Bayesian inference on the Allee effect in cancer cell line populations using time-lapse microscopy images. (English) Zbl 1528.92015
Summary: The Allee effect describes the phenomenon that the per capita reproduction rate increases along with the population density at low densities. Allee effects have been observed at all scales, including in microscopic environments where individual cells are taken into account. This is great interest to cancer research, as understanding critical tumour density thresholds can inform treatment plans for patients. In this paper, we introduce a simple model for cell division in the case where the cancer cell population is modelled as an interacting particle system. The rate of the cell division is dependent on the local cell density, introducing an Allee effect. We perform parameter inference of the key model parameters through Markov chain Monte Carlo, and apply our procedure to two image sequences from a cervical cancer cell line. The inference method is verified on in silico data to accurately identify the key parameters, and results on the in vitro data strongly suggest an Allee effect.
Keywords:
agent based models/individual based model; MCMC; population size; reaction-diffusion mechanisms; stochastic differential equations; cancer modellingSoftware:
PRMLTReferences:
| [1] | Agrawal, R.; Squires, C.; Yang, K.; Shanmugam, K.; Uhler, C., Abcd-strategy: Budgeted experimental design for targeted causal structure discovery, (The 22nd International Conference on Artificial Intelligence and Statistics (2019), PMLR), 3400-3409 |
| [2] | Basanta, D.; Anderson, A. R., Exploiting ecological principles to better understand cancer progression and treatment, Interface Focus, 3, 4, Article 20130020 pp. (2013) |
| [3] | Bishop, C. M.; Nasrabadi, N. M., Pattern Recognition and Machine Learning. Vol. 4 (2006), Springer · Zbl 1107.68072 |
| [4] | Boukal, D. S.; Berec, L., Single-species models of the Allee effect: Extinction boundaries, sex ratios and mate encounters, J. Theoret. Biol., 218, 3, 375-394 (2002) |
| [5] | Browning, A. P.; McCue, S. W.; Binny, R. N.; Plank, M. J.; Shah, E. T.; Simpson, M. J., Inferring parameters for a lattice-free model of cell migration and proliferation using experimental data, J. Theoret. Biol., 437, 251-260 (2018) · Zbl 1394.92019 |
| [6] | Cassini, M. H., Consequences of local Allee effects in spatially structured populations, Oecologia, 165, 3, 547-552 (2011) |
| [7] | Cleves, M.; Gould, W.; Gutierrez, R.; Marchenko, Y., An Introduction to Survival Analysis Using Stata (2008), Stata Press |
| [8] | Courchamp, F.; Berec, L.; Gascoigne, J., Allee Effects in Ecology and Conservation (2008), OUP: OUP Oxford |
| [9] | Da Silva, J. G.; De Morais, R. M.; Da Silva, I. C.R.; Adimy, M.; De Arruda Mancera, P. F., A mathematical model for treatment of papillary thyroid cancer using the Allee effect, J. Biol. Systems, 28, 03, 701-718 (2020) · Zbl 1451.92163 |
| [10] | Delitala, M.; Ferraro, M., Is the Allee effect relevant in cancer evolution and therapy?, AIMS Mathematics, 5, 6, 7649-7660 (2020) · Zbl 1484.92072 |
| [11] | dos Santos, R. V.; Ribeiro, F. L.; Martinez, A. S., Models for Allee effect based on physical principles, J. Theor. Biol., 385, 143-152 (2015) · Zbl 1343.92452 |
| [12] | Fadai, N. T.; Johnston, S. T.; Simpson, M. J., Unpacking the Allee effect: determining individual-level mechanisms that drive global population dynamics, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 476, 2241, Article 20200350 pp. (2020) · Zbl 1472.92174 |
| [13] | Fadai, N. T.; Simpson, M. J., Population dynamics with threshold effects give rise to a diverse family of Allee effects, Bull. Math. Biol., 82, 6, 74 (2020) · Zbl 1444.92086 |
| [14] | Fieberg, J.; Ellner, S. P., When is it meaningful to estimate an extinction probability?, Ecology, 81, 7, 2040-2047 (2000) |
| [15] | Gerlee, P.; Altrock, P. M.; Malik, A.; Krona, C.; Nelander, S., Autocrine signaling can explain the emergence of Allee effects in cancer cell populations, PLoS Comput. Biol., 18, 3, Article e1009844 pp. (2022) |
| [16] | González-Olivares, E., Gonzalez-Yanez, B., Mena-Lorca, J., Ramos-Jiliberto, R., 2006. Modelling the Allee effect: are the different mathematical forms proposed equivalents. In: Proceedings of the International Symposium on Mathematical and Computational Biology BIOMAT, Vol. 2007. pp. 53-71. |
| [17] | Hörmander, L., The Analysis of Linear Partial Differential Operators IV: Fourier Integral Operators (2009), Springer · Zbl 1178.35003 |
| [18] | Huan, X.; Marzouk, Y., Gradient-based stochastic optimization methods in Bayesian experimental design, Int. J. Uncertain. Quantif., 4, 6 (2014) · Zbl 1497.62069 |
| [19] | Johnson, K. E.; Howard, G.; Mo, W.; Strasser, M. K.; Lima, E. A.; Huang, S.; Brock, A., Cancer cell population growth kinetics at low densities deviate from the exponential growth model and suggest an Allee effect, PLoS Biol., 17, 8, Article e3000399 pp. (2019) |
| [20] | Klebaner, F. C., Introduction to Stochastic Calculus with Applications (2012), World Scientific Publishing Company · Zbl 1274.60005 |
| [21] | Kynaston, J. C.; Guiver, C.; Yates, C. A., Equivalence framework for an age-structured multistage representation of the cell cycle, Phys. Rev. E, 105, 6, Article 064411 pp. (2022) |
| [22] | Li, C.; Godsill, S., Sequential inference methods for non-homogeneous poisson processes with state-space prior, IEEE Trans. Signal Process., 69, 1154-1168 (2021) · Zbl 1543.62495 |
| [23] | Masters, J. R., Hela cells 50 years on: the good, the bad and the ugly, Nat. Rev. Cancer, 2, 4, 315-319 (2002) |
| [24] | Menon, R.; Korolev, K. S., Public good diffusion limits microbial mutualism, Phys. Rev. Lett., 114, 16, Article 168102 pp. (2015) |
| [25] | Morris, D. W., Measuring the Allee effect: Positive density dependence in small mammals, Ecology, 83, 1, 14-20 (2002) |
| [26] | Neumann, B.; Walter, T.; Hériché, J.-K.; Bulkescher, J.; Erfle, H.; Conrad, C.; Rogers, P.; Poser, I.; Held, M.; Liebel, U., Phenotypic profiling of the human genome by time-lapse microscopy reveals cell division genes, Nature, 464, 7289, 721-727 (2010) |
| [27] | Obeyesekere, M. N.; Zimmerman, S. O.; Tecarro, E. S.; Auchmuty, G., A model of cell cycle behavior dominated by kinetics of a pathway stimulated by growth factors, Bull. Math. Biol., 61, 5, 917-934 (1999) · Zbl 1323.92073 |
| [28] | Sapsis, T. P., Output-weighted optimal sampling for Bayesian regression and rare event statistics using few samples, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 476, 2234, Article 20190834 pp. (2020) · Zbl 1439.62177 |
| [29] | Simpson, M. J.; Browning, A. P.; Warne, D. J.; Maclaren, O. J.; Baker, R. E., Parameter identifiability and model selection for sigmoid population growth models, J. Theoret. Biol., 535, Article 110998 pp. (2022) · Zbl 1483.92113 |
| [30] | Sun, G.-Q., Mathematical modeling of population dynamics with Allee effect, Nonlinear Dynam., 85, 1-12 (2016) |
| [31] | Tilman, D.; May, R. M.; Lehman, C. L.; Nowak, M. A., Habitat destruction and the extinction debt, Nature, 371, 6492, 65-66 (1994) |
| [32] | Ulman, V.; Maška, M.; Magnusson, K. E.; Ronneberger, O.; Haubold, C.; Harder, N.; Matula, P.; Matula, P.; Svoboda, D.; Radojevic, M., An objective comparison of cell-tracking algorithms, Nat. Methods, 14, 12, 1141-1152 (2017) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
