Towards a unified theory for morphomechanics

Larry A. Taber

Abstract

Mechanical forces are closely involved in the construction of an embryo. Experiments have suggested that mechanical feedback plays a role in regulating these forces, but the nature of this feedback is poorly understood. Here, we propose a general principle for the mechanics of morphogenesis, as governed by a pair of evolution equations based on feedback from tissue stress. In one equation, the rate of growth (or contraction) depends on the difference between the current tissue stress and a target (homeostatic) stress. In the other equation, the target stress changes at a rate that depends on the same stress difference. The parameters in these morphomechanical laws are assumed to depend on stress rate. Computational models are used to illustrate how these equations can capture a relatively wide range of behaviours observed in developing embryos, as well as show the limitations of this theory. Specific applications include growth of pressure vessels (e.g. the heart, arteries and brain), wound healing and sea urchin gastrulation. Understanding the fundamental principles of tissue construction can help engineers design new strategies for creating replacement tissues and organs in vitro.

Footnotes

  • One contribution of 12 to a Theme Issue ‘Mechanics in biology: cells and tissues’.

  • 1 Clearly, an axon actually grows by adding material as it extends over long distances, but an HR response is more consistent with the stress-rate criteria defined above. How the axon reaches equilibrium at the end of phase 1 is immaterial here, so long as tension is maintained.

  • 2 Because force was measured in the experiments, it would be more consistent to examine the first Piola–Kirchhoff stress P, which is proportional to the applied force. Calculations show, however, that the fundamental behaviour is the same, and so Cauchy stress is used for clarity in comparing with the target stress.

  • 3 For convenience, the term ‘dimple region’ refers only to the region containing the initial contraction, even as the actual invagination continues to spread.

  • 4 Theoretical aspects of anisotropy and mechanically based growth laws are discussed in some recent papers (see Maugin & Imatani 2003; Ambrosi & Guana 2007; Menzel 2007).

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