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Collective transport through channels shows surprising properties under one-dimensional confinement: particles in a single file exhibit subdiffusive behavior, while liquid confinement causes distance-independent correlations between the particles. Such interactions in channels are well studied for passive Brownian motion, but driven transport remains largely unexplored. Here, we demonstrate gating of transport due to a speed-up effect for actively driven particle transport through microfluidic channels. We prove that particle velocity increases with particle density in the channel due to hydrodynamic interactions under electrophoretic and gravitational forces. Numerical models demonstrate that the observed speed-up of transport originates from a hydrodynamic pistonlike effect. Our discovery is fundamentally important for understanding protein channels and transport through porous materials and for designing novel sensors and filters.