Unravelling hagfish slime

Abstract

Hagfish slime is a unique predator defence material containing a network of long fibrous threads each ∼10 cm in length. Hagfish release the threads in a condensed coiled state known as skeins (∼100 µm), which must unravel within a fraction of a second to thwart a predator attack. Here we consider the hypothesis that viscous hydrodynamics can be responsible for this rapid unravelling, as opposed to chemical reaction kinetics alone. Our main conclusion is that, under reasonable physiological conditions, unravelling due to viscous drag can occur within a few hundred milliseconds, and is accelerated if the skein is pinned at a surface such as the mouth of a predator. We model a single skein unspooling as the fibre peels away due to viscous drag. We capture essential features by considering simplified cases of physiologically relevant flows and one-dimensional scenarios where the fibre is aligned with streamlines in either uniform or uniaxial extensional flow. The peeling resistance is modelled with a power-law dependence on peeling velocity. A dimensionless ratio of viscous drag to peeling resistance appears in the dynamical equations and determines the unraveling time scale. Our modelling approach is general and can be refined with future experimental measurements of peel strength for skein unravelling. It provides key insights into the unravelling process, offers potential answers to lingering questions about slime formation from threads and mucous vesicles, and will aid the growing interest in engineering similar bioinspired material systems.

Figure 1.

Slime defends hagfish against predator attacks. (a) Sequence of events during a predator attack (adapted from Zintzen et al. [8]). On being attacked, the hagfish produces a large quantity of slime that chokes the predator. The process of secretion and slime creation took less than 0.4 s. (b) Slime is formed from the secreted biomaterial, in part containing prolate-shaped skeins. (c) A skein unravels under the hydrodynamic forces from the surrounding flow field and produces a micrometre-width fibre of length 10–15 cm. (d) The unravelled fibres and mucous vesicles entrain a large volume of water to form a cohesive network. Details on materials and microscopy are provided in the electronic supplementary material, section I. (Online version in colour.)

Figure 2.

Unravelling a thread skein by pulling, as viewed with brightfield microscopy. Bottom right scale bar 50 μm.

Figure 3.

Simplified model of thread being drawn from a skein. The thread has length $L(t)$ with initial length $L(0)=L_0$. Here s is the arclength material (Lagrangian) coordinate along the unravelled thread, with $0\le s\le L(t)$. The fixed laboratory (Eulerian) coordinate of the thread is $\mathit{x}(s,t)$, with the thread peeling from the skein at $\mathit{x}(L(t),t)=\mathit{X}(t)$. (Online version in colour.)

Figure 4.

Numerical solution (solid line) of (4.2) for the parameter values R₀ = 50 μm, $L_0=2R_0$, ℘ = 10, m = 1/2, U = 1 m s⁻¹. The dashed line (purple) is the upper bound $L=L_0+Ut$. The horizontal dashed line is at $L=L_{\max }$, when the skein is fully unravelled. Even for such a moderate force ratio ℘ = 10 the thread unravels almost as fast as the upper bound. (Online version in colour.)

Figure 5.

Numerical solution (solid line) of (4.10) for the parameter values R₀ = 50 μm, $L_0=2R_0$, ℘ = 1/2, m = 1/2, U = 1 m s⁻¹. The dashed line (purple) is the upper bound $L=L_0+Ut$. The horizontal dashed line is at $L=L_{\max }$, when the skein is fully unravelled. Even for such a small force ratio $\mathrm{\wp }$ the thread unravels almost as fast as the upper bound. (Online version in colour.)

Figure 6.

Numerical solution (solid line) of (4.14) for the parameter values R₀ = 50 μm, $L_0=2R_0$, ℘ = 10, m = 1/2, λ = 10 s⁻¹. The dashed line (purple) is the upper bound $L_0\exp (\frac{\lambda }{\hspace{0.17em}}t/2)$. The horizontal dashed line is at $L_1=L_{\max }$, when the skein is fully unravelled. (Online version in colour.)

Figure 7.

Thread being drawn from two skeins. (Online version in colour.)

Figure 8.

Numerical solution (solid line) for the thread half-length $L_1(t)$ using the force for two symmetric free skeins (equation (4.24)) for the parameter values R₁(0) = 50 μm, $L_1(0)=2R_1(0)$, ℘ = 10, m = 1/2, λ = 10 s⁻¹. The dashed line (purple) is the upper bound $L_1(0)\exp (\lambda t)$. The horizontal dashed line is at $L_1={L_1}_{\max }$, when the skein is fully unravelled. (Online version in colour.)

Figure 9.

Parameter dependence of ‘effective’ unravelling. Comparison of time scale $t_{\mathrm{dep},50\text{\%}}$ for unravelling half the total length of the fibre for different values of m, as the dimensionless quantity $\mathrm{\wp }$ is varied in different unravelling scenarios. (a) Pinned thread in uniform flow, (b) pinned skein in uniform flow, (c) free thread and skein in straining flow and (d) symmetric free skeins in straining flow. Other parameters used are r = 1 μm, R₀ = 50 μm, $L_0=2R_0$, U = 1 m s⁻¹ and λ = 10 s⁻¹. The dotted horizontal line represents the physiologically observed time scale (=0.4 s). (Online version in colour.)

Figure 10.

(a) Mucous vesicles aggregating on unravelling thread (adapted from Koch et al. [21]). (b) Mucous vesicles aggregated on unravelling thread elongated along with the fibre under the flow (adapted from Winegard & Fudge [22]).