Statistical properties of autonomous flows in 2D active nematics

Abstract

We study the dynamics of a tunable 2D active nematic liquid crystal composed of microtubules and kinesin motors confined to an oil-water interface. Kinesin motors continuously inject mechanical energy into the system through ATP hydrolysis, powering the relative microscopic sliding of adjacent microtubules, which in turn generates macroscale autonomous flows and chaotic dynamics. We use particle image velocimetry to quantify two-dimensional flows of active nematics and extract their statistical properties. In agreement with the hydrodynamic theory, we find that the vortex areas comprising the chaotic flows are exponentially distributed, which allows us to extract the characteristic system length scale. We probe the dependence of this length scale on the ATP concentration, which is the experimental knob that tunes the magnitude of the active stress. Our data suggest a possible mapping between the ATP concentration and the active stress that is based on the Michaelis-Menten kinetics that governs motion of individual kinesin motors.

Topological chaos in active nematics

“…(Methods: PIV velocity analysis.) varies only modestly with ATP concentration, consistent with Lemma et al [23] for ATP concentrations larger than 10µM. Refs.…”

“…Refs. [23,45] establish that the correlation length arises from balancing the elastic bend energy of the microtubule bundles with motor activity. Thus, if only the activity were increased, should decrease, and indeed, except for the 250 µM data, our results are consistent with a small downward trend.…”

“…Following Refs. [23,45], we chose to be the length at which the velocity-velocity correlation function, computed from PIV velocities, decays to half its maximum value, Fig. 5c.…”

“…We also used the PIV velocities to compute the velocity-velocity correlation length for each data run, as in Ref. [23,45]. The velocity autocorrelation function was computed as C(r) = ijv i ·v j δ(r − r ij ), where the indices i and j range over all frames and all grid points within a frame,v i = v i /|v i | is the unit velocity vector, and r ij = |r i −r j |, for grid points r i and r j .…”

“…Nature provides many examples of active matter, ranging from flocks of birds [1], fish [2], and insects [3] to sheets of cells [4][5][6] and swarms of bacteria [7][8][9]. In the lab, various attempts have been made to develop biomimetic and synthetic active materials, from self-propelled colloids [10,11] and mechanically agitated flocks [12], to dense phases of biopolymers driven by molecular motors [13][14][15][16][17][18][19][20][21][22][23]. This is a rich field of research, and to date, much theoretical work has been dedicated to understanding the fundamental physics of these fascinating and diverse systems [24,25].…”