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¹ Escola Politécnica, Departamento de Engenharia de Telecomunicaçoes e Controle
² Departmento de Fisiologia e Biofísica, Instituto de Ciencias Biomédicas, Universidade de São Paulo, 05508-900 São Paulo, Brazil

Address correspondence to Francisco Lacaz-Vieira, Departmento de Fisiologia e Biofísica, Instituto de Ciencias Biomédicas, Universidade de São Paulo, 05508-900 São Paulo, Brazil. Fax: (55) 11-3091.7285; E-mail: flacaz{at}usp.br

Tight junction (TJ) permeability responds to changes of extracellular Ca²⁺ concentration. This can be gauged through changes of the transepithelial electrical conductance (G) determined in the absence of apical Na⁺. The early events of TJ dynamics were evaluated by the fast Ca²⁺ switch assay (FCSA) (Lacaz-Vieira, 2000), which consists of opening the TJs by removing basal calcium (Ca²⁺_bl) and closing by returning Ca²⁺_bl to normal values. Oscillations of TJ permeability were observed when Ca²⁺_bl is removed in the presence of apical calcium (Ca²⁺_ap) and were interpreted as resulting from oscillations of a feedback control loop which involves: (a) a sensor (the Ca²⁺ binding sites of zonula adhaerens), (b) a control unit (the cell signaling machinery), and (c) an effector (the TJs). A mathematical model to explain the dynamical behavior of the TJs and oscillations was developed. The extracellular route (ER), which comprises the paracellular space in series with the submucosal interstitial fluid, was modeled as a continuous aqueous medium having the TJ as a controlled barrier located at its apical end. The ER was approximated as a linear array of cells. The most apical cell is separated from the apical solution by the TJ and this cell bears the Ca²⁺ binding sites of zonula adhaerens that control the TJs. According to the model, the control unit receives information from the Ca²⁺ binding sites and delivers a signal that regulates the TJ barrier. Ca²⁺ moves along the ER according to one-dimensional diffusion following Fick's second law. Across the TJ, Ca²⁺ diffusion follows Fick's first law. Our first approach was to simulate the experimental results in a semiquantitative way. The model tested against experiment results performed in the frog urinary bladder adequately predicts the responses obtained in different experimental conditions, such as: (a) TJ opening and closing in a FCSA, (b) opening by the presence of apical Ca²⁺ and attainment of a new steady-state, (c) the escape phase which follows the halt of TJ opening induced by apical Ca²⁺, (d) the oscillations of TJ permeability, and (e) the effect of Ca²⁺_ap concentration on the frequency of oscillations.

Key Words: calcium • tight junctions • cell adhesion • models, theoretical • calcium-binding proteins

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