Fourier-Based Diffraction Analysis of Live <em>Caenorhabditis elegans</em>

Abstract

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 "roller" C. elegans. Wild type worms exhibit a rapid oscillation pattern in solution. The "roller" 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 "roller" 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.

Live &lt;i&gt;C. elegans&lt;/i&gt; Diffraction at a Single Point

“…We have used the transparent nematode, Caenorhabditis elegans, to develop methodologies for examining microscopic organismal shape and locomotion in real-time in 3 dimensions without using microscopes [1] [4] [5]. The simple rhythmic motions and small size of these free-living organisms have allowed us to develop techniques and mathematical reconstruction processes to allow us to explore locomotion dynamics.…”

“…can be established with the precision corresponding to the resolution of the microscope and the precision of the specifications associated with the optics. Using diffraction and shadowing methods forces [1] [4], movements on the order of the wavelength are used. The frequency analysis of a live diffraction signal contains information about the cumulative movements of every single point on the microscopic object as the Fraunhofer diffraction pattern is proportional to the magnitude of the Fourier transform (FT) squared of the diffracting nematode shape containing a superposition of the EM radiating from all points on the diffracting object's outline.…”