Real (Zre) and imaginary (Zim) part of the complex total impedance ZT
The derivation of the real (Zre) and imaginary (Zim) part of the complex total impedance, ZT, has recently been revisited (Krug et al, 2009) and is
briefly explained here for the three parameter model depicted in the main text (Fig. 1B). In this model, impedance of the (ohmic) epithelial resistor
is Repi, that of the subepithelial resistor is Rsub. Impedance of the epithelial capacitor depends on the angular frequency ( = 2··f) and amounts to
1/(i··Cepi) where i   1 denotes the phase shift by -90° and Cepi the epithelial capacitance. Applying Kirchhoff’s laws, the total impedance ZT is
calculated as:
Z 
T

1    R
R epi  1  i    R epi  C epi
epi
C

epi 2
 R
sub
(Eq. S1)
ZT is a complex number and can be rearranged to obtain the form Zre + i·Zim (Zre, real part of the impedance or resistance; Zim, imaginary part of the
impedance or reactance):
Z re 

R epi
1    R epi  C epi

2
 R sub ;
Z im 
   (R epi ) 2  C epi

1    R epi  C epi
(Eqs. S2; S3)

2
For the six parameter model (main text, Fig. 1D), the derivation can be carried out analogously.
The equation for ZT is given in the main text (Eq. 6) and can be rearranged to yield
2
2
R para  {(R ap  R bl )  (R para  R ap  R bl )   2  [(R ap   bl  R bl   ap ) 2  R para  (R ap   bl  R bl   ap )]}
Z  
 R sub
para
ap
bl
2
para
ap
bl 2
2
para
ap
para
bl
ap
bl
bl
ap 2
(R  R  R    R     )    (R    R    R    R   )
re
(Eq. S4)
and
Z im  
(R para
   (R para ) 2  {R ap   ap  [1  (   bl ) 2 ]  R bl   bl  [1  (   ap ) 2 ]}
 R ap  R bl  2  R para   ap   bl ) 2  2  (R para   ap  R para   bl  R ap   bl  R bl   ap ) 2
(Eq. S5)
References
Krug, S. M., M. Fromm, and D. Günzel. 2009. Two-path impedance spectroscopy for measuring paracellular and transcellular epithelial resistance.
Biophys. J. 97:2202–2211.