Modeling cancer immunoediting in tumor microenvironment with system characterization through the ising-model Hamiltonian

Abstract

Background and objective Cancer Immunoediting (CI) describes the cellular-level interaction between tumor cells and the Immune System (IS) that takes place in the Tumor Micro-Environment (TME). CI is a highly dynamic and complex process comprising three distinct phases (Elimination, Equilibrium and Escape) wherein the IS can both protect against cancer development as well as, over time, promote the appearance of tumors with reduced immunogenicity. Herein we present an agent-based model for the simulation of CI in the TME, with the objective of promoting the understanding of this process. Methods Our model includes agents for tumor cells and for elements of the IS. The actions of these agents are governed by probabilistic rules, and agent recruitment (including cancer growth) is modeled via logistic functions. The system is formalized as an analogue of the Ising model from statistical mechanics to facilitate its analysis. The model was implemented in the Netlogo modeling environment and simulations were performed to verify, illustrate and characterize its operation. Results A main result from our simulations is the generation of emergent behavior in silico that is very difficult to observe directly in vivo or even in vitro. Our model is capable of generating the three phases of CI; it requires only a couple of control parameters and is robust to these. We demonstrate how our simulated system can be characterized through the Ising-model energy function, or Hamiltonian, which captures the “energy” involved in the interaction between agents and presents it in clear and distinct patterns for the different phases of CI. Conclusions The presented model is very flexible and robust, captures well the behaviors of the target system and can be easily extended to incorporate more variables such as those pertaining to different anti-cancer therapies. System characterization via the Ising-model Hamiltonian is a novel and powerful tool for a better understanding of CI and the development of more effective treatments. Since data of CI at the cellular level is very hard to procure, our hope is that tools such as this may be adopted to shed light on CI and related developing theories.

Use of monoclonal antibodies in cancer immunotherapy: types and mechanisms of action

“…Second, the equilibrium phase, characterized by the dynamic equilibrium between tumor cells and the immune system; these cells may remain quiescent or continue to accumulate changes that modulate the expression of tumor-specific antigens or stress-induced antigens. Third, the escape phase, in which the continuous pressure exerted on tumor cells causes a decrease in immunogenicity and immunosuppressive mechanisms that attenuate the immune response and favor tumor growth and invasion of other organs (metastasis) 8 .…”

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“…An interesting perspective to formulate models is to consider the cell as a basic unit, i.e., a virtual cell [124,125], with a set of rules for behaviour. The unit is sometimes called an "agent", with rules to proliferate, reproduce or transform depending on interactions with its external microenvironment [111] and probabilistic rules [126]. Different types of cells (tumour, immune or dendritic) constitute different agents [127].…”

Mathematically mapping the network of cells in the tumor microenvironment

“…However, the TME exhibits emergent behavior that cannot be explained by individual cell- or protein types 3,4 and focusing only on individual parts of the TME hinders the development of more comprehensive treatment strategies. For example, the tumor necrosis factor alpha (TNF-α) protein can elicit both a pro- or anti-tumor reaction based on further context cues in the TME 5 .…”