Direct coupling analysis of epistasis in allosteric materials.

In allosteric proteins, the binding of a ligand modifies function at a distant active site. Such allosteric pathways can be used as target for drug design, generating considerable interest in inferring them from sequence alignment data. Currently, different methods lead to conflicting results, in particular on the existence of long-range evolutionary couplings between distant amino-acids mediating allostery. Here we propose a resolution of this conundrum, by studying epistasis and its inference in models where an allosteric material is evolved in silico to perform a mechanical task. We find in our model the four types of epistasis (Synergistic, Sign, Antagonistic, Saturation), which can be both short or long-range and have a simple mechanical interpretation. We perform a Direct Coupling Analysis (DCA) and find that DCA predicts well the cost of point mutations but is a rather poor generative model. Strikingly, it can predict short-range epistasis but fails to capture long-range epistasis, in consistence with empirical findings. We propose that such failure is generic when function requires subparts to work in concert. We illustrate this idea with a simple model, which suggests that other methods may be better suited to capture long-range effects.

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.

Mechanics of Allostery: Contrasting the Induced Fit and Population Shift Scenarios.

In allosteric proteins, binding a ligand can affect function at a distant location, for example, by changing the binding affinity of a substrate at the active site. The induced fit and population shift models, which differ by the assumed number of stable configurations, explain such cooperative binding from a thermodynamic viewpoint. Yet, understanding what mechanical principles constrain these models remains a challenge. Here, we provide an empirical study on 34 proteins supporting the idea that allosteric conformational change generally occurs along a soft elastic mode presenting extended regions of high shear. We argue, based on a detailed analysis of how the energy profile along such a mode depends on binding, that in the induced fit scenario, there is an optimal stiffness ka∗ ∼ 1/N for cooperative binding, where N is the number of residues. We find that the population shift scenario is more robust to mutations affecting stiffness because binding becomes more and more cooperative with stiffness up to the same characteristic value ka∗, beyond which cooperativity saturates instead of decaying. We numerically confirm these findings in a nonlinear mechanical model. Dynamical considerations suggest that a stiffness of order ka∗ is favorable in that scenario as well, supporting that for proper function, proteins must evolve a functional elastic mode that is softer as their size increases. In consistency with this view, we find a fair anticorrelation between the stiffness of the allosteric response and protein size in our data set.

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.

A minimal scenario for the origin of non-equilibrium order.

Extant life contains numerous non-equilibrium mechanisms to create order not achievable at equilibrium; it is generally assumed that these mechanisms evolved because the resulting order was sufficiently beneficial to overcome associated costs of time and energy. Here, we identify a broad range of conditions under which non-equilibrium order-creating mechanisms will evolve as an inevitable consequence of self-replication, even if the order is not directly functional. We show that models of polymerases, when expanded to include known stalling effects, can evolve kinetic proofreading through selection for fast replication alone, consistent with data from recent mutational screens. Similarly, replication contingent on fast self-assembly can select for non-equilibrium instabilities and result in more ordered structures without any direct selection for order. We abstract these results into a framework that predicts that self-replication intrinsically amplifies dissipative order-enhancing mechanisms if the distribution of replication times is wide enough. Our work suggests the intriguing possibility that non-equilibrium order can arise more easily than assumed, even before that order is directly functional, with consequences impacting mutation rate evolution and kinetic traps in self-assembly to the origin of life.

Bottlenecks, Modularity, and the Neural Control of Behavior.

In almost all animals, the transfer of information from the brain to the motor circuitry is facilitated by a relatively small number of neurons, leading to a constraint on the amount of information that can be transmitted. Our knowledge of how animals encode information through this pathway, and the consequences of this encoding, however, is limited. In this study, we use a simple feed-forward neural network to investigate the consequences of having such a bottleneck and identify aspects of the network architecture that enable robust information transfer. We are able to explain some recently observed properties of descending neurons-that they exhibit a modular pattern of connectivity and that their excitation leads to consistent alterations in behavior that are often dependent upon the desired behavioral state of the animal. Our model predicts that in the presence of an information bottleneck, such a modular structure is needed to increase the efficiency of the network and to make it more robust to perturbations. However, it does so at the cost of an increase in state-dependent effects. Despite its simplicity, our model is able to provide intuition for the trade-offs faced by the nervous system in the presence of an information processing constraint and makes predictions for future experiments.

Allostery in Its Many Disguises: From Theory to Applications.

Allosteric regulation plays an important role in many biological processes, such as signal transduction, transcriptional regulation, and metabolism. Allostery is rooted in the fundamental physical properties of macromolecular systems, but its underlying mechanisms are still poorly understood. A collection of contributions to a recent interdisciplinary CECAM (Center Européen de Calcul Atomique et Moléculaire) workshop is used here to provide an overview of the progress and remaining limitations in the understanding of the mechanistic foundations of allostery gained from computational and experimental analyses of real protein systems and model systems. The main conceptual frameworks instrumental in driving the field are discussed. We illustrate the role of these frameworks in illuminating molecular mechanisms and explaining cellular processes, and describe some of their promising practical applications in engineering molecular sensors and informing drug design efforts.