Spatiotemporal dynamics of different growth-diffusion systems on a percolation lattice

Liang, Yiqin; Yang, Renlong; Guo, Yifan; Jiang, Chongming; Liu, Lizhi; Wan, Yanzi; Shao, Youxiang

doi:10.1103/physreve.99.042401

Cited by 3 publications

(3 citation statements)

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“…In the studies of (Jiang et al, 2014, 2016) and (Liang et al, 2019), the used parameters were cited from various references and thus lacked consistency. As a result, uncertainty assessment of the parameters could be hindered.…”

Section: Introductionmentioning

confidence: 99%

“…As a result, uncertainty assessment of the parameters could be hindered. More-over, the spatiotemporal mean-field approximations used in partial differential equations (PDE) in (Liang et al, 2019) could neglect some fluctuation details, especially under the circumstances with low cell densities featuring the Allee effect of concern. Simpson et al (2010) have studied different mesoscopic migration patterns and concluded that formal continuous description might not exist for dynamic systems with strong mesoscopic patterns.…”

Section: Introductionmentioning

confidence: 99%

“…However, the Logistic growth model they used proved inaccurate when cell density is low (Johnson et al, 2019; Korolev et al, 2014; Neufeld et al, 2017). Liang et al (2019) have tried to analyze such invasiveness theoretically and introduced the Allee effect for higher accuracy, and they proved theoretically that the Logistic model and the Allee model behave differently. They also calculated the critical exponents of corresponding growth-migration processes with the finite size scaling (FSS) method, using the successful penetration rate (SPR) as the order parameter.…”

Section: Introductionmentioning

confidence: 99%

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Invasiveness of Cancer Populations in a Two-dimensional Percolation cluster: a Stochastic Mathematical Approach

Yang

Shao

Jiang

2022

Preprint

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A framework for the software Unstructured Reaction-Diffusion Master Equation (URDME) was developed. A mitogenic paracrine signaling pathway was introduced phenomenologically to show how cells cooperate with one another. We modeled the emerging Allee effect using low seeding density culture (LSDC) assays to fit the model parameters. Finite time scaling (FTS) was found to be a useful tool for quantifying invasiveness in cancer populations. Through simulation, we analyzed the growth-migration dynamics of BT474 cancer cell populations in-vitro in a 2D percolation cluster and calculated the SPR (successful penetration rate). By analyzing the temporal trajectories of the SPR, we could determine the critical exponents of the critical SPR scaling relation $RT^{-\beta}\sim\widetilde f\left(T^{1/\nu}\left(p-p_c\right)\right) $. Moreover, the SPR transition point defined according to the FTS theory, $p_c $, is negatively correlated with the invasiveness of cancer cell populations. The $p_c $ of the three virtual cancer populations distinctly designated by varying the parameter set of the same model are 0.3408, 0.3675, and 0.4454, respectively. Therefore, the FTS algorithm may be useful in determining invasiveness. Through the simplistic phenomenological paracrine model, inter-cell cooperation and mutual mitogenic boosting are enabled, causing the Allee effect to occur. Such a method could be applied to other circumstances as an example of the quantitatively falsifiable emerging theory.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%