Simple biophysical model of tumor evasion from immune system control

Abstract

The competitive nonlinear interplay between a tumor and the host's immune system is not only very complex but is also time-changing. A fundamental aspect of this issue is the ability of the tumor to slowly carry out processes that gradually allow it to become less harmed and less susceptible to recognition by the immune system effectors. Here we propose a simple epigenetic escape mechanism that adaptively depends on the interactions per time unit between cells of the two systems. From a biological point of view, our model is based on the concept that a tumor cell that has survived an encounter with a cytotoxic T-lymphocyte (CTL) has an information gain that it transmits to the other cells of the neoplasm. The consequence of this information increase is a decrease in both the probabilities of being killed and of being recognized by a CTL. We show that the mathematical model of this mechanism is formally equal to an evolutionary imitation game dynamics. Numerical simulations of transitory phases complement the theoretical analysis. Implications of the interplay between the above mechanisms and the delivery of immunotherapies are also illustrated.

Abscopal Benefits of Localized Radiotherapy Depend on Activated T-cell Trafficking and Distribution between Metastatic Lesions

“…A myriad of factors contribute to this challenge, including (i) heterogeneity of mechanisms a tumor can use to resist immune attack; (ii) heterogeneity of the capacity for an anticancer response by different components of the immune system; and (iii) anatomic-and time-dependent treatment effects. Numerous mathematical models have been developed to describe tumor-immune interactions at different phases of tumor progression (18)(19)(20) or to look at different pathways that can be exploited for immunotherapy (21)(22)(23)(24)(25). However, to our knowledge, models of metastatic cancer and both local and systemic immune system interactions currently do not exist.…”

A model for effects of adaptive immunity on tumor response to chemotherapy and chemoimmunotherapy

“…However, some studies have employed stochastic differential equations, to capture natural fluctuations in immune levels. Notable among such studies are Caravagna et al [28], D'Onofrio [29], and D'Onofrio and Ciancio [30]; these works showed that stochastic effects can have a significant influence on tumor control.…”

“…The term "immunoediting" [33] has been variously applied to all such forms of evolution, albeit without a consensus yet on its precise definition. Mathematical models have been developed to capture the effects of such time-evolution processes [30,34].…”

Mathematical models of immune-induced cancer dormancy and the emergence of immune evasion

“…Other theoretical investigations have been made [32,[34][35][36][37]40], but these lacked a connection to experimental cancer dormancy data. We have made many simplifying assumptions in this work to distil the process of cancer escape down to the fundamental players: cancer cells and CTLs.…”

“…Additionally, in the same paper, the role of immunoediting in cancer evasion through mutation to a resistant clone was studied analytically. Effects of both direct cell contact [37,38] and bounded noise [39] have also been investigated. Interestingly, a spatio-temporal model of emerging cancer cell resistance suggests that escape may occur through declining recognition or increasing resistance (or both) [40].…”