Temperature-dependent sex determination, realized by hormonal dynamics with enzymatic reactions sensitive to ambient temperature

Temperature-dependent sex determination (TSD) is adopted by many animal taxa, including reptiles and fishes. In some species, the eggs develop into females under a low hatching temperature, whereas they will develop into males under a high hatching temperature (called the FM-pattern). In other species, the eggs develop into males (or females) under a low (or high) hatching temperature (MF-pattern). Still, in other species, the eggs develop into females, males, or females, respectively, when under a low, intermediate, or high hatching temperature (FMF-pattern). In this paper, we study a mechanism for realizing TSD. Specifically, we explore a hypothesis that the temperature dependence of enzymatic reaction rates causes a clear switching of sex hormone levels with gradual change of temperature. Herein, we analyze a simple hormonal-dynamics with temperature-sensitive rates of enzymatic reactions included in the sex-determining gene-protein regulatory network. We first examined the cases in which the enzymatic reactions followed Arrhenius equation. The MF-pattern appeared when the rates of aromatase production and/or estradiol production depend more strongly on temperature than do the rates of their decay. By contrast, the FM-pattern appeared when the temperature dependence is stronger for the decay rates of aromatase and/or estradiol than their production rates. However, the FMF-pattern appeared only when some enzymatic reactions follow Berthelot-Hood equation, which exhibits a stronger temperature dependence under higher temperatures than Arrhenius equation. We discuss the possible mechanisms for TSD of FMF-pattern, including alternative splicing and post-translational modification.