Session S35: Control Strategies in Soft Matter and Biological Systems

Three ways to control dynamical systems robustly

Robustness is widely considered a desirable feature for a decision strategy, yet the concept itself is often only loosely defined.   In this talk, I review three classes of strategies for controlling dynamical systems robustly:  feedforward, feedback, and worst case.  The first class, feedforward strategies, control the dynamics knowing only the initial state of the system and thus do not require sensors.  Surprisingly, there are systematic ways to make feedforward commands more robust, combining damping and clever manipulations of control parameters.  I illustrate the basic ideas on a toy model (transport of a harmonic oscillator) that is related to the problem of designing broadband antireflection coatings in optics.  Another example is the control of the time it takes a eukaryotic cell to complete DNA replication.  The second class of strategies is to apply feedback.  Generic feedback strategies are effective for simple systems subject to small disturbances and are widely used in biological systems, for example to reduce variations in transcription levels (proportional feedback) or to give robustness against constant disturbances in chemotaxis (integral feedback).  More general feedback strategies linearize about nonlinear feedforward commands generated using optimal control and again are effective for moderate disturbances and uncertainties.   But these local feedback techniques can fail in the face of larger uncertainties, leading to a third class of “worst-case” control strategies having roots in game theory, economics and notions of risk.   The main idea is to partition events into two classes, “normal” and “disaster,”and optimize among normal events assuming that one encounters the worst case among that set.  Disasters are dealt with via contingency plans.  Too often, the partition process itself is not made explicit, and the implicit choices become apparent only when disaster strikes.  I argue for a more up-front accounting of partitioning.   

Controlling the nonlinear configuration space of mechanical and dynamical systems

From decision making in neural systems to cooperativity in proteins, soft and biological systems exhibit an extraordinarily diverse yet carefully crafted complexity. The specific interactions between constituent elements such as neurons and amino acids enforce dynamical and mechanical constraints, thereby enabling these systems to evolve according to the precise algorithms that govern biological functions such as neural representations and enzyme catalysis. To control these functions, we require knowledge of both the forward map from known interactions to their corresponding dynamical and mechanical functions, and the inverse map from the desired functions to the interactions that evoke them. However, knowledge of these maps is made difficult due to the nonlinearities in both the interactions and the functions. In this talk, I will discuss several strategies for how to obtain these maps to wield control over the nonlinear configuration space. For dynamical systems, I will demonstrate how to embed nonlinear and controllable dynamics into a recurrent neural network (RNN) via its connectivity weights, and how to decode the dynamics learned by trained RNNs. For mechanical systems, I will demonstrate how to control the nonlinear sequence and geometry of conformational shape change in mechanical linkages.   

Bounds on Information Transfer for Stabilization of Insect Flight

Many insects are passively unstable in flight, requiring active control to remain stable. In the fly, an organ called the haltere measures angular velocities and provides fast feedback directly to the wing muscles, bypassing the brain and allowing flies to stabilize themselves. The clear and specific goal of the halteres makes them ideal for understanding how information flows through a nervous system. Here, we ask how much information must be communicated to the wings to stabilize flight. From these bounds we can begin to ask quantitative functional questions about fly flight stabilization: is fly flight information-efficient, and is it as stable as possible given the fidelity of the halteres as sensors?   

Nonlinear effects of electrical stimulation strength on tissue-scale collective migration

Tissues are essentially agent-based active matter that exhibit numerous complex, essential collective behaviors such as healing. Thus, approaches to formally control the many cells within a tissue as a group are quite valuable, necessitating new control frameworks suitable for large-scale agent-based systems. We have been developing a unique approach to do this in living tissues that harnesses a natural process called electrotaxis—directed cell migration to ionic currents/DC electric fields. Such currents form naturally in tissues due to ion transport, damage, and development. Further, electrotaxis is nearly universal in multicellular organisms, and we have been able to demonstrate numerous examples of steering collective cell migration of 10,000+ cells in tissues spanning kidney, skin, and gut systems by mimicking and shaping these natural electric fields to accelerate healing and accelerate tissue growth. While electrotaxis is clearly powerful, it has nearly entirely been studied as a biological phenomenon rather than as a control framework for living active matter. For instance, even the most basic question of how the strength of an applied DC field affects the group-level collective cell electrotaxis in a tissue is poorly explored. Here, we investigate how tissue-scale electrotaxis varies with electrical stimulation strength and specifically evaluate the spatiotemporal response of epithelial sheets (skin, kidney, etc.). Our preliminary findings demonstrate a distinct difference between the 'bulk' response of the tissue (in the center of a tissue) and the edge effects that varies with increasing field strength. While the bulk 'speed' of collective migration goes up, the edges of the tissue (such as at the edge of an injury) respond differently. Clearly such systems can be optimally controlled, which is what we are pushing towards and will be discussing here.   

Nonequilibrium free energy calculations from time-reversed path ensembles through stochastic optimal control

As free energy calculations come to occupy central roles in research fronts throughout chemistry, physics, biology, and data science, it is timely to address computational cost-efficiency challenges for applications in and out of thermodynamic equilibrium.  For equilibrium applications, free energy calculations relying on extensive sampling of Boltzmann--Gibbs conformational ensembles can prove prohibitively expensive when screening vast swaths of chemical space; for nonequilibrium applications, burgeoning interest in driven systems and active matter has opened a new market for methods to quantify free energy distortions due to persistent currents originating from thermal gradients and active forces.  Both sets of applications are addressed by the fluctuation relations of Jarzynski, Kawasaki, and Crooks, which relate free energy differences to path-wise work/heat averages and suggest ways to enable (in nonequilibrium applications) or accelerate (in equilibrium applications) free energy calculations by reweighing trajectory data from short, irreversible transformations.  Yet, many numerical implementations of fluctuation relations have been fraught with numerical issues due to statistically inefficient choices of the nonequilibrium switching protocol.  In our work, we build from Jarzynski's observed connection between time-reversed driven trajectory ensembles and statistically optimal nonequilibrium averages [C. Jarzynski, Phys. Rev. E  73, 046105 (2006)] to characterize switching protocols that render rare, time-reversed trajectories typical via optimally controlled overdamped Langevin dynamics.  For several test diffusions featuring both additive and multiplicative noise, we adaptively learn optimal switching protocols by fitting a Hilbert or neural-network ansatz to experimental or simulated trajectory data, from which we estimate equilibrium free energy landscapes and their nonequilibrium distortions.   

Curiosity-driven discovery of novel non-equilibrium behaviors

Exploring the spectrum of novel behaviors a physical system can produce can be a labor-intensive task. Active learning is a collection of iterative sampling techniques developed in response to this challenge. However, these techniques often require a pre-defined metric, such as distance in a space of known order parameters, in order to guide the search for new behaviors. Order parameters are rarely known for non-equilibrium systems a priori, especially when possible behaviors are also unknown, creating a chicken-and-egg problem. Here, we combine active and unsupervised learning for automated exploration of novel behaviors in non-equilibrium systems with unknown order parameters. We iteratively use active learning based on current order parameters to expand the library of known behaviors and then relearn order parameters based on this expanded library. We demonstrate the utility of this approach in Kuramoto models of coupled oscillators of increasing complexity. In addition to reproducing known phases, we also reveal previously unknown behavior and the related order parameters.   

Chemomechanical Sensing and Feedback in Active Nematics

Biological systems seamlessly integrate chemical and chemomechanical feedback loops to regulate dynamics and create or maintain complex forms. Active matter systems built from reconstituted biological components have yet to achieve a comparable level of programmable autonomous behavior. In my talk, I distinguish between exogenous and endogenous control of active materials and discuss the role each has in developing self-regulating materials. Using extensile active nematics as an exemplar, I propose PDE models that couple structural features in the nematic director to chemical patterns. I posit that such coarse-grained models motivate the design of biomolecular constituents that enable the creation of materials with desired emergent properties.   

Spatiotemporal control of 2D active nematics

In this work, we examine how spatiotemporal patterns of activity affect the dynamical organization of a model two-dimensional active nematic. We prepare two dimensional nematics composed of rodlike microtubules driven by light-sensitive kinesin motors. In this design, patterns of activity are prescribed through the projection of light onto the sample. We examine the response of the nematic defect density and the flow to spatially- and temporally-varying patterns of light. This data is used to develop data-driven models of the active nematic behavior. Further, we apply spatiotemporal patterns of light to shape the material flow and structure into desired configurations. We examine the success of various strategies of control to impose specific material configuations in a material whose dynamics are instrinsically chaotic.   

Network control of jammed materials

Amorphous and jammed particulate matter constitutes a wide range of natural and synthetic materials. The way in which these systems' disordered and extended chain-like mesoscale structures evolve under stress, leading to particle rearrangements and eventual yield, has profound consequences for phenomena ranging from landscape evolution to cellular unjamming during tumor metastasis. While traditional methods have made progress in relating this mesoscale structure to rearrangement dynamics, the lack of obvious structural order on multiple length scales suggests the need for novel physical theories to better predict yielding behavior. Here, we model disordered solids as spatially-embedded spring networks, and bring linear network control theory to bear on the problem of predicting dynamics from structure. We utilize this network control framework, which has previously proven successful in describing the dynamics and function of various biological, neurological, and mechanical networks, in a manner that is novel in the context of jammed materials. Our work shows that node controllability in this context correlates strongly with particle rearrangement under stress. In general, this work demonstrates that network control theory is a promising mathematical framework for predicting and designing yield behavior in disordered media.