Lose the stress: Viscoelastic materials for cell engineering

Abstract

Biomaterials are widely used to study and control a variety of cell behaviors, including stem cell differentiation, organogenesis, and tumor invasion. While considerable attention has historically been paid to biomaterial elastic (storage) properties, it has recently become clear that viscous (loss) properties can also powerfully influence cell behavior. Here we review advances in viscoelastic materials for cell engineering. We begin by discussing collagen, an abundant naturally occurring biomaterial that derives its viscoelastic properties from its fibrillar architecture, which enables dissipation of applied stresses. We then turn to two other naturally occurring biomaterials that are more frequently modified for engineering applications, alginate and hyaluronic acid, whose viscoelastic properties may be tuned by modulating network composition and crosslinking. We also discuss the potential of exploiting engineered fibrous materials, particularly electrospun fiber-based materials, to control viscoelastic properties. Finally, we review mechanisms through which cells process viscous and viscoelastic cues as they move along and within these materials. The ability of viscoelastic materials to relax cell-imposed stresses can dramatically alter migration on two-dimensional surfaces and confinement-imposed barriers to engraftment and infiltration in three-dimensional scaffolds. STATEMENT OF SIGNIFICANCE: Most tissues and many biomaterials exhibit some viscous character, a property that is increasingly understood to influence cell behavior in profound ways. This review discusses the origin and significance of viscoelastic properties of common biomaterials, as well as how these cues are processed by cells to influence migration. A deeper understanding of the mechanisms of viscoelastic behavior in biomaterials and how cells interpret these inputs should aid the design and selection of biomaterials for specific applications.

Keywords: Alginate; Cell migration; Collagen; Electrospun fibers; Hyaluronic acid; Mechanobiology; Stress relaxation; Viscoelastic.

Figure 1.. Shear Rheology for Polymer Systems.

(a) In an oscillatory rheological measurement, the rheometer probe rotates sinusoidally at a given frequency (or over a “sweep” of frequencies, see (h) below), and thus (b) strain ($\mathrm{\lambda }$) and (c) stress ($\mathrm{\top }$) oscillate with time (t). In a purely elastic material, $\mathrm{\top }$ and $\mathrm{\lambda }$ are instantaneously coupled, whereas in a purely viscous material the two quantities are offset by a phase angle $(\mathrm{\delta })=\mathrm{\pi }/2$ (see text). Materials between these two extremes are considered viscoelastic. Unlike oscillatory tests, (d) stress-relaxation tests are performed at constant strain, so (e) strain and the resulting (f) stress change monotonically with time. A purely elastic material, such as an elastic solid, resists with a constant stress, reflecting storage rather than dissipation of the mechanical input. For a viscoelastic solid, stress falls (relaxes) with time to some plateau value, where the initial and plateau stress correspond to effective spring constants for the material (${\mathrm{\mu }}_1+{\mathrm{\mu }}_2$ and ${\mathrm{\mu }}_1$, respectively). For a viscoelastic fluid, such as a non-crosslinked polymer solution, stress eventually falls to zero. A purely viscous material does not hold stress at all. (g) All of these materials can be abstracted into models of springs and dashpots, where a purely elastic and purely viscous materials comprise of simply a spring or dashpot, respectively. Viscoelastic solids follow the standard-linear solid model, comprised of a spring in parallel with a spring and dashpot in series. Viscoelastic liquids, typically follow the Maxwell (spring and dashpot in series) model. (h) Each type of material responds characteristically when frequency is systematically varied (“frequency sweep”). Here storage (elastic) and viscous (loss) moduli are represented as G’ and G” respectively (see text), and the blue arrows represent progression from elastic to viscous character. G’ (solid lines) is constant for a purely elastic solid and increases with frequency for a viscoelastic material, as expected from (f) given that frequency represents a sort of inverse time. For a viscoelastic solid, ${\mathrm{G}}^{’}={\mathrm{\mu }}_1$ at zero frequency and increases to a plateau value of ${\mathrm{G}}^{’}={\mathrm{\mu }}_1+{\mathrm{\mu }}_2$ at high frequency. For viscoelastic liquid, ${\mathrm{G}}^{’}$ decays to 0 at the 0 limit. For G”, systems with a spring and dashpot in series have a maximum at ${\mathrm{\mu }}_2/\mathrm{\eta }$. Schematics are adapted from figures and text in the following references [–29].

Figure 2.. Architecture and stress-relaxation relationships for Collagen.

(a) Schematic showing the multiscale architecture of collagen, along with how properties of the network lead to viscoelastic properties. Collagen hydrogels are characterized by a hierarchical, fibrillar structure encoded within the primary sequences of the protein chains. Collagen hydrogels derive viscoelastic properties from a combination of entanglement, crosslinking (covalent and noncovalent), and fibril/fiber deformation and sliding. (b) Experimental stress-relaxation curves compiled and reformatted from two different studies [16, 18]. Collagen hydrogels [16, 18] relax stress faster than HA-collagen IPNs [16].

Figure 3.. Architecture and stress-relaxation relationships for Alginate.

(a) Schematic of alginate network architecture, showing how the network may be modified to tune viscoelastic properties by controlling alginate molecular weight and by introducing PEG spacers between the alginate chains. (b) Experimental stress-relaxation data compiled and reformatted from two different studies [18, 74]. Decreasing alginate MW and increasing PEG spacer MW tends to enhance viscous character. Further, a smaller degree of saturation (DS) is needed for a larger PEG spacer [74].

Figure 4.. Architecture and stress-relaxation relationships for Hyaluronic Acid (HA).

(a) Schematic of HA network architecture of HA, showing how HA networks may be modified to enhance viscoelastic properties. HA hydrogels may be transiently crosslinked to introduce viscoelastic character via IPNs, hydrogen bonds, coordinated metal ions, and host-guest chemistries. (b) Experimental stress-relaxation data compiled and reformatted from three different studies. Cd-Ad-based crosslinking [12] and IPN networks of HA-collagen [21] stress relaxes faster than hydrazone crosslinking (HA-ALD and HA-BLD single networks) [16].

Figure 5.. Architecture and stress-relaxation relationships for Electrospun Fibers.

(a) Schematic showing network architecture of electrospun fibers, along with how this network facilitates viscoelastic properties. Electrospun fibers derive viscoelastic properties analogously to collagen, due to their common fibrillar architecture, where fiber diameter, sliding, and density all play a role. (b) Experimental stress-relaxation curves compiled and reformatted from a single study [98]. As fiber diameter increases, the extent of stress dissipation also increases.

Figure 6. 2D Cell Spreading.

A general theme from 2D motility studies is that when a sufficiently high density of adhesive ligands is provided on stiff, fast-relaxing hydrogels, cells spread more on viscoelastic surfaces than on their elastic counterparts.

Figure 7. 3D Cell Motility.

(a) In 3D viscoelastic hydrogels, cells can viscoplastically deform and displace network chains to open cell-sized pores to facilitate migration. (b) This network rearrangement allows large groups of cells in tumors and organoids to facilitate branching and budding