The role of Allee effect in modelling post resection recurrence of glioblastoma

Neufeld, Zoltán; Witt, William von; Lakatos, Dóra; Wang, Jiaming; Hegedűs, Balázs; Czirók, András

doi:10.1371/journal.pcbi.1005818

Cited by 56 publications

(71 citation statements)

References 47 publications

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“…The possibility of exploiting ecology for the treatment of tumors based on studies in conservation biology about extinction and control of invasive species has been proposed (13)(14)(15)(16)(17)(18)(19)(20)(21)(22), but this is the first work to our knowledge that has explicitly tested for the presence of the Allee effect in a regime in which low cancer cell populations can be measured and fit to a number of stochastic model structures representing different biological hypotheses about the Allee effect. Our finding is consistent with pre-clinical(2) and clinical observations (3,56) of threshold-like behavior of tumor growth or slowed tumor growth following resection. Evidence for the Allee effect is also consistent with evidence of cooperation among cancer cell subclones as has been amply demonstrated (5-7,57-59) An understanding of subpopulation interactions and their molecular mediators that drive the observed Allee effect offer new approaches to manipulate cancer cell growth dynamics in favor of extinction.…”

Section: Discussionsupporting

confidence: 91%

“…However, the ability to measure early stage tumor growth, at a stage when only low cell numbers are present, is not feasible in the clinic, as patients present only after the tumor has exceeded the lower limit of detection (about 1 million cells on a typical CT scan (1)). Recent findings in preclinical mouse models (2) and from clinical outcomes following tumor resection (3) reveal that tumor growth at low tumor cell densities does not match the expectation of exponential growth. These findings give rise to an intriguing possibility: does tumor cell growth deviate from the model of exponential growth at low tumor cell densities?…”

Section: Introductionmentioning

confidence: 99%

“…A mechanistic view for deviations from (near) exponential early growth is the Allee effect which results from cell-cell interactions in the low-cell number regime which can promote growth. Indeed, recently deviations from exponential growth in early stages of tumor growth have been observed in glioblastoma, where patient brain tumors were resected and monitored over time for relapse (3). These studies of relapsed tumor growth revealed that the observed growth rate at the clinically detectable stages of tumor growth failed to match models of simple logistic growth, and instead were better described by a weak Allee effect model.…”

Section: Introductionmentioning

confidence: 99%

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Cancer cell population growth kinetics at low densities deviate from the exponential growth model and suggest an Allee effect

Johnson

Howard

et al. 2019

Preprint

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Models of cancer cell population expansion assume exponential growth kinetics at low cell densities, with deviations from exponential growth only at higher densities due to limited resources such as space and nutrients. However, recent pre-clinical and clinical observations of tumor initiation or recurrence indicate the presence of tumor growth kinetics in which growth rates scale with cell numbers. These observations are analogous to the cooperative behavior of species in an ecosystem described by the ecological principle of the Allee effect. In preclinical and clinical models however, tumor growth data is limited by the lower limit of detection (i.e. a measurable lesion) and confounding variables, such as tumor microenvironment and immune responses may cause and mask deviations from exponential growth models. In this work, we present alternative growth models to investigate the presence of an Allee effect in cancer cells seeded at low cell densities in a controlled in vitro setting. We propose a stochastic modeling framework to consider the small number of cells in this low-density regime and use the moment approach for stochastic parameter estimation to calibrate the stochastic growth trajectories. We validate the framework on simulated data and apply this approach to longitudinal cell proliferation data of BT-474 luminal B breast cancer cells. We find that cell population growth kinetics are best described by a model structure that considers the Allee effect, in that the birth rate of tumor cells depends on cell number. This indicates a potentially critical role of cooperative behavior among tumor cells at low cell densities with relevance to early stage growth patterns of emerging tumors and relapse. Author SummaryThe growth kinetics of cancer cells at very low cell densities are of utmost clinical importance as the ability of a small number of newly transformed or surviving cells to grow exponentially and thus, to "take off" underlies tumor formation and relapse after treatment. Mathematical models of stochastic tumor cell growth typically assume a stochastic birth-death process of cells impacted by limited nutrients and space when cells reach high density, resulting in the widely accepted logistic growth model. Here we present an in-depth investigation of alternate growth models adopted from ecology to describe potential deviations from a simple cell autonomous birth-death model at low cell densities. We show that our stochastic modeling framework is robust and can be used to identify the underlying structure of stochastic growth trajectories from both simulated and experimental data taken from a controlled in vitro setting in which we can capture data from the relevant low cell density regime. This work suggests that the assumption of cell autonomous proliferation via a constant exponential growth rate at low cell densities may not be appropriate for all cancer cell growth dynamics. Consideration of cooperative behavior amongst tumor cells in this regime is critical for elucidating strategies for controll...

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Section: Discussionsupporting

confidence: 91%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Cancer cell population growth kinetics at low densities deviate from the exponential growth model and suggest an Allee effect

Johnson

Howard

et al. 2019

Preprint

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“…To detect cell-occupied area, a global threshold was applied to the local standard deviation of image brightness following the procedures outlined in Neufeld et al (2017).…”

Section: Image Processingmentioning

confidence: 99%

SPECC1L-deficient palate mesenchyme cells show speed and directionality defect

Goering

Isai

Hall

et al. 2019

Preprint

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Clefts of the lip and/or palate (CL/P) are common anomalies that occur in 1/800 live births. Pathogenic SPECC1L variants identified in patients with rare atypical clefts and syndromic CL/P suggest the gene plays a primary role in face and palate development. We have generated Specc1l gene-trap (Specc1l cGT ) and truncation (Specc1l DC510 ) alleles that cause embryonic or perinatal lethality, respectively.Specc1l cGT/DC510 compound mutants show delayed and abnormal palatal shelf elevation at E14.5. By E15.5, the mutant shelves do elevate and fuse, however, the palatal rugae form abnormally. Palatogenesis requires extensive mesenchymal remodeling, especially during palatal shelf elevation. We posit that this remodeling involves collective movement of neural crest-derived palatal mesenchyme cells. Live time-lapse microscopy was performed to visualize in vitro wound-repair assays with wildtype and SPECC1L-deficient primary mouse embryonic palatal mesenchyme (MEPM) cells. SPECC1L-deficient MEPM cells consistently showed delayed closure in wound-repair assays. To evaluate which features of cellular movement were responsible, we performed automated particle image velocimetry (PIV) and manual cell tracking. The analyses revealed that both cell speed and directionality are disrupted in SPECC1L-deficient cells compared to controls.To determine if primary MEPM cells can move collectively, we assayed stream formation, which is a hallmark of collective movement. Indeed, MEPM cultures displayed correlated movement of neighboring cells. Importantly, correlation length was reduced in SPECC1Ldeficient cultures, consistent with a role for SPECC1L in collective migration.Furthermore, we demonstrated that activation of the PI3K-AKT pathway with the 740Y-P small molecule can rescue the wound-closure delay in SPECC1L-deficient MEPM cells. 3Cell tracking analyses showed that this rescue was due to both increased speed and improved directionality. Altogether, our data showed a novel role for SPECC1L in guided movement through modulation of PI3K-AKT signaling.

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“…3, as well as videos presented in the Supplementary Information, we show that averaged density data from the IBM, C , agrees very well with C, conrming Comparison of data from the IBM with the solution of the corresponding global population description for dierent suites of proliferation rates. Simulations of the IBM are shown with three dierent familes of proliferation rates p n (a,d,g), described in equation(8), along with the resulting per-capita rate of the global population model (b,e,h), described in equation(9). The three dierent families of proliferation rates are referred to as Case 1 (ac,j), Case 2 (df,k), and Case 3 (gi,l), respectively.…”

mentioning

confidence: 99%

Unpacking the Allee effect: determining individual-level mechanisms that drive global population dynamics

Fadai

Johnston

Simpson

2019

Preprint

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We present the rst solid theoretical foundation for interpreting the origin of Allee eects by providing the missing link in understanding how local individual-based mechanisms translate to global population dynamics. Allee eects were originally proposed to describe population dynamics that cannot be explained by exponential and logistic growth models. However, standard methods simply calibrate continuum models incorporating Allee eects to match observed global population dynamics, without providing any mechanistic insight. By introducing a stochastic individual-based model, with proliferation, death, and motility rates that depend on local density, we present the rst modelling framework that gives rise to a range of global Allee eects. Using data from ecology and cell biology, we unpack individual-level mechanisms implicit in an Allee eect model and provide simulation tools for others to repeat this analysis.

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The role of Allee effect in modelling post resection recurrence of glioblastoma

Cited by 56 publications

References 47 publications

Cancer cell population growth kinetics at low densities deviate from the exponential growth model and suggest an Allee effect

Cancer cell population growth kinetics at low densities deviate from the exponential growth model and suggest an Allee effect

SPECC1L-deficient palate mesenchyme cells show speed and directionality defect

Unpacking the Allee effect: determining individual-level mechanisms that drive global population dynamics

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