An in silico model to study the impact of carbonic anhydrase IX expression on tumour growth and anti-PD-1 therapy

Abstract

Immune checkpoint inhibitors (ICIs) are revolutionary cancer treatments. However, the mechanisms behind their effectiveness are not yet fully understood. Here, we aimed to investigate the role of the pH-regulatory enzyme carbonic anhydrase IX (CAIX) in ICI success. Consequently, we developed an in silico model of the tumour microenvironment. The hybrid model consists of an agent-based model of tumour–immune cell interactions, coupled with a set of diffusion-reaction equations describing substances in the environment. It is calibrated with data from the literature, enabling the study of its qualitative behaviour. In our model, CAIX-expressing tumours acidified their neighbourhood, thereby reducing immune infiltration by 90% (p < 0.001) and resulting in a 25% increase in tumour burden (p < 0.001). Moreover, suppression of CAIX improved the response to anti-PD-1 (23% tumour reduction in CAIX knockouts and 6% in CAIX-expressing tumours, p < 0.001), independently of initial PD-L1 expression. Our simulations suggest that patients with CAIX-expressing tumours could respond favourably to combining ICIs with CAIX suppression, even in the absence of pre-treatment PD-L1 expression. Furthermore, when calibrated with tumour-type-specific data, our model could serve as a high-throughput tool for testing the effectiveness of such a combinatorial approach.

1. Introduction

Immune checkpoint inhibitors (ICIs), such as anti-PD-1 and anti-CTLA-4, reinvigorate the immune response and thereby deter immune evasion by tumours. They have revolutionized the treatment of various malignancies, particularly metastatic melanoma [1,2]. Nowadays, ICIs are a cornerstone of the treatment of malignancies of almost any organ system, including cancer of the lungs, breast, skin, gastrointestinal and genitourinary tract. However, while some patients exhibit durable benefits, the majority do not respond to the treatment [3–6]. Moreover, ICI therapy is associated with a high incidence of immune-related adverse effects (irAEs) with some of the PD-1 inhibitors causing irAEs in ca 70% of patients and severe irAEs in 10–13% of patients [7,8]. Therefore, it is critical to understand what separates responders from non-responders. Furthermore, there is an acute need for the development of combination therapies that target factors driving resistance to ICI.

Over the past 10 years, considerable effort has been put into the search for ICI biomarkers. The most extensively investigated factor is the expression of the PD-1 ligand PD-L1 on tumour cells [9]. However, this does not discriminate fully between responders and non-responders. For example, some PD-L1-negative patients respond to anti-PD-1 therapy, presumably due to measurement errors such as assay limitations or insufficient sampling that does not capture the heterogeneous and dynamic expression [10]. Furthermore, other patients respond despite the lack of PD-L1 on tumour cells, since it is PD-L1-expressing immune cells that block the immune response [10]. On the other hand, not all PD-L1-positive patients benefit from the therapy because of other inhibitory pathways subduing the immune response [10]. A comprehensive review of the investigated biomarkers with their limitations has been prepared by Havel et al. [11]. Ultimately, there is no definite predictive marker yet. It is believed that finding a single biomarker might be impossible as numerous factors influence the success of immunotherapy. This poses an opportunity for computational modelling, which enables us to quickly and inexpensively build a predictive model that incorporates various elements contributing to ICI effectiveness.

The effect of the immune system on tumour growth has been modelled in various ways, including differential equations [12,13], agent-based or hybrid models [14] and evolutionary game theory models [15], offering new insights into the intricate tumour–immune system interactions. A deeper understanding of the role of immune cells in tumour development has paved the way for the modelling of immunotherapies such as ICI. Gong et al. [16] developed an agent-based model (ABM) simulating the effects of pre-treatment PD-L1 expression and tumour neoantigen profile on anti-PD-1 therapy. Lai et al. [17] built and analysed a continuous model of anti-PD-1 coupled with anti-TNF-α therapy. Byun et al. [18] used a compartmental model to study the synergistic combination of anti-PD-1 and radiotherapy. However, the intricacies of the influence of the tumour microenvironment (TME) on the success of ICI therapy are still underexplored [19,20].

Here, we have developed a hybrid model, which combines an ABM of tumour–immune system interactions with a partial-differential equation model describing the substances present in the TME. While there are models of tumour metabolism and the resulting acidic niche in the TME [21–24] and models of tumour–immune interactions [25,26], to our knowledge, this is the first computational model which takes into account both of these factors. Therefore, it allows us to study combination therapies that target immune response and the immuno-suppressive TME.

In particular, we focus on the combination of PD-1 and carbonic anhydrase IX (CAIX) inhibitors, such as SLC-0111, which has been deemed safe in a Phase 1 clinical trial [27]. CAIX is an enzyme present on the surface of cancer cells, which acidifies the microenvironment by catalysing the hydration of CO₂. The extracellular acidification contributes to immune escape as low pH subdues T-cell cytotoxicity [28], while CAIX expression protects the cancer cells from the effects of acidosis by regulating their intracellular pH [29,30]. It is thus not surprising that CAIX expression has recently piqued the interest of researchers investigating ICIs. A preclinical study has shown CAIX inhibition in combination with ICI to be a promising treatment in mouse tumour models of melanoma and breast cancer [31]. However, treatments tested in mouse models rarely translate to actual patients [32]. We believe that in silico models, especially when calibrated with clinical data, may bridge the gap between in vivo experiments and clinical practice.

In the present study, we have used our model to study the role of CAIX expression in ICI therapy success. We simulated the influence of CAIX on tumour growth, immune response and the TME and evaluated the effectiveness of combining PD-1 and CAIX inhibitors. Thanks to its bottom-up approach, our ABM allows us to simulate emergent behaviour, such as ICI effectiveness, based on simple assumptions about the interactions between cells and their environment [33], making it a well-suited model for biomarker investigation. Due to its dynamical nature and three-dimensionality, the model provides insights into the composition of the simulated TME, as well as the dynamic evolution of markers such as PD-L1 expression. Furthermore, our model is built in a modular fashion, hence it can be easily extended to incorporate other components contributing to ICI effectiveness.

2. Materials and methods

2.1. Model assumptions and implementation

We have built a three-dimensional computational framework based on a previously developed well-characterized ABM [25,26]. It is a hybrid model, composed of an on-grid agent-based part responsible for the modelling of tumour–immune interactions and a partial-differential equation model describing the substances present in the TME. The previous model simulated tumour growth in the presence of immune cells, fibrotic stroma accumulation and necrosis induction due to the lack of oxygen. The influence of the TME on immune cells was considered via an umbrella variable termed adjuvanticity. To adapt this model to our research problem, we expanded the notion of the TME by incorporating tumour cell metabolism, which is responsible for an acidic and nutrient-depleted TME, which impairs the immune response. We assume that tumour cells consume oxygen and glucose available in their neighbourhood and in turn produce ATP and protons via aerobic and anaerobic respiration. Nutrient scarcity may lead to the death or impairment of tumour and immune cells. In particular, if the amount of ATP produced by a certain tumour cell is too small, the cell becomes necrotic. On the other hand, the accumulation of protons may turn both cell types quiescent, i.e. suppress their proliferation, or induce cell death. A more detailed explanation of how tumour metabolism and the influence of substances present in the TME on the agents are modelled is given in the electronic supplementary material.

Furthermore, to focus on targeted therapies, we included CAIX and PD-L1 expression on tumour cells in our model. We assume that each new tumour cell may express CAIX with a fixed probability CAIXfreq. CAIX acidifies the TME and increases the tumour cell's resistance to low pH, as described in the electronic supplementary material. On the other hand, PD-L1 expression is dependent on T-cell activity [34,35]. Attacking T cells produce IFN-γ in their vicinity, and, once the IFN-γ concentration surpasses a certain threshold, cancer cells in the neighbourhood start expressing PD-L1. When lymphocytes try to attack cancer cells with PD-L1 expression, the attack fails, and they become exhausted, i.e. they irreversibly lose their ability to attack.

The previous model contained two types of immune cells, T cells and macrophages. Since the current model had already been heavily extended by modelling the TME in more detail, thereby increasing computation costs, we simplified the immune response to cut down on computation time, memory requirements and the number of parameters. As T cells were more fundamental to the mechanisms we wanted to model, and their infiltration was supported by the experimental data we tried to recreate, we removed macrophages from the model. Similarly, we assumed that stroma was fully permeable to both lymphocytes and tumour cells, as we were not focusing on stroma-targeting therapies.

Finally, the previous model represented colorectal cancer, which usually consists of densely packed cells. Due to this property, it was assumed that immune cells could not occupy the same grid cell as tumour cells. However, we performed our simulations without focusing on a specific tumour type, so we removed this simplification. We set the grid size equal to the average tumour cell diameter and thus assumed that only one tumour cell can occupy one grid cell. This applied to both active tumour cells and necrotic cells. Lymphocytes, however, are much smaller than tumour cells; hence we allowed them to occupy the same grid cell without limits. Moreover, since T cells can usually slip in between tumour cells to infiltrate tumours, we assumed that they can also occupy the same grid cell as tumour cells.

In short, we have an on-grid ABM that considers two types of agents: tumour cells and lymphocytes. Their actions are stochastic but depend on the environment (in particular, on other agents in their neighbourhood and the substance gradient in their grid cell (figure 1a)). Moreover, agents have certain properties such as stemness or proliferation capacity, which influence their actions and thereby take into account the history of the given agent (figure 1b,c). Simplified diagrams explaining the rules that govern their behaviour in each iteration are presented in electronic supplementary material, figure S1.

Figure 1.

Short overview of the ABM. (a) Diagram of the interactions between the agents and the environment. (b) Actions (dark grey) and properties (white) of tumour cells. (c) Actions (dark grey) and properties (white) of T cells.

The main simulation engine is implemented in the C++ programming language. The simulations have been run and visualized using Matlab 2020Rb. All source codes are freely available at https://github.com/JuliaGrajek/acidicTumorABM3D.

2.2. Treatment optimization in heterogeneous tumours

For the comparison of ICI efficacy in heterogeneous tumour groups, we simulated anti-PD-1 treatment at three dose levels: d = 33%, 66%, 100% of the maximal dose. For this experiment, we assumed that anti-PD-1 decreases the probability of T-cell suppression by PD-L1, denoted PDL1SuppProb, by 25%, 50% and 75%, respectively, for the entire duration of the simulation.

To test several treatment schedules, we then introduced simple pharmacokinetics in the model. We assume that the serum concentrations of anti-PD-1 and CAIX inhibitors decay exponentially with rate constant k = ln(2)/t_1/2, where t_1/2 is the serum elimination half-life specific for the drug. Additionally, CAIX inhibitors are administered orally, their concentration at the administration site again decreases monoexponentially, and it is fully absorbed into the bloodstream. The absorption rate constant can be calculated by knowing the time of maximal drug concentration in the body t_max in the following way: maximal drug concentration occurs when the absorption rate equals the elimination rate, i.e. $k_a{(X_a)}_{t_{max}}=\hspace{0.17em}k{(X)}_{t_{max}}$, where X_a denotes the drug concentration at the site of administration and X the drug serum concentration. From this, we get $t_{max}=\ln (k_a/k)/(k_a-k)$ and can determine the value of k_a. By contrast, anti-PD-1 is administered intravenously and is absorbed immediately. We assume that drug concentration linearly corresponds to the drug effect, i.e. $\mathrm{PDL}1\mathrm{SuppProb}=1-0.75\times X_{\mathrm{antiPD}1}$, where $X_{\mathrm{antiPD}1}$ is the anti-PD-1 concentration in serum. The coefficient 0.75 was chosen to correspond to the maximal dose tested in the prior experiment. Similarly, CAIX inhibitors suppress CAIX expression on cancer cells, i.e. they increase the probability that a cancer cell stops expressing CAIX in the given iteration, which we denote $\mathrm{CAIXSup}=X_{\mathrm{antiCAIX}}$.

2.3. Statistical analysis and visualization

Pairwise comparisons between CAIX knockout and CAIX tumours were carried out on the results of the simulations without treatment. Statistical significance was analysed using the two-sided Wilcoxon rank-sum test implemented in Matlab (Mathworks Inc. Matlab 2020Rb) in the ranksum function. Visualization of the obtained data was performed using Python's matplotlib library.

Comparisons between multiple groups (treatment efficacy) were analysed using the Kruskal–Wallis test with Dunn post hoc analysis. Bonferroni correction was applied. Results were plotted using Python's seaborn library.

Survival analysis was performed in The Cancer Genome Atlas (TCGA) database using the Kaplan–Meier Plotter developed by Lanczky et al. and presented in [36]. Significance was measured with the log-rank test. The cut-off value distinguishing high and low CAIX expression was determined for each tumour type by computing all possible cut-off values between the upper and lower quartile and choosing the best performing one, i.e. the most significant one in terms of the log-rank test. To account for this multiple hypothesis testing, we also report the false discovery rate. The follow-up threshold was set to 60 months.

3. Results

3.1. Carbonic anhydrase IX induces acidification of the tumour microenvironment and supports tumour growth

To validate that the model is biologically plausible, we independently simulated n = 20 CAIX knockout tumours (CAIX KO) and n = 20 CAIX-expressing tumours (CAIX). Simulations started from a spheroid with a radius of 30 tumour cells. Starting with a spheroid as opposed to a single tumour cell allowed us to drastically cut simulation time. At the same time, the initialized tumours were still too small to cause significant nutrient shortage that would induce a less homogeneous tumour spheroid, e.g. having a significant necrotic core. The nutrient gradients were always calculated as a steady state solution, hence, this initialization did not have an impact on the TME. As this was simply due to an efficiency issue, the publicly available codes allow to start the simulation from a single tumour cell as well. A randomly sampled fraction of CAIXfreq tumour cells expressed CAIX at the beginning of the simulation in CAIX tumours, while CAIX expression was non-existent in CAIX KO tumours. We recorded tumour behaviour and changes in TME for 40 days, taking measurements every 2.5 days.

Our model showed that CAIX expression significantly and durably decreased mean extracellular pH (from 7 to ca 6.6; p < 0.001) (figure 2a). This decrease in pH seemed favourable to tumour growth, as our simulated CAIX tumours were considerably bigger in terms of the number of tumour cells (figure 2b). More specifically, CAIX tumours consisted on average of ca 25% more tumour cells than CAIX KO tumours (p < 0.001).

Figure 2.

Influence of CAIX expression on the tumour and the TME. The mean results of 20 simulations are plotted. Error bars indicate s.d. (a) For each independent simulation mean pH over the entire domain is measured. (b) Tumour burden is here defined as the number of tumour cells in the domain. (c,d) Volume denotes the number of tumour cells and necrotic cells, either including stromal cells or not. (e,f) Tumour composition is shown as the fraction of cell types that make up the tumour. Lymphocytes are much smaller than tumour cells, hence they are omitted.

Since tumours consist of more than just cancer cells, we also analysed tumour volume, defined as the number of tumour cells, necrotic cells and stromal cells. We decided to omit lymphocytes as their diameters are much smaller than those of tumour cells and the grid cells of our domain, and hence we may assume that they can slip in between other cells and do not contribute to the tumour volume. Contrary to the tumour cell burden, we observed that CAIX KO tumours had a larger volume than CAIX tumours (p < 0.001) (figure 2c). This could be explained by the salient change in tumour composition (figure 2e,f). CAIX tumours consisted mainly of tumour cells (more than 60% of tumour composition), whereas CAIX KO tumours had a considerable fibrotic stroma fraction. Removing stroma from our calculations induced a dramatic difference in tumour volume between CAIX and CAIX KO tumours, in favour of the CAIX tumours (figure 2d, p < 0.001).

3.2. Carbonic anhydrase IX expression impairs immune response and PD-L1 expression

The abundant accumulation of stroma (figure 2e,f) implied a superior immune response in CAIX KO tumours, which could explain the hampered tumour growth. To quantify T-cell infiltration in our simulations, we calculated the probability of finding a T cell in the vicinity of a tumour cell, i.e. the fraction of tumour cells that have a T cell present within the distance of two grid cells. We found that tumours lacking CAIX expression have significantly increased T-cell infiltration (92% versus 10%, p < 0.001, figure 3a). Moreover, we observed higher PD-L1 expression in CAIX KO (figure 3b), which supports the notion of an enhanced immune response, since PD-L1 is induced by T-cell activity.

Figure 3.

Influence of CAIX on the immune response. The mean results of 20 simulations are plotted. Error bars indicate s.d. (a) T-cell infiltration is measured as the probability of finding a T cell with a distance smaller or equal to two grid cells to a tumour cell. (b) Fraction of tumour cells with PD-L1 expression. (c) Types of T cells in the TME: exhausted cells have either used up their killing capacity or been suppressed by PD-L1 and cannot ever recover their cytotoxicity. Quiescent cells are reversibly suppressed by low pH.

Furthermore, our computational model allowed us to look deeper and analyse the composition of the infiltrating T-cell population (figure 3c). In CAIX KO tumours, we observed more active T cells. However, there was also a dramatic increase in exhausted T cells, indicating that immune cells launch more attacks in CAIX KO tumours. On the other hand, in CAIX tumours, we found a fraction of quiescent T cells, which are cells suppressed by low pH that are thus unable to attack.

3.3. Testing treatment efficacy in heterogeneous tumour types

Having established that CAIX expression is beneficial to tumour growth, we wanted to test whether CAIX inhibition can improve anti-PD-1 treatment effectiveness. In addition, we decided to investigate the significance of PD-L1 expression at beginning of treatment on therapy success. Therefore, we simulated ICI treatment for three different doses in four distinct tumour groups: CAIX KO without initial PD-L1 expression, CAIX KO with initial PD-L1 expression, CAIX-expressing tumours without initial PD-L1 expression and CAIX-expressing tumours with initial PD-L1 expression. Again, tumours were grown from a sphere with a radius of 30 tumour cells. We conducted 80 simulations per tumour group (20 independent repeats per tested anti-PD-1 dose and 20 control tumours that did not receive anti-PD1 treatment) and measured the change in tumour cell number in the treatment group relative to the appropriate control group. Treatment was administered on day 0 and response was assessed on day 40.

ICI therapy was significantly more effective in the CAIX KO groups than in the CAIX groups (figure 4). In the groups without initial PD-L1 expression, we observed on average 22% tumour reduction for CAIX KO versus 6% tumour reduction for CAIX for the highest studied anti-PD-1 dose, 14% for CAIX KO versus 4% for CAIX for the medium dose (66% of maximum dose) and 7% for CAIX KO versus 2% for CAIX for the lowest dose (33% of maximum dose). All of these differences were significant with p < 0.05 (Kruskal–Wallis test and post hoc Dunn analysis with Bonferroni correction, see electronic supplementary material, figure S2). On the contrary, initial PD-L1 expression was not required for long-term efficacy, and we did not observe any statistically significant difference in the median treatment effectiveness between the PD-L1-expressing tumours and their PD-L1 non-expressing counterparts. The only factor in which these groups differed was the effectiveness of the lowest anti-PD-1 dose, which was significantly better in the CAIX KO no PD-L1 group than the CAIX no PD-L1 (p = 0.03), while there was no difference between the CAIX KO PD-L1 and CAIX PD-L1 groups. Concerning dose escalation, in CAIX KO tumours, the highest dose was significantly more effective than the lowest dose (p < 0.001). In the CAIX KO group without initial PD-L1 expression, there was no difference between the low and medium dose, unlike in the group with initial PD-L1 expression, where we observed a slight difference (p = 0.047).

Figure 4.

Efficacy of anti-PD1 treatment in four heterogeneous tumour groups at three dose levels (33%, 66% and 100% of maximum dose). Per dose and tumour group, 20 tumours were simulated and compared with the control group that did not receive anti-PD-1. Black circles indicate individual repeats. Immune checkpoint blockade was significantly more effective in CAIX KO than CAIX tumours (p < 0.001 for medium and high drug dose, p = 0.03 for low dose for tumours without initial PD-L1 expression; Bonferroni correction was applied). There was no significant difference between tumours without PD-L1 expression at treatment begin and tumours with 10% PD-L1 expression at beginning of treatment. Significance between doses within the same tumour group is marked on the plots with their given p-value.

Exemplary tumours treated with the maximal anti-PD-1 dose for each studied tumour type are shown in figure 5. We can see that all tumours have a necrotic core. CAIX KO tumours are fully infiltrated by T cells and filled with fibrotic stroma. It is clear that CAIX tumours have lower T-cell infiltration and that the present lymphocytes tend to stay outside of the tumour, where the pH is higher. In short, the immune response is not only greater in CAIX KO tumours, but the immune cells are also better distributed.

Figure 5.

Examples of tumours treated with the maximal anti-PD1 dose 40 days after treatment start. The first column shows the entire tumour, while the other columns focus on a certain cell type and the remaining cells are plotted with increased transparency.

3.4. Simulation of combination therapy schedules

The results discussed in the previous section urged us to study combination therapy between CAIX inhibition and anti-PD1 treatment more in depth and perform a preliminary study of possible therapy schedules. Considering that CAIX KO tumours had superior immune infiltration and response to anti-PD-1, we hypothesized that administering CAIX inhibitors prior to anti-PD-1 might increase the effectiveness of combination therapy compared with simultaneous administration. The reasoning for this hypothesis was that CAIX inhibition would induce a hotter TME, thus increasing immunotherapy effectiveness. To test this hypothesis, we simulated seven treatment schedules in 20 independent in silico tumours. We started each simulation from a spherical tumour with a radius of 30 tumour cells and let it grow for 5 days. Daily anti-CAIX administration (in line with the protocol in [27]) started on day 5.5. As shown in figure 6a, T-cell infiltration reached its peak on day 8.5. Hence, we tested treatment schedules during which anti-PD-1 was injected once on days 5.5 to 8.5. Anti-PD-1 is administered at two- to four-week intervals, so we decided to look at the change in tumour burden within two weeks after the anti-PD-1 treatment start. We did not observe any significant difference between the treatment schedules (figure 6b).

Figure 6.

Initial analysis of combination therapy schedules. The CAIX inhibitor SLC-0111 is being administered on day 5.5. (a) T-cell infiltration into the tumour after pH normalization. The line plot represents averages of 20 simulations, the error bars represent s.d. (b) Change in tumour cell number within two weeks after anti-PD-1 administration. We observe no statistically significant difference between the treatment schedules. TIL: tumour-infiltrating lymphocyte.

3.5. Carbonic anhydrase IX is a prognostic biomarker in certain tumour types

To initially test our hypothesis that CAIX benefits tumour progression in clinical data, we performed a survival analysis for 21 tumour types divided into high and low CAIX-expressing cohorts (overall n = 7489). We observed decreased overall survival, determined by the HR and the p-value of the log-rank test, in the CAIX-expressing cohort for 10 tumour types, and a reversed relationship in two tumour types (see electronic supplementary material, table S2). However, out of these 12 tumour-type-specific analyses, only two had a low FDR (liver hepatocellular carcinoma: HR 2.4, p < 0.001, FDR = 1% and lung adenocarcinoma: HR 1.72, p < 0.001, FDR = 10%). In both cases, high CAIX expression was associated with poor prognosis.

4. Discussion

Driven by the clinical need for increasing the effectiveness of ICI therapy, we have developed a computational model of tumour–immune interactions. Using this model, we studied the influence of CAIX expression on tumour development and ICI success. To our knowledge, this is the first ABM that incorporates tumour metabolism and the resulting acidosis, as well as immune cells, and allows thus for the modelling of combination therapies that target both immune checkpoints and the immuno-suppressive low pH. Our in silico simulations produced a TME with pH values that are in line with the literature, where the pH of the TME is reported to fall within 5.7–7 [37] and most commonly oscillates around 6.5–6.8 [28]. Moreover, we showed that CAIX expression significantly impairs immune response and is therefore beneficial to tumour growth. Furthermore, CAIX-expressing tumours did not respond to ICIs, as opposed to CAIX KO tumours. This indicates that CAIX expression might be one of the factors driving resistance to ICI treatment. Our results provide a basis for further research into CAIX as a biomarker for ICI therapy and as a target for combination therapy. Importantly, our model may be used as a high-throughput tool for testing combination therapy protocols, when calibrated with tumour-specific data.

According to our simulations, CAIX-expressing tumours are 25% larger than CAIX KO tumours in terms of tumour cell number. This implies that CAIX-expressing tumours might be more aggressive, which corroborates experimental findings in [31], where Chafe et al. identified CAIX as a biomarker for worse overall survival in melanoma, which was associated with increased grade and risk of metastasis. Similarly, we also observed an association between high CAIX expression and poor prognosis in liver hepatocellular carcinoma and lung adenocarcinoma. It must be noted that we have only performed a preliminary survival analysis, which did not take into account other variables which might influence ICI effectiveness. Further multivariate analysis should be performed to rule out any confounding variables. Moreover, we observed that the decreased tumour burden of CAIX KO tumours might not be observed by volume measurements alone, as the tumour composition changes significantly when suppressing CAIX. In particular, CAIX KO tumours seem to have a high stroma fraction, which might mask the decrease in the number of tumour cells.

In our simulations, we also observed that CAIX expression dramatically decreases T-cell infiltration and suppresses their effector function. As T-cell quiescence is reversible [4], inhibiting CAIX might reinvigorate immune response by increasing T-cell infiltration and cytotoxicity. Taken together with the observation that CAIX expression inhibits PD-L1 expression on tumour cells, this supports our hypothesis that combination therapy with anti-CAIX might improve ICI efficacy. Considering that our model assumed that PD-L1 is induced by lymphocyte activity, this was also another indicator of improved immune response in CAIX KO tumours.

The enhanced immune response in CAIX KO tumours led to abundant stroma accumulation in our in silico experiments. Studying the effects of stroma on treatment success was out of the scope of this study, but remains an interesting question for further research that focuses on cancer types that are linked to chronic-inflammation-induced fibrosis. In [25], Kather et al. postulated that fibrosis might have both pro-tumorigenic and tumour-suppressive properties, depending on the immune cell infiltration. Hence, research considering combination approaches consisting of immunotherapy and treatments targeting stroma and CAIX expression seems promising.

Finally, our simulations of anti-PD1 therapy in CAIX-expressing and CAIX KO tumours suggest that CAIX is a potential biomarker for ICIs and combination therapy might be more effective for patients with CAIX-expressing tumours than monotherapies. On the other hand, PD-L1 expression at beginning of treatment was not crucial for ICI therapy effectiveness. This might be explained by the fact that PD-L1 expression is dynamic, which is a limitation of this biomarker that has been raised before, see [10]. In particular, we believe PD-L1 expression in the pre-treatment TME to be a misleading biomarker for combination therapy with anti-CAIX, as CAIX expression induces a T-cell-depleted TME. Inhibiting CAIX may then reinvigorate immune response and therefore upregulate PD-L1 expression. Hence, PD-L1 negative patients should not be excluded from the treatment based on this marker alone.

Our simulations did not find a significant difference between treatment protocols that assume simultaneous administration of anti-PD1 and anti-CAIX versus protocols with a time delay. However, our model's smallest discrete time step is equal to 12 h. Therefore, it cannot be assumed that simultaneous administration of both drugs is the best treatment strategy, based on our results alone. For future investigations, the model could be recalibrated to allow for smaller time steps and more precise modelling of treatment response. Yet, this would significantly increase the already quite time-consuming computation time. Hence, we believe that a continuous model would be more suitable to optimize the exact treatment protocol. Such a simpler and computationally cheaper model would also allow for the simulation of longer treatment and various treatment cycles that could actually eradicate the tumour instead of slowing down its growth. Moreover, it could be interesting to evaluate more complex pharmacodynamics models which represent the treatment effect more accurately.

It should be noted that in our simulations treatment was administered while the tumour consisted of less than 200 000 cells. This obviously does not reflect clinical reality, where such a small tumour would probably not be detected and treated. Since the behaviour of the agents depends only on the TME and the interactions between the single agents, as opposed to the absolute number of modelled cells, we believe that our simulations reflect realistic qualitative results despite the smaller scale. If our model were to be used for quantitative analysis, larger tumours should be simulated. To avoid drastically increasing computation costs, the model could be modified. One idea would be to forgo the three-dimensional structure and perform two-dimensional simulations, which would of course be a simplification, but would allow to model larger tumours without increasing the number of modelled agents. Another very interesting approach would be to recalibrate the model in such a way that each grid cell would represent a packet of homogeneous cancer cells, as proposed in [38].

Our study's limitation is that our model is currently only calibrated with data from the literature. We aimed at elucidating the general impact of CAIX expression on tumour growth and immune response, and therefore decided on performing qualitative simulations. An obvious future step would be the thorough calibration and validation of the model with tumour-type-specific data to conduct quantitative analyses. Moreover, as with all computational models, our framework is a simplification of reality. For example, our model assumes that CAIX expression is random, although CAIX is a known hypoxia-related biomarker [39]. This simplification allowed us to decrease model complexity without significantly impacting qualitative model results. However, if somebody were interested in studying the spatial distribution of CAIX, our model could be extended by incorporating this mechanism. Furthermore, our model is ignorant of other pH regulatory pathways, such as other carbonic anhydrases, anion exchangers and monocarboxylate transporters [40]. While it has been shown that inhibiting CAIX alone increases extracellular pH and decreases tumour growth, some studies report that CAIX suppression may result in CAXII upregulation, and suppressing both enzymes simultaneously results in superior tumour eradication [41,42]. Hence, it could be interesting to incorporate more pH regulatory mechanisms into our model to study their interplay and impact on treatment effectiveness. Finally, our model neglects other factors driving resistance to ICIs, such as the presence of immune-suppressive cells in the TME, like regulatory T cells, pro-tumour macrophages or myeloid-derived suppressor cells. Nevertheless, we were able to capture emergent behaviour which agrees with studies performed on mice, while giving us deeper insight into the underlying mechanisms, providing a bridge between animal and human models. Thanks to its modular fashion, it can be easily extended to test other hypotheses or treatment strategies to quickly and inexpensively determine which are worth further investigation.

Data accessibility

Survival analysis was performed on the n = 7489 samples available for pan-cancer mRNA analysis in the Kaplan–Meier Plotter database [36]. The data are publicly available at TCGA (https://portal.gdc.cancer.gov/). Source codes for the ABM are freely available at https://github.com/JuliaGrajek/acidicTumorABM3D.

The data are provided in the electronic supplementary material [43].

Authors' contributions

J.G.: conceptualization, formal analysis, methodology, software, visualization and writing—original draft; J.N.K.: formal analysis, methodology and writing—review and editing; J.P.: conceptualization, methodology, software, supervision and writing—review and editing.

All authors gave final approval for publication and agreed to be held accountable for the work performed therein.

Conflict of interest declaration

The authors declare no potential conflicts of interest.

Funding

Project is supported by ESF, POWR.03.02.00-00-I028/17-00.