Energetic variational modeling of active nematics: coupling the Toner-Tu model with ATP hydrolysis

Abstract

We present a thermodynamically consistent energetic variational model for active nematics driven by ATP hydrolysis, with a focus on the coupling between chemical reactions and mechanical dynamics. Extending the classical Toner-Tu framework, we introduce a chemo-mechanical coupling mechanism in which the self-advection and polarization dynamics are modulated by the ATP hydrolysis rate. The model is derived using an energetic variational approach that integrates both chemical free energy and mechanical energy into a unified energy-dissipation law. The reaction rate equation explicitly incorporates mechanical feedback, revealing how active transport and alignment interactions influence chemical fluxes and vice versa. This formulation not only preserves consistency with nonequilibrium thermodynamics but also provides a transparent pathway for modeling energy transduction in active systems. We also present numerical simulations demonstrating how ATP consumption drives the merging of topological defects and enables the system to escape a quasi-equilibrium, a phenomenon not observed in passive nematic systems. This framework offers new insights into energy transduction and regulation mechanisms in biologically related active systems.