. The Biological bulletin. Biology; Zoology; Biology; Marine Biology. 98 M. ISHIKAWA ET AL. 400 350 300 3 200 ro £ 150 =3 O 100 50 0. Attractant cone, []. 1000 ju,m) while they are far from the attractant source (~5 mm), and smaller trajectories (-200 jum) near the attractant source (— mm). However, this dependence on distance from the attractant was lost in the absence of external Ca2 + , which suggests that Ca2 + influx is involved in the modula- tion of the curvature of trajectories. We incorporated these findings into the assumptions set in the model as follows: (a) Curv
. The Biological bulletin. Biology; Zoology; Biology; Marine Biology. 98 M. ISHIKAWA ET AL. 400 350 300 3 200 ro £ 150 =3 O 100 50 0. Attractant cone, []. 1000 ju,m) while they are far from the attractant source (~5 mm), and smaller trajectories (-200 jum) near the attractant source (— mm). However, this dependence on distance from the attractant was lost in the absence of external Ca2 + , which suggests that Ca2 + influx is involved in the modula- tion of the curvature of trajectories. We incorporated these findings into the assumptions set in the model as follows: (a) Curvature decreases as intracellular Ca2+ concentra- tion, ([Ca2* ],), increases ( a negative correlation). (b) [Ca2+], positively correlates with c(p), the attractant concentration which is sensed by the sperm. Assumption (a) also agrees with the evidence that sper- matozoa treated with a Ca2+ ionophore showed a curvature of —200 /am. which increased up to -800 /am at lower Ca24" concentration. Since any quantitative relationship among these factors in real spermatozoa is not yet available, we set some trial functions and studied the behavior. We first tried a simple linear correlation between [Ca2+], and c(p), and a cubic function for [Ca2 + ], and r(t) (Fig. 3A): [Ca: + ], = dp) (0 < c < 1; [arbitral unit ()]) (Eq. 6) ,-(,) = 400(1 - [Ca;T],)- [jam] (0 < < 1; []) (Eq. 7) This now allows us to study how spermatozoa swim under these conditions. The results show that the trajectories gen- erated by such conditions are far from chemotactic behav- ior. Spermatozoa do circle around the attractant source but never finally approach the egg (Fig. 3B). This result is not surprising because our present system is fully symmetric in terms of time and space components. When using functions other than those of equations (6 and 7), no chemotaxis is observed at all. However, a remarkable change occurs if we incorporate an additional condition: (c) |Ca2' |, has
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Keywords: ., bookauthorlilliefrankrat, booksubjectbiology, booksubjectzoology
