Experimental Investigation on the Validity of Population Dynamics Approach to Bacterial Colony Formation

Wakita, Jun–ichi; Kono, Kenji; Nakahara, Akio; Matsuyama, Tohey; Matsushita, Mitsugu

doi:10.1143/jpsj.63.1205

Cited by 119 publications

(124 citation statements)

References 18 publications

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“…Melbourne and Hastings (31) have carried out a very detailed comparison between theory and experiment for a laboratory population of flour beetles and showed that the unavoidable heterogeneity of the founding organisms leads to large variation in the rate of spread between replica populations. At the microscopic scale, Wakita et al (32) tested the expected relation between the rate of spread and nutrient availability in Escherichia coli, and Giometto et al (33) used the theory of pulled waves to describe the expansion of tetrahymena in linear channels. All of these studies, however, focused only on the rate of invasion and did not test theoretical predictions for the shape of the invading fronts.…”

Section: Significancementioning

confidence: 99%

Range expansions transition from pulled to pushed waves as growth becomes more cooperative in an experimental microbial population

Gandhi

Yurtsev

Korolev

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

117

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Range expansions are becoming more frequent due to environmental changes and rare long-distance dispersal, often facilitated by anthropogenic activities. Simple models in theoretical ecology explain many emergent properties of range expansions, such as a constant expansion velocity, in terms of organism-level properties such as growth and dispersal rates. Testing these quantitative predictions in natural populations is difficult because of large environmental variability. Here, we used a controlled microbial model system to study range expansions of populations with and without intraspecific cooperativity. For noncooperative growth, the expansion dynamics were dominated by population growth at the low-density front, which pulled the expansion forward. We found these expansions to be in close quantitative agreement with the classical theory of pulled waves by Fisher [Fisher RA (1937) Ann Eugen 7(4):355-369] and Skellam [Skellam JG (1951) Biometrika 38(1-2):196-218], suitably adapted to our experimental system. However, as cooperativity increased, the expansions transitioned to being pushed, that is, controlled by growth and dispersal in the bulk as well as in the front. Given the prevalence of cooperative growth in nature, understanding the effects of cooperativity is essential to managing invading species and understanding their evolution.Allee effect | Fisher wave | biological invasion F rom a local disturbance by an invasive species to the global expansion of the biosphere after an ice age, range expansions have been a major ecological and evolutionary force (1, 2). Range expansions and range shifts are becoming increasingly frequent due to the deliberate introduction of foreign species (3, 4), unintentional introductions caused by global shipping (5), and temperature changes associated with climate change (6, 7). Many invasions disturb ecosystem functions, reduce biodiversity, and impose significant economic costs (8, 9). The interest in invasion forecasting and management resulted in a substantial effort to develop predictive mathematical models of range expansions (4, 10-13), but empirical tests of these models have been less extensive.Species invade new territory through a combination of dispersal and local growth. Mathematically, these dynamics can be described by a variety of models depending on the details of the species ecology or simplifying assumptions (14). For example, the invasion of house finches in North America has been successfully modeled with integrodifference equations (4). Continuous reactiondiffusion equations have been used to describe the expansion of trees following the end of an ice age and the expansion of muskrats from central Europe (15), whereas metapopulation models with disjoint patches of suitable habitat and discrete generations are more appropriate for certain butterflies living in temperate climates (16). One of the great achievements of mathematical ecology is the discovery that all these diverse models of population expansion can be divided into two broad classes of pulled...

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Section: Significancementioning

confidence: 99%

Range expansions transition from pulled to pushed waves as growth becomes more cooperative in an experimental microbial population

Gandhi

Yurtsev

Korolev

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

117

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“…The FKE has been used to model the spread of advantageous genes in animal populations (6), the growth of bacterial colonies (23)(24)(25), and the growth of complex cell organizations such as spreading of tumors (26), brain tumor growth (27), and wound healing (28), epidemics such as the spread of plague (29) and other pandemic diseases, social developments such as the spread of Neolithic farming practices (30), and the spread of Indo-European languages across Europe (31). Other important examples from biology include the frontal polymerization of actin (32) and microtubules (33).…”

Section: Implications Of Observationsmentioning

confidence: 99%

Propagating waves of self-assembly in organosilane monolayers

Douglas

Efimenko

Fischer

et al. 2007

Proc. Natl. Acad. Sci. U.S.A.

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Wavefronts associated with reaction-diffusion and self-assembly processes are ubiquitous in the natural world. For example, propagating fronts arise in crystallization and diverse other thermodynamic ordering processes, in polymerization fronts involved in cell movement and division, as well as in the competitive social interactions and population dynamics of animals at much larger scales. Although it is often claimed that self-sustaining or autocatalytic front propagation is well described by mean-field ''reaction-diffusion'' or ''phase field'' ordering models, it has recently become appreciated from simulations and theoretical arguments that fluctuation effects in lower spatial dimensions can lead to appreciable deviations from the classical mean-field theory (MFT) of this type of front propagation. The present work explores these fluctuation effects in a real physical system. In particular, we consider a high-resolution near-edge x-ray absorption fine structure spectroscopy (NEXAFS) study of the spontaneous frontal self-assembly of organosilane (OS) molecules into self-assembled monolayer (SAM) surface-energy gradients on oxidized silicon wafers. We find that these layers organize from the wafer edge as propagating wavefronts having well defined velocities. In accordance with two-dimensional simulations of this type of front propagation that take fluctuation effects into account, we find that the interfacial widths w(t) of these SAM self-assembly fronts exhibit a power-law broadening in time, w(t) Ϸ t ␤ , rather than the constant width predicted by MFT. Moreover, the observed exponent values accord rather well with previous simulation and theoretical estimates. These observations have significant implications for diverse types of ordering fronts that occur under confinement conditions in biological or materials-processing contexts.fluctuation-induced interfacial broadening ͉ frontal self-assembly ͉ mean-field Fisher-Kolmogorov equation ͉ reaction-diffusion fronts ͉ self-assembled monolayers I n the early 1990s, Chaudhury and Whitesides developed an extremely facile method of creating surface energy gradients using self-assembled monolayers (SAMs) (1). Rather than using a solution as a carrier for adsorption or a rubber stamp for direct deposition of SAM molecules, these researchers simply placed a volatile fluid of organosilane (OS) molecules at the edge of a silica-covered substrate and enclosed the entire system in a container to avoid convection effects (Fig. 1). The symmetry-breaking perturbation associated with placing the source of diffusing material to the side of the wafer imparts a direction to the self-assembly of the SAM layer and leads to the spontaneous formation of a concentration gradient of OS molecules on the substrate. This gradient may be fixed into position at any point in its development by simply removing the wafer from OS exposure (2). These kinetically ''frozen'' SAM patterns are then ready for further measurements in which surface energy gradients are required.Although this method of ...

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“…The colony morphology depends upon various factors such as nutrient concentration, cell motility, growth-proliferation and death dynamics, and other chemical and physical variables [12][13][14][15][16][17][18][19][20]. In a classic experiment, Wakita et al [4] obtained the phase-diagram of Bacillus subtilis colony morphology as a function of nutrient concentration and solidity of agar medium and identified five basic morphologies: (A) diffusion limited aggregation (DLA), (B) Eden-like, (C) concentric ring-like, (D) homogeneous spreading, and (E) dense branching morphology (DBM). Similar morphological patterns have also been observed in growing yeast colonies [21].…”

Section: Introductionmentioning

confidence: 99%

“…Several studies have incorporated the effect of the nutrient concentration and bacteria motility by coupling Eq. (1.1) with an additional equation for each of these variables to obtain different morphological patterns that were discussed above [4][5][6][7][8][9][10][11][33][34][35]. Studies designed to investigate the role of demographic noise use the stochastic variants of Eq.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we explore the morphological spatial dynamics of non motile bacteria growing on a hard agar plate with varying initial nutrient concentration and diffusivity. Our numerical investigation using agent based and continuum models are designed to mimic the experiments of Wakita et al [4] which show a transition from branching to an Eden like pattern. Our approach is different than earlier studies [7,8,33,41,42] where the bacterial morphological patterns were attributed to substrate properties such as irregularities on the agar substrate [41], substrate hardness that depends on the agar concentration and local lubrication created by bacteria [42], and nutrient concentration.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Spreading of nonmotile bacteria on a hard agar plate: Comparison between agent-based and stochastic simulations

2017

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We study spreading of a non-motile bacteria colony on a hard agar plate by using agent-based and continuum models. We show that the spreading dynamics depends on the initial nutrient concentration, the motility and the inherent demographic noise. Population fluctuations are inherent in an agent based model whereas, for the continuum model we model them by using a stochastic Langevin equation. We show that the intrinsic population fluctuations coupled with non-linear diffusivity lead to a transition from Diffusion Limited Aggregation (DLA) type morphology to an Eden-like morphology on decreasing the initial nutrient concentration.

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Experimental Investigation on the Validity of Population Dynamics Approach to Bacterial Colony Formation

Cited by 119 publications

References 18 publications

Range expansions transition from pulled to pushed waves as growth becomes more cooperative in an experimental microbial population

Range expansions transition from pulled to pushed waves as growth becomes more cooperative in an experimental microbial population

Propagating waves of self-assembly in organosilane monolayers

Spreading of nonmotile bacteria on a hard agar plate: Comparison between agent-based and stochastic simulations

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