We thank Juan Vasquez for his computational contributions with this project. We are grateful for the support of the Vassar College Undergraduate Research Summer Institute (URSI), the Lucy Maynard Salmon Research Fund and the NSF award No. 1058385.

1. C. elegans Growth and Maintenance
<ol>
	<li>Prepare nematode culture dishes.
	<ol>
		<li>Fill the Petri dishes with an agar solution and leave them to solidify, then seed with an E. coli culture of the OP50 strain9,10.</li>
	</ol>
	</li>
	<li>Prepare a starting population of adult nematodes on each plate by moving several adult worms to fresh agar-filled Petri dishes with an E. coli patch. Maintain the nematode cultures at 20 &#176;C in an incubator. 
	NOTE: Nematode strains can be obtained from the Caenorhabditis elegans Genome Center. For this study, the wild type, N2, strain and the OH7547 (otls199[cat-2::GFP + rgel-1(F25B3.3)::dsRed + rol-6(su1006)]) strain, which exhibits a roller phenotype, were utilized.</li>
	<li>Propagate worms for future cultures.
	<ol>
		<li>Remove the Petri dish containing C. elegans and an unused habitat Petri dish from the temperature-controlled incubator. Place them on the stage of a dissecting microscope.</li>
		<li>Light the Bunsen burner and sterilize the platinum nematode pick by placing the metal into the flame until it glows red. Allow the pick to cool to room temperature. Do not set the pick down or let the pick come into contact with contaminants.</li>
		<li>Gently touch the tip of the pick to the edge of the circle of bacteria. This substance is sticky and will make picking individual adult nematodes easier.</li>
		<li>Transfer up to 4 gravid nematodes to a Nematode Growth Medium (NGM) agar-filled Petri plate and incubate at 20 &#176;C. The worms will lay eggs that will mature in four days.</li>
		<li>Return the remaining nematodes to the incubator after moving four adult nematodes.</li>
	</ol>
	</li>
</ol>
2. Optical Setup (Figure 1)
<ol>
	<li>Secure the helium-neon laser near the back-left corner of the optical workbench and connect it to a power source. 
	NOTE: The laser&#39;s beam must fulfill the requirements for oversampling. The C. elegans are approximately 1 mm long, therefore the laser beam should have a diameter greater than 2 mm while incident on the nematode, but no larger than 5 mm so that the diffraction pattern is not difficult to locate.</li>
	<li>Place a neutral density filter between the helium-neon laser and the sample such that the laser beam travels through the filter before reaching the sample.</li>
	<li>Using two front surface aluminum steering mirrors, build a periscope by securing the first mirror after the neutral density filter. Secure the second mirror about 10 cm below the first mirror to give room to steer the laser beam and insert the cuvette between the mirrors. Align the laser beam and cuvette so that the laser beam travels vertically through the cuvette. 
	NOTE: The distance from the diffracting organism to the photodiode must be much larger than the organism itself to achieve far-field diffraction. In this experiment, the distance from the cuvette to the photodiode is 20 cm.</li>
	<li>Secure the photodiode directly across from the second mirror with its sensor facing the mirror. 
	NOTE: The cuvette containing the nematode will be placed between the two mirrors using chemistry clamps. See sections 4 and 5.</li>
	<li>Place a water-filled cuvette on the stand. Adjust the height of the stand. Adjust the heights and angles of mirror 1 and mirror 2 so that the laser beam travels through the cuvette aimed near but not directly at the photodiode.</li>
	<li>Use a level to ensure the stands form a leveled surface for the cuvette. Adjust the mirrors further if necessary.</li>
	<li>Connect the photodiode to the digital oscilloscope using the USB cable provided with the digital oscilloscope. Connect the digital oscilloscope to the computer that will be used to record and save the data.</li>
</ol>
3. Oscilloscope Setup
<ol>
	<li>Using the software for the oscilloscope on the computer, set the sample rate to at least 8 Hz to resolve the thrashing cycle of the worm sufficiently. 
	NOTE: The sample rate should be more than twice that of the expected thrashing frequencies of the species so that the Nyquist theorem11 is satisfied.</li>
</ol>
4. Preparing the Worm and Cuvette for Data Collection
<ol>
	<li>Transfer four adult nematodes to a fresh NGM10 agar-filled Petri plate using a thin, flattened platinum wire pick (see section 1.3).</li>
	<li>Remove one disposable plastic cuvette from its package, being careful to only touch the cuvette on its ridged sides.</li>
	<li>Use a micropipette to pipette distilled water into the cuvette until the cuvette is approximately 80% filled with distilled water. 
	NOTE: It is important to only use distilled water or ionized buffers such as M910 or phosphate-buffered saline (PBS) when handling the nematodes, as tap water contains microorganism-killing compounds.</li>
	<li>Place the Petri dish containing the C. elegans to be used under a dissecting scope.</li>
	<li>Using the platinum pick, remove one mature C. elegans from the Petri dish and submerge the pick into the cuvette, moving the pick in circles if necessary to dislodge the nematode.</li>
	<li>To prevent bubbles forming in the cuvette, fill the cuvette with water until it slightly bulges over the cuvette&#39;s top. Fill the cuvette&#39;s cap entirely with water then quickly put the cap onto the cuvette.</li>
	<li>Use an optical cleaning cloth to remove water droplets that may have spilled over and optical cleaning paper to clean any small remaining droplets.</li>
</ol>
5. Real Time Data-Acquisition of Diffraction Pattern Intensity Changes
<ol>
	<li>Turn on the helium-neon laser and adjust the frequency/color setting so that it produces a red beam. Turn on the sensor. 
	Caution: Use a low-energy beam at 632 nm, as C. elegans avoid high-frequency (blue) light12.</li>
	<li>Locate the worm in the cuvette. Holding the cuvette on its ridged sides, gently tilt the cuvette until nematode is approximately in the center of the portion of the cuvette. 
	NOTE: Shaking or tilting the cuvette violently causes the worm to collide with the walls of the cuvette. This can damage the nematode.
	<ol>
		<li>Place the cuvette onto the stand in the optical system, centering the worm within the laser&#39;s beam reflected from Mirror 1 to Mirror 2. Be sure to eliminate stray light.</li>
	</ol>
	</li>
	<li>Center the worm in the laser beam.
	<ol>
		<li>Place the photodiode in the diffraction pattern so that the location of the photodiode and the central maximum of the diffraction pattern do not coincide.</li>
		<li>Adjust the neutral density filter to prevent saturation of the photodiode. Rotating the neutral density filter wheel regulates the light intensity.
		<ol>
			<li>Rotate the neutral density filter so that the voltage output from the photodiode increases. 
			NOTE: The voltage output is observed using the software for the digital photodiode. The photodiode is saturated if the voltage does not change. In that case, rotate the neutral density filter until the voltage reduces without flattening out at a minimum reading. Ensure that the voltage signal does not flatten at the peak readings, indicating saturation of the photodiode. Reduce the light intensity by rotating the neutral density filter wheel if saturation is observed.</li>
		</ol>
		</li>
		<li>Once the moving diffraction pattern is visible, collect data with the photodiode by clicking the start button on the software controlling the oscilloscope while monitoring the worm&#39;s movement. Continue taking measurements until the worm moves out of the laser beam and the diffraction pattern disappears, which usually takes about 20 s.
		<ol>
			<li>Stop the data collecting process by clicking the stop button on the software for the oscilloscope. Save each trial&#39;s data in .csv or .txt format.</li>
		</ol>
		</li>
	</ol>
	</li>
	<li>Repeat steps 5.2 - 5.3 until at least 50 data sets have been collected for each phenotype. Use eight to ten animals per trial.</li>
	<li>If the cuvette is scratched dispose of it and the worm, and repeat step 4. If the worm is harmed in the transfer, dispose of it and rinse the cuvette with distilled water before repeating step 4 using the same cuvette.</li>
	<li>Repeat step 5 using the OH7547 &#34;Roller&#34; strain, being careful to label the data to indicate the worm strain.</li>
</ol>
6. Fourier Spectrum of Data
<ol>
	<li>Import the data acquired into a data analysis program capable of performing Discrete Fourier transforms3.</li>
	<li>Perform Fourier transforms on each data set using the fast Fourier transform (FFT) option of the software.</li>
	<li>Average the frequencies from the FFT results for each amplitude for the N2 wild type worms.</li>
	<li>Repeat step 6.3 using the FFTs from the OH7547 &#34;roller&#34; worms.</li>
</ol>
7. Modeling of the Fourier Spectrum
<ol>
	<li>Program a binary model of the nematode locomotion (see program included in the supplemental materials). 
	NOTE: This model is a rough approximation, which at first displays the prominent characteristics of worm motion. The model can be refined as the outcomes are compared with actual worms. Worm shapes are approximations using microscope images13.
	<ol>
		<li>Create sequential frames of the binary model moving through at least two worm cycles (Figure 2a). See the videos in the supplemental materials; C Worm video (CWorm.avi) and W Worm video (WWorm.avi).</li>
	</ol>
	</li>
	<li>Produce sequential diffraction patterns. See the videos in the supplemental materials. C Worm Diffraction video (CWormDiff.avi) and W Worm video (WWormDiff.avi).
	<ol>
		<li>Fourier transform each binary frame of the worm image. The larger the padding of the frame around the worm, the better the resolution of the diffraction image will be. 
		NOTE: The absolute value of each Fourier transformed frame is proportional to the corresponding diffraction pattern (Figure 2b).</li>
		<li>Tune the contrast of the diffraction pattern by mapping the intensities of the diffraction pattern to a logarithmic scale. 
		NOTE: Cameras and eyes tend to function on a non-linear scale. A logarithmic scale can simulate how a diffraction pattern is typically perceived by the human eye.</li>
	</ol>
	</li>
	<li>Extract the modeled diffraction signal.
	<ol>
		<li>Pick an off-center location that corresponds to the location of the photodiode in the diffraction pattern.</li>
		<li>Add the neighboring matrix elements surrounding the location of the photodiode to simulate the size of the photodiode. The size of the photodiode is typically 0.1% of the modeled diffraction pattern.</li>
		<li>Record and plot the sequence of the magnitude of the diffraction signals. Check that the signal is physically reasonable (i.e., in the case of periodic thrashing, the signal from the photodiode should be periodic as well).</li>
	</ol>
	</li>
	<li>Fourier transform the diffraction signal obtained in 7.3 and compare results with the experimental data.</li>
	<li>Repeat for various worm strains and compare.</li>
</ol>

<ol>
	<li>Magnes, J., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Analysis+of+Freely+Swimming+C.+elegans+Using+Laser+Diffraction.">Analysis of Freely Swimming C. elegans Using Laser Diffraction.</a> Open J. Biophys. 2, 101-107 (2012).</li><li>Magnes, J., Raley-Susman, K. M., Eells, R. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Quantitative+Locomotion+Study+of+Freely+Swimming+Micro-organisms+Using+Laser+Diffraction.">Quantitative Locomotion Study of Freely Swimming Micro-organisms Using Laser Diffraction.</a> J. Vis. Exp. (68), (2012).</li><li>James, J. F. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> A Student's Guide to Fourier Transforms with Applications in Physics and Engineering. , (1995).</li><li>Korta, J., Clark, D. A., Gabel, C. V., Mahadevan, L., Samuel, A. D. T. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Mechanosensation+and+mechanical+load+modulate+the+locomotory+gait+of+swimming+C.+elegans.">Mechanosensation and mechanical load modulate the locomotory gait of swimming C. elegans.</a> J. Exp. Biol. 210, (2007).</li><li>Martin-Garcia, J. M., Conrad, C. E., Coe, J., Roy-Chowdhury, S., Fromme, P. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Serial+femtosecond+crystallography:+A+revolution+in+structural+biology.">Serial femtosecond crystallography: A revolution in structural biology.</a> Arch. Biochem. Biophys. 602, 32-47 (2016).</li><li>Thibault, P., Rankenburg, I. C. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Optical+diffraction+microscopy+in+a+teaching+laboratory.">Optical diffraction microscopy in a teaching laboratory.</a> Amer. J. Phys. 75 (9), 827-832 (2007).</li><li>Miao, J., Ishikawa, T., Anderson, E. H., Hodgson, K. O. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Phase+retrieval+of+diffraction+patterns+from+non+crystalline+samples+using+the+oversampling+method.">Phase retrieval of diffraction patterns from non crystalline samples using the oversampling method.</a> Phys. Rev. B. 67, 174104 (2003).</li><li>Zhang, Y. P., Zhang, J. Q., Xu, W. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Method+for+eliminating+zero-order+diffraction+in+lensless+Fourier+transform+digital+holography.">Method for eliminating zero-order diffraction in lensless Fourier transform digital holography.</a> Optik - International Journal for Light and Electron Optics. 124 (21), 4873-4875 (2013).</li><li>Brody, A. H., Chou, E., Gray, J. M., Pokrywka, N. J., Raley-Susman, K. M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Mancozeb-induced+behavioral+deficits+precede+structural+neural+degeneration.">Mancozeb-induced behavioral deficits precede structural neural degeneration.</a> NeuroToxicology. 34, 74-81 (2013).</li><li>Stiernagle, T. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Maintenance+of+C.+elegans.">Maintenance of C. elegans.</a> WormBook. , (2006).</li><li>Dasalukunte, D., &#214;wall, V., Rusek, F., Anderson, J. B. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> Faster than Nyquist Signaling. Algorithms to Silicon. , (2014).</li><li>Edwards, S. L., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=A+novel+molecular+solution+for+ultraviolet+light+detection+in+Caenorhabditis+elegans.">A novel molecular solution for ultraviolet light detection in Caenorhabditis elegans.</a> PLoS Biol. 6 (8), e198 (2008).</li><li>Bilbao, A., Wajnryb, E., Vanapalli, S. A., Blawzdziewicz, J. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Nematode+Locomotion+in+Confined+and+Unconfined+Fluids.">Nematode Locomotion in Confined and Unconfined Fluids.</a> Phys. Fluids. 25, 081902 (2013).</li></ol>

The authors have nothing to disclose.

Including stretches of data with inactivity will skew the results since artificial lower frequencies will be averaged into the results. Saturating the photodiode can be recognized by flat peaks or &#34;cut off&#34; peaks in the raw data. Dividing each raw data set by peak intensities will help with accounting for fluctuations in the laser intensity.
The peak frequencies are an indicator of the overall thrashing frequency; however, complicated motion causes interference at beat frequencies in the diffraction pattern and need to be examined carefully.
This method can be used to investigate the locomotion of other nematodes. The environment can be changed to another medium. Wavelengths may be changed as well. Working in the visible range of the electromagnetic spectrum is easiest and safest.
A more refined model will simulate the diffraction spectra more realistically in the future. A future model may include a worm that can change orientations, which would not affect frequency locations but relative peak heights. A more realistic model would allow for a probabilistic distribution of thrashing frequencies, which would broaden the peaks as in the experimental data. A spread in frequencies would account for variations in thrashing frequencies.
The current worm shape is crude, especially in the head and tail region, which should be more tapered than in the current model. It may be interesting to conduct a detailed analysis of the time series of the signal since it could give clues about the complexity of the locomotion in different mutants.
It is worth considering the practicality of expanding this technique into characterizing multiple nematodes simultaneously. This method should be understood as a complementary method to existing methods using traditional microscopes. This method has an advantage in not requiring a microscope during the data-acquisition so that the worm may move out of the focal plane. The averaged frequency spectra show clear differences in worm motion and can be quantified by the prevalent frequency peaks, which is a novel method in quantifying worm locomotion. Data analysis of the diffraction signatures is in further development and will hopefully lead to an automated identification process of multiple mutants and individuals.

This method compares experimental and modeled frequency spectra of the locomotion of C. elegans using two strains with very different locomotory patterns. The results show that the frequency spectrum depends on temporal changes as the nematode swims in a water column so that clear microscopic images are not needed for analysis. This method allows for quantitative real-time analysis and provides complementary information to images/videos obtained with traditional microscopes. Fraunhofer diffraction, also called far-field diffraction, provides the basis for obtaining live diffraction data1,2. The light intensity at any single point in the diffraction pattern is the result of superimposing light from every point in the outline of the nematode3. As a result, the light intensity collected over time carries information about the locomotion of the nematode. Analyzing the time-dependent diffraction signal can identify the characteristic motion of the corresponding mutant since analyzing all the frequencies involved in the locomotion complements the traditional video analysis. In this case, the characteristic differences between the locomotion of the &#34;roller&#34; and wild type C. elegans are confirmed by comparing the frequency spectra of the two different strains of nematode.
Some previous characteristics have been confirmed using frequency analysis of diffraction signals such as swimming frequencies2,4. More importantly, this method can be used as a complementary method to traditional microscopy to observe locomotion in real time on a computer screen as the data are being collected. The frequency spectrum of worms with distinct locomotory patterns can be quantified by considering the Fourier transformed signal of the diffraction signal.
The multidisciplinary nature of Fourier-based diffraction in this work involves the fields of biology and physics. Diffraction by under sampling has long been used to investigate crystal structures in biology5 and other fields. In this experiment, however, oversampling6,7 creates the far-field diffraction pattern so that the organism is centered in the laser beam. Oversampling is typically used for lens-less imaging8 in conjunction with a phase retrieval algorithm that reconstructs an image of the original object. Phase retrieval is difficult to achieve when scatterers are present as is the case with a nematode. The temporal diffraction signature is enough to evaluate key frequencies of the worm motion. This method is less computationally taxing and provides an optical way to quantify locomotion. This technique could readily be adapted for analysis of mutations or environmental conditions that alter behavior.

<table><tbody><tr><td>Tunable Helium-Neon laser</td><td>Research Electro-Optics</td><td>30602</td><td>Four wavelengths can be selected between 543 nm and 633 nm.</td></tr><tr><td>2 Front Surface Aluminum Mirrors</td><td>Thorlabs</td><td>PF10-03-F01</td><td></td></tr><tr><td>Photodiode: SI Amplified Detector</td><td>Thorlabs</td><td>PDA 100A</td><td></td></tr><tr><td>Quartz Cuvette</td><td>Starna Cells</td><td>21/G/5</td><td>Plastic cells may be used as well.</td></tr><tr><td>MatLab (Software)</td><td>MathWorks</td><td>R2016b (9.1.0.441655)</td><td>Use the fft command to simulate diffraction</td></tr><tr><td>Excel</td><td>Microsoft</td><td>14.7.1</td><td>Used for data analysis of Figure 4</td></tr><tr><td>&lt;em&gt;Caenorhabditis elegans&lt;/em&gt; Roller</td><td>&lt;em&gt;University of Minnesota Caenorhabditis elegans Center (CGC)&lt;/em&gt;</td><td>Strain: OH7547&lt;br/&gt; Genotype: otIs199.</td><td>https://cbs.umn.edu/cgc/home</td></tr><tr><td>&lt;em&gt;Caenorhabditis elegans&lt;/em&gt; Wild Type</td><td>&lt;em&gt;University of Minnesota Caenorhabditis elegans Center (CGC)&lt;/em&gt;</td><td>Strain:N2 Genotype: C. elegans wild isolate</td><td>https://cbs.umn.edu/cgc/home</td></tr></tbody></table>

fourier-based diffraction analysis of live caenorhabditis elegans

This manuscript describes how to classify nematodes using temporal far-field diffraction signatures. A single C. elegans is suspended in a water column inside an optical cuvette. A 632 nm continuous wave HeNe laser is directed through the cuvette using front surface mirrors. A significant distance of at least 20-30 cm traveled after the light passes through the cuvette ensures a useful far-field (Fraunhofer) diffraction pattern. The diffraction pattern changes in real time as the nematode swims within the laser beam. The photodiode is placed off-center in the diffraction pattern. The voltage signal from the photodiode is observed in real time and recorded using a digital oscilloscope. This process is repeated for 139 wild type and 108 &#34;roller&#34; C. elegans. Wild type worms exhibit a rapid oscillation pattern in solution. The &#34;roller&#34; worms have a mutation in a key component of the cuticle that interferes with smooth locomotion. Time intervals that are not free of saturation and inactivity are discarded. It is practical to divide each average by its maximum to compare relative intensities. The signal for each worm is Fourier transformed so that the frequency pattern for each worm emerges. The signal for each type of worm is averaged. The averaged Fourier spectra for the wild type and the &#34;roller&#34; C. elegans are distinctly different and reveal that the dynamic worm shapes of the two different worm strains can be distinguished using Fourier analysis. The Fourier spectra of each worm strain match an approximate model using two different binary worm shapes that correspond to locomotory moments. The envelope of the averaged frequency distribution for actual and modeled worms confirms the model matches the data. This method can serve as a baseline for Fourier analysis for many microscopic species, as every microorganism will have its unique Fourier spectrum.

The optical experimental setup shown in Figure 1 allows for the study of microorganisms without being tied to a focal plane. The thrashing signal from the photodiode can be observed in real time on the computer screen as the data is collected. Unusual patterns will be visible immediately without having to analyze a video in detail.
Examples of modeled sequential worm movement and corresponding diffraction patterns are shown in Figure 2. The modeled diffraction patterns qualitatively resemble experimental patterns1 and are an initial indication that the simulations successfully model the nematode.
A sample temporal diffraction signature of the two types of C. elegans studied here is shown in Figure 3. It can be seen qualitatively that each nematode thrashes at different rates and amplitudes. Some of the differences can be quantified through curve fitting as was done in a previous publication1. The discrete Fourier transform, however, reveals more details regarding embedded frequencies:
<img alt="Equation 1" src="/files/ftp_upload/56154/56154eq1.jpg" />, (1)
where Fk is the digital Fourier transform (FT) and fn is the time-dependent raw diffraction signal with the discrete time variable n and the discrete frequency variable k. N is the total number of data points. The average digital Fourier transform allows for the nematode to be identified by amplitude of its diffraction frequency spectrum (Figure 4). The wild type spectrum is dominated by lower frequencies than the roller motion spectrum.
A model that approximates the wild type versus the roller C. elegans notes the wild type tends to thrash in a wavelike (W or S shape) motion (Figure 2a) while the roller tends to favor one side that roughly resembles an oscillating C shape (Figure 5). This offers some explanation for the different spectra. The roller will mostly form a C to one side while the W oscillation can be thought of as two opposing C motions. For this reason, the W motion is more complex revealing more secondary low frequencies than the C motion. This result is confirmed in the computational model. The W shape has a much higher frequency density than the C shape (Figure 6). This is confirmed in the FFT in Figure 4 where the roller frequencies are more clustered while not completely discrete. The statistics of the roller are skewed since the roller can revert to wild type locomotion temporarily.
The smoothed power spectra of roller type C. elegans shows a broad peak at ~1.5 Hz, while the swimming wild type C. elegans exhibits a multimodal spectrum (including peaks at ~1.0 Hz and 1.75 Hz). The photodiode (PD) has a finite size spreading over several matrix elements. Individual matrix elements or points on the diffraction pattern vary in intensity since constructive and destructive interference varies; nevertheless, the frequencies at which the intensities vary are the same for all matrix elements, as can be seen in Figure 7. Considering the time derivative Eq. 1, it can be seen that the frequency fluctuations do not depend on the phase matrix but only on the original object&#39;s fluctuations:
<img alt="Equation 2" src="/files/ftp_upload/56154/56154eq2.jpg" />, (2)
As the PD spreads over several matrix elements, the peak locations average to a consistent frequency profile. Some variation can be expected and can give clues about the orientation of the worm. The frequency distribution will change as the gait of the worm changes. The current model is a simple model that only allows for the evaluation of peak locations rather than relative peak heights. Different locomotory patterns will average to different peak locations.

<img alt="Figure 1" class="xfigimg" src="/files/ftp_upload/56154/56154fig1.jpg" /> 
Figure 1. Experimental Setup. The low power laser beam travels through the neutral density filter, is reflected by mirror M1 down through the cuvette containing the worm onto mirror M2, and travels towards the photodiode. <a href="https://cloudflare.jove.com/files/ftp_upload/56154/56154fig1large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 2" class="xfigimg" src="/files/ftp_upload/56154/56154fig2.jpg" /> 
Figure 2. Sequential Worm Shapes and Corresponding Diffraction Patterns. (a) Some select sequential binary images of modeled W shape nematodes and the (b) corresponding sequential diffraction patterns. <a href="https://cloudflare.jove.com/files/ftp_upload/56154/56154fig2large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 3" class="xfigimg" src="/files/ftp_upload/56154/56154fig3.jpg" /> 
Figure 3. Experimental Sample Diffraction Signatures. Diffraction signatures collected for (a) OH7547 &#34;roller&#34; and (b) N2 wild type C. elegans using a single photodiode in the diffraction pattern. <a href="https://cloudflare.jove.com/files/ftp_upload/56154/56154fig3large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 4" class="xfigimg" src="/files/ftp_upload/56154/56154fig4.jpg" /> 
Figure 4. Experimental Averaged Power Spectra of Roller and Wild Type Fraunhofer Diffraction Series. The spectra show the frequencies present in averaged Fourier transform of the time series recorded with the photodiode. A Gaussian filter of standard deviation 0.075 Hz, truncated at 3 standard deviations, is used for smoothing. Note the broad spectral peak at ~1.5 Hz in the smoothed roller spectrum, compared with the multimodal smoothed wild type spectrum (including peaks at ~1.0 and 1.75 Hz). <a href="https://cloudflare.jove.com/files/ftp_upload/56154/56154fig4large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 5" class="xfigimg" src="/files/ftp_upload/56154/56154fig5.jpg" /> 
Figure 5. Diffraction Formation Illustration. Diffraction patterns can be modeled by thinking of each line segment as an infinitesimally small straight line (left). Superimposing these lines (right) demonstrates the construction of far-field diffraction patterns generated by a C shaped nematode. <a href="https://cloudflare.jove.com/files/ftp_upload/56154/56154fig5large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 6" class="xfigimg" src="/files/ftp_upload/56154/56154fig6.jpg" /> 
Figure 6. Simulated Power Spectra of Roller and Wild Type Fraunhofer Diffraction Series. (a) C shape and (b) W shape worms with the photodiode centered at the matrix elements 200 (vertical) and 175 (horizontal). The W shape shows a higher density of frequencies due to the more complex locomotion. <a href="https://cloudflare.jove.com/files/ftp_upload/56154/56154fig6large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 7" class="xfigimg" src="/files/ftp_upload/56154/56154fig7.jpg" /> 
Figure 7. Simulated Power Spectra of Roller and Wild Type Fraunhofer Diffraction Series at Different Photodiode Locations. (a) W shape worm and the (b) C shape worm for single matrix elements at various locations simulating various locations of the photodiode. Peak heights vary for various locations; however, peak locations remain the same for specific shapes. <a href="https://cloudflare.jove.com/files/ftp_upload/56154/56154fig7large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>

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Fourier-Based Diffraction Analysis of Live Caenorhabditis elegans

This manuscript describes how to distinguish different nematodes using far-field diffraction signatures. We compare the locomotion of 139 wild type and 108 &#34;Roller&#34; C. elegans by averaging frequencies associated with the temporal Fraunhofer diffraction signature at a single location using a continuous wave laser.

Fourier-Based Diffraction Analysis of Live Caenorhabditis elegans

This manuscript describes how to classify nematodes using temporal far-field diffraction signatures. A single C. elegans is suspended in a water column ...

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7.9K Views.  Vassar College. Dit manuscript wordt beschreven hoe onderscheiden verschillende nematoden ver-veld diffractie handtekeningen gebruiken. We vergelijken de motoriek van 139 wild type en 108 "Roller" C. elegans door gemiddeld frequenties de temporele Fraunhofer diffractie handtekening op een enkele plaats met behulp van een continu wave laser is gekoppeld.

Video: Fourier-Based Diffraction Analysis of Live Caenorhabditis elegans

Single Wavelength Shadow Imaging of Caenorhabditis elegans Locomotion Including Force Estimates

This study demonstrates an inexpensive and straightforward technique that allows the measurement of physical properties such as position, velocity, acceleration and forces involved in the locomotory behavior of nematodes suspended in a column of water in response to single wavelengths of light. We demonstrate how to evaluate the locomotion of a microscopic organism using Single Wavelength Shadow Imaging (SWSI) using two different examples.
The first example is a systematic and statistically viable study of the average descent of C. elegans in a column of water. For this study, we used living and dead wildtype C. elegans. When we compared the velocity and direction of nematode active movement with the passive descent of dead worms within the gravitational field, this study showed no difference in descent-times. The average descent was 1.5 mm/sec &#177; 0.1 mm/sec for both the live and dead worms using 633 nm coherent light.
The second example is a case study of select individual C. elegans changing direction during the descent in a vertical water column. Acceleration and force are analyzed in this example. This case study demonstrates the scope of other physical properties that can be evaluated using SWSI while evaluating the behavior using single wavelengths in an environment that is not accessible with traditional microscopes. Using this analysis we estimated an individual nematode is capable of thrusting with a force in excess of 28 nN.
Our findings indicate that living nematodes exert 28 nN when turning, or moving against the gravitational field. The findings further suggest that nematodes passively descend in a column of water, but can actively resist the force of gravity primarily by turning direction.

Single Wavelength Shadow Imaging of Caenorhabditis elegans Locomotion Including Force Estimates

The technique presented here measures the path of freely swimming microscopic species using single wavelength exposure. C. elegans are used to demonstrate shadow imaging as an inexpensive alternative to costly microscopes. This technique can be adapted to accommodate various orientations, environments and species to measure direction, speed, acceleration and forces.

This study demonstrates an inexpensive and straightforward technique that allows the measurement of physical properties such as position, velocity, ...

Quantitative Locomotion Study of Freely Swimming Micro-organisms Using Laser Diffraction

Soil and aquatic microscopic organisms live and behave in a complex three-dimensional environment. Most studies of microscopic organism behavior, in contrast, have been conducted using microscope-based approaches, which limit the movement and behavior to a narrow, nearly two-dimensional focal field.1 We present a novel analytical approach that provides real-time analysis of freely swimming C. elegans in a cuvette without dependence on microscope-based equipment. This approach consists of tracking the temporal periodicity of diffraction patterns generated by directing laser light through the cuvette. We measure oscillation frequencies for freely swimming nematodes.
Analysis of the far-field diffraction patterns reveals clues about the waveforms of the nematodes. Diffraction is the process of light bending around an object. In this case light is diffracted by the organisms. The light waves interfere and can form a diffraction pattern. A far-field, or Fraunhofer, diffraction pattern is formed if the screen-to-object distance is much larger than the diffracting object. In this case, the diffraction pattern can be calculated (modeled) using a Fourier transform.2
C. elegans are free-living soil-dwelling nematodes that navigate in three dimensions. They move both on a solid matrix like soil or agar in a sinusoidal locomotory pattern called crawling and in liquid in a different pattern called swimming.3 The roles played by sensory information provided by mechanosensory, chemosensory, and thermosensory cells that govern plastic changes in locomotory patterns and switches in patterns are only beginning to be elucidated.4 We describe an optical approach to measuring nematode locomotion in three dimensions that does not require a microscope and will enable us to begin to explore the complexities of nematode locomotion under different conditions.

Microscopic organisms like the free-swimming nematode C. elegans, live and behave in a complex three-dimensional environment. We report on a novel approach that provides analysis of C. elegans using diffraction patterns. This approach consists of tracking the temporal periodicity of diffraction patterns generated by directing laser light through a cuvette.

Soil and aquatic microscopic organisms live and behave in a complex three-dimensional environment. Most studies of microscopic organism behavior, in ...

Bioengineering

Microfluidic-based Electrotaxis for On-demand Quantitative Analysis of Caenorhabditis elegans' Locomotion

The nematode Caenorhabditis elegans is a versatile model organism for biomedical research because of its conservation of disease-related genes and pathways as well as its ease of cultivation. Several C. elegans disease models have been reported, including neurodegenerative disorders such as Parkinson's disease (PD), which involves the degeneration of dopaminergic (DA) neurons 1. Both transgenes and neurotoxic chemicals have been used to induce DA neurodegeneration and consequent movement defects in worms, allowing for investigations into the basis of neurodegeneration and screens for neuroprotective genes and compounds 2,3.
Screens in lower eukaryotes like C. elegans provide an efficient and economical means to identify compounds and genes affecting neuronal signaling. Conventional screens are typically performed manually and scored by visual inspection; consequently, they are time-consuming and prone to human errors. Additionally, most focus on cellular level analysis while ignoring locomotion, which is an especially important parameter for movement disorders.
We have developed a novel microfluidic screening system (Figure 1) that controls and quantifies C. elegans' locomotion using electric field stimuli inside microchannels. We have shown that a Direct Current (DC) field can robustly induce on-demand locomotion towards the cathode ("electrotaxis") 4. Reversing the field's polarity causes the worm to quickly reverse its direction as well. We have also shown that defects in dopaminergic and other sensory neurons alter the swimming response 5. Therefore, abnormalities in neuronal signaling can be determined using locomotion as a read-out. The movement response can be accurately quantified using a range of parameters such as swimming speed, body bending frequency and reversal time.
Our work has revealed that the electrotactic response varies with age. Specifically, young adults respond to a lower range of electric fields and move faster compared to larvae 4. These findings led us to design a new microfluidic device to passively sort worms by age and phenotype 6.
We have also tested the response of worms to pulsed DC and Alternating Current (AC) electric fields. Pulsed DC fields of various duty cycles effectively generated electrotaxis in both C. elegans and its cousin C. briggsae 7. In another experiment, symmetrical AC fields with frequencies ranging from 1 Hz to 3 KHz immobilized worms inside the channel 8.
Implementation of the electric field in a microfluidic environment enables rapid and automated execution of the electrotaxis assay. This approach promises to facilitate high-throughput genetic and chemical screens for factors affecting neuronal function and viability.

Microfluidic-based Electrotaxis for On-demand Quantitative Analysis of Caenorhabditis elegans' Locomotion

A semi-automated micro-electro-fluidic method to induce on-demand locomotion in Caenorhabditis elegans is described. This method is based on the neurophysiologic phenomenon of worms responding to mild electric fields (&#x201C;electrotaxis&#x201D;) inside microfluidic channels. Microfluidic electrotaxis serves as a rapid, sensitive, low-cost, and scalable technique to screen for factors affecting neuronal health.

The nematode Caenorhabditis elegans is a versatile model organism for biomedical research because of its conservation of disease-related genes and ...

Computational Analysis of the Caenorhabditis elegans Germline to Study the Distribution of Nuclei, Proteins, and the Cytoskeleton

The Caenorhabditis elegans (C. elegans) germline is used to study several biologically important processes including stem cell development, apoptosis, and chromosome dynamics. While the germline is an excellent model, the analysis is often two dimensional due to the time and labor required for three-dimensional analysis. Major readouts in such studies are the number/position of nuclei and protein distribution within the germline. Here, we present a method to perform automated analysis of the germline using confocal microscopy and computational approaches to determine the number and position of nuclei in each region of the germline. Our method also analyzes germline protein distribution that enables the three-dimensional examination of protein expression in different genetic backgrounds. Further, our study shows variations in cytoskeletal architecture in distinct regions of the germline that may accommodate specific spatial developmental requirements. Finally, our method enables automated counting of the sperm in the spermatheca of each germline. Taken together, our method enables rapid and reproducible phenotypic analysis of the C. elegans germline.

Computational Analysis of the Caenorhabditis elegans Germline to Study the Distribution of Nuclei, Proteins, and the Cytoskeleton

We present an automated method for three-dimensional reconstruction of the Caenorhabditis elegans germline. Our method determines the number and position of each nucleus within the germline and analyses germline protein distribution and cytoskeletal structure.

The Caenorhabditis elegans (C. elegans) germline is used to study several biologically important processes including stem cell development, apoptosis, and ...

Developmental Biology

Calcium Imaging in Freely Behaving Caenorhabditis elegans with Well-Controlled, Nonlocalized Vibration

Nonlocalized mechanical forces, such as vibrations and acoustic waves, influence a wide variety of biological processes from development to homeostasis. Animals cope with these stimuli by modifying their behavior. Understanding the mechanisms underlying such behavioral modification requires quantification of neural activity during the behavior of interest. Here, we report a method for calcium imaging in freely behaving Caenorhabditis elegans with nonlocalized vibration of specific frequency, displacement, and duration. This method allows the production of well-controlled, nonlocalized vibration using an acoustic transducer and quantification of evoked calcium responses at single-cell resolution. As a proof of principle, the calcium response of a single interneuron, AVA, during the escape response of C. elegans to vibration is demonstrated. This system will facilitate understanding of neural mechanisms underlying behavioral responses to mechanical stimuli.

Calcium Imaging in Freely Behaving Caenorhabditis elegans with Well-Controlled, Nonlocalized Vibration

Reported here is a system for calcium imaging in freely behaving Caenorhabditis elegans with well-controlled, nonlocalized vibration. This system allows researchers to evoke nonlocalized vibrations with well-controlled properties at nano-scale displacement and to quantify calcium currents during responses of C. elegans to the vibrations.

Nonlocalized mechanical forces, such as vibrations and acoustic waves, influence a wide variety of biological processes from development to homeostasis. ...

Behavior

Comparative Analysis of Experimental Methods to Quantify Animal Activity in Caenorhabditis elegans Models of Mitochondrial Disease

Caenorhabditis elegans is widely recognized for its central utility as a translational animal model to efficiently interrogate mechanisms and therapies of diverse human diseases. Worms are particularly well-suited for high-throughput genetic and drug screens to gain deeper insight into therapeutic targets and therapies by exploiting their fast development cycle, large brood size, short lifespan, microscopic transparency, low maintenance costs, robust suite of genomic tools, mutant repositories, and experimental methodologies to interrogate both in vivo and ex vivo physiology. Worm locomotor activity represents a particularly relevant phenotype that is frequently impaired in mitochondrial disease, which is highly heterogeneous in causes and manifestations but collectively shares an impaired capacity to produce cellular energy. While a suite of different methodologies may be used to interrogate worm behavior, these vary greatly in experimental costs, complexity, and utility for genomic or drug high-throughput screens. Here, the relative throughput, advantages, and limitations of 16 different activity analysis methodologies were compared that quantify nematode locomotion, thrashing, pharyngeal pumping, and/or chemotaxis in single worms or worm populations of C. elegans at different stages, ages, and experimental durations. Detailed protocols were demonstrated for two semi-automated methods to quantify nematode locomotor activity that represent novel applications of available software tools, namely, ZebraLab (a medium-throughput approach) and WormScan (a high-throughput approach). Data from applying these methods demonstrated similar degrees of reduced animal activity occurred at the L4 larval stage, and progressed in day 1 adults, in mitochondrial complex I disease (gas-1(fc21)) mutant worms relative to wild-type (N2 Bristol) C. elegans. This data validates the utility for these novel applications of using the ZebraLab or WormScan software tools to quantify worm locomotor activity efficiently and objectively, with variable capacity to support high-throughput drug screening on worm behavior in preclinical animal models of mitochondrial disease.

Comparative Analysis of Experimental Methods to Quantify Animal Activity in Caenorhabditis elegans Models of Mitochondrial Disease

This study presents protocols for two semi-automated locomotor activity analysis approaches in C. elegans complex I disease gas-1(fc21) worms, namely, ZebraLab (a medium-throughput assay) and WormScan (a high-throughput assay) and provide comparative analysis among a wide array of research methods to quantify nematode behavior and integrated neuromuscular function.

Caenorhabditis elegans is widely recognized for its central utility as a translational animal model to efficiently interrogate mechanisms and therapies of ...

Agarose Microchambers for Long-term Calcium Imaging of Caenorhabditis elegans

Behavior is controlled by the nervous system. Calcium imaging is a straightforward method in the transparent nematode Caenorhabditis elegans to measure the activity of neurons during various behaviors. To correlate neural activity with behavior, the animal should not be immobilized but should be able to move. Many behavioral changes occur during long time scales and require recording over many hours of behavior. This also makes it necessary to culture the worms in the presence of food. How can worms be cultured and their neural activity imaged over long time scales? Agarose Microchamber Imaging (AMI) was previously developed to culture and observe small larvae and has now been adapted to study all life stages from early L1 until the adult stage of C. elegans. AMI can be performed on various life stages of C. elegans. Long-term calcium imaging is achieved without immobilizing the animals by using short externally triggered exposures combined with an electron multiplying charge-coupled device (EMCCD) camera recording. Zooming out or scanning can scale up this method to image up to 40 worms in parallel. Thus, a method is described to image behavior and neural activity over long time scales in all life stages of C. elegans.

Agarose Microchambers for Long-term Calcium Imaging of Caenorhabditis elegans

Imaging behavior and neural activity over long time scales without immobilization of the animal is a prerequisite to understand behavior. Agarose microfluidic chambers imaging (AMI) can be used to image neural activity and behavior for all life stages of Caenorhabditis elegans.

Behavior is controlled by the nervous system. Calcium imaging is a straightforward method in the transparent nematode Caenorhabditis elegans to measure ...

Neuroscience

A Microfluidic Platform for Longitudinal Imaging in Caenorhabditis elegans

In the last decade, microfluidic techniques have been applied to study small animals, including the nematode Caenorhabditis elegans, and have proved useful as a convenient live imaging platform providing capabilities for precise control of experimental conditions in real time. In this article, we demonstrate live imaging of individual worms employing WormSpa, a previously-published custom microfluidic device. In the device, multiple worms are individually confined to separate chambers, allowing multiplexed longitudinal surveillance of various biological processes. To illustrate the capability, we performed proof-of-principle experiments in which worms were infected in the device with pathogenic bacteria, and the dynamics of expression of immune response genes and egg laying were monitored continuously in individual animals. The simple design and operation of this device make it suitable for users with no previous experience with microfluidic-based experiments. We propose that this approach will be useful for many researchers interested in longitudinal observations of biological processes under well-defined conditions.

A Microfluidic Platform for Longitudinal Imaging in Caenorhabditis elegans

In this article, we demonstrate live imaging of individual worms employing a custom microfluidic device. In the device, multiple worms are individually confined to separate chambers, allowing multiplexed longitudinal surveillance of various biological processes.

In the last decade, microfluidic techniques have been applied to study small animals, including the nematode Caenorhabditis elegans, and have proved ...

Tracking Calcium in the Early Developmental Phases of C. elegans

In Vivo Visualization of Calcium Transients during Fertilization and Early Development in C. elegans

Calcium is an important signaling molecule during the oocyte-to-embryo transition (OET) and early embryogenesis. The hermaphroditic nematode Caenorhabditis elegans provides several unique advantages for the study of the OET as it is transparent and has an ordered gonad that produces one mature oocyte every ~23 min at 20 &#176;C. We have modified the genetically encoded calcium indicator jGCaMP7s to fluorescently indicate the moment of fertilization within a living organism. We have termed this reporter &#34;CaFE&#34; for Calcium during Fertilization in C. elegans. The CaFE reporter was&#160;engineered into a safe harbor locus in single copy, has no significant impact on physiology or fecundity, and produces a robust signal upon fertilization. Here, a series of protocols is presented for utilizing the CaFE reporter as an in vivo tool for dissecting the OET and embryogenesis. We include methods to synchronize worms, examine the effects of RNAi knockdown, mount worms for imaging, and to visualize calcium in oocytes and embryos. Additionally, we present the generation of additional worm strains to aid in this type of analysis. Demonstrating the utility of the CaFE reporter to visualize the timing of fertilization, we report that double ovulation occurs when ipp-5 is targeted by RNAi and that only the first oocyte undergoes immediate fertilization. Furthermore, the discovery of single-cell calcium transients during early embryogenesis is reported here, demonstrating that the CaFE reporter persists into early development. Importantly, the CaFE reporter in worms is simple enough to use for incorporation into course-based undergraduate research (CURE) laboratory classes. The CaFE reporter, coupled with the ordered gonad and ease of RNAi in worms, facilitates inquiry into the cell-cell dynamics required to regulate internal fertilization and early embryogenesis.

Here, we present protocols and tools for visualizing calcium during fertilization and early embryogenesis using a genetically encoded calcium reporter expressed in the germline of the model nematode C. elegans.

Calcium is an important signaling molecule during the oocyte-to-embryo transition (OET) and early embryogenesis. The hermaphroditic nematode ...

Investigating the Spreading and Toxicity of Prion-like Proteins Using the Metazoan Model Organism C. elegans

Prions are unconventional self-propagating proteinaceous particles, devoid of any coding nucleic acid. These proteinaceous seeds serve as templates for the conversion and replication of their benign cellular isoform. Accumulating evidence suggests that many protein aggregates can act as self-propagating templates and corrupt the folding of cognate proteins. Although aggregates can be functional under certain circumstances, this process often leads to the disruption of the cellular protein homeostasis (proteostasis), eventually leading to devastating diseases such as Alzheimer&#8217;s disease (AD), Parkinson&#8217;s disease (PD), Amyotrophic lateral sclerosis (ALS), or transmissible spongiform encephalopathies (TSEs). The exact mechanisms of prion propagation and cell-to-cell spreading of protein aggregates are still subjects of intense investigation. To further this knowledge, recently a new metazoan model in Caenorhabditis elegans, for expression of the prion domain of the cytosolic yeast prion protein Sup35 has been established. This prion model offers several advantages, as it allows direct monitoring of the fluorescently tagged prion domain in living animals and ease of genetic approaches. Described here are methods to study prion-like behavior of protein aggregates and to identify modifiers of prion-induced toxicity using C. elegans.

Investigating the Spreading and Toxicity of Prion-like Proteins Using the Metazoan Model Organism C. elegans

Prion-like propagation of protein aggregates has recently emerged as being implicated in many neurodegenerative diseases. The goal of this protocol is to describe, how to use the nematode C. elegans as a model system to monitor protein spreading and to investigate prion-like phenomena.

Prions are unconventional self-propagating proteinaceous particles, devoid of any coding nucleic acid. These proteinaceous seeds serve as templates for ...

Fourier-Based Diffraction Analysis of Live Caenorhabditis elegans

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