Bacteria in the deep oceans are a key determinant of remineralization of sinking carbon particles and thus global climate. However, most marine ecosystem models overlook how bacteria aggregate on particles and the microscale interactions between particle-associated bacteria, making it difficult to obtain mechanistic insights on their vertical power-law decay pattern. Here, we present a spatial population model where the attachment and detachment processes of bacterial cells depend on the local density of particle-associated bacteria. We first derived the equilibrium frequency distribution of particle-associated bacteria between particles under density-dependent interactions, which follows a novel type of exponentially-weighted Poisson (EWP) distribution that is under-dispersed relative to the Poisson distribution. We then showed that the vertical power-law distribution of bacterial abundance only emerges with the EWP distribution. Furthermore, the comparison between model behavior and empirical patterns in the Pacific and Southern Ocean indicated that temperature-dependent hydrolysis rate and sinking rate of particles depending on nutrient conditions are key parameters to explain the regional variations of power-law exponent. The mechanistic approach developed here provides a pathway to link micro-scale interactions between individuals to macro-scale food chain structures and carbon cycle.