Destabilization of CAR T-cell treatment efficacy in the presence of dexamethasone

Chimeric antigen receptor (CAR) T-cell therapy is potentially an effective targeted immunotherapy for glioblastoma, yet there is presently little known about the efficacy of CAR T-cell treatment when combined with the widely used anti-inflammatory and immunosuppressant glucocorticoid, Dexamethasone. Here we present a mathematical model-based analysis of three patient-derived glioblastoma cell lines treated in vitro with CAR T-cells and Dexamethasone. Advanced in vitro experimental cell killing assay technologies allow for highly resolved temporal dynamics of tumor cells treated with CAR T-cells and Dexamethone, making this a valuable model system for studying the rich dynamics of nonlinear biological processes with translational applications. We model the system as a non-autonomous, two-species predator-prey interaction of tumor cells and CAR T-cells, with explicit time-dependence in the clearance rate of Dexamethasone. Using time as a bifurcation parameter, we show that (1) the presence of Dexamethasone destabilizes coexistence equilibria between CAR T-cells and tumor cells and (2) as Dexamethasone is cleared from the system, a stable coexistence equilibrium returns in the form of a Hopf bifurcation. With the model fit to experimental data, we demonstrate that high concentrations of Dexamethasone antagonizes CAR T-cell efficacy by exhausting, or reducing the activity of CAR T-cells, and by promoting tumor cell growth. Finally, we identify a critical threshold in the ratio of CAR T-cell death to CAR T-cell proliferation rates that predicts eventual treatment success or failure that may be used to guide the dose and timing of CAR T-cell therapy in the presence of Dexamethasone in patients. Author summary Bioengineering and gene-editing technologies have paved the way for advance immunotherapies that can target patient-specific tumor cells. One of these therapies, chimeric antigen receptor (CAR) T-cell therapy has recently shown promise in treating glioblastoma, an aggressive brain cancer often with poor patient prognosis. Dexamethasone is a commonly prescribed anti-inflammatory medication due to the health complications of tumor associated swelling in the brain. However, the immunosuppressant effects of Dexamethasone on the immunotherapeutic CAR T-cells are not well understood. To address this issue, we use mathematical modeling to study in vitro dynamics of Dexamethasone and CAR T-cells in three patient-derived glioblastoma cell lines. We find that in each cell line studied there is a threshold of tolerable Dexamethasone concentration. Below this threshold, CAR T-cells are successful at eliminating the cancer cells, while above this threshold, Dexamethasone critically inhibits CAR T-cell efficacy. Our modeling suggests that in the presence of Dexamethasone reduced CAR T-cell efficacy, or increased exhaustion, can occur and result in CAR T-cell treatment failure.

Chimeric antigen receptor (CAR) T-cell therapy is a novel immunotherapy for the 2 treatment of cancer. While initially demonstrating efficacy in haematologic cancers, 3 CAR T-cell therapy also has potential for treating solid tissue tumours, including the 4 highly aggressive brain cancer glioblastoma (GBM) [1][2][3][4]. To further develop CAR 5 T-cell therapy for the clinical treatment of GBM, it is essential to understand how CAR 6 T-cells interact with commonly administered medications which may impact CAR T-cell 7 efficacy. The anti-inflammatory synthetic glucocorticoid Dexamethasone (Dex) is a 8 ubiquitous medication for patients with GBM due to the propensity for brain tissue 9 inflammation that accompanies tumor development in GBM, and the severity of the 10 associated medical complications that accompanies inflammation. To study the effects 11 of Dex on CAR T-cell proliferation, killing, and exhaustion, we extend mathematical 12 models developed by us and others to study highly resolved temporal in vitro dynamics 13 of patient-derived GBM cell lines under various concentrations of Dexamethasone and 14 CAR T-cells [5]. 15 Glioblastoma is a highly aggressive and unfortunately common form of primary 16 malignant brain tumor. It is noted for its high rates of proliferation and poor survival 17 following chemotherapy, radiotherapy, and surgical resection. The recent development of 18 adoptive CAR T-cell therapy using patient-specific T cells has shown promise in 19 treating GBM targeting the glioma antigen IL13Rα2 [1]. In this study we examine the 20 treatment response to CAR T-cell therapy of three human derived primary brain tumor 21 (PBT) cell lines with high levels of expression of the IL13Rα2 antigen. These treatment 22 experiments are conducted with varying concentrations of Dexamethasone and 23 effector-to-target (E:T) ratios of CAR T-cells to examine the effects of combination 24 therapy. 25 In a clinical context, patients diagnosed with GBM are commonly prescribed the 26 glucocorticoid steroid Dexamethasone (Dex) to manage inflammation surrounding the 27 site of tumor burden. Importantly, recent work has demonstrated contradictory 28 outcomes in the use of Dex for treating GBM. Specifically, the anti-and 29 pro-proliferative effects of Dex on GBM have been shown to depend on cell type [6]. 30 Furthermore, a previous proof-of-concept experiment demonstrated the ability of high 31 Dex doses (5 mg/kg) to compromise successful CAR T-cell therapy in mice with 32 xenograft GBM tumors, whereas lower doses (0.2-1 mg/kg) had limited effect on in vivo 33 antitumor potency [7]. This data suggests a threshold at which Dex negatively impacts 34 CAR T-cell therapy and reinforces the importance of mathematical modeling to infer 35 and understand how Dex influences CAR T-cell therapy efficacy for GBM. 36 Mathematical modeling has demonstrated value in quantitatively characterizing the 37 interactions between GBM cells and CAR T-cells. Previous work validated this 38 September 30, 2021 2/21 approach in which the principle components necessary for accurate predictions were 39 identified as: rates of GBM proliferation and cell killing, and CAR T-cell proliferation, 40 exhaustion, and death. These factors were combined into a predator-prey system called 41 CARRGO: Chimeric Antigen Receptor T-cell treatment Response in GliOma [5]. Here 42 we extend this work by incorporating the Dex concentration as a new model parameter, 43 and assume that it follows exponentially depleting pharmacokinetics. We posit that Dex 44 has directly measurable effects on GBM proliferation and CAR T-cell death, and 45 indirectly measurable effects on all other model parameters. We use our extended model 46 to investigate the consequences of combination CAR T-cell and Dex therapy on three in 47 vitro GBM cell lines. We establish an experimental protocol that measures treatment Primary brain tumor GBM cell lines were derived as described in [1,8] IL13Rα2-targeting CAR as described in [7]. Summary information regarding cell lines 60 can be found in Table 1. hours after seeding and followed for 6-8 days (144-192 hrs). CAR T-cell treatments were 75 performed with E:T ratios of 1:4, 1:8, and 1:20. Dex treatment concentrations used were 76 10 −4 , 10 −3 , 10 −2 , 10 −1 , and 1 µg/ml. The experiment design is diagrammed in Fig 1(a), 77 and treatment conditions are presented in Table 1. A follow-up experiment was 78 conducted to examine the potential for Dex-induced changes to tumor cell morphology 79 using the IncuCyte live cell imaging system (Fig 2). In this second experiment, E:T Dexamethasone, we extend the predator-prey inspired CARRGO model from Sahoo et 86 al. [5]. We use the principle of mass-action to model the effect of Dex on tumor and

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CAR T-cell populations, without an explicit assumption of a positive or negative effect 88 of Dex on those cell populations. A compartmental representation of the model is 89 presented in Fig 1(b), and all model variables and parameters are presented in Table 2. killing assay measurement system [5,10,11]. Expressing the compartmental model as a 93 system of equations, 94 where x is the tumor cell population, y is the CAR T-cell population, and D is the Pharmacokinetic studies report the plasma half-life of Dex as being approximately 101 200 minutes, resulting in σ = ln(2)/3.3 hr −1 [12,13]. We do not explicitly model the 102 mechanism by which Dex is cleared from the system, which can be through cell uptake, 103 evaporation, or absorption into the culture media. Here we simply assume the 104 elimination of Dex is equivalent to the Dex plasma half-life. While the Dex interaction 105 terms are explicitly subtracted from the population growth rates, we make no 106 presumptions on the signs of the interaction constants, c 0 and c 3 . This has the effect of 107 allowing for both scenarios where Dex can be either anti-proliferative (i.e. c 0 , c 3 < 0) or 108 pro-proliferative (i.e. c 0 , c 3 > 0) to either the CAR T-cells or tumor growth [6,14]. 109 We next convert this three-species, autonomous population model into a two-species, 110 non-autonomous model. We formulate the model this way to study how the 111 concentration of Dex influences the predicted long-term stability of the CAR T-cell and 112 tumor cell populations, which essentially considers time as a bifurcation parameter. To 113 perform this conversion, note that Eq. (3) can be solved separately as D(t) = D 0 e −σt . 114 Upon substitution for D(t), we arrive at the following system of equations where we factored terms to reflect the anti/pro-proliferative potential of Dex, and 116 re-scaled the constants c 0 and c 3 . Letting ρ(t) = ρ − c 0 e −σt , K(t) = ρ(t)K/ρ, and 117 θ(t) = θ + c 3 e −σt , our model takes the simplified form of which is reminiscent of the original CARRGO model [5]. The fitting procedure used to estimate model parameters consisted of a combination of 129 particle swarm optimization (PSO) and the Levenberg-Marquardt algorithm (LMA).

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PSO is a stochastic global optimization procedure inspired by biological swarming [15]. 131 September 30, 2021 6/21 PSO has been used recently for parameter estimation in a variety of initial value 132 problems across cancer research and systems biology [16][17][18][19]. These optimization 133 procedures were used to minimize the weighted sum-of-squares error between measured 134 and predicted tumor cell and CAR T-cell populations. PSO was used first to determine 135 rough estimates of model parameters. This was followed by use of LMA to fine-tune where (x, y) = (tumor cells, CAR T-cells). These 156 solutions are referred to as 'Death', 'Tumor Proliferation', and 'Coexistence' respectively. 157 Given the structure of the dynamical system in Eqs. (6)- (7), eigenvalue analysis shows 158 that the 'Death' and 'Tumor Proliferation' equilibria are never stable solutions (see 159 Supplemental Information). Interestingly, this does not preclude our ability to predict 160 tumor death or proliferation. On the contrary, observed and measured tumor death and 161 proliferation occur within the parameter space that defines the coexistence equilibrium. 162 Careful examination of the coexistence equilibrium stability can elucidate this point.

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In the 'Coexistence' scenario, the equilibrium is . 164 Importantly, the model parameters that determine the final tumor cell population are 165 the ratio of the CAR T-cell death rate and the CAR T-cell proliferation/exhaustion 166 after the Dex has cleared, θ/κ 2 . Thus, if either CAR T-cell death is low with respect to 167 CAR T-cell proliferation, or CAR T-cell proliferation is high with respect to death, then 168 θ/κ 2 ≈ 0, and tumor death can occur as the coexistence equilibrium. We next examine 169 how the conditions for stability depend on the model parameters, in particular the Dex 170 concentration.

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The eigenvalues of the Jacobian for the coexistence equilibrium are Substitution 173 of the expressions for the time-dependent growth rate, carrying capacity, and death rate 174 results in In Eq. (9), the term underlined in blue determines oscillatory behavior, while the term 176 underlined in red determines the stability of the oscillatory states (spiraling in, spiraling 177 out, or as a fixed limit cycle). By convention, only the parameters characterising the 178 effects of Dex on tumor growth and CAR T-cell death, c 0 and c 3 , can take on negative 179 values. Thus, after the Dex has cleared, any oscillatory coexistence state will be stable. 180 This consequence highlights the value of our decision to model the system as 181 non-autonomous. In the event that Dex is pro-proliferative to the CAR T-cells such 182 that c 3 < −θ, then there will always be at least one positive eigenvalue (with or without 183 oscillations), and the equilibrium will be temporarily unstable until the Dex has 184 sufficiently cleared the system.

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To determine the condition for oscillatory states, we require non-zero imaginary 186 components of the eigenvalues, (λ ± ) = 0, which results in the following condition In Eq. (10) we can see that the existence of oscillations about the coexistence 188 equilibrium are again determined by the relative sizes of θ(t) and κ 2 . incorporates Dex can predict these changes in CAR T-cell efficacy and connect them to 199 key features of CAR T-cell function (e.g. proliferation, exhaustion, and death). 200 Our modeling identifies that Dex treatment destabilizes the coexistence equilibrium 201 and forces the system into a new equilibrium state upon Dex clearance (Fig 5). We 202 predict that this process is a result of a Dex-induced increase in CAR T-cell 203 proliferation, c 3 < −θ, followed by an increase in CAR T-cell death, θ increasing, and 204 either a decrease or fixation of cancer cell stimulated proliferation of CAR T-cells, κ 2 205 decreasing or approx. constant. We interpret these combined effects as facilitating CAR 206 T-cell exhaustion (Fig 6). These responses are manifest in a cycle of pseudo-progression, 207 pseudo-regression, and a final stage of tumor progression. Importantly, we identify a 208 threshold on the ratio of CAR T-cell death to CAR T-cell proliferation/exhaustion 209 rates, (θ/κ 2 ≈ 0.4 CI), that appears to predict successful tumor eradication (θ/κ 2 < 0.4 210 CI), or proliferation (θ/κ 2 > 0.4 CI). We find that this threshold is valid across all three 211 PBT cell lines, initial CAR T-cell populations, and Dex concentrations (Fig 7).   This effect was also observed in PBT030 (again in the absence of CAR T-cells), but not 239 PBT138, and led to our omission of the Dex-only treatments in this analysis.

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Dexamethasone induced destablization of coexistence 241 Analysis of the coexistence eigenvalue stability helps to elucidate the effect that Dex has 242 on the system dynamics. In the scenario with an initial Dex concentration of 1 × 10 −3 µg/ml (Fig 5 a), the 253 coexistence equilibrium begins as a stable spiral for the duration of the Dex clearance 254 and the remainder of the experiment. As the Dex clears, the real and imaginary 255 components of the eigenvalues decrease in magnitude. These temporal changes in the 256 eigenvalues shift the location and shape of the system trajectory, as shown in the figure 257 inset. In particular, during the times t 1 = 32 hrs and t 2 = 40 hrs, as the Dex is still 258 clearing, the system is predicted and observed to oscillate about the changing 259 coexistence equilibrium P 3 . At the times t 1 and t 2 real component of the eigenvalue is 260 large enough to facilitate in-spiraling. By t 3 = 60 hrs, effectively all of the Dex has 261 cleared, and the phase space trajectory is soon to pass through a zero in tumor cell 262 population, terminating the dynamics.

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In the scenario with a higher initial Dex concentration of 1 × 10 −1 µg/ml (Fig 5 b), 264 the coexistence equilibrium begins as an unstable fixed point (times t 1 = 32 hrs and 265 t 2 = 38 hrs). After twice the half-life of Dex (≈ 7 hrs), a Hopf bifurcation occurs and 266 the system transitions through a limit cycle (time t ≈ 40 hrs) and into a stable spiral 267 (time t 3 = 42 hrs). When the system is in an unstable state, the instantaneous 268 trajectory predicted by Eqs. (6)-(7) show pseudo-progressive growth. As in the previous 269 scenario with 1 × 10 −3 µg/ml of Dex, the system enters a stable spiral by the time all of 270 the Dex has cleared (t 3 = 60 hrs) that would result in zero tumor cells. However, in this 271 scenario, once the Dex has fully cleared the system the coexistence eigenvalue is a stable 272 spiral that importantly no longer passes through a zero in the tumor cell population. Dex-gradient of treatment failure (Fig 6 a, c, and e for cell lines PBT030, PBT128, and 279 PBT138, respectively). Accompanying each growth trajectory are barplots of the 280 inferred model parameters (Fig 6 b, d, and f), which help to identify how Dex interacts 281 separately with the tumor cells and CAR T-cells. We chose not to examine Dex only 282 treatments as flow cytometry measurements indicated a loss in the strength of the 283 correlation between xCelligence cell index and flow cytometry-measured cell number in 284 these treatment scenarios [10,11]. The correlation was observed to be maintained in In (a) the initial Dex concentration of 1 × 10 −3 µg/ml is too small to facilitate exhaustion of the CAR T-cells, thus the coexistence equilibrium is a stable spiral. However, the equilibrium position is still seen to translate through the phase space, and the predicted trajectory deform, while Dex is clearing. In (b) the initial Dex concentration of 1 × 10 −1 µg/ml is sufficiently large enough to facilitate exhaustion of the CAR T-cells, thus the coexistence equilibrium is an unstable fixed point (dashed lines) until a sufficient level of Dex has cleared and the system returns to a stable spiral (solid lines). Unlike the lower initial Dex concentration scenario in (a), the coexistence equilibrium has translated, and the predicted trajectory has narrowed, such that the tumor population no longer reaches a value of zero, resulting in tumor progression.  the cancer cell stimulated CAR T-cell proliferation. After Dex clears, CAR T-cell death 298 returns to a small rate resulting in treatment success. In the failure scenario Dex again 299 promotes CAR T-cell growth, c 3 < 0, yet increases CAR T-cell exhaustion by reducing 300 the size of κ 2 . Our interpretation of these combined effects is that Dex results in CAR 301 T-cell exhaustion. In this work we demonstrate how mathematical modeling can be leveraged to identify 317 and quantify how the commonly used anti-inflammatory synthetic glucocorticoid 318 Dexamethasone may undermine CAR T-cell treatment efficacy in glioblastoma.

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In modeling this system, we chose to use a non-autonomous (explicit in time) 320 approach in order to assess the dynamical stability of the system as a function of Dex 321 concentration. By treating time as a bifurcation parameter, variations in system 322 stability and predicted phase space trajectories can be visualized (Fig 5). This approach 323 facilitates understanding of treatment success and failure due to an overabundance of 324 Dex and in the context of stability analysis. Specifically, in scenarios where treatment 325 succeeded, as in Fig 5(a), the coexistence equilibrium remained stable throughout the 326 duration of Dex clearance. On the other hand, in scenarios where high levels of Dex led 327 to treatment failure and tumor outgrowth, as in Fig 5(b), the coexistence equilibrium 328 was initially unstable until sufficient Dex cleared from the system. growth and CAR T-cell growth at early times (due to c 3 < −θ), yet once the Dex has 336 cleared the CAR T-cells become exhausted, no longer proliferating enough to keep up 337 with natural death or facilitate tumor cell killing. CAR T-cell exhaustion, indicated by 338 a decrease in κ 2 , is a primary cause of tumor progression as determined by the increase 339 in the predicted final tumor cell population, θ/κ 2 (Fig 6). Importantly, this 340 Dex-induced shift from CAR T-cell proliferation to exhaustion is highlighted by the 341 differences in phase space trajectories between treatment success and treatment failure 342 presented in Fig 5.

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A notable feature of the mathematical model is the fact that it captures a wide 344 range of dynamics observed in multiple experimental conditions [5]. This is despite its 345 relative simplicity compared to other mathematical models of immunotherapies [21][22][23][24]. 346 A recent commentary regarding predator-prey like models, including the model 347 presented here, is the possibility of oscillating solutions which are unlikely to be 348 observed in patients [25,26]. We note that the coexistence equilibrium is accompanied 349 with phase-space trajectories that accurately describe experimental data. This includes 350 scenarios of treatment success and tumor death (x = 0), allowing for informative and 351 quantitative biological inference.  [25,27], a population of macrophages [24], or explicitly accounting for 360 the pharmacodynamic and pharmacokinetics of CAR T-cell dynamics [28]. Interestingly, 361 recent theoretical work has shown that a two T-cell type predator-prey model with 362 Holling Type I interactions can, in the appropriate limits and conditions, reduce to a 363 single T-cell type predator-prey model with a Holling Type II interaction [23]. While assay is an in vitro system lacking an immune system naturally limits the model 371 complexity that is experimentally accessible. Related to this is the clearance rate of the 372 Dexamethasone, assumed here to have a fixed value of approximately 200 minutes. In 373 patient populations, some level of variation in the clearance rate is to be expected due 374 to physiological differences [12,13]. Future work examining how variation in the 375 clearance rate affects treatment success would be of interest. Furthermore, the fact that 376 T-cells are non-adherent to the cell killing assay precludes proposed models that require 377 high temporal resolution of the T-cell dynamics. Presently, our experimental protocol 378 includes only 2 datapoints for the CAR T-cells: the initial and final timepoints. Translating our findings to clinical applications requires refining understanding of the 389 treatment success or failure threshold in terms of clinically accessible information for a 390 typical GBM patient. Presently, typical clinically relevant Dex dosage levels for GBM 391 related inflammation are believed to be below the threshold of Dex-induced treatment 392 failure identified in this study [7]. However, as advances in personalized medicine 393 continue to develop patient-specific treatment plans, the question is no longer how much 394 Dex is too much, but instead how many CAR T-cells are too few? This question is 395 essential for designing patient specific adaptive therapies and in use of clinical decision 396 support software. Furthermore, it requires knowledge of the spatial extent of individual 397 tumors, the in vivo spatial heterogeneity of CAR T-cells and Dexamethasone 398 concentrations, and patient response and tolerance to timed-drug delivery.

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A growing subject of importance is understanding sex and age-based differences in 400 the immunological responses of patient derived cell lines, and how those difference 401 translate to an individual level in clinical applications [29]. In this work, all GBM cell 402 lines were derived from male patients of a similar age (43, 52, and 59 years old), 403 suggesting that future in vitro work would benefit from including a greater diversity of 404 patients across both age and sex.

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The strategy of adaptive therapy involves reducing cancer killing treatments away 406 from the maximum tolerated dosages, as they can lead to the emergence of treatment 407 resistant clones. Instead, these therapies are aimed toward minimum necessary dosages 408 in order to maintain genetically diverse tumor populations that remain susceptible to 409 treatment [30]. In such scenarios it becomes vital to know if the reduced CAR T-cell 410 dosing begins approaching the treatment success or failure threshold in comparison to 411 the Dex dosage that patient is likely to be receiving already.

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Alternatively, one can vary the concentration and timing of the Dexamethasone 413 dosages to still provide therapeutic levels of Dex yet avoid compromising CAR T-cell 414 efficacy. Previous theoretical work analysing pulsed drug delivery shows promise for this 415 alternative approach [31]. Yet still, another treatment strategy could be patient preconditioning with Dexamethasone followed with delayed, and perhaps pulsed, CAR 417 T-cell delivery. Recent simulated studies investigating preconditioning with 418 chemotherapy [32] or targeted radionuclide therapy [33] followed with CAR T-cells 419 suggests that combination pretreatment and time-delay approaches have clinical value, 420 in particular for providing therapeutic dosages at lower total concentrations. Based on 421 the duration of observable changes to the phase-space trajectory in Fig 5, we suggest a 422 time-delay of 2-3 Dexamethasone half-lives.

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While adaptive therapy protocols have yet to be fully implemented in CAR T-cell 424 treatment plans, data driven methods such as clinical decision support systems and 425 other machine learning inspired approaches have been proposed for patient 426 monitoring [34]. Here, algorithms are trained on historical patient treatment data in an 427 effort to assess the likelihood that new patients will develop cytokine release syndrome 428 or immune effector cell-associated neurotoxicity syndrome as a result of CAR T-cell spatially-dependent models that can accurately account for observed variation. Recent 440 work in this direction has shown promise, demonstrating the ability of mathematical 441 models to combine genotypic evolution with spatial aggregation to describe 442 heterogeneous tumor growth [35].

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In this work, we present an analysis of experimental data designed to untangle the 445 interaction between glioblastoma cancer cells, CAR T-cells, and the anti-inflammatory 446 glucocorticoid, Dexamethasone. We examined three different human derived primary 447 brain tumor glioblastoma cell lines and found that Dexamethasone can act to promote 448 tumor growth and exhaust CAR T-cells, thereby undermining treatment success. In