Modelling the Immune Response to Cancer: An Individual-Based Approach Accounting for the Difference in Movement Between Inactive and Activated T Cells

Abstract

A growing body of experimental evidence indicates that immune cells move in an unrestricted search pattern if they are in the pre-activated state, whilst they tend to stay within a more restricted area upon activation induced by the presence of tumour antigens. This change in movement is not often considered in the existing mathematical models of the interactions between immune cells and cancer cells. With the aim to fill such a gap in the existing literature, in this work we present a spatially structured individual-based model of tumour-immune competition that takes explicitly into account the difference in movement between inactive and activated immune cells. In our model, a Lévy walk is used to capture the movement of inactive immune cells, whereas Brownian motion is used to describe the movement of antigen-activated immune cells. The effects of activation of immune cells, the proliferation of cancer cells and the immune destruction of cancer cells are also modelled. We illustrate the ability of our model to reproduce qualitatively the spatial trajectories of immune cells observed in experimental data of single-cell tracking. Computational simulations of our model further clarify the conditions for the onset of a successful immune action against cancer cells and may suggest possible targets to improve the efficacy of cancer immunotherapy. Overall, our theoretical work highlights the importance of taking into account spatial interactions when modelling the immune response to cancer cells.

Sputum from chronic obstructive pulmonary disease patients inhibits T cell migration in a microfluidic device

“…In our study, we applied, for the first time, a microfluidics‐based assay to the quantitative analysis of T cell migration and chemotaxis in COPD. The results showed that T cells from COPD patients and healthy controls migrated in the two DTT control gradient groups (Medium:DTT = 1:1 or PBS:DTT = 1:1), which is consistent with the known basal motility of activated T cells . However, the migration of T cells from COPD patients and healthy controls was significantly inhibited in the presence of a gradient of sputum supernatant from COPD patients compared to the DTT gradient control groups.…”

“…The results showed that T cells from COPD patients and healthy controls migrated in the two DTT control gradient groups (Medium:DTT = 1:1 or PBS:DTT = 1:1), which is consistent with the known basal motility of activated T cells. 21,[24][25][26] However, the migration of T cells from COPD patients and healthy controls was significantly inhibited in the presence of a gradient of sputum supernatant from COPD patients compared to the DTT gradient control groups. We further tested the migration of T cells from both COPD patients and healthy subjects in the Medium & DTT and PBS & DTT controls with increasing DTT concentration (i.e., DTT:Medium or DTT:PBS = 1:1 to have a final DTT concentration of 0.05%; 2:1 to have a final DTT concentration of 0.067%; 1:0 to have the final DTT concentration of 0.1%).…”

Mathematical modeling of tumor-immune cell interactions

“…Overall, the results of the model imply that more effective immunotherapy treatment protocols could be achieved by modifying the injection location and schedule. (Macfarlane et al, 2018) presented a spatially structured model of tumor-immune competition taking into account the difference in movement between activated and inactive immune cells.…”

Quantitative Systems Pharmacology Approaches for Immuno‐Oncology: Adding Virtual Patients to the Development Paradigm

“…Other modeling formalisms that describe and investigate different mechanisms of cancer and immune cell dynamics include: (i) a spatial model that accounts for the difference in trajectories between pre-activated and activated immune cells, 56 (ii) a model that accounts for the interaction between multiple tumors competing for resources and immune response, 57 and (iii) models that investigate the roles of oncogenes and anti-oncogenes in controlling cell proliferation, and that explores how immune cells respond to inactivation of the driving oncogene. [58][59][60] Not all models listed in the lineage map Figure 1 are reviewed in this section; however, the entire list of these models is available in the Supplementary Material.…”