Cardiomyopathies, often caused by mutations in genes encoding muscle proteins, are traditionally treated by phenotyping hearts and addressing symptoms post irreversible damage. With advancements in genotyping, early diagnosis is now possible, potentially introducing earlier treatment. However, the intricate structure of muscle and its myriad proteins make treatment predictions challenging. Here, we approach the problem of estimating therapeutic targets for a mutation in mouse muscle using a spatially explicit half sarcomere muscle model. We selected nine rate parameters in our model linked to both small molecules and cardiomyopathy-causing mutations. We then randomly varied these rate parameters and simulated an isometric twitch for each combination to generate a large training data set. We used this data set to train a conditional variational autoencoder, a technique used in Bayesian parameter estimation. Given simulated or experimental isometric twitches, this machine learning model is able to then predict the set of rate parameters that are most likely to yield that result. We then predict the set of rate parameters associated with twitches from control mice with the cardiac troponin C (cTnC) I61Q variant and control twitches treated with the myosin activator Danicamtiv, as well as model parameters that recover the abnormal I61Q cTnC twitches.

We characterize the connectivity structure of feed-forward, deep neural networks (DNNs) using network motif theory. To address whether a particular motif distribution is characteristic of the training task, or function of the DNN, we compare the connectivity structure of 350 DNNs trained to simulate a bio-mechanical flight control system with different randomly initialized parameters. We develop and implement algorithms for counting second- and third-order motifs and calculate their significance using their Z-score. The DNNs are trained to solve the inverse problem of the flight dynamics model in Bustamante, et al. (2022) (i.e., predict the controls necessary for controlled flight from the initial and final state-space inputs) and are sparsified through an iterative pruning and retraining algorithm Zahn, et al. (2022). We show that, despite random initialization of network parameters, enforced sparsity causes DNNs to converge to similar connectivity patterns as characterized by their motif distributions. The results suggest how neural network function can be encoded in motif distributions, suggesting a variety of experiments for informing function and control.

Systems in nature are stochastic as well as nonlinear. In traditional applications, engineered filters aim to minimize the stochastic effects caused by process and measurement noise. Conversely, a previous study showed that the process noise can reveal the observability of a system that was initially categorized as unobservable when deterministic tools were used. In this paper, we develop a stochastic framework to explore observability analysis and sensor placement. This framework allows for direct studies of the effects of stochasticity on optimal sensor placement and selection to improve filter error covariance. Numerical results are presented for sensor selection that optimizes stochastic empirical observability in a bioinspired setting.

The sarcomeric protein troponin regulates the timing of muscle contraction by undergoing a dramatic shape change following calcium binding. This shape change ultimately allows tropomyosin to move away from prospective binding sites along the thin filament and myosin motors to bind to the thin filament. Mutations in troponin can disrupt its function, and several are implicated in cardiomyopathies. In this study, we explore how mutations within TnC alter its structure and dynamics using molecular dynamics simulations.

Flight control requires active sensory feedback, and insects have many sensors that help them estimate their current locomotor state, including campaniform sensilla, which are mechanoreceptors that sense strain resulting from deformation of the cuticle. Campaniform sensilla on the wing detect bending and torsional forces encountered during flight, providing input to the flight feedback control system. During flight, wings experience complex spatio-temporal strain patterns. Because campaniform sensilla detect only local strain, their placement on the wing is presumably critical for determining the overall representation of wing deformation; however, how these sensilla are distributed across wings is largely unknown. Here, we test the hypothesis that campaniform sensilla are found in stereotyped locations across individuals of Manduca sexta, a hawkmoth. We found that although campaniform sensilla are consistently found on the same veins or in the same regions of the wings, their total number and distribution can vary extensively. This suggests that there is some robustness to variation in sensory feedback in the insect flight control system. The regions where campaniform sensilla are consistently found provide clues to their functional roles, although some patterns might be reflective of developmental processes. Collectively, our results on intraspecific variation in campaniform sensilla placement on insect wings will help reshape our thinking on the utility of mechanosensory feedback for insect flight control and guide further experimental and comparative studies.

The timing and magnitude of force generation by a muscle depend on complex interactions in a compliant, contractile filament lattice. Perturbations in these interactions can result in cardiac muscle diseases. In this study, we address the fundamental challenge of connecting the temporal features of cardiac twitches to underlying rate constants and their perturbations associated with genetic cardiomyopathies. Current state-of-the-art metrics for characterizing the mechanical consequence of cardiac muscle disease do not utilize information embedded in the complete time course of twitch force. We pair dimension reduction techniques and machine learning methods to classify underlying perturbations that shape the timing of twitch force. To do this, we created a large twitch dataset using a spatially explicit Monte Carlo model of muscle contraction. Uniquely, we modified the rate constants of this model in line with mouse models of cardiac muscle disease and varied mutation penetrance. Ultimately, the results of this study show that machine learning models combined with biologically informed dimension reduction techniques can yield excellent classification accuracy of underlying muscle perturbations.

Sensory feedback is essential to both animals and robotic systems for achieving coordinated, precise movements. Mechanosensory feedback, which provides information about body deformation, depends not only on the properties of sensors but also on the structure in which they are embedded. In insects, wing structure plays a particularly important role in flapping flight: in addition to generating aerodynamic forces, wings provide mechanosensory feedback necessary for guiding flight while undergoing dramatic deformations during each wingbeat. However, the role that wing structure plays in determining mechanosensory information is relatively unexplored. Insect wings exhibit characteristic stiffness gradients and are subject to both aerodynamic and structural damping. Here we examine how both of these properties impact sensory performance, using finite element analysis combined with sensor placement optimization approaches. We show that wings with nonuniform stiffness exhibit several advantages over uniform stiffness wings, resulting in higher accuracy of rotation detection and lower sensitivity to the placement of sensors on the wing. Moreover, we show that higher damping generally improves the accuracy with which body rotations can be detected. These results contribute to our understanding of the evolution of the nonuniform stiffness patterns in insect wings, as well as suggest design principles for robotic systems.

How does neural activity drive muscles to produce behavior? The recent development of genetic lines in Hydra that allow complete calcium imaging of both neuronal and muscle activity, as well as systematic machine learning quantification of behaviors, makes this small cnidarian an ideal model system to understand and model the complete transformation from neural firing to body movements. To achieve this, we have built a neuromechanical model of Hydra ’s fluid-filled hydrostatic skeleton, showing how drive by neuronal activity activates distinct patterns of muscle activity and body column biomechanics. Our model is based on experimental measurements of neuronal and muscle activity and assumes gap junctional coupling among muscle cells and calcium-dependent force generation by muscles. With these assumptions, we can robustly reproduce a basic set of Hydra ’s behaviors. We can further explain puzzling experimental observations, including the dual timescale kinetics observed in muscle activation and the engagement of ectodermal and endodermal muscles in different behaviors. This work delineates the spatiotemporal control space of Hydra movement and can serve as a template for future efforts to systematically decipher the transformations in the neural basis of behavior.

Nonlinear model order reduction has opened the door to parameter optimization and uncertainty quantification in complex physics problems governed by nonlinear equations. In particular, the computational cost of solving these equations can be reduced by means of local reduced-order bases. This article examines the benefits of a physics-informed cluster analysis for the construction of cluster-specific reduced-order bases. We illustrate that the choice of the dissimilarity measure for clustering is fundamental and highly affects the performances of the local reduced-order bases. It is shown that clustering with an angle-based dissimilarity on simulation data efficiently decreases the intra-cluster Kolmogorov N-width. Additionally, an a priori efficiency criterion is introduced to assess the relevance of a ROM-net, a methodology for the reduction of nonlinear physics problems introduced in our previous work in Daniel et al. (2020) [48]. This criterion also provides engineers with a very practical method for ROM-nets' hyperparameters calibration under constrained computational costs for the training phase. On five different physics problems, our physics-informed clustering strategy significantly outperforms classic strategies for the construction of local reduced-order bases in terms of projection errors.

Muscle cells contain a highly organized and complexly regulated filament lattice with repetitive structure, where both inter- and intra-filament interactions control muscle activation and relaxation. Genetic cardiomyopathies, such as hypertrophic cardiomyopathy (HCM), can arise from dysfunction in any of the major components of muscle (thin, thick and titin filaments). We hypothesize that cellular scale (twitch) metrics contain enough information to predict specific protein perturbations, and lend insights into targeted compensatory interventions.

Insect flight is a strongly nonlinear and actuated dynamical system. As such, strategies for understanding its control have typically relied on either model-based methods or linearizations thereof. Here we develop a framework that combines model predictive control on an established flight dynamics model and deep neural networks (DNN) to create an efficient method for solving the inverse problem of flight control. We turn to natural systems for inspiration since they inherently demonstrate network pruning with the consequence of yielding more efficient networks for a specific set of tasks. This bio-inspired approach allows us to leverage network pruning to optimally sparsify a DNN architecture in order to perform flight tasks with as few neural connections as possible, however, there are limits to sparsification. Specifically, as the number of connections falls below a critical threshold, flight performance drops considerably. We develop sparsification paradigms and explore their limits for control tasks. Monte Carlo simulations also quantify the statistical distribution of network weights during pruning given initial random weights of the DNNs. We demonstrate that on average, the network can be pruned to retain a small amount of original network weights and still perform comparably to its fully-connected counterpart. The relative number of remaining weights, however, is highly dependent on the initial architecture and size of the network. Overall, this work shows that sparsely connected DNNs are capable of predicting the forces required to follow flight trajectories. Additionally, sparsification has sharp performance limits.

Macroalgae provide surfaces where other organisms live. Unlike organisms on rigid substrata, epibionts on host macroalgae sit on flexible surfaces that bend, stretch, and move in turbulent water currents and waves. We used blade-like red algae, Mazzaella splendens, and encrusting bryozoans, Membranipora membranacea, to investigate the biomechanical and hydrodynamic effects of encrusting epibionts on macroalgae, and of flexible hosts on epibiotic bryozoans. Passive flapping by algae in wave-driven ambient flow enhanced renewal of water near hosts and epibionts. Wave exposure and the presence of a surrounding canopy of flexible algae altered the locations along algal blades where bryozoans encountered the highest time-averaged boundary shear velocities. Hydrodynamic forces on flexible algae moving back-and-forth with the water were lower in waves than in unidirectional flow. Bryozoan epibionts increased hydrodynamic forces on host algae by affecting their reconfiguration in moving water. Encrusting bryozoans increased the flexural stiffness of algal blades, but the elastic modulus, extensibility, and strength of blade tissue was unaffected by bryozoan epibionts. Algal blades were more extensible and stronger than bryozoans, so bryozoans fractured or popped off stretched algae. Algae in rapid-flow habitats had few epibionts, and encrusted algae transplanted from a protected to a wave-exposed habitat lost their epibionts.

Plants cover a large fraction of the Earth’s land mass despite most species having limited to no mobility. To transport their propagules, many plants have evolved mechanisms to disperse their seeds using the wind 1 – 4 . A dandelion seed, for example, has a bristly filament structure that decreases its terminal velocity and helps orient the seed as it wafts to the ground 5 . Inspired by this, we demonstrate wind dispersal of battery-free wireless sensing devices. Our millimetre-scale devices weigh 30 milligrams and are designed on a flexible substrate using programmable, off-the-shelf parts to enable scalability and flexibility for various sensing and computing applications. The system is powered using lightweight solar cells and an energy harvesting circuit that is robust to low and variable light conditions, and has a backscatter communication link that enables data transmission. To achieve the wide-area dispersal and upright landing that is necessary for solar power harvesting, we developed dandelion-inspired, thin-film porous structures that achieve a terminal velocity of 0.87 ± 0.02 metres per second and aerodynamic stability with a probability of upright landing of over 95%. Our results in outdoor environments demonstrate that these devices can travel 50–100 metres in gentle to moderate breeze. Finally, in natural systems, variance in individual seed morphology causes some seeds to fall closer and others to travel farther. We adopt a similar approach and show how we can modulate the porosity and diameter of the structures to achieve dispersal variation across devices.

Research on insect flight control has focused primarily on the role of wings. Yet abdominal deflections during flight can potentially influence the dynamics of flight. This paper assesses the role of airframe deformations in flight, and asks to what extent the abdomen contributes to flight maneuverability. To address this, we use a combination of both a Model Predictive Control (MPC)-inspired computational inertial dynamics model, and free flight experiments in the hawkmoth, Manduca sexta. We explored both underactuated (i.e., number of outputs are greater than the number of inputs) and fully actuated (equal number of outputs and inputs) systems. Using metrics such as the non-dimensionalized tracking error and cost of transport to evaluate flight performance of the inertial dynamics model, we show that fully actuated simulations minimized the tracking error and cost of transport. Additionally, we tested the effect of restricted abdomen movement on free flight in live hawkmoths by fixing a carbon fiber rod over the thoracic-abdomen joint. Moths with a restricted abdomen performed worse than sham treatment moths. This study finds that abdominal motions contribute to flight control and maneuverability. Such motions of non-aerodynamic structures, found in all flying taxa, can inform the development of multi-actuated micro air vehicles.

Cardiac muscle cells consist of a highly organized filament lattice with repetitive structure. Both inter- and intra-filament interactions control muscle activation and relaxation, and even small perturbations of these interactions can result in the development of cardiomyopathies. Building on an existing spatially explicit computational model of muscle contraction at the half-sarcomere level, we simulated different mutations by changing model parameters using published biochemical or biomechanical data. Importantly, we added the ability to specify profiles of protein properties and their frequency (penetrance) within the model. We assigned the mutant properties to a portion of the proteins, with the remainder retaining wildtype properties. The current model consists of 8 thin filaments, with a four state cardiac troponin-tropomyosin regulation cycle, determining accessibility of actin binding sites for myosin motor heads arising from the 4 thick filaments. Upon binding, the myosin motors follow a three-state model of the crossbridge cycle to generate axial tension. We simulated the cardiac troponin c (cTnC) mutation L48Q, which has increased calcium binding affinity, and the non-functional cTnC mutation D65A, which prevents calcium from binding at site II (contraction trigger site). Additionally, we co-varied cross-bridge cycle transition rates, increasing the attachment rate and decreasing the detachment rates to simulate the effect of myosin mutations, to study how this affected contraction with different dosages of L48Q. We simulated isometric twitch force, the force-pCa relationship, and filament material properties assays. For the isometric twitches, we specified a calcium transient derived from published intra-lattice measurements. Our results show emergent contractile dynamics similar to the respective experimental phenotypes. L48Q, with increasing penetrance, increases calcium sensitivity and linearly increases maximum tension, as well as time at maximum tension. D65A decreases maximum tension, and our myosin treatment increases maximum tension, and slows relaxation.

A highly organized and densely packed lattice of molecular machinery within the sarcomeres of muscle cells powers contraction. Although many of the proteins that drive contraction have been studied extensively, the mechanical impact of fluid shearing within the lattice of molecular machinery has received minimal attention. It was recently proposed that fluid flow augments substrate transport in the sarcomere, however, this analysis used analytical models of fluid flow in the molecular machinery that could not capture its full complexity. By building a finite element model of the sarcomere, we estimate the explicit flow field, and contrast it with analytical models. Our results demonstrate that viscous drag forces on sliding filaments are surprisingly small in contrast to the forces generated by single myosin molecular motors. This model also indicates that the energetic cost of fluid flow through viscous shearing with lattice proteins is likely minimal. The model also highlights a steep velocity gradient between sliding filaments and demonstrates that the maximal radial fluid velocity occurs near the tips of the filaments. To our knowledge, this is the first computational analysis of fluid flow within the highly structured sarcomere.

Model order reduction has been extensively studied over the last two decades. Projection-based methods such as the Proper Orthogonal Decomposition and the Reduced Basis Method enjoy the important advantages of Galerkin methods in the derivation of the reduced problem, but are limited to linear data compression for which the reduced solution is sought as a linear combination of spatial modes. Nonlinear data compression must be used when the solution manifold is not embedded in a low-dimensional subspace. Early methods involve piecewise linear data compression, by constructing a dictionary of reduced-order models tailored to a partition of the solution manifold. In this work, we introduce the concept of optimal partition of the solution manifold in terms of normalized Kolmogorov widths, and prove that the optimal partitions can be found by means of a representative-based clustering algorithm using the sine dissimilarity measure on the solution manifold.

During muscle contraction, myosin motors anchored to thick filaments bind to and slide actin thin filaments. These motors rely on energy derived from ATP, supplied, in part, by diffusion from the sarcoplasm to the interior of the lattice of actin and myosin filaments. The radial spacing of filaments in this lattice may change or remain constant during contraction. If the lattice is isovolumetric, it must expand when the muscle shortens. If, however, the spacing is constant or has a different pattern of axial and radial motion, then the lattice changes volume during contraction, driving fluid motion and assisting in the transport of molecules between the contractile lattice and the surrounding intracellular space. We first create an advective-diffusive-reaction flow model and show that the flow into and out of the sarcomere lattice would be significant in the absence of lattice expansion. Advective transport coupled to diffusion has the potential to substantially enhance metabolite exchange within the crowded sarcomere. Using time-resolved x-ray diffraction of contracting muscle, we next show that the contractile lattice is neither isovolumetric nor constant in spacing. Instead, lattice spacing is time varying, depends on activation, and can manifest as an effective time-varying Poisson ratio. The resulting fluid flow in the sarcomere lattice of synchronous insect flight muscles is even greater than expected for constant lattice spacing conditions. Lattice spacing depends on a variety of factors that produce radial force, including cross-bridges, titin-like molecules, and other structural proteins. Volume change and advective transport varies with the phase of muscle stimulation during periodic contraction but remains significant at all conditions. Although varying in magnitude, advective transport will occur in all cases in which the sarcomere is not isovolumetric. Akin to "breathing," advective-diffusive transport in sarcomeres is sufficient to promote metabolite exchange and may play a role in the regulation of contraction itself.