Journal ArticleDOI
Free boundary morphogenesis in living matter.
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TLDR
A novel approach for studying free boundary problems during morphogenesis is proposed in this work, where the presence of mass fluxes inside a biological system is coupled with the local gradient of diffusing morphogens.Abstract:
Morphogenetic theories investigate the creation and the emergence of form in living organisms. A novel approach for studying free boundary problems during morphogenesis is proposed in this work. The presence of mass fluxes inside a biological system is coupled with the local gradient of diffusing morphogens. The contour stability of a growing material is studied using a two-dimensional system model with a rectilinear free border inside a Hele-Shaw cell. Modeling mass transport during morphogenesis allows fixing the velocity at the traveling wave solution as a function of one-dimensionless parameter. Performing a perturbation of the free boundary, the dispersion relation is derived in an implicit form. Although both the velocity of the moving front and the surface tension act as stabilizing effects at small wavelengths, the dispersion diagrams show that the rectilinear border is always unstable at large wavelengths. Further applications of this model can help give insights into a number of free boundary problems in biological systems.read more
Citations
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Journal ArticleDOI
Emerging morphologies in round bacterial colonies: comparing volumetric versus chemotactic expansion
TL;DR: This work provides a new interpretation of the emergence of branched patterns in living aggregates, depicted as the results of a complex interplay among chemical, mechanical and size effects.
Journal ArticleDOI
On the morphological stability of multicellular tumour spheroids growing in porous media.
TL;DR: The proposed model of heterogeneous MCTSs within a porous material, taking into account a diffusing nutrient from the surrounding material directing both the proliferation rate and the mobility of tumour cells, demonstrates that the integration of mathematical tools in biological research could be crucial for better understanding the tumour’s ability to invade its host environment.
Book ChapterDOI
Mathematical Modeling of Morphogenesis in Living Materials
TL;DR: This chapter introduces a continuous chemo-mechanical approach of morphogenesis, deriving the balance principles and evolution laws for both volumetric and interfacial processes.
Journal ArticleDOI
Mechanically Driven Branching of Bacterial Colonies
TL;DR: The analytical analysis demonstrates that the front of the colony is linearly unstable for a proper choice of the parameters, and simulation of the model in the nonlinear regime confirms the development of fingers with typical wavelength controlled by the size parameters of the problem.
References
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Journal ArticleDOI
Stress-dependent finite growth in soft elastic tissues
TL;DR: A general continuum formulation for finite volumetric growth in soft elastic tissues is proposed and it is shown that transmurally uniform pure circumferential growth, which may be similar to eccentric ventricular hypertrophy, changes the state of residual stress in the heart wall.
Journal ArticleDOI
Cell surface mechanics and the control of cell shape, tissue patterns and morphogenesis.
TL;DR: A range of developmental phenomena can be explained by the regulation of cell surface tension, and the framework that emerges from diverse disciplines such as cell biology, physics and developmental biology points to adhesion and cortical actin networks as regulators ofcell surface mechanics.
Journal ArticleDOI
Collective migration of an epithelial monolayer in response to a model wound
M. Poujade,Erwan Grasland-Mongrain,A. Hertzog,J. Jouanneau,Philippe Chavrier,Benoit Ladoux,A. Buguin,Pascal Silberzan +7 more
TL;DR: Dealing with Madin–Darby canine kidney cells on various surfaces, it is found that a sudden release of the available surface is sufficient to trigger collective motility, which is characterized by a duality between collective and individual behaviors.
Journal ArticleDOI
Modelling solid tumour growth using the theory of mixtures.
Helen M. Byrne,Luigi Preziosi +1 more
TL;DR: Variation of parameters such as the maximum cell proliferation rate and the rate of natural cell death yield results which are consistent with analyses performed on simpler tumour growth models and indicate that the two-phase formulation is a natural extension of the earlier models.
Journal ArticleDOI
A single-cell-based model of tumor growth in vitro: monolayers and spheroids.
TL;DR: A phenomenological growth law in early expansion phases in which specific biological small-scale processes are subsumed in a small number of effective parameters is proposed.