Viscoelastic properties of the nematode Caenorhabditis elegans , a self-similar, shear-thinning worm

Abstract

Undulatory motion is common to many creatures across many scales, from sperm to snakes. These organisms must push off against their external environment, such as a viscous medium, grains of sand, or a high-friction surface; additionally they must work to bend their own body. A full understanding of undulatory motion, and locomotion in general, requires the characterization of the material properties of the animal itself. The material properties of the model organism Caenorhabditis elegans were studied with a micromechanical experiment used to carry out a three-point bending measurement of the worm. Worms at various developmental stages (including dauer) were measured and different positions along the worm were probed. From these experiments we calculated the viscoelastic properties of the worm, including the effective spring constant and damping coefficient of bending. C. elegans moves by propagating sinusoidal waves along its body. Whereas previous viscoelastic approaches to describe the undulatory motion have used a Kelvin-Voigt model, where the elastic and viscous components are connected in parallel, our measurements show that the Maxwell model, where the elastic and viscous components are in series, is more appropriate. The viscous component of the worm was shown to be consistent with a nonNewtonian, shear-thinning fluid. We find that as the worm matures it is well described as a self-similar elastic object with a shear-thinning damping term and a stiffness that becomes smaller as one approaches the tail.biomechanics | viscoelasticity

Worms under Pressure: Bulk Mechanical Properties of C. elegans Are Independent of the Cuticle

“…S2. Thus, the observed stiffness is a purely passive mechanical property of C. elegans, consistent with previous studies (26).…”

“…However, it is known to be very thin (0.5 mm, roughly 2% of the diameter of the worm), and thus its contribution to the overall stiffness of the worm need not be significant (42). Consistent with this, our measured value for the worm bulk modulus, k ¼ 140 5 20 kPa, is in close agreement with bending measurements of the worm body (26), provided the worm is modeled as a uniform cylinder, rather than as a hollow tube comprised solely of the cuticle. The worm's bulk mechanical properties thus reflect coarse-grained properties of the entire worm, rather than its cuticle alone.…”

“…Another recent study measured the worm's bending modulus using deflection of the entire body under actuation from a single point (26). Calculating the Young's modulus of the worm's body yields a value ranging from 110 kPa to 1.3 MPa, depending on whether the worm is modeled as a uniform cylinder or cylindrical shell (26).…”

ComparingCaenorhabditis elegansgentle and harsh touch response behavior using a multiplexed hydraulic microfluidic device

“…This may be because the worm’s elastic modulus is much smaller than that of PDMS. Studies that consider the worm as a whole have estimated its modulus to be the range of 110–140 kPa 30,31 , compared to ~1 MPa for PDMS with a 20:1 base:curing agent ratio 32 . However, the stiffness of C. elegans and other biological tissues is known to increase sharply with strain 31 , so it is possible that valve deflection with and without a worm are not equal at higher pressures.…”

“…Our confocal measurements suggest that touch valve deflection is similar with and without a worm up to at least 15 psi, the pressure tested. A deflection of 9.3 µm causes a response in WT animals 50% of the time, and the Young’s modulus of the worm, based on an average of literature values, is approximately E=125 kPa (average of two estimates 30,31 ). Since the worm’s modulus is much smaller than that of PDMS, the force on the worm is dominated the worm’s elasticity.…”