Mechanical and biochemical organization of three-dimensional biofilm architectures
Final Report Abstract
Right at the beginning of my fellowship at MIT the coronavirus pandemic began. Bound to take a perspective that was less dependent on experimental data, we therefore decided to focus on a general methodological question that was raised by the proposed project: How can microscale-resolved, highly multi-modal experimental data of living and non-equilibrium systems be effectively coarse-grained into quantitative and predictive models that recapitulate collective organization on larger scales? Building on the success of known coarse-graining approaches in equilibrium systems, we started by considering a liquid crystal (LC) toy model of k-fold symmetric particles (k-atic LC) interacting via their orientational degree of freedom. Such k-atic LCs support defects with fractional topological charge. Inspired by the transformation properties of anyonic quantum particles that carry an apparent fractional spin charge, I studied the exchange properties of a pair of fractional defects in k-atic LCs and found that their exchange properties are analog to those of anyonic quantum particles. A universal mean-field equation I derived predicted a novel spontaneous chiral symmetry breaking in k-atic orientation patterns, which was subsequently reproduced by the particle model. We proposed several experimental systems to implement realizations of these theoretical predictions and published the work in Physical Review X. We then wondered how such coarse-graining approaches can inform analog techniques in more complex living systems. Together with PhD students from MIT, we developed a coarsegraining and hydrodynamic equation inference framework that could directly be applied to synthetic and experimental data: active chiral Brownian particle simulations and recent experiments on Quincke micro-rollers, a fish school and single-cells migrating during early zebrafish gastrulation. In all cases, we could infer hydrodynamic models that recapitulated symmetry breaking events as spatio-temporally self-organized processes and, if experiments were available, correctly predicted the dynamics in alternative geometries or for different microscopic parameters. Key methodological insights came from the realization that non-linearities in hydrodynamic equations – crucial to capture feedback and self-organization in dynamic systems – are most strongly affected by the central assumptions typically made in analytic approaches. The data-driven approach developed in this work circumvents several of these assumptions and is thus more likely to infer suitable closure-relations and non-linearities therein. Together with experimental collaborators, I could build on these experiences when we studied the self-organized formation of large living chiral crystals formed near fluid surfaces by thousands of starfish embryos with the goal to connect single-embryo to macroscopic crystal properties. A theoretical analysis of fluid flows around embryos rationalized the stability of spinning embryos and orbiting embryo groups, as well as the finite-time stability of whole crystals. An experimentally parameterized minimal model quantitatively recapitulated key emergent features of crystal growth. Interestingly, the minimal model suggested the possibility for living chiral crystals to exhibit ‘odd’ elastic material properties. In two dimensions, these unconventional properties can only exist in chiral out-of-equilibrium systems – precisely the microscopic ingredients provided by living chiral crystals. By quantifying crystal deformations surrounding lattice defects, we could confirm the presence of such odd material properties in a living system and provided estimates of their amplitudes. The corresponding work was recently published in Nature.
Publications
- Learning developmental mode dynamics from single-cell trajectories. eLife 10, e68679 (2021)
N. Romeo , A. Hastewell , A. Mietke , and J. Dunkel
(See online at https://doi.org/10.7554/elife.68679) - Anyonic defect braiding and spontaneous chiral symmetry breaking in dihedral liquid crystals. Physical Review X, Vol. 12, 011027 (2022)
A. Mietke , and J. Dunkel
(See online at https://doi.org/10.1103/PhysRevX.12.011027) - Learning hydrodynamic equations for active matter from particle simulations and experiments. arXiv
R. Supekar, B. Song, A. Hastewell, G. P. T. Choi, A. Mietke, and J. Dunkel
(See online at https://doi.org/10.48550/arXiv.2101.06568) - Odd dynamics of living chiral crystals. Nature, Vol. 607, 287–293 (2022)
T. H. Tan , A. Mietke , J. Li, Y. Chen, H. Higinbotham, P. J. Foster, S. Gokhale, J. Dunkel, and N. Fakhri
(See online at https://doi.org/10.1038/s41586-022-04889-6)
