Applicability of mathematical methods to quantify the Lag phase in Rhinella arenarum oocytes maturation

URUEÑA LA; ZELARAYÁN LI; FERNÁNDEZ L; BENZAL G

BIOCELL

Biocell

Año: 2019 vol. 43 p. 80 - 80

The Gompertz model fits the dynamics of biological processes, as we demonstrated for the steroid-induced maturation of Rhinella arenarum oocytes. The Gompertz curve explains the behavior of the different phases of the maturation process. The lag phase is the period of time elapsed from the oocyte hormonal induction to the morphological signs of the rupture of the germinal vesicle. The aim of this study was to quantify the duration of the lag phase in the R. arenarum oocyte maturation induced by different hormones. The experimental data were obtained from ovarian follicles of R. arenarum treated in vitro with progesterone (P4) and prostaglandins PGE1 and PGF2α. In order to estimate the lag time (λ), the experimental data were subjected to modeling and simulation with MATLAB and corresponding parameters were estimated with NLIN. In addition, two traditional mathematical methods were applied to the Gompertz growth curve: tangent at the inflection point and the third derivative. Experimental data indicate that λ varies according to the induced hormone, around 4 hours (h) for PGE1 and PGF2α and only 3h for P4. However, the mathematical methods applied showed that the lag phase is greater when the maturation is induced with P4 (λ≈4:47h) than with PGE1 (λ≈4:30h) or PGF2α (λ≈3:46h). The methods fit the effect of the PG more accurately than that of P4. This is explained by the formulation for the calculation of λ that depends on the growth rate in the exponential phase, given by of the parameter r (PG with r