Complex Mechanics Within Hydrogel Systems

Many materials used to study cell behaviors are linearly elastic for most relevant cell level strains, including PA (Storm, Pastore et al. 2005), hyaluronic acid, and PEGDA hydrogels (de Molina, Lad et al. 2015). The initial reason for using these simple systems in mechanobiology experiments was in part due their availability, and in part to minimize complexity in the system to the greatest extent possible. That is, an ideal material would remain linearly elastic within a cellular deformation range, and this would maintain the

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material formulation as simple as possible in order to avoid introducing unnecessary complexities. Even with these simple systems, a great deal has been discovered regarding the role of passive stiffness cues on cell behaviors (as noted above). This linear elasticity has also enabled development of tools to measure cell force generation, where linear assumptions are crucial for simplifying computationally efficient analytical solutions (e.g., solving the system of equations in traction force microscopy) (Sabass, Gardel et al. 2008, Polacheck, Chen et al. 2016). Other systems commonly used for studying cell mechanobiology, such as alginate and collagen are slightly more complex due to their crosslinking mechanism, as many types of alginate are only linearly elastic up to 6% strain, effectively making them behave as nonlinear materials in the range of most cellular strains (Siviello, Greco et al. 2015). On top of these synthetic materials, most tissues are simply not linearly elastic due to the fact that their constitutive ECM components, including collagen, fibrin, etc. are non-linear materials (Storm, Pastore et al. 2005). As such, cells in their normal in vivo microenvironment are likely interacting with mechanically complex materials, potentially altering important cellular functionalities that depend on cellular contractility.

Mechanical properties of native tissues vary markedly across tissue types, and are based on their function and composition. Most tissues have high water content, thus making them viscoelastic, where the applied forces on the tissue gradually dissipate under a constant deformation. In these cases, the materials can be characterized by a storage modulus (G’, elastic) and a loss modulus (G’’, viscous). Early work exploring cell mechanosensing in viscoelastic environments was carried by Cameron and coauthors, where they took the standard PA gel system with a constant elastic storage modulus (~5 kPa) and varied the loss modulus by altering that ratio of acrylamide to bis-acrylamide. When cells were plated

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on materials containing a significant viscous mechanical contribution, focal adhesions were smaller but cell spread area and proliferation rate increased (Cameron, Frith et al. 2011). Additionally, the authors found an influence of loss modulus on MSC differentiation, where increased loss modulus increased MSC osteogenesis in differentiation media. Other work using such viscoelastic substrates also revealed that a more viscous substrate enhanced collective cell migration (Murrell, Kamm et al. 2011).

In a similar vein, a series of recent publications have centered on the use of ionic and covalently crosslinked alginate-based systems that enable creation of hydrogels that undergo stress-relaxation, in which there is a time-dependent dissipation of stress. When cells were cultured on top of 2D thin films of these stress-relaxing alginate hydrogels, differential responses were seen on low elastic modulus substrates. In this scenario, cells on stress-relaxing gels were more spread and exhibited higher levels of YAP/TAZ localization (Chaudhuri, Gu et al. 2015)(Figure 2-2). However, on stiff hydrogels or at lower ligand densities, the stress-relaxation properties of this hydrogel had no effect on cellular behavior. This suggests that, when stiffness is high or when cells cannot effectively cluster sufficient ligand, cells get enough mechanical feedback and there is no impetus for clustering of these RGD adhesions. In 3D microenvironments, varying the molecular weight of these stress-relaxing alginate materials caused them to behave as a Bingham solid – where above a threshold force the solid material exhibited viscous flow. The faster stress-relaxation times of the alignate hydrogel led to increased cell spreading and increased proliferation at high RGD densities. This suggests that, similar to work in fibrous scaffold systems, the mechanical properties of the surrounding ECM can dictate how cells are able to remodel their microenvironment by acting locally to cluster ligands (and thereby

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increase generation of contractile stress). However, important questions remain regarding the biophysical mechanism underlying these results. What is the amount of contractile stress in the cytoskeleton of these cells and is this achieved through focal adhesion activation? Additionally, over long timescales, how do these stress-relaxing gels regulate matrix deposition in these contexts. Long-term differentiation experiments bring up other interesting mechanistic questions in this system – perhaps the hydrogels are acting as a barrier to matrix deposition in 3D, and as such hydrogels that can stress-relax may promote increased matrix deposition, similar to effects of agarose concentration on matrix deposition and morphology as highlighted by McLeod and Mauck (McLeod and Mauck 2016).

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Figure 2-2 – Overview of stress-relaxing alginate hydrogels and MSC culture inside of these hydrogels. (top) Tuning of the stress-relaxation parameters was accomplished through changing molecular weight parameters and inserting PEG

spacers. (middle) Cell spreading increased with faster stress-relaxation time scales. (bottom) MSCs could remodel the biomaterial to locally increase ligand density following culture in a fast stress-relaxing alginate hydrogel. Adapted from

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Others have attempted to create stress-stiffening materials that mimic the nonlinear native mechanical response of collagen. One such example came in the form of 3D polyisocyanopeptide (PIC) hydrogels in the 200-400 Pa modulus range, and through tuning polymer length, altered the critical stress at which these hydrogels entered the nonlinear stress-stiffening regime (Das, Gocheva et al. 2016). Unlike collagen gels however, these PIC gels were not degradable. Thus, despite being strain stiffening, cell morphology in these 3D hydrogels did not match those of cells embedded in fibrin or collagen gels in which there was cellular spreading and polarization. These changes in stem cell morphology were dependent on integrin-binding, suggesting that despite a rounded morphology, local changes in modulus and integrin clustering drove these responses. Coupling these strain-stiffening systems with degradable crosslinks could further develop a mechanistic understanding of how cellular mechanobiology adapts to changes in modulus with applied force, and how these changes engender long-term feedback and memory in cellular processes.