However, current engineering technologies, based on inhomogeneous actuation across the thickness of slender structures, are intrinsically limited to one-directional bending5. Shape-morphing structures are at the core of future applications in aeronautics1, minimally invasive surgery2, tissue engineering3 and smart materials4. We discuss the implications of forming undulated biofilm morphologies, which may enhance the availability of nutrients and signaling molecules and serve as a “bet hedging” strategy. Our results, which establish that nonuniform growth and friction are fundamental determinants of stress anisotropy and hence biofilm morphology, are broadly applicable to bacterial biofilms with similar morphologies and also provide insight into how other bacterial biofilms form distinct wrinkle patterns. Our model shows quantitative agreement with experimental measurements of biofilm expansion dynamics, and it accurately predicts two distinct spatiotemporal patterns observed in the experiments-the wrinkles initially appear either in the peripheral region and propagate inward (soft substrate/low friction) or in the central region and propagate outward (stiff substrate/high friction). To gain mechanistic insights into this dynamic pattern-formation process, we developed a model that considers diffusion of nutrients and their uptake by bacteria, bacterial growth/biofilm matrix production, mechanical deformation of both the biofilm and the substrate, and the friction between them.
Expanding biofilms are initially flat but later undergo a mechanical instability and become wrinkled. To circumvent this issue, here we present a study of developing Vibrio cholerae biofilms grown on agar substrates in which the spatiotemporal morphological patterns were altered by varying the agar concentration.
While basic mechanisms underlying morphogenesis are known in eukaryotes, it is often difficult to manipulate them in vivo. Armed with our simple rules, and the methodology underlying them, one can anticipate the creation of designer wrinkle patterns.ĭuring development, organisms acquire three-dimensional (3D) shapes with important physiological consequences. Finally, they explain how the sign of the shell's initial curvature dictates the presence or lack of disorder.
#A WRINKLE IN TIME VEX MOVIES DRIVER#
They also unveil the role of the shell's medial axis, a distinguished locus of points that we show is a basic driver in pattern selection. They predict the surprising coexistence of orderly wrinkles alongside disordered regions where the response appears stochastic, which we confirm in experiment and simulation. Our rules apply to shells whose initial Gaussian curvatures are of one sign, such as cutouts of saddles and spheres. Building on the theoretical foundation of, we derive a complete and simple rule set for wrinkles in the model system of a curved shell on a liquid bath.
The challenge is to explain the patterns in any given setup, even when they fail to be robust. This is due, in part, to the promise of lithography-free micropatterning, but also to the observation that similar patterns arise in biological systems from growth. Such patterns continue to receive attention across science and engineering. Thin elastic membranes form complex wrinkle patterns when put on substrates of different shapes.
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