Date Published: March 27, 2015
Publisher: Public Library of Science
Author(s): Claire Christophe, Sabina Müller, Magda Rodrigues, Anne-Elisabeth Petit, Patrick Cattiaux, Loïc Dupré, Sébastien Gadat, Salvatore Valitutti.
The dynamics of the interaction between Cytotoxic T Lymphocytes (CTL) and tumor cells has been addressed in depth, in particular using numerical simulations. However, stochastic mathematical models that take into account the competitive interaction between CTL and tumors undergoing immunoediting, a process of tumor cell escape from immunesurveillance, are presently missing. Here, we introduce a stochastic dynamical particle interaction model based on experimentally measured parameters that allows to describe CTL function during immunoediting. The model describes the competitive interaction between CTL and melanoma cell nodules and allows temporal and two-dimensional spatial progression. The model is designed to provide probabilistic estimates of tumor eradication through numerical simulations in which tunable parameters influencing CTL efficacy against a tumor nodule undergoing immunoediting are tested. Our model shows that the rate of CTL/tumor nodule productive collisions during the initial time of interaction determines the success of CTL in tumor eradication. It allows efficient cytotoxic function before the tumor cells acquire a substantial resistance to CTL attack, due to mutations stochastically occurring during cell division. Interestingly, a bias in CTL motility inducing a progressive attraction towards a few scout CTL, which have detected the nodule enhances early productive collisions and tumor eradication. Taken together, our results are compatible with a biased competition theory of CTL function in which CTL efficacy against a tumor nodule undergoing immunoediting is strongly dependent on guidance of CTL trajectories by scout siblings. They highlight unprecedented aspects of immune cell behavior that might inspire new CTL-based therapeutic strategies against tumors.
CTL destroy virally infected cells and tumor cells via the secretion of lytic molecules stored in intracellular granules . CTL are key components of the anti-cancer immune response and it is therefore crucial to study in depth, and possibly enhance, their biological responses against tumors . Accordingly, therapeutic protocols designed to potentiate CTL responses against tumor cells are currently at the frontline of cancer clinical research . The molecular mechanisms of tumor recognition by CTL and the biological responses of CTL against tumors have been thoroughly investigated. However, since CTL/tumor cell interactions are highly dynamic, it is crucial to define the cell motility and interaction parameters that might influence CTL efficacy against tumor cells and tumor eradication.
The theoretical model presents the stochastic evolution of a growing tumor undergoing immunoediting, facing motile CTL that have the capacity to kill tumor cells. The model provides a basis to run multiple simulations, which are used to compute the probability of success/loss in tumor eradication. All the experimental parameters used for the numerical simulations of the model are issued from  or have been measured by us in this study (Supporting Information S1 Table lists the parameters used in the model).
In the present work, we applied mathematical modeling to dissect the multiparametric confrontation between CTL and a growing tumor nodule that undergoes immunoediting. We report that, for the given parameters, the success of a CTL population in tumor eradication strongly depends on the rate of CTL/tumor nodule productive collisions occurring during the initial period of CTL/tumor confrontation. In this view, we show that, when keeping the number of CTL constant, a bias in CTL motility inducing their attraction towards the tumor nodule is a major CTL functional parameter favoring CTL/tumor early collisions and tumor eradication.