Publications

The structure and dynamics of important biological quasi-two-dimensional systems, ranging from cytoskeletal gels to tissues, are controlled by nematic order, flow, defects and activity. Continuum hydrodynamic descriptions combined with numerical simulations have been used to understand such complex systems. The development of thermodynamically consistent theories and numerical methods to model active nemato-hydrodynamics is eased by mathematical formalisms enabling systematic derivations and structured-preserving algorithms. Alternative to classical nonequilibrium thermodynamics and bracket formalisms, here we develop a theoretical and computational framework for active nematics based on Onsager's variational formalism to irreversible thermodynamics, according to which the dynamics result from the minimization of a Rayleighian functional capturing the competition between free-energy release, dissipation and activity. We show that two standard incompressible models of active nemato-hydrodynamics can be framed in the variational formalism, and develop a new compressible model for density-dependent active nemato-hydrodynamics relevant to model actomyosin gels. We show that the variational principle enables a direct and transparent derivation not only of the governing equations, but also of the finite element numerical scheme. We exercise this model in two representative examples of active nemato-hydrodynamics relevant to the actin cytoskeleton during wound healing and to the dynamics of confined colonies of elongated cells.

JTD Keywords: Active nematics, Bracket formulation, Equations, Finite element metho, Hydrodynamics, Instabilities, Model, Nematic defects, Onsager's variational formalism, Principle, Wound healing

Various locomotion strategies employed by microorganisms are observed in complex biological environments. Spermatozoa assemble into bundles to improve their swimming efficiency compared to individual cells. However, the dynamic mechanisms for the formation of sperm bundles have not been fully characterized. In this study, we numerically and experimentally investigate the locomotion of spermatozoa during the transition from individual cells to bundles of two cells. Three consecutive dynamic behaviors are found across the course of the transition: hydrodynamic attraction/repulsion, alignment, and synchronization. The hydrodynamic attraction/repulsion depends on the relative orientation and distance between spermatozoa as well as their flagellar wave patterns and phase shift. Once the heads are attached, we find a stable equilibrium of the rotational hydrodynamics resulting in the alignment of the heads. The synchronization results from the combined influence of hydrodynamic and mechanical cell-to-cell interactions. Additionally, we find that the flagellar beat is regulated by the interactions during the bundle formation, whereby spermatozoa can synchronize their beats to enhance their swimming velocity.

JTD Keywords: behavior, cilia, collective locomotion, collective motion, competition, flagellar propulsion, hydrodynamics, motility, propulsion, sperm cooperation, tracking, Collective locomotion, Flagellar propulsion, Flagellar synchronization, Spermatozoa bundle

The principles underlying the biomechanics of morphogenesis are largely unknown. Epiboly is an essential embryonic event in which three tissues coordinate to direct the expansion of the blastoderm. How and where forces are generated during epiboly, and how these are globally coupled remains elusive. Here we developed a method, hydrodynamic regression (HR), to infer 3D pressure fields, mechanical power, and cortical surface tension profiles. HR is based on velocity measurements retrieved from 2D+T microscopy and their hydrodynamic modeling. We applied HR to identify biomechanically active structures and changes in cortex local tension during epiboly in zebrafish. Based on our results, we propose a novel physical description for epiboly, where tissue movements are directed by a polarized gradient of cortical tension. We found that this gradient relies on local contractile forces at the cortex, differences in elastic properties between cortex components and the passive transmission of forces within the yolk cell. All in all, our work identifies a novel way to physically regulate concerted cellular movements that might be instrumental for the mechanical control of many morphogenetic processes.

JTD Keywords: Epiboly, Hydrodynamics, Mechanics, Morphogenesis, Zebrafish