pH as a potential therapeutic target to improve temozolomide antitumor efficacy : A mechanistic modeling study

Abstract Despite intensive treatments including temozolomide (TMZ) administration, glioblastoma patient prognosis remains dismal and innovative therapeutic strategies are urgently needed. A systems pharmacology approach was undertaken to investigate TMZ pharmacokinetics‐pharmacodynamics (PK‐PD) incorporating the effect of local pH, tumor spatial configuration and micro‐environment. A hybrid mathematical framework was designed coupling ordinary differential equations describing the intracellular reactions, with a spatial cellular automaton to individualize the cells. A differential drug impact on tumor and healthy cells at constant extracellular pH was computationally demonstrated as TMZ‐induced DNA damage was larger in tumor cells as compared to normal cells due to less acidic intracellular pH in cancer cells. Optimality of TMZ efficacy defined as maximum difference between damage in tumor and healthy cells was reached for extracellular pH between 6.8 and 7.5. Next, TMZ PK‐PD in a solid tumor was demonstrated to highly depend on its spatial configuration as spread cancer cells or fragmented tumors presented higher TMZ‐induced damage as compared to compact tumor spheroid. Simulations highlighted that smaller tumors were less acidic than bigger ones allowing for faster TMZ activation and their closer distance to blood capillaries allowed for better drug penetration. For model parameters corresponding to U87 glioma cells, inter‐cell variability in TMZ uptake play no role regarding the mean drug‐induced damage in the whole cell population whereas this quantity was increased by inter‐cell variability in TMZ efflux which was thus a disadvantage in terms of drug resistance. Overall, this study revealed pH as a new potential target to significantly improve TMZ antitumor efficacy.

involving surgery, radiation, and chemotherapy mainly based on the alkylating agent temozolomide (TMZ). 1 No major therapeutic advance has been accomplished since this current standard of care was established more than 10 years ago. Moreover, this treatment is associated with moderate to severe toxicity events, which can be life threatening in some cases. 2 Hence, innovative therapeutic strategies are urgently needed and there is scope for great progress in terms of patients survival and quality of life. TMZ is the cornerstone of GBM management but has also been approved for the treatment of other solid tumors including pituitary tumors. 3 TMZ is a prodrug that spontaneously converts into its metabolite 5-(3-methyltriazen-1-yl)imidazole-4-carboxamide (MTIC), which is subsequently degraded into 4-amino-5-imidazole-carboxamide (AIC)-an inactive metabolite and a methyldiazonium cation, the DNA-methylating species. The methyldiazonium cation creates DNA adducts-a marker of TMZ pharmacodynamics (PD)-that trigger DNA damage responses and potentially induce cell death. 4,5 Both TMZ and MTIC degradation rates are highly pH-dependent as they exponentially increase and decrease with pH values, respectively. 6 Healthy and tumor cells present different regulations of extraand intracellular pH values which may influence TMZ PK although this has not been studied mechanistically up to our knowledge.
Cancer cells can acidify their micro-environment which may favor the development of resistant clones, promote tumor invasion and suppress the antitumor immune response. [7][8][9] Furthermore, cancer cells may present an abnormal regulation of their intracellular pH which allow them to evade from acid-mediated toxicities whereas healthy cells would not survive in acidic environment. 10,11 Several anticancer strategies currently under development rely on targeting the tumor pH such as the administration of proton pump inhibitors to invert extracellular/intracellular pH gradient or the design of pHcontrolled nanoparticles releasing the active compound at acid pH. 10 Mathematical modeling of tumor acidity is not new 12 and the integration of the intracellular pH regulation of tumor cell has also been considered a while ago 13 by incorporating the effects of the different membrane transporters. The complex tumor cell metabolism and its evolution from aerobic to glycolysis were also considered in tumor models [14][15][16] to establish the extracellular pH dynamics accompanying the tumor evolution. More recently cellular automaton approaches were developed so as to integrate the pH as an environmental constraint. 17 Such more general and often multiscale hybrid models have now proved very useful to further evaluate consequences of treatments. 18 We here intend to investigate TMZ pH-dependent pharmacokinetics (PK) and simplified pharamcodynamics (PD) in solid tumors through such hybrid mathematical modeling and validate the potential of pH as a therapeutic target to increase TMZ exposure benefit both in terms of efficacy and tolerability. We build on a previously published non-spatial model of TMZ PK-PD which has been incorporated into a spatial hybrid framework to analyze TMZ efficacy in a space-and pH-dependent manner. 4,19 2 | MATERIALS AND METHODS

| Non-spatial model of TMZ cellular PK-PD
TMZ cellular PK-PD was firstly represented by an Ordinary Differential Equations (ODE)-based model. 4 This model considers both an extra-and an intracellular compartment ( Figure 1). In both compartments, TMZ pH-dependent activation into MTIC and MTIC subsequent degradation into AIC are represented by the law of mass action. MTIC dissociation produces a methyldiazonium cation that can create DNA adducts, which is also represented by the law of mass action. Because TMZ is highly lipophilic and constitutes a poor substrate of ATP-Binding Cassette (ABC) transporters, its cellular transport is modeled as passive diffusion using Ficks first law. As MTIC displays limited ability to cross cell membranes and as the methyldiazonium cation is a highly reactive species, their transport between the extra-and intracellular compartments were not considered.
Regarding TMZ PD, the methyldiazonium cation is the sole species able to form DNA adducts that are considered as an early marker of TMZ efficacy.
The system of ODEs for TMZ extracellular concentration (T o ) and for the intracellular dynamics of TMZ (T i ), MTIC (M i ), Cation (C i ) and DNA adducts (Add) concentrations ( Figure 2) are defined by: where (k 0 T , λ T ) and (k 0 M , λ M ) are non-physiological parameters to estimate. All model parameters were estimated from in vitro studies in buffer solutions or in U87 glioma cells and the best-fit model achieved a very good fit to data 4 ; Table 1).

| Spatial hybrid model of TMZ PK-PD
In order to account for tumor heterogeneities depending on spatial cell location in its environment or inter-cell variability, the ODEbased model was coupled to a spatial cellular automaton (CA). The if there is one tumor cell at location (i; j) and 0 otherwise. The tumor cell population in the CA is thus defined as follows: where D ¼ 1:7 Â 10 À5 cm 2 /s is the TMZ diffusion coefficient 20 and  This results in the appearance of large spatial heterogeneities.

| Extracellular pH
One characteristics of the tumor cells is their high level of glucose consumption. 21 Positron emission tomography (PET scan) is now standardly used to highlight the tumor sites thanks to this specific signature. 22 25 however since we will only consider short-term events (of a few hours) in this study, we assume that the oxygen level can be taken as a good indicator of local acidity. Therefore, we constructed a function that directly gives the extracellular pH given the stationary oxygen concentration since this quantity can easily be computed through the cellular automaton 26,27 (Appendix C).
Given the local oxygen concentration (Oxy) and a threshold value for oxygen (Oxy thr ) below which the pH is assumed to saturate to its minimum pH min (due to the limited production rate of H+ by the cells), the pH is computed as follows: if Oxy>Oxy thr then pH ¼ pH max À Δ pH ΔOxy Oxy max À Oxy ð Þ (10) else pH ¼ pH min (11) where pH max is the pH in normal healthy tissues (ie, normally oxygenated tissue, corresponding to Oxy max ) and is typically 7.4 and pH min is the lower pH level found in tumors which can be as low as 6.5. 28, 29 We set these two values to pH max and pH min respectively. ΔOxy ¼ Oxy max À Oxy thr and Δ pH ¼ pH max À pH min (Appendix Figure A2).

| Intracellular pH
One hallmark of the tumor cells is their ability to survive in an acidic environmentthat they contribute to generateby maintaining their intracellular pH at physiological levels. On the other hand, this acidic environment is detrimental to normal cells that have not acquire this ability. 28 Intracellular pH regulation is a complex process that is not completely elucidated yet. 30,31 However, simultaneous measurements of extra and intracellular pH were made in several T A B L E 1 Model parameters of TMZ PK, all taken from the original -experimentally validated-model by (4), except parameters with symbol (*) that were rescaled as described in Appendix A

Parameters Unit Value Description
Methylating cation degradation k add h À1 0.005 DNA adducts formation rate tumor cell types that all exhibit the reversed pH property where the intracellular pH is higher than the extracellular one. 30,[32][33][34] For this study, we needed to evaluate the intracellular pH given the extracellular one. give the pH e -pH i relationship for tumor cells (Figure 3, f x ð Þ): For normal cells, the physiological status point was well characterized in different cell types with pH e =7.4 and pH i =7. [35][36][37][38] The intracellular pH is found to evolve passively with the extracellular pH, being around half a unit lower 39 which gives a; b ð Þ¼ 1; 0:4 ð Þfor normal cells ( Figure 3, g x ð Þ).

| Data and Statistical analysis
The simulations for the in vitro settings were realized with Matlab  Figure 4D). For all considered exposure durations, maximum antitumor efficacy was computationally obtained for pH values between 6.65 and 7.9, optimal pH decreasing with exposure time.
Optimal pH values inducing the largest difference between DNA damage in tumor and healthy cells were comprised between 6.8 and 7.5 and decreased with exposure duration ( Figure 4E).

| TMZ pH-and space-dependent PK-PD in an in vivo solid tumor
The next step was to computationally investigate TMZ PK-PD in a solid tumor within its environment. Tumor tissues may present (a) modified micro-environment and in particular abnormal vascular network, (b) different spatial configurations. In this section, we intend to specifically study these two elements and their influence on local pH and TMZ PK-PD. Our hybrid approach that involves a cellular automaton is particularly well adapted to that task since the model simultaneously accounts for spatialization and cell individualization.

| TMZ PK-PD dependency on tumor microenvironment
We here considered two major sources of environmental heterogeneities that can impact on TMZ PK-PD: the pH that affects the successive stages of TMZ transformation into its active compound, and the tumor vascularization that affects TMZ delivery in the tissues. The resources (oxygen, nutrients) and the drugs are delivered through the capillary network. In a normal healthy tissue, this network is homogeneously covering the volume of the tissue. On the opposite, in tumors, the capillary network is degraded: (i) vessels are crushed by the proliferating tumor cells, (ii) the increased acidity triggers apoptosis of the normal endothelial cells, (iii) growth factors destabilize the capillaries by stimulating vessels sprouting for angiogenesis. 27 As a consequence, two scenari were simulated with the model: (a) the capillary network was considered to be intact and TMZ was initially homogeneously distributed to the tumor cells, (b) the capillary network was degraded, TMZ was delivered from the intact capillary network outside of the tumor mass which then diffused to reach the tumor cells ( Figure 5B, t = 0 h). In reality, the capillary network may be mostly degraded inside the tumor, although not completely destroyed. We compared these two extreme cases to better highlight the consequences on TMZ PK-PD.
Simulations were performed for a circular tumor mass of radius TMZ PK-PD results were presented for three cells located at three different points in the tumor from the center to the periphery: tumor cells often disseminate in the healthy brain tissue. 41 Therefore, we here considered three different tumor configurations to better assess the importance of spatiality: a spheroid (case 1, as before), cell clusters (case 2), spread cells (case 3) ( Figure 6A). In the three cases, the total amount of cells was conserved. Furthermore, we considered a degraded capillary network so that TMZ was initially only in the tumor peripheral tissues. As before, pH distribution was first computed for each tumor configuration from the oxygen local concentration ( Figure 6A). Simulations were madeusing the same set of parameters for all three cases-to evaluate the in vivo availability of TMZ and its impact based on DNA adduct generation ( Figure 6B). For all three cases, tumor cells were not all homoge-

| Influence on TMZ PK-PD of inter-cell variability in drug cellular transport
One important hallmark of cancer cells is their large inter-cell heterogeneity regarding intracellular gene and protein levels. We used our models of TMZ PK-PD to assess the impact of inter-cell variability

| Inter-cell variability in an in vitro setting in acidic conditions
For this simulations, we assumed an in vitro setting in which cells have uniformly access to TMZ and in which pH is constant and equal to an acidic value. In acidic conditions, TMZ is not metabolized and the sole reactions occurring were the drug cellular uptake and efflux. Since TMZ is stabilized, we assumed that TMZ total quantity was conserved and equal to T tot so that The steady state of TMZ intracellular concentration T Ã i can then easily be derived from equations (1 and 2), and is equal to: The two considered sources of heterogeneity in the medium. (A) pH spatial variations (the dotted line represents the tumor boundary); (B) temporal evolution of TMZ concentration for a homogeneous capillary network and for a degraded one. In the homogeneous case, TMZ is initially (t = 0 h) homogeneously distributed whereas when the capillary network is degraded inside the tumor mass, the tumor does not have access to TMZ initially. Comparison of TMZ PK depending on the cell location in the tumor spheroid, for the homogeneous capillary network (left column) and for the degraded one (right column). The PK is represented for three cells located at three different distance x from the center of the 2D tumor: where p T and p T2 are the rate constants of TMZ cellular uptake and efflux, respectively. Interestingly, TMZ intracellular steady state level varied with respect to p T and p T2 in a non-linear manner ( Figure 7A).
We then studied a heterogeneous cell population in which each cell TMZ intracellular steady state level was predicted to be similar in the homogeneous cell population and in the cell population presenting variability in TMZ uptake when p T2 was set to its value estimated from U87 data p y T2 and p T was varied around its data-derived value ( Figure 7B). However, simulations for different values of the fixed parameter p y T2 and of mean p T yielded different results ( Figure 7D). For small p T mean values, TMZ accumulated more in the heterogeneous cell population compared to the homogeneous one whereas for p T mean values larger than some threshold value, the situation was reversed. p T threshold value increased with p y T2 and was comprised between 0.0025 and 0.0035 h À1 . The same study was performed for the parameter p T2 which was varied uniformly in 0:2p y T2 ; 1:8p y T2 h i , p y T2 denoting the value estimated from data.  Figure 7E). For small p T2 mean values, TMZ accumulation was larger in the homogeneous cell population as compared to the population with inter-cell variability in TMZ efflux. When p T2 was larger than a threshold value in [0.0056, 0.0073], increasing with p y T value, the situation was reversed.

| Inter-cell variability in a solid tumor
We then used the hybrid model to investigate the impact of intercell variability on TMZ PK-PD in a solid tumor. As for the in vitro study, we varied p T and p T2 parameters which correspond to TMZ uptake and efflux rate constants, respectively. One advantage of using a cellular automaton was the possibility to test variability in individual cell properties. Thus, we randomly assigned to each cell a perturbed value of p T and p T2 separately (ie, in two different simulations). Different perturbation amplitudes were considered and the effects only started to be visible for AE80% amplitude ( Figure 7F,G, H). Interestingly, the impact of these two parameters was very close to the results in the in vitro setting. Perturbation of the efflux parameter p T2 produced a bigger impact on the resulting mean DNA adducts level in the whole cell population. On the other hand, the impact of varying p T was small compared to the unperturbed case with only a slight decrease in the mean DNA adducts concentration.

| DISCUSSION
Although pH is known to critically influence TMZ PK-PD, 4 its potential impact on the drug efficacy has not yet been fully investigated.
Thus, we designed a complete theoretical framework to study TMZ PK-PD in both in vitro and in vivo settings, incorporating pH dependency, spatial heterogeneities, and inter-cell variability in TMZ transport. Overall, all simulations in all scenari predicted that optimal TMZ efficacy was obtained when tumor pH was close to physiological pH. This is clearly an argument for considering pH as a therapeutic target and advocates for future research on the combination of TMZ with pH-regulating agents.
We first evaluated the differential response to TMZ of tumor and healthy cells presenting different intracellular pH regulations. Interestingly, the model provided quantitative predictions regarding the drug differential impact on normal or cancer cells and optimal pH values leading to an advantage for healthy cells. Tumor cells were able to maintain relatively high intracellular pH in acidic environment, whereas normal cells were assumed to regulate their pH proportionally to the extracellular one. As a consequence, at the same extracellular pH, both cell types presented different sensitivity to TMZ. Indeed, our simulation results showed that, for extracellular pH between 5.8 and 8.2, TMZ transformation into its active compound and subsequent DNA damage were larger in tumor cells as compared to normal cells thanks to less acidic intracellular pH in cancer cells. This indicated that the local acidity often encountered in tumor tissues was still a favorable ground for TMZ effectiveness.
However, optimality of TMZ efficacy defined as a maximum difference between drug-induced damage in tumor and healthy cells was reached between 6.8 and 7.5 which is closer to physiological values.
Next, we computationally investigated TMZ PK-PD in a solid tumor taking into account its environment. In vivo cells are not homogeneously exposed to the same pH, nor to the same drug concentration. These essentially depend on the location of the cells in the tumor tissue (central parts versus periphery). Non-spatial PK-PD approaches only describe temporal aspects assuming that the whole cell population is homogeneously exposed to the same environmental conditions and reacts in the same way to the drug. To overcome these limitations, we proposed a hybrid framework incorporating a cellular automaton that allowed to explicitly compute TMZ PK-PD for each individual tumor cell given its particular local environment.
Our simulations showed that spread cancer cells or fragmented tumors presented higher TMZ-induced damage as compared to compact tumor spheroid. The model provided insights into molecular explanations for this result. First, pH values close to normal in smaller tumors micro-environment allowed for TMZ activation whereas bigger tumors were more acidic and prevented the drug from transformation into its active metabolites. This potential mechanism of resistance to TMZ has not been described in the literature up to our knowledge. The model also confirmed as expected that isolated cancer cells or fragmented tumors could be reached by the drug whereas, at the heart of a tumor spheroid, the most inner cells had no access to the drug due to damaged vascular network and insufficient drug diffusion in the interstitial fluid.
Our in vivo simulations were performed for a generic solid tumor as TMZ is approved for the treatments of several types of malignancies, although the drug is mainly used against brain tumors. To specifically represent a brain tumor and surrounding healthy brain tissues, one needs to incorporate the blood-brain barrier (BBB) along the capillaries. While the BBB is intact in the normal tissues and decreases TMZ penetration rate in the interstitial fluid, the barrier is often altered at the neighborhood of the tumor mass where the combination of acidity, growth factors stimulating angiogenesis and increased cell density destabilize blood vessels and increase their permeability. Adding the BBB component to our hybrid model may modify TMZ efficacy on spread cells if they are located in normal tissues where the BBB is too weakly altered to allow for TMZ brain penetration.
In the last paragraph, we considered the importance of inter-cell variability in TMZ cellular transport. We provided a counter-intuitive prediction regarding a differential effect of inter-cell variations on TMZ uptake or efflux, respectively. Indeed, for model parameters F I G U R E 7 Effect of TMZ transport parameters variability in cells. (A) TMZ intracellular concentration at steady state with respect to TMZ uptake parameter (p T ) or efflux parameter (p T2 ); (B) TMZ cumulative steady state intracellular concentration in a homogeneous cell population (no noise) or a heterogeneous population presenting inter-cell variability in TMZ uptake (p T ± 80%); (C) TMZ cumulative steady state intracellular concentration in a homogeneous cell population (no noise) or a heterogeneous population presenting inter-cell variability in TMZ efflux (p T2 ± 80%); (D) TMZ cumulative steady state intracellular concentration with respect to p T and p T2 in a homogeneous cell population (dark curve) or a heterogeneous population presenting inter-cell variability in TMZ uptake (light curve); (E) TMZ cumulative steady-state intracellular concentration with respect to p T and p T2 in a homogeneous cell population (dark curve) or a heterogeneous population presenting inter-cell variability in TMZ efflux (light curve);(F) DNA adducts accumulation in the perturbed and non-perturbed cases; (G) mean amount of DNA adducts accumulation per cells for perturbed inflow (p T ) and outflow (p T2 ) parameters; (H) close up of (G) with standard deviation (SD) bars removed. Note: the mean amount of DNA adducts is calculated over the all tumor cell population for each case STÉPHANOU AND BALLESTA | 11 of 15 pharmacology and thus inform on drug optimal scheduling and combinations. This is further advocated by the fast developing fields of systems oncology and systems pharmacology. 41,42 Specifically, our model has allowed to show that pH and drug access are determining factors and depend on the cell type and tumor configuration which gives fundamental insights to decipher the impacts of interrelated conditions. On the prospective plan, the model highlights potential means to enhance the TMZ efficacy by acting dynamically on the local pH. 10 The realization of which opens up new challenging paths for research with potential high benefit for patients.

AUTHOR CONTRIBU TI ONS
A.S. and A.B performed the simulations that concern the in vivo and in vitro cases, respectively. Both authors equally contributed in the writing of the manuscript.

Volumes
In the original ODE model, 4 the extracellular medium is covering in vitro an overall population of 10 6 tumor cells. The volume of the medium, that is, the extracellular volume, is taken as V o ¼ 2mL. The volume of each single cell is approximately 7pL so the total intracellular volume is V i ¼ 7μL.
In the cellular automaton, the simulation domain is taken as a 5 mm long square box. The extracellular medium is assumed to cover the cells in the automaton grid up to 1mm high. The extracellular medium thus represents a volume V o ¼ 25μL.

Transport parameters
The transport parameters of TMZ through the tumor cell membrane are available for the in vitro experiments where V pop i was representing the intracellular volume for the entire cell population (see above).
In the cellular automaton, each cell is considered individually so the intracellular volume V i now concerns a single cell. The influx and efflux parameters p T and p T2 are rescaled according to the volume as follows: The parameters for the cell population are given in Ballesta et al., 4 The transport parameters across the membrane of one single tumor cells are then:

COMPUTATION OF THE TUMOR OXYGENATION
The oxygen concentration can be computed using the cellular automaton grid as in 26,27 where full details can be found. To sum up, the simulation domain that represents the tissue is assumed to be homogeneously paved with capillaries from which oxygen is delivered depending on the oxygen concentration locally available O x; y; t ð Þ and the vessels permeability γ p . The oxygen then diffuses in the tissue and is consumed by the tumor cells that occupy the automaton grid at positions i; j ð Þ with uptake rate α. The resulting equations for the spatiotemporal evolution of oxygen is given by:

COMPUTATION OF TMZ INTRACELLULAR STEADY STATE CONCENTRATION IN A CELL POPULATION
The steady state of TMZ intracellular concentrationT Ã i in a single cell can easily be derived from equations (1 and 2), and is equal to: where p T and p T2 are the rate constants of TMZ cellular uptake and efflux, respectively.
We then computed TMZ cumulative intracellular steady state level in an heterogeneous cell population in which each cell displayed a different value of p T , respectively p T2 . The studied intervals were here ½a T ; b T ¼ ½0:2p y T ; 1:8p y T and ½a T2 ; b T2 ¼ ½0:2p y T2 ; 1:8p y T2 , respectively, which corresponded to a deviation of 80% of the value of p y T or p y T2 estimated from experimental data in U87 cells. TMZ cumulative steady state level was then computed by integrating T Ã i with respect to p T (denoted I 1 ), respectively p T2 (denoted I 2 ) on the studied interval. This is equivalent to model an infinity of cells whose parameters are uniformly selected in the predefined intervals.
The same quantities were computed for a homogeneous cell population with no inter-cell variability, that is, in which p T ¼ p y T and p T2 ¼ p y T2 for all cells (denoted I T 0 and I T2 0 ). The following formulas were derived: Since H+ production by the cells is limited it is here assumed to saturate beyond a threshold level of oxygen (Oxy thr ) indicated by the lower dashed line. The upper level of oxygen (Oxy max ) correspond to the normal physiological level of oxygen in the tissue. The oxygen variation between these 2 levels (ΔOxy) is assumed to correspond to the maximum pH variation between the center of the tumor and the surrounding tissue (ΔpH)