Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

With this research, we aim to characterize the locomotion of a microscopic species, with the aim to gain a better understanding of the neural circuit of the locomotion. More specifically, we have established that the locomotion of the C.elegans is chaotic with low experimental noise. Experimental chaos can be difficult to analyze to experimental noise.

Dynamic optical diffraction, or DOD, is relatively new. It does not have any counterparts in the field and it's easy to implement, it is cost-effective, and provides multi-scale data. The multi-scale dynamic information provides a check for a modeled neural circuit.

Once we build a neural circuit with matching dynamic information, we know that we've understood the circuit. In the future, our research will be focused on exploring, but other biological quantities we can characterize with the largest Lyapunov exponent. Additionally, we'll build a model of locomotory neurons.

To begin, pipette 0.5 milliliters of Escherichia coli with an OD600 onto each Nematode Growth Medium Agar Plate to provide food for the nematodes. Wait for the Escherichia coli to dry completely on the surface of each agar plate. Obtain a control plate of Caenorhabditis elegans from a biological material supplier to use for generating age-synchronized nematode populations.

Using a Bunsen burner, sterilize a platinum pick in the flame until it glows orange. Under a dissecting microscope, use the sterilized pick to collect five to 10 adult wild-type Caenorhabditis elegans. Transfer the picked worms onto a prepared agar plate.

After the egg laying period of four to five hours, remove the adult worms from the plate using a platinum pick. Incubate the remaining plate to allow the eggs to develop until the desired day of use. On the day of data collection, fill a 4.5 milliliter optical-grade quartz cuvette with room temperature distilled water just below the rim to prevent spillage.

Use a platinum pick to gently transfer two to three nematodes into the cuvette. Once the nematodes are inside, place the cuvette on its side to facilitate alignment of the worm with the laser beam. Observe the swimming motion of the fully-immersed nematodes, which may float toward the bottom, but remain active.

Set up the experimental system with a modification involving the construction of a periscope using two mirrors. Position the cuvette on its side between the two mirrors to simplify alignment of the worm in the laser beam. Instead of a camera, position a photo detector in the diffraction pattern to collect optical signals.

Then, turn on the helium neon laser and allow it to warm up for approximately 15 minutes until it reaches thermal equilibrium. Start the digital oscilloscope to initiate data collection. To configure the oscilloscope, set the time interval to 100 seconds and select a memory buffer of at least 100 kilo samples per second.

Set the data acquisition resolution to one kilohertz. Adjust the bit resolution to 12 bits to ensure sensitivity to small-scale amplitude variations. Use the auto AC offset function on the oscilloscope to center the intensity oscillations at zero volts.

Next, use a sterilized platinum pick to gently pick two to three nematodes and transfer them into a cuvette filled with distilled water. Insert the cuvette containing the nematodes into the periscope assembly and adjust the setup to center one nematode precisely in the laser beam path. Observe the formation of a far field diffraction pattern approximately 50 centimeters beyond the periscope once a Caenorhabditis elegans is centered in the laser beam.

Position the photo diode in the far field diffraction pattern as a nematode traverses the laser beam. Record data for at least 10 seconds to collect a minimum of 10, 000 data points, which is necessary for accurate calculation of the largest Lyapunov exponent. Examine the time series to identify segments where the nematode is freely swimming within the laser beam.

Analyze the time series to evaluate the signal-to-noise ratio. Establish the baseline noise level by recording a time series without a nematode in the cuvette. Confirm that both the amplitude and features of the experimental signal exceed twice the noise level.

Discard any portion of the time series containing saturated data. Identify the first minimum in the mutual information graph within the time range of 0.140 to 0.240 seconds. Select a lag value that effectively separates the phase trajectories to allow for clear divergence measurements.

Determine the embedding dimension using the false nearest neighbors method. Select the lowest dimension at which the percentage of false nearest neighbors stabilizes at a minimum. The largest Lyapunov exponent peaked at day five, then declined steadily from day six through day 12.

The divergence of nearby trajectories initially increased exponentially before reaching a plateau, confirming the bounded chaotic behavior of the system. A linear slope was observed in the early portion of the log divergence curve, providing a reliable estimate of the largest Lyapunov exponent. Mean swimming frequency declined from day three to day 12, with a noticeable breakdown in the trend on day 12.