Search tips
Search criteria 


Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
Cancer Res. Author manuscript; available in PMC 2010 November 15.
Published in final edited form as:
PMCID: PMC2783510

Microenvironmental independence associated with tumor progression


Tumor-microenvironment interactions are increasingly recognized to influence tumor progression. To understand the competitive dynamics of tumor cells in diverse microenvironments, we experimentally parameterized a hybrid discrete-continuum mathematical model with phenotypic trait data from a set of related mammary cell lines with normal, transformed, or tumorigenic properties. Surprisingly, in a resource-rich microenvironment, with few limitations on proliferation or migration, transformed but not tumorigenic cells were most successful and outcompeted other cell types in heterogeneous tumor simulations. Conversely, constrained microenvironments with limitations on space and/or growth factors gave a selective advantage to phenotypes derived from tumorigenic cell lines. Analysis of the relative performance of each phenotype in constrained versus unconstrained microenvironments revealed that, although all cell types grew more slowly in resource-constrained microenvironments, the most aggressive cells were least affected by microenvironmental constraints. A game theory model testing the relationship between microenvironment resource availability and competitive cellular dynamics supports the concept that microenvironmental independence is an advantageous cellular trait in resource-limited microenvironments.

Major Findings

These results suggest that a critical feature of the process of tumor progression is selection of cells that can escape from resource limitations by achieving a relative microenvironmental independence.


The microenvironment can either suppress or promote tumor progression, depending on the context (1). Due to the complex, multivariate nature of tumor-microenvironment interactions, traditional reductionist approaches may not be sufficient to achieve a complete mechanistic understanding of the process. A complementary method to probe tumor progression mechanisms is mathematical and computational modeling, to integrate and test in silico interactions between tumor cells and various aspects of the microenvironment.

We previously described a hybrid discrete-continuum (HDC) mathematical model that drives computer simulations of tumor growth by integrating cellular and microenvironmental variables (2, 3). In the HDC model, individual cells with different phenotypic traits interact spatially with each other and with microenvironmental variables, such as extracellular matrix (ECM) or oxygen. Analysis of evolving simulated tumors can provide mechanistic understanding, by allowing in silico testing of factors that affect tumor progression. For example, the interaction of cell phenotypes with “harsh” microenvironments (limiting oxygen, heterogeneous ECM) was found to produce tumors with invasive morphology, dominated by few cancer cell phenotypes with aggressive traits (high proliferation, low adhesion, high motility) (2). In contrast, under “mild” microenvironmental conditions (spatially homogeneous, abundant oxygen) there was little clonal selection and noninvasive morphologies.

In our previous work, theoretical phenotypes were parameterized with diverse values from the literature (2, 3). However, an important step is to incorporate experimental data gathered under comparable conditions in order to connect simulation predictions with biological context. For this purpose, we collected a homogeneous experimental phenotypic trait dataset from a panel of related breast epithelial cell lines with varying aggressiveness. Surprisingly, differences between measured phenotypic traits of normal, transformed, and tumorigenic cell lines were much smaller than those previously used for the theoretical cell phenotypes. Nonetheless, in simulated tumors run with growth factor-deprived and space-constrained microenvironments tumorigenic phenotypes became dominant. Conversely, simulations run with a non-limiting microenvironment instead favored transformed cell types. Analysis of the performance of single phenotype tumors in diverse microenvironments revealed that all cell types grew more slowly in resource-limited environments; however, the most aggressive cells were least affected. A non-zero sum game theory analysis confirms the general advantage conferred by microenvironmental independence for cells competing in resource-constrained microenvironments. These results suggest that tumorigenesis is an evolving process for which the increasing acquisition of independence from microenvironmental constraints is a critical feature.

Materials and Methods

MCF10A parent, pBabe, neuN, neuT were from Dr. Joan Brugge (Harvard Medical School), authenticated by 3D culture, and cultured as described (4); MCF10AT1, CA1a and CA1d were from the original source Dr. Fred Miller (Karmanos Institute) (5). Experimental raw data are shown in Supplemental Figs 1-3.

Extraction of model parameters from experimental data, scaling and fitting were as follows:


Data were obtained from in vitro experiments with cells grown under sparse, exponential growth conditions. In vivo growth rates would likely be difficult to use in simulations since they represent not only intrinsic cell doubling times, but also responses to contact inhibition and unknown factors in the tumor microenvironment (e.g. GF, hypoxia). Experimental growth data (Supp Fig 1) were assessed for a best fit model using the ‘curve estimation tool’ in GraphPad Prism. Exponential growth fits were significantly better than other tested models (R2 values between 0.904 and 0.995). From experimental data, we fitted exponential growth curves of the form y=aegt using SPSS, where y is cell number, a is a scaling constant, g is growth rate, and t is time (in hours). Doubling times (Table 1) were calculated from ln2/g (i.e., pBabe in full serum, g=0.031; ln2/0.031=22.36 h). See Quick Guide for model input of doubling times (M).

Table 1
Parameter Values for Phenotypic Traits

Cell-Cell Adhesion

Experimental cell-cell adhesion measurements were obtained using in vitro dispase assays (Supp Fig 3, (6)), and are presented as average percentage of cell-cell dissociation, where 100% is equivalent to complete dissociation after pipetting. Since MCF10A-p120-knockdown cells exhibit very little cell-cell adhesion (~96% dissociation), they were used as a positive control. Experimental dissociation values were normalized against p120-knockdown values, to achieve recalculated % dissociations (i.e., out of 100%).

Cell-cell adhesion (Ai) is modeled by designating a value for each cell that represents its likelihood to adhere to other cells. Movement is restricted based on these values and on the number of neighboring cells (see Supp Table 1 and (2, 3) for details). These internal cell-cell adhesion values are represented by 4 integers, ranging from 0 (no adhesion) to 3 (maximal adhesion), which must be derived from experimental values prior to input (see Quick Guide).

ECM Degradation

Experimental ECM degradation measurements were obtained using an invadopodia assay (Supp Fig 2, (7)), and presented as average degradation area/cell area. Since a cell is represented as a single lattice site, the cell area should match that of the model and the timescale is reasonably close. However, in simulations using these raw values ECM degradation occurred slowly. Thus, to minimize computation time, we used an arbitrary scaling of 5 to enhance each cell type’s degradation ability (δ). Control simulations run under various ECM constraints without this scaling and for a 5-fold longer time period gave the same clonal dominance ranking, but a slightly more ruffled edge due to greater impact of ECM heterogeneity (results not shown).

Unbiased Migration

Single cell velocities (μm/hr, Table 1) were measured as described (8) and converted into diffusion rates (Dn) by using the relationship between cell velocity and diffusion. We find that cells under these conditions follow a random walk, as defined by a linear relationship between mean squared displacement and time (9) and by 4 hours enter a fully diffusive regime (unpublished data). See Quick Guide for diffusion coefficient calculations.

Quick Guide to Equations and Assumptions

HDC Model

Model Assumptions

Cell life-cycle assumptions

Each cell can move, proliferate, degrade ECM and adhere to other cells on the two-dimensional lattice. The first step in the cell life-cycle (Fig 1) is examination of the ECM concentration and number of immediate neighbors. Next, depending on the phenotype, cells proliferate, become quiescent, or migrate. The six cell phenotypes, along with non-dimensionalized parameters for phenotypic traits (M = doubling time, Dn = migration, Ai = cell-cell adhesion, δ = ECM degradation) are shown in colored boxes.

Figure 1
HDC model. Cell life-cycle (A) and ECM domain (B). See Quick Guide for details.

ECM and cell movement assumptions

As shown in Fig 1, ECM is modeled as a heterogeneous mixture with pixels modeled at the cell scale (diameter h) and with concentrations from 0-100% (heat map). When space constraints are modeled, the “ECM threshold” represents the concentration below which cells are allowed to move or proliferate. Cells (Ni) can modify the ECM concentration (f) through localized degradation (δ). Cells can only move one step to their four orthogonal neighboring lattice sites with a probability P1 (left), P2 (right), P3 (down) and P4 (up) or remain stationary (P0) each time step (k). Further detailed description of all HDC assumptions are in Supplemental Table 1.

Data Input Equations

Proliferation (M)

We scaled calculated doubling times by the time-scale (| =24 h) multiplied by the simulation time-step (k = 0.00005) to obtain the final value. Thus, the proliferation parameter M = doubling time/(|*k) (i.e., pBabe in full serum, M= 22.36/(24*0.00005) ~ 18,600 time steps). Time units are 1/10th of the time scale, e.g. 2.4 h.

Migration (Dn)

To obtain diffusion coefficients, we used the relationship, Dn=(ts2)/2, where s is the experimentally measured speed of motion for each cell line for a given time t (9). Dn has units of μm2/hour. To non-dimensionalize this parameter we scaled it by the time (24hrs) and length scales (1cm2) of the model to obtain Dn=s2*12/108 with units of cm2 /hour. To implement unbiased migration from a diffusion coefficient, we use the relationship between a random walk and the diffusion equation (Supp Table 1). This relationship allows definition of movement probabilities for cells modulated by diffusion coefficients (Figure 1) and has been formally defined in the HDC model (10) and for reinforced random walks (11).

Cell-cell Adhesion (Ai)

To scale experimental dissociation values, normalized measurements were divided into 4 equally spaced bins derived from setting the highest dissociation value (p120-knockdown=100.0%) to 0, and the lowest % dissociation value (AT1=10.73%) to 3, to define outer limits of the data range. The 4 established bins were set to 0 (77.69-100%), 1 (55.37-77.68%), 2 (33.05-55.36%), and 3 (10.73-33.04%); all phenotypes were then assigned an integer (between 0-3), according to the appropriate bin.

Game theory model

Model Assumptions

We assume that the tumor is made of cells that do (mED) or do not (mEI) depend on their microenvironment for survival. The interactions between mEI and mED cells can be summarized as follows: although the maximum fitness for any cell is 1, mEI cells are assumed to have a constant fitness (h<1), regardless of the presence of other cells. Conversely, mED cells change their fitness if they are surrounded by mEI cells (which do not take resources from the mE) versus other mED cells (which do compete for those resources). Thus the change in fitness of a mED cell interacting with mEI cells is 1-c whereas this value is 1-nc if an mED cell interacts with other mED cells. c represents the cost of relying on the mE (c~0 in a microenvironment with easy access to GF, space, or other resources). n represents the increase in microenvironmental dependance cost due to available mE resources being shared between multiple mED cells.


The fitness of microenvironment-independent (mEI) and -dependent (mED) cells is as follows: h=fitness of mEI cells and is independent of cellular interactions. c=cost of of extracting resources from the microenvironment. n is a constant that accounts for greater extraction of resources by various (more than one) mED competing cells.

To calculate the proportion p of mEI cells in a population with both types of cells, we assume that in equilibrium, the fitness of the two populations is equal (see appendix for details). Assuming that the cost of relying on the mE is twice as much in environments in which more than one mED cell has to share available resources (n=2) then the proportion p of mEI cells is:

(EQ 1)

The magnitude of this coexistence region is dependent on both mEI fitness and mE parameters and defined as (see Supp Appendix):

(EQ 2)

The cost for relying on the mE is traded against the cost for mE independence (related to fitness, h).


To experimentally parameterize the HDC model, we adopted a panel of cultured cell lines (Table 1) based on the non-tumorigenic, immortalized breast epithelial cell line MCF10A (4). These cell lines were produced by introduction of genes known to be involved in breast cancer and in some cases by passaging the cells through mice: pBabe (vector control); neuN (overexpressed normal c-neu oncogene); neuT (oncogenic mutant of neu) (10); AT1 (activated ras); CA1a and CA1d (ras plus multiple in vivo passages). pBabe is immortalized but nontransformed, neuN and neuT are transformed but not tumorigenic, AT1 is poorly tumorigenic, and CA1a and CA1d are consistently tumorigenic and metastatic in tail vein injection assays (5). Thus, these cell lines can be taken to represent different tumor progression stages.

Experimental measurements and data integration

Key parameters in the HDC model include rates of proliferation (M), ECM degradation (δ), and motility (Dn), and cell-cell adhesion values (Ai, Table 1, Fig 1) (2). These parameters were measured in each cell line, under conventional tissue culture conditions. Raw experimental values, detailed graphs and images are shown in Table 1, and Supp Figs 1-3, respectively. Interestingly, the measured trait values do not immediately distinguish cell lines with respect to known tumorigenicity (Table 1). Only ECM degradation was higher in the consistently tumorigenic CA1a and CA1d cell lines, compared with other cell lines. Proliferation in growth-factor-deprived media was the highest in the CA1d cells but was equivalent between the strongly and weakly tumorigenic CA1a and AT1 cells, respectively.

To introduce these values into the model, the data were analyzed and nondimensionalized (Experimental Procedures). Each simulated “cell” is endowed with a collection of experimentally-derived phenotypic traits and can interact with other cells (through cell-cell adhesion) and the microenvironment (Fig 1, Supp Table 1). Cells can move and proliferate if there is adjacent lattice space and if their internal cell-cell adhesion value is less than the number of cellular neighbors. This latter rule gives cells with low cell-cell adhesion values a higher probability of moving away from neighboring cells than cells with high cell-cell adhesion values ((3), Supp Table 1). Movement at each time step is also modulated by the migration speed of each phenotype. Migration and proliferation are considered as continuous processes with one following the other at each time step, e.g. first a cell moves then it proliferates, as constrained by cell phenotype (Table 1) and availability of adjacent lattice sites.

Incorporation of experimental data inevitably led to model changes. We originally used two partial differential equations to model ECM degradation with cellular production and diffusion of proteases coupled to ECM disappearance. The direct measurement of cell-associated ECM degradation obviated the need for separate equations and made the process more realistic, since transmembrane proteases such as MT1-MMP are necessary and sufficient for cell invasion and ECM degradation (11-14). In addition, haptotaxis and oxygen consumption are not modeled in this study. It is unclear whether haptotaxis is a critical component of tumor cell motility, since it has only been measured in vitro, and in tissues proteolytic activity is more likely to result in rearrangement of ECM fibers than generation of smooth haptotactic gradients (15, 16). Oxygen consumption is not modeled because it became apparent that it should be treated as a separate study with measurement of metabolic parameters and incorporation of glycolytic switch equations (17, 18). Cell death is not explicitly modeled, but rather implicitly modeled using net cell doubling times, experimentally gathered in the presence or absence of growth factors.

Transformed and tumorigenic phenotypes coexist in a resource-rich microenvironment

To examine tumor population dynamics in a resource-rich microenvironment, simulations of heterogeneous tumor growth were run in which equal numbers of the 6 experimentally-parameterized cell types were mixed together. We define a microenvironment as “resource-rich” when the microenvironment imposes no limitations; that is, cells compete only for space on the lattice. Analysis of tumor cell dynamics shows that transformed neuT and neuN phenotypes become dominant over time, with some competition from the tumorigenic CA1d phenotype. By contrast, the normal pBabe, and respectively weakly and strongly tumorigenic AT1 and CA1a cells are quickly suppressed by other phenotypes (Fig 2A). Similar trends are evident in single phenotype simulations (Fig 2B), with the most “fit” phenotypes being neuT, neuN, and CA1d. However, small differences in fitness are critical in the competition for space during heterogeneous tumor development (Fig 2A). Normalization of cell-cell adhesion values to either 1 (NeuT value, Fig 2C) or 3 (CA1d value, not shown), leads to a shift in the order of phenotype dominance, with CA1d>NeuN>NeuT. In all simulations, AT1, CA1a, and pBabe were least fit regardless of cell-cell adhesion, indicating lower fitness with regard to other traits.

Figure 2
Tumor evolution in a resource-rich microenvironment

In the resource-rich microenvironment, tumor growth in HDC simulations depends heavily on migration and proliferation. The classic work of Fisher (19) considers a gene spreading through a population as an invading wave travelling at constant speed and similarly driven by diffusion and proliferation. In the case where only migration and proliferation differentially affect cellular behavior (Fig 2C, equalized cell-cell adhesion), it is possible to calculate Fisher wave speeds and obtain the same ranking of phenotype dominance (results not shown). However, this relationship breaks down when cell-cell adhesion and degradation are modifying factors and phenotypes are placed under microenvironmental constraints.

Comparison of simulation results with known biological behavior leads to an obvious discrepancy: neuT and neuN cells are not tumorigenic yet occupy the largest fraction of simulated tumors (together ~80%, Fig 2A). Since the simulations were run under environmental conditions without resource limitations and our previous work implicated microenvironmental selection in tumor invasiveness (2), we hypothesized that a more realistic microenvironment might alter competitive cellular dynamics during tumor evolution. In general, tumor microenvironments are considered to be stressful, with limited availability of growth factors (GF), nutrients or oxygen (20, 21), as well as spatial constraints likely to limit tumor growth (11). To test effects of resource limitation on tumor dynamics and composition, we modeled GF deprivation and ECM constraints, as detailed below.

Implementation of resource limitation promotes dominance of the tumorigenic CA1d cells

To model the effect of GF-deprivation on heterogeneous tumor evolution, GF-deprived cell doubling times (bracketed parameters for M, Table 1) were used in simulations along with the other phenotypic parameters. The pBabe phenotype was unable to grow, due to lack of proliferation. AT1 and CA1a phenotypes initially grew well, however their levels declined after time unit ~40 due to increasing dominance of the CA1d phenotype and “trapping” inside the tumor. NeuN and neuT each maintained a steady fraction of 16% and 12% in the growing tumor, respectively (Fig 3A).

Figure 3
GF- or space-constrained environments promote dominance of tumorigenic CA1d phenotype

In comparison to the resource-rich microenvironment, GF-deprivation leads to an earlier and larger degree of clonal dominance. Thus, the tumorigenic CA1d phenotype occupies 63% of the tumor at the simulation end, with no other phenotype occupying more than 16% (Fig 3A). By contrast, under unconstrained conditions, NeuN, NeuT, and CA1d coexist to a greater extent, with respective tumor fractions of 50%, 35%, and 12% (Fig 2A).

To model tissue space constraints, movement and proliferation of cells was limited by ECM concentrations above a certain threshold. ECM is represented in a generalized manner, without specification of molecular details or structure (Fig 1, (2, 3)). Cellular ECM degradation lowers the ECM level at a given lattice site, allowing movement or proliferation if the new ECM level falls below the threshold. Although the ECM threshold is the same for all cells within a given simulation, each cell type has a different ability to degrade ECM based on the measured trait parameter δ (Table 1, Fig 1B). At stringent thresholds (e.g. ECM concentrations ≤80% allow cell movement or proliferation), tumors become smaller and more compact (Fig 3B). Furthermore, neuT no longer dominates, giving way to neuN at intermediate (90-86% ECM threshold) and CA1d under high (≤84% ECM threshold) spatial constraints. Thus, similar to the GF-deprived environment, imposition of high space constraints leads to dominance of CA1d (Fig 3B), with suppression of other phenotypes. Similarly, in recently published in vitro colony expansion assays, we find that CA1d colonies expand further than MCF10A colonies in the presence but not absence of space constraints and CA1d cells dominate the periphery of mixed MCF10A:CA1d space-constrained cultures (22). Similar to cell-cell adhesion in the resource-rich environment, ECM degradation accounts for the dominance switch between neuN/neuT/CA1d under high ECM constraints, since equalizing cellular degradation rates leads to coexistence of neuN/neuT/CA1d under high ECM constraints (Fig 3C).

Tumor progression in a dually constrained microenvironment

In vivo, tumors grow and progress under multiple microenvironmental constraints. In an environment that is both GF- and space-constrained, CA1d once again becomes dominant with the highest degree of suppression of other phenotypes (Fig 4A, ~90% of the tumor population in GF-deprived + highest ECM constraint compared with ~60% of the tumor population in the GF-deprived + lowest ECM constraint). This finding validates the aggressiveness of the tumorigenic CA1d phenotype and indicates that microenvironment constraints can combine to further drive clonal dominance and tumor progression. However, this is not an entirely surprising result since the CA1d phenotype is more successful in each of the separate GF-deprived and space-constrained environments (Fig 3).

Figure 4
Dually-constrained microenvironment drives tumor progession

To test whether tumor evolution would occur differently in the absence of CA1d cells, simulations were run with a mixture of the remaining 5 phenotypes under GF-deprivation and in the presence or absence of space constraints (Fig 4B). Interestingly, under minimal space constraints (90-98% ECM threshold), AT1 and CA1a initially dominate equally but are overtaken quickly by the better-migrating neuN and neuT phenotypes. Under intermediate space constraints (80% threshold), AT1 and CA1a gain an increasing share of the tumor, to the disadvantage of neuT. However, as stringent space constraints are imposed (≤60% threshold), CA1a becomes dominant, holding a >50% fraction of the tumor. This clonal dominance is likely due to the slight advantage that CA1a holds in ECM degradation capacity (Table 1) over the other phenotypes. Thus, in the absence of CA1d, the next phenotype that is predicted to dominate under highly selective microenvironmental conditions is the only other consistently tumorigenic cell line, CA1a. These findings suggest that a key feature of tumorigenicity is the ability to survive under adverse circumstances and that the process of tumor progression selects for cells that can do so.

Remarkably, CA1a was never competitive for dominance in simulations when all 6 phenotypes were mixed (compare Fig 4B to Figs Figs4A4A,,22,,3).3). Instead, the main competition for dominance appeared to take place between CA1d and the neuN/neuT phenotypes, which constituted the largest fraction of the tumor. Thus, when both CA1a and CA1d are present, the similarity between phenotypes with a slight advantage to CA1d may lead to intense competition within the same tumor niche and suppression of CA1a by its next of kin, CA1d.

Independence from microenvironmental constraints as an aggressive cancer cell trait

To understand why resource constraints give an advantage to tumorigenic phenotypes, we analyzed the relative fitness of each phenotype in resource-constrained environments. To do so, we divided the final cell number at the end of resource-constrained simulations by the final cell number at the end of resource-rich simulations (microenvironment independence values, shown underneath appropriate simulation images in Fig 5A). In order to isolate microenvironment effects, we analyzed single phenotype simulation results. Interestingly, although all cells grow slowly in resource-constrained microenvironments, normal cells are severely affected and tumorigenic cells are least affected by resource restriction (Fig 5A). Thus, in the dually-constrained microenvironment, the aggressive CA1d phenotype achieves 38% of its performance in the resource-rich environment. By contrast, normal pBabe cells perform at 1% in this comparison and the other cells are intermediate, with a slight advantage to CA1a. In singly-constrained environments, the best separation between tumorigenic and transformed cell lines occurs with ECM constraint, consistent with invasion as a late stage in tumor progression and association of growth-factor independence with early stages of cellular transformation. Overall, these results suggest that microenvironmental independence is a critical cellular feature acquired during the process of tumor progression.

Figure 5
Tumorigenic cells exhibit relative independence from microenvironment constraints

Game Theory Model

To investigate further the role of microenvironmental independence, we used a game theoretical (GT) model that studies how different microenvironments (defined by cost of obtaining resources from them) explain tumour population composition. GT models have been used to study evolutionary dynamics in biological populations (23), including cancer (24). Model assumptions and equations are described in Quick Guide and Supplemental Appendix.

The GT analysis shows that mEs with a low cost of reliance favor mED cells (Fig 5B,C). However, resource-limited mEs favor mEI cells. The 2-D plots in Fig 5B show the expected proportion of mED or mEI cells as a function of varying cost (c) for extracting resources. Note the region of coexistence of mEI and mED populations (which is broader for low than high fitness (h) values) as the cost of obtaining microenvironment resources increases, similar to the crossover that occurs in the plot of tumor cell number versus ECM threshold in Fig 3b. In both cases, mEI cells are not as fit as mED cells in a low cost microenvironment; however, within high cost microenvironments they are comparatively fitter. The 3D plot in Fig 5C shows how the proportion of mED cells in the tumour population varies based on the cost (c) of relying on external mE factors and the fitness (h) of mEI cells.


To understand the role of the microenvironment in tumor progression, we gathered experimental parameter data from breast epithelial cells with normal, transformed, and tumorigenic properties for integration into the HDC model. We find that tumorigenic cells are predicted to dominate simulated tumors only under resource-constrained (GF-deprived or space-constrained) conditions. Analysis of tumor growth of each cell type in diverse simulated environments revealed that all phenotypes grew less well with limited resources; however, biological aggressiveness correlated with a relative resistance to microenvironmental constraints. A game theory analysis suggests that, in general, the ability to achieve microenvironment independence without a large fitness loss is advantageous to cells and likely to be selected for in high-cost environments. In aggregate, our results suggest that independence from microenvironmental constraints is a critical feature of tumor progression.

Microenvironmental independence as a key feature of carcinogenesis

Microenvironmental independence as a defining feature of cancer is consistent with cancer as a disease of deregulation, in which proliferation is unchecked by normal controls. Thus, it is not rampant proliferation that characterizes cancer cells (as is frequently assumed), but rather the ability to continue proliferating despite microenvironmental context that would inhibit normal cells. In considering the “hallmarks of cancer” (20), almost all of them can be connected to microenvironmental independence. Cell-intrinsic changes that allow cells to ignore their microenvironment include evading apoptosis, self-sufficiency in growth signals, and insensitivity to antigrowth signals. Active modification of the microenvironment to make it more favorable includes angiogenesis and tissue invasion (20). In light of our study, we speculate that the acquisition of microenvironment-independent traits should correlate with each step of tumor progression. Indeed, aggressive metastatic cells are extremely microenvironment-independent, colonizing diverse tissue sites.

In colon cancer, a specific series of genetic changes (the “vogelgram”) was shown to correlate with the progression from a normal cell to advanced carcinoma and includes loss of APC, activation of k-ras, loss of DCC, and loss of p53 genes (25). As opposed to a model in which genetic alterations remove intrinsic cell barriers to tumorigenesis that are unrelated to local microenvironment, our study is instead consistent with a model in which microenvironment-dependent selection accounts for the frequency of tissue-specific genetic changes. In light of that concept, how might one consider the well-defined “vogelgram”? APC mutations usually represent the first hit in colon tumorigenesis and decouple transit-amplifying and crypt base cell responses from extracellular Wnt ligand concentrations by upregulating beta-catenin levels (26). Activation of the signaling protein k-ras occurs most frequently at the transition from early to intermediate adenomas and allows growth-factor independence (20, 25). DCC is frequently lost at the intermediate to large adenoma transition and is a “dependence receptor” that promotes apoptosis when not bound to its ligand netrin (25, 27). Thus, loss of DCC confers microenvironment-independence to evolving adenomas by allowing survival in areas of low netrin (e.g. at the tip of intestinal villi) (27). Loss of p53 function is a late event in many cancers, occuring at the late adenoma to carcinoma transition and regulates cell cycle arrest, apoptosis, and cellular senescence. Although many p53 functions appear to be cell-intrinsic, e.g. cell-cycle arrest in response to DNA damage, p53 is important in regulating cellular responses to many microenvironmental stresses including hypoxia and osmotic stress (25, 28, 29).

Recent studies have shown that normal host cells can promote tumor progression (30-32). Our findings are not inconsistent with that view. We would argue that cancer cells in fact do not evolve independently from their microenvironment but rather that a normal tissue environment provides a variety of microenvironmental barriers that must be overcome during the process of tumorigenesis and progression. Whether those barriers are overcome entirely by cancer cells themselves or through the recruitment and activation of professional cells, such as inflammatory cells or fibroblasts, is a matter of strategy. The creation of a permissive environment may be more easily achieved via helper cells, such as activated fibroblasts that can lay down matrix, secrete angiogenic and growth factors, and/or remodel matrix (31), than through multiple changes in the carcinoma cell itself. Over time, such a permissive environment may allow fixation of stable genetic changes in cancer cells, e.g. progression.

Modeling approach

Many individual-based models of tumor growth and progression exist (18, 33-40). We focused on the current model because it fits easily into current biological and experimental frameworks. The theoretical focus of the HDC model on cell-microenvironment interactions is relevant to current debates on mechanisms of tumor progression (32), clonal expansion (25, 41), rates of mutation acquisition (42), and metastasis (43). Model limitations are primarily associated with representation of cells as lattice points, such that. ECM is not given elastic or force properties, molecular specificity, or tissue architecture and cell-cell adhesion is represented in an abstract manner, without cell geometry and associated forces. Modeling approaches that more naturally represent these elements include lattice-based cellular Potts (38, 40), lattice-free, center-based (34, 44) and the immersed boundary models (45). Nonetheless, the model has other advantages, including easy incorporation of individual phenotypes and experimental data, that allow analysis of competition between cellular phenotypes. Future inclusion of more accurate representations of ECM structure and mechanics and cell shape could be achieved by linking with models that already have these in place, albeit with fewer cells (46).

Implications and Future directions

If microenvironmental independence is a critical, defining feature of cancer, therapies that reverse this process might be effective. One possibility is differentiation therapy to limit the cellular response range by inducing maturation, e.g. ATRA for promyelocytic leukemia or potentially HDAC inhibitors +/- PPARγ ligands for lung adenocarcinomas (47, 48). Another approach is inhibition of genes or processes that promote adaptability to the microenvironment.

Future testing of microenvironmental independence as a driving force for tumor progression will require characterizing cell performance in additional microenvironments, including acidic, hypoxic, inflammatory, or drug-treated, along with in vivo validation of simulation results. Another future direction could include investigation of the role of tissue architecture and other tissue-specific microenvironment barriers in driving tumor progression. We anticipate that future integration of experimentation with modeling will continue to provide insight into the process of tumor progression.

Supplementary Material


Funding was provided by U54CA113007 to VQ and K22CA109590 to AMW.


1. Witz IP. Yin-yang activities and vicious cycles in the tumor microenvironment. Cancer Res. 2008;68:9–13. [PubMed]
2. Anderson AR, Weaver AM, Cummings PT, Quaranta V. Tumor morphology and phenotypic evolution driven by selective pressure from the microenvironment. Cell. 2006;127:905–15. [PubMed]
3. Anderson ARA. A hybrid mathematical model of solid tumour invasion: the importance of cell adhesion. Mathematical Medicine and Biology-a Journal of the Ima. 2005;22:163–86. [PubMed]
4. Debnath J, Muthuswamy SK, Brugge JS. Morphogenesis and oncogenesis of MCF-10A mammary epithelial acini grown in three-dimensional basement membrane cultures. Methods. 2003;30:256–68. [PubMed]
5. Santner SJ, Dawson PJ, Tait L, et al. Malignant MCF10CA1 cell lines derived from premalignant human breast epithelial MCF10AT cells. Breast Cancer Res Treat. 2001;65:101–10. [PubMed]
6. Huen AC, Park JK, Godsel LM, et al. Intermediate filament-membrane attachments function synergistically with actin-dependent contacts to regulate intercellular adhesive strength. J Cell Biol. 2002;159:1005–17. [PMC free article] [PubMed]
7. Clark ES, Whigham AS, Yarbrough WG, Weaver AM. Cortactin is an essential regulator of matrix metalloproteinase secretion and extracellular matrix degradation in invadopodia. Cancer Res. 2007;67:4227–35. [PubMed]
8. Bryce NS, Clark ES, Leysath JL, Currie JD, Webb DJ, Weaver AM. Cortactin promotes cell motility by enhancing lamellipodial persistence. Curr Biol. 2005;15:1276–85. [PubMed]
9. Potdar AA, Lu J, Jeon J, Weaver AM, Cummings PT. Bimodal analysis of mammary epithelial cell migration in two dimensions. Ann Biomed Eng. 2009;37:230–45. [PMC free article] [PubMed]
10. Bargmann CI, Hung MC, Weinberg RA. Multiple independent activations of the neu oncogene by a point mutation altering the transmembrane domain of p185. Cell. 1986;45:649–57. [PubMed]
11. Hotary KB, Allen ED, Brooks PC, Datta NS, Long MW, Weiss SJ. Membrane type I matrix metalloproteinase usurps tumor growth control imposed by the three-dimensional extracellular matrix. Cell. 2003;114:33–45. [PubMed]
12. Sabeh F, Ota I, Holmbeck K, et al. Tumor cell traffic through the extracellular matrix is controlled by the membrane-anchored collagenase MT1-MMP. J Cell Biol. 2004;167:769–81. [PMC free article] [PubMed]
13. Artym VV, Zhang Y, Seillier-Moiseiwitsch F, Yamada KM, Mueller SC. Dynamic interactions of cortactin and membrane type 1 matrix metalloproteinase at invadopodia: defining the stages of invadopodia formation and function. Cancer Res. 2006;66:3034–43. [PubMed]
14. Weaver AM. Invadopodia: specialized cell structures for cancer invasion. Clin Exp Metastasis. 2006;23:97–105. [PubMed]
15. Friedl P, Wolf K. Tube travel: the role of proteases in individual and collective cancer cell invasion. Cancer Res. 2008;68:7247–9. [PubMed]
16. Provenzano PP, Eliceiri KW, Campbell JM, Inman DR, White JG, Keely PJ. Collagen reorganization at the tumor-stromal interface facilitates local invasion. BMC Med. 2006;4:38. [PMC free article] [PubMed]
17. Gatenby RA, Smallbone K, Maini PK, et al. Cellular adaptations to hypoxia and acidosis during somatic evolution of breast cancer. British Journal of Cancer. 2007;97:646–53. [PMC free article] [PubMed]
18. Gerlee P, Anderson ARA. An evolutionary hybrid cellular automaton model of solid tumour growth. Journal of Theoretical Biology. 2007;246:583–603. [PMC free article] [PubMed]
19. Fisher RA. The wave of advance of advantageous genes. Ann Eugenics. 1937;7:355–69.
20. Hanahan D, Weinberg RA. The hallmarks of cancer. Cell. 2000;100:57–70. [PubMed]
21. Smalley KS, Brafford PA, Herlyn M. Selective evolutionary pressure from the tissue microenvironment drives tumor progression. Semin Cancer Biol. 2005;15:451–9. [PubMed]
22. Kam Y, Karperien A, Weidow B, Estrada L, Anderson AR, Quaranta V. Nest expansion assay: a cancer systems biology approach to in vitro invasion measurements. BMC Res Notes. 2009;2:130. [PMC free article] [PubMed]
23. Smith J Maynard. Evolution and the theory of games. Cambridge University Press; Cambridge ; New York: 1982.
24. DaD A. Basanta. A game theoretical perspective on the somatic evolution of cancer. In: Bellomo N, editor. Selected topics on cancer modeling: genesis, evolution, immune competition, therapy. Birkhauser; Boston: 2008. MCaED.
25. Vogelstein B, Kinzler KW. The multistep nature of cancer. Trends Genet. 1993;9:138–41. [PubMed]
26. Reya T, Clevers H. Wnt signalling in stem cells and cancer. Nature. 2005;434:843–50. [PubMed]
27. Arakawa H. Netrin-1 and its receptors in tumorigenesis. Nat Rev Cancer. 2004;4:978–87. [PubMed]
28. Murray-Zmijewski F, Slee EA, Lu X. A complex barcode underlies the heterogeneous response of p53 to stress. Nat Rev Mol Cell Biol. 2008;9:702–12. [PubMed]
29. Staib F, Robles AI, Varticovski L, et al. The p53 tumor suppressor network is a key responder to microenvironmental components of chronic inflammatory stress. Cancer Res. 2005;65:10255–64. [PMC free article] [PubMed]
30. Chung LW, Baseman A, Assikis V, Zhau HE. Molecular insights into prostate cancer progression: the missing link of tumor microenvironment. J Urol. 2005;173:10–20. [PubMed]
31. Kalluri R, Zeisberg M. Fibroblasts in cancer. Nat Rev Cancer. 2006;6:392–401. [PubMed]
32. Rubin H. Microenvironmental regulation of the initiated cell. Adv Cancer Res. 2003;90:1–62. [PubMed]
33. Dormann S, Deutsch A. Modeling of self-organized avascular tumor growth with a hybrid cellular automaton. In Silico Biol. 2002;2:393–406. [PubMed]
34. Drasdo D, Hohme S. A single-cell-based model of tumor growth in vitro: monolayers and spheroids. Phys Biol. 2005;2:133–47. [PubMed]
35. Jiang Y, Pjesivac-Grbovic J, Cantrell C, Freyer JP. A multiscale model for avascular tumor growth. Biophys J. 2005;89:3884–94. [PubMed]
36. Rejniak KA. A single cell aproach in modeling the dynamics of tumor microregions. Mathematical Biosciences and Engineering. 2005;2:643–55. [PubMed]
37. Stott E, Britton NF, Glazier JA, Zajac M. Stochastic Simulation of Benign Avascular Tumor Growth using the Potts Model. J Theor Biol. 1999;30:183–98.
38. Turner S, Sherratt JA. Intercellular adhesion and cancer invasion: a discrete simulation using the extended Potts model. J Theor Biol. 2002;216:85–100. [PubMed]
39. Zhang L, Athale CA, Deisboeck TS. Development of a three-dimensional multiscale agent-based tumor model: simulating gene-protein interaction profiles, cell phenotypes and multicellular patterns in brain cancer. J Theor Biol. 2007;244:96–107. [PubMed]
40. Poplawski NJ, Agero U, Gens JS, Swat M, Glazier JA, Anderson AR. Front Instabilities and Invasiveness of Simulated Avascular Tumors. Bull Math Biol. 2009 [PMC free article] [PubMed]
41. Jones S, Chen WD, Parmigiani G, et al. Comparative lesion sequencing provides insights into tumor evolution. Proc Natl Acad Sci U S A. 2008;105:4283–8. [PubMed]
42. Beerenwinkel N, Antal T, Dingli D, et al. Genetic progression and the waiting time to cancer. PLoS Comput Biol. 2007;3:e225. [PubMed]
43. Bernards R, Weinberg RA. A progression puzzle. Nature. 2002;418:823. [PubMed]
44. Ramis-Conde I, Drasdo D, Anderson AR, Chaplain MA. Modeling the influence of the E-cadherin-beta-catenin pathway in cancer cell invasion: a multiscale approach. Biophys J. 2008;95:155–65. [PubMed]
45. Rejniak KA. An immersed boundary framework for modelling the growth of individual cells: an application to the early tumour development. J Theor Biol. 2007;247:186–204. [PubMed]
46. Rejniak KA, Anderson ARA. A computational study of the development of epithelial acini: I. Sufficient conditions for the formation of a hollow structure. Bulletin of Mathematical Biology. 2008;70:677–712. [PubMed]
47. Chang TH, Szabo E. Enhanced growth inhibition by combination differentiation therapy with ligands of peroxisome proliferator-activated receptor-gamma and inhibitors of histone deacetylase in adenocarcinoma of the lung. Clin Cancer Res. 2002;8:1206–12. [PubMed]
48. Nowak D, Stewart D, Koeffler HP. Differentiation therapy of leukemia - three decades of development. Blood. 2009 [PubMed]