of Neurology, 2 Petru Rares Str., 200349, Craiova, Romania Titu Maiorescu University Department of Pharmacology, 189 Gheorghe Sincai Blvd., 040317, Bucharest, Romania University of Medicine and Pharmacy,Department of Thoracic Surgery, 2 Petru Rares Str., 200349, Craiova, Romania

GBM is the most aggressive type of brain tumour and although advances have been made in recent years, the prognosis for patients suffering from this cancer remains abysmal [1]. This is due, in part, to a very poor knowledge of the dynamics of growth and proliferation which confer the distinctively aggressive nature of this particular tumor. GBM is more common in adults, with a median overall survival of approximately 14.6 months and a progression-free survival of 6.9 months. Additionally, the 5-year survival rate is under 10%, making GBMs one of the most aggressive and hard to treat tumors in oncological practice [2,3]. Even with the constant improvement of the surgical techniques employed in current practice, recurrences happen in almost 99% of the cases mainly because of the malignant cells capacity to detach and invade adjacent structures. The incidence of GBM is 3 to 5 cases per 100 000 people in Europe and United States of America [4,5]. Additionally, it was observed that the incidence of GBM increases with age (75-84 years old) and it is more common in white males [6].
The standard of care treatment has a relative poor prognostic due to the GBM's high recurrence. Although many new treatment options have emerged, the best approach for the initial treatment is based on maximal surgical resection followed by concomitant temozolomide (TMZ) and radiotherapy with adjuvant TMZ chemotherapy shortly afterwards [1]. New molecular-based approaches have been under investigation for primary and recurrent GBMs with bevacizumab (Avastin®) a VEGF (vascular endothelial growth factor) inhibitor, erlotinib (Tarceva®) or gefitinib (Iressa®) both EGFR (epidermal growth factor receptor) inhibitors providing promising results in preclinical settings [7]. However, all of these agents presented mediocre results in clinical trials, remaining viable options only as salvage therapy after recurrence or progression, which usually happens in 99% of recorded cases [5,[8][9][10].
Many studies have presented the importance of mathematical models that help in the prognosis and behavior of untreated and treated GBMs.
Researchers from several groups have studied the in vivo mathematical models for the growth and proliferation rate of gliomas. A mathematical model was developed for glioma growth and invasion of the brain tissue, using the equation for the "rate of change for the cell population density" [11]. In addition, mathematical models are important https://doi.org/10.37358/RC. 20.2.7903 for understanding the biological mechanisms responsible for the differences in proliferative kinetic of patients with same type of cancer [11,12]. Swanson et al developed a mathematical model that can help to estimate the efficacy of tumour treatments, in patients diagnosed with GBM [13,14].
The description in an abstract form of a behavioral system of the tumour cells through mathematical models is the base of numerical simulation, with important implications for the knowledge of cells complex developments. In this study, we aim to build a mathematical model, focused on the interactions between the tumour cells' proliferation rate, aggression and saturation rates.
We used one cell line derived from a primary tumour (GBM). Based on the evolution of this cell line we made a model analysis of the biological system variables.

Reagents
Cell culture media, Tyrphostine AG1433, SU1498 and Imatinib® were purchased from Sigma-Aldrich (St. Louis, MO, USA). The drugs were diluted in dimethyl sulfoxide (DMSO) to a stock concentration of 10 mM and stored at -20 °C. The DMSO concentration was below 0.1% when the inhibitors were added in the cultured medium. Fetal Bovine Serum (FBS), Penicillin/Streptomycin antibiotics, Trypsin, Phosphate-buffered saline (PBS) were obtained from Gibco by Life Technologies TM .

Cell culture and treatment
Low passage cell culture used in this study was established from tissue obtained from a patient diagnosed with GBM at the "Bagdasar-Arseni" Emergency Hospital, Bucharest, Romania. The cell line was established according to standard procedures [15]. For experimental purposes, cells were seeded in 6 wells plates in DMEM and treated with different concentrations of small molecule inhibitors tyrosine kinases, SU1498, AG1433 and STI-571 (1 μM, 2 μM, 5 μM, 10 μM, 20 μM, 40 μM, 80 μM), for 3 days. Appropriate control groups with culture medium and 0.01% DMSO were included. Each of the three experiments was performed in triplicate.

IC50 calculation
In order to determine the inhibitory concentration for the used drugs that kills 50% of GB10B cells (IC50 values) the applied formula was: IC50 = [(50-M)/(N-M)] x (P-Q) + Q, with M being the first percent inhibition that is less than 50%, N representing the first percent inhibition that is higher or equal to 50%, Q and P being the concentrations of inhibitors that corresponds to X% and respectively Y% inhibition.

Cell proliferation and survival
For assay proliferation, cells were seeded into 6-well plates at a concentration of 2×10 5 cells/well. Cells were incubated in standard MEM medium overnight and then treated with various concentrations of SU1498, AG1433 and STI-571 and incubated for 3 days.
After the incubation time, the cells were trypsinized and a uniform cell suspension was counted in a Bürker hemocytometer, using trypan blue. Each experiment was performed in triplicate and repeated three times.

Mathematical models
The mathematical models are based on the first order transfer function, FT1: where: K1 corresponds to the value of D/IC50 = 0; K1= 100%, K2 represents the system-imposed minimal value for cellular proliferation (K2=10%). The 1/E constant results from mathematical simulation after validation of the simulation model, based on the correlation between the data series.
Cellular viability was determined using the fn function (unaffected cellular fraction) calculated as a percentage of cells alive in comparison to the control group, which represent 100% by default. The mathematical simulation was designed using the Matlab tool with the Simulink extension. The statistical analysis was expressed as mean ± standard deviation (±SD) and statistical comparison was expressed using Student t-test. Statistically significant was considered for a p-value ˂0.05. All experiments were performed in triplicate.
Pearson's R correlation coefficient was used to estimate the correlation in linear regression. A Pearson R value between 0.5 and 1 was considered to be a positive correlation between the experimental values and the simulation.

Results and discussion
Very little is known about the intrinsic mechanisms which make up for the highly invasive nature of GBMs. One of the greatest setbacks in developing a viable approach for treating GBMs is the lack of therapeutic agents which can be used in a clinical setting. This is due to a couple of factors. The first and the most important is the presence of the blood brain barrier (BBB) which blocks the passage for over 90% of the agents used in the current clinical setting [16,17]. Secondly, GBMs have a propensity to quickly develop resistance to the therapeutic agents which penetrate the BBB, through multiple molecular pathways [18][19][20].
In our experiment we established a mathematical model based on the IC50 observed in an experimental setting for each therapeutic agent used on the GB10B GBM cell line. We compared the simulated results obtained using the mathematical model with the observed experimental value. A Pearson R value between 0.5 and 1 was considered to be a positive correlation between the experimental values and the simulation ( fig. 1). Several clinical trials have, so far, presented no significant clinical results for patients with recurrent malignant gliomas being treated with Imatinib [21,22]. This poor response can be attributed, in part, to the very low perfusion rate of Imatinib through the BBB, with Imatinib levels being 92-times lower in the cerebrospinal fluid in comparison to the blood of patients receiving the drug [23].

Conclusions
We have conducted a study that demonstrates that treatment with Imatinib, SU 1498 and AG 1433 inhibitors induces cell death in the GB10B GBM cell line, in vitro. A mathematical model was proposed using Matlab for describing the dose-response activity of the Imatinib, SU 1498 and AG1433 inhibitors, based on the results observed in the experimental setting. After comparing the experimental and predicted results using the mathematical model, the Pearson R coefficient was positive, with values between 0.5 and 1 for all the three inhibitors used in our experiment. This indicated a very strong correlation between the two sets of values, thus validating the value of the mathematical model in predicting the dose-dependent behavior of inhibitors used in preclinical settings.