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Designing allostery-inspired response in mechanical networks
Open accessAbstract
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.
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“Optimizing the networks for a geometric task, by selecting network structures where binding a ligand leads to a defined displacement on the other side of the network (“active site”), yields networks displaying a powerful lever at the active site, where the signal is required (Flechsig, 2017; Rocks et al., 2017; Yan et al., 2017a, 2017b).”
From Allostery in Its Many Disguises: From Theory to Applications (2019) · cites this paper as Rocks et al., 2017
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Auxetic metamaterials from disordered networks
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“[10] Jason W.”
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“Elastic network calculations were performed using a specialized bench-marked set of computational tools, used earlier for research on tuned networks [5, 23].”
BackgroundMethodInfluentialDemonstration of Decentralized Physics-Driven Learning
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“Allostery is a common feature of proteins [27], in which an input signal, namely strain applied to a local region of the protein by binding a regulatory molecule, gives rise to a desired strain or conformational change elsewhere in the protein, enabling or preventing binding of a substrate molecule.”
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“For example, principles of topological protection can be used to design materials where forces at specific sites lead to localized deformations (1, 2), while other principles (3) can help communicate that deformation to a specific distant site.”
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Rocks, J. W., Ronellenfitsch, H., Liu, A. J., Nagel, S. R., & Katifori, E. (2019) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1806790116 · Cited by 76
“Network Tuning Protocol Our method for tuning networks follows the general scheme described in our previous work (15) with slight modifications.”
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“After finishing the article I became aware of two quite recently appeared works, in which the design of mechanical networks with allosteric coupling had also been undertaken (46,47).”
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Adhikari, M., & Sastry, S. (2018) · The European Physical Journal E · doi:10.1140/epje/i2018-11717-5 · Cited by 57
Inverse design of discrete mechanical metamaterials
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Theoretical search for heterogeneously architected 2D structures
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Periodic training of creeping solids
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“[9] Jason W Rocks, Nidhi Pashine, Irmgard Bischofberger, Carl P Goodrich, Andrea J Liu, and Sidney R Nagel.”
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Berthier, E., Porter, M. A., & Daniels, K. E. (2019) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1900272116 · Cited by 41
“From an engineering perspective, such materials are promising because of their light weights and their tunable, designable properties: a Poisson ratio from the auxetic (4, 8, 9) to the incompressible limits (4), a targeted local response to a remote perturbation (5), or the ability to change shape (3).”
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Hagh, V. F., Nagel, S. R., Liu, A. J., Manning, M. L., & Corwin, E. I. (2022) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2117622119 · Cited by 40
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Simple mechanics of protein machines
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Colloquium : Proteins: The physics of amorphous evolving matter
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MethodMemory Formation in Jammed Hard Spheres
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Principles for Optimal Cooperativity in Allosteric Materials
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Hidden Topological Structure of Flow Network Functionality
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“[4]).”
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“It is also possible to computationally simulate a network’s training and print it out in its trained state [20], but there are good reasons to build a network with tunable components: A printed network that has been designed for a single task is static in nature, and could not be re-trained for…”
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“For example, one can control the ratio of high-frequency and lowfrequency modes by choosing the link density above or below the connectivity percolation, since the low-frequency mode sets in when ρ>ρc , and the remaining high-frequency modes decrease significantly once ρ>ρr , the rigidity percolation threshold, with r…”
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“The bonds were made thinner near the nodes to minimize angle-bending interactions in the networks as was done in previous work [4].”
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Structural hierarchy confers error tolerance in biological materials
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Mechanics of Allostery: Contrasting the Induced Fit and Population Shift Scenarios
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Optimal Elasticity of Biological Networks
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BackgroundThirumalai, D., & Hyeon, C. (2018) · Philosophical Transactions of the Royal Society B Biological Sciences · doi:10.1098/rstb.2017.0182 · Cited by 20
A Simple Mechanical Model for Synthetic Catch Bonds
Dansuk, K. C., & Keten, S. (2019) · Matter · doi:10.1016/j.matt.2019.06.005 · Cited by 20
Residue-Level Allostery Propagates through the Effective Coarse-Grained Hessian
Lake, P. T., Davidson, R. B., Klem, H., Hocky, G. M., & McCullagh, M. (2020) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.9b01149 · Cited by 20
“89,90 The derivative edge metric identifies the formation of new edges across the HisF-HisH interfaces as being impactful on the covariance between sources and sinks.”
BackgroundAutonomous codesign and fabrication of multistimuli-responsive material systems
Wang, L., Evenchik, A. L., Yang, J. M., Truby, R. L., & Chen, W. (2025) · Science Advances · doi:10.1126/sciadv.adx4409 · Cited by 20
“They open opportunities for the accelerated production of autonomous and robotic materials ( 89 ), material systems for mechanical computing ( 90 , 91 ), biocompatible morphing structures for biomedicine ( 28 , 92 ), and more.”
Memory Formation in Adaptive Networks
Bhattacharyya, K., Zwicker, D., & Alim, K. (2022) · Physical Review Letters · doi:10.1103/physrevlett.129.028101 · Cited by 19
Rigidity percolation and geometric information in floppy origami
Chen, S., & Mahadevan, L. (2019) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1820505116 · Cited by 20
“The presence of a percolation transition points toward some intriguing applications that include (i) a framework for multibit mechanical information storage, going beyond a recent 1-bit origami-based storage device (28); (ii) strategies for the optimal control of the number of DoF in a floppy origami structure in the…”
BackgroundSoft Modes as a Predictive Framework for Low-Dimensional Biological Systems Across Scales
Russo, C. J., Husain, K. B., & Murugan, A. (2025) · Annual Review of Biophysics · doi:10.1146/annurev-biophys-081624-030543 · Cited by 25
“Allosteric communication: soft modes have been shown to facilitate allostery in proteins, i.e., communication between distal residues in the protein (83, 108, 12, 105, 104).”
Rigidity of epithelial tissues as a double optimization problem
Arzash, S., Tah, I., Liu, A. J., & Manning, M. L. (2025) · Physical Review Research · doi:10.1103/physrevresearch.7.013157 · Cited by 19
“Simultaneous minimization of the cost function and energy/power with respect to tunable and physical degrees of freedom ( double optimization ) can be used to generate an auxetic [1, 3, 4] or allosteric response [2, 5].”
Designed Elastic Networks: Models of Complex Protein Machinery
Flechsig, H., & Togashi, Y. (2018) · International Journal of Molecular Sciences · doi:10.3390/ijms19103152 · Cited by 18
“implemented a computational strategy to tune mechanical networks towards developing allosteric responses [18].”
MethodDirect coupling analysis of epistasis in allosteric materials
Bravi, B., Ravasio, R., Brito, C., & Wyart, M. (2020) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1007630 · Cited by 21
Tah, I., Haertter, D., Crawford, J. M., Kiehart, D. P., Schmidt, C. F., & Liu, A. J. (2024) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2322732121 · Cited by 16
Conformational Freedom and Topological Confinement of Proteins in Biomolecular Condensates
Scholl, D., & Deniz, A. A. (2021) · Journal of Molecular Biology · doi:10.1016/j.jmb.2021.167348 · Cited by 16
Building blocks of protein structures: Physics meets biology
Škrbić, T., Maritan, A., Giacometti, A., Rose, G. D., & Banavar, J. R. (2021) · Physical review. E · doi:10.1103/physreve.104.014402 · Cited by 16
“Proteins (1-40) [we apologize that we have only included a limited selection of papers], the”
BackgroundFluctuation correlations as major determinants of structure- and dynamics-driven allosteric effects
Yu, M., Chen, Y.-X., Wang, Z.-L., & Liu, Z. (2019) · Physical Chemistry Chemical Physics · doi:10.1039/c8cp07859a · Cited by 14
Disordered auxetic networks with no reentrant polygons
Hagh, V. F., & Thorpe, M. F. (2018) · Physical review. B./Physical review. B · doi:10.1103/physrevb.98.100101 · Cited by 14
“[52] Jason W Rocks, Nidhi Pashine, Irmgard Bischofberger, Carl P Goodrich, Andrea J Liu, and Sidney R Nagel.”
BackgroundFrom complex to simple : hierarchical free-energy landscape renormalized in deep neural networks
Yoshino, H. (2020) · SciPost Physics Core · doi:10.21468/scipostphyscore.2.2.005 · Cited by 16
“The present work may also have implications on various complex systems with spatial heterogeneity, including ultra-stable glass [54–56] mentioned above, gene regulatory networks [62–64] which are often viewed like perceptrons and allosteric systems [65–67].”
BackgroundZhu, C., Fang, C., Jin, Z., Li, B., Shen, X., & Xu, L. (2024) · Applied Physics Reviews · doi:10.1063/5.0199530 · Cited by 12
Three-body problem for Langevin dynamics with different temperatures
Wang, M., & Grosberg, A. Y. (2020) · Physical review. E · doi:10.1103/physreve.101.032131 · Cited by 13
“This behavior has some connection with allostery-inspired mechanical networks [43], where the motion or activity of nodes in one part of a mechanical network can affect the response in another part differently depending on how one removes bonds (analogous to changing the interaction strengths between nodes).”
BackgroundReprogrammable allosteric metamaterials from disordered networks.
Pashine, N., Nasab, A. M., & Kramer-Bottiglio, R. (2023) · Soft Matter · doi:10.1039/d2sm01284g · Cited by 10
Enzymes as viscoelastic catalytic machines
Weinreb, E., McBride, J. M., Siek, M., Rougemont, J., Renault, R., Peleg, Y., Unger, T., Albeck, S., Fridmann‐Sirkis, Y., Lushchekina, S. V., et al. (2025) · Nature Physics · doi:10.1038/s41567-025-02825-9 · Cited by 11
“Our viscoelastic model complements and advances beyond the standard treatment of proteins in terms of elastic networks 19,46,49,57,58,68,74,76,85,86 , which are particularly useful in analysing the motions involved in binding 34 .”
InfluentialExcess floppy modes and multibranched mechanisms in metamaterials with symmetries
Lubbers, L. A., & van Hecke, M. (2019) · Physical review. E · doi:10.1103/physreve.100.021001 · Cited by 12
Chennakesavalu, S., Manikandan, S. K., Hu, F., & Rotskoff, G. M. (2024) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2310238121 · Cited by 13
“Mechanical response in soft materials is dictated by both intrinsic material properties of the constituents and also their spatial organization [23, 24].”
Putting a spin on metamaterials: Mechanical incompatibility as magnetic frustration
Pisanty, B., Oğuz, E. C., Nisoli, C., & Shokef, Y. (2021) · SciPost Physics · doi:10.21468/scipostphys.10.6.136 · Cited by 13
“For instance, a pruning process selectively applied to random spring networks can cause them to approach either the incompressible or completely aux-etic limits [5], as well as tune specific long-range coupled mechanical responses [6].”
Metadata
- Authors
- Rocks, J. W., Pashine, N., Bischofberger, I., Goodrich, C. P., Liu, A. J., & Nagel, S. R.
- Affiliations
- University of Pennsylvania (US)
- University of Chicago (US)
- Massachusetts Institute of Technology (US)
- Harvard University (US)
- ORCID
- Venue
- Proceedings of the National Academy of Sciences
- Publisher
- National Academy of Sciences
- Published
- 2017-02-21
- Volume
- 114
- Issue
- 10
- Pages
- 2520-2525
- ISSN
- 0027-8424 (ISSN-L)
- 1091-6490
- PMC
- PMC5347623
- OpenAlex
- W2485975781
- Cited by
- 204
- References
- 33
- Citations by year
- 2026: 17 · 2025: 34 · 2024: 18 · 2023: 22 · 2022: 12 · 2021: 27 · 2020: 22 · 2019: 29 · 2018: 14 · 2017: 8
- FWCI
- 15.50
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Proceedings of the National Academy of Sciences (publishedVersion)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- DSpace@MIT (Massachusetts Institute of Technology) (submittedVersion, cc-by-nc)
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
- arXiv (Cornell University)
- Funders
- U.S. Department of Energy (DE-FG02-05ER46199, DE-FG02-03ER46088)
- National Science Foundation Graduate Research Fellowship Program (DGE-1321851)
- Simons Foundation (305547, 327939)
- DOC | National Institute of Standards and Technology (60NANB15D055)
- Topics
- Physical Sciences › Engineering › Mechanical Engineering › Advanced Materials and Mechanics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Cell Biology › Cellular Mechanics and Interactions
- Physical Sciences › Physics and Astronomy › Acoustics and Ultrasonics › Acoustic Wave Phenomena Research
- Keywords
- allosteric regulation, mechanical metamaterials, spring networks, strain amplification, disordered networks, protein conformational change, network design
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