## 4 Discussion and Conclusions
(**B**) Impact of ZA concentration and exposure time of tumor cells on V\(\gamma\)9\(\prime\)82 T cell immune response. In this cartoon, a patient is represented during intravenous ZA infusion, and the possible effects on his tumor cells localised in the gut are also represented. We aim to translate the knowledge acquired by our models on in vitro cell experiments onto patients by focusing on the events occurring in tumor cells upon long treatment of ZA. Finally, we show that IPP accumulation acts on the activation and proliferation of \(\gamma\delta\) T cells, promoting their anti-tumoral function. **(C)** Illustration of the inhibition mechanism of ZA on FPP synthase determined by a conformational change of enzyme. The first conformation shows in the a pocket site the Mg\({}^{2+}\) involved in the ZA binding. After this opened conformation follows a partially closed conformation, in which the catalytic site is occupied by ZA. The last conformation is the most stable thank to the IPP binding that determines the closed and inactive function of the enzyme [45; 50]. It is interesting to note that [PERSON] and colleagues repeated the pulse experiment in 2011 [51], changing the modality of treatment (starvation of serum for 18 h before ZA treatment) and the incubation time (3 h instead of 1 h). This may suggest the possibility that the authors were not completely satisfied with the original experimental procedure and why some aspects of it, not explicit and not incorporated in the model, may underlie the different dynamics of ZA uptake in the two assays. Finally, the analytic methods used have a lower detection limit for ZA and IPP concentrations, which may determine some unappreciated errors that could not be added to the model. Regarding the Ag dynamics sub-model, while the formulation differs between Model 1 and Model 2, both models can still follow the data well, both for continuous and pulse experiments. Model 2 considers the ZA + enzyme + Ag complex formation and can be considered more representative of the real biological processes. To maintain a biological correspondence between two \(G(t)\) models equations, the same parameter for the total IPP elimination rate (\(k_{XG}^{tot}\)) was used, although its computation is model-specific. In particular, \(k_{XG}^{tot}\) was evaluated as the sum of two different terms: the first term, the irreducible antigen elimination rate (\(k_{XG}\)), is equal in both formulations; the second term in Model 1 represents the antigen elimination rate that can be suppressed in the presence of ZA (\(k_{XG}\)), and in Model 2, it represents the antigen elimination rate per percentage of an unbound enzyme (\(k_{XGU}\)). The numerical evaluations for \(k_{XG}^{tot}\) in two models for pulse and continuous experiments are reported in Tables 3 and 4. While models of the response to therapy and the dynamical models for body distribution have already been reported for ZA [36; 52], a model of the dynamics of cellular response to ZA has not yet been formulated to the best of our knowledge. In clinical cancer, the effect of ZA on metastatic bone disease is mostly related to its ability to decrease osteoclast-mediated bone resorption and its direct anti-tumor activity. Thus, a mathematical model that incorporates the dynamics of cellular response to ZA and the accumulation of IPP appears to be needed. Our models provide a tool to predict the effects of ZA treatment on the accumulation of IPP, focusing attention on the timing of the accumulation to better perform \(\gamma\delta\) T cell expansion assays applied to immunotherapeutic procedures. The importance of this issue is made evident by a recent publication [38], in which the authors optimised the protocol to expand efficient V\(\gamma\)9V\(\delta\)2 T cells by restimulating short-term-expanded \(\gamma\delta\) T cells with phospho-modified Vitamin C (pVC).