Modular analysis of the control of flagellar Ca2+-spike trains produced by CatSper and CaV channels in sea urchin sperm
In A and B, the graphs show the numerical solutions of the indicated variables under the reference parameters of the CaV+BK (as in Fig 4) and the CatSper+NHE (as in Fig 6) modules. In both cases, the normal response to SAP release at time 0 s (vertical dashed line) develops until it is perturbed by an artificial raise in pHi (indicated by the second vertical dashed line) to a constant value maintained thereafter. Variables representing pHi and NHE in the model were coupled to those of the CaV+BK module with the same reference parameters used in the CatSper module. The grey dots are a rescaled trace of the relative intensity of a Ca-sensitive fluorescent probe in S. purpuratus individual sperm cell bound to a coverslip obtained by adding first 100 nM Speract (vertical dashed line) and subsequently 10 mM NH4Cl (second vertical line). C) Parameter vectors projected onto the plane (gcv, gcs) (as in Fig 8A) were coloured according to predicted model responsiveness during identical pHi manipulation protocol: if alkalinisation results in sustained, slow decaying C dynamics the parameter set is representing according to the cluster’s colour, otherwise it is depicted in grey. D) Plot of the fraction of open CatSper channels vs pHi in the numerical solutions of the model parameterised under the reference CatSper+NHE module, the reference CaV+BK module, and with the parameter vectors singled out from the clusters c, d, e and f illustrated in Fig 8. The trajectories are displayed for the interval 2-12 s to avoid transients.