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Not AvailableTransporters play key roles in regulating the movement of molecules into and out of cells. Uniporters, the simplest class of transporters, use facilitated diffusion to translocate molecules across membranes down their concentration gradient. This process can be affected by the presence of additional substrates in the intra- and extracellular environment, which can either increase the net transport rate of a molecule via trans acceleration or decrease it via competitive inhibition. In this study, we derived mathematical models to describe the net transport rate of uniporters in the presence of multiple extracellular substrates or inhibitors. Analyses of these models identified four possible states for the system when two substrates are present, with two states leading to trans acceleration and the other two states resulting in inhibition. Finally, we found that the relation between kinetic constants that controls the fraction of transporters in the inward-facing open state is responsible for these behaviors. Our theoretical results provide a mathematical framework for understanding the dynamic response of uniporters in the presence of multiple substrates and inhibitors, which could have implications for various processes, from nutrient utilization to metabolic engineering.