Biphasic modulation of cancer stem cell‐driven solid tumour dynamics in response to reactivated replicative senescence

Abstract

Objectives

Cell senescence is a physiological programme of irreversible mitotic arrest that is triggered after a variety of intracellular and extracellular events. Its purpose is to protect tissue integrity by disabling mitosis in stressed or damaged cells. The senescence program serves as a tumour suppressor, and cancer cells are believed to bypass senescence to advance to malignancy. Recent studies have shown that senescence can be reactivated in cancer cells through a number of external perturbations, including oncogene activation, tumour suppressor gene withdrawal and irradiation.

Materials and methods

We have developed an agent‐based model of solid tumour growth whose input population composition is based on the cancer stem‐cell hypothesis. It is used to show how cancer stem cells can drive tumour progression, while non‐stem cancer cells (CCs) interfere with this by impeding cancer stem‐cell dynamics.

Results

Here we show that intratumoural competition between the two cell types may arise to modulate tumour progression and ultimately cancer presentation risk. Model simulations reveal that reactivation of the replicative senescence programme in CCs initially increases total tumour burden, as attrition from cell death is partially averted, but evolves to provide tumour control in the long‐term through increasing constraints on stem‐cell compartment kinetics.

Conclusions

Reactivation of replicative senescence can prolong CC competition with cancer stem cells, thereby ultimately inhibiting malignant progression regardless of tumour size.

Introduction

In 1961, Hayflick and Moorhead reported that extensively cultured human primary cells cease to proliferate after a finite number of divisions 1 yet remain viable and metabolically active 2, 3. Experiments with transfected telomerase, an enzyme that rebuilds telomeric DNA 4, revealed that proliferation exhaustion is a consequence of telomere erosion 5, 6. This irreversible cytostasis is termed replicative senescence. Several other factors can lead to different forms of irreversible mitotic arrest, such as DNA damage and oxidative stress [stress‐induced senescence; 3], oncogenic activation [oncogene‐induced senescence; 7], or loss of tumour suppressor genes [PTEN loss‐induced cellular senescence; 8]. Senescent cells display altered cell morphology, overexpress plasminogen activator protein 1 and present β‐galactosidase 9, 10. Initially, cellular senescence was believed to be a side effect of culturing cells in vitro, but recently senescent cells have also been detected in vivo in a variety of tissues in a number of different organs 11. The senescence program is believed to protect tissue integrity by disabling mitosis in stressed or damaged cells – thus probably acting as a tumour suppressor 12. During carcinogenesis, cells acquire traits that enable circumvention of replicative senescence – a hallmark of cancer 13, 14, 15. It has been suggested, however, that the cellular senescence pathways remain intact in tumours 16 and can be reactivated through cell autonomous programs 17. It has been reported that cellular senescence can also be triggered, and might actually be the predominant response to ionizing radiation and many currently used chemotherapeutic drugs 3, 15, 18. Cell population growth arrest in these cases is achieved and maintained, in part, by increased expression of specific cyclin‐dependent kinase inhibitors, including p16Ink4a 19.

Replicative senescence might play an important role in tumour growth kinetics. If cell death is averted in favour of senescence, the number of cells inevitably increases. Senescent cells, however, do not actively contribute to population expansion, and might even hinder non‐senescent cell proliferation through competition for common resources. At the same time, there is a growing body of evidence supporting the cancer stem‐cell (CSC) hypothesis as a hierarchical model for tumour cell populations 20, 21. To rigorously understand the action of senescence within this hierarchical population structure, a theoretical framework has been developed that is capable of tracking how these dynamics interact.

The CSC hypothesis itself offers one unifying explanation for the seemingly disparate observations that (i) locally recurring cancers are commonly more aggressive than the original primary tumour from which they arise 22, 23, while (ii) indolent tumours are exceedingly common among asymptomatic adults 24, 25, 26. We propose that these phenomena may be reconciled by the prospect that a sensitive cancer cell subpopulation competes with a minor, but more resistant and aggressive cancer cell subpopulation to prevent its enrichment beyond a small fraction. In the context of the CSC hypothesis, the sensitive fraction would be identified with non‐stem cancer cells (CCs), and the resistant fraction with CSCs 27, 28, 29, 30. Unique to CSCs is the capacity for self‐renewal and for tumour initiation 31, 32. CCs, in contrast, although being fully transformed, have only a limited lifespan and proliferation capacity and hence are incapable of initiating, reinitiating and sustaining tumours 33. CSCs have been shown to be intrinsically less sensitive to conventional types of treatment 28, 34 and thus be likely to drive the frequent, aggressive recurrences seen after apparently eradicative tumour treatment 35. Cells sensitive to radiation and chemotherapeutic cell killing might also be susceptible to agents that work by other means. It has been shown that cancer cell fate can be shifted towards senescence using irradiation or moderate doses of chemotherapy 36, Kras or c‐Myc inactivation in oncogene‐addicted tumours 7, 17 or loss of tumour suppressor Pten 8. Here we present a quantitative model of CSC‐driven tumour progression, and investigate how re‐induction of replicative senescence in CCs modulates tumour growth kinetics in early tumour development as well as in tumours that are already advanced.

Materials and methods

We introduce a theoretical framework to investigate reactivation of senescence as a modulator of tumour progression. While a number of quantitative models have been proposed to study a variety of aspects of cellular senescence 37, 38, 39, 40, 41, 42, 43, the model presented here considers growth modulation of CSC‐driven tumours. We use an agent‐based model to simulate the dynamics and interactions of single cells and observe emergent tumour formation 33, 44. Agent‐based modelling is a computational methodology for simulating intercellular and cell–environment interactions that can reveal emerging properties of a dynamic system in time and space; it has been widely used in diverse areas of biomedical research 45, 46 including cancer and tumour biology 47, 48, 49, 50, 51, 52, 53, 54. In agent‐based models, the system is represented as a collection of autonomous, decision‐making agents, or cells, that have a set of intrinsic state variables and predefined instructions that determine how they behave and interact with each other and their local environment. Full details of cells and their interactions as the simulation progresses are visualizable, measurable and accessible to intervention 55. Stochastic simulations of the interaction of single cells and multiple cell populations with one another as well as with their immediate environment result in complex population dynamics such as cooperation or competition 56. The agent‐based framework can capture the complex interactive consequences of these dynamics while allowing for distinction of the various participating cell populations of CSCs, CCs and senescent non‐stem cancer cells (SCCs).

The model is based on asynchronous cellular automata in which all cell events are stochastically driven. A cell is an individual entity that occupies a single grid point of 100 μm² on a two‐dimensional or 1000 μm³ on a three‐dimensional cubic lattice. All tumour subpopulations, CSCs, CCs and SCCs, are characterized by their proliferation potential. We have assumed that only CSCs and CCs are able to divide and produce daughter cells, while SCCs are in an irreversible post‐mitotic state. According to the CSC hypothesis, CSCs are immortal and have infinite proliferative potential. At each division, CSCs produce either another CSC with probability 0 < P _s ≤ 1 (symmetric division) or a CC with probability 1 − P _s (asymmetric division). CCs that are direct offspring of a CSC are equipped with a limited proliferation capacity ρ = ρ_max (Fig. 1a) that reduces with each cell division, a quantitative rendering of telomere shortening 9. At ρ = 0, CCs either die or become senescent. We assume that post‐mitotic fate is decided randomly with probability 0 ≤ σ ≤ 1, where σ = 0 simulates cell kinetics without senescence (that is, all cells will die after exhaustion of proliferation capacity), and σ = 1 simulates exclusive induction of senescence after exhaustion of proliferation capacity. Dead cells are instantaneously removed from the simulation, whereas senescent cells remain components of the tumour system. Due to continued metabolic activity and absence of cell division, senescent cells commonly increase in size but have reduced motility 57, 58, 59. While CSCs and CCs are equipped with fixed migration rate μ, we have investigated senescent cells with either an equivalent migration rate μ_s = μ or lower motility assumed to be μ_s = 0.25 μ, which represents 75% reduction in cell motility. Cell proliferation and cell migration are dependent on the intracellular state as well as the local environment. We assume that cells need adjacent space for migration and proliferation, and cells that are completely surrounded by other cells (eight or twenty‐six on a two‐ or three‐dimensional lattice respectively) become quiescent (Fig. 1b,c) until neighbouring space opens up via cell migration or spontaneous cell death. In unsaturated environments, cells proliferate and migrate into vacant adjacent space at random.

Figure 1.

(a) Proliferation hierarchy of cancer stem cells ( CSC s), non‐stem cancer cells ( CC s) and senescent cancer cells ( SCC s). (b, c) Tumour cells populate the computational lattice by cell migration and cell proliferation. A cell can randomly migrate to, or place a daughter cell in, one of the eight (b) or twenty‐six (c) adjacent lattice points subject to availability. A cell becomes quiescent if all adjacent lattice points are occupied.

To simulate tumour progression, we have initialized tumour growth with one CSC in the centre of the computational lattice. We chose lattice sizes of 600 × 600 (representing a 36 mm² domain) in two dimensions and 500 × 500 × 500 (representing a 125 mm³ domain) in three dimensions respectively. We assume that cells divide on average once per day and set cell cycle length to be 24 h 60. Furthermore, in line with previous models, we assume cell migration to be in the order of μ = 150 μm/day 33, and thus migration into adjacent lattice points (10–14 μm away) can occur within 96 min. Therefore, we advance time at discrete time intervals Δt = 1/24 day (60 min). At each simulation time step, cells are considered in random order and behaviour of each is updated. Cell proliferation and migration are temporally mutually exclusive events, and spontaneous cell death, as for example, due to metabolic catastrophe 61, occurs during proliferation attempts. We set spontaneous cell death rate to α = 0.01 to allow for natural, attrition‐dependent tumour progression. We assume migration probabilities P _m = μ × Δt for CCs and CSCs and P _m = μ_s × Δt for SCCs, where parameters μ and μ_s (μ_s ≤ μ) denote motility of non‐senescent and senescent cancer cells (SCCs), respectively. To reflect the low frequency of CSCs in solid tumours reported in the literature 29, we set probability of symmetric CSC division (which yields two CSCs) to P _s = 0.01. With probability 1 − P _s, CSC division yields a CSC and a CC. Motivation for and variation of mentioned parameters α, μ and P _s and their impact on tumour progression have been discussed in detail elsewhere 33, 44, 62, 63. Figure 2 summarizes the simulation procedure for the presented model. Due to the model's stochastic nature, we performed 100 independent simulations for each discussed parameter set and report average values and standard deviations.

Figure 2.

Schematic representation of the simulation process.

Results

We first simulated CSC‐driven tumour growth without replicative senescence. Then we investigated how early replicative senescence modulates intrinsic tumour progression, and studied effects of reactivated replicative senescence in established tumours of different sizes.

Cancer stem cell‐driven self‐metastatic tumour progression

We simulated tumour progression initiated by one CSC for t = 1460 days (4 years). We compared tumour progression as a function of the CC proliferation capacity ρ_max (c.f. Fig. 1a) – low proliferation capacity ρ_max = 10 and larger proliferation capacity ρ_max = 20 divisions. As previously discussed 33, 44, with low probability of symmetric CSC division P _s = 0.01, tumour growth is limited by tumour mass 64. The founding CSC quickly produces CCs that go on and produce exclusively more CCs. As symmetric CSC division is an infrequent event, the CSC rapidly becomes engulfed in the CC population. The interior of the population enters quiescence due to spatial constraints (c.f. Fig. 1b,c) and proliferation is limited to the outer rim of the growing population. Proliferation capacities of proliferating CCs near the outer rim continuously reduce and peripheral cell death sets in after proliferation capacity is exhausted (ρ = 0; σ = 0). Previously quiescent CCs become active again and follow the kinetics of their predecessors. Tumour population size oscillates until the CSC becomes liberated and recommences proliferation, subject to (a)symmetric division. If symmetric division produces a new CSC, the two CSCs can opportunistically spatially separate and form independent clusters of self‐limited size in the vicinity of each other (Fig. 3). This process repeats with increasing frequency as a continuously increasing number of CSCs seed new CSCs and new tumour clusters nearby – a process we and others have termed self‐metastatic tumour progression 44, 63, 65.

Figure 3.

Self‐metastatic tumour growth. Cancer stem cells (CSC, yellow) form small tumour clusters and seed independent clusters in their vicinity. Efficiency of self‐metastatic seeding depends on inhibition by non‐stem cancer cells. Larger proliferation potentials (ρ_max = 20) can inhibit self‐metastatic seeding and induce prolonged phases of dormancy.

Figure 3 shows that tumours with a larger CC proliferation capacity ρ_max = 20 have significantly slower tumour growth. Inhibition of the founding CSC by its early progeny CCs and their subsequent offspring is so profound that in the simulated time interval of 4 years, no tumour progression beyond the initial self‐limited population is observed. A second CSC forms, but inhibition by progeny of both CSCs limits spatial separation and self‐metastatic progression 44. Faster advance of the population with ρ_max = 10 occurs despite the fact that a CC with ρ_max = 10 will over time generate a population of 2¹⁰ = 1024 cells, whereas the population arising from a CC with ρ_max = 20 will consist of 2²⁰ = 1 048 576 cells – more than three orders of magnitude (>1000 times) more cells. In the next sections, we report our investigation of impact of replicative senescence on slowly progressing (ρ_max = 20) and rapidly progressing (ρ_max = 10) CSC‐driven self‐metastatic tumours.

Replicative senescence and early tumour progression modulation

We then introduced replicative senescence into the model. We first assumed σ = 1, total deferment of cell death in favour of senescence. A CC that exhausts its replicative potential, ρ = 0, will become senescent (SCC) and avoid apoptosis. To account for reduced motility of SCCs 58, 59 we compared migration rates of μ_s for the cases μ_s = {μ, 0.25 μ}. Effect of SCC presence on tumour progression is biphasic. Initially, introduction of replicative senescence yields larger tumours with larger total number of cells compared to self‐metastatic tumour progression, as cell death is averted. As one would expect 44, lower SCC migration rate μ_s = 0.25 μ results in smaller tumours as competition with and restrictions on mitotic populations are increased. Interestingly, tumour morphology changes from a self‐metastatic phenotype to compact circular tumours with a diffuse rim (Fig. 4) that is characteristic of cell diffusion‐driven tumours 66, 67. As SCCs cease to proliferate and thus no longer increase cell number, and further refrain from vacating the space they occupy and therefore inhibit CC and CSC proliferation, tumour progression is severely impaired in the long term. Consequently, a reverse trend in tumour numbers can be observed and tumours with SCCs become smaller with significantly reduced growth rates at later times compared to self‐metastatic tumours without senescence (Fig. 4). Rapidly growing self‐metastatic tumours (i.e. ρ_max = 10) contain an order of magnitude more cells and two orders of magnitude more CSCs than SCC‐harbouring tumours, in which only 1.05% (for μ_s = μ) and 1.19% (μ_s = 0.25 μ) are non‐senescent with remaining proliferation capacity ρ > 0.

Figure 4.

Comparison of tumour growth dynamics over time in two‐dimensional lattice in cases of presence (light and dark green) or absence (Control, light yellow) of senescence, and for different replicative potential ρ _max  = 10, 20 and two migration potentials of senescent cells, μ _s  = μ or 0.25 μ. (a) Typical tumour morphologies at t = 1460 days. s: CSC count; n: CC+SCC count. (b–d) Average statistics after 1460 days (bar plots) and (e) tumour evolution over time for ρ_max = 10.

The effect of early replicative senescence in slowly progressing self‐metastatic tumours is remarkably different. If self‐metastatically progressing tumours have a long initial self‐limited, dormant phase (i.e. ρ_max = 20), introduction of senescence increases total tumour cell count as cell death is averted, but has little effect on CSC numbers or non‐senescent CC counts (Fig. 4). To ensure that observed dynamics are not artefactual of the two‐dimensional simulation setup, we extended the model into three dimensions (Fig. 5). Induction of replicative senescence in CC was confirmed biphasic as discussed above with initial increase in tumour cell count followed by reduction of tumour growth rate and inhibited tumour progression compared to self‐metastatic tumour progression. Regardless of SCC migration rate μ_s, non‐senescent cells (CSCs + CCs) make up less than 1% of the total population. Biphasic modulation of CSC‐driven solid tumour growth can be observed even if only a very small fraction of CC avert replicative cell death in favour of senescence. Figure 6 shows the case for σ = 0.02, that is, 2% of CCs become senescent when their replicative potential is exhausted.

Figure 5.

Comparison of tumour growth dynamics over time in three‐dimensional lattice in cases of presence (light and dark green) or absence (Control, light yellow) of senescence for P _s  = 0.01, ρ _max  = 15, μ = 10 and μ _s  = μ or 0.25 μ. (a) Examples of tumour morphologies after 530 days. (b) Evolution of tumours over time.

Figure 6.

Analysis of senescence induction at very low rate σ = 0.02 (i.e. 2% of cancer cell enter senescence instead of replicative cell death). (a) Total cell count. (b) Cancer stem‐cell count. (c) Cancer stem‐cell fraction. (d) Pre‐senescent fraction.

Reactivation of replicative senescence in established tumours

We simulated rapid self‐metastatic tumour progression (ρ_max = 10) and introduced exclusive replicative senescence with σ = 1, after tumours had reached sizes of 10 000, 50 000 or 100 000 cells. Induction of replicative senescence initially increased total population size as cell death was averted, but, in the long term, impeded tumour progression compared to unperturbed self‐metastatic growth (Fig. 7). Interestingly, dynamics of the tumour response to reactivated replicative senescence was independent of tumour size. For all studied tumour sizes, evolution of total cell count after reactivation of senescence exhibited the biphasic initial increase and later reduced growth rate, and differences in times until intersections of senescent tumour growth trajectories with untreated control were insignificant (see Table 1). Number of CSCs and thus total number of non‐senescent cells was significantly lower regardless of tumour size (Fig. 7).

Figure 7.

Effect of reactivation of the senescence program in non‐stem cancer cells. (a) Examples of tumour morphologies after 100, 200 and 800 days. s: CSC, n: CC+SCC. (b) Evolution of tumour populations of different initial sizes.

Table 1.

Average time until intersection of the senescent tumour growth trajectories with non‐senescent control for different initial population sizes and senescent cells' migrations potentials

Tumour size at senescence reactivation	μs = μ	μs = 0.25 μ
10 000 cells	646 days	343 days
50 000 cells	599 days	333 days
100 000 cells	607 days	337 days

Discussion

Transformed cells ‘learn’ to bypass physiological programs of irreversible growth arrest as part of the carcinogenic cascade. Pathways underlying cellular senescence, however, have been shown to remain intact in tumours and thus are reactivatable and potentially exploitable for therapeutic intervention. Here, we have presented a theoretical model of CSC‐driven solid tumour progression and explored how tumour dynamics are modulated if replicative senescence is reactivated. We have described solid tumour growth as self‐metastatic expansion resulting from competition for space between CSCs and their non‐stem progeny. Large CC populations inhibit CSC kinetics required for tumour growth. In this model, replicative senescence works to impede tumour progression – independent of tumour size – by further increasing pressure on the CSC population that is inevitably forced to remain in the core of the population. Initial response to senescence activation, however, is an undesirable rapid increase in cell number, and thus tumour burden, as cell death is averted.

Introduction of irreversible growth arrest in cancer cells utilizing a built‐in, but currently under‐appreciated, program might, nevertheless, present an attractive therapeutic target. Pro‐senescence treatments may have been prematurely dismissed for a number of reasons. First, senescent cells may alter the tissue microenvironment by expressing growth factors, degradative enzymes and inflammatory cytokines 68, which may induce proliferation, dedifferentiation and invasion by premalignant cells 69. Secondly, growth‐promoting signalling of residual populations of cancer cells, albeit senescent, may still be of concern 15, and only recently have studies emerged reporting that senescent cells may be cleared by the immune system 70. In contrast to conventional cancer treatments with rapid gross tumour reduction and eradicative intent, pro‐senescent treatment might initially increase number of cancer cells as cell death is averted. In terms of later response, however, reactivated senescence might avoid eradicating most tumour cells altogether, instead causing subpopulations to ultimately compete so as to push the tumour as a whole into a self‐limiting state. The result would be to therapeutically maintain the tumour in a dormant state as a chronic asymptomatic condition as opposed to a frank disease. In conclusion, response of a tumour population to potential therapeutic induction of senescence, with its short‐term burst but longer term suppression, may comprise a welcome dynamic reversal vis‐à‐vis conventional types of treatment where an initial reduction is seen in tumour volume– often many orders of magnitude below level of clinical detection – followed by accelerated repopulation beyond initial tumour burden 23, 35 that often proves fatal. These observations motivate investigations into combining conventional treatments that reduce tumour volume with subsequent pro‐senescence therapy to maintain the reduced tumour in a controlled, dormant‐like state.

In the presented model, senescent cells were shown to act to inhibit kinetics of pre‐senescent cells. Clearance of senescent cells dampen the observed modulation towards tumour control, which suggests that failure to remove these post‐mitotic cells may not be a major concern. The model, however, needs to be extended to account complex crosstalk of senescent cells with pre‐senescent populations, adjacent non‐transformed tissue cells and the host immune system 10, 69, 71 – all of which are expected to alter intrinsic tumour kinetics directly as well as indirectly by modulation of the senescent cell population and the supporting host.