Organization of cytoskeletal networks creates non-equilibrium energy gradients through space and time.

Abstract

Active matter systems consume fuel to form organized, dynamical patterns and structures. These ordered states do not exist in the absence of an energy source. As such, a more general description of energy-driven behavior than is offered by near-equilibrium approaches is required to describe active matter. To gain insight into the energetic cost to form and maintain structure, we investigate the assembly of an ordered aster from a disordered, homogeneous mixture of microtubules and their attendant kinesin motors. This formation 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 through space and time on an in vitro cytoskeletal network. We additionally develop reaction-diffusion models to predict how a given motor profile results in non-equilibrium ATP distributions. Comparing the theoretical versus measured ATP profiles provides insight into the dynamics of structure formation and properties of the motors, such as if motors operate cooperatively. Our experiments reveal global and spatial gradients in ATP consumption. The concentration of ATP depletes over time, first in the center of the aster and then propagating outward. This is inversely related to the concentration of motors, which are most concentrated in the aster center. Our theoretical models qualitatively match the experimental depletion profiles of ATP. This work is a first 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 the larger effort of developing generalized theories of non-equilibrium systems.