Mathematical Modeling of Dynamic Cellular Association Patterns in Seminiferous Tubules

In vertebrates, sperm is generated in testicular tube-like structures called seminiferous tubules. The differentiation stages of spermatogenesis exhibit a dynamic spatiotemporal wavetrain pattern. There are two types of pattern—the vertical type, which is observed in mice, and the helical type, which is observed in humans. The mechanisms of this pattern difference remain little understood. In the present study, we used a three-species reaction–diffusion model to reproduce the wavetrain pattern observed in vivo. We hypothesized that the wavelength of the pattern in mice was larger than that in humans and undertook numerical simulations. We found complex patterns of helical and vertical pattern frequency, which can be understood by pattern selection using boundary conditions. From these theoretical results, we predicted that a small number of vertical patterns should be present in human seminiferous tubules. We then found vertical patterns in histological sections of human tubules, consistent with the theoretical prediction. Finally, we showed that the previously reported irregularity of the human pattern could be reproduced using two factors: a wider unstable wavenumber range and the irregular geometry of human compared with mouse seminiferous tubules. These results show that mathematical modeling is useful for understanding the pattern dynamics of seminiferous tubules in vivo.