Designing allostery-inspired response in mechanical networks

Abstract

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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