Nonuniversality of front fluctuations for compact colonies of nonmotile bacteria

Abstract

The front of a compact bacterial colony growing on a Petri dish is a paradigmatic instance of non-equilibrium fluctuations in the celebrated Eden, or Kardar-Parisi-Zhang (KPZ), universality class. While in many experiments the scaling exponents crucially differ from the expected KPZ values, the source of this disagreement has remained poorly understood. We have performed growth experiments with B. subtilis 168 and E. coli ATCC 25922 under conditions leading to compact colonies in the classically alleged Eden regime, where individual motility is suppressed. Non-KPZ scaling is indeed observed for all accessible times, KPZ asymptotics being ruled out for our experiments due to the monotonic increase of front branching with time. Simulations of an effective model suggest the occurrence of transient nonuniversal scaling due to diffusive morphological instabilities, agreeing with expectations from detailed models of the relevant biological reaction-diffusion processes.

Eden model with nonlocal growth rules and kinetic roughening in biological systems

“…The actual universality class of this non-local Eden model needs further theoretical investigations. One natural possibility is to consider non-local KPZ equations [63][64][65], as recently done in the context of non-universal biological growth [8].…”

“…Pattern formation in biological growth is a nonequilibrium process that has attracted a lot of attention [1][2][3]. Particular interest is given to the rough interfaces of compact and spherical patterns observed in bacterial colonies [4][5][6][7][8] and clusters of normal [9][10][11] and tumor [12,13] cells grown on culture under controlled experimental conditions. The Eden model [14] is a benchmark of stochastic processes, in the important class of growth models on expanding substrates [15][16][17][18][19][20][21], which forms radial clusters with irregular (fractal) borders.…”

“…The situation has changed recently after a thorough statistical analysis of patterns produced between distinct turbulent phases of liquid crystals [45][46][47] which was followed by other experiments reporting KPZ exponents [9,10,13,[48][49][50]. Regarding biological growth, essentially all experimental essays on compact bacteria colonies [4,5,7,8] or cell aggregates [12,51] ruled out KPZ universality class until quite recently when in vitro experiments with eukaryotic cells, namely Vero [9,10] and cancer HeLa [13] cells, yielded exponents in pretty good agreement with the KPZ class. The necessary conditions to observe the KPZ exponents are high renewal rate of the culture medium granting sufficient nutrients for cells and removing the waste products produced by the cellular processes and soft medium permitting cell motility.…”

Instability and fingering of interfaces in growing tissue

“…In growing bacterial colonies of E. coli inside a microfluidic device, a streaming instability has been oberseved due to steric interactions between large, slow-moving and small, fast-moving cells [11]. During growth of bacterial colonies on a petri dish, instabilities of the advancing front arise, displaying different levels of complexity, which range from a small number of fingers to densely-branched, dentritic structures [12][13][14][15].…”

Mechanism underlying dynamic scaling properties observed in the contour of spreading epithelial monolayer

“…Dynamic scaling has been identified in a wide range of phenomena, including bacteria colonies on agar [16,17], propagation of slow combustion of paper [18], and growing interfaces in a turbulent liquid crystal [19]. In collective migration of vertebrate cells, the contours of cell colonies of HeLa and Vero cell lines were also found to exhibit dynamic scaling, with α = 0.50 and β = 0.32 [20,21].…”