  The cytoskeleton, consisting of biopolymer filaments, molecular motors, and
passive crosslinking proteins, provides the internal structure of cells that
facilitate movement, growth, and cell division. Understanding the microscopic
motor-filament kinetics and dynamics is essential for comprehending macroscopic
behaviors of reconstituted cytoskeletal assemblies, such as self-organized flow
and active stress. In this study, we employ an adaptive fast Chebyshev
approximator based on tree search and parallel computing to accurately recover
the equilibrium distribution of crosslinking proteins. Therefore, it satisfies
detailed balance in binding through kinetic Monte Carlo sampling while
maintaining cost-effectiveness. Additionally, we offer expandable features,
including segregating the simulation process via pre-building and allowing the
free-loading of different closed-form formulations of the motor's potential
energy. Overall, this research contributes to computational advancement in
function approximation and has the potential to better describe the evolution
of cytoskeletal active matter.
