arXiv subjects

Michael M. Norton

Publications and source records attributed to Michael M. Norton.

17 recordsLinked to original sources

arXiv2025

3D pattern formation of a protein-membrane suspension

Many essential cellular processes, including cell division and the establishment of cell polarity during embryogenesis, are regulated by pattern-forming proteins. These proteins often need to bind to a substrate, such as the cell membrane, onto which they interact and form two-dimensional (2D) patterns. It is unclear how the membrane's continuity and dimensionality impact pattern formation. Here, we address this gap using the MinDE system, a prototypical example of pattern-forming membrane proteins. We show that when the lipid substrate is fragmented into submicrometer-sized diffusive liposomes, ATP-driven protein-protein interactions generate three-dimensional (3D) spatially extended patterns, despite the complete loss of membrane continuity. Remarkably, these 3D patterns emerge at scales four orders of magnitude larger than the individual liposomes. By systematically varying protein concentration, liposome size, and density, we observed and characterized a variety of 3D dynamical patterns not seen on continuous 2D membranes, including traveling waves, dynamical spirals, and a coexistence phase. Simulations and linear stability analysis of a coarse-grained model revealed that the physical properties of the dispersed membrane effectively rescale both the protein-membrane binding rates and diffusion, two key parameters governing pattern formation and wavelength selection. These findings highlight the robustness of Min's pattern-forming ability, suggesting that protein-membrane suspensions could serve as an adaptable template for studying out-of-equilibrium self-organization in 3D, beyond in vivo contexts.

cond-mat.soft↗

arXiv2025

Emergence of Anti-chemotactic Flocking in Active Biomimetic Colloids

Competition for resources is a fundamental constraint that guides the self-organization of natural, biological, and human systems, ranging from urban planning and ecosystem development to intracellular pattern formation. Here, we reveal that competition for resources is at the origin of the collective dynamics that emerge in a population of colloids propelled by actin treadmilling, an out-of-equilibrium process where filaments grow from one end while shrinking from the other. Using a combination of experiments and theory, we show that symmetry-breaking, self-propulsion, and flocking emerge from the local competition for actin monomers. We demonstrate that beads propelled by actin treadmilling are anti-chemotactic and spontaneously generate asymmetric actin gradients that trigger and sustain directed motility. Flocking emerges from the combined effects of anti-chemotaxis and local competition for monomers. The flocking transition depends on the actin polymerization rate, actin monomer diffusivity, and the bead's motility, whose interplay controls the emergence of short-range attractive interactions between the colloids. Our findings demonstrate that active stress generation coupled to reaction-diffusion is a generic mechanism that can lead to a multiscale cascade of behaviors when active agents remodel their environment. Actin treadmilling offers a platform to study how motile agents that interact through a field self-organize in novel dynamical phases, with potential applications in non-reciprocal and trainable active matter.

cond-mat.soft↗

arXiv2024

Closed-loop control of active nematic flows

Living things enact control of non-equilibrium, dynamical structures through complex biochemical networks, accomplishing spatiotemporally-orchestrated physiological tasks such as cell division, motility, and embryogenesis. While the exact minimal mechanisms needed to replicate these behaviors using synthetic active materials are unknown, controlling the complex, often chaotic, dynamics of active materials is essential to their implementation as engineered life-like materials. Here, we demonstrate the use of external feedback control to regulate and control the spatially-averaged speed of a model active material with time-varying actuation through applied light. We systematically vary the controller parameters to analyze the steady-state flow speed and temporal fluctuations, finding the experimental results in excellent agreement with predictions from both a minimal coarse-grained model and full nematohydrodynamic simulations. Our findings demonstrate that proportional-integral control can effectively regulate the dynamics of active nematics in light of challenges posed by the constituents, such as sample aging, protein aggregation, and sample-to-sample variability. As in living things, deviations of active materials from their steady-state behavior can arise from internal processes and we quantify the important consequences of this coupling on the controlled behavior of the active nematic. Finally, the interaction between the controller and the intrinsic timescales of the active material can induce oscillatory behaviors in a regime of parameter space that qualitatively matches predictions from our model. This work underscores the potential of feedback control in manipulating the complex dynamics of active matter, paving the way for more sophisticated control strategies in the design of responsive, life-like materials.

cond-mat.soft↗

arXiv2024

Mechanochemical Topological Defects in an Active Nematic

We propose a reaction-diffusion system that converts topological information of an active nematic into chemical signals. We show that a curvature-activated reaction dipole is sufficient for creating a system that dynamically senses topology by producing a concentration field possessing local extrema coinciding with $\pm\frac{1}{2}$ defects. The enabling term is analogous to polarization charge density seen in dielectric materials. We demonstrate the ability of this system to identify defects in both passive and active nematics. The model demonstrates that a relatively simple feedback scheme in the form of a PDE system is capable of producing chemical signals in response to inherently non-local structures in anisotropic media. We posit that such coarse-grained systems can help generate testable hypotheses for regulated processes in biological systems such as morphogenesis and motivate the creation of bioinspired materials that utilize dynamic coupling between nematic structure and biochemistry.

cond-mat.soft↗

arXiv2023

Exploring regular and turbulent flow states in active nematic channel flow via Exact Coherent Structures and their invariant manifolds

This work is a unified study of stable and unstable steady states of 2D active nematic channel flow using the framework of Exact Coherent Structures (ECS). ECS are stationary, periodic, quasiperiodic, or traveling wave solutions of the governing equations that, together with their invariant manifolds, organize the dynamics of nonlinear continuum systems. We extend our earlier work on ECS in the preturbulent regime by performing a comprehensive study of stable and unstable ECS for a wide range of activity values spanning the preturbulent and turbulent regimes. In the weakly turbulent regime, we compute more than 200 unstable ECS that co-exist at a single set of parameters, and uncover the role of symmetries in organizing the phase space geometry. We provide conclusive numerical evidence that in the preturbulent regime, generic trajectories shadow a series of unstable ECS before settling onto an attractor. Finally, our studies hint at shadowing of quasiperiodic type ECS in the turbulent regime.

physics.flu-dyn↗

arXiv2023

From Disks to Channels: Dynamics of Active Nematics Confined to an Annulus

Confinement can be used to systematically tame turbulent dynamics occurring in active fluids. Although periodic channels are the simplest geometries to study confinement numerically, the corresponding experimental realizations require closed racetracks. Here, we computationally study 2D active nematics confined to such a geometry -- an annulus. By systematically varying the annulus inner radius and channel width, we bridge the behaviors observed in the previously studied asymptotic limits of the annulus geometry: a disk and an infinite channel. We identify new steady-state behaviors, which reveal the influence of boundary curvature and its interplay with confinement. We also show that, below a threshold inner radius, the dynamics are insensitive to topological constraints imposed by boundary conditions. We explain this insensitivity through a simple scaling analysis. Our work sheds further light on design principles for using confinement to control the dynamics of active nematics.

cond-mat.soft↗

arXiv2021

A Generalized Unscented Transformation for Probability Distributions

The unscented transform uses a weighted set of samples called sigma points to propagate the means and covariances of nonlinear transformations of random variables. However, unscented transforms developed using either the Gaussian assumption or a minimum set of sigma points typically fall short when the random variable is not Gaussian distributed and the nonlinearities are substantial. In this paper, we develop the generalized unscented transform (GenUT), which uses 2n+1 sigma points to accurately capture up to the diagonal components of the skewness and kurtosis tensors of most probability distributions. Constraints can be analytically enforced on the sigma points while guaranteeing at least second-order accuracy. The GenUT uses the same number of sigma points as the original unscented transform while also being applicable to non-Gaussian distributions, including the assimilation of observations in the modeling of infectious diseases such as coronavirus (SARS-CoV-2) causing COVID-19.

stat.ME↗

arXiv2021

Exact coherent structures and phase space geometry of pre-turbulent 2D active nematic channel flow

Confined active nematics exhibit rich dynamical behavior, including spontaneous flows, periodic defect dynamics, and chaotic `active turbulence'. Here, we study these phenomena using the framework of Exact Coherent Structures, which has been successful in characterizing the routes to high Reynolds number turbulence of passive fluids. Exact Coherent Structures are stationary, periodic, quasiperiodic, or traveling wave solutions of the hydrodynamic equations that, together with their invariant manifolds, serve as an organizing template of the dynamics. We compute the dominant Exact Coherent Structures and connecting orbits in a pre-turbulent active nematic channel flow, which enables a fully nonlinear but highly reduced order description in terms of a directed graph. Using this reduced representation, we compute instantaneous perturbations that switch the system between disparate spatiotemporal states occupying distant regions of the infinite dimensional phase space. Our results lay the groundwork for a systematic means of understanding and controlling active nematic flows in the moderate to high activity regime.

cond-mat.soft↗

arXiv2021

Multiscale Microtubule Dynamics in Active Nematics

In microtubule-based active nematics, motor-driven extensile motion of microtubule bundles powers chaotic large-scale dynamics. We quantify the interfilament sliding motion both in isolated bundles and in a dense active nematic. The extension speed of an isolated microtubule pair is comparable to the molecular motor stepping speed. In contrast, the net extension in dense 2D active nematics is significantly slower; the interfilament sliding speeds are widely distributed about the average and the filaments exhibit both contractile and extensile relative motion. These measurements highlight the challenge of connecting the extension rate of isolated bundles to the multi-motor and multi-filament interactions present in a dense 2D active nematic. They also provide quantitative data that is essential for building multiscale models.

cond-mat.soft↗

arXiv2021

The Symmetry Basis of Pattern Formation in Reaction-Diffusion Networks

In networks of nonlinear oscillators, symmetries place hard constraints on the system that can be exploited to predict universal dynamical features and steady-states, providing a rare generic organizing principle for far-from-equilibrium systems. However, the robustness of this class of theories to symmetry-disrupting imperfections is untested. Here, we develop a model experimental reaction-diffusion network of chemical oscillators to test applications of this theory in the context of self-organizing systems relevant to biology and soft robotics. The network is a ring of 4 identical microreactors containing the oscillatory Belousov-Zhabotinsky reaction coupled to nearest neighbors via diffusion. Assuming perfect symmetry, theory predicts 4 categories of stable spatiotemporal phase-locked periodic states and 4 categories of invariant manifolds that guide and structure transitions between phase-locked states. In our experiments, we observed the predicted symmetry-derived synchronous clustered transients that occur when the dynamical trajectories coincide with invariant manifolds. However, we observe only 3 of the 4 phase-locked states that are predicted for the idealized homogeneous system. Quantitative agreement between experiment and numerical simulations is found by accounting for the small amount of experimentally determined heterogeneity. This work demonstrates that a surprising degree of the network's dynamics are constrained by symmetry in spite of the breakdown of the assumption of homogeneity and raises the question of why heterogeneity destabilizes some symmetry predicted states, but not others.

nlin.PS↗

arXiv2020

Machine Learning Forecasting of Active Nematics

Active nematics are a class of far-from-equilibrium materials characterized by local orientational order of force-generating, anisotropic constitutes. Traditional methods for predicting the dynamics of active nematics rely on hydrodynamic models, which accurately describe idealized flows and many of the steady-state properties, but do not capture certain detailed dynamics of experimental active nematics. We have developed a deep learning approach that uses a Convolutional Long-Short-Term-Memory (ConvLSTM) algorithm to automatically learn and forecast the dynamics of active nematics. We demonstrate our purely data-driven approach on experiments of 2D unconfined active nematics of extensile microtubule bundles, as well as on data from numerical simulations of active nematics.

cond-mat.soft↗

arXiv2020

Optimal Control of Active Nematics

In this work we present the first systematic framework to sculpt active nematics systems, using optimal control theory and a hydrodynamic model of active nematics. We demonstrate the use of two different control fields, (1) applied vorticity and (2) activity strength, to shape the dynamics of an extensile active nematic that is confined to a disk. In the absence of control inputs, the system exhibits two attractors, clockwise and counterclockwise circulating states characterized by two co-rotating topological $+\frac{1}{2}$ defects. We specifically seek spatiotemporal inputs that switch the system from one attractor to the other; we also examine phase-shifting perturbations. We identify control inputs by optimizing a penalty functional with three contributions: total control effort, spatial gradients in the control, and deviations from the desired trajectory. This work demonstrates that optimal control theory can be used to calculate non-trivial inputs capable of restructuring active nematics in a manner that is economical, smooth, and rapid, and therefore will serve as a guide to experimental efforts to control active matter.

cond-mat.soft↗

arXiv2019

Dynamics of Reaction-Diffusion Oscillators in Star Networks

We experimentally and theoretically investigate the dynamics of inhibitory coupled self-driven oscillators on a star network in which a single central hub node is connected to $k$ peripheral arm nodes. The system consists of water-in-oil Belousov-Zhabotinsky $\sim$100$μ$m emulsion drops contained in storage wells etched in silicon wafers. We observed three dynamical attractors by varying the number of arms in the star graph and the coupling strength; ($i$) unlocked; uncorrelated phase shifts between all oscillators, ($ii$) locked; arm-hubs synchronized in-phase with a $k$-dependent phase shift between the arm and central hub, and ($iii$) center silent; central hub stopped oscillating and the arm-hubs oscillated without synchrony. We compare experiment to theory. For case ($ii$), we identified a logarithmic dependence of the phase shift on star degree, and were able to discriminate between contributions to the phase shift arising from star topology and oscillator chemistry.

nlin.AO↗

arXiv2019

Self-organized dynamics and the transition to turbulence of confined active nematics

We study how confinement transforms the chaotic dynamics of bulk microtubule-based active nematics into regular spatiotemporal patterns. For weak confinements, multiple continuously nucleating and annihilating topological defects self-organize into persistent circular flows of either handedness. Increasing confinement strength leads to the emergence of distinct dynamics, in which the slow periodic nucleation of topological defects at the boundary is superimposed onto a fast procession of a pair of defects. A defect pair migrates towards the confinement core over multiple rotation cycles, while the associated nematic director field evolves from a distinct double spiral towards a nearly circularly symmetric configuration. The collapse of the defect orbits is punctuated by another boundary-localized nucleation event, that sets up long-term doubly-periodic dynamics. Comparing experimental data to a theoretical model of an active nematic, reveals that theory captures the fast procession of a pair of $+\frac{1}{2}$ defects, but not the slow spiral transformation nor the periodic nucleation of defect pairs. Theory also fails to predict the emergence of circular flows in the weak confinement regime. The developed confinement methods are generalized to more complex geometries, providing a robust microfluidic platform for rationally engineering two-dimensional autonomous flows.

cond-mat.soft↗

arXiv2017

Dynamics of nanoscale bubbles growing in a tapered conduit

We predict the dynamics and shapes of nanobubbles growing in a supersaturated solution confined within a tapered, Hele-Shaw device with a small opening angle $Φ\ll 1$. Our study is inspired by experimental observations of the growth and translation of nanoscale bubbles, ranging in diameter from tens to hundreds of nanometers, carried out with liquid-cell transmission electron microscopy. In our experiments, the electron beam plays a dual role: it supersaturates the solution with gaseous radiolysis products, which lead to bubble nucleation and growth, and it provides a means to image the bubbles in-situ with nanoscale resolution. To understand our experimental data, we propose a migration mechanism, based on Blake-Haynes theory, which is applicable in the asymptotic limits of zero capillary and Bond numbers and high confinement. Consistent with experimental data, our model predicts that in the presence of confinement, growth rates are orders of magnitude slower compared to a bubble growing in the bulk and that the combination of a tapered channel and contact line pinning create tear-drop shaped bubbles.

physics.flu-dyn↗

arXiv2017

Insensitivity of active nematic dynamics to topological constraints

Confining a liquid crystal imposes topological constraints on the orientational order, allowing global control of equilibrium systems by manipulation of anchoring boundary conditions. In this article, we investigate whether a similar strategy allows control of active liquid crystals. We study a hydrodynamic model of an extensile active nematic confined in containers, with different anchoring conditions that impose different net topological charges on the nematic director. We show that the dynamics are controlled by a complex interplay between topological defects in the director and their induced vortical flows. We find three distinct states by varying confinement and the strength of the active stress: a topologically minimal state, a circulating defect state, and a turbulent state. In contrast to equilibrium systems, we find that anchoring conditions are screened by the active flow, preserving system behavior across different topological constraints. This observation identifies a fundamental difference between active and equilibrium materials.

cond-mat.soft↗

arXiv2017

Engineering reaction-diffusion networks with properties of neural tissue

We present an experimental system of networks of coupled non-linear chemical reactors, which we theoretically model within a reaction-diffusion framework. The networks consist of patterned arrays of diffusively coupled nanoliter-scale reactors containing the Belousov- Zhabotinsky (BZ) reaction. Microfluidic fabrication techniques are developed that provide the ability to vary the network topology, the reactor coupling strength and offer the freedom to choose whether an arbitrary reactor is inhibitory or excitatory coupled to its neighbor. This versatile experimental and theoretical framework can be used to create a wide variety of chemical networks. Here we design, construct and characterize chemical networks that achieve the complexity of central pattern generators (CPGs), which are found in the autonomic nervous system of a variety of organisms.

nlin.PS↗