BBC Russian

Editors' Suggestion

Fingering Instability Accelerates Population Growth of a Proliferating Cell Collective

Yiyang Ye (叶毅扬) and Jie Lin (林杰)

Phys. Rev. Lett. 132, 018402 – Published 3 January 2024

Abstract

During the growth of a cell collective, such as proliferating microbial colonies and epithelial tissues, the local cell growth increases the local pressure, which in turn suppresses cell growth. How this pressure-growth coupling affects the growth of a cell collective remains unclear. Here, we answer this question using a continuum model of a cell collective. We find that a fast-growing leading front and a slow-growing interior of the cell collective emerge due to the pressure-dependent growth rate. The leading front can exhibit fingering instability, and we confirm the predicted instability criteria numerically with the leading front explicitly simulated. Intriguingly, we find that fingering instability is not only a consequence of local cell growth but also enhances the entire population’s growth rate as positive feedback. Our work unveils the fitness advantage of fingering formation and suggests that the ability to form protrusions can be evolutionarily selected.

Received 20 June 2023
Accepted 17 November 2023

DOI:https://doi.org/10.1103/PhysRevLett.132.018402

Physics Subject Headings (PhySH)

Cell growth Cell migration Fingering instability Growth

Living matter & active matter

Physics of Living Systems

Authors & Affiliations

Yiyang Ye (叶毅扬)¹ and Jie Lin (林杰)^1,2,*

¹Center for Quantitative Biology, Peking University, Beijing, China
²Peking-Tsinghua Center for Life Sciences, Peking University, Beijing, China

^*Corresponding author: [email protected]

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 132, Iss. 1 — 5 January 2024

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
A schematic of a cell collective growing in the $x$ direction. In the continuum model, the velocity field under active cell growth is described as Eqs. (1) and (2). In numerical simulations, we use a level-set function $ϕ$ to distinguish the cell collective from the passive fluid, where $ϕ = 0$ corresponds to the interface.
Reuse & Permissions
Figure 2
Theoretical predictions (dashed lines) in the absence of fingering instability are compared with numerical simulations (solid lines) at two threshold pressures $p_{c}$ .
Reuse & Permissions
Figure 3
Conditions of fingering instability and numerical verifications. (a) In the linear instability analysis, instability occurs when ${\dot{ξ}}_{k} / ξ_{k} > 0$ . Circles mark the critical wave numbers where ${\dot{ξ}}_{k} / ξ_{k} = 0$ . Triangles mark the wave numbers with the maximum ${\dot{ξ}}_{k} / ξ_{k}$ . (b) A sinusoidal perturbation is applied to the flat interface in the numerical simulations. A negative correlation between the perturbation and the interface velocity change leads to a stable interface and vice versa for an unstable interface. The unstable example corresponds to $x_{I} = 0.7$ , $k = 12 π$ in (c), and the stable example corresponds to $x_{I} = 0.7$ , $k = 16 π$ in (c). (c),(d) Phase diagram for the interface stability. The solid line represents the theoretical result of the linear instability analysis. According to simulations, stable interfaces are marked as green dots, while unstable ones are marked as red crosses. In (c), the interface instability is dominated by the pressure gradient difference across the interface, and the dashed line is the prediction merely considering the effects of the pressure gradient. In (d), the interface instability is purely induced by active cell growth since $α \equiv ζ_{1} / ζ_{2} = 1$ . The dashed line represents the asymptotic result in the limit $x_{I} ≫ 1 / k_{c} ≫ x_{c}$ .
Reuse & Permissions
Figure 4
Fingering instability accelerates population growth. (a) The local growth rate of a cell collective at a specific time, free of instability, is displayed with a color bar on the left. The arrows represent the velocity field, and its magnitude is displayed in the color bar on the right. Here, $α = 9.35 \times 10^{- 2}$ , $γ = 1 \times 10^{- 3}$ . The interface is highlighted as the gray curve. (b) The pressure pattern of the same simulation as (a). The contour lines of the pressure field are shown with the pressure values on the right. The pressure value decreases from left to right. (c) In contrast to (a), we use a small $γ = 3.73 \times 10^{- 6}$ and apply a perturbation to the initial flat interface so that the cell collective exhibits fingering instability. In this case, cells in the fingers have higher growth rates and larger velocity magnitudes than in the bulk. (d) The pressure pattern of the same simulation as (c), which is significantly lower than the case without instability, as shown in (a). (e) The population growth rate of the cell collective $Λ_{p}$ as a function of the current volume $V_{cell}$ given different surface tension constants. The curves stop when any part of the collective reaches the boundary in simulations. (f) The population growth rate of a cell collective without pressure-growth coupling does not depend on $γ$ and is always equal to the local cell growth rate $Λ_{p} = 1$ . (g) Heat map of the population growth rate $Λ_{p}$ at a given total cell volume $V_{cell} = 0.232$ as a function of $α$ and $γ$ .
Reuse & Permissions

Physical Review Letters

Fingering Instability Accelerates Population Growth of a Proliferating Cell Collective

Yiyang Ye (叶毅扬) and Jie Lin (林杰)

Phys. Rev. Lett. 132, 018402 – Published 3 January 2024

Abstract

Physics Subject Headings (PhySH)

Authors & Affiliations

Article Text (Subscription Required)

Supplemental Material (Subscription Required)

References (Subscription Required)

Issue

Access Options

Authorization Required

Other Options

Download & Share

Images

Figure 1

Figure 2

Figure 3

Figure 4

Log In

Search

Article Lookup

Paste a citation or DOI

Enter a citation