Organization of Cytoskeletal Networks Creates Non-Equilibrium Energy Gradients Through Space and Time*

Active matter systems consume fuel to form organized, dynamic structures and patterns. These ordered states do not exist in the absence of an energy source. To gain insight into the energetic cost of structure formation, we investigate the assembly of an ordered aster from a disordered, uniform mixture of microtubules and kinesin motors. This self-organization occurs due to optogenetically-controllable crosslinking of motor proteins that walk on microtubules and hydrolyze ATP. Here, we perform the first careful measurement of ATP consumption, and power usage, through space and time on an in vitro cytoskeletal network. We additionally develop reaction-diffusion models and corresponding finite element simulations to predict how a given motor profile results in non-equilibrium ATP distributions. Our experiments and models both reveal radial spatial gradients in ATP, with the lowest ATP concentration in the aster core, where the motors are most dense. The expended power correlates with aster contraction, where the largest changes in aster radius accompany the greatest power usage. These results suggest that loading of motors, due to high motor densities at small aster radii, creates slower contraction. This work is a step toward understanding the role of energy consumption through space and time to produce organization in this active matter system. More broadly, our work provides a case study towards developing generalized theories of non-equilibrium systems connecting energy, entropy, and order.