A Strong Non-equilibrium Bound for Sorting of Crosslinkers on Growing Biopolymers*

Actin networks at the leading edge of cells generate protrusion forces against cell membranes to facilitate cell migration and cytoskeletal deformation. There is an emerging paradigm for regulation in the actin networks whereby components are passively sorted to their correct locations due to network growth. The tradeoff between actin growth speeds and network patterns under non-equilibrium driving is still a subject of active investigation. Here we use the framework of stochastic thermodynamics to investigate how the actin polymerization rates tune the sorting of actin binding proteins(ABPs) in a growing actin bundle. Our main results show that thermodynamics can be used to elucidate the role of actin polymerization in the sorting of ABPs in the growing actin bundle. In particular, we derive a thermodynamic uncertainty relation between non-equilibrium driving, emergent actin structure, and growth speed. Our work can be viewed as a starting point that reveals how the energy dissipation accompanying polymerization dynamics governs the emerging structure of networks formed by force transmitting biological agents.