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

Intracellular calcium ([Ca 2+ ] i ) is a basic, versatile and ubiquitous cellular signal controlling a wide variety of biological processes. A remarkable example is the steering of sea urchin spermatozoa towards the conspecific egg by a spatially and temporally orchestrated series of cytosolic [Ca 2+ ] i spikes. Although this process has been an experimental paradigm for reproduction and sperm chemotaxis studies, the composition and regulation of the signalling network underlying the cytosolic calcium fluctuations are hitherto not fully understood. Here, we used a differential equations model of the signalling network to assess which set of channels can explain the characteristic envelop and temporal organisation of the [Ca 2+ ] i -spike trains. The signalling network comprises an initial membrane hyperpolarisation/repolarisation produced by an upstream module triggered by the egg-released chemoattractant peptide, via receptor activation, cGMP synthesis and decay. Followed by downstream modules leading to pH i , voltage and [Ca 2+ ] i fluctuations. The upstream module outputs were fitted to kinetic data on cGMP activity and early membrane potential changes measured in bulk cell populations. Two candidate modules featuring voltage-dependent Ca 2+ -channels link these outputs to the downstream dynamics and can independently explain the typical decaying envelop and the progressive spacing of the spikes. In the first module, [Ca 2+ ] i -spike trains require the concerted action of a classical Ca V -like channel and a potassium channel, BK (Slo1), whereas the second module relies on pH i -dependent, [Ca 2+ ] i -inactivated CatSper dynamics alone. The model predicts that these two modules interfere with each other and produce unreasonable dynamics when present at similar proportions, which suggests that one may predominate over the other in vivo . To assess these alternatives, several quantitative predictions were derived from each module and confronted to experimental observations. We show that the [Ca 2+ ] I dynamics observed experimentally after sustained alkalinisation can be reproduced by a model featuring the CatSper module but not by one including the pH-independent Ca V and BK module. We conclude in favour of the module containing CatSper.