Abstract

BackgroundIn this work a mathematical model describing the growth of a solid tumour in the presence of an immune system response is presented. Specifically, attention is focused on the interactions between cytotoxic T-lymphocytes (CTLs) and tumour cells in a small, avascular multicellular tumour. At this stage of the disease the CTLs and the tumour cells are considered to be in a state of dynamic equilibrium or cancer dormancy. The precise biochemical and cellular mechanisms by which CTLs can control a cancer and keep it in a dormant state are still not completely understood from a biological and immunological point of view. The mathematical model focuses on the spatio-temporal dynamics of tumour cells, immune cells, chemokines and “chemorepellents” in an immunogenic tumour. The CTLs and tumour cells are assumed to migrate and interact with each other in such a way that lymphocyte-tumour cell complexes are formed. These complexes result in either the death of the tumour cells (the normal situation) or the inactivation of the lymphocytes and consequently the survival of the tumour cells. In the latter case, we assume that each tumour cell that survives its “brief encounter” with the CTLs undergoes certain beneficial phenotypic changes.ResultsWe explore the dynamics of the model under these assumptions and show that the process of immuno-evasion can arise as a consequence of these encounters. We show that the proposed mechanism not only shape the dynamics of the total number of tumor cells and of CTLs, but also the dynamics of their spatial distribution. We also briefly discuss the evolutionary features of our model, by framing them in the recent quasi-Lamarckian theories.ConclusionsOur findings might have some interesting implication of interest for clinical practice. Indeed, immuno-editing process can be seen as an “involuntary” antagonistic process acting against immunotherapies, which aim at maintaining a tumor in a dormant state, or at suppressing it.ReviewersThis article was reviewed by G. Bocharov (nominated by V. Kuznetsov, member of the Editorial Board of Biology Direct), M. Kimmel and A. Marciniak-Czochra.

Highlights

  • In this work a mathematical model describing the growth of a solid tumour in the presence of an immune system response is presented

  • Chemotactic motion of immune system cells is a hallmark of the defence of the human body against “non-self agents”, including tumours, since cells belonging to both the innate immune system (e.g. Natural Killers, Macrophages, Dendritic Cells, etc.. [3]) and adaptive immune system (e.g. Cytotoxic T Lymphocites, etc.. [3]) are able to reach their targets thanks to the gradients of various kinds of chemicals [3,14], e.g. inflammation-related substances produced by tumour cells

  • Chemotaxis is of paramount importance in the interplay between tumours and the immune system, since it influences the control of tumour growth and the immune surveillance

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Summary

Introduction

In this work a mathematical model describing the growth of a solid tumour in the presence of an immune system response is presented. Tumour cells are characterized by a large number of genetic and epigenetic events leading to the appearance of specific antigens (e.g. mutated proteins, under/overexpressed normal proteins and many others) triggering reactions by the both the innate and the adaptive immune system [3,4,5,6,7]. These observations have provided a theoretical basis to the empirical hypothesis of immune surveillance, i.e. that the immune system may act to eliminate tumours [8], only recently experimentally and epidemiologically confirmed [9]. Chemotaxis is of paramount importance in the interplay between tumours and the immune system, since it influences the control of tumour growth and the immune surveillance

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