Modelling the mechanics of epithelial sheets on soft substrates: nonlinearity, feedback and dissipation

The rapid expansion of experimental biophysics is driving a new realisation of the fundamental importance of mechanical forces in biology. Cells are now seen to be exquisitely sensitive to their mechanical microenvironments, exhibiting very different behaviours when exposed to e.g. soft or stiff gels. Particularly striking is work showing that stem cells can turn into very different cell types ranging from brain, bone to muscle depending on the stiffness of the gel they are grown on. As a result of such studies it has become clear that successful tissue engineering is dependent on making tissue scaffolds that are finely tuned not just in their biochemical, but also in their mechanical properties.

A primary mechanism by which cells sense the mechanical properties of their environments is by exploiting the contractility of their internal cytoskeletal networks to 'pull' on the external gel. For single cells, the strength of this pulling force is traditionally measured using Traction Force Microscopy (TFM). In TFM the amount that a cell displaces the gel is carefully measured and correlated to the mechanical activity of the individual cell. However in tissues, obtaining and interpreting such experimental data is significantly complicated and instead the magnitudes of cellular forces are usually inferred through indirect methods such as by mechanical relaxation after laser cutting.

We propose here a different approach using mathematical abstraction to couple descriptions of active cellular behaviours into classical elasticity models. The result will be an innovative suite of continuum models that integrate cell contractility, cell mechanotransduction, stress relaxation and the complex material properties of the underlying gel matrix into a complete model of tissue-gel interaction. This work can be used to interpret experimental data and predict cellular response to changes in the mechanical properties of the surrounding environment. The models developed will also inform future biomechanical modelling work as applied to tissue development and morphogenesis.

The modelling work is split into various steps that build up the complete picture that we are aiming for. The modules are: A) A model for the bonding of a contractile epithelial tissue to an underlying gel incorporating stress relaxation; B) Incorporating feedback control of cellular behaviour into the system; and C) A consideration of the physical complexities of the gel underlying the tissue layer.

Fundamental to all tissue development and morphogenesis is the ability of cells to generate and respond to force. Striking examples of feedback control in tissues include stem cells differentiating into different cell types on gels of different stiffnesses and that mechanical stress regulates tissue size in a wide variety of tissues. Equally in disregulated tissues, for example in cancers, the ability of cells to evade physical cues from the microenvironment is being seen to have a profound influence on malignancy, tumour progression and metastasis. As a result the proposed work, which will produce intuitive and applicable models for tissue gel-matrix interactions, has the potential to have a significant impact in a wide variety of contexts. I highlight below some specific areas of impact and their beneficiaries.

A) Tissue engineering and medical technologies - the proposed work will have significant downstream impact in this area spanning the engineering of artificial scaffolds for regenerative medicine and the design of medical implants. As well as informing the design of new technologies I expect the knowledge acquired from this work to, for example, prevent unexpected and unwelcome results from current implants.

Beneficiaries include the general public through improvements in healthcare and the medical technology industrial sector, which in the UK "has a turnover of around £16 billion, and employs 70,000 people in 3,000 countries" (Innovation in medical technology, (2013) Royal Academy of Engineering). For industry the potential impact of the work also includes a reduction in research costs. This will achieved by the computational models here developed being used for in silico experiments and also by being able to focus attention on those aspects that the work highlights as most significant. The reduction of animal experimentation that this in silico modelling enables entails an additional impact of the work, benefitting both public and commercial partners (see e.g. NC3Rs).

B) Systems biologists and modellers - there is a large community of systems biologists and modellers not just within academia but also within industry. For example, the biosystems group at the University of Surrey has strong links with industrial partners at Syngenta, Pfizer and MedImmune. Commercial research that will be impacted by the proposed work include in healthcare specific companies (e.g. GSK) and in lifestyle focused industries (e.g. Unilever). As the proposed model is designed to be generally applicable to cell-gel interactions it is envisaged that the framework will be easily incorporated into other tissue simulations. The model will thus impact research on a wide variety of epithelial tissues (including intestinal tissues and skin).

C) Training of research staff - the research here developed will inform the work of an EPSRC funded PhD student in the group of the PI who will be working on projects in the area of biomechanical modelling and continuum mechanics starting from Oct. 2014.

D) Indirect impact - the significance of the work to academic beneficiaries including experimental biophysicists and cell biologists (as detailed above) will mean that the proposed models will feed through indirectly as well directly into the areas detailed above. This will increase the the total impact of the work in all areas.