Caenorhabditis elegans (C. elegans) is a free-living nematode that has an average lifespan of about two to three weeks. Since the mid-1960's, C. elegans has played an integral role in molecular and developmental biology. It is considered a model organism due to its high degree of homology to other eukaryotic systems as well as its complex developmental processes. It is made up of 959 somatic cells, of which about 300 comprise its nervous system. Its overall shape is characterized by a long cylindrical body, tapering to a cone on either end. The following image depicts a typical example of C. elegans (the scale bar is 100 um):
For the purposes of this lab, we evaluated a wide range of C.elegans worms. We characterized their average dimensions and explored their modes of motility. The worms we examined were all grown on plates coated with agar media. The following table highlights the recorded measurements from a sample group of eight worms:
Worm # Thickness (um) Length (um) l1 (um) l2 (um) Velocity (um/sec) Cross-sectional Area (um2) 1 13.98 288.92 149.12 144.46 55.92 153.4985312 2 9.32 265.62 125.82 116.5 65.24 68.22156943 3 18.64 265.62 153.78 272.8862777 4 18.64 428.72 209.7 58.25 272.8862777 5 55.92 405.42 34.17333333 2455.976499 6 13.98 279.6 149.12 153.4985312 7 46.6 312.22 41.94 1705.539236 8 13.98 307.56 163.1 167.76 153.4985312
The worms move in a sine wave fashion across the agar, using chemotaxis to detect food sources that may be present. Columns 4 and 5 in the table above describe the measured wavelengths of these motions. The following images demonstrate this characteristic sinusoidal pattern of the worm paths:
The measurements in the table above were taken from the two movies we captured of the dynamic behavior of a group of C. elegans on the agar media. Each of these movies is presented below. The first is embedded in this page and should have begun playing when the page was loaded. The second movie is provided as a hyperlink in order to conserve bandwidth:
From the data presented in the above table, we calculated the average velocity of a C. elegans to be approximately 51.1 mm/second. We then decided to calculate the amount of power output required from these creatures in order for them to move at such a rate in the observed environment. In order to perform this calculation, we first needed to calculate the force of drag on these worms from the surrounding medium. We used the following equation to calculate this drag force (from Smits, p.324):
FD = 1/2 rV2ACD
Where r is the density of the medium (kg/m3), V is velocity of the worm (m/s), A is the cross-sectional area of the worm (m2), and CD is the drag coefficient of the worm.
In order to simplify our calculations, we estimated the front of the worms to be a disk, which gives CD = 1.17 (Smits, p. 318). Since some of the worms were burrowing through the agar and others were on the surface of the agar, we decided to calculate the drag force that the worms encountered in both agar and the air. The only difference between these calculations was in the density of the medium. ragar = 1000 kg/m3 (from Lebedev et al.), rair = 1.184 kg/m3 (at 25?C; Smits, p.486). The following table gives our calculations for the drag force and power output for each of the worms in our sample group:
Worm # FD in agar (N) FD in air (N) Area (m2) Power in agar(W) Power in air (W) 1 1.29307E-09 1.531E-12 1.53499E-10 1.55169E-10 1.8372E-13 2 7.82229E-10 9.26159E-13 6.82216E-11 1.09512E-10 1.29662E-13 3 2.72886E-10 4 2.49435E-09 2.95331E-12 2.72886E-10 3.11794E-10 3.69164E-13 5 7.7265E-09 9.14818E-12 2.45598E-09 5.6661E-10 6.70866E-13 6 1.53499E-10 7 8.0817E-09 9.56873E-12 1.70554E-09 7.27353E-10 8.61186E-13 8 1.53499E-10
The average FD in agar was 4.1 x 10-9 N. The average FD in air was 4.8 x 10-12 N. Due to the disparate densities of agar and of air, the difference was about three orders of magnitude.
We calculated the power required for the worms' movement with the following equation (from Smits, p.324):
Power = FD x V
The average power output of the worms moving through agar was 3.7x10-10 W. The average power output moving through air was 4.4x10-13 W.
References:
Lebedev, M., Dyabilin, K., Eidmann, K., Fortov, V., Grabovskij, E., and Smirnov, V. "Supersonic heat wave in low density foams generated by soft X-radiation from a Z-pinch plasma." Web site: http://epsppd.epfl.ch/Praha/WEB/98ICPP_W/C066PR.PDF
Smits, A.J. (2000). A Physical Introduction to Fluid Mechanics (New York: John Wiley & Sons, Inc.).