From predicting to learning dissipation from pair correlations of active liquids.

Active systems, which are driven out of equilibrium by local non-conservative forces, can adopt unique behaviors and configurations. An important challenge in the design of novel materials, which utilize such properties, is to precisely connect the static structure of active systems to the dissipation of energy induced by the local driving. Here, we use tools from liquid-state theories and machine learning to take on this challenge. We first analytically demonstrate for an isotropic active matter system that dissipation and pair correlations are closely related when driving forces behave like an active temperature. We then extend a nonequilibrium mean-field framework for predicting these pair correlations, which unlike most existing approaches is applicable even for strongly interacting particles and far from equilibrium, to predicting dissipation in these systems. Based on this theory, we reveal a robust analytic relation between dissipation and structure, which holds even as the system approaches a nonequilibrium phase transition. Finally, we construct a neural network that maps static configurations of particles to their dissipation rate without any prior knowledge of the underlying dynamics. Our results open novel perspectives on the interplay between dissipation and organization out of equilibrium.

Mean-field theory for the structure of strongly interacting active liquids.

Active systems, which are driven out of equilibrium by local non-conservative forces, exhibit unique behaviors and structures with potential utility for the design of novel materials. An important and difficult challenge along the path toward this goal is to precisely predict how the structure of active systems is modified as their driving forces push them out of equilibrium. Here, we use tools from liquid-state theories to approach this challenge for a classic minimal active matter model. First, we construct a nonequilibrium mean-field framework that can predict the structure of systems of weakly interacting particles. Second, motivated by equilibrium solvation theories, we modify this theory to extend it with surprisingly high accuracy to systems of strongly interacting particles, distinguishing it from most existing similarly tractable approaches. Our results provide insight into spatial organization in strongly interacting out-of-equilibrium systems.

High-Resolution ENDOR Spectroscopy Combined with Quantum Chemical Calculations Reveals the Structure of Nitrogenase Janus Intermediate E4(4H).

We have shown that the key state in N2 reduction to two NH3 molecules by the enzyme nitrogenase is E4(4H), the "Janus" intermediate, which has accumulated four [e-/H+] and is poised to undergo reductive elimination of H2 coupled to N2 binding and activation. Initial 1H and 95Mo ENDOR studies of freeze-trapped E4(4H) revealed that the catalytic multimetallic cluster (FeMo-co) binds two Fe-bridging hydrides, [Fe-H-Fe]. However, the analysis failed to provide a satisfactory picture of the relative spatial relationships of the two [Fe-H-Fe]. Our recent density functional theory (DFT) study yielded a lowest-energy form, denoted as E4(4H)(a), with two parallel Fe-H-Fe planes bridging pairs of "anchor" Fe on the Fe2,3,6,7 face of FeMo-co. However, the relative energies of structures E4(4H)(b), with one bridging and one terminal hydride, and E4(4H)(c), with one pair of anchor Fe supporting two bridging hydrides, were not beyond the uncertainties in the calculation. Moreover, a structure of V-dependent nitrogenase resulted in a proposed structure analogous to E4(4H)(c), and additional structures have been proposed in the DFT studies of others. To resolve the nature of hydride binding to the Janus intermediate, we performed exhaustive, high-resolution CW-stochastic 1H-ENDOR experiments using improved instrumentation, Mims 2H ENDOR, and a recently developed pulsed-ENDOR protocol ("PESTRE") to obtain absolute hyperfine interaction signs. These measurements are coupled to DFT structural models through an analytical point-dipole Hamiltonian for the hydride electron-nuclear dipolar coupling to its "anchoring" Fe ions, an approach that overcomes limitations inherent in both experimental interpretation and computational accuracy. The result is the freeze-trapped, lowest-energy Janus intermediate structure, E4(4H)(a).

Energy dissipation and fluctuations in a driven liquid.

Minimal models of active and driven particles have recently been used to elucidate many properties of nonequilibrium systems. However, the relation between energy consumption and changes in the structure and transport properties of these nonequilibrium materials remains to be explored. We explore this relation in a minimal model of a driven liquid that settles into a time periodic steady state. Using concepts from stochastic thermodynamics and liquid state theories, we show how the work performed on the system by various nonconservative, time-dependent forces-this quantifies a violation of time reversal symmetry-modifies the structural, transport, and phase transition properties of the driven liquid.

Transmembrane helix connectivity in Orai1 controls two gates for calcium-dependent transcription.

The channel Orai1 requires Ca2+ store depletion in the endoplasmic reticulum and an interaction with the Ca2+ sensor STIM1 to mediate Ca2+ signaling. Alterations in Orai1-mediated Ca2+ influx have been linked to several pathological conditions including immunodeficiency, tubular myopathy, and cancer. We screened large-scale cancer genomics data sets for dysfunctional Orai1 mutants. Five of the identified Orai1 mutations resulted in constitutively active gating and transcriptional activation. Our analysis showed that certain Orai1 mutations were clustered in the transmembrane 2 helix surrounding the pore, which is a trigger site for Orai1 channel gating. Analysis of the constitutively open Orai1 mutant channels revealed two fundamental gates that enabled Ca2+ influx: Arginine side chains were displaced so they no longer blocked the pore, and a chain of water molecules formed in the hydrophobic pore region. Together, these results enabled us to identify a cluster of Orai1 mutations that trigger Ca2+ permeation associated with gene transcription and provide a gating mechanism for Orai1.