Short-range migration can alter evolutionary dynamics in solid tumors

Azimzade, Youness; Saberi, Abbas Ali

doi:10.1088/1742-5468/ab4983

“…To implement a spatially explicit model for population dynamics that captures complex spatiotemporal interactions, we use the two species Eden model [39,40]. This model has been used in a wide variety of research on population dynamics [16,38,41,42], primarily due to an accurate representation of bacteria range expansion [11,40]. We consider two population kinds, (A) and (B), living in a (2+1)D environment of sizes w × l × l where populations can live and expand in z direction (see FIG.…”

Section: Modelmentioning

confidence: 99%

“…These domain walls separate different types and play a crucial role in the evolutionary dynamics of biofilms [11,13]. Due to such a role, quantitative understanding of domain wall structures has gained increasing attention in the past few years [14][15][16][17]. Based on such studies, we know that the geometry of individuals [18] alongside ecological processes and underlying physical interactions [12,19,20] regulate the geometry of domain walls and evolutionary dynamics.…”

mentioning

confidence: 99%

Geometrically Regulating Evolutionary Dynamics in Biofilms

Azimzade,

Saberi

2021

Preprint

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Theoretical understanding of evolutionary dynamics in spatially structured populations often relies on non-spatial models. Biofilms are among such populations where a more accurate understanding is of theoretical interest and can reveal new solutions to existing challenges. Here, we studied how the geometry of the environment affects the evolutionary dynamics of expanding populations, using the Eden model. Our results show that fluctuations of sub-populations during range expansion in 2D and 3D environments are not Brownian. Furthermore, we found that the substrate's geometry interferes with the evolutionary dynamics of populations that grow upon it. Inspired by these findings, we propose a periodically wedged pattern on surfaces prone to develop biofilms. On such patterned surfaces, natural selection becomes less effective and beneficial mutants would have a harder time establishing. Additionally, this modification accelerates genetic drift and leads to less diverse biofilms. Both interventions are highly desired for biofilms.INTRODUCTION.

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“…Discrete models have been developed to study invasion as well [18][19][20][21] . Stepping Stone Model (SSM) is one of the best-known models to describe population dynamics 22 .…”

Section: ξmentioning

confidence: 99%

Invasion front dynamics in disordered environments

Azimzade

¹

,

Sasar

²

,

Maleki

³

2020

Sci Rep

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Invasion occurs in environments that are normally spatially disordered, however, the effect of such a randomness on the dynamics of the invasion front has remained less understood. Here, we study Fisher’s equation in disordered environments both analytically and numerically. Using the Effective Medium Approximation, we show that disorder slows down invasion velocity and for ensemble average of invasion velocity in disordered environment we have $$\bar{v}=v_0 (1-|\xi |^2/6)$$ v ¯ = v 0 ( 1 - | ξ | 2 / 6 ) where $$|\xi |$$ | ξ | is the amplitude of disorder and $$v_0$$ v 0 is the invasion velocity in the corresponding homogeneous environment given by $$v_0=2\sqrt{RD_0}$$ v 0 = 2 R D 0 . Additionally, disorder imposes fluctuations on the invasion front. Using a perturbative approach, we show that these fluctuations are Brownian with a diffusion constant of: $$D_{C}= \dfrac{1}{8} \xi ^2\sqrt{RD_0 (1-|\xi |^2/3)}$$ D C = 1 8 ξ 2 R D 0 ( 1 - | ξ | 2 / 3 ) . These findings were approved by numerical analysis. Alongside this continuum model, we use the Stepping Stone Model to check how our findings change when we move from the continuum approach to a discrete approach. Our analysis suggests that individual-based models exhibit inherent fluctuations and the effect of environmental disorder becomes apparent for large disorder intensity and/or high carrying capacities.

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“…In invasive tumors, cancer cells take over the host tissue by pushing existing healthy cells 9 and degrading the physical structure of extracellular matrix (ECM) 10 – 12 alongside various chemical and mechanical interactions 13 , 14 . Facing such a barrier can affect the evolutionary dynamics of tumors in different aspects 15 , 16 . More importantly, tumor cells that push the healthy tissue belong to different clones 17 .…”

Section: Introductionmentioning

confidence: 99%

Invasion front dynamics of interactive populations in environments with barriers

Azimzade

¹

2022

Sci Rep

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Invading populations normally comprise different subpopulations that interact while trying to overcome existing barriers against their way to occupy new areas. However, the majority of studies so far only consider single or multiple population invasion into areas where there is no resistance against the invasion. Here, we developed a model to study how cooperative/competitive populations invade in the presence of a physical barrier that should be degraded during the invasion. For one dimensional (1D) environment, we found that a Langevin equation as $$dX/dt=V_ft+\sqrt{D_f}\eta (t)$$ d X / d t = V f t + D f η ( t ) describing invasion front position. We then obtained how $$V_f$$ V f and $$D_f$$ D f depend on population interactions and environmental barrier intensity. In two dimensional (2D) environment, for the average interface position movements we found a Langevin equation as $$dH/dt=V_Ht+\sqrt{D_H}\eta (t)$$ d H / d t = V H t + D H η ( t ) . Similar to the 1D case, we calculate how $$V_H$$ V H and $$D_H$$ D H respond to population interaction and environmental barrier intensity. Finally, the study of invasion front morphology through dynamic scaling analysis showed that growth exponent, $$\beta$$ β , depends on both population interaction and environmental barrier intensity. Saturated interface width, $$W_{sat}$$ W sat , versus width of the 2D environment (L) also exhibits scaling behavior. Our findings show revealed that competition among subpopulations leads to more rough invasion fronts. Considering the wide range of shreds of evidence for clonal diversity in cancer cell populations, our findings suggest that interactions between such diverse populations can potentially participate in the irregularities of tumor border.

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Short-range migration can alter evolutionary dynamics in solid tumors

Cited by 7 publications

References 71 publications

Geometrically Regulating Evolutionary Dynamics in Biofilms

Geometrically Regulating Evolutionary Dynamics in Biofilms

Invasion front dynamics in disordered environments

Invasion front dynamics of interactive populations in environments with barriers

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