Intracellular calcium ([Ca2+]i) is a basic 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 [Ca2+]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 envelope and temporal organisation of the [Ca2+]i-spike trains. The signalling network comprises an initial membrane hyperpolarisation 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 intraflagellar pH (pHi), voltage and [Ca2+]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 Ca2+-channels link these outputs to the downstream dynamics and can independently explain the typical decaying envelope and the progressive spacing of the spikes. In the first module, [Ca2+]i-spike trains require the concerted action of a classical CaV-like channel and a potassium channel, BK (Slo1), whereas the second module relies on pHi-dependent CatSper dynamics articulated with voltage-dependent neutral sodium-proton exchanger (NHE). We analysed the dynamics of these two modules alone and in mixed scenarios. We show that the [Ca2+]i dynamics observed experimentally after sustained alkalinisation can be reproduced by a model featuring the CatSper and NHE module but not by those including the pH-independent CaV and BK module or proportionate mixed scenarios. We conclude in favour of the module containing CatSper and NHE and highlight experimentally testable predictions that would corroborate this conclusion.