Daniel M. Zuckerman

Gap junction channels formed by connexins mediate direct intercellular communication and are essential for electrical signaling and tissue homeostasis. Despite their large, solvent-accessible pores, connexin channels exhibit distinct conductance, selectivity, and rectification properties, but the molecular mechanisms underlying these behaviors remain incompletely understood. Here, we performed ∼67 μs of all-atom computational electrophysiology simulations of connexin-46 (Cx46), connexin-50 (Cx50), and heterotypic Cx46/50 gap junction channels based on high-resolution open-state structures, enabling characterization of both ion permeation and long-timescale channel dynamics. Simulations reveal a multi-ion, multi-pathway permeation mechanism governed by isoform-specific energetic barriers and transient ion coordination sites that shape conductance and selectivity. In heterotypic Cx46/50 channels, asymmetric energetic landscapes establish a mechanistic basis for rectification. Unexpectedly, the microsecond-timescale simulations further revealed dynamic interactions between the intracellular loop (ICL) region and N-terminal domain (NT) that transiently constrict the pore and attenuate ionic currents. These findings suggest that the open-state comprises an ensemble of rapidly interconverting conductance microstates rather than a single static conformation, providing structural information of potential mechanistic importance beyond what has been learned from cryo-EM studies. Together, our results provide a mechanistic basis for ion permeation and current modulation in gap junction channels and highlight the importance of long-timescale protein dynamics in shaping intercellular communication.

Multiple AI prediction tools for protein structural ensembles have recently been released, building on the much heralded advances from AlphaFold, large language models, and other machine-learning approaches. Here we report on a comparison of several tools (BioEmu, AFSample2, ESMFlow) using a small test set of proteins, including three which exhibit well-studied structural transitions. Overall, while the AI platforms generate structurally diverse ensembles with overlapping regions, each tool produces clearly distinct conformational distributions. Thus, it is impossible that all the tools generate ensembles of high biophysical quality, analogous to a Boltzmann distribution. Experimental structures are often, but not always, covered by the ensembles in dimensionally reduced spaces. In cases where point mutations are known experimentally to cause large structural shifts, the AI tools exhibit either small or negligible shifts. Although our current analysis cannot evaluate the absolute quality of an ensemble, and hence cannot identify a best-performing AI tool, the results suggest users pursuing downstream applications such as protein engineering or drug design should interpret these ensembles with caution.

A significant challenge in molecular dynamics (MD) simulations is ensuring that sampled configurations converge to the equilibrium or nonequilibrium stationary distribution of interest. Lack of convergence constrains the estimation of free energies and of rates and mechanisms for molecular transitions. Here, we introduce the “Randomized ITErative trajectory reWeighting” (RiteWeight) algorithm to estimate a stationary distribution from unconverged simulation data. This method iteratively reweights trajectory segments in a self-consistent way by solving for the stationary distribution of a Markov state model (MSM), updating segment weights, and employing a new random clustering in each iteration. The repeated clustering mitigates the configuration-space discretization error inherent in existing trajectory reweighting techniques and yields quasi-continuous configuration-space distributions. RiteWeight accurately recovers the stationary distribution even without requiring the Markov property at the cluster level. We present mathematical analysis of the RiteWeight fixed point. We empirically validate the method using both synthetic MD Trp-cage trajectories, for which the stationary solution is exactly calculable, and standard atomistic MD Trp-cage trajectories, which are extracted from a long reference simulation. In both test systems, RiteWeight corrects flawed distributions and generates accurate observables for equilibrium and nonequilibrium steady states. The results highlight the value of correcting the underlying trajectory distribution rather than using a standard MSM.

Determining the stationary distribution from a set of stochastic-process trajectory data, e.g., molecular dynamics, has long been a challenging if under-appreciated problem. We recently proposed a randomized iterative reweighting algorithm, “RiteWeight,” which provided a solution given unbiased trajectory data, i.e., trajectories generated directly from the dynamics of interest (potential surface, temperature, etc.). However, numerous sampling methodologies use biased dynamics, typically generated from a smoothed energy surface. Here, we introduce the bRiteWeight algorithm, which modifies RiteWeight for biased dynamics based on Girsanov (importance sampling) weights for trajectory snippets. We show theoretically and with simple examples that the new algorithm can correct biased dynamics to yield the stationary distribution of the unbiased system. As with RiteWeight, the algorithm is suitable both for equilibrium and nonequilibrium steady states.

Recently, a number of tools have been released that generate ensembles of protein structures based on artificial intelligence (AI) approaches. Although ensembles generated by the tools differ significantly, we demonstrate a computational path to harmonizing the various outputs under a stationary condition using two complementary physics-based approaches. In the first stage, the AI ensemble is used to seed a weighted ensemble (WE) simulation, promoting relaxation toward the steady state. In the second stage, trajectory segments generated by WE are reweighted to steady state using the recently developed RiteWeight (RW) algorithm. We applied this approach to generate an atomically-detailed equilibrium ensemble of unliganded adenylate kinase conformations, starting from ensembles produced by three AI tools: AFSample2, ESMFlow-PDB (trained from PDB structures), and ESMFlow-MD (trained from molecular dynamics simulation data). Dramatic differences in the AI-generated ensembles are largely erased during the WE-RW process, yielding a consistent description of the equilibrium ensemble for a given force field.

Accurate estimation of equilibrium and nonequilibrium steady-state distributions from molecular simulation data remains challenging for systems exhibiting timescales longer than can be accessed with typical computing resources. The recently introduced RiteWeight algorithm iteratively reweights trajectory segments using randomized clustering to recover stationary distributions without discretization bias. However, with smaller data sets or a large number of iterations, the original RiteWeight algorithm may exhibit instability in weight updates due to noisy cluster-level stationary estimates. Here, we introduce a simple smoothed reweighting scheme that modifies the RiteWeight update rule by interpolating between the “raw” RiteWeight weights and average cluster weights. This formulation improves iterative convergence in under-sampled datasets while introducing a small, but tunable, bias. We demonstrate the value of smoothing using downsampled Trp-cage trajectory data previously employed in the original RiteWeight study. With smaller datasets, the smoothed update procedure substantially stabilizes convergence and improves estimation of stationary densities relative to unsmoothed RiteWeight. These results establish smoothing as a practical regularization strategy for iterative trajectory reweighting in sparse-data settings, extending the applicability of RiteWeight to a wider variety of simulation workflows.