Fig 1.
Schematic of active microrheology measurements of Chaetopterus marine worm mucus.
(A) Typical Chaetopterus worm used for experiments, with body parts labeled. Mucus is extracted from the head and parapodia. (B) Image of viscoelastic mucus excreted by the worm. (C) Schematic of microspheres embedded in the mucus. Bead sizes are labeled and colored as they appear in the rest of the figures. Here, the 4.5 μm bead is trapped and sinusoidally oscillated at an amplitude Δx while the force F on the bead is measured. (D) Sample force F (blue) and stage position x (black) curves are shown for a 6 μm bead. Fmax is the amplitude of the force exerted by the mucus on the bead, xmax is the oscillation amplitude, and Δϕ is the phase difference between the force and stage curves.
Fig 2.
Force response reveals lengthscale-dependent material properties of mucus mesh.
(A) Sample force curves normalized by corresponding bead radii (F/R) show scale-dependent material response. Force curves shown are for an oscillation amplitude of 3.6 μm and frequency of 10 Hz for probe sizes of 2 (green), 4.5 (cyan), 6 (blue), and 10 μm (magenta). F/R for 4.5 and 6 μm beads are nearly identical indicating the mucus is responding as a continuum fluid at these lengthscales (l2). The ~2× reduction in F/R for 2 μm probes indicates a transition to a water-like regime (l1). The ~3× reduced F/R for the 10 μm probe indicates that the bead is being forced out of the trap and does not track with the trap position during the complete oscillation. This forcing, unique to 10 μm probes, indicates the presence of stiffer structures at this lengthscale (l3). (B) The force peaks from the boxed regions in (A) show that F/R for 10 μm probes drop nearly to zero at the maximum position, as the bead is forced out of the trap. (C) The average normalized force amplitude, <Fmax>/R, as a function of bead diameter clearly shows the described distinction between the three different lengthscales (l1 (green), l2 (cyan, blue), l3 (magenta)).
Fig 3.
Viscosity vs oscillation amplitude reveals a critical lengthscale of ~4 μm controlling mechanics.
Viscosity, η (Pa-s), as a function of oscillation amplitude for 2 (green), 4.5 (cyan), 6 (blue) and 10 μm (magenta) probes. Note that the viscosities for 4.5 and 6 μm probes are nearly identical. Smaller η values for 2 μm probes indicate a water-like regime (l1) which only transitions to the continuum regime for amplitudes >4 μm (l2, dashed line). The reduced η for 10 μm probes is an artifact of the probe being forced out of the trap, likely by larger stiffer structures in the mucus (l3).
Fig 4.
Frequency-dependent viscoelastic moduli indicate that the mesoscale polymer mesh is highly viscous while elasticity is a largescale phenomenon.
Elastic modulus, G', (closed squares) and viscous modulus, G'', (open squares) as a function of amplitude for four different probes sizes. Note the similar values for the 4.5 and 6 μm beads and the increase in G′ for the 2 μm probe at xmax > 4 μm. The reduced gap between G′ and G" for 10 μm probes indicates a more elastic response.
Fig 5.
Elasticity dominates the macroscale response, while viscosity is comparable on multiple lengthscales.
Elastic (closed) and viscous (open) modulus measured via macrorheology (red) and microrheology using 4.5 (cyan) and 6 μm (blue) microspheres. Macrorheology measurements exhibit G′>G" (in contrast to microrheology data) indicating that elasticity is a macroscale phenomenon. G" for both macrorheology and microrheology data are similar, indicating that the dissipative mechanics arise from the loosely entangled polymers in the mucus.
Fig 6.
Lengthscale-dependent viscoelastic effects of mucus.
G'(ω) and G"(ω) for 2 (green), 4.5 (cyan), 6 (blue), and 10 μm (magenta) probe sizes. The scaling of G′ and G" for 2 μm beads indicates that the mucus is responding principally as a Newtonian fluid with minimal elasticity, indicated by the terminal regime scaling laws represented by dashed lines. For the larger probes, the scaling of both G′ and G" deviate from terminal regime scaling indicating the onset of viscoelastic effects. Consistent with our proposed model, the values for 4.5 and 6 μm beads coincide (l2), and for 10 μm beads G′ approaches G" and both G′ and G" approach frequency-independent plateaus.
Fig 7.
Relative elasticity <G′/G"> of mucus increases with increasing lengthscales.
(A) Average relative elasticity <G′/G"> for 2 (green), 4.5 (cyan), 6 (blue), 10 μm (magenta) beads and macrorheology data (red). Closed squares are < G′/G"> values averaged over all amplitudes while open squares are averaged over all frequencies. The relative elasticity increases as probe size increases, approaching <G′/G"> for macrorheology data. (B) <G′/G"> as a function of amplitude shows that elastic effects begin to play a role in mechanics beyond 4 μm.
Fig 8.
Lengthscale-dependent microrheology measurements suggest that mucus can be modeled as a coupled two-fluid system.
Cartoon of the proposed structure of the marine worm mucus. l1 is the water-like regime, where the mesh plays little role in the response and particles can freely pass through the mucus. l2 is the mesoscale continuum regime comprised of loosely entangled polymers. l3 is the regime where the stiff scaffold produces the elastic-like macroscopic mucus properties. Coupling of the two meshes at l2 and l3 may be achieved via steric entanglements or chemical crosslinking.