We investigate a two-dimensional lattice model representation of intercellular Ca2+ signalling in a population of epithelial cells coupled by gap junctions. The model is based on and compared with Ca2+ imaging data from globally bradykinin-stimulated MDCK-I (Madin-Darby canine kidney)-I cell layers. We study large-scale synchronization of relevance to our laboratory experiments. The system is found to express a wealth of dynamics, including quasiperiodic, chaotic and multiply-periodic behaviour for intermediate couplings. We take a particular interest in understanding the role of "pacemaker cells" in the synchronization process. It has been hypothesized that a few highly hormone-sensitive cells control the collective frequency of oscillation, which is close to the natural frequencies (without coupling) of these cells. The model behaviour is consistent with the conjectures of the pacemaker cell hypothesis near the critical coupling where the cells lock onto a single frequency. However, the simulations predict that the frequency in globally connected systems decreases with increasing coupling. It is found that a pacemaker is not defined by its natural frequency alone, but that other intrinsic or local factors must be considered. Inclusion of partly sensitized cells that do not oscillate autonomously in the cell layer increases the coupling necessary for global synchronization. For not excessively high coupling, these cells oscillate irregularly and with distinctive lower frequencies. In summary, the present study shows that the frequency of synchronized oscillations is not dictated by one or few fast-responding cells. The collective frequency is the result of a two-way communication between the phase-advanced pacemaker and its environment.