Emergent programmable behavior and chaos in dynamically driven active filaments

Kinetically arrested periodic clusters in active filament arrays

We study the dynamics and pattern formation of ordered arrays of active semi-flexible filaments, each of which is pinned at one end and free at the other. The filaments are modeled as connected chains of polar active particles with activity incorporated through local follower forces acting along their local tangent. Using Brownian dynamics simulations in two dimensions, we show that for a range of activity and filament separation, the filament array self-assembles into regularly spaced, kinetically arrested compact clusters. Activity, array geometry, filament elasticity, and grafting density are each seen to crucially influence the show size, shape, and spacing of these emergent clusters. Furthermore, cluster shapes for different grafting densities can be rescaled into self-similar forms with activity-dependent scaling exponents. We derive theoretical expressions that relate the number of filaments in a cluster and the spacing between adjacent clusters to filament activity, filament elasticity, and grafting density. Our results provide insight into the physical mechanisms involved in the initiation of clustering and suggest that steric contact forces and friction balance active forces and filament elasticity to shape and stabilize emergence clusters.

Biological computations: Limitations of attractor-based formalisms and the need for transients

Living systems, from single cells to higher vertebrates, receive a continuous stream of non-stationary inputs that they sense, for e.g. via cell surface receptors or sensory organs. By integrating these time-varying, multi-sensory, and often noisy information with memory using complex molecular or neuronal networks, they generate a variety of responses beyond simple stimulus-response association, including avoidance behavior, life-long-learning or social interactions. In a broad sense, these processes can be understood as a type of biological computation. Taking as a basis generic features of biological computations, such as real-time responsiveness or robustness and flexibility of the computation, we highlight the limitations of the current attractor-based framework for understanding computations in biological systems. We argue that frameworks based on transient dynamics away from attractors are better suited for the description of computations performed by neuronal and signaling networks. In particular, we discuss how quasi-stable transient dynamics from ghost states that emerge at criticality have a promising potential for developing an integrated framework of computations, that can help us understand how living system actively process information and learn from their continuously changing environment.

Curved crease origami and topological singularities enable hyperextensibility of L. olor

Fundamental limits of cellular deformations, such as hyperextension of a living cell, remain poorly understood. Here, we describe how the single-celled protist Lacrymaria olor, a 40-micrometer cell, is capable of reversibly and repeatably extending its necklike protrusion up to 1200 micrometers in 30 seconds. We discovered a layered cortical cytoskeleton and membrane architecture that enables hyperextensions through the folding and unfolding of cellular-scale origami. Physical models of this curved crease origami display topological singularities, including traveling developable cones and cytoskeletal twisted domain walls, which provide geometric control of hyperextension. Our work unravels how cell geometry encodes behavior in single cells and provides inspiration for geometric control in microrobotics and deployable architectures.

Conformation and dynamics of partially active linear polymers

We perform numerical simulations of isolated, partially active polymers, driven out-of-equilibrium by a fraction of their monomers. We show that, if the active beads are all gathered in a contiguous block, the position of the section along the chain determines the conformational and dynamical properties of the system. Notably, one can modulate the diffusion coefficient of the polymer from active-like to passive-like just by changing the position of the active block. Further, we show that a slight modification of the self-propulsion rule may give rise to an enhancement of diffusion under certain conditions, despite a decrease of the overall polymer activity. Our findings may help in the modelisation of active biophysical systems, such as filamentous bacteria or worms.

Curved crease origami and topological singularities at a cellular scale enable hyper-extensibility of Lacrymaria olor

Eukaryotic cells undergo dramatic morphological changes during cell division, phagocytosis and motility. Fundamental limits of cellular morphodynamics such as how fast or how much cellular shapes can change without harm to a living cell remain poorly understood. Here we describe hyper-extensibility in the single-celled protist Lacrymaria olor, a 40 μm cell which is capable of reversible and repeatable extensions (neck-like protrusions) up to 1500 μm in 30 seconds. We discover that a unique and intricate organization of cortical cytoskeleton and membrane enables these hyper-extensions that can be described as the first cellular scale curved crease origami. Furthermore, we show how these topological singularities including d-cones and twisted domain walls provide a geometrical control mechanism for the deployment of membrane and microtubule sheets as they repeatably spool thousands of time from the cell body. We lastly build physical origami models to understand how these topological singularities provide a mechanism for the cell to control the hyper-extensile deployable structure. This new geometrical motif where a cell employs curved crease origami to perform a physiological function has wide ranging implications in understanding cellular morphodynamics and direct applications in deployable micro-robotics.

Emergent programmable behavior and chaos in dynamically driven active filaments

How the behavior of cells emerges from their constituent subcellular biochemical and physical parts is an outstanding challenge at the intersection of biology and physics. A remarkable example of single-cell behavior occurs in the ciliate Lacrymaria olor, which hunts for its prey via rapid movements and protrusions of a slender neck, many times the size of the original cell body. The dynamics of this cell neck is powered by a coat of cilia across its length and tip. How a cell can program this active filamentous structure to produce desirable behaviors like search and homing to a target remains unknown. Here, we present an active filament model that allows us to uncover how a "program" (time sequence of active forcing) leads to "behavior" (filament shape dynamics). Our model captures two key features of this system-time-varying activity patterns (extension and compression cycles) and active stresses that are uniquely aligned with the filament geometry-a "follower force" constraint. We show that active filaments under deterministic, time-varying follower forces display rich behaviors including periodic and aperiodic dynamics over long times. We further show that aperiodicity occurs due to a transition to chaos in regions of a biologically accessible parameter space. We also identify a simple nonlinear iterated map of filament shape that approximately predicts long-term behavior suggesting simple, artificial "programs" for filament functions such as homing and searching space. Last, we directly measure the statistical properties of biological programs in L. olor, enabling comparisons between model predictions and experiments.