Transport of partially active polymers in chemical gradients

The transport of molecules for chemical reactions is critically important in various cellular biological processes. Despite thermal diffusion being prevalent in many biochemical processes, it is unreliable for any sort of directed transport or preferential accumulation of molecules. In this paper, we propose a strategy for directed motion in which the molecules are transported by partially active polymeric structures. These polymers are assumed to be Rouse chains, in which the monomers are connected via harmonic springs and these chains are studied in environments that have activity varying spatially. The transport of such polymers is facilitated by these chemical/activity gradients which generate an effective drift. By marginalizing out the active degrees of freedom of the system, we obtain an effective Fokker-Planck equation for the Rouse modes of the polymer. In particular, we solve for the steady state distribution of the center of mass and its mean first passage time to reach an intended destination. We focus on how the arrangement of active units within the polymer affects its steady-state and dynamic behavior and how they can be optimized to achieve high accumulation or rapid motility.