Locomotion of flagellates with mastigonemes

Theoretical hydrodynamic analyses of the locomotion of flagellates with mastigonemes are presented and particular comparison is made within experimental data on Ochromonas malhamensis. The first part of the paper analyses locomotion assuming the mastigonemes are rigid and maintain a fixed and normal position relative to the flagellum. The predicted propulsive velocity of 60 mum/sec for Ochromonas agrees well with the observed values of 55-60 mum/sec. It is shown that the propulsive system of Ochromonas represents a compromise between the need for efficient rectilinear propulsion and the need to manoeuvre and accelerate. The effect of rigid mastigonemes which are maintained at non-zero angles to the flagellar normal is also calculated and demonstrates a significant degradation of performance when this angle is greater than about 10 degrees. The latter part of the paper investigates the more complex but more realistic situation in which the mastigonemes flex during the motion according to the instantaneous hydrodynamic forces imposed upon them. The cyclical flexing history of a mastigoneme with passage of a flagellar wave and the consequent velocity of propulsion are obtained for a variety of geometric configurations and structural mastigoneme stiffnesses. It is demonstrated that there exists a relatively small transition range in the values of mastigoneme flexibility below which the mastigonemes are essentially rigid and above which they become totally ineffective hydrodynamically so that the flagellum can be regarded as essentially smooth. Since the transition value of the modulus of elasticity is about 5 dynes/mum2 (or stiffness of 3.5 X 10(-16) dyne cm2) for the mastigonemes of Ochromonas it would appear that the actual value must be in excess of this. Comparison is made with the structural properties of the micro-tubules in eukaryote cilia and flagella and with prokaryote flagella. The latter comparison suggests that the mastigonemes of Ochromonas are just rigid enough to produce the observed propulsive effect.