Undulatory locomotion of finite filaments: lessons fromCaenorhabditis elegans

Abstract

Undulatory swimming is a widespread propulsion strategy adopted by many small-scale organisms including various single-cell eukaryotes and nematodes. In this work, we report a comprehensive study of undulatory locomotion of a finite filament using (i) approximate resistive force theory (RFT) assuming a local nature of hydrodynamic interaction between the filament and the surrounding viscous liquid and (ii) particle-based numerical computations taking into account the intra-filament hydrodynamic interaction. Using the ubiquitous model of a propagating sinusoidal waveform, we identify the limit of applicability of the RFT and determine the optimal propulsion gait in terms of (i) swimming distance per period of undulation and (ii) hydrodynamic propulsion efficiency. The occurrence of the optimal swimming gait maximizing hydrodynamic efficiency at finite wavelength in particlebased computations diverges from the prediction of the RFT. To compare the model swimmer powered by sine wave undulations to biological undulatory swimmers, we apply the particle-based approach to study locomotion of the 6

Structured light enables biomimetic swimming and versatile locomotion of photoresponsive soft microrobots

“…Although our subject here was generating sophisticated functions from simple robots by structured light fields, even more powerful and exotic behaviours can be expected when complicated fields are combined with intrinsically functional microrobot designs 48 . While we have focused on metachronal waves used by ciliates, it should be noted that nematodes, whose size is comparable to our swimmers, swim by another propulsion mechanism: undulation 49 . The implementation of undulation is in principle possible with the system we describe, but would require a modified fabrication procedure for the swimmers.…”

Taylor line swimming in microchannels and cubic lattices of obstacles

“…To discuss directed swimming more quantitatively, we introduce the swimming velocity (12) and indicated in Fig. 3(b).…”

“…2 They have developed various swimming strategies to cope with the strong viscous forces 2 including beating flagellar appendages of sperm cells, 3,4 metachronal waves of collectively moving cilia on the cell surface of a paramecium, 5 rotating helical flagella in E. coli, [6][7][8][9][10] and periodic deformations of the whole cell body. [11][12][13] The first expression for the swimming speed of a simplified flagellar model was given by Taylor in 1951. 14,15 In this model a prescribed bending wave moves along a filament, which we call the Taylor line in the following.…”

Modeling Fluid Flow Induced by C. elegans Swimming at Low Reynolds Number

“…Their wavelike movement has an average amplitude of 0.25 mm and a frequency of 2 Hz [16,2], meaning that a full beating cycle is completed in 0.5 seconds. The average forward swimming speed has been found to be 0.36 ± 0.06 mm/s by [16] and to be 0.12 mm/s at James Madison University's Wiggling Organism Research and Modeling (WORM) lab (the discrepancy here is likely due to the age, adult and L4 respectively, and size of the worms used in the respective experiments).…”

“…The past decade has evinced significant research into the locomotion of microorganisms, in particular that of the nematode Caenorhabditis elegans both theoretical and experimental [16,15,17,2,3,11,14]. However, while there have been a number of experimental investigations into the induced fluid movement of bacterial flagella or carpets [10,7], artificial helices [18], and nematodes [16], to the authors' knowledge, there has been little theoretical investigations into the induced fluid flows, particularly at the intermediate scale of C. elegans, a 1mm long, unsegmented round worm.…”