Effect of cell coupling between pacemaker cells on the biological pacemaker in cardiac tissue model

Biological pacemaker is a therapy for cardiac rhythm disease, which can be transformed from ventricular myocytes (VMs) by overexpressing HCN gene which codes the expression of hyperpolarization-activated current (${\mathrm {I}}_{\mathrm{f}}$) and knocking off Kir2.1 gene which codes inward-rectifier potassium current (${\mathrm {I}}_{\mathrm{K1}}$). Our previous study built a biological pacemaker single cell model and clarified the underlying mechanisms of how gene expressing levels influence the pacemaking activity of single pacemaker cell. But the pacemaking ability of pacemaker tissue has not been researched systematically. And what factors may have effects on pacemaker’s synchronization and spontaneous beating propagation are not clear. Biological research indicated that both sinoatrial node and pacemaker cells has less expression of connexin than unexcitable cardiac cells, which provides a possibility that improve pacemaking ability of pacemaker by decreasing its cell coupling. Another possible factor is the number of pacemaker cells. According to the common sense, increasing cell number can promote pacemaking behaviours, but overmuch pacemaker cells is unreasonable in clinic. As a result, the balance between pacemaker number and cell coupling is important when applying biological pacemaker. In this study, we constructed a two-dimensional cardiac tissue model with the description of electrophysiology to illustrate the relationship between gap junction and cell number. Based on this model, we modified the cell coupling between pacemaker cells by adjusting the diffusion coefficient of tissue with different pacemaker number. In different condition, the synchronization, pacemaking cycle length and electrical signal propagation were evaluated. It can be concluded that weakening cell coupling among pacemaker cells can lift the efficiency of bio-pacemaker therapy. This study may contribute to produce effective pacemaker in clinic.