Computational analysis of the influence of the microenvironment on carcinogenesis

tugHall: a simulator of cancer-cell evolution based on the hallmarks of cancer and tumor-related genes

Summary

The flood of recent cancer genomic data requires a coherent model that can sort out the findings to systematically explain clonal evolution and the resultant intra-tumor heterogeneity (ITH). Here, we present a new mathematical model designed to computationally simulate the evolution of cancer cells. The model connects the well-known hallmarks of cancer with the specific mutational states of tumor-related genes. The cell behavior phenotypes are stochastically determined, and the hallmarks probabilistically interfere with the phenotypic probabilities. In turn, the hallmark variables depend on the mutational states of tumor-related genes. Thus, our software can deepen our understanding of cancer-cell evolution and generation of ITH.

Availability and implementation

The open-source code is available in the repository https://github.com/nagornovys/Cancer_cell_evolution.

Contact

mamkato@ncc.go.jp

Supplementary information

Supplementary data are available at Bioinformatics online.

Effects of motion in structured populations

In evolutionary processes, population structure has a substantial effect on natural selection. Here, we analyse how motion of individuals affects constant selection in structured populations. Motion is relevant because it leads to changes in the distribution of types as mutations march towards fixation or extinction. We describe motion as the swapping of individuals on graphs, and more generally as the shuffling of individuals between reproductive updates. Beginning with a one-dimensional graph, the cycle, we prove that motion suppresses natural selection for death-birth (DB) updating or for any process that combines birth-death (BD) and DB updating. If the rule is purely BD updating, no change in fixation probability appears in the presence of motion. We further investigate how motion affects evolution on the square lattice and weighted graphs. In the case of weighted graphs, we find that motion can be either an amplifier or a suppressor of natural selection. In some cases, whether it is one or the other can be a function of the relative reproductive rate, indicating that motion is a subtle and complex attribute of evolving populations. As a first step towards understanding less restricted types of motion in evolutionary graph theory, we consider a similar rule on dynamic graphs induced by a spatial flow and find qualitatively similar results, indicating that continuous motion also suppresses natural selection.

Homeostasis Back and Forth: An Ecoevolutionary Perspective of Cancer

The role of genetic mutations in cancer is indisputable: They are a key source of tumor heterogeneity and drive its evolution to malignancy. But, the success of these new mutant cells relies on their ability to disrupt the homeostasis that characterizes healthy tissues. Mutated clones unable to break free from intrinsic and extrinsic homeostatic controls will fail to establish a tumor. Here, we will discuss, through the lens of mathematical and computational modeling, why an evolutionary view of cancer needs to be complemented by an ecological perspective to understand why cancer cells invade and subsequently transform their environment during progression. Importantly, this ecological perspective needs to account for tissue homeostasis in the organs that tumors invade, because they perturb the normal regulatory dynamics of these tissues, often coopting them for its own gain. Furthermore, given our current lack of success in treating advanced metastatic cancers through tumor-centric therapeutic strategies, we propose that treatments that aim to restore homeostasis could become a promising venue of clinical research. This ecoevolutionary view of cancer requires mechanistic mathematical models to both integrate clinical with biological data from different scales but also to detangle the dynamic feedback between the tumor and its environment. Importantly, for these models to be useful, they need to embrace a higher degree of complexity than many mathematical modelers are traditionally comfortable with.

Analysis of behaviour transitions in tumour growth using a cellular automaton simulation

The authors used computational biology as an approach for analysing the emergent dynamics of tumour growth at cellular level. They applied cellular automata for modelling the behaviour of cells when the main cancer cell hallmarks are present. Their model is oriented to mimic the development of multicellular spheroids of tumour cells. In their modelling, cells have a genome associated with the different cancer hallmarks, indicating if those are acquired as a consequence of mutations. The presence of the cancer hallmarks defines cell states and cell mitotic behaviours. These hallmarks are associated with a series of parameters, and depending on their values and the activation of the hallmarks in each of the cells, the system can evolve to different dynamics. With the simulation tool the authors performed an analysis of the first phases of cancer growth, using different and alternative strategies: firstly, studying the evolution of cancer cells and hallmarks in different representative situations regarding initial conditions and parameters, analysing the relative importance of the hallmarks for tumour progression; secondly, being the focus of this work, inspecting the behaviour transitions when the cancer cells are killed with a given probability during the cellular system progression.

Treatment Analysis in a Cancer Stem Cell Context Using a Tumor Growth Model Based on Cellular Automata

Cancer can be viewed as an emergent behavior in terms of complex system theory and artificial life, Cellular Automata (CA) being the tool most used for studying and characterizing the emergent behavior. Different approaches with CA models were used to model cancer growth. The use of the abstract model of acquired cancer hallmarks permits the direct modeling at cellular level, where a cellular automaton defines the mitotic and apoptotic behavior of cells, and allows for an analysis of different dynamics of the cellular system depending on the presence of the different hallmarks. A CA model based on the presence of hallmarks in the cells, which includes a simulation of the behavior of Cancer Stem Cells (CSC) and their implications for the resultant growth behavior of the multicellular system, was employed. This modeling of cancer growth, in the avascular phase, was employed to analyze the effect of cancer treatments in a cancer stem cell context. The model clearly explains why, after treatment against non-stem cancer cells, the regrowth capability of CSCs generates a faster regrowth of tumor behavior, and also shows that a continuous low-intensity treatment does not favor CSC proliferation and differentiation, thereby allowing an unproblematic control of future tumor regrowth. The analysis performed indicates that, contrary to the current attempts at CSC control, trying to make CSC proliferation more difficult is an important point to consider, especially in the immediate period after a standard treatment for controlling non-stem cancer cell proliferation.

Glucose-lactate metabolic cooperation in cancer: insights from a spatial mathematical model and implications for targeted therapy

A recent study has hypothesised a glucose-lactate metabolic symbiosis between adjacent hypoxic and oxygenated regions of a developing tumour, and proposed a treatment strategy to target this symbiosis. However, in vivo experimental support remains inconclusive. Here we develop a minimal spatial mathematical model of glucose-lactate metabolism to examine, in principle, whether metabolic symbiosis is plausible in human tumours, and to assess the potential impact of inhibiting it. We find that symbiosis is a robust feature of our model system-although on the length scale at which oxygen supply is diffusion-limited, its occurrence requires very high cellular metabolic activity-and that necrosis in the tumour core is reduced in the presence of symbiosis. Upon simulating therapeutic inhibition of lactate uptake, we predict that targeted treatment increases the extent of tissue oxygenation without increasing core necrosis. The oxygenation effect is correlated strongly with the extent of wild-type hypoxia and only weakly with wild-type symbiotic behaviour, and therefore may be promising for radiosensitisation of hypoxic, lactate-consuming tumours even if they do not exhibit a spatially well-defined symbiosis. Finally, we conduct in vitro experiments on the U87 glioblastoma cell line to facilitate preliminary speculation as to where highly malignant tumours might fall in our parameter space, and find that these experiments suggest a weakly symbiotic regime for U87 cells, thus raising the new question of what relationship might exist between symbiosis and tumour malignancy.

Studying the capability of different cancer hallmarks to initiate tumor growth using a cellular automaton simulation. Application in a cancer stem cell context

We used a cellular automaton model for cancer growth simulation at cellular level, based on the presence of different cancer hallmarks acquired by the cells. The presence of the hallmarks in each of the cells determines cell mitotic and apoptotic behaviors. Depending on the presence of the different hallmarks and some associated parameters of the hallmarks, the system can evolve to different dynamics. We used the cellular automaton model to inspect the capability of different hallmarks to generate tumor growth in different conditions, using this study in a cancer stem cell context to analyze the capability of the hallmarks to tumor regrowth in different circumstances.

The role of chromosome missegregation in cancer development: a theoretical approach using agent-based modelling

Many cancers are aneuploid. However, the precise role that chromosomal instability plays in the development of cancer and in the response of tumours to treatment is still hotly debated. Here, to explore this question from a theoretical standpoint we have developed an agent-based model of tissue homeostasis in which to test the likely effects of whole chromosome mis-segregation during cancer development. In stochastic simulations, chromosome mis-segregation events at cell division lead to the generation of a diverse population of aneuploid clones that over time exhibit hyperplastic growth. Significantly, the course of cancer evolution depends on genetic linkage, as the structure of chromosomes lost or gained through mis-segregation events and the level of genetic instability function in tandem to determine the trajectory of cancer evolution. As a result, simulated cancers differ in their level of genetic stability and in their growth rates. We used this system to investigate the consequences of these differences in tumour heterogeneity for anti-cancer therapies based on surgery and anti-mitotic drugs that selectively target proliferating cells. As expected, simulated treatments induce a transient delay in tumour growth, and reveal a significant difference in the efficacy of different therapy regimes in treating genetically stable and unstable tumours. These data support clinical observations in which a poor prognosis is correlated with a high level of chromosome mis-segregation. However, stochastic simulations run in parallel also exhibit a wide range of behaviours, and the response of individual simulations (equivalent to single tumours) to anti-cancer therapy prove extremely variable. The model therefore highlights the difficulties of predicting the outcome of a given anti-cancer treatment, even in cases in which it is possible to determine the genotype of the entire set of cells within the developing tumour.

A general reaction-diffusion model of acidity in cancer invasion

We model the metabolism and behaviour of a developing cancer tumour in the context of its microenvironment, with the aim of elucidating the consequences of altered energy metabolism. Of particular interest is the Warburg Effect, a widespread preference in tumours for cytosolic glycolysis rather than oxidative phosphorylation for glucose breakdown, as yet incompletely understood. We examine a candidate explanation for the prevalence of the Warburg Effect in tumours, the acid-mediated invasion hypothesis, by generalising a canonical non-linear reaction-diffusion model of acid-mediated tumour invasion to consider additional biological features of potential importance. We apply both numerical methods and a non-standard asymptotic analysis in a travelling wave framework to obtain an explicit understanding of the range of tumour behaviours produced by the model and how fundamental parameters govern the speed and shape of invading tumour waves. Comparison with conclusions drawn under the original system--a special case of our generalised system--allows us to comment on the structural stability and predictive power of the modelling framework.

Evolution of tumor invasiveness: the adaptive tumor microenvironment landscape model

Interactions between cancer cells and their microenvironment are crucial for promoting tumor growth and invasiveness. In the tumor adaptive landscape model, hypoxic and acidic microenvironmental conditions reduce the fitness of cancer cells and significantly restrict their proliferation. This selects for enhanced motility as cancer cells may evolve an invasive phenotype if the consequent cell movement is rewarded by proliferation. Here, we used an integrative approach combining a mathematical tumor adaptive landscape model with experimental studies to examine the evolutionary dynamics that promote an invasive cancer phenotype. Computer simulation results hypothesized an explicit coupling of motility and proliferation in cancer cells. The mathematical modeling results were also experimentally examined by selecting Panc-1 cells with enhanced motility on a fibroblast-derived 3-dimensional matrix for cells that move away from the unfavorable metabolic constraints. After multiple rounds of selection, the cells that adapted through increased motility were characterized for their phenotypic properties compared with stationary cells. Microarray and gene depletion studies showed the role of Rho-GDI2 in regulating both cell movement and proliferation. Together, this work illustrates the partnership between evolutionary mathematical modeling and experimental validation as a potentially useful approach to study the complex dynamics of the tumor microenvironment.