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Research Papers

Mechanically Driven Branching of Bacterial Colonies

[+] Author and Article Information
Chiara Giverso

MOX - Department of Mathematics,
Politecnico di Milano and Fondazione CEN,
P.za Leonardo da Vinci, 32,
Milan 20133, Italy
e-mail: chiara.giverso@polimi.it

Marco Verani

MOX - Department of Mathematics,
Politecnico di Milano,
P.za Leonardo da Vinci, 32,
Milan 20133, Italy
e-mail: marco.verani@polimi.it

Pasquale Ciarletta

CNRS and Institut Jean le Rond d'Alembert,
UMR 7190,
Université Paris 6,
4 place Jussieu case 162,
Paris 75005, France
e-mail: pasquale.ciarletta@upmc.fr

Manuscript received December 21, 2014; final manuscript received March 12, 2015; published online June 2, 2015. Assoc. Editor: Pasquale Vena.

J Biomech Eng 137(7), 071003 (Jul 01, 2015) (10 pages) Paper No: BIO-14-1636; doi: 10.1115/1.4030176 History: Received December 21, 2014; Revised March 12, 2015; Online June 02, 2015

A continuum mathematical model with sharp interface is proposed for describing the occurrence of patterns in initially circular and homogeneous bacterial colonies. The mathematical model encapsulates the evolution of the chemical field characterized by a Monod-like uptake term, the chemotactic response of bacteria, the viscous interaction between the colony and the underlying culture medium and the effects of the surface tension at the boundary. The analytical analysis demonstrates that the front of the colony is linearly unstable for a proper choice of the parameters. The simulation of the model in the nonlinear regime confirms the development of fingers with typical wavelength controlled by the size parameters of the problem, whilst the emergence of branches is favored if the diffusion is dominant on the chemotaxis or for high values of the friction parameter. Such results provide new insights on pattern selection in bacterial colonies and may be applied for designing engineered patterns.

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Figures

Grahic Jump Location
Fig. 1

Dispersion diagrams for different values of the model parameters β and σ. The solid lines are obtained through interpolation of the discrete values of λ, solutions of the dispersion equation for k ∈ N,k≥1. The dispersion curves are reported in (a) and (b) for the case n0>>nmax and in (c) and (d) for the case n0≪nmin.

Grahic Jump Location
Fig. 2

Morphological diagram of the expanding bacterial colony for increasing values (from left to right) of the parameter β, while keeping the other parameters fixed. In particular, the simulations were obtained setting Rout = 220, σ = 0.01,n0 = 0.5, and Rout/R0* = 5. The contour of the colony is plotted at different instants of time (reported at the bottom of each contour plot).

Grahic Jump Location
Fig. 3

Morphological diagram of the expanding bacterial colony for different values of the dimensionless surface tension σ, maintaining fixed the dimensionless Petri dish radius (Rout = 220) and the initial radius of the colony (Rout = 44). In the simulations, it is set β = 1 and n0 = 0.5.

Grahic Jump Location
Fig. 4

Morphological diagram of the expanding bacterial colony for different values of Rout and R0*, while keeping the value q = Rout/R0* = 5 fixed. The other parameters are equal to β = 1, σ = 0.01, and n0 = 0.5. The contour of the colony is plotted at different instants of time (reported at the bottom of each contour plot).

Grahic Jump Location
Fig. 5

Morphological diagram of the expanding bacterial colony for different values of the initial size of the colony, R0*, maintaining fixed the dimensionless Petri dish radius. The other parameters in the model are: Rout = 220, σ = 0.01, β = 1, and n0 = 0.5. The contour of the colony is plotted at different instants of time (reported at the bottom of each contour plot).

Grahic Jump Location
Fig. 6

Morphological diagram of the expanding bacterial colony for different values of n0, regulating the Monod dynamic. The other parameters in the model are: Rout = 100, σ = 0.01, β = 1, and Rout/R0* = 5. At the bottom of each morphological diagram, the evolution of the nutrients concentration along a diameter of the Petri dish is reported for different instants of time.

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