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<img src='content_image/368759.jpg'>

is finite and it increases when the number of cells is increased. The increase of relaxation decrement when m → ∞ is physically limited by σ$_{S}$ ≪ δ (1 / 2 − χ$_{k}$ ) σ$_{1}$ , since the membrane conductivity is not strictly 0. 

Due to cluster’s shape and membrane properties, the variation of P$_{k,}$$_{1}$/ (1 / 2 − χ$_{k}$ ) and (1 / 2 − χ$_{k}$ ) with respect the eigenmode k determines a low frequency relaxation when the dipole-active eigenvalue χ$_{k}$ is close to 1/2. We note here that for dipole-active eigenmodes of ellipsoids the term (1 / 2 − χ$_{k}$ ) is called the depolarization factor and has analytical expression [37]. Prolate spheroids with longitudinal axis much larger than the transverse axis (needles) have the longitudinal depolarization factor approaching 0 and the transverse depolarization factor approaching 1/2. More precisely, for a long prolate spheroid, the longitudinal depo- larization factor scales as (1 / 2 − χ$_{2}$ ) ∝ a 2 $_{x}$/a 2 $_{z}$, a$_{z}$ > a$_{x}$ = a$_{y}$ , as a$_{x}$ → 0. On the other hand, extensive numerical calculations support the fact that cylinders with the same aspect ratio behave similarly to prolate spheroids [37]. Thus, it is not hard to observe that the low-frequency relaxation of linear clusters of cells connected by tight junctions is similar to that of a needle or a thin cylinder as long as the cluster and as thick as the junction. 

