Data-driven model discovery for an active nematic system

Author

Connor Robertson, Anand Oza (NJIT), Travis Askham (NJIT)

Active nematics refer to active matter systems made up of self-propelled rod-like material in nematic order (loosely aligned without being spatially organized). This seemingly obscure system actually appears in a variety of, mostly biological, settings. Most prominently, active nematics play a large role in the cell cytoplasm, where suspensions of microtubules moved by kinesin proteins are key in the structural integrity of the cell and in transporting nutrients and organelles within the cell [1]. High quality video of this microtubule-kinesin system in a 2D plane were taken in a pioneering experiment by Zvonimir Dogic and collaborators [2] as seen below:

Several models have been proposed for this system via a continuum “Q-tensor” theory. The models consist of coupled partial differential time-evolution equations for the orientation and velocity of the microtubules (and occasionally the concentration). Though successful in recreating some of the most salient qualitative behavior, there has been some disagreement on the model form and the exact quantitative agreement [2–5].

This project aims to provide a data-driven model that can lend insight into the various proposed model forms using the Sparse Identification of Nonlinear Dynamics (SINDy) modeling framework [6]. It involves:

  1. Accurately extracting the orientation, concentration, and velocity of the microtubles in the above video
  2. Generating a library of possible terms for each evolution equation via symbolic computation, data fitting, and numerical differentiation of noisy data
  3. Using techniques in sparse regression and variable selection to identify the most probable form for the evolution equations
  4. Simulating the resulting models and comparing the results both qualitatively and quantitatively with the information extracted from the experimental images

This work was presented at the APS March meeting 2022, APS DFD meeting 2022, and SIAM CSE 2023.

References

[1]
J. Pringle, A. Muthukumar, A. Tan, L. Crankshaw, L. Conway, and J. L. Ross, Microtubule Organization by Kinesin Motors and Microtubule Crosslinking Protein MAP65, Journal of Physics: Condensed Matter 25, 374103 (2013).
[2]
S. J. DeCamp, G. S. Redner, A. Baskaran, M. F. Hagan, and Z. Dogic, Orientational Order of Motile Defects in Active Nematics, Nature Materials 14, 1110 (2015).
[3]
A. Doostmohammadi, J. Ignés-Mullol, J. M. Yeomans, and F. Sagués, Active Nematics, Nature Communications 9, 1 (2018).
[4]
A. U. Oza and J. Dunkel, Antipolar Ordering of Topological Defects in Active Liquid Crystals, New Journal of Physics 18, 093006 (2016).
[5]
T. Gao, M. D. Betterton, A.-S. Jhang, and M. J. Shelley, Analytical Structure, Dynamics, and Coarse Graining of a Kinetic Model of an Active Fluid, Physical Review Fluids 2, 093302 (2017).
[6]
S. L. Brunton, J. L. Proctor, and J. N. Kutz, Discovering Governing Equations from Data by Sparse Identification of Nonlinear Dynamical Systems, Proceedings of the National Academy of Sciences 113, 3932 (2016).