Mechanics of 3D Cell-Hydrogel Interactions: Experiments, Models, and Mechanisms.

Hydrogels are highly water-swollen molecular networks that are ideal platforms to create tissue mimetics owing to their vast and tunable properties. As such, hydrogels are promising cell-delivery vehicles for applications in tissue engineering and have also emerged as an important base for ex vivo models to study healthy and pathophysiological events in a carefully controlled three-dimensional environment. Cells are readily encapsulated in hydrogels resulting in a plethora of biochemical and mechanical communication mechanisms, which recapitulates the natural cell and extracellular matrix interaction in tissues. These interactions are complex, with multiple events that are invariably coupled and spanning multiple length and time scales. To study and identify the underlying mechanisms involved, an integrated experimental and computational approach is ideally needed. This review discusses the state of our knowledge on cell-hydrogel interactions, with a focus on mechanics and transport, and in this context, highlights recent advancements in experiments, mathematical and computational modeling. The review begins with a background on the thermodynamics and physics fundamentals that govern hydrogel mechanics and transport. The review focuses on two main classes of hydrogels, described as semiflexible polymer networks that represent physically cross-linked fibrous hydrogels and flexible polymer networks representing the chemically cross-linked synthetic and natural hydrogels. In this review, we highlight five main cell-hydrogel interactions that involve key cellular functions related to communication, mechanosensing, migration, growth, and tissue deposition and elaboration. For each of these cellular functions, recent experiments and the most up to date modeling strategies are discussed and then followed by a summary of how to tune hydrogel properties to achieve a desired functional cellular outcome. We conclude with a summary linking these advancements and make the case for the need to integrate experiments and modeling to advance our fundamental understanding of cell-matrix interactions that will ultimately help identify new therapeutic approaches and enable successful tissue engineering.

Moving while you're stuck: a macroscopic demonstration of an active system inspired by binding-mediated transport in biology.

Diffusive motion is typically constrained when particles bind to the medium through which they move. However, when binding is transient and the medium is made of flexible filaments, each association or dissociation event produces a stochastic force that can overcome the medium stickiness and enable motion. This mechanism is amply used by biological systems where the act of balancing binding and displacement robustly achieves key functionalities, including bacterial locomotion or selective active filtering in cells. Here we demonstrate the feasibility of making a dynamic system with macroscopic features, in which analogous binding-mediated motion can be actively driven, precisely tuned, and conveniently studied. We find an optimal binding affinity and number of binding sites for diffusive motion, and an inverse relationship between viscosity and diffusivity.

Spatiotemporal neocartilage growth in matrix-metalloproteinase-sensitive poly(ethylene glycol) hydrogels under dynamic compressive loading: an experimental and computational approach.

Enzyme-sensitive hydrogels containing encapsulated chondrocytes are a promising platform for cartilage tissue engineering. However, the growth of neotissue is closely coupled to the degradation of the hydrogel and is further complicated due to the encapsulated cells serving as the enzyme source for hydrogel degradation. To better understand these coupled processes, this study combined experimental and computational methods to analyze the transition from hydrogel to neotissue in a biomimetic MMP-sensitive poly(ethylene glycol) (PEG) hydrogel with encapsulated chondrocytes. A physics-based computational model that describes spatial heterogeneities in cell distribution was used. Experimentally, cell-laden hydrogels were cultured for six weeks under free swelling or subjected daily to one-hour of dynamic compressive loading. Extracellular matrix (ECM) synthesis rates were used as model inputs, and the model was fit to the experimentally determined construct modulus over time for the free swelling condition. Experimentally, ECM accumulation comprising collagen II and aggrecan increased over time concomitant with hydrogel degradation observed by a loss in PEG. Simulations demonstrated rapid degradation in regions of high cell density (i.e., cell clusters) reaching complete degradation by day 13, which facilitated localized ECM growth. Regions of low cell density degraded more slowly, had limited ECM, and led to the decrease in construct modulus during the first two weeks. The primary difference between the two culture environments was greater ECM accumulation in the clusters under free swelling, which facilitated a faster recovery in construct modulus. By 6 weeks the compressive modulus increased 2.5-fold to 107 kPa under free swelling, but dropped 1.6-fold to 26 kPa under loading. In summary, this biomimetic MMP-sensitive hydrogel supports neocartilage growth by facilitating rapid ECM growth within cell clusters, which was followed by slower growth in the rest of the hydrogel. Subtle temporal differences in hydrogel degradation and ECM accumulation, however, had a significant impact on the evolving mechanical properties.

A Statistical Model of Expansive Growth in Plant and Fungal Cells: The Case of Phycomyces.

Expansive growth is a process by which walled cells of plants, algae, and fungi use turgor pressure to mediate irreversible wall deformation and regulate their shape and volume. The molecular structure of the primary cell wall must therefore perform multiple functions simultaneously, including providing structural support by combining elastic and irreversible deformation and facilitating the deposition of new material during growth. This is accomplished by a network of microfibrils and tethers composed of complex polysaccharides and proteins that can dynamically mediate the network topology via periodic detachment and reattachment events. Lockhart and Ortega have provided crucial macroscopic understanding of the expansive growth process through global biophysical models, but these models lack the connection to molecular processes that trigger network rearrangements in the wall. Interestingly, the helical growth of the fungal sporangiophores of Phycomyces blakesleeanus is attributed to a limited region (called the growth zone) where microfibrils are deposited, followed by reorientation and slip. Based on past evidence of dominant shear strain between microfibrils (slippage), we propose a mechanistic model of a network of sliding fibrils connected by tethers. A statistical approach is introduced to describe the population behavior of tethers that have elastic properties and the ability to break and reform in time. These properties are responsible for global cell wall mechanics such as creep and stress relaxation. Model predictions are compared with experiments from literature on stress relaxation and turgor pressure step up for the growing cells of P. blakesleeanus, which are later extended to incised pea (Pisum sativus L.) and the algae Chara corallina using the unique dimensionless number Πpe for each species. To our knowledge, this research is the first attempt to use a statistical approach to model the cell wall during expansive growth, and we believe it provides critical insights on cell wall dynamics at a molecular level.

The Chain Distribution Tensor: Linking Nonlinear Rheology and Chain Anisotropy in Transient Polymers.

Transient polymer networks are ubiquitous in natural and engineered materials and contain cross-links that can reversibly break and re-form. The dynamic nature of these bonds allows for interesting mechanical behavior, some of which include nonlinear rheological phenomena such as shear thickening and shear thinning. Specifically, physically cross-linked networks with reversible bonds are typically observed to have viscosities that depend nonlinearly on shear rate and can be characterized by three flow regimes. In slow shear, they behave like Newtonian fluids with a constant viscosity. With further increase in shear rate, the viscosity increases nonlinearly to subsequently reach a maximum value at the critical shear rate. At this point, network fracture occurs followed by a reduction in viscosity (shear-thinning) with a further increase in shear rate. The underlying mechanism of shear thickening in this process is still unclear with debates between a conversion of intra-chain to inter-chain cross-linking and nonlinear chain stretch under high tension. In this paper, we provide a new framework to describe the nonlinear rheology of transient polymer networks with the so-called chain distribution tensor using recent advances from the transient network theory. This tensor contains quantitatively and statistical information of the chain alignment and possible anisotropy that affect network behavior and mechanics. We investigate shear thickening as a primary result of non-Gaussian chain behavior and derive a relationship for the nonlinear viscosity in terms of the non-dimensional Weissenberg number. We further address the criterion for network fracture at the critical shear rate by introducing a critical chain force when bond dissociation is suddenly accelerated. Finally, we discuss the role of cross-linker density on viscosity using a "sticky" reptation mechanism in the context of previous studies on metallo-supramolecular networks with reversible cross-linkers.

Heterogeneity is key to hydrogel-based cartilage tissue regeneration.

Degradable hydrogels have been developed to provide initial mechanical support to encapsulated cells while facilitating the growth of neo-tissues. When cells are encapsulated within degradable hydrogels, the process of neo-tissue growth is complicated by the coupled phenomena of transport of large extracellular matrix macromolecules and the rate of hydrogel degradation. If hydrogel degradation is too slow, neo-tissue growth is hindered, whereas if it is too fast, complete loss of mechanical integrity can occur. Therefore, there is a need for effective modelling techniques to predict hydrogel designs based on the growth parameters of the neo-tissue. In this article, hydrolytically degradable hydrogels are investigated due to their promise in tissue engineering. A key output of the model focuses on the ability of the construct to maintain overall structural integrity as the construct transitions from a pure hydrogel to engineered neo-tissue. We show that heterogeneity in cross-link density and cell distribution is the key to this successful transition and ultimately to achieve tissue growth. Specifically, we find that optimally large regions of weak cross-linking around cells in the hydrogel and well-connected and dense cell clusters create the optimum conditions needed for neo-tissue growth while maintaining structural integrity. Experimental observations using cartilage cells encapsulated in a hydrolytically degradable hydrogel are compared with model predictions to show the potential of the proposed model.