# Immunoediting: evidence of the multifaceted role of the immune system in self-metastatic tumor growth

- Heiko Enderling
^{1}, - Lynn Hlatky
^{1}and - Philip Hahnfeldt
^{1}Email author

**9**:31

**DOI: **10.1186/1742-4682-9-31

© Enderling et al.; licensee BioMed Central Ltd. 2012

**Received: **15 March 2012

**Accepted: **16 May 2012

**Published: **28 July 2012

## Abstract

### Background

The role of the immune system in tumor progression has been a subject for discussion for many decades. Numerous studies suggest that a low immune response might be beneficial, if not necessary, for tumor growth, and only a strong immune response can counter tumor growth and thus inhibit progression.

### Methods

We implement a cellular automaton model previously described that captures the dynamical interactions between the cancer stem and non-stem cell populations of a tumor through a process of self-metastasis. By overlaying on this model the diffusion of immune reactants into the tumor from a peripheral source to target cells, we simulate the process of immune-system-induced cell kill on tumor progression.

### Results

A low cytotoxic immune reaction continuously kills cancer cells and, although at a low rate, thereby causes the liberation of space-constrained cancer stem cells to drive self-metastatic progression and continued tumor growth. With increasing immune system strength, however, tumor growth peaks, and then eventually falls below the intrinsic tumor sizes observed without an immune response. With this increasing immune response the number and proportion of cancer stem cells monotonically increases, implicating an additional unexpected consequence, that of cancer stem cell selection, to the immune response.

### Conclusions

Cancer stem cells and immune cytotoxicity alone are sufficient to explain the three-step “immunoediting” concept – the modulation of tumor growth through inhibition, selection and promotion.

## Background

Tumor growth dynamics are usually marked by the defining features of immunoediting; initial growth amidst productive immune response, an equilibrium state where tumor growth and suppression by immune response are more or less in balance, and malignant progression, as tumor subpopulations selected for immune resistance or evasion during the previous phase drive tumor expansion [1, 4]. The selection of tumor cells resistant to infiltrating immune cells might explain the strong correlation between number of tumor-associated macrophages and poor prognosis [11]. The tumor-promoting effect of macrophages and the immune system in general has been attributed to second-order events such as production of angiogenic factors and matrix metalloproteinases (MMPs), because the primary cytotoxic cell killing is intuitively tumor-inhibiting [11]. However, it has been shown recently that cell kill might paradoxically benefit tumor progression in heterogeneous tumors [12] and in particular, that a sufficient source for this heterogeneity may lie in the tumor-intrinsic interactions between cancer stem cell and non-stem cell fractions that give rise to a ‘self-metastatic’ phenotype [13, 14]. Here we present a model of self-metastatic tumor growth subject to immune action, and show in this setting that the basic cytotoxic function of the immune system alone can reproduce the experimentally- and clinically-observed multifaceted features of immunoediting – elimination, equilibrium, and escape.

## Methods

_{max}, after which they become unviable and die. Throughout this study we assumed ρ

_{max}= 10, in line with previous observations of fast tumor growth [26]. With every cell division, cancer stem cells can either divide symmetrically with probability p

_{s}to produce two daughter cancer stem cells, or asymmetrically with probability 1-p

_{s}to produce a cancer stem cell and a non-stem progenitor cancer cell. We set p

_{s}= 0.01 (i.e., 1%) to reflect the low frequency of cancer stem cells reported in the literature [32]. To initiate the simulation of tumor growth and immune response, we seed single cancer stem cells in the center of a computational domain of 350 × 350 grid points, representing a square lattice of 3,500 μm × 3500 μm subdivided into 100 μm

^{2}units that can hold at the most one cell at any time. Cells have a random motility μ (in units of cell widths per day) and accordingly, are considered for migration to an adjacent unit every 1/μ days. In line with previous studies we set μ = 15 (i.e., 15 cell widths or ≈150 μm day

^{-1}) [13]. Cells can divide after reaching ‘maturation’, which for simplicity is attempted every 1 day. When it is time to attempt migration or division, the moving cell, or the progeny of the dividing cell, will be randomly assigned to an adjacent vacant unit. If there is no adjacent vacant unit the movement (or division) does not take place. Accordingly, a cell that is completely surrounded by other cells is forced to become quiescent, and migration and proliferation are only possible once adjacent lattice points become vacant again. For simplicity we ignore tumor cell interaction with host cells in the immediate tumor microenvironment, as well as density-dependent modulation of cellular fates [33].

*c*is modeled as a diffusing continuum

*d*

_{ c }= 10

^{-9}cm

^{2}s

^{-1}is the diffusion coefficient comparable to cell motility estimated experimentally [34] and

*β*is the decay rate of immune reactants. We further assume immune system sources to be located at the domain boundary, and as the tumor grows, immune agents are produced with either (

*i*) a constant strength ξ, reflecting the probability of cell kill at the boundary ∂Ω of the total domain Ω, from which it follows that 0 ≤ ξ ≤ 1, equated with the (presumed fixed) boundary concentration, i.e.,

or (*ii*) dependent on the tumor size in response to a growing cell population, as later described. The probability *α*of immune reactant-induced death for a non-stem cancer cell at position (*x**y*) at time *t*is equated to the immune reactant concentration at this position at that time, i.e., *α=c*(*x**y**t*). In line with recent literature we assume cancer stem cells evade the immune response [6, 7, 35, 36]. A schematic of the cell dynamics and the hybrid two-layer architecture is shown in Figure 2.

## Results

### Dual effect of the immune system

**Simulation statistics**

ξ | Total population | Cancer stem cells | Cancer stem cell ratio (%) |
---|---|---|---|

0 | 16,749 | 15 | 0.09 |

0.04 | 29,596 | 44 | 0.15 |

0.1 | 58,134 | 219 | 0.38 |

0.4 | 25,502 | 1,018 | 3.99 |

1 | 2,365 | 1,177 | 49.8 |

### Self-metastastic morphology and immune selection

### Early and late effects of an adaptive immune response

*m*that diffuses (with comparable diffusion rate d

_{m}= 10

^{-9}cm

^{2}s

^{-1}) into the domain Ω and triggers an immune response at the boundary ${c|}_{\partial \Omega}$according to the strength of the signal there. Specifically,

*P*(

*x*

*y*

*t*) represents the occupation status in the discrete cell layer (1 if a cell is present at (

*x*

*y*) at time

*t*and 0 otherwise). What is seen after simulation is that a small tumor cluster triggers only a low response, whereas a large conglomerate of self-metastases induces a strong immune reaction. Tumor growth dynamics (Figure 5) feature a promotion of tumor growth early on while the immune reaction is low, followed by a late strong reaction that is inhibiting – the early and late function of an initially weak and later strong immune system response to a growing tumor, another effect hypothesized by Prehn [2].

## Discussion

We presented a cellular automaton model of heterogeneous tumor growth and the impact of an induced immune response on tumor dynamics. Intrinsically, without an immune response, a heterogeneous tumor population comprised of cancer stem cells and non-stem progenitors grows as conglomerates of self-metastases [13, 14]. This morphological phenomenon results from the interplay of cell proliferation, cell migration and cell death. With increasing cell death intra-tumoral spatial inhibitions are loosened, which in turn enable cancer stem cell cycling and thus, counter-intuitively, tumor progression. Focusing only on the cytotoxic function of the immune system we were able to observe all immunoediting roles of the immune system: immune promotion at weak immune responses, immunoinhibition at strong immune responses, and immunoselection at all levels. Simulations of our model support a hypothesis previously put forward by Prehn [2, 8–10] that comparable tumor sizes can be observed for weak and strong immune reactions (either side of the peak in Figures 1and 3). Our model augments these studies by highlighting the different tumor compositions expected, including a malignant enrichment in cancer stem cells following a strong immune response. We conclude that tumors that progress to clinical presentation, particularly after strong immune responses, are likely to be heavily enriched in cancer stem cells. Moreover, when the immune system selection force is removed, the initial ratio of cancer stem cells to non-stem cells is re-established, showing that long-term cancer stem cell enrichment requires continuous dynamic maintenance. We propose more generally that a stem-cell-expansive influence may take the form of anything that encourages morphological fingering. Beyond immune response, this could include cell death, or even growth within restricted thin channels, as might be expected e.g. during invasion of host tissue.

## Declarations

### Acknowledgements

The work of P.H. and H.E was supported by DOE-DE-SC0001434, Office of Science (Office of Biological and Environmental Research [BER]), US Department of Energy (to P.H.). The work of L.H. was supported by DOE-DE-SC0002606, Office of Science (Office of Biological and Environmental Research [BER]), US Department of Energy (to L.H.).

## Authors’ Affiliations

## References

- de Visser KE, Eichten A, Coussens LM: Paradoxical roles of the immune system during cancer development. Nat Rev Cancer. 2006, 6: 24-37. 10.1038/nrc1782.View ArticlePubMedGoogle Scholar
- Prehn RT: The immune reaction as a stimulator of tumor growth. Science. 1972, 176: 170-171. 10.1126/science.176.4031.170.View ArticlePubMedGoogle Scholar
- Saudemont A, Quesnel B: In a model of tumor dormancy, long-term persistent leukemic cells have increased B7-H1 and B7.1 expression and resist CTL-mediated lysis. Blood. 2004, 104: 2124-2133. 10.1182/blood-2004-01-0064.View ArticlePubMedGoogle Scholar
- Dunn GP, Bruce AT, Ikeda H, Old LJ, Schreiber RD: Cancer immunoediting: from immunosurveillance to tumor escape. Nat Immunol. 2002, 3: 991-998. 10.1038/ni1102-991.View ArticlePubMedGoogle Scholar
- Levina V, Marrangoni AM, DeMarco R, Gorelik E, Lokshin AE: Drug-selected human lung cancer stem cells: cytokine network, tumorigenic and metastatic properties. PLoS One. 2008, 3: e3077-10.1371/journal.pone.0003077.PubMed CentralView ArticlePubMedGoogle Scholar
- Liu K, Caldwell SA, Abrams SI: Immune selection and emergence of aggressive tumor variants as negative consequences of Fas-mediated cytotoxicity and altered IFN-gamma-regulated gene expression. Cancer Res. 2005, 65: 4376-4388. 10.1158/0008-5472.CAN-04-4269.View ArticlePubMedGoogle Scholar
- Reim F, Dombrowski Y, Ritter C: Immunoselection of Breast and Ovarian Cancer Cells with Trastuzumab and Natural Killer Cells: Selective Escape of CD44high/CD24low/HER2low Breast Cancer Stem Cells. Cancer Res. 2009, 69: 8058-8066. 10.1158/0008-5472.CAN-09-0834.View ArticlePubMedGoogle Scholar
- Prehn RT: An immune reaction may be necessary for cancer development. Theor Biol Med Model. 2006, 3: 6-10.1186/1742-4682-3-6.PubMed CentralView ArticlePubMedGoogle Scholar
- Prehn RT: Does the immune reaction cause malignant transformation by disrupting cell-to-cell or cell-to-matrix communications?. Theor Biol Med Model. 2007, 4: 16-10.1186/1742-4682-4-16.PubMed CentralView ArticlePubMedGoogle Scholar
- Prehn RT: Immunostimulation and immunoinhibition of premalignant lesions. Theor Biol Med Model. 2007, 4: 6-10.1186/1742-4682-4-6.PubMed CentralView ArticlePubMedGoogle Scholar
- Allavena P, Sica A, Garlanda C, Mantovani A: The Yin-Yang of tumor-associated macrophages in neoplastic progression and immune surveillance. Immunol Rev. 2008, 222: 155-161. 10.1111/j.1600-065X.2008.00607.x.View ArticlePubMedGoogle Scholar
- Wodarz D, Komarova N: Can loss of apoptosis protect against cancer?. Trends Genet. 2007, 23: 232-237. 10.1016/j.tig.2007.03.005.View ArticlePubMedGoogle Scholar
- Enderling H, Hlatky L, Hahnfeldt P: Migration rules: tumours are conglomerates of self-metastases. Br J Cancer. 2009, 100: 1917-1925. 10.1038/sj.bjc.6605071.PubMed CentralView ArticlePubMedGoogle Scholar
- Norton L: Conceptual and Practical Implications of Breast Tissue Geometry: Toward a More Effective, Less Toxic Therapy. Oncologist. 2005, 10: 370-381. 10.1634/theoncologist.10-6-370.View ArticlePubMedGoogle Scholar
- Sherratt JA, Nowak MA: Oncogenes, anti-oncogenes and the immune response to cancer: a mathematical model. Proc Biol Sci. 1992, 248: 261-271. 10.1098/rspb.1992.0071.View ArticlePubMedGoogle Scholar
- Owen MR, Sherratt JA: Pattern formation and spatiotemporal irregularity in a model for macrophage-tumour interactions. J Theor Biol. 1997, 189: 63-80. 10.1006/jtbi.1997.0494.View ArticlePubMedGoogle Scholar
- Owen MR, Sherratt JA: Modelling the macrophage invasion of tumours: effects on growth and composition. IMA J Math Appl Med Biol. 1998, 15: 165-185. 10.1093/imammb/15.2.165.View ArticlePubMedGoogle Scholar
- de Pillis LG, Radunskaya AE, Wiseman CL: A validated mathematical model of cell-mediated immune response to tumor growth. Cancer Res. 2005, 65: 7950-7958.PubMedGoogle Scholar
- Mallet DG, de Pillis LG: A cellular automata model of tumor-immune system interactions. J Theor Biol. 2006, 239: 334-350. 10.1016/j.jtbi.2005.08.002.View ArticlePubMedGoogle Scholar
- Eikenberry S, Thalhauser CJ, Kuang Y, Bergstrom CT: Tumor-Immune Interaction, Surgical Treatment, and Cancer Recurrence in a Mathematical Model of Melanoma. PLoS Comp Biol. 2009, 5: e1000362-10.1371/journal.pcbi.1000362.View ArticleGoogle Scholar
- d'Onofrio A: A general framework for modeling tumor-immune system competition and immunotherapy: Mathematical analysis and biomedical inferences. Physica D. 2005, 208: 220-235. 10.1016/j.physd.2005.06.032.View ArticleGoogle Scholar
- Brazzoli I, De Angelis E, Jabin PE: A mathematical model of immune competition related to cancer dynamics. Math Meth Appl Sci. 2010, 33: 733-750.Google Scholar
- Kuznetsov V: Modeling tumor regrowth and immunotherapy. Math Comput Model. 2001, 33: 1275-1287. 10.1016/S0895-7177(00)00314-9.View ArticleGoogle Scholar
- d'Onofrio A, Ciancio A: Simple biophysical model of tumor evasion from immune system control. Phys Rev E. 2011, 84: 031910-View ArticleGoogle Scholar
- d'Onofrio A: Tumor evasion from immune control: Strategies of a MISS to become a MASS. Chaos, Solitons & Fractals. 2007, 31: 261-268. 10.1016/j.chaos.2005.10.006.View ArticleGoogle Scholar
- Enderling H, Anderson ARA, Chaplain MAJ, Beheshti A, Hlatky L, Hahnfeldt P: Paradoxical dependencies of tumor dormancy and progression on basic cell kinetics. Cancer Res. 2009, 69: 8814-8821. 10.1158/0008-5472.CAN-09-2115.View ArticlePubMedGoogle Scholar
- Enderling H, Park D, Hlatky L, Hahnfeldt P: The Importance of Spatial Distribution of Stemness and Proliferation State in Determining Tumor Radioresponse. Math Model Nat Phenom. 2009, 4: 117-133. 10.1051/mmnp/20094305.View ArticleGoogle Scholar
- Enderling H, Hlatky L, Hahnfeldt P: Tumor morphological evolution: directed migration and gain and loss of the self-metastatic phenotype. Biol Direct. 2010, 5: 23-10.1186/1745-6150-5-23.PubMed CentralView ArticlePubMedGoogle Scholar
- Enderling H, Hlatky L, Hahnfeldt P: The promoting role of a tumour-secreted chemorepellent in self-metastatic tumour progression. Math Med Biol. 2012, 29: 21-29. 10.1093/imammb/dqq015.View ArticlePubMedGoogle Scholar
- Anderson ARA: A hybrid mathematical model of solid tumour invasion: the importance of cell adhesion. Math Med Biol. 2005, 22: 163-186. 10.1093/imammb/dqi005.View ArticlePubMedGoogle Scholar
- Rejniak KA, Anderson ARA: Hybrid models of tumor growth. Wiley Interdiscip Rev Syst Biol Med. 2011, 3: 115-125. 10.1002/wsbm.102.PubMed CentralView ArticlePubMedGoogle Scholar
- Visvader JE, Lindeman GJ: Cancer stem cells in solid tumours: accumulating evidence and unresolved questions. Nat Rev Cancer. 2008, 8: 755-768. 10.1038/nrc2499.View ArticlePubMedGoogle Scholar
- Rubin H: What keeps cells in tissues behaving normally in the face of myriad mutations?. Bioessays. 2006, 28: 515-524. 10.1002/bies.20403.View ArticlePubMedGoogle Scholar
- Bray D: Cell movements: from molecules to motility. 1992, New York: Garland PublishingGoogle Scholar
- Kawasaki BT, Farrar WL: Cancer stem cells, CD200 and immunoevasion. Trends Immunol. 2008, 29: 464-468. 10.1016/j.it.2008.07.005.View ArticlePubMedGoogle Scholar
- Reiman JM, Knutson KL, Radisky DC: Immune Promotion of Epithelial-mesenchymal Transition and Generation of Breast Cancer Stem Cells. Cancer Res. 2010, 70: 3005-3008. 10.1158/0008-5472.CAN-09-4041.PubMed CentralView ArticlePubMedGoogle Scholar

## Copyright

This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.