Active forces and elastic resistances within the flagellar axoneme

Charles B. Lindemann, Dominic W. Pelle, Kathleen A. Lesich

The focus of recent work in our laboratory has been to gain a better understanding of the forces that are acting within a beating flagellum. Force-calibrated glass microprobes have been used to measure the stalling force of beating flagella of reactivated bull sperm. The force to arrest the flagellum averaged 2.52 ( 0.68) 10-10 N ( SD) in the presence of 1 mM Mg ATP. From this, the torque acting across the axoneme diameter was calculated. On the basis of the number of dyneins in the active region of the flagellum pushing against the probe, we found that each dynein head must contribute approximately 5 pN. As it is unlikely that a single dynein head could produce much more than this amount of force, our result suggest that all of the dynein heads must contribute. Based on this estimate of the force produced by dynein in an arrested flagellum, we were able to find the t-force in a bull sperm flagellum that is arrested by shortening. The t-force near the switch-point of the beat is about 0.5 nN/micron, approximately the same as the total dynein force generated per micron of flagellar length. This value of the t-force requires that the spokes must bear substantial t-force both before and after dynein switching. After dynein releases its connections to the B-subtubule during the beat, spoke #1 should experience approximately 7 pN of force, pulling it away from the central pair apparatus. This should cause significant distortion of the axoneme after dynein switching, a concrete prediction that should be subject to experimental verification. Most recently, we have been observing and measuring the passive elastic properties of the flagellum after the action of dynein has been eliminated with sodium metavanadate. We measured the passive stiffness of the flagellum and observed that the passive flagellum develops a counter-bend in the distal part of the flagellum, when the proximal portion is bent with a microprobe. The counter-bend phenomenon is most likely a property which results from passive elastic linkages between the doublets. We have observed the counter-bend formation in rat, mouse, bull and sea urchin sperm flagella. Analyzing the behavior of the counter-bend, we have obtained estimates of the interdoublet elasticity, and found that the elasticity is non-linear. At large shear displacements the elasticity reaches a value of approximately 2.0 x 10-5 N/m per nexin link. This would support the presence of permanent elastic linkages in the axoneme that can stretch to many times their resting length. Supported by Grant MCB-0110024 from the National Science Foundation.