. The Biological bulletin. Biology; Zoology; Biology; Marine Biology. B. Figure 2. (A) A schematic drawing that shows the four parameters used in the calculation of sperm trajectory. O, the origin; p, position at t (vector); v, velocity (vector); (j>, angular component of v (scalar); r, radius of curvature (scalar). (B) A computed snapshot of the chemoattractant gradient used in the present study. The attractant concentration profile in the square area of ± I mm of the .v-y plane is plotted in the z-axis. The peak (hilltop) corresponds to the chemoattractant source located at the origin (.v
. The Biological bulletin. Biology; Zoology; Biology; Marine Biology. B. Figure 2. (A) A schematic drawing that shows the four parameters used in the calculation of sperm trajectory. O, the origin; p, position at t (vector); v, velocity (vector); (j>, angular component of v (scalar); r, radius of curvature (scalar). (B) A computed snapshot of the chemoattractant gradient used in the present study. The attractant concentration profile in the square area of ± I mm of the .v-y plane is plotted in the z-axis. The peak (hilltop) corresponds to the chemoattractant source located at the origin (.v = v = 0). lation of error during the integrations for a long time period. All the calculations and graphical outputs were done by using the Mathematica program (Wolfram Research). Attractant profile For most observations of chemotaxis, the following ex- perimental design was adopted: a glass pipette filled with chemoattractant or any fluid (within agar-gel in many cases) to be tested was placed in a drop of water containing dispersed sperm cells. This allows a spatial gradient of attractant concentration to be established rapidly: sperm located in the vicinity of an attractant source usually ap- proach it within no more than tens of seconds. Since mol- ecules such as an organic compound or a small protein normally have diffusion coefficients in water of -10"'" nr/s or smaller, it is an acceptable approximation that the attractant profile does not change much during the approach of the spermatozoon. In our model, therefore, we simply used a computed snapshot of a solution of a diffusion equation as an attractant profile (Fig. 2B). Moreover, the drop is largely spread on the slide but is much thinner in the ;-axis, so variation of attractant concentration along the c-axis should be small. Therefore, we consider the attractant gradient field with a two-dimensional diffusion equation with a coefficient of D: 8c/8t = D(82c/8.\2 + 82c/8\2) (Eq. 3) In the polar coordin
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Keywords: ., bookauthorlilliefrankrat, booksubjectbiology, booksubjectzoology
