Non-stem cancer cell kinetics modulate solid tumor progression

Abstract

Background: Solid tumors are heterogeneous in composition. Cancer stem cells (CSCs) are believed to drive tumor progression, but the relative frequencies of CSCs versus non-stem cancer cells span wide ranges even within tumors arising from the same tissue type. Tumor growth kinetics and composition can be studied through an agent-based cellular automaton model using minimal sets of biological assumptions and parameters. Herein we describe a pivotal role for the generational life span of non-stem cancer cells in modulating solid tumor progression in silico.

Results: We demonstrate that although CSCs are necessary for progression, their expansion and consequently tumor growth kinetics are surprisingly modulated by the dynamics of the non-stem cancer cells. Simulations reveal that slight variations in non-stem cancer cell proliferative capacity can result in tumors with distinctly different growth kinetics. Longer generational life spans yield self-inhibited tumors, as the emerging population of non-stem cancer cells spatially impedes expansion of the CSC compartment. Conversely, shorter generational life spans yield persistence-limited tumors, with symmetric division frequency of CSCs determining tumor growth rate. We show that the CSC fraction of a tumor population can vary by multiple orders of magnitude as a function of the generational life span of the non-stem cancer cells.

Conclusions: Our study suggests that variability in the growth rate and CSC content of solid tumors may be, in part, attributable to the proliferative capacity of the non-stem cancer cell population that arises during asymmetric division of CSCs. In our model, intermediate proliferative capacities give rise to the fastest-growing tumors, resulting in self-metastatic expansion driven by a balance between symmetric CSC division and expansion of the non-stem cancer population. Our results highlight the importance of non-stem cancer cell dynamics in the CSC hypothesis, and may offer a novel explanation for the large variations in CSC fractions reported in vivo.

Figure 1

Cancer stem cells (CSCs, yellow) may divide symmetrically (curved black arrows) to generate two identical CSCs; or asymmetrically (red arrows) to self-renew and yield a non-stem cancer cell with a discrete maximum proliferative capacity. Non-stem cancer cells may divide only symmetrically (straight horizontal black arrows), with both parent and daughter experiencing a decrement in proliferative capacity. Mortal non-stem cancer cells with exhausted proliferative capacity die upon the ensuing division attempt. Non-stem cancer cells inherit generational life spans from the parent CSCs, resulting in a hierarchy depth (red to black gradient) that determines tumor population heterogeneity. Shown are hierarchical progressions of tumor populations originating from A) a CSC conferring ρ_max = 4 and B) a CSC conferring ρ_max = 1.

Figure 2

Flow of control in the agent-based model. All cells require available adjacent space to either migrate or proliferate, or they remain quiescent for the given time interval. Cells that have maturated through the cell cycle may proliferate, and the resulting progeny will initially occupy a neighboring grid locus. Non-stem cancer cells with no remaining replicative potential die upon a decision to proliferate, leaving the previously occupied grid locus empty.

Figure 3

Simulation results representing the set of conditions at which tumors most rapidly reach 5x104 total cell population when symmetric CSC division frequency ps = 1%. A) Simulation results representing the set of conditions to most rapidly reach 5 × 10⁴ total cell population at symmetric CSC division frequency p_s = 1%. Shown from left to right: migration rates (μ) of 0, 5, 10, and 15 cell widths per day. Yellow CSCs enlarged for visibility. B) Corresponding growth curves for model tumors at all values of replicative potential ρ_max = 0-10. Error bars correspond to SEM (n = 10).

Figure 4

Simulation results representing the set of conditions at which tumors most rapidly reach 5x104 total cell population when symmetric CSC division frequency ps = 10%. A) Simulation results representing the set of conditions to most rapidly reach 5 × 10⁴ total cell population at symmetric CSC division frequency p_s = 10%. Shown from left to right: migration rates (μ) of 0, 5, 10, and 15 cell widths per day. Yellow CSCs enlarged for visibility. B) Corresponding growth curves for model tumors at all values of replicative potential ρ_max = 0-10. Error bars correspond to SEM (n = 10).

Figure 5

Comparison of tumor populations across all generational life spans at tcritical when symmetric CSC division frequency ps=1%. A) Time to simulation termination when p_s = 1% and B) average population size at t_critical for all ρ_max values and migration speeds. Non-zero migration values demonstrate non-monotonic behavior and distinct optima at intermediate values of replicative potential. At t_critical, model tumors from all ρ_max values demonstrate a wide range of sizes. C) Matching pairs of model tumors for non-zero migration values differing only by the replicative potential of the seeding CSC. In most cases, morphologies are sufficiently distinguishable to enable estimation of CSC content and therefore the replicative potential of the cell of tumor origin. Top: μ = 5, left ρ_max = 2, right ρ_max = 8. Middle: μ = 10, left ρ_max = 3, right ρ_max = 10. Bottom: μ = 15, left ρ_max = 5, right ρ_max = 10. Yellow CSCs enlarged for visibility.

Figure 6

Comparison of tumor populations across all generational life spans at tcritical when symmetric CSC division frequency ps=10%. A) Time to simulation termination when p_s = 10% and B) average population size at t_critical for all ρ_max values and migration speeds. Non-zero migration values demonstrate non-monotonic behavior and distinct optima at intermediate values of replicative potential. At t_critical, model tumors from all ρ_max values demonstrated a wide range of sizes. C) Matching pairs of model tumors for non-zero migration values differing only by the replicative potential of the seeding CSC. In most cases, macroscopic appearances are so similar that analysis for CSC content would be necessary to identify the replicative potential of the cell of tumor origin. Top: μ = 5, left ρ_max = 2, right ρ_max = 5. Middle: μ = 10, left ρ_max = 3, right ρ_max = 7. Bottom: μ = 15, left ρ_max = 1, right ρ_max = 9. Yellow CSCs enlarged for visibility.

Figure 7

The relative size of the CSC compartment of model tumors is inversely proportional to the generational life span of the non-stem cancer cell progeny. Top row, p_s = 1%; bottom row, p_s = 10%. From left to right, μ = 0, 5, 10, and 15 cell widths/day. Model tumors seeded by CSC with low replicative potentials depended more strongly on symmetric division for macroscopic expansion and as such comprised a higher CSC fraction than those comprising deeper mortal non-stem cancer cell hierarchies. Early high amplitude fluctuations are attributable to the stochastic nature of growth, but in all cases, CSC fraction approaches a pseudo steady-state composition consistent with self-metastatic expansion.