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. Variants of ecological predator-prey models can capture the dynamics of such cancer control mechanisms by adaptive immune system cells. These dynamical systems describe, e.g., tumor cell-effector T cell conjugation, immune cell activation, cancer cell killing, and T cell exhaustion. Target (tumor) cell-T cell conjugation is integral to the adaptive immune system's cancer control and immunotherapy. However, whether conjugate dynamics should be explicitly included in mathematical models of cancer-immune interactions is incompletely understood. Here, we analyze the dynamics of a cancer-effector T cell system and focus on the impact of explicitly modeling the conjugate compartment to investigate 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 (i) change long-term steady-state, (ii) critically change the time to reach an equilibrium, (iii) alter the probability of tumor escape, and (iv) lead to very different extinction time distributions. Thus, we demonstrate the importance of the conjugate compartment in defining tumor-effector T cell interactions. Accounting for transitionary compartments of cellular interactions may better capture the dynamics of tumor control and progression.