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Modular analysis of the control of flagellar Ca2+-spike trains produced by CatSper and CaV channels in sea urchin sperm

Fig 8

Exploration of mixed scenarios involving the components of the CaV+BK and CatSper+NHE modules.

The state space of the model was extended to {S, RF, RH, RL, G, ,, V,,,,,, C, H}. A large number of parameter vectors resulting from a search of parameter space for coherence with experimental time series is illustrated in this figure according to clustering in the projection plane (gcv, gcs), predicted dynamics, and predicted functionality of the components of the two modules. During the exploration, coherence with experimental time series required that the resting C(0) is about 100nM, the average spike interval is in the range 0.37s-1.38 s, the predicted (bT, bA) point falls within the convex hull of most representative experimental values in the bottom right quadrant (polygon in A, right). A) On the left, the clustering of the parameter vectors in projection in the (gcv, gcs) plane is shown. On the right, the envelope and temporal organisation of Ca-spike trains predicted by each of these parameter vectors is represented as the bivariate plot of the spike-amplitude coefficient bA vs the interspike interval coefficient bT. In both graphs the dots represent individual parameter vectors which are coloured according to the cluster if they are fully coherent with experimental time series (selected) and grey otherwise (unselected). For each cluster in the plane (gcv, gcs) a parameter vector has been singled out (smaller filled circles). The two larger filled circles represent the reference parameter vectors for CaV+BK and CatSper+NHE modules. B) Illustration of the dynamics corresponding to the parameters vectors singled out in clusters c (top left), d (top right), e (bottom left) and f (bottom right) in A. The curves are the numerical solutions of the variable C in the model under the full parameter vector (coloured according to the cluster), setting gcs = 0 (black) and setting gcv = gbk = 0 (grey). Notice the overlap between coloured and black curves on the graphs on top.

Fig 8

doi: https://doi.org/10.1371/journal.pcbi.1007605.g008