Mechanics of the axoneme: self-organized beating patterns and vortex arrays of spermatozoa

Cilia and eukaryotic flagella are long, thin extensions of cells that contain a structure known as axoneme. The key components of the axoneme are microtubule filaments and the motor proteins dynein. These dynein motors force the microtubules to slide in an oscillatory fashion leading to a wave pattern along the axoneme. How these motors are coordinated and how this phenomenon can be described quantitatively is not understood. I therefore studied the waveforms of sperm tails that contain such an axoneme. I observed these waveforms under different conditions with a high-speed camera and developed an automated image analysis tool allowing the extraction of long time series of this waveform. In a subsequent Fourier analysis I increased the precision by obtaining an averaged waveform. I then compared the data to the predictions of a theoretical framework (Camalet, Julicher et al. 1999) and found that they do not agree. I suggested extending this theoretical framework by considering a visco-elastic element at the base of the axoneme, which leads to a satisfactory agreement. This project leaves open questions hence further work is discussed. As a side finding, I discovered a new phenomenon on how spermatozoa form dynamic vortex arrays. I described this pattern in detail and introduced a novel order parameter to quantify the order among many particles. I showed that the array only forms above a critical sperm density. I suggested a model to explain the origin of the pattern and showed by simulation that the model can account for the main features of the pattern. Finally I estimated the typical interaction force between beating axonemes to be 0.1 pN and drew conclusions about their collective action in general that might be relevant for sperm cooperation or metachronal waves of cilia