Patterns in biofilms: From contour undulations to fold focussing

Laboratoire de Physique Statistique, Ecole Normale Supérieure, UPMC Univ Paris 06, Université Paris Diderot, CNRS - 24 rue Lhomond, 75005 Paris, France and Institut Universitaire de Cancérologie, Faculté de médecine, Université Pierre et Marie Curie-Paris 6 91 Bd de l'Hôpital, 75013 Paris, France

Received: 1 August 2014
Accepted: 10 October 2014

Abstract

Morphologies of soft materials in growth, swelling or drying have been extensively studied recently. Shape modifications occur as the size varies transforming ordinary spheres, cylinders and thin plates into more or less complex objects. Here we consider the genesis of biofilm patterns when a simple disc containing initially bacteria with moderate adhesion to a rigid substrate grows according to very simple rules. The initial circular geometry is lost during the growth expansion, contour undulations and buckling appear, ultimately a rather regular periodic focussing of folds repartition emerges. We theoretically predict these morphological instabilities as bifurcations of solutions in elasticity, characterized by typical driving parameters established here. The substrate plays a critical role limiting the geometry of the possible modes of instabilities and anisotropic growth, adhesion and toughness compete to eventually give rise to wrinkling, buckling or both. Additionally, due to the substrate, we show that the ordinary buckling modes, vertical deviation of thin films, are not observed in practice and a competitive pattern with self-focussing of folds can be found analytically. These patterns are reminiscent of the blisters of delamination in material sciences and explain recent observations of bacteria biofilms. The model presented here is purely analytical, is based on a neo-Hookean elastic energy, and can be extended without difficulties and applied to polymer materials.