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Mesoscale Continuum (L2) Not accessing full mesh (L1) Rigid mesh revealed (L3) Active microrheology reveals molecular-level variations in the viscoelastic properties of Chaetopterus mucus William Weigand 1 , Ashley Messmore 2 , Dimitri Deheyn 3 , Jeff Urbach 4 ,Rae M Robertson-Anderson 1 1 Department of Physics and Biophysics, University of San Diego; 2 UC San Diego; 3 Scripps Institution of Oceanography, 4 Department of Physics, Georgetown University Abstract: The sea annelid, Chaetopterus Variopedatus, secretes a bioluminescent mucus that also exhibits complex viscoelastic properties. The constituents of the mucus are relatively unknown but it does play an important role in the development of the worms’ parchment-like housing tubes. In order to determine how and why this mucus can exhibit material properties ranging from fluidity to rigidity we perform microrheology experiments. We determine the microscale viscoelastic properties by using optical tweezers to produce small oscillations in the mucus which allow us to determine both the linear storage and loss moduli (G’,G’’) along with the viscosity of the fluid. By varying the size of the microspheres (2-10 μm) and oscillation amplitude (.5-10 μm) we are able to determine the dominant intrinsic length scales of the molecular mesh comprising the mucus. By varying the oscillation frequency (1-15Hz) we determine the crossover frequency at which G’ surpasses G’’, to quantify the longest relaxation time of the mesh network. Initial results show a strong dependence on bead size which indicate that the dominant entanglement lengthscale of the mucus mesh is ~5 um. Microspheres of this size exhibit a wide variety of stress responses in different regions of the mucus demonstrating the substantial microscale heterogeneity of the mucus. We carry out measurements on a population of worms of varying size and age to determine mucus variability between worms. Mucus response to microscale force oscillations Sample preparation: Worms are kept in a salt water tank at ~15°C. To extract mucus, we remove the head and the arms from the rest of the body, place them in a syringe and lightly squeeze. 1 10μL of mucus from the head and the arms is mixed with 3 μL BSA coated microspheres ranging in size from 2-10μm and 0.015% Tween-20 to prevent microspheres from adhering to the microscope slide. The mucus mixture is mixed and pipetted into a microchannel comprised of two strips of double sided taped applied lengthwise along a microscope slide with a coverslip adhered to the top. Force oscillations: Microspheres are trapped using a 1064nm Nd:YAG fiber laser focused by a 60x objective. The trapped microsphere is kept stationary and the surrounding fluid is sinusoidally oscillated by a piezoelectric stage. To measure the force, we use a position sensing detector measures the deflection of the laser which is proportional to the force. We then fit the data to sine curves using the least squares method 2 . We vary both the oscillation frequency (3-15Hz) and oscillation amplitude(1-8μm). Calculating elastic and viscous moduli and viscosity: From the fits to the force data, we calculate the elastic modulus, G’, the viscous modulus, G’’, and the viscosity η. . G’ = cos() 6 , G’’ = sin() 6 , and η = (( ′2 + ′′2 )/(ω 2 ))^(1/2),, where F max is the amplitude of the force on the bead, x stage is the displacement of the stage, Δϕ is the phase difference between force and displacement and R is the radius of the bead 3 . The equations above tell us that material properties (η,G’,G’’) are proportional to Force/Radius (F/R) of the probe. In continuum fluids such as honey, these material properties are constant at all lengthscales, so the ratio F/R should be independent of probe size. For the mucus: F/R is constant for 4.5 and 6μm beads • at this lengthscale the mucus acts as a continuum fluid F/R is substantially lower for 2μm beads • the discrete nature of the mucus becomes important (the probe is moving largely through water). F/R is even lower for 10μm probes with flat peaks • the bead is forced out of the trap by the mucus preventing it from travelling the full oscillation distance. evidence for a rigid scaffolding with pore sizes of ~10μm Force response reveals lengthscale dependent material properties of mucus mesh Viscosity vs oscillation amplitude shows that the mucus mesh size is ~ 4 um The 10 μm bead η is even lower • probe is being forced out of the trap, for oscillations >4μm, η continues to drop as the bead can only travel a partial distance despite trying to move it further • rigid scaffold dominates response above 10 μm Elasticity dominates macroscale response, fluidity is comparable on multiple lengthscales Comparing G’ and G” for 4.5 and 6µm beads to macrorheology data reveals: • elasticity is a largely macroscopic phenomenon as G’ is ~10x larger for macrorheology data compared to microrheology. • G” for both micro- and macroscopic data are equal indicating that loosely entangled microscale mesh is responsible for fluidity at all scales. Ratio of G’ to G’’ quantifies relative elasticity of mucus network • Mucus elasticity increases with increasing probe size approaching macroscale elasticity (dashed line) for 10μm beads. • Loosely entangled polymer mesh leads to enhanced viscosity above L1 • large scale rigid scaffold beyond L2 controls the elastic response seen at the macroscale Conclusion: Using active microrheology we determine that Chaetopterus sp. mucus contains three distinct lengthscales that govern the material properties. • Below ~4 um the mucus responds similarly to water with minimal contribution from the biopolymer mesh • A mesoscale continuum regime exists for 4 – 10 um where the mucus acts as a continuum viscoelastic fluid comprised of loosely entangled polymers. • Beyond 10 um, a more rigid mesh, likely comprised of bundled polymers, responds elastically to perturbations and is responsible for the macroscopic elastic gel response that is typically found in mucus. Understanding the lengthscales intrinsic to mucus provides important insight into how it is able to perform its highly varied functions – from lubrication and digestion to protection from pathogens 4 and has potential application in developing novel drug delivery systems. Macrorheology References 1. Deheyn, D.D., et al. “Optical and Physicochemical Characterization of the Luminous Mucous Secreted by the Marine Worm Chaetopterus sp.”, Physiological and Biochemical Zoology, 86, 702-715 (2013). 2. Chapman, C.D., et al. “Onset of Non-Continuum Effect in Microrhelogy of Entangled Biopolymer Solutions.” MacroMolecules, 47, 1181-1186 (2014) 3. Ziemann, F., et al. “Local measurements of viscoelastic moduli of entangled actin networks using anoscillating magnetic bead micro-rheometer.” Biophysical Journal, 66, 2210-2216 (1994). 4. Lai, S.K, et al. “Micro- and macrorheology of mucus.” Advanced Drug Delivery Reviews, 61, 86-100 (2009). G’, (closed squares) quantifies elasticity, G’’, (open squares) quantifies fluidity Mesoscale polymer mesh is highly viscous but elasticity is a largescale phenomenon controlled by larger rigid polymer scaffold For 2μm beads G’’ ≈ 10G’, both G’ and G’’ are lower than for 4.5 and 6µm beads • probe is moving largely through water between the mucus mesh For 4.5 and 6µm spheres, G’’ ≈ 2G’ • probes are moving mainly through the viscoelastic mucus mesh but the elastic contribution is relatively weak indicating loose polymer entanglements For the 10µm probes G’’ ≈ G’ • mucus is responding much more elastically due to a large scale elastic rigid scaffold Mesoscale Continuum (L2) (L1) (L3) Microrheology measurements suggest that the biopolymer mesh comprising the mucus contains three intrinsic lengthscales Acknowledgments: We thank the Air Force Office of Scientific Research for funding this project. L 1 <4μm: a largely viscous response similar to that of water. Probes move largely through water occasionally encountering the mesh. L 2 ≈ 4.5-10μm: probe-independent response indicates continuum limit. The discrete nature of the mesh can be ignored. Probes move largely through polymer mesh. L3 >10μm: elastic response indicates more rigid mesh that is strong enough to prevent the bead from staying trapped. Response is similar to macroscopic rheology response Viscosity for 4.5 and 6 μm beads is the same • the mucus is responding as a continuum fluid at these lengthscales For 2μm beads η is ~3x smaller and constant up to ~4 μm oscillation amplitude, after which η increases approaching η of 4.5 and 6μm beads. • the probe is traveling mostly through water for amplitudes <4 um, accessing continuum mucus mesh beyond 4 μm G’/G’’ - averaged over range of amplitudes (closed squares) and frequencies (open squares) - quantifies the relative elasticity of the mucus mesh at varying lengthscales
