Antibiotic resistance exerts a metabolic cost on bacteria and presumably a fitness disadvantage in the absence of antibiotics. However, several studies have shown that bacteria can evolve to eliminate this cost. Escherichia coli can adapt to the plasmid pBR322 carrying the tetA tetracycline-resistance gene (codes for the TetA efflux pump) by a chromosome mutation, which requires an intact tetA gene on the plasmid. The TetA pump can mediate potassium uptake. Here, the hypothesis that TetA replaces the endogenous K+ uptake system Trk is explored using a multi-level modeling approach that explicitly resolves relevant intracellular processes (e.g., metabolism and K+ uptake) and simulates individual bacteria in competition. The general behavior of the model is consistent with observations from the literature (e.g., growth rate and K+ limitation). In competition experiments without tetracycline, the model correctly predicts the fitness advantage of naive susceptible over naive resistant, evolved resistant over naive resistant and evolved resistant over evolved susceptible strains. Trk takes up about 10 times the K+ required, which costs energy. TetA takes up less K+, which is more efficient and leads to the evolution of the Trk mutant. The evolved Trk mutant relies on TetA to take up K+, and thus, carrying the plasmid is advantageous even in the absence of the antibiotic.