In Silico Reconstruction of Sperm Chemotaxis

Abstract

In echinoderms, sperm swims in random circles and turns in response to a chemoattractant. The chemoattractant evokes transient Ca²⁺ influx in the sperm flagellum and induces turning behavior. Recently, the molecular mechanisms and biophysical properties of this sperm response have been clarified. Based on these experimental findings, in this study, we reconstructed a sperm model in silico to demonstrate an algorithm for sperm chemotaxis. We also focused on the importance of desensitizing the chemoattractant receptor in long-range chemotaxis because sperm approach distantly located eggs, and they must sense the chemoattractant concentration over a broad range. Using parameters of the sea urchin, simulations showed that a number of sperm could reach the egg from millimeter-order distances with desensitization, indicating that we could organize a functional sperm model, and that desensitization of the receptor is essential for sperm chemotaxis. Then, we compared the model with starfish sperm, which has a different desensitization scheme and analyzed the properties of the model against various disturbances. Our approach can be applied as a novel tool in chemotaxis research.

Keywords: desensitization; fertilization; modeling of cell; sperm chemotaxis.

Figure 1

Design of sperm models. (A) Conceptual diagram of modeled sperm. Sperm movement was chosen between the circular motion and turn, depending on (Chemoattractant) and (GC). B and D: Sperm curvatures of sea urchin (B) and starfish (D) in turn mode. The y-axis indicates the curvature in relative change to the circular-motion mode. The x-axis is a time series in 60 ms frames. C and E: Sperm movement pattern of turn mode in the sea urchin model (C) and starfish model (E). The colors of the tracks correspond to the colors of lines B and D. (F) An example of the shape of the (Chemoattractant) gradient defined within a radius of 5000 μm. The z-axis indicates (Chemoattractant) at each point calculated in the 2D surface represented as an x-y plane, where the egg is located at the origin with (Chemoattractant)s = 0.1 nM.

Figure 2

Results of simulations with the sea urchin model. (A) Summary of simulation results. The x-axis indicates the distance between the sperm start-point and the center of the egg, and egg-arrival rates of sperm from these points are shown as the longitudinal axis (n = 10,000). The blue symbols represent the results of the desensitization model, and the red symbols represent the results of a model in which the desensitization function is frozen. The length of the simulation was 30 min. (B) Magnification of a part of A. (C) Representative trajectories in the simulation. The black circle at the center indicates the egg, and the sperm started swimming from the four gray circles. Trajectories 1 and 2, 3 and 4, 5 and 6, and 7 and 8 start from the same points. Trajectories 2, 4, 6, and 8 show successful examples, whereas the others represent failures.

Figure 3

Result of simulations with starfish model. (A,B) Summary of the simulation results with the starfish model. The axes and colors are the same as in Figure 2A,B. (C) Representative trajectories in the simulation using the starfish model. The black circle indicates the egg, and the sperm started from the four gray circles. Trajectories 1 and 2, 3 and 4, 5 and 6, and 7 and 8 start from the same points. Trajectories 2, 4, 6, and 8 show successful examples, whereas the others represent failures.

Figure 4

Further analysis of models. (A–F) Summarized graphs of simulations with modification in parameters and the threshold for [cGMP]_i, K_1/2, and [Chemoattractant]_s. The y-axis shows the egg-arrival rates of sperm (n = 10,000), with the modification in each parameter shown as the abscissa axis. (A,C,E) correspond to the sea urchin models. (B,D,F) represent the starfish models. Green lines indicate the original values of the parameters. (G,H) Effects of physical disturbances in the sea urchin model (G) and starfish model (H). The y-axis shows the egg-arrival rates of sperm (n = 10,000), with the frequency of sine-wave oscillation shown as the x-axis. The broken line represents 0.01 Hz, and the arrowhead in G indicates a local maximum at 100 Hz.