Mathematical Models for Immune Checkpoint Blockade and Delayed Responses

Abstract

Immune checkpoint blockades have transformed oncology, yet a persistent clinical puzzle remains: Why do some patients exhibit delayed responses, with tumours that initially grow or plateau before abruptly regressing? This thesis tackles that question with a multi-scale mathematical study that couples analytically tractable ordinary differential equation (ODE) models with a spatial, stochastic agent-based model (ABM). In ODE form, we show that delayed responses can arise intrinsically, without imposed time lags, via costimulation bottlenecks and slow passages near tipping points associated with special saddle-node bifurcations. We map delayed responses to a statistically-thin part of the model parameter space, suggesting their rarity. Our ODE results enable us to propose an immune profile framework that maps patient prognosis to the natural strength of their immune system---an idea that has become increasingly popular in clinical research since COVID-19.

To move beyond mean-field assumptions, we develop an ABM tracking cancer cells, dendritic cells (DCs), CD8+ T cells, and Tregs at single-cell resolution, with molecular attributes and cell-level rules. Mechanistically, our ABM explains why combination therapy outperforms monotherapy: anti-CTLA-4 'reopens the gate' while anti-PD-1 'lifts the brake', yielding a larger and fitter effector CD8+ T cell pool. Our results supports two hypothesised mechanisms of action underlying CTLA-4 blockades---Treg depletion in humans and Treg-driven stripping of B7 ligands---highlighting how depleting suppressors and protecting strategically-important ligands reopen the costimulatory pathway. We characterise delayed responses as an alignment of a multitude of immune events, followed by a fast cascade of killing. This suggests that DC therapies prioritising net DC recruitment and T cell therapies that prioritise tumour-infiltrating lymphocyte (TIL) survivability synergise well with immune checkpoint blockades.