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## Universality in Bacterial Colonies

### Citations

593 |
Novel type of phase transition in a system of self-deriven particles
- Vicsek, Cziroók, et al.
- 1995
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Citation Context ...g the application of statistical mechanics to ecological or metabolic networks [1, 2], or the use of phase transition theory and correlation functions to understand the behavior of animal collectives =-=[3, 4]-=-. One of the most remarkable instances of marriage between physics and biology concerns the emergent spatial patterns produced by growing bacterial colonies. Beginning with a strip or drop of bacteria... |

343 |
Dynamic scaling of growing interfaces
- Kardar, Parisi, et al.
- 1986
(Show Context)
Citation Context ...onent α. For interfaces showing anomalous roughening, however, the values of local exponents are not necessarily universal [23], and we therefore cannot infer 3 β α z αloc αexp STANDARD SELF-AFF. KPZ =-=[26]-=- 1/3 1/2 3/2 1/2 − X qKPZ[27] 3/5 3/4 5/4 3/4 − X qKPZ (F > Fc) 0.62(3) 0.75(5) 1.19(5) 0.68(5) ∗ 0.72(5); 0.68(5) X Experiments [12, 17] − − − − 0.74− 0.78(7) − Theoretical Model 0.65 [25] 0.80 [25] ... |

265 | Functional cartography of complex metabolic networks. Nature
- Guimera, Amaral
- 2005
(Show Context)
Citation Context ...ravel biological problems has yielded many novel insights into the living world. Numerous examples can be cited, including the application of statistical mechanics to ecological or metabolic networks =-=[1, 2]-=-, or the use of phase transition theory and correlation functions to understand the behavior of animal collectives [3, 4]. One of the most remarkable instances of marriage between physics and biology ... |

203 |
Diffusion-limited aggregation, a kinetic critical phenomenon
- Witten, Sander
- 1981
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Citation Context ...tterns similar to the DBM, but with fewer, thicker branches due to limited cell movement [11, 12, 13]. These patterns (zone IV) resemble those created by diffusion-limited aggregation (DLA) processes =-=[16]-=-, with a very similar fractal dimension [7, 8]. For medium-to-high nutrient levels, the colony patterns are compact again, but with more irregular fronts than those obtained with low agar concentratio... |

191 |
Fractal concepts in surface growth
- Barabasi, Stanley
- 1995
(Show Context)
Citation Context ...e Diagram of Bacterial Colonies More than two decades ago, Matsuyama et al. [7] and Fujikawa and Matsushita [8] showed that bacterial colony patterns obtained in the laboratory can be fractal objects =-=[9]-=-. The properties of the emergent fractal depend mainly on two factors: i) nutrient concentration, C, strongly influences cell growth rate, and ii) agar concentration, CA, controls cell mobility by alt... |

187 |
Fractals, Scaling and Growth far from Equilibrium
- Meakin
- 1998
(Show Context)
Citation Context ...causing lateral correlations to develop more quickly [12]. Such a large α exponent value is also found in systems with different stochastic terms, like non-Gaussian thermal noises, or quenched noises =-=[9, 39]-=-. If we replace the thermal noise of Eq.(7) by a quenched noise, η(x, h), the interface changes its universal behavior. For F < Fc, the advance of the surface is hindered and eventually prevented by p... |

96 | La technique de culture continue: Théorie et applications. - Monod - 1950 |

64 |
The architecture of mutualistic networks minimizes competition and increases biodiversity.
- Bastolla, Fortuna, et al.
- 2009
(Show Context)
Citation Context ...ravel biological problems has yielded many novel insights into the living world. Numerous examples can be cited, including the application of statistical mechanics to ecological or metabolic networks =-=[1, 2]-=-, or the use of phase transition theory and correlation functions to understand the behavior of animal collectives [3, 4]. One of the most remarkable instances of marriage between physics and biology ... |

41 | Finger formation in biofilm layers
- Dockery, Klapper
- 2002
(Show Context)
Citation Context ...ont is therefore reduced in these “valleys” (see Fig.4). Competition between cells for the available resource can thus generate points at the interface with substantially reduced propagation velocity =-=[41]-=-. Moreover, this inequality of propagation is subject to positive feedback: the slower the propagation of the front at a site in comparison with the neighbors, the deeper the valley becomes and the mo... |

32 | The formation of patterns in non-equilibrium growth", Nature 343 - Ben-Jacob, Garik - 1990 |

23 |
Fractal growth of Bacillus subtilis on agar plates
- Fujikawa, Matsushita
- 1989
(Show Context)
Citation Context ... front, different physical properties of the system must be analyzed. The Morphological Phase Diagram of Bacterial Colonies More than two decades ago, Matsuyama et al. [7] and Fujikawa and Matsushita =-=[8]-=- showed that bacterial colony patterns obtained in the laboratory can be fractal objects [9]. The properties of the emergent fractal depend mainly on two factors: i) nutrient concentration, C, strongl... |

23 | Reaction diffusion modelling of bacterial colony patterns, Phys. A 282 - Mimura, Sakaguchi, et al. - 2000 |

21 |
The evolution of quorum sensing in bacterial biofilms.
- Nadell, Xavier, et al.
- 2008
(Show Context)
Citation Context ...oaches. For instance, we can analyze the influence of cell group structure on the evolution of cooperative or competitive secretion phenotypes, measuring the reproductive fitness of idealized strains =-=[5, 6]-=-. On the other hand, if we are interested in a morphological characterization of the colony’s propagating front, different physical properties of the system must be analyzed. The Morphological Phase D... |

19 |
A framework for multidimensional modelling of activity and structure of multispecies biofilms. Environ Microbiol 7(8): 1085–1103 Simulating Microbial Community Patterning Using Biocellion
- JB, Picioreanu, et al.
- 2005
(Show Context)
Citation Context ...imulation framework. Our framework is derived from the latest generation of agent-based models developed by chemical engineers to predict the structure and metabolic activity of bacterial communities =-=[30]-=-. The model has already been used to study colony structure patterns in the high agar concentration regime (zones IV and V), with excellent experimental support [30, 31, 32]. With this simulation fram... |

16 | A molecular mechanism that stabilizes cooperative secretions in Pseudomonas aeruginosa - JB, Kim, et al. - 2011 |

14 | Fluctuation-induced diffusive instabilities, - Kessler, Levine - 1998 |

10 | Emergence of spatial structure in cell groups and the evolution of cooperation.
- Nadell, Foster, et al.
- 2010
(Show Context)
Citation Context ...oaches. For instance, we can analyze the influence of cell group structure on the evolution of cooperative or competitive secretion phenotypes, measuring the reproductive fitness of idealized strains =-=[5, 6]-=-. On the other hand, if we are interested in a morphological characterization of the colony’s propagating front, different physical properties of the system must be analyzed. The Morphological Phase D... |

9 |
Fractal spreading growth of Serratia marcescens which produces surface active exolipids. FEMSMicrobiol. Lett
- Matsuyama, Sogawa, et al.
- 1989
(Show Context)
Citation Context ...tion of the colony’s propagating front, different physical properties of the system must be analyzed. The Morphological Phase Diagram of Bacterial Colonies More than two decades ago, Matsuyama et al. =-=[7]-=- and Fujikawa and Matsushita [8] showed that bacterial colony patterns obtained in the laboratory can be fractal objects [9]. The properties of the emergent fractal depend mainly on two factors: i) nu... |

9 |
Modeling of spatiotemporal patterns in bacterial colonies,
- Lacasta, Cantalapiedra, et al.
- 1999
(Show Context)
Citation Context ...− X qKPZ[27] 3/5 3/4 5/4 3/4 − X qKPZ (F > Fc) 0.62(3) 0.75(5) 1.19(5) 0.68(5) ∗ 0.72(5); 0.68(5) X Experiments [12, 17] − − − − 0.74− 0.78(7) − Theoretical Model 0.65 [25] 0.80 [25] 1.15 [25] − 0.74 =-=[24]-=- − Present Work 0.61(5) 0.68(5)∗ 1.11(17)∗ 0.68(5) 0.67(5) X Table 1: Value of the exponents for the different universality classes, experiments and numerical simulations mentioned in the text. The va... |

7 |
Cuerno R., Superroughening versus intrinsic anomalous scaling of surfaces
- López, Rodríguez
- 1997
(Show Context)
Citation Context ...β for t < t′x lαloc for t > t′x . (5) Systems in which α 6= αloc show what is called anomalous roughening, while regular self-affine interfaces fulfill the standard scaling for the roughness α = αloc =-=[22]-=-. For l ∼ a, where a is the grid spacing (or, in this case, the cell diameter), w(l ∼ a, t) exhibits power-law behavior with positive exponent for cases of anomalous roughening, while it is constant o... |

6 |
Scaling Properties of the Surface of the Eden Model
- Jullien, Botet
- 1985
(Show Context)
Citation Context ...to determining the universality class to which the system belongs. A Universality Class for the Compact, Rough Patterns The Eden model is the paradigm of toy models representing growing cell colonies =-=[35, 36, 37]-=-. In one of its versions, a site along the colony front is randomly chosen each time step and one new cell is placed at any of its free surrounding locations [36]. The basic ingredients of this model ... |

5 |
Self-affinity for the growing interface of bacterial colonies
- Wakita, Itoh, et al.
- 1997
(Show Context)
Citation Context ...work will be focused on the shaded zone, called here the rough regime. patterns may be classified with a two-dimensional phase diagram. Using Bacillus subtilis, Fujikawa, Matsushita and collaborators =-=[8, 11, 12]-=- defined a phase diagram that comprises five regions with different qualitative behaviors resulting from the interaction between biological and physical factors (see Fig.1): At low agar concentratio... |

5 |
Generic Model of Morphological Changes in Growing Colonies of Fungi. Phys
- López, Jensen
(Show Context)
Citation Context ...in velocity between the growing parts of the front and the pinned sites make the β exponent take unusually large values around β = 1 (with patterns similar to those reported for the “groovy” phase in =-=[42]-=-). At even smaller bulk nutrient concentrations, we enter a phase in which wide pinning regions are developed, but the colony continues to grow at a slow pace. Here, branches arise and the colony can ... |

4 |
Diversity of the Growth Patterns of Bacillus Subtilis Colonies on Agar Plates. FEMS ¡icrobiol
- Fujikawa
- 1994
(Show Context)
Citation Context ...work will be focused on the shaded zone, called here the rough regime. patterns may be classified with a two-dimensional phase diagram. Using Bacillus subtilis, Fujikawa, Matsushita and collaborators =-=[8, 11, 12]-=- defined a phase diagram that comprises five regions with different qualitative behaviors resulting from the interaction between biological and physical factors (see Fig.1): At low agar concentratio... |

4 |
Periodic Growth of Bacillus Subtilis Colonies on Agar Plates
- Fujikawa
- 1992
(Show Context)
Citation Context ...centration and relatively high nutrient availability, colonies consist of concentric rings that result from periodic alternation between static and motile stages with positive growth rates (zone III) =-=[14, 15]-=-. At high agar concentration, the substratum becomes hard and dry enough that cells cannot move by active means. Thus, low nutrient concentration results in patterns similar to the DBM, but with few... |

4 |
Scaling Approach to Calculate Critical Exponents in Anomalous Surface Roughening
- López
- 1999
(Show Context)
Citation Context ...he measurement of finite size effects over the roughness of the interface [12, 17]. Let us briefly analyze this observable, which we designate wexp. If we define the “local roughness” of the front as =-=[21]-=-: w(l, t) = 〈 〈[h(x, t) − 〈h〉l] 2 〉l 〉1/2 , (4) where < . >l represents a spatial average over boxes of size l, the behavior of this local observable resembles that of the global variable, but with di... |

4 |
Absorbing States and Elastic Interfaces in Random Media: Two Equivalent Descriptions of Self-Organized Criticality
- Bonachela, Dornic, et al.
(Show Context)
Citation Context ...this local roughness provides a good measurement of the global, universal exponent α. For interfaces showing anomalous roughening, however, the values of local exponents are not necessarily universal =-=[23]-=-, and we therefore cannot infer 3 β α z αloc αexp STANDARD SELF-AFF. KPZ [26] 1/3 1/2 3/2 1/2 − X qKPZ[27] 3/5 3/4 5/4 3/4 − X qKPZ (F > Fc) 0.62(3) 0.75(5) 1.19(5) 0.68(5) ∗ 0.72(5); 0.68(5) X Experi... |

2 |
Dependence of Local Cell Density on Concentric Ring Colony Formation by Bacterial Species Bacillus Subtilis
- Shimada, Ikeda, et al.
(Show Context)
Citation Context ... cell motility [10], bacterial colony ∗Corresponding author: jabo@princeton.edu 1 Figure 1: Sketch of the morphological phase diagram shown by bacterial spatial patterns (adapted with permission from =-=[15]-=-; copyrighted by the Physical Society of Japan). Our work will be focused on the shaded zone, called here the rough regime. patterns may be classified with a two-dimensional phase diagram. Using Bacil... |

2 |
Scaling of the Active Zone
- Family, Vicsek
- 1985
(Show Context)
Citation Context ...pending on the environmental conditions. If the colony pattern is fractal or compact, the front can be treated a priori as a self affine object, and the so-called Family-Vicsek scaling may be assumed =-=[20]-=-: W (L, t) ∼ tβ for t < tx Lα for t > tx . (2) That is, for short times the colony roughness follows a power law behavior defined by the growth exponent, β; at time t = tx, it saturates to a size... |

2 |
Dynamic Scaling of the Growing Rough Surfaces
- Kobayashi, Moriyama, et al.
(Show Context)
Citation Context ...F-AFF. KPZ [26] 1/3 1/2 3/2 1/2 − X qKPZ[27] 3/5 3/4 5/4 3/4 − X qKPZ (F > Fc) 0.62(3) 0.75(5) 1.19(5) 0.68(5) ∗ 0.72(5); 0.68(5) X Experiments [12, 17] − − − − 0.74− 0.78(7) − Theoretical Model 0.65 =-=[25]-=- 0.80 [25] 1.15 [25] − 0.74 [24] − Present Work 0.61(5) 0.68(5)∗ 1.11(17)∗ 0.68(5) 0.67(5) X Table 1: Value of the exponents for the different universality classes, experiments and numerical simulatio... |

2 |
Fifth Berkeley Symp. on Mathematical Statistics and Probability
- MacQueen, Proc
- 1967
(Show Context)
Citation Context ...to determining the universality class to which the system belongs. A Universality Class for the Compact, Rough Patterns The Eden model is the paradigm of toy models representing growing cell colonies =-=[35, 36, 37]-=-. In one of its versions, a site along the colony front is randomly chosen each time step and one new cell is placed at any of its free surrounding locations [36]. The basic ingredients of this model ... |

2 |
Universality Class of Isotropic On-Lattice Eden Clusters
- Paiva, Jr
(Show Context)
Citation Context ...to determining the universality class to which the system belongs. A Universality Class for the Compact, Rough Patterns The Eden model is the paradigm of toy models representing growing cell colonies =-=[35, 36, 37]-=-. In one of its versions, a site along the colony front is randomly chosen each time step and one new cell is placed at any of its free surrounding locations [36]. The basic ingredients of this model ... |

2 | Modelling and Numerical Analysis of the Colony Formation of Bacteria - Kobayashi, Sato, et al. |

1 |
Dynamics of Surface Roughening in Disordered Media
- Csahók, Honda, et al.
- 1993
(Show Context)
Citation Context ...ng anomalous roughening, however, the values of local exponents are not necessarily universal [23], and we therefore cannot infer 3 β α z αloc αexp STANDARD SELF-AFF. KPZ [26] 1/3 1/2 3/2 1/2 − X qKPZ=-=[27]-=- 3/5 3/4 5/4 3/4 − X qKPZ (F > Fc) 0.62(3) 0.75(5) 1.19(5) 0.68(5) ∗ 0.72(5); 0.68(5) X Experiments [12, 17] − − − − 0.74− 0.78(7) − Theoretical Model 0.65 [25] 0.80 [25] 1.15 [25] − 0.74 [24] − Prese... |

1 |
Loosdrecht. Assesment of Three-Dimensional Biofilm Models Through Direct Comparison with Confocal Microscopy Imaging
- Xavier, Picioreanu, et al.
(Show Context)
Citation Context ... activity of bacterial communities [30]. The model has already been used to study colony structure patterns in the high agar concentration regime (zones IV and V), with excellent experimental support =-=[30, 31, 32]-=-. With this simulation framework, we can monitor the state of every cell and its interaction with the nutrient field and the rest of the group. Also, we have total control over environmental condition... |

1 |
our simulations it is assumed a Monod-like relation between the growth rate and the nutrient concentration
- In
(Show Context)
Citation Context ...n with the nutrient field and the rest of the group. Also, we have total control over environmental conditions and individual traits, including maximum growth rate and the ability to absorb nutrients =-=[33]-=-. The tractability offered by these individual-based simulations allows us to perform a finer exploration of the space of parameters that contribute to colony pattern formation. This will be useful no... |