We propose a new multiscale method to incorporate active transport of cargo particles in biological cells in stochastic, mesoscopic models of reaction-transport processes. Given a discretization of the computational domain, we find stochastic, convective mesoscopic molecular fluxes over the edges or facets of the subvolumes and relate the process to a corresponding first order finite volume discretization of the linear convection equation. We give an example of how this can be used to model active transport of cargo particles on a microtubule network by the motor proteins kinesin and dynein. In this way we extend mesoscopic reaction-diffusion models of biochemical reaction networks to more general models of molecular transport within the living cell.
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