We study wrinkling instability in a one-dimensional tension-based model of epithelial tissue with apico-basal asymmetry. Starting from a discrete model, we derive the governing Euler-Lagrange equations in the continuum limit and study their linear stability. We obtain an algebraic equation for the dominant wavenumber of the wrinkling pattern, whose solutions provide closed-form expressions for the critical apico-basal differential tension, the wrinkling wavelength, and an expression for the local thickness modulation of the wrinkled tissue. Vertex-model simulations validate the analytical results. Our results show how the apico-basal asymmetry in cellular mechanics may affect the emergent tissue patterns and they motivate a nonlinear analysis as well as a three-dimensional generalization of the model.
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