Adaptive elastic networks as models of supercooled liquids

Principles for Optimal Cooperativity in Allosteric Materials

Allosteric proteins transmit a mechanical signal induced by binding a ligand. However, understanding the nature of the information transmitted and the architectures optimizing such transmission remains a challenge. Here we show, using an in silico evolution scheme and theoretical arguments, that architectures optimized to be cooperative, which efficiently propagate energy, qualitatively differ from previously investigated materials optimized to propagate strain. Although we observe a large diversity of functioning cooperative architectures (including shear, hinge, and twist designs), they all obey the same principle of displaying a mechanism, i.e., an extended soft mode. We show that its optimal frequency decreases with the spatial extension L of the system as L^-d/2, where d is the spatial dimension. For these optimal designs, cooperativity decays logarithmically with L for d = 2 and does not decay for d = 3. Overall, our approach leads to a natural explanation for several observations in allosteric proteins and indicates an experimental path to test if allosteric proteins lie close to optimality.

Entropy favors heterogeneous structures of networks near the rigidity threshold

The dynamical properties and mechanical functions of amorphous materials are governed by their microscopic structures, particularly the elasticity of the interaction networks, which is generally complicated by structural heterogeneity. This ubiquitous heterogeneous nature of amorphous materials is intriguingly attributed to a complex role of entropy. Here, we show in disordered networks that the vibrational entropy increases by creating phase-separated structures when the interaction connectivity is close to the onset of network rigidity. The stress energy, which conversely penalizes the heterogeneity, finally dominates a smaller vicinity of the rigidity threshold at the glass transition and creates a homogeneous intermediate phase. This picture of structures changing between homogeneous and heterogeneous phases by varying connectivity provides an interpretation of the transitions observed in chalcogenide glasses.

Architecture and coevolution of allosteric materials

We introduce a numerical scheme to evolve functional elastic materials that can accomplish a specified mechanical task. In this scheme, the number of solutions, their spatial architectures, and the correlations among them can be computed. As an example, we consider an "allosteric" task, which requires the material to respond specifically to a stimulus at a distant active site. We find that functioning materials evolve a less-constrained trumpet-shaped region connecting the stimulus and active sites, and that the amplitude of the elastic response varies nonmonotonically along the trumpet. As previously shown for some proteins, we find that correlations appearing during evolution alone are sufficient to identify key aspects of this design. Finally, we show that the success of this architecture stems from the emergence of soft edge modes recently found to appear near the surface of marginally connected materials. Overall, our in silico evolution experiment offers a window to study the relationship between structure, function, and correlations emerging during evolution.