Free energy and kinetics of cAMP permeation through connexin26 via applied voltage and milestoning

Dissecting current rectification through asymmetric nanopores

Rectification, the tendency of bidirectional ionic conductors to favor ion flow in a specific direction, is an intrinsic property of many ion channels and synthetic nanopores. Despite its frequent occurrence in ion channels and its phenomenological explanation using Eyring's rate theory, a quantitative relationship between the rectified current and the underlying ion-specific and voltage-dependent free energy profile has been lacking. In this study, we designed nanopores in which potassium and chloride current rectification can be manipulated by altering the electrostatic pore polarity. Using molecular dynamics-based free energy simulations, we quantified voltage-dependent changes of free energy barriers in six ion-nanopore systems. Our results illustrate how the energy barriers for inward and outward fluxes become unequal in the presence of an electromotive driving force, leading to varying degrees of rectification for cation and anion currents. By establishing a direct link between potential of mean force and current rectification rate, we demonstrate that rectification caused by energy barrier asymmetry depends on the nature of the permeating ion, can be tuned by pore polarity, does not require ion binding sites, conformational flexibility, or specific pore geometry, and, as such, may be widespread among ion channels.

Calcium induced N-terminal gating and pore collapse in connexin-46/50 gap junctions

Gap junctions facilitate electrical and metabolic coupling essential for tissue function. Under ischemic conditions ( e.g., heart attack or stroke), elevated intracellular calcium (Ca 2+ ) levels uncouple these cell-to-cell communication pathways to protect healthy cells from cytotoxic signals. Using single-particle cryo-EM, we elucidate details of the Ca 2+ -induced gating mechanism of native connexin-46/50 (Cx46/50) gap junctions. The resolved structures reveal Ca 2+ binding sites within the channel pore that alter the chemical environment of the permeation pathway and induce diverse occluded and gated states through N-terminal domain remodeling. Moreover, subunit rearrangements lead to pore collapse, enabling steric blockade by the N-terminal domains, reminiscent of the "iris model" of gating proposed over four decades ago. These findings unify and expand key elements of previous gating models, providing mechanistic insights into how Ca 2+ signaling regulates gap junction uncoupling and broader implications for understanding cell stress responses and tissue protection.

Molecular permeation through large pore channels: computational approaches and insights

Computational methods such as molecular dynamics (MD) have illuminated how single-atom ions permeate membrane channels and how selectivity among them is achieved. Much less is understood about molecular permeation through eukaryotic channels that mediate the flux of small molecules (e.g. connexins, pannexins, LRRC8s, CALHMs). Here we describe computational methods that have been profitably employed to explore the movements of molecules through wide pores, revealing mechanistic insights, guiding experiments, and suggesting testable hypotheses. This review illustrates MD techniques such as voltage-driven flux, potential of mean force, and mean first-passage-time calculations, as applied to molecular permeation through wide pores. These techniques have enabled detailed and quantitative modeling of molecular interactions and movement of permeants at the atomic level. We highlight novel contributors to the transit of molecules through these wide pathways. In particular, the flexibility and anisotropic nature of permeant molecules, coupled with the dynamics of pore-lining residues, lead to bespoke permeation dynamics. As more eukaryotic large-pore channel structures and functional data become available, these insights and approaches will be important for understanding the physical principles underlying molecular permeation and as guides for experimental design.

Large-pore connexin hemichannels function like molecule transporters independent of ion conduction

Connexin hemichannels were identified as the first members of the eukaryotic large-pore channel family that mediate permeation of both atomic ions and small molecules between the intracellular and extracellular environments. The conventional view is that their pore is a large passive conduit through which both ions and molecules diffuse in a similar manner. In stark contrast to this notion, we demonstrate that the permeation of ions and of molecules in connexin hemichannels can be uncoupled and differentially regulated. We find that human connexin mutations that produce pathologies and were previously thought to be loss-of-function mutations due to the lack of ionic currents are still capable of mediating the passive transport of molecules with kinetics close to those of wild-type channels. This molecular transport displays saturability in the micromolar range, selectivity, and competitive inhibition, properties that are tuned by specific interactions between the permeating molecules and the N-terminal domain that lies within the pore-a general feature of large-pore channels. We propose that connexin hemichannels and, likely, other large-pore channels, are hybrid channel/transporter-like proteins that might switch between these two modes to promote selective ion conduction or autocrine/paracrine molecular signaling in health and disease processes.

Connexin Gap Junction Channels and Hemichannels: Insights from High-Resolution Structures

Connexins (Cxs) are a family of integral membrane proteins, which function as both hexameric hemichannels (HCs) and dodecameric gap junction channels (GJCs), behaving as conduits for the electrical and molecular communication between cells and between cells and the extracellular environment, respectively. Their proper functioning is crucial for many processes, including development, physiology, and response to disease and trauma. Abnormal GJC and HC communication can lead to numerous pathological states including inflammation, skin diseases, deafness, nervous system disorders, and cardiac arrhythmias. Over the last 15 years, high-resolution X-ray and electron cryomicroscopy (cryoEM) structures for seven Cx isoforms have revealed conservation in the four-helix transmembrane (TM) bundle of each subunit; an αβ fold in the disulfide-bonded extracellular loops and inter-subunit hydrogen bonding across the extracellular gap that mediates end-to-end docking to form a tight seal between hexamers in the GJC. Tissue injury is associated with cellular Ca2+ overload. Surprisingly, the binding of 12 Ca2+ ions in the Cx26 GJC results in a novel electrostatic gating mechanism that blocks cation permeation. In contrast, acidic pH during tissue injury elicits association of the N-terminal (NT) domains that sterically blocks the pore in a "ball-and-chain" fashion. The NT domains under physiologic conditions display multiple conformational states, stabilized by protein-protein and protein-lipid interactions, which may relate to gating mechanisms. The cryoEM maps also revealed putative lipid densities within the pore, intercalated among transmembrane α-helices and between protomers, the functions of which are unknown. For the future, time-resolved cryoEM of isolated Cx channels as well as cryotomography of GJCs and HCs in cells and tissues will yield a deeper insight into the mechanisms for channel regulation. The cytoplasmic loop (CL) and C-terminal (CT) domains are divergent in sequence and length, are likely involved in channel regulation, but are not visualized in the high-resolution X-ray and cryoEM maps presumably due to conformational flexibility. We expect that the integrated use of synergistic physicochemical, spectroscopic, biophysical, and computational methods will reveal conformational dynamics relevant to functional states. We anticipate that such a wealth of results under different pathologic conditions will accelerate drug discovery related to Cx channel modulation.

Unifying Single-Channel Permeability From Rare-Event Sampling and Steady-State Flux

Various all-atom molecular dynamics (MD) simulation methods have been developed to compute free energies and crossing rates of ions and small molecules through ion channels. However, a systemic comparison across different methods is scarce. Using a carbon nanotube as a model of small conductance ion channel, we computed the single-channel permeability for potassium ion using umbrella sampling, Markovian milestoning, and steady-state flux under applied voltage. We show that a slightly modified inhomogeneous solubility-diffusion equation yields a single-channel permeability consistent with the mean first passage time (MFPT) based method. For milestoning, applying cylindrical and spherical bulk boundary conditions yield consistent MFPT if factoring in the effective bulk concentration. The sensitivity of the MFPT to the output frequency of collective variables is highlighted using the convergence and symmetricity of the inward and outward MFPT profiles. The consistent transport kinetic results from all three methods demonstrated the robustness of MD-based methods in computing ion channel permeation. The advantages and disadvantages of each technique are discussed, focusing on the future applications of milestoning in more complex systems.

Markovian Weighted Ensemble Milestoning (M-WEM): Long-Time Kinetics from Short Trajectories

We introduce a rare-event sampling scheme, named Markovian Weighted Ensemble Milestoning (M-WEM), which inlays a weighted ensemble framework within a Markovian milestoning theory to efficiently calculate thermodynamic and kinetic properties of long-time-scale biomolecular processes from short atomistic molecular dynamics simulations. M-WEM is tested on the Müller-Brown potential model, the conformational switching in alanine dipeptide, and the millisecond time-scale protein-ligand unbinding in a trypsin-benzamidine complex. Not only can M-WEM predict the kinetics of these processes with quantitative accuracy but it also allows for a scheme to reconstruct a multidimensional free-energy landscape along additional degrees of freedom, which are not part of the milestoning progress coordinate. For the ligand-receptor system, the experimental residence time, association and dissociation kinetics, and binding free energy could be reproduced using M-WEM within a simulation time of a few hundreds of nanoseconds, which is a fraction of the computational cost of other currently available methods, and close to 4 orders of magnitude less than the experimental residence time. Due to the high accuracy and low computational cost, the M-WEM approach can find potential applications in kinetics and free-energy-based computational drug design.