Elastic extension and jump of the flagellar nexin links: A theoretical mechanical cycle

The functions of the nexin links of a flagellar axoneme have not been clear ly demonstrated. Taking into account both the elastic (Hookean) characteris tics and the possible jump of the nexin links, we calculated the sliding to bending conversion of a theoretical model in a tip-ward direction step by step, according to the essential principles proposed by the geometric clutc h hypothesis [Lindemann, 1994: J Theoret Biol 168:175-189]: the activity of the dynein arms depends on the transverse forces induced by the axonemal c urvature. In our calculations, however, the transverse forces that are invo lved in the regulation of the activities of the dynein arms were due to the extension of the nexin links located upstream of a given abscissa. This al lowed us to define a bent segment as the axonemal portion at whose proximal and distal ends the nexin links were relaxed, and as fully extended as pos sible, respectively. The model creates an apparent disorder in the orientat ion of the nexin links as already observed [Bozkurt and Wooley, 1993: Cell Motil Cytoskeleton 24:109-118; Wooley, 1997: J Cell Sci 110:85-94]. We prop ose that the nexin links are involved in a mechanical cycle, whose 3 stages are (1) rapid extension, (2) slow relaxation, and (3) stand-by. The rapid extension is compatible with the mechanical interactions between the nexin links and the inner dynein arms with which they form the dynein regulatory complex. This was correlated with the oscillating properties of the nexin l inks along the axoneme that allow them to be one of the regulatory elements of the local ATPase activity of the dynein arms. (C) 2001 Wiley-Liss, Inc.