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Burrowing dynamics of aquatic worms in soft sediments
Edited by David A. Weitz, Harvard University, Cambridge, MA, and approved October 31, 2019 (received for review July 1, 2019)

Significance
The physical principles of locomotion inside sediment beds at the bottom of water bodies are poorly understood because of the remoteness and opacity of the medium. We show that the common oligochaete Lumbriculus variegatus moves faster in sediments compared with water, while using a similar combination of elongation–contraction and transverse undulatory strokes, exploiting a higher drag anisotropy of its body. Tracking the worm inside transparent sediments, we show that its speed can be captured by a linear combination of calculated speeds with resistive-force theory and an anchor model of peristaltic motion. We then demonstrate that these locomotion strategies can be observed in composting worms and can be used to move effectively in media with a wide range of yield strengths.
Abstract
We investigate the dynamics of Lumbriculus variegatus in water-saturated sediment beds to understand limbless locomotion in the benthic zone found at the bottom of lakes and oceans. These slender aquatic worms are observed to perform elongation–contraction and transverse undulatory strokes in both water-saturated sediments and water. Greater drag anisotropy in the sediment medium is observed to boost the burrowing speed of the worm compared to swimming in water with the same stroke using drag-assisted propulsion. We capture the observed speeds by combining the calculated forms based on resistive-force theory of undulatory motion in viscous fluids and a dynamic anchor model of peristaltic motion in the sediments. Peristalsis is found to be effective for burrowing in noncohesive sediments which fill in rapidly behind the moving body inside the sediment bed. Whereas the undulatory stroke is found to be effective in water and in shallow sediment layers where anchoring is not possible to achieve peristaltic motion. We show that such dual strokes occur as well in the earthworm Eisenia fetida which inhabits moist sediments that are prone to flooding. Our analysis in terms of the rheology of the medium shows that the dual strokes are exploited by organisms to negotiate sediment beds that may be packed heterogeneously and can be used by active intruders to move effectively from a fluid through the loose bed surface layer which fluidizes easily to the well-consolidated bed below.
Organisms burrowing in the benthic layer composed of organic and inorganic granular sediments at the bottom of water bodies can be found widely across our planet. While the strategies used by freely swimming waterborne organisms have been well studied, those used by limbless organisms which burrow in the loose sediment bed are far less known beyond the wide use of water jets to fluidize the sediments (1). For example, earthworms use peristalsis to move through terrestrial environments (2, 3), but their use in moving through noncohesive water-saturated sediments which fluidize easily is unclear because of the difficulty in visualizing the strokes in situ. It has been observed that undulatory body motion is employed to burrow through water-saturated sediments by sand lances (4) and opheliid polychaete Armandia brevis (5, 6), and it has been suggested that peristalsis may be insufficient to overcome fracture resistance or anchor small worms in unconsolidated sediments (5). Interestingly in this context, the nematode Caenorhabditis elegans is well documented to modify its undulatory gait from high to low frequencies from swimming in water to crawling on surfaces and through agarous (7). However, they appear to always undulate their bodies even while moving through loosely packed sediment monolayers (8) and fixed micropillar arrays (9).
While body undulations can be readily identified across a wide range of limbless organisms (10), the physical mechanism by which locomotion is accomplished varies significantly even in water, depending on the size and speed of the swimmer. It is long established that the drag of the body used by the swimmer to propel itself forward can be dominated by viscous forces at low speeds and by inertia at high speeds, as measured by the Reynolds number (11, 12). Measurements with spheres and rods moving in water-saturated soft sediments have found that the drag scaled by the buoyancy-subtracted weight of the grains can be used to define an effective friction
Here, we use the California blackworm Lumbriculus variegatus (Fig. 1A) as a paradigm to understand limbless burrowing in water-saturated soft sediments that can fluidize easily. This common freshwater oligochaete shows peristaltic motion while crawling on wet surfaces with waves of circular and longitudinal muscle contraction that move in the direction opposite to motion (17). However, their dynamics inside noncohesive water-saturated sediments have neither been observed directly nor analyzed in terms of the drag experienced in the medium. By using clear hydrogel grains, which appear transparent when immersed in water, we visualize the shape of the body while burrowing inside a sedimented bed (Fig. 1B and Methods) and compare it to that while swimming in water.
(A) An Image of L. variegatus. (B) The tracked head, tail, and centroid of a worm of length
Results
Observations with L. variegatus.
The projected shapes of a L. variegatus released just above a sedimented bed in a water-filled container, shown schematically in Fig. 1C, is plotted at 1-s time intervals in Fig. 1D. The worm is observed to swim above the bed surface for a few seconds before burrowing rapidly down through the bed, turning, rising, and then further exploring the surface of the sedimented bed. Magnified views with higher time resolution of each phase can be found in SI Appendix, Fig. S1. It can be observed that the worm moves in a narrow sinusoidal path which is not much wider than its body width while burrowing in the sediments. Whereas greater lateral body motion is observed while it is swimming in water near the bed surface. Further, the worm can be also observed to reflect off the side walls and sometimes move backward. Similar behavior is observed as well in a sedimented bed inside thinner quasi-2D containers and wider cuboid containers (SI Appendix, Fig. S2). We also observe that the worms do not crawl up the side walls and slide on glass and acrylic surfaces when fully immersed in water. Thus, the container walls serve as a physical barrier and do not appear to aid the locomotion of the worm. Because the image analysis and tracking are far simpler in 2D, we discuss worm dynamics in a container with internal dimensions
The projected shapes of a worm of length
(A and B) Worm trajectory in the laboratory frame of reference in the sediments (A) and water (B). The worm of length
To compare the form of the strokes used while burrowing and swimming, we use the body reference frame which is oriented along the average direction in which the worm points and where its origin is located at the worm centroid as shown in Fig. 1B. We plot the same measured shapes in Fig. 2 C and D in the body reference frame, but where the centroid is shifted vertically by time denoted by the vertical axis. We observe that transverse undulations and that the worm elongations and length contraction can be observed in fact in both media. To show that the shortening of the worm indeed arises due its changes, and not simply because of the transverse undulations, we obtain the difference of dynamic worm length from its mean length
Then, we obtain the component of worm speed over a short time interval
(A) The measured worm speed versus its length shows significant scatter from worm to worm. However,
Transverse Body Undulations.
We measure the transverse undulations using the root-mean-square (rms) transverse amplitude in the body frame of reference
Then, to determine the relevant regime for its dynamics, we use the Reynolds number
Drag-Assisted Propulsion in Sediments.
To find the appropriate drag encountered by the worm while undulating in the sediments, we performed complementary measurements with a thin rod corresponding to the worm body over the typical range of speeds encountered by the worm. As discussed in more detail in SI Appendix, Drag Measurements, we observe a drag which increases sublinearly with speed and depends on the orientation of the rod axis relative to the direction of motion. Over the range of speeds U from 0.1 to 10 mm
The estimated
Peristaltic Motion.
To extract the dominant oscillation frequency, we obtain the longitudinal amplitude correlation function
(A and B) The length correlation function
Then, we calculate the velocity correlation function
Anchor Model.
To understand these correlations, we consider an idealized anchor model of peristaltic motion (3) as illustrated in Fig. 4E, Upper Left Inset. Here, the worm is represented in the form of a pair of beads connected by a spring which travels forward by elongating its body through a length ϵ while anchoring its tail and then moving forward by contracting its body through the same length ϵ while anchoring its head to regain its initial length, as indicated by the arrows. Then, the distance moved by the worm centroid is
Assuming that the primary oscillation of the worm length occurs sinusoidally with period of longitudinal oscillation
Medium Rheology and Locomotion Speed.
L. variegatus is known to dynamically deploy 10- to 20-μm-long hair-like projections called chaetae (22) along with muscle contractions to change the relative friction during the sliding and anchoring phase while crawling on solid surfaces (17). Given the small size of chaetae relative to
Thus, the yield-stress nature of the medium is also important to achieving anchoring needed for peristaltic motion. This strength characterized by
Then, assuming that the locomotion speed of the worm occurs due to a linear superposition of the contributions due to the undulatory and the peristaltic motion, we have
The calculated versus the measured speeds corresponding to the trails listed in SI Appendix, Table S1 are in good agreement. A dashed line with slope 1 is drawn for reference.
Dual Strokes in Eisenia fetida.
We further investigate the dynamics of the common composting earthworm Eisenia fetida to examine whether dual peristaltic and undulatory strokes are observed in other organisms as well. The general behavior of the earthworms and their physical characteristics are discussed in SI Appendix, Earthworm Dynamics. Fig. 6A shows the projected shapes of the earthworm as it burrows straight down in a container with
(A and B) Tracked snapshots of the composting earthworm E. fetida of length
To access the period of the longitudinal stroke, we plot
Discussion and Concluding Remarks
Thus, by directly tracking L. variegatus and E. fetida inside water and sediments, we have demonstrated that limbless worms can move in media with wide-ranging rheological properties using a combination of peristaltic and undulatory strokes. While the stroke amplitude can be modified somewhat as evidenced by the decrease of transverse undulations in sediments compared to in water, the nature of the medium has a significant impact on the effectiveness of these strokes. When the worm cannot anchor itself, as when moving in water or near the surface of a sedimented bed, our study shows that only the transverse undulatory motion is important to achieving locomotion. But deep in the sediment bed, where the overburden pressure causes the grains to stay in close contact, we observe clear importance of peristaltic motion in achieving locomotion. Conversely, lacking the dual strokes, a worm would be at a disadvantage while swimming in the water or in the unconsolidated grains very near the bed surface. Whereas an undulating worm would be increasingly at a disadvantage as it burrows deeper because the drag in moving perpendicular to its body grows more rapidly than parallel to its body, making that motion prohibitive at large enough depth. In fact, peristaltic motion can be expected to dominate as an active intruder moves deeper based on our analysis. This suggests that active intruders, whether biological or synthetic, can be designed to exploit these dual strokes to move between fluid-like regions with negligible yield stress and frictional granular regions with large yield stress.
Methods
Specimens.
L. variegatus were obtained from Carolina Biological Supply Company (https://www.carolina.com) on October 3, 2017 and were sustained in a freshwater aquarium. E. fetida were obtained from Uncle Jim’s Worm Farm (https://unclejimswormfarm.com/) on June 6, 2017 and were maintained in a wet soil-filled container. The worms used to perform quantitative measurements are listed in SI Appendix, Table S1. Both were housed in an air-conditioned laboratory maintained at
Medium.
We use clear hydrogel grains (Acrylic Acid Polymer Sodium Salt; Sumitomo Seika Chemicals Co.) with density
Worm Tracking.
Because the refractive indexes of these grains and water are essentially the same, the medium appears transparent, allowing us to visualize the worm dynamics through transparent glass sidewalls. Images are thresholded to identify a connected set of pixels associated with the worm body. Its head, tail, and skeletal shape are then found using the operation bwmorph in the Image Processing Toobox in MATLAB.
SI Datasets.
The data corresponding to the measured worm speed, worm length, specimens, and containers used can be found in SI Appendix and in Datasets S1–S5.
Acknowledgments
We thank Andreea Panaitescu, Gregory Jones, Rausan Jewel, and Benjamin Allen for assistance with experiments and Alex Petroff for comments on the manuscript. This work was supported by the National Science Foundation under Grant CBET-1805398.
Footnotes
- ↵1To whom correspondence may be addressed. Email: akudrolli{at}clarku.edu.
Author contributions: A.K. and B.R. designed research, performed research, analyzed data, and wrote the paper.
The authors declare no competing interest.
This article is a PNAS Direct Submission.
This article contains supporting information online at https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1911317116/-/DCSupplemental.
Published under the PNAS license.
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