We study a transmission problem of Neumann-Robin type involving a parameter $\alpha$ and perform an asymptotic analysis with respect to $\alpha$. The limits $\alpha \to 0$ and $\alpha \to +\infty$ correspond respectively to complete decoupling and full unification of the problem, and we derive error estimates for both regimes. Biologically, the model describes two cells connected by the gap junction with permeability $\alpha$: the case $\alpha \to 0$ corresponds to a situation where the gap junction is closed, leaving only the tight junctions between the cells, so that no substance exchange occurs, while $\alpha \to +\infty$ corresponds to cell fusion. We also consider time-dependent permeability and analyze the case where $\alpha$ blows up in finite time. Under suitable regularity assumptions, we rigorously show that the solution can be extended beyond the blow-up time, remaining in the cell fusion regime.