Before revision:  In this work , we propose a mean-field mathematical model of the mechanical interactions of two populations of molecular motors with diffusion of the cargo (thermal fluctuations ) as the fundamental noise source. By studying a simplified model, the delayed response of motors to rapid fluctuations in the cargo  is quantified, allowing for the reduction of the full model to two "characteristic positions " of each of the motor populations .
After revision:  In this work , we propose a mean-field mathematical model of the mechanical interactions of two populations of molecular motors with cargo thermal fluctuations (diffusion) is presented to study this phenomenon. The delayed response of motors to rapid fluctuations in the cargo is quantified, allowing for the reduction of the full model to two "characteristic positions " of each of the motor populations .