Tight junctions are dynamic structures that are crucial in establishing the diffusion and electrical barrier of epithelial monolayers. Dysfunctions in the tight junctions can impede this barrier function and lead to many pathological conditions. Unfortunately, detailed understanding of the non-specific permeation pathway through the tight junctions, the so-called leak pathway, is lacking. We created computational models of the leak pathway to describe the two main barrier measures, molecular permeability and transepithelial electric resistance while using common structural dynamics. Our results showed that the proposed alternatives for the leak pathway, the bicellular strand opening dynamics and the tricellular pores, contribute together with distinct degrees, depending on the epithelium. The models can also capture changes in the tight junction barrier caused by changes in tight junction protein composition. In addition, we observed that the molecular permeability was markedly more sensitive to changes in the tight junction structure and strand dynamics compared with transepithelial electric resistance. The results highlight that our model creates a good methodological framework to integrate knowledge on the tight junction structure as well as to provide insights and tools to advance tight junction research.