Sticking around: Optimal cell adhesion patterning for energy minimization and substrate mechanosensing

Abstract

Cell mechanotransduction, in which cells sense and respond to the physical properties of their micro-environments, is proving fundamental to understanding cellular behaviours across biology. Tissue stiffness (Youngs modulus) is typically regarded as the key control parameter and bioengineered gels with defined mechanical properties have become an essential part of the toolkit for interrogating mechanotransduction. We here, however, show using a mechanical cell model that the effective substrate stiffness experienced by a cell depends not just on the engineered mechanical properties of the substrate but critically also on the particular arrangement of adhesions between cell and substrate. In particular, we find that cells with different adhesion patterns can experience two different gel stiffnesses as equivalent and will generate the same mean cell deformations. For small adhesive patches, which mimic experimentally observed focal adhesions, we demonstrate that the observed dynamics of adhesion growth and elongation can be explained by energy considerations. Significantly we show different focal adhesions dynamics for soft and stiff substrates with focal adhesion growth not preferred on soft substrates consistent with reported dynamics. Equally, fewer and larger adhesions are predicted to be preferred over more and smaller, an effect enhanced by random spot placing with the simulations predicting qualitatively realistic cell shapes in this case. The model is based on a continuum elasticity description of the cell and substrate system, with an active stress component capturing cellular contractility. This work demonstrates the necessity of considering the whole cell-substrate system, including the patterning of adhesion, when investigating cell stiffness sensing, with implications for mechanotransductive control in biophysics and tissue engineering. Author summaryCells are now known to sense the mechanical properties of their tissue micro-environments and use this as a signal to control a range of behaviours. Experimentally, such cell mechanotransduction is mostly investigated using carefully engineered gel substrates with defined stiffness. Here we show, using a model integrating active cellular contractility with continuum mechanics, that the way in which a cell senses its environment depends critically not just on the stiffness of the gel but also on the spatial patterning of adhesion sites. In this way, two gels of substantially different stiffnesses can be experienced by the cell as similar, if the adhesions are located differently. Exploiting this insight, we demonstrate that it is energetically favourable for small adhesions to grow and elongate on stiff substrates but that this is not the case on soft substrates. This is consistent with experimental observations that nascent adhesions only mature to stable focal adhesion (FA) sites on stiff substrates where they also grow and elongate. These focal adhesions (FAs) have been the focus of work on mechanotransduction. However, our paper demonstrates that there is a fundamental need to consider the combined cell and micro-environment system moving beyond a focus on individual FAs.