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Strategies for tumor elimination and control under immune evasion and chemotherapy resistance

Nazanin Mokari, Bryce Morsky

Abstract

The evolutionary and ecological dynamics of tumors under immune responses and therapeutic interventions pose major challenges to long-term treatment success. Although treatment may initially achieve short-term disease control, resistant cancer cell subpopulations often arise, leading to relapse with more aggressive and treatment-resistant forms of the disease. Here, we develop and analyze mathematical models describing the interactions among effector cells, chemo-resistant tumor cells, and immuno-resistant tumor cells under distinct immune-evasion strategies. The models incorporate competition and cooperation between resistant and sensitive tumor subpopulations. We identify threshold conditions governing tumor persistence, elimination, and phenotype dominance under varying therapeutic intensities. These findings provide a theoretical framework for designing targeted and combination therapies and offer insights into strategies for mitigating the treatment resistance.

Strategies for tumor elimination and control under immune evasion and chemotherapy resistance

Abstract

The evolutionary and ecological dynamics of tumors under immune responses and therapeutic interventions pose major challenges to long-term treatment success. Although treatment may initially achieve short-term disease control, resistant cancer cell subpopulations often arise, leading to relapse with more aggressive and treatment-resistant forms of the disease. Here, we develop and analyze mathematical models describing the interactions among effector cells, chemo-resistant tumor cells, and immuno-resistant tumor cells under distinct immune-evasion strategies. The models incorporate competition and cooperation between resistant and sensitive tumor subpopulations. We identify threshold conditions governing tumor persistence, elimination, and phenotype dominance under varying therapeutic intensities. These findings provide a theoretical framework for designing targeted and combination therapies and offer insights into strategies for mitigating the treatment resistance.

Paper Structure

This paper contains 14 sections, 1 theorem, 24 equations, 11 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Methods
  3. Model Summary
  4. Immune Evasion
  5. Results
  6. Equilibrium and Stability Analysis
  7. Tumor-free equilibrium:
  8. $T_1$-only equilibrium:
  9. $T_2$-only equilibrium:
  10. Coexistence equilibria (CE):
  11. Bifurcation diagrams for Immuno-resistance Only
  12. Bifurcation Diagrams for Chemo-resistance and Immuno-resistance
  13. Discussion
  14. Further Bifurcation Diagrams

Key Result

Proposition 1

The tumor-free equilibrium $\mathcal{E}_0 = (0,0,\sigma/(\delta+\omega\chi))$ is stable iff Otherwise, the model admits a nontrivial equilibrium in which at least one tumor population persists. $\blacktriangleleft$$\blacktriangleleft$

Figures (11)

  • Figure 1: Tumor ($T_i$) and effector ($E$) cells can combine into a conglomerate ($C_i$) for $i=1,2$. $C_i$ may then dissociate leaving either one or no cells damaged with damaged cells marked by $\dagger$. Rates of these reaction are $\gamma_{i,j}$ for $T_i$ and for $j=-1,1,2,3$.
  • Figure 2: Bifurcation diagrams when $T_1$ employs immune checkpoint evasion. $\theta_1=0.6$ and $\theta_1=0.8$ for the $T_1$-only and $T_2$-only equilibria, respectively.
  • Figure 3: Bifurcation diagrams when $T_1$ employs reduced antigen presentation. $\theta_1 = 0.6$ and $\theta_1 = 0.8$ for the $T_1$-only and $T_2$-only equilibria, respectively.
  • Figure 4: Bifurcation diagrams for $\chi$, $\delta$, and $\sigma$ when $T_2$ is chemo-resistant and $T_1$ employs immune checkpoint evasion. $\theta_1=\theta_2=0.5$ and $\theta_1=0.5 < \theta_2=0.8$ in the left and right columns, respectively.
  • Figure 5: Bifurcation diagrams for $\theta_1$, $\mu$, and $\rho$ when $T_2$ is chemo-resistant and $T_1$ employs immune checkpoint evasion. Except when varying $\theta_1$, $\theta_1=\theta_2=0.5$ and $\theta_1=0.5 < \theta_2=0.8$ in the left and right columns, respectively.
  • ...and 6 more figures

Theorems & Definitions (1)

  • Proposition 1