Machine learning active-nematic hydrodynamics

Physical Review E

Uniaxial rods in a nematic phase diffuse preferentially in the direction parallel to the nematic directorn. The nematic director fieldn(r) of a chiral twist-bend nematic (N TB) phase of achiral banana-shaped particles, recently discovered experimentally, displays a heliconical twist of given handedness and periodicity. Using simulations, we investigate the long-time macroscopic diffusion in N TB phases, and find that the predilection of curved rods to diffuse in the direction of the twistingn(r) yields a fascinating chiral dynamics along helices, even though achiral curved rods display Brownian motion with a nontrivial rototranslational coupling. We devise a machine learning protocol to characterize the helicoidal particle trajectories, finding that their pitch and radius are determined by the pitch and conical angle of the N TB phase thereby connecting its structural and dynamical properties.

Proceedings of the National Academy of Sciences, 2015

Significance Animals have muscles to act on their environment. The molecules endowing them with this faculty are actin and myosin and are also present in nonmuscle cells. Our modelling breaks down the motor-like properties of the actomyosin network in single nonmuscle cells, which show striking similarity to the properties of muscles. In particular, an internal friction sets the maximum speed of contraction of both cells and muscles when myosins do not have time to detach after pulling, just as rowers lifting their oars too slowly after their stroke. The same modelling explains cell-scale mechanosensing: the combination of myosin-driven contraction and actin polymerization-driven protrusivity regulates cell length in a force-dependent manner, making response to rigidity a property of the very material of the cell cortex.

Fluids

Simulations of fluid flows at the nanoscale feature massive data production and machine learning (ML) techniques have been developed during recent years to leverage them, presenting unique results. This work facilitates ML tools to provide an insight on properties among molecular dynamics (MD) simulations, covering missing data points and predicting states not previously located by the simulation. Taking the fluid flow of a simple Lennard-Jones liquid in nanoscale slits as a basis, ML regression-based algorithms are exploited to provide an alternative for the calculation of transport properties of fluids, e.g., the diffusion coefficient, shear viscosity and thermal conductivity and the average velocity across the nanochannels. Through appropriate training and testing, ML-predicted values can be extracted for various input variables, such as the geometrical characteristics of the slits, the interaction parameters between particles and the flow driving force. The proposed technique co...

Complexity, 2007

S elf-organization has been a hot topic in the second half of last century when physicists and chemists discovered a variety of nonequilibrium phenomena that could be subsumed under a common heading. Self-organizing systems form ordered states in space and time spontaneously and without an external template. The patterns are characterized as dissipative structures because their maintenance requires a flow of energy or matter. After introducing a flow of increasing strength into a system at equilibrium, patterns form instantaneously at certain critical values of the flux. In the language of dynamical systems theory the patterns emerge at bifurcation points corresponding to some critical intensity of the flow. At present we know many well-studied examples of self-organizing systems at many time scales and largely different spatial extensions. Examples are the gigantic red spot on Jupiter, cloud patterns in the atmosphere, the Bénard phenomenon in the coffee cup, the Taylor-Cuvette flow, the Belusov-Zhabotinskii reaction, Liesegang rings, and many other nonlinear phenomena. 2 Recent progress in all fields where self-organization is important confirmed the original concepts and, in addition, gave rise to a new formulation of the old paradigms that allows for a distinction of different forms of self-organizing dynamics in physics, chemistry, and biology. We distinguish here three cases that involve different levels of complexity: self-organization of (i) structure, (ii) function, and (iii) intention or seeming purpose. Structural self-organization became a central issue of nonequilibrium dynamics ever since Alan Turing published his seminal work on chemical morphogenesis [1]. Turing suggested a chemical mechanism based on slow diffusion of an activator and fast diffusion of an inhibitor that can lead to spontaneous formation of stable stationary nonequilibrium patterns through diffusion of some key compounds and argued that such a mechanism could be responsible for the formation of biological patterns. It took 20 years before the Turing mechanism was incorporated into a conceptual framework for pattern formation in early embryonic development that results eventually in the patterns we find in adult organisms [2-6]. Activator and inhibitor are thought to represent two "morphogens," leading to short-range activation and long-range inhibition. For a long time no diffusing morphogen was known in developmental biology and, more-After introducing a flow of increasing strength into a system at equilibrium, patterns form instantaneously at certain critical values of the flux.

BMC Biology

Background The dynamics of the actomyosin machinery is at the core of many important biological processes. Several relevant cellular responses such as the rhythmic compression of the cell cortex are governed, at a mesoscopic level, by the nonlinear interaction between actin monomers, actin crosslinkers, and myosin motors. Coarse-grained models are an optimal tool to study actomyosin systems, since they can include processes that occur at long time and space scales, while maintaining the most relevant features of the molecular interactions. Results Here, we present a coarse-grained model of a two-dimensional actomyosin cortex, adjacent to a three-dimensional cytoplasm. Our simplified model incorporates only well-characterized interactions between actin monomers, actin crosslinkers and myosin, and it is able to reproduce many of the most important aspects of actin filament and actomyosin network formation, such as dynamics of polymerization and depolymerization, treadmilling, network ...

Journal of Scientific Computing

Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode model equations, like Partial Differential Equations (PDE), as a component of the neural network itself. PINNs are nowadays used to solve PDEs, fractional equations, integral-differential equations, and stochastic PDEs. This novel methodology has arisen as a multi-task learning framework in which a NN must fit observed data while reducing a PDE residual. This article provides a comprehensive review of the literature on PINNs: while the primary goal of the study was to characterize these networks and their related advantages and disadvantages. The review also attempts to incorporate publications on a broader range of collocation-based physics informed neural networks, which stars form the vanilla PINN, as well as many other variants, such as physics-constrained neural networks (PCNN), variational hp-VPINN, and conservative PINN (CPINN). The study indicates that most research has focused on customizing the P...

Nature Physics, 2019

Active nematics are out-of-equilibrium fluids composed of rod-like subunits, which can generate large-scale, self-driven flows. We examine a microtubule-kinesin-based active nematic confined to two-dimensions, exhibiting chaotic flows with moving topological defects. Applying tools from chaos theory, we investigate self-driven advection and mixing on different length scales. Local fluid stretching is quantified by the Lyapunov exponent. Global mixing is quantified by the topological entropy, calculated from both defect braiding and curve extension rates. We find excellent agreement between these independent measures of chaos, demonstrating that the extensile stretching between microtubules directly translates into macroscopic braiding of positive defects. Remarkably, increasing extensile activity (via ATP concentration) does not increase the dimensionless topological entropy. This study represents the first application of chaotic advection to the emerging field of active nematics and the first time that the collective motion of an ensemble of defects has been quantified (via topological entropy) in a liquid crystal.

Topological defects in the nematic order of actin fibres as organization centres of Hydra morphogenesis, 2021

A nimal morphogenesis involves multiple mechanical and biochemical processes, spanning several orders of magnitude in space and time, from local dynamics at the molecular level to global, organism-scale morphology. How these numerous processes are coordinated and integrated across scales to form robust, functional outcomes remains an outstanding question 1-4. Developing an effective, coarse-grained description of morphogenesis can provide essential insights towards addressing this important challenge. Here we focus on whole-body regeneration in Hydra, a small freshwater predatory animal, and provide an effective description of the mor-phogenesis process that is based on the dynamic organization of the supracellular actin fibres in regenerating tissues 5,6. Hydra is a classic model system for morphogenesis, owing to its simple body plan and remarkable regeneration capabilities. Historically, research on Hydra regeneration inspired the development of many of the fundamental concepts on the biochemical basis of morphogenesis, including the role of an 'organizer' 7 , the idea of pattern formation by reaction-diffusion dynamics of mor-phogens 8,9 and the concept of positional information 10. However, in these studies, as well as in the majority of subsequent works, the role of mechanics in Hydra morphogenesis was largely overlooked. Here we revisit this classic model system, and investigate the cytoskeletal dynamics during the regeneration process from a biophysical point of view, revealing a relation between cytoskeletal organization and the morphogenesis process. A mature Hydra has a simple uniaxial body plan, with a head on one end and a foot on the other. Its tubular body consists of a double layer of epithelial cells, which contain highly organized arrays of parallel supracellular actin fibres (Extended Data Fig. 1). The fibres are globally aligned along the body axis in the outer (ectoderm) layer, and perpendicular to the body axis in the inner (endoderm) layer 5. The actin fibres are decorated with myosin motors, forming contractile bundles called myonemes, which are akin to muscular structures in other organisms. The fibres lie along the basal surfaces of each epithelial layer and are connected through cell-cell junctions to form supracellular bundles, which exhibit long-range directional order over scales comparable to the size of the animal, ranging from ~300 μm in small regenerated Hydra to several millimetres in fully grown Hydra. The myonemes are coupled via adhesion complexes to a thin, viscoelastic extracellular matrix layer (the mesoglea) sandwiched between the two cell layers (Extended Data Fig. 1) 11. Large-scale supracellular arrays of contractile actin-myosin fibres are a common organizational theme found in many animal tissues 12-14. Although the mechanism for the development of these parallel fibre arrays is not entirely clear, mechanical feedback has been shown to play a central role in their formation and alignment 14,15. Such parallel alignment is characteristic of systems with nematic order; that is, systems in which the microscopic constituents tend to locally align parallel to each other, exhibiting long-range orientational order 16. Nematic systems can be described by a director field that denotes the local orientation, and its spatio-temporal evolution reflects the dynamics of the system. Such systems can be further classified as 'active' if their constituents consume energy and generate forces, giving rise to a wealth of interesting dynamic behaviours 17. Recently, the framework of active nematics has been found to be informative in understanding various phenomena in a variety of biophysical systems 17,18 including in vitro cytoskeletal networks 19-23 , cell monolayers 24-26 and bacterial cultures 27. Here we describe the organization of the supracellular actin fibres in regenerating Hydra as an active nematic system. Hydra contains two distinct perpendicular arrays of nematic supracellular actin fibres in the ectoderm and in the endoderm (Extended Data Fig. 1). Here we primarily consider the thicker and more continuous ectodermal actin fibres, which are the most prominent cytoskeletal feature affecting Hydra mechanics 5,6. The director field describing the alignment of the ectodermal fibres defines a Topological defects in the nematic order of actin fibres as organization centres of Hydra morphogenesis Animal morphogenesis arises from the complex interplay between multiple mechanical and biochemical processes with mutual feedback. Developing an effective, coarse-grained description of morphogenesis is essential for understanding how these processes are coordinated across scales to form robust, functional outcomes. Here we show that the nematic order of the supra-cellular actin fibres in regenerating Hydra defines a slowly varying field, whose dynamics provide an effective description of the morphogenesis process. We show that topological defects in this field, which are long-lived yet display rich dynamics, act as organization centres with morphological features developing at defect sites. These observations suggest that the nematic orientation field can be considered a 'mechanical morphogen' whose dynamics, in conjugation with various biochemical and mechanical signalling processes, result in the robust emergence of functional patterns during morphogenesis. NATurE PhYSicS | www.nature.com/naturephysics

2012

Non-equilibrium processes which convert chemical energy into mechanical motion enable the motility of organisms. Bundles of inextensible filaments driven by energy transduction of molecular motors form essential components of micron-scale motility engines like cilia and flagella. The mimicry of cilia-like motion in recent experiments on synthetic active filaments supports the idea that generic physical mechanisms may be sufficient to generate such motion. Here we show, theoretically, that the competition between the destabilising effect of hydrodynamic interactions induced by force-free and torque-free chemomechanically active flows, and the stabilising effect of nonlinear elasticity, provides a generic route to spontaneous oscillations in active filaments. These oscillations, reminiscent of prokaryotic and eukaryotic flagellar motion, are obtained without having to invoke structural complexity or biochemical regulation. This minimality implies that biomimetic oscillations, previously observed only in complex bundles of active filaments, can be replicated in simple chains of generic chemomechanically active beads.

Recent experiments imaging fluid flow around swimming microorganisms have revealed complex time-dependent velocity fields that differ qualitatively from the stresslet flow commonly employed in theoretical descriptions of active matter. Here we obtain the most general flow around a finite sized active particle by expanding the surface stress in irreducible Cartesian tensors. This expansion, whose first term is the stresslet, must include, respectively, third-rank polar and axial tensors to minimally capture crucial features of the active oscillatory flow around translating Chlamydomonas and the active swirling flow around rotating Volvox. The representation provides explicit expressions for the irreducible symmetric, antisymmetric and isotropic parts of the continuum active stress. Antisymmetric active stresses do not conserve orbital angular momentum and our work thus shows that spin angular momentum is necessary to restore angular momentum conservation in continuum hydrodynamic descriptions of active soft matter.