Integration of immune cell-target cell conjugate dynamics changes the time scale of immune control of cancer

The human immune system can recognize, attack, and eliminate cancer cells, but cancers can escape this immune surveillance. The dynamics of these cancer control mechanisms by cells of the adaptive immune system can be captured by variants of ecological predator-prey models. These dynamical systems can describe the interaction of cancer cells and, e.g., effector T cells to form tumor cell-immune cell conjugates, cancer cell killing, immune cell activation, and T cell exhaustion. Target (tumor) cell-T cell conjugation is integral to the adaptive immune systems cancer control or immunotherapy dynamics. However, it is incompletely understood whether conjugate dynamics should be explicitly included in mathematical models of cancer-immune interactions. Here, we analyze the dynamics of a cancer-effector T cell system regarding the impact of explicitly modeling the conjugate compartment to elucidate the role of cellular conjugate dynamics. We formulate a deterministic modeling framework to compare possible equilibria and their stability, such as tumor extinction, tumor-immune coexistence (tumor control), or tumor escape. We also formulate the stochastic analog of this system to analyze the impact of demographic fluctuations that arise when cell populations are small. We find that explicit consideration of a conjugate compartment can change long-term steady-state, critically change the time to reach an equilibrium, alter the probability of tumor escape, and lead to very different extinction time distributions. Thus, we demonstrate the importance of the conjugate compartment in defining tumor-effector interactions. Accounting for transitionary compartments of cellular interactions may better capture the dynamics of tumor control and progression.