Ex vivo rheology of spider silk

Over the past decade, numerous studies have shown that spider dragline silk has a number of unique material properties(Becker et al., 2003; Gosline et al., 1999; Shao and Vollrath, 2002), yet how exactly the spider processes its fiber remains unclear. Recent experiments with recombinant spider silk (Lazaris et al., 2002) and other studies performed with silkworms(Shao and Vollrath, 2002) show that careful control of the processing conditions for fiber spinning is key to obtaining superior mechanical properties in spun silks. Forced silking at different rates results in modified kinematics in the spinning canal and substantial changes in the mechanical properties of the resulting silk fibers(Perez-Rigueiro et al., 2005). A detailed microscopic study of spider silk spinning involving whole spider silk glands suggests that at least two physical processes are important(Knight and Vollrath, 1999):(1) shear-thinning of the silk solution in the ducts that deliver the fluid towards the spinneret (this is, in turn, related to the liquid crystallinity of the protein solution) and (2) pronounced elongation of the long protein chains during the spinning process results in a highly aligned microstructure after the silk dries.

To further understand this complex flow process it is essential to elucidate the rheological properties of the initial liquid spinning material,commonly referred to as `spinning dope'(Vollrath and Knight, 2001),that is stored in the spinning glands of the spider(Chen et al., 2002). Although the spinning dope is a concentrated aqueous solution containing 25-30 wt%protein, all rheological experiments to date have been performed with diluted solutions (typically <5 wt% of protein)(Chen et al., 2002).

Recently, processing experiments have been performed with reconstituted silk solutions obtained from the silkworm Bombyx mori(Jin and Kaplan, 2003). Micellar solutions with ∼8 wt% silk were reconstituted using dialysis. However, in order to produce spinnable fibers, a high-molecular-mass linear polymer (polyethylene oxide with molecular mass of 0.9 ×10⁶ g mol^-1) was added to the reconstituted solutions. This additional component augments the `spinnability' of the dope by increasing the extensional or `tensile' viscosity of the fluid and prevents capillary break-up of the fluid jet. The resulting spun fibers exhibited morphological features, such as increased birefringence and alignment, that are similar to the native silk fiber (Magoshi et al.,1994). The birefringence properties of raw spider silk have also been observed and investigated by Knight and Vollrath(Knight and Vollrath, 1999). These experiments suggest that native silkworm and spider silk solutions possess significant non-Newtonian fluid properties(Chen et al., 2002; Terry et al., 2004), however more insight would be gained through direct rheological characterization of the native, concentrated spider silk dope. For clarity, we provide in the Appendix a glossary of some of the most important rheological concepts that are essential for understanding the properties of this complex protein solution.

Recently published results (Terry et al., 2004) of bulk shear rheometry on larger scale samples of silkworm silk solutions indicate strong viscoelastic properties for silk dope with a zero-shear-rate viscosity on the order of 10³ Pa.s and a critical rate of the onset of shear thinning on the order of 1 s^-1. Phase separation and unstable flow conditions above this critical rate were interpreted as indication for a shear-induced beta-sheet formation.

The volume of spinning dope that can be harvested from a single major ampullate gland of N. clavipes is approximately 5-10 μl. Besides the minute quantity available, the dope is viscous(Willcox et al., 1996) and tends to dry with time, making it difficult to obtain reliable viscometric data. Many of these difficulties can be overcome by using micro-rheometry. The majority of micro-rheometric techniques available for the characterization of complex biofluids rely on Brownian forcing of microscopic tracer beads. The rheological properties of the surrounding fluid matrix are obtained from the time-correlated displacement of the bead via a deconvolution process(Mukhopadhyay and Granick,2001; Solomon and Lu,2001). Such techniques are inherently limited to studies of linear viscoelastic properties of the test fluid at small shearing strains. By contrast, the silk spinning process involves large strains and both shearing and extensional kinematic components(Knight and Vollrath, 1999). These large deformations influence the development of non-equilibrium texture morphologies in the spun silk (Vollrath and Knight, 2001) that lead to observational phenomena such as super-contraction (Vollrath et al.,1996) and shape-memory effects(Emile et al., 2006). In order to address these issues, two new micro-rheometric instruments have been constructed: a flexure-based micro-rheometer(Clasen et al., 2006; Clasen and McKinley, 2004; Gudlavalleti et al., 2005) for steady and oscillatory shearing measurements and a capillary break-up micro-rheometer for extensional rheometry(Bazilevsky et al., 1990; McKinley and Tripathi,2000).

Here, we describe the application of these instruments in measuring the rheological properties of dragline silk solutions extracted from the major ampullate gland of Nephila spiders.

Both of the experimental devices utilized in the present study have been specifically designed to accommodate the small quantities (∼1 μl) of fluid available from a single major ampullate gland of the Nephila clavipes L. spider, as shown in Fig. 1. Thus, these micro-rheometric devices enable ex vivotesting of the native spinning dope from which the spider spins dragline and web frame fibers (Gosline et al.,1999; Vollrath and Knight,2001).

Dissections were performed using a standard dissecting microscope, and the ampullate glands were extracted and stored under distilled water for less than 5 min whilst being transferred to the micro-rheometers for testing. Each sample was only utilized once due to progressive evaporation of the aqueous phase to the environment.

The flexure-based micro-rheometer generates a plane Couette shearing flow between two plates that are aligned using white light interferometry and separated by a precisely controlled gap of 1-150 μm(Fig. 2a). The plates consist of cylindrical optical flats that are then diamond-machined to provide the required rectangular test surface area. The shear stress exerted on the sample(ranging from 2 to 10⁴ Pa) is calculated from the deflection of the upper flexure as the lower one is actuated. The imposed shear rate(⁠

Here, σ is the surface tension of the liquid, R(t)is the midpoint radius of the thread measured with the laser micrometer, and the numerical prefactor is derived from a slender-body lubrication theory for a viscous incompressible Newtonian fluid in order to account for deviations from a purely cylindrical geometry in the vicinity of the endplates(McKinley and Tripathi,2000).

Due to the high viscosity of the silk and the evaporation of the aqueous solvent, it was not possible to directly measure the surface tension of the silk, and furthermore we are not aware of any published data on this topic. However, we may estimate the range of values to be 30×10^-3≤σ≤60×10^-3 N m^-1. The upper bound is consistent with measured values for other aqueous polymer solutions (Adamson and Gast, 1997; Christanti and Walker, 2001; Cooper-White et al., 2002). The presence of any additional surfactant components in the silk dope may lower this number to values closer to those of non-water-soluble hydrocarbon-based polymers that are typically of the order of 30×10^-3 N m^-1.

where λ is a measure of the relaxation time of the viscoelastic fluid (its inverse is the critical shear rate that marks the onset of shear thinning), n is the power-law exponent characterizing the shear-thinning regime observed at high shear rates, and the coefficient a describes the rate of transition between the zero-shear-rate region and the power-law region.

Nonlinear regression of these parameters to our data yields values ofλ=0.40 s, a=0.68 and n=0.18, which are characteristic for a strongly shear-thinning fluid(Yasuda et al., 1981). We are not aware of any other published data on the ex vivo rheology of native Nephila dope with which we can compare these values. A comparison to rheological measurements for B. mori dope, determined with the same experimental setup and shown in Fig. 2b, gives similar viscoelastic properties for the silk dopes obtained from the silkworm and the spider. The constitutive parameters obtained with each sample are tabulated in Table 1. The shear-thinning behavior measured in our silkworm dope is consistent with recent experiments performed with a commercial rheometer(Terry et al., 2004), in which the zero-shear-rate viscosity measured was reported to be `approximately 2 kPa.s' (we measured 5±1 kPa.s). Their measurements also showed that the critical shear-rate above which shear-thinning occurs is of the order 0.5 s^-1 (we determined 1.7 s^-1). No reports of standard error or sample-to-sample variability were reported in this earlier study; the relatively small differences between the two sets of measurements may be due to biological variability as well as to handling of the dope sample.

The data in Fig. 3b show that at small strains the extensional viscosity η_e is three times larger than the zero-shear-rate viscosity measured with the shearing micro-rheometer. This observation is consistent with the classical results of Trouton for a Newtonian liquid (Trouton,1906). However, at large strains, the necking dynamics are greatly retarded as the filament simultaneously strain-hardens and undergoes mass transfer to the surroundings (i.e. evaporative drying). This strain-hardening stabilizes the spinline and leads to the formation of axially uniform filaments (Olagunju, 1999). The apparent extensional viscosity therefore diverges and the thinning fluid thread ultimately dries to become a solid filament with a fixed finite radius. In contrast to an actual dragline filament, which is spun under a constant force corresponding to the weight of a spider(Gosline et al., 1999), in our capillary break-up device there is no externally imposed tension. The final thread radius is measured to be R_f≈20 μm. The solid red line in Fig. 3a corresponds to a one-dimensional model of this drying process, which is discussed in detail below.

Here, λ and n are obtained from the Carreau-Yasuda model(Eqn 2). This relation is only valid in the shear-thinning regime when the shear rate is larger than the critical shear rate (1/λ) and the viscosity is thus well approximated by

The pressure drop ΔP_silk necessary to push the silk dope through the spinneret at the typical flow rate of Q̇=0.25 nl s^-1 is approximately 4 ×10⁷ Pa. The corresponding energy dissipation rate ΔP_silkQ̇∼10 μW (due to viscous flow of the silk dope) is comparable to the release rate of potential energy, MgV_spin∼20 μW, for a spider descending on a dragline, where M is the mass of the spider (∼0.1 g), gis the gravitational constant, and V_spin=20 mm s^-1 is a typical silking speed. By contrast, if the silk dope did not exhibit this pronounced shear-thinning behavior (which is associated with its liquid crystallinity), the viscous dissipation rate required to sustain the corresponding flow rate of a Newtonian fluid would be 5000 μW and hence would significantly exceed the potential energy release rate. Additional sources of energy input would have to be provided by the spider or,conversely, a much lower natural spinning speed would be selected.

This shear-thinning property of the silk dope may also act in conjunction with other proposed mechanisms that facilitate the spinning of the thread,such as a shear-induced transition to a liquid crystalline phase(Vollrath and Knight, 2001),localised slip of the polymer solution on the tube wall(Migler et al., 1993), or a subtle form of lubrication, such as a watery surfactant layer(Vollrath and Knight, 2001) or an analogue to the sericin coat surrounding fibroin fibers spun by B. mori (Kaplan et al.,1994).

In contrast to the observations of shear-thinning, the measurements of the transient extensional rheology in the micro-capillary break-up extensional rheometer (or μCABER) show that in an elongational flow the material's resistance to stretching increases with elapsed time (and imposed strain). The importance of this strain-hardening phenomena for the spinning of dragline silk appears to have been first noted by Ferguson and Walters(Ferguson and Walters, 1988)and prevents the capillary break-up of an elongating viscoelastic fluid filament (Olagunju, 1999).

This rate of stretching can be compared with the liquid relaxation time via the Deborah number [see Appendix as well as Bird et al.(Bird et al., 1987a)], defined as

Combining this time-dependent viscosity with Eqn 1 results in an integro-differential equation for calculating the evolution of the radius of the thinning thread.

Alternatively, it is possible to apply this theory directly to the present microcapillary break-up measurements treating P as an arbitrary fitting parameter. The results of using a best-fit value of P=2.715×10^-2 are shown in Fig. 3a by the solid red line. This best fit value of the processability parameter is in good agreement with the a priori estimate given above.

The resistance of the fluid thread to further stretching is characterized by the apparent extensional viscosity (derived from Eqns 1, 6) as presented in Fig. 3b over the entire course of the filament evolution. At large strains, the filament undergoes strain-hardening due to the combined action of molecular elongation and solvent evaporation and ultimately becomes a solid thread with a constant diameter. The extensional viscosity increases by 100-fold during the capillary thinning of the filament radius. This strain-hardening plays an important role in the fiber spinning process by inhibiting capillary thread break-up and stabilizing the spinline.

In this work, we have used two new micro-rheometric devices that utilize less than 5 μl of fluid for a test and enable the measurement of the steady and transient rheological properties of ex vivo samples of biopolymer solutions such as spider and silkworm spinning dope. The devices are able to impose large deformation rates and large strains that match the range of deformations experienced in vivo. Our measurements show that the steady shear viscosities

Orb-weaving spiders use a specialized fiber-spinning process that exploits the nonlinear rheology of a complex fluid. In the spinning canal of N. clavipes, the shear viscosity of the spinning dope decreases by an order of magnitude and thus reduces the pressure-drop along the canal, whereas the extensional viscosity increases by a factor of 100 to stabilise the fluid thread and inhibit capillary break-up of the spun thread. Tailoring the rheological properties of artificial spinning dopes containing genetically modified or reconstituted silks to match the ex vivo properties of the natural dope may prove essential in enabling us to successfully process novel synthetic materials with mechanical properties comparable to, or better than, those of natural spider silk.

In this glossary we provide brief working definitions for some of the most important rheological concepts utilized in this work and provide references to other primary sources for additional reading.

Also often described as a `rheological equation of state'. Such equations relate the tensorial state of stress in a complex fluid to the entire deformation history imposed on it. If the relationship between an imposed shear-rate and the resulting shear stress is nonlinear then the fluid is`non-Newtonian'. Constitutive equations may be constructed empirically or derived from molecular-based kinetic theories(Bird et al., 1987a; Bird et al., 1987b).

One of the most common rheological features of complex fluids is a nonlinear relationship between the shear stress (⁠

Liquid crystalline solutions are distinguished by the rigidity and local ordering of the constituent molecules (in contrast to the random walk conformation associated with flexible macromolecules). This local molecular ordering can lead to phase transitions as the concentration is increased or the system temperature is reduced. In addition, the coupling between imposed mechanical deformations and molecular ordering leads to optical anisotropy in the solutions that is manifested in effects such as flow-induced birefringence(Burghardt, 1998). Such effects have been measured in protein solutions obtained from silkworms and from spiders (Magoshi et al., 1994; Willcox et al., 1996) and are discussed in detail in the review of Vollrath and Knight(Vollrath and Knight,2001).

The extensional viscosity of a fluid is a measure of the resistance to elongational (stretching) deformations and is defined as a ratio of the measured tensile stress difference to the imposed rate of stretching. Although perhaps this concept is initially puzzling to contemplate, some physical understanding may be attained by recognizing that the extensional viscosity holds the same relationship to the shear viscosity of a fluid as the Young's modulus (E) does to the shear modulus (G) for an elastic solid. Indeed, for an incompressible Newtonian fluid, the extensional viscosity is precisely three times the shear viscosity, a result first obtained by Trouton 100 years ago(Trouton, 1906), just as the Young's modulus is three times the shear modulus for an incompressible Hookean solid. For non-Newtonian fluids such as polymer solutions, the extensional viscosity is an independent material function that cannot be determined from the shear viscosity. Typically, the extensional viscosity of a complex fluid is a function of both the rate of elongation and the total strain imposed and this governs the `spinnability' of a fluid thread(Macosko, 1994).

For many polymeric systems it is found that the extensional viscosity increases with the total strain imposed on the system. This is a consequence of the increasing molecular elongation of the flexible polymer chains as the external strain is increased and is referred to as strain-hardening or sometimes `strain-stiffening' (Nguyen and Kausch, 1999). This increase in the extensional viscosity is only to be expected if the rate of deformation imposed on the fluid is sufficiently rapid to exceed local relaxation of the chain back towards equilibrium; this criterion is parameterized by the Deborah number of the flow.

The Deborah number provides a dimensionless measure of how important non-Newtonian effects are expected to be in a given deformation. The Deborah number represents a ratio of the intrinsic relaxation time of the polymeric liquid to the characteristic flow time scale (or equivalently the product of relaxation time with the rate of deformation) of a particular flow process(McKinley, 2005). For example,if a polymer chain can relax back to its equilibrium configuration (through Brownian motion) faster than it is deformed (De<1) then the material will not show strain-hardening in elongation, or shear-thinning in steady shear flow and will instead flow in the same manner as a viscous Newtonian fluid.

This research was supported by funds from the NASA Biologically-Inspired Technology Program, the DuPont-MIT Alliance and in part by the U.S. Army through the Institute for Soldier Nanotechnologies, under Contract DAAD-19-02-D0002 with the U.S. Army Research Office. Adult female Nephila clavipes spiders were kindly provided by Rachel Rogers of the Miami MetroZoo.