Recent advances in designing metamaterials have demonstrated that global mechanical properties of disordered spring networks can be tuned by selectively modifying only a small subset of bonds. Here, using a computationally efficient approach, we extend this idea to tune more general properties of networks. With nearly complete success, we are able to produce a strain between any two target nodes in a network in response to an applied source strain on any other pair of nodes by removing only ∼1% of the bonds. We are also able to control multiple pairs of target nodes, each with a different individual response, from a single source, and to tune multiple independent source/target responses simultaneously into a network. We have fabricated physical networks in macroscopic 2D and 3D systems that exhibit these responses. This work is inspired by the long-range coupled conformational changes that constitute allosteric function in proteins. The fact that allostery is a common means for regulation in biological molecules suggests that it is a relatively easy property to develop through evolution. In analogy, our results show that long-range coupled mechanical responses are similarly easy to achieve in disordered networks. mechanical metamaterials | allostery | tunable response | proteins | disordered networks T he ability to tune the response of mechanical networks has significant applications for designing metamaterials with unique properties. For example, the ratio G/B of the shear modulus G to the bulk modulus B can be tuned by over 16 orders of magnitude by removing only 2% of the bonds in an ideal spring network (1). Such a pruning procedure allows one to create a network that has a Poisson ratio ν anywhere between the auxetic limit (ν = − 1) and the incompressible limit. In another example, the average coordination number of a network controls the width of a failure zone under compression or extension (2). Both these results are specific to tuning the global responses of a material. However, many applications rely on targeting a local response to a local perturbation applied some distance away. For example, allostery in a protein is the process by which a molecule binding locally to one site affects the activity at a second distant site (3). Often this process involves the coupling of conformational changes between the two sites (4). Here we ask whether disordered networks, which generically do not exhibit this behavior, can be tuned to develop a specific allostery-inspired structural response by pruning bonds.We introduce a formalism for calculating how each bond contributes to the mechanical response, anywhere in the network, to an arbitrary applied source strain. The formalism allows us to develop algorithms to control how the strain between two arbitrarily chosen target nodes responds to the strain applied between two arbitrary source nodes. In the simplest case, bonds are removed sequentially until the desired target strain is reached. For almost all of the initial networks studied, only a small fraction of th...

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SignificanceFunctionally optimized networks are ubiquitous in nature, e.g., in allosteric proteins that change conformation upon binding to a ligand or vascular networks that distribute oxygen and nutrients in animals or plants. Many of these networks are multifunctional, with proteins that can catalyze more than one substrate or vascular networks that can deliver enhanced flow to more than one localized region of the network. This work investigates the question of how many simultaneous functions a given network can be designed to fulfill, uncovering a phase transition that is related to other constraint–satisfaction transitions such as the jamming transition.

In the beating heart, cardiac myocytes (CMs) contract in a coordinated fashion, generating contractile wave fronts that propagate through the heart with each beat. Coordinating this wave front requires fast and robust signaling mechanisms between CMs. The primary signaling mechanism has long been identified as electrical: gap junctions conduct ions between CMs, triggering membrane depolarization, intracellular calcium release, and actomyosin contraction. In contrast, we propose here that, in the early embryonic heart tube, the signaling mechanism coordinating beats is mechanical rather than electrical. We present a simple biophysical model in which CMs are mechanically excitable inclusions embedded within the extracellular matrix (ECM), modeled as an elastic-fluid biphasic material. Our model predicts strong stiffness dependence in both the heartbeat velocity and strain in isolated hearts, as well as the strain for a hydrogel-cultured CM, in quantitative agreement with recent experiments. We challenge our model with experiments disrupting electrical conduction by perfusing intact adult and embryonic hearts with a gap junction blocker, β-glycyrrhetinic acid (BGA). We find this treatment causes rapid failure in adult hearts but not embryonic hearts-consistent with our hypothesis. Last, our model predicts a minimum matrix stiffness necessary to propagate a mechanically coordinated wave front. The predicted value is in accord with our stiffness measurements at the onset of beating, suggesting that mechanical signaling may initiate the very first heartbeats. mechanotransduction | excitable media | cardiac development | heartbeat | reaction-diffusion

The plasticity of amorphous solids undergoing shear is characterized by quasi-localized rearrangements of particles. While many models of plasticity exist, the precise relationship between the plastic dynamics and the structure of a particle’s local environment remains an open question. Previously, machine learning was used to identify a structural predictor of rearrangements called “softness.” Although softness has been shown to predict which particles will rearrange with high accuracy, the method can be difficult to implement in experiments where data are limited and the combinations of descriptors it identifies are often difficult to interpret physically. Here, we address both of these weaknesses, presenting two major improvements to the standard softness method. First, we present a natural representation of each particle’s observed mobility, allowing for the use of statistical models that are both simpler and provide greater accuracy in limited datasets. Second, we employ persistent homology as a systematic means of identifying simple, topologically informed, structural quantities that are easy to interpret and measure experimentally. We test our methods on two-dimensional athermal packings of soft spheres under quasi-static shear. We find that the same structural information that predicts small variations in the response is also predictive of where plastic events will localize. We also find that an excellent accuracy is achieved in athermal sheared packings using simply a particle’s species and the number of nearest neighbor contacts.