Revealing intermediate states of voltage-gated potassium channels with physics-informed deep learning: application to Kv7.1

Voltage-gated potassium channels translate membrane-voltage changes into pore opening through coordinated conformational rearrangements, yet the intermediate states connecting these events remain difficult to capture. Revealing such hidden intermediates is essential for reconstructing protein motions as continuous, interpretable pathways. We use Kv7.1/KCNQ1 as a stringent demonstration case because its extensive experimental characterization enables testing whether endpoint data can recover the intervening transition. We applied and tuned a general physics-informed deep-learning pipeline to molecular dynamics ensembles of tetrameric Kv7.1. A convolutional autoencoder was trained only on resting and activated endpoint conformations, while an independent intermediate ensemble was withheld. Structural reconstruction was combined with molecular-physics regularization and an electrostatic descriptor of charge displacement across the membrane field. Independent cryogenic electron microscopy structures were introduced after training as benchmarks. Generated conformations were assessed through voltage-sensor progression, contact rearrangements, pore opening, stereochemical quality, and stability in an explicit membrane. The workflow was also applied to KCNQ1-KCNE1 channel-complex ensembles containing either one or two phosphatidylinositol 4,5-bisphosphate molecules per KCNQ1 monomer. The model recovered a continuous structural progression and positioned the withheld intermediate ensemble between the endpoints. Experimental structures followed the expected resting-to-intermediate-to-activated sequence. Generated intermediates showed coordinated voltage-sensor displacement, reorganization of stabilizing interactions, and later widening of the activation gate, despite the absence of intermediate structures or pore-radius information during training. In the KCNQ1-KCNE1 complex, the approach distinguished the two lipid-stoichiometry conditions and revealed remodeling of networks linking the voltage sensor, linker, and pore gate. Physics-informed generative modeling can connect sparse endpoint data to pathway-resolved atomic hypotheses for protein conformational changes, particularly ion-channel gating. The inferred trajectories are not unique kinetic or free-energy pathways, but testable mechanistic models consistent with structural and biophysical information. More broadly, the framework offers a transferable strategy for investigating conformational transitions and modulation in proteins.

Voltage-gated ion channels are dynamic membrane proteins whose biological function depends on transitions between metastable conformational states rather than on a single static structure. Recent advances in cryo-electron microscopy have transformed the field by revealing multiple functional states of voltage-gated channels and, increasingly, their complexes with endogenous modulators, toxins, and pharmacological ligands (Huang et al., 2024). This structural progress is especially important because voltage-gated ion channels are major therapeutic targets, and state-dependent conformations can expose pharmacological sites that are absent or inaccessible in other states (Huang et al., 2024; Willegems et al., 2022). However, structural snapshots alone do not define the transition routes that connect these states. A major remaining challenge is therefore to reconstruct the intermediate conformations and pathways that underlie voltage-dependent gating, and to relate them to measurable observables such as voltage-sensor activation, pore opening, ion selectivity, and state-specific modulation (Wang et al., 2020; Taylor et al., 2020; Hou et al., 2020).

From a computational perspective, this problem is still limited by a central bottleneck in biophysics: obtaining physically meaningful descriptions of rare membrane-protein transitions at biologically relevant scales. Conventional molecular dynamics provides atomistic trajectories without imposing a transition pathway, but the timescales relevant to biomolecular conformational changes often extend far beyond what can be sampled directly, especially for slow gating events in large membrane proteins (Chodera and Noé, 2014; Corradi et al., 2018). Enhanced-sampling approaches can accelerate conformational exploration, but they often require predefined collective variables, reaction coordinates, or biasing schemes, so the resulting pathways may depend strongly on assumptions made before sampling begins (Abrams and Bussi, 2014). This creates a need for complementary approaches that can use available structural and simulation data to generate physically plausible transition hypotheses while remaining interpretable in terms of experimentally measurable features.

Deep learning has recently become a useful tool for moving beyond single protein structures toward conformational ensembles and latent representations of structural variability. Recent approaches include AlphaFold2 perturbation strategies, such as MSA subsampling or modified sampling protocols, which can recover alternative conformations and approximate conformational populations (Monteiro da Silva et al., 2024; Kalakoti and Wallner, 2025); flow- or diffusion-based generative models such as AlphaFlow and ESMFlow, which adapt structure-prediction architectures to sample sequence-conditioned ensembles (Jing et al., 2024); and large-scale protein ensemble emulators such as BioEmu, which uses static structures, extensive molecular dynamics simulations, and stability data to rapidly sample approximate equilibrium ensembles (Lewis et al., 2025). These methods represent an important shift from static structure prediction toward ensemble-aware modeling. At the same time, they mostly address conformational diversity or equilibrium sampling, whereas the problem considered here is an ordered transition-path problem. This distinction is important for voltage-gated ion channels, where intermediate conformations should follow the physical progression of voltage-sensor activation rather than simply represent diverse plausible structures. It is also relevant at the level of molecular representation: BioEmu, for example, operates primarily in a backbone-frame representation with side chains reconstructed after sampling, whereas analyses of channel gating often depend on side-chain interactions, pore constrictions, lipid contacts, and all-atom energetic terms (Lewis et al., 2025).

Alongside this, physics- and experiment-guided learning approaches have shown that molecular-mechanics losses or experimental distance restraints can improve the physical realism or interpretability of generated structures (Albano et al., 2024; Wu et al., 2025). This was the context for the physics-informed approach we have been developing, the first version of which was previously applied to Kv1.2 voltage sensor domain (Kacher et al., 2024). In that framework, known channel endpoint states are embedded into a low-dimensional learned manifold, and decoded intermediates are constrained by geometric reconstruction, physics-based structural terms, and a gating-charge-specific component. The gating-charge term gives the manifold a physical direction, encouraging generated structures to follow the expected progression of voltage sensing.

Here, we extend this framework and apply it to Kv7.1/KCNQ1, a system where the central difficulty of pathway prediction is now matched by an unusually rich experimental context. Kv7.1 is a tetrameric voltage-gated potassium channel with major roles in cardiac repolarization, epithelial transport, and inner-ear potassium homeostasis, and its dysfunction is linked to long QT syndrome, short QT syndrome, deafness, and other channelopathies (Wang et al., 2020; S et al., 2020).

Mechanistically, it is more informative than a simple closed-to-open channel model. Functional studies have shown that its voltage sensor activates through at least two distinguishable steps, producing resting, intermediate, and activated voltage-sensor configurations that are differentially coupled to pore opening (Taylor et al., 2020). This multi-state behavior has motivated a two-stage electromechanical coupling model in which distinct VSD-pore interfaces are engaged during successive activation steps (Hou et al., 2020). Recent structural work has made this benchmark substantially stronger. Mandala and MacKinnon’s polarized-vesicle structures support a mechanism in which the membrane electric field regulates the PIP2-binding site, making voltage-dependent gating indirectly dependent on PIP2 affinity and pore coupling (Mandala and MacKinnon, 2023). The newly resolved high-resolution intermediate-state structure of Kv7.1 provides an experimental landmark for a physiologically relevant intermediate conformation (Mandala and MacKinnon, 2023; Kyriakis et al., 2025a).

Alongside this, recent KCNQ1-KCNE1 structures suggest that accessory subunits and dual PIP 2 binding reshape the coupling landscape in the cardiac IKs complex (Zhong et al., 2025; Cui et al., 2025; De La Cruz and Larsson, 2025). Thus, Kv7.1 offers exactly the kind of test case needed here: a channel with experimentally distinguishable functional states and emerging structural landmarks along the activation pathway. Its regulation by PIP2 and auxiliary KCNE subunits adds a separate layer of complexity, but also provides an opportunity to test whether the framework can capture not only a transition path, but also how that path is reshaped by modulatory context. Previous work in our laboratory has also generated atomistic state models and MD-derived conformational ensembles for Kv7.1 and IKs across resting, intermediate, and activated configurations. These data provide a practical basis for training and allow us to evaluate the learned transition landscape on the tetrameric transmembrane channel core, including both voltage-sensor and pore domains, rather than on an isolated domain alone.

Together, these data make it possible to test the framework in the setting it was designed for: a full channel-core transition where intermediate states can be evaluated against independent structural and biophysical landmarks. We therefore use Kv7.1/KCNQ1 to assess whether a scalable physics-informed deep learning pipeline can reconstruct gating transitions that are both structurally plausible and biophysically interpretable. Specifically, we benchmark predicted intermediates against the experimental structural context now available for Kv7.1, incorporate a Kv7.1-specific gating-charge parametrization as a physically grounded descriptor of voltage sensing, and evaluate the resulting pathway using manifold placement, structural comparison, and pore-level descriptors of channel opening.

MD-derived datasets and preprocessing

The primary learning dataset was constructed from previously generated atomistic molecular dynamics simulations of Kv7.1/KCNQ1 state models. These models were developed before the availability of the recent high-resolution cryo-EM intermediate-state structures and therefore provide an independent computational source for training and internal validation. The source simulations described the tetrameric transmembrane channel core in three state-specific conformations: resting/closed (RC), intermediate/open (IO), and activated/open (AO). These state definitions follow the two-stage electromechanical coupling model of Kv7.1, in which the channel can conduct when the VSD occupies either the intermediate or activated configuration (Hou et al., 2020). In the original systems, the Kv7.1 channel was embedded in a POPC membrane, solvated with 150 mM KCl, and simulated with PIP 2 present in the membrane environment, with one PIP 2 molecule per Kv7.1 subunit in the earlier Kv7.1 simulations (Hou et al., 2020; Deyawe et al., 2018).

For the present learning task, only endpoint conformational ensembles were used for model training. Frames from the RC and AO trajectories were combined to form the training dataset, whereas the IO trajectory was withheld and used as an internal MD-derived validation set. The final Kv7.1 full-channel dataset was intentionally based on relatively modest state-local sampling: 500 ns simulations were available for each modeled state, yielding 7515 training frames from the RC and AO endpoint ensembles and 3676 withheld validation frames from the IO ensemble, following the dataset partitioning used in our earlier implementation of the full-channel workflow (Kacher, 2024). Thus, the model was not trained on long unbiased trajectories containing spontaneous gating transitions, but on short equilibrium ensembles around predefined endpoint states. This design tests whether the framework can infer pathway-relevant intermediate conformations from accessible end-state sampling rather than from exhaustive transition sampling.

A secondary dataset derived from IKs/Kv7.1-KCNE1 simulations was prepared to assess the same workflow in a modulatory context. In the underlying IKs models, the corresponding state set is RC, IC, and AO, reflecting the suppression of intermediate-state pore opening by KCNE1 (Deyawe et al., 2018; Deyawe et al., 2023). Although KCNE1 and PIP 2 were present in the original IKs molecular systems, including simulations designed to examine PIP 2 stoichiometry effects, they were not included in the learning atom selection used here. In particular, the later IKs simulations compared systems with one versus two PIP 2 molecules per Kv7.1 subunit and suggested that two PIP2 binding sites per monomer stabilize the IKs state models more effectively (Deyawe et al., 2023). Thus, the IKs-derived dataset was used to evaluate the Kv7.1 channel-core transition under a KCNE1/PIP 2 -shaped structural context.

For all learning datasets, the coordinate representation consisted of Kv7.1 protein heavy atoms only. Hydrogens, water molecules, ions, membrane lipids, and PIP 2 were not used for training. In the IKs-derived dataset, the atom selection was additionally restricted to Kv7.1 α -subunit heavy atoms, so that KCNE1 was excluded from the learned coordinate space. This representation preserves the tetrameric voltage-sensor and pore-domain architecture. The same atom order and topology reference were maintained across training, internal validation, generation, and inference steps.

Trajectory preprocessing was performed using the pipeline data-loading module built on MDAnalysis (Michaud-Agrawal et al., 2011; Gowers et al., 2016). Along with the atom selection, coordinates are centered and aligned before training. The coordinate representation used for learning and the atom set used for alignment were intentionally defined separately. All selected Kv7.1 heavy atoms were retained as model input, whereas global rigid-body motion was removed using backbone atoms from the stable transmembrane scaffold. This alignment scaffold included the pore-domain transmembrane helices and S1–S3 of the voltage-sensing domains, while excluding flexible loop regions. The S4 helices were not used as the primary fitting scaffold, so that voltage-sensor displacement along the activation pathway was not artificially removed. For membrane-protein trajectories, rotational/translational fitting was restricted to the xy plane, removing global lateral drift and rotation while preserving z-directed displacements relevant to voltage-sensor motion. The processed coordinates, selected-atom topology, and normalization parameters were saved and reused for subsequent model training, generation, and inference. The same preprocessing convention was applied to endpoint training frames, IO validation frames, and later external test structures to ensure that all conformations were comparable.

No cryo-EM structures were included in either the training dataset or the internal MD-validation dataset. Experimental structures were introduced only after model training, as external structural landmarks for projection into the learned manifold and comparison with generated intermediates.

Neural network architecture and composite loss function

The model is based on the physics-informed autoencoder framework previously developed for voltage-sensor-domain activation-pathway prediction (Kacher et al., 2024) and implemented in PyTorch (Paszke et al., 2019). A schematic of the network architecture and composite loss is provided in Supplementary Figure S1. In the present work, the pipeline was extended from an isolated voltage-sensor-domain application to the tetrameric Kv7.1 transmembrane channel core. The main technical improvements were introduced at the level of the physics-loss implementation, which made it feasible to retain molecular-mechanics-based regularization during training on full-channel coordinate sets. Input conformations were represented as ordered Cartesian coordinate tensors of the selected Kv7.1 heavy atoms. The encoder maps each conformation into a two-dimensional latent representation, and the decoder reconstructs Cartesian coordinates from latent points. A two-dimensional latent space was retained because it allows direct visualization of the learned conformational manifold and the predicted transition pathway.

For the full-channel Kv7.1 datasets, the network used a one-dimensional convolutional autoencoder architecture with residual blocks, batch normalization, and nonlinear activation layers. Compared with the earlier voltage-sensor-domain implementation, the full-channel model used a deeper architecture to accommodate the larger number of atoms and the broader range of collective motions in the tetrameric transmembrane channel core. Model hyperparameters, including convolutional depth, number of residual blocks, latent dimensionality, batch size, learning rate, and loss-component weighting coefficients, were kept fixed within each reported run and are provided in the Supplementary Material (Supplementary Figure S1.2).

The composite loss function follows the general form introduced in our previous work (Kacher et al., 2024), as shown in Equation 1:

where M S E is the coordinate reconstruction loss, L phys penalizes physically unfavorable decoded conformations, and the two gating-charge terms constrain the organization of the latent path. Q path encourages decoded structures to follow the expected ordering of voltage-sensor activation, whereas Q lin promotes a smooth progression of the gating-charge descriptor along the interpolated pathway. The Kv7.1-specific parametrization of the gating-charge descriptor is described separately below. The coefficients are set to 1 for α 1, and the auxiliary physics and gating-charge terms were assigned default weights of 0.1. The auxiliary weights were chosen to preserve coordinate reconstruction while discouraging physically unfavorable decoded structures and enforcing smooth voltage-sensor ordering, following the balance established in our first implementation (Kacher et al., 2024).

The physics-based component was designed to discourage decoded conformations that are geometrically plausible in latent space but physically unrealistic at the molecular level. It includes bonded, angular, torsional, and non-bonded terms derived from classical molecular-mechanics force-field expressions. This part of the framework was initially inspired by the force-field-based regularization introduced in the molearn workflow from the Degiacomi group, which provides tools for learning protein conformational spaces from molecular simulation or experimental ensembles (Degiacomi, 2019; Ramaswamy et al., 2021). In the present pipeline, this idea was reimplemented and extended for voltage-gated ion-channel transition modeling. In particular, we refactored the physics-loss implementation to support full-channel coordinate sets, introduced atom-name and atom-type conversion routines to accommodate MD datasets generated in different force-field contexts, and coupled the structural regularization to the Kv-channel-specific gating-charge terms described below. In this context, Lphys was used as a soft structural regularizer rather than as an absolute molecular-mechanics energy estimate.

The non-bonded contribution was the main computational bottleneck for extending the workflow from isolated voltage-sensor domains to the full tetrameric channel core. A naive implementation based on explicit all-pairs distance tensors becomes memory-limiting for full-channel systems. To address this, we implemented a custom CUDA/Numba backend (Lam et al., 2015) for the Lennard-Jones/Coulomb non-bonded term, avoiding storage of the full pairwise distance matrix and substantially reducing the memory footprint of the physics loss (Kacher, 2024) (Supplementary Figure S2). This kernel-based implementation was the main technical change that made it feasible to retain non-bonded regularization during training on the full tetrameric transmembrane channel core. Numerical consistency checks and timing/memory benchmarks for the kernel implementation are reported in the Supplementary Material.

In the current version of the pipeline, the non-bonded physics term is backend-modular. In addition to the custom CUDA/Numba implementation, the same loss framework can be run with an OpenMM-based backend (Eastman et al., 2013). This backend uses OpenMM as the molecular-mechanics engine while preserving the original physics-loss interface. This provides a reference implementation, similar to the recent OpenMM-Loss, when the molecular-mechanics potential energy is incorporated as a differentiable loss to improve the physical quality of deep-learning-generated protein structures (Albano et al., 2024). In the present work, the physics loss is not used for static protein structure prediction. Instead, it acts as a structural regularizer for decoded Kv7.1 transition intermediates, while the gating-charge terms impose the voltage-sensing direction of the learned pathway.

Production runs were performed on an NVIDIA GeForce RTX 3090 GPU with 24 GB memory. In the representative Kv7.1 full-channel run, 200 epochs completed in approximately 4 h 34 min, corresponding to approximately 50,000 optimization steps, or about 0.33 s per optimization step. Under comparable in-house settings, this full-channel training was approximately fivefold slower than the earlier single-VSD implementation, reflecting the larger atom selection and tetrameric channel-core representation. This wall time is reported as a run-specific value rather than as a general benchmark, because computation time depends strongly on atom selection, number of frames, batch size, GPU hardware, validation set, validation frequency, and logging scope and frequency. Backend-level timing was therefore evaluated separately on the non-bonded physics-loss term using an NVIDIA GeForce GTX 1070 GPU with 8 GB memory as a conservative memory-limited test case. Comparisons between the custom kernel backend and the OpenMM-based implementation are provided in the Supplementary Material (Supplementary Figure S2.2, S2.3). The latter showed faster isolated physics-loss evaluation and lower memory use, motivating its use as the preferred backend in the current version of the pipeline, while the CUDA/Numba backend remains the backend used for the production run reported here and a useful alternative.

Generation, postprocessing, and structural validation of intermediates

After training, transition intermediates are generated by sampling the learned latent space between the closed and open endpoint regions–the primary pathway is generated in an automated cluster-center mode. In this mode, representative latent points were selected from the RC and AO endpoint ensembles, and a lowest-score route was traced between the corresponding endpoint cluster centers on the learned two-dimensional latent manifold. Here, the score refers to the model-derived latent energy-like landscape and should not be interpreted directly as a free-energy surface. Twenty equally spaced latent points are then decoded into Cartesian coordinates to produce a first-generation series of Kv7.1 intermediate conformations. The number of generated structures can be increased for higher pathway resolution, and alternative path-generation modes, including paths based on manually defined endpoints, were used for exploratory analyses.

The generated structures are first analyzed directly as decoded protein conformations. Because the learned coordinate representation contains Kv7.1 heavy atoms only, the initial outputs do not include hydrogens, solvent, membrane lipids, ions, PIP2, or KCNE1 in the IKs case. To test whether generated intermediates could be used as simulation-ready atomic models, selected decoded structures were reintroduced into an explicit membrane/solvent environment using an automated OpenMM pipeline. Since the autoencoder outputs Kv7.1 heavy-atom coordinates only, missing atoms and hydrogens were added, after which each structure was embedded in a POPC membrane, solvated, neutralized, and ionized with 150 mM KCl using OpenMM Modeller with Amber14, lipid17, and TIP3P parameters. The systems were energy-minimized, restrained during equilibration at 310 K, and then propagated in unrestrained simulations. This step was used as a practical stability test, to determine whether decoded intermediates could seed new simulations. Structural validation is performed at several complementary levels. First, global and domain-specific structural similarity is evaluated by RMSD after alignment to the same reference frame used for the validation dataset at the model inference. Second, local structural quality is evaluated using stereochemical and statistical-potential metrics. MolProbity is used to assess local model quality, including steric clashes, Ramachandran outliers, and side-chain rotamer quality, following its standard all-atom structure-validation framework (Williams et al., 2018). DOPE scores are used as an additional statistical-potential-based assessment of relative model quality, particularly for comparing generated structures along the same pathway and after relaxation (Shen and Sali, 2006). These metrics are interpreted as quality-control readouts. Third, the generated structures are evaluated using Kv7.1-specific structural descriptors. Contact maps and residue-pair distances are calculated for known state-sensitive interaction networks, including VSD salt-bridge patterns, VSD-pore coupling interfaces, S4-S5/S6 contacts, and the SFF-region hydrophobic-gate environment. Particular attention is given to residues previously implicated in Kv7.1 pore gating and coupling, including the S6/PAG-region and SFF/F339-F340 region, because these features provide a direct link to earlier MD-based analyses of Kv7.1 and IKs state models.

Finally, pore geometry is assessed using HOLE pore-radius calculations (Smart et al., 1996). For each generated and relaxed structure, the pore profile was calculated along the central conduction pathway, and bottleneck radii were compared across RC, generated intermediates, IO validation structures, AO, and external structural references. HOLE results are therefore used as structural descriptors of pore opening rather than as direct conductance estimates.

Together, these postprocessing and validation steps were designed to separate three questions: whether the decoded intermediates are geometrically and stereochemically reasonable, whether they follow the expected voltage-sensor and pore-domain progression, and whether selected structures remain stable enough after reinsertion into an explicit membrane environment to serve as starting points for downstream simulations.

Projection of cryo-EM structures and external models into the learned manifold

Experimental structures and external models were used only after model training and were not included in either the endpoint training dataset or the internal MD-derived validation dataset. They were introduced as external structural landmarks to assess how independently determined Kv7.1/KCNQ1 conformations are organized in the learned latent space and how experimentally resolved or experimentally derived states align with the generated intermediates.

The Mandala and MacKinnon polarized-vesicle structures 8SIN, 8SIM, and 8SIK were used as voltage-sensor-state landmarks corresponding to VSD-down, VSD-intermediate, and VSD-up conformations, respectively (Mandala and MacKinnon, 2023). These structures are particularly useful for testing voltage-sensor placement in the manifold because they provide an experimental series of KCNQ1 VSD conformations obtained in lipid vesicles under an applied electric field. However, their use for pore-state validation is limited because the structures were obtained in the absence of PIP2-dependent pore opening. In the Mandala and MacKinnon model, voltage-sensor motion regulates the pore indirectly by altering access to the PIP2-binding site; therefore, a VSD-up conformation in this series does not necessarily correspond to an activated/open pore state in the sense used for the MD-derived AO ensemble (Mandala and MacKinnon, 2023). Consistently, all three structures have a closed pore in the absence of PIP2 (Mandala and MacKinnon, 2023).

The Kyriakis/Fedida structures were included as high-resolution experimental references for the KCNQ1 intermediate-state mechanism (Kyriakis et al., 2025a). In this dataset, 9MY3 corresponds to the experimentally determined Xenopus WT KCNQ1-CaM structure, whereas 9MY4 corresponds to the xE1R/R2E charge-reversal construct stabilized in the intermediate VSD state. 9MY3 was retained as the same-species WT structural reference from the same study, while 9MY4 captures the intermediate-state VSD arrangement. Both structures were resolved in the PIP2-free environment and retain a closed inner gate.

The Kyriakis/Fedida intermediate structure is especially informative because it is not simply a geometric midpoint between resting and activated states. In the xE1R/R2E structure, the upper parts of S1 and S2 are straightened and displaced away from the filter helix by approximately 6 Å relative to xWT, whereas the S4 helix, S4-S5 linker, and pore-domain helices remain close to the activated-state arrangement. Residue numbering differs between Xenopus KCNQ1 structures and the human Kv7.1/KCNQ1 models used for training. Therefore, structural comparisons were performed after sequence-based residue mapping, but for the principal VSD gating residues, Xenopus residues map to human KCNQ1 residues with an approximately +10 shift, making the downstream analysis straightforward (Kyriakis et al., 2025a). The reported C α RMSD between xE1R/R2E and xWT is only 0.37 Å for the pore-domain residues 249–349, indicating that the major intermediate-state signature is concentrated in the VSD, especially S1/S2, rather than in the pore domain. The same study compares xE1R/R2E with the lower-resolution Mandala/MacKinnon intermediate structure 8SIM and notes that both share related charge-transfer-center features, although xE1R/R2E displays a more pronounced straightened S1/S2 conformation.

We were particularly interested in the WT-reverted intermediate model from the Kyriakis/Fedida MD dataset. This model, xWT-R (derived from 9MY4 and referred to as 9MY4-rWT in the figures) was generated in the original study by reverting the xE1R/R2E mutations back to the WT sequence in the xE1R/R2E coordinate file and then evaluating the resulting structure by molecular dynamics (Kyriakis et al., 2025b). The final conformations from the WT-system replicas were therefore treated as computational WT-reverted intermediate models derived from the xE1R/R2E cryo-EM state.

To assess PIP2-associated open/coupled conformations, we also included the human KCNQ1-CaM-ML277-PIP2 structures 7XNL and 7XNN (Ma et al., 2022). These structures could not be treated as native PIP2-only references because both contain CaM, PIP2, and the small-molecule state stabilizer ML277. Instead, they were used as drug- and lipid-stabilized open/coupled references. 7XNL corresponds to state A and 7XNN to state B of the KCNQ1-CaM-ML277-PIP2 complex, with reported cryo-EM resolutions of 3.10 Å and 2.50 Å, respectively (Ma et al., 2022). The major distinction between states A and B involves intracellular CaM/CTD rearrangement and PIP2 coordination rather than only the transmembrane channel core, so these structures were still useful references. However, because ML277 binds at the VSD-pore coupling interface and stabilizes channel opening pharmacologically, ML277-containing structures should not be interpreted as unliganded physiological open states (Ma et al., 2022).

In addition to cryo-EM structures, we included the historical Smith et al. closed-state KCNQ1 model as an external model reference (Smith et al., 2007). This structure was treated separately from the experimental landmarks because it is a pre-cryo-EM comparative/Rosetta model generated to rationalize mutation-phenotype relationships, not an experimentally resolved Kv7.1 state. It was therefore used only as a historical closed-model reference and not as a primary validation target for the learned transition pathway.

All external structures and models were prepared to match the training atom selection before projection. Non-Kv7.1 components, including CaM, ML277, PIP2, lipids, ions, detergents, waters, and other non-protein molecules, were removed unless required for separate structural inspection. The remaining Kv7.1/KCNQ1 channel-core coordinates were mapped onto the same selected-atom representation used for model training. Missing atoms within the selected atom set were completed when necessary using OpenMM Modeller (Eastman et al., 2013), whereas unresolved or ambiguous regions outside the selected atom set were omitted from the learning representation.

Because the trained model uses a fixed atom order and fixed chain ordering, whereas tetrameric experimental structures may be deposited with arbitrary chain labels, chain-order matching was performed before manifold projection. For each external tetramer, symmetry-consistent chain permutations were generated, prepared with the same atom selection, and aligned to the training reference using the preprocessing convention described above. This step was used to prevent arbitrary chain-label mismatch from being interpreted as a genuine conformational difference, and it represents a practical limitation of applying fixed-order coordinate autoencoders to multimeric proteins. Each prepared structure was then passed through the trained encoder in inference mode and projected into the two-dimensional latent space together with the training and validation datasets and the generated intermediates.

The resulting projections were analyzed together with the structural metrics described above, including RMSD, domain-wise comparisons, contact signatures, gating-charge descriptors, and pore-radius profiles. Thus, external structures were not used to train or tune the model, but provided independent landmarks for evaluating the performance of the pipeline.

Table 1 summarizes the external references used for post-training manifold projection and structural comparison.

Kv7.1 gating charge parametrization

Voltage-gated ion channels respond to changes in membrane potential because charged groups within the voltage-sensing domain move through the membrane electric field. In Kv channels, the dominant contribution comes from positively charged residues on the S4 helix, which move outward during activation and exchange interactions with acidic residues and lipid headgroups along the voltage sensor. This charge displacement gives rise to a small capacitive current, the gating current. The time integral of this current reports the charge displaced by voltage-sensor rearrangement and is commonly referred to as gating charge (Sigworth, 1994; Silva et al., 2009; Treptow and Tarek, 2006; Khalili-Araghi et al., 2006; Souza et al., 2014; Delemotte et al., 2011; Ishida et al., 2015). Structurally, this quantity can be interpreted as a compact descriptor of how far the S4 charges have progressed through the focused electric field of the VSD. In our previous work, this property was incorporated into the network loss function because it connects conformational interpolation to the physical direction of voltage-sensor activation (Kacher et al., 2024).

A distinction is important here. In electrophysiology, “gating charge” usually refers to a transferred charge, i.e., a difference between limiting states or between states sampled by a voltage protocol. This is the quantity obtained by integrating gating currents or inferred from voltage-dependent activation. Some studies report an apparently absolute value such as Q per channel, but this value still represents the total movable charge over the experimentally accessible activation process, usually normalized by channel number or inferred from the limiting slope. In contrast, a structure-based calculation produces a state-dependent descriptor whose zero depends on the chosen electrical-distance convention, reference frame, and selected charges. Therefore, in this work we denote the raw structural descriptor as Q *, and we compare with experimental gating-charge estimates only through differences between states, Δ Q.

The theoretical basis follows previous computational treatments of voltage-sensor activation, in which the contribution of a charged residue depends not only on its formal charge but also on its position within the local membrane electric field (Silva et al., 2009; Treptow and Tarek, 2006; Khalili-Araghi et al., 2006; Souza et al., 2014; Delemotte et al., 2011). In this framework, the electrical distance δ reports the fraction of the transmembrane potential experienced by a charge at a given position. The structural descriptor can then be approximated as the sum of charge contributions weighted by their electrical distances. This formalism has been used in molecular simulations of voltage sensors and in multiscale channel modeling to connect S4 charge displacement with voltage-dependent energetics and gating-current-like observables (Silva et al., 2009; Treptow and Tarek, 2006; Khalili-Araghi et al., 2006; Souza et al., 2014; Delemotte et al., 2011).

In the present work, we used a Kv7.1-specific Q * descriptor both as a training constraint and as a post hoc analysis coordinate. The descriptor was incorporated into the learning objective through Q path and Q lin, and it was also used to label and compare training structures, generated intermediates, relaxed structures, and external references projected into the learned manifold. The descriptor is not intended to replace experimental gating-current measurements. Rather, it acts as an effective structural proxy for S4 charge displacement, calculated consistently for all conformations considered in the workflow.

For Kv7.1, the electrical-distance coefficients were estimated from independent VSD/PIP2 systems prepared from our state models. Individual VSDs were extracted from the full-channel Kv7.1 simulations together with the associated PIP2 molecule and a local POPC lipid environment. These assemblies were embedded into pre-equilibrated POPC bilayers, solvated with 150 mM KCl, and simulated as independent systems representing resting, intermediate, and activated VSD configurations. In the thesis-stage implementation, twelve systems were prepared, corresponding to the four VSDs from each of the three modeled states, and equilibrated before electrostatic-potential analysis. The original setup used OpenMM, OpenMM Modeller for system editing and solvation, CHARMM36m parameters, the TIP3P water model, and PIP2 with a net charge of − 4.

To estimate the electrical-distance profile, we used the charge-imbalance protocol previously introduced by our group (Delemotte et al., 2008). The simulation box was extended along the membrane normal, and ion-imbalance configurations were generated to impose different electrostatic conditions across the membrane. In the original implementation, electrostatic potential profiles were obtained from these trajectories using GROMACS-based potential analysis (Abraham et al., 2015). In the updated workflow, the same conceptual analysis can be performed using the SCIM electrostatic-potential pipeline, avoiding dependence on a complete GROMACS setup. In both implementations, potential profiles are compared across imposed electrostatic conditions, converted into electrical-distance curves, and fitted with a sigmoidal function.

The electrical distance was modeled as δ (z) = 1 1 + e − α (z − β), where z is the position of the selected gating-charge atom along the membrane normal in the VSD reference frame, α the steepness of the transition across the focused electric field, and β defines the midpoint of the effective field profile. The gating-charge descriptor for a given conformation λ was then calculated as Q (λ) = ∑ i q i δ (z i), where q i is the formal charge assigned to the selected S4 charge-carrying atom or group and z i is its position along the membrane-normal coordinate. For Kv7.1, the selected S4 gating charges included the principal positively charged residues involved in voltage sensing, including R228, R231, R237, and R243, whose state-dependent interactions with E160, E170, and D202 provide a structural signature of VSD progression.

The initial Kv7.1-specific fits from the thesis-stage implementation yielded effective coefficients of α = 1.2044 and β = − 0.1808. With these coefficients, Q * increased by approximately 5 e 0 between resting/closed and activated/open-like conformational ensembles in reasonable agreement with available experimental estimates for Kv7.1 total gating charge. Barro-Soria et al. estimate the total transferred charge for KCNQ1/KCNE1 as 4.13 e 0 per channel in their six-state model, composed of a main independent VSD movement plus a smaller concerted movement coupled to opening (Barro-Soria et al., 2014). At the same time, it remains lower than values reported for more highly charged Kv channels such as Kv1.2, for which Ishida et al. estimated a total movable charge close to 10 e 0 per channel (Ishida et al., 2015). It is also within the broader range discussed for KCNQ1 channels: direct Q1 gating current measurements by Ruscic et al. gave a Q-V slope of approximately z = 2.2, which under a simplified two-state interpretation corresponds to roughly 8–9 elementary charges per Kv7.1 channel, although the authors emphasize that z should not be equated directly with total effective valence for a multi-state channel (Ruscic et al., 2013).

We also evaluated whether the fitted α and β parameters could be treated as universal across states and subunits, as suggested by earlier work proposing that the focused electric-field profile is relatively conserved across voltage-sensor domains (Supplementary Figure S4) (Souza et al., 2014). Our Kv7.1 VSD/PIP2 calculations indicate that the fitted parameters are not perfectly identical across resting, intermediate, and activated systems and may also differ between subunits. This variability is especially apparent in β, consistent with the idea that the local lipid, PIP2, and protein environment can shift the effective midpoint of the focused-field region. Nevertheless, the differences were small enough for the present purpose, where the descriptor is used primarily to regularize and orient the learned transition pathway rather than to compute an absolute electrostatic observable. For the main production workflow, we therefore used averaged Kv7.1-specific α and β coefficients to provide a single consistent ordering descriptor across the full tetrameric channel. State- and subunit-specific coefficients were retained as sensitivity controls and are reported in the Supplementary Material after recalculation with the updated electrostatic-potential workflow (Supplementary Figure S4).

Finally, the current framework also allows α and β coefficients to be treated as trainable or weakly restrained parameters during model optimization. This extension is useful for testing whether the data support small adjustments of the electrical-distance profile while preserving the physically motivated sigmoidal shape. However, unless otherwise stated, the main analyses reported here use fixed Kv7.1-specific coefficients, because fixed coefficients make the gating-charge descriptor directly comparable across training, generated, relaxed, and externally projected structures. Trainable-coefficient experiments were therefore treated as exploratory controls rather than as the default parametrization for the present manuscript.

Visualization and statistical analysis

Structural visualization was performed using VMD (Humphrey et al., 1996) for publication figures, structural overlays, and inspection of cryo-EM-derived models and external references. Trajectory and structure analyses were performed using Python-based workflows. MDAnalysis was used for trajectory handling, atom selection, alignment, and coordinate extraction (Michaud-Agrawal et al., 2011; Gowers et al., 2016). NumPy and SciPy were used for numerical analysis (Harris et al., 2020; Virtanen et al., 2020), performance-critical custom routines were accelerated with Numba where appropriate (Lam et al., 2015), and Matplotlib was used for plotting (Hunter, 2007).

Structural descriptors, including RMSD, contact distances, pore radii, MolProbity scores (Williams et al., 2018), DOPE scores (Shen and Sali, 2006), and Q * descriptors, were compared across training ensembles, validation structures, generated intermediates, relaxed intermediates, and external structural references. Unless otherwise stated, ensemble quantities are reported as means and standard deviations, while individual cryo-EM structures and external models are reported as single-structure reference values. Generated intermediates were ordered according to their position along the predicted latent-space path and compared with Q *, pore-radius, RMSD, and contact-signature progression.

No statistical hypothesis testing was used to assign functional states. The analysis was treated as a structural-validation and pathway-consistency problem, where generated conformations were evaluated against internal MD validation data, independent structural landmarks, stereochemical quality metrics, pore descriptors, and gating-charge progression.

The goal of this study was twofold. First, we asked whether a physics-informed autoencoder trained only on modest endpoint MD ensembles could infer pathway-relevant intermediates for a large tetrameric membrane protein without requiring either long spontaneous transitions or biased pathway-sampling trajectories. Second, we asked whether the resulting learned manifold could be interpreted in the biological context of Kv7.1 gating, where voltage-sensor activation, PIP2-dependent VSD-pore coupling, and accessory-subunit modulation make the transition more complex than a simple closed-to-open structural interpolation. The Results are therefore organized around these two questions: we first evaluate whether the endpoint-trained model learns an ordered Kv7.1 transition manifold and generates structurally plausible intermediates, and then test whether the inferred pathway is consistent with voltage-sensor progression, pore/coupling descriptors, follow-up MD relaxation, and independent cryo-EM structural landmarks.

Endpoint-trained model learns a Kv7.1 transition manifold

We first asked whether local conformational sampling around endpoint states is sufficient for a physics-informed autoencoder to recover a transition-relevant organization of the Kv7.1 channel. The model was trained on MD conformations drawn from two state-local endpoint ensembles, corresponding to resting/closed-like and activated/open-like channel states, referred to as RC and AO. The independently generated intermediate/open-like ensemble was withheld during training and used only after model optimization as an internal validation set. This design deliberately imposed a stringent learning problem: the network was trained only on very limited MD data coming from endpoints. The question was therefore whether this sampling, together with physics-informed regularization, was sufficient to organize Kv7.1 conformations along a biologically meaningful activation coordinate.

This task is substantially more demanding than learning a reduced voltage-sensor-only representation, as in our previous study (Kacher et al., 2024). The input coordinates contain the tetrameric channel core, including four voltage-sensor domains, the central pore domain, and the S4–S5/S6 coupling interface. The model therefore must represent not only local S4 rearrangements, but also the coordinated organization of homologous subunits and the pore scaffold. Successful training on this full channel-core representation was thus an important technical prerequisite for the biological analysis that follows (as described in the Methods and Supplementary Figure S2). It established that the architecture and optimized physics-loss implementation could be applied to a large tetrameric membrane protein without reducing the system to a single isolated voltage sensor.

Projection of the training data into the learned two-dimensional latent space revealed a clear separation between the RC and AO endpoint ensembles (Figure 1, training data). When the withheld IO ensemble was subsequently encoded into the trained model, these conformations projected to a biologically interpretable region of the same manifold: displaced toward the AO side, consistent with their open/coupled character, but not collapsed into the AO cluster, consistent with the distinct intermediate-open state described for Kv7.1. This behavior indicates that the autoencoder did not simply memorize endpoint-specific structural features. Instead, it learned an ordered low-dimensional organization in which independently generated intermediate conformations fall along the inferred route between the endpoint states. This result is consistent with the established two-step activation behavior of Kv7.1/KCNQ1, in which voltage-sensor activation proceeds through intermediate and activated configurations rather than a single binary resting-to-activated transition. Barro-Soria et al. showed that KCNQ1/KCNE1 voltage-sensor movement is divided into two steps, and Hou et al. later linked these voltage-sensor steps to two-stage electromechanical coupling in Kv7.1 (Hou et al., 2020; Barro-Soria et al., 2014). We further quantified this internal validation in the Supplementary Material (Supplementary Figure S3) by directly comparing generated intermediates with the withheld IO ensemble.

We next sampled the latent organization to generate a discrete transition hypothesis. Using the cluster-center path-generation mode, we selected 20 evenly spaced latent points between representative RC and AO regions and decoded each point back into Cartesian coordinates. This generated a first-generation series of Kv7.1 intermediate structures. We interpret this series as the preferred latent-space transition hypothesis under the present training conditions, not as a unique physical pathway or a fully equilibrated dynamical trajectory. The generated route necessarily depends on the endpoint MD ensembles used for training, the molecular context of those simulations, and the regularization terms included in the model. Consequently, the decoded structures are treated here as physically informed structural hypotheses.

To test whether the inferred path was ordered along an electromechanically meaningful voltage-sensor coordinate, we colored the manifold and decoded structures by a computed absolute gating charge descriptor (Figure 1). We estimated this descriptor from the electrical-distance profile of the Kv7.1 voltage sensor and used that profile to weight the displacement of charged groups along the membrane electric field. In this formulation, each charge contributes according to the fraction of the transmembrane potential it senses (Silva et al., 2009; Treptow and Tarek, 2006; Khalili-Araghi et al., 2006; Souza et al., 2014; Delemotte et al., 2011). The learned landscape was ordered by this descriptor: closed/resting references localized near the low-charge region of the manifold, whereas activated/open references localized near the high-charge region. Run-to-run robustness is summarized in the Supplementary Material S6. Across independently trained autoencoder-style models, the exact two-dimensional geometry varied, but RC/AO separation, intermediate IO placement, and ordered q-charge progression were preserved.

In the model shown, resting/closed structures fall near 5 e 0, while activated/open structures are near 10 e 0; RC-to-AO displacement is close to Δ q ≈ 5 e 0. As an external check, applying the same electrical-distance coefficients to IKs systems reproduced the experimentally inferred KCNQ1/KCNE1 total gating-charge estimate of 4.13 e 0 /channel reported by Barro-Soria et al., whereas Kv7.1 alone yielded a slightly larger value.

Cryo-EM structures as benchmarks for the learned manifold

Kv7.1 is an unusually favorable test case for pathway prediction because several recent cryo-EM studies have resolved structures corresponding to distinct voltage-sensor, pore, lipid-bound, and ligand-stabilized contexts (Mandala and MacKinnon, 2023; Kyriakis et al., 2025a; Zhong et al., 2025; Cui et al., 2025; Ma et al., 2022). These structures provide independent landmarks for evaluating the learned manifold; therefore, we used them as external benchmarks after training. However, they should not be interpreted as interchangeable state labels because each was obtained in a specific experimental and molecular context.

The Mandala and MacKinnon polarized-vesicle structures provide a useful voltage-sensor series: 8SIN corresponds to a VSD-down conformation, 8SIM to a VSD-intermediate conformation, and 8SIK to a VSD-up conformation (Mandala and MacKinnon, 2023). These structures are especially valuable because they were obtained in lipid vesicles under an applied membrane electric field and therefore directly report voltage-dependent VSD rearrangements. However, they are less suitable as direct pore-opening references. In the same study, the channel was analyzed in a PIP2-free context, and the main mechanistic conclusion was that the membrane electric field regulates access to the PIP2-binding site rather than opening the pore directly (Mandala and MacKinnon, 2023). Thus, even the VSD-up structure 8SIK should be treated as an activated-VSD landmark, not as a native AO-like open-pore reference. 8SIM is an intermediate-conformation KCNQ1 structure with a 6.20 Å cryo-EM resolution, which further supports using it primarily as a state-level VSD landmark.

The recent Kyriakis/Fedida structures provide a complementary intermediate-state benchmark. 9MY3 is the same-study Xenopus WT KCNQ1-CaM reference, whereas 9MY4 is the xE1R/R2E charge-reversal construct stabilized in the intermediate VSD state (Kyriakis et al., 2025a). Although these structures are Xenopus KCNQ1, the regions used here for voltage-sensor and pore-core comparison are highly conserved and map straightforwardly to human Kv7.1. The reported high-resolution intermediate 9MY4 structure shows straightened upper S1 and S2 helices, an S4 position similar to the fully activated structure, and little change in the S4-S5 linker between intermediate and activated states (Kyriakis et al., 2025a). We included the WT-reverted intermediate models from the Kyriakis/Fedida MD dataset as WT intermediate-state references (Kyriakis et al., 2025b). These xWT-R conformations were generated by reverting the xE1R/R2E mutations back to the WT sequence and evaluating the resulting intermediate-like state by MD. Their role in the present analysis is to bridge the engineered 9MY4 intermediate state and a WT-sequence intermediate-like conformation.

For open/coupled references, we used the full-length human KCNQ1-CaM-ML277-PIP2 structures 7XNL and 7XNN from Ma et al. (Ma et al., 2022). These structures provide valuable references for ligand- and lipid-stabilized open conformations, but they also cannot be interpreted as unliganded AO states. Both contain CaM, PIP2, and the small-molecule activator ML277; 7XNL corresponds to state A at 3.10 Å resolution and 7XNN to state B at 2.50 Å resolution. The primary publication reports that ML277 binds at an “elbow” pocket above the S4-S5 linker, while PIP2 binds in the VSD-pore cleft; together, these ligands act as electro-mechanical coupling enhancers (Ma et al., 2022). Nevertheless, 7XNL and 7XNN are best used as open/coupled structural landmarks.

After preparation with the same atom selection and alignment convention used for the MD-derived data, the external structures were encoded into the trained latent space (Figure 1). Overall, the external structures occupied interpretable regions of the manifold. The Mandala/MacKinnon structures followed the expected VSD ordering from down to intermediate to up. Notably, despite their PIP2-free closed-pore context, these structures did not project far from the predicted transition path, suggesting that the learned manifold is strongly organized by voltage-sensor state, while pore opening and PIP2-dependent coupling contribute additional context-dependent differences. The Kyriakis/Fedida WT-reverted intermediate MD conformations projected near the intermediate region and had a gating-charge value comparable to the average MD-derived IO validation ensemble. The ML277/PIP2/CaM structures occupied the activated/open side of the landscape and projected directly into the AO region, consistent with their ligand- and lipid-stabilized open/coupled context. Importantly, this latent-space proximity should not be interpreted as implying that structures decoded from nearby points are atomistically identical to the corresponding cryo-EM models. Rather, the projection indicates that the network recognized shared state-defining features, such as VSD charge state and coupling-region organization, while individual decoded structures may still inherit context-specific traits from the training ensembles.

We next asked whether the decoded intermediates also reproduce local voltage-sensor signatures expected for Kv7.1 state progression. For this analysis, we focused on the exchange interactions of the S4 basic residues with conserved acidic countercharges during voltage-sensor activation (Osteen et al., 2012). We computed charged-atom minimum distances between the Kv7.1 S4 basic residues R228, R231, R237, and R243 and the acidic residues E160, E170, and D202 (Figure 2). Distances were first computed per subunit and then averaged, preserving the possibility of subunit-specific heterogeneity (Supplementary Material S5) while providing a compact state-level contact fingerprint. Intermediates might contain mixed local VSD charge-pairing signatures across the four subunits, consistent with the interpretation of the decoded path as a tetramer-averaged transition coordinate rather than a strictly synchronous C4-symmetric sequence.

This contact-level analysis motivates a more direct visual comparison with the available cryo-EM intermediate structure. We therefore compared the most similar interpolation to 8SIM using local VSD alignment (Figure 3). The tetrameric overlay shows that the decoded intermediate preserves the overall channel-core architecture, but the HOLE pore-profile comparison between the interpolated intermediate and 8SIM gave an RMS profile difference of approximately 2.5 Å, and tetrameric core alignment gave an RMSD of 3.5 Å. This level of difference is expected because 8SIM is a PIP2-free intermediate-state structure with a closed pore, whereas decoded intermediates in this region of the learned path already show open-like activation-gate widening. Thus, the comparison should be interpreted primarily at the VSD level and we focused the structural interpretation on a locally aligned VSD comparison. The local alignment was performed using the VSD scaffold selection. In this view, the decoded intermediate and 8SIM show a comparable helices arrangement and S4 architecture in particular.

Together, this comparison supports the structural plausibility of the decoded intermediate; however, the generated structure is not claimed to reproduce the full 8SIM tetramer atom by atom. Instead, it occupies an intermediate-like region of the learned manifold, and preserves VSD features that can be compared meaningfully with the cryo-EM intermediate-state landmark.

Decoded intermediates are structurally suitable for downstream MD simulations

After comparing selected generated intermediates with cryo-EM intermediate-state references, we next evaluated whether the decoded structures could be used as atomistic models for downstream analysis and simulation. This step is important because the network generates Cartesian coordinates directly; therefore, even if a structure is well positioned in latent space, it must still satisfy local stereochemical requirements and tolerate reinsertion into an explicit membrane/solvent environment before it can be used as an MD starting model.

We first assessed the structural quality of the decoded intermediates using complementary validation metrics. DOPE scores were calculated with Modeller as a statistical-potential measure of relative model quality across the generated pathway (Shen and Sali, 2006). Backbone ϕ / ψ geometry was evaluated using a deterministic Ramachandran-region classifier and compared with sampled frames from the original MD ensembles. Across the decoded path, DOPE scores remained within a continuous range rather than showing abrupt failures, although the middle of the path was less favorable than endpoint-proximal structures (Figure 4A). This behavior is expected because middle-path conformations are furthest from the endpoint MD ensembles used for training and represent the most extrapolative decoded structures. Ramachandran outliers remained limited across the interpolations, ranging from approximately 0.5%–2.5%, while the fraction of favored backbone conformations decreased in the middle of the path but recovered toward the late intermediates (Figures 4A,B). Overall, the generated structures preserve sufficient quality to support relaxation and downstream applications.

As an initial test of MD compatibility, a representative decoded intermediate was simulated in three independent replicas for 250 ns each, including an initial restrained equilibration phase of 50 ns followed by unrestrained dynamics. The trajectories did not show any structural failure after release of restraints. Domain-wise RMSD analysis showed that the pore-core backbone remained comparatively stable, increasing to approximately 1.4 Å during the unrestrained portion of the simulations (Figure 4C). Larger deviations were observed when the analysis included the TMD/linker/pore region and the full channel backbone, which reached approximately 3 Å and 4 Å, respectively, by the end of the current trajectories. This pattern is consistent with the expected flexibility of the structure rather than with global unfolding or collapse of the channel-core architecture.

These simulations provide a small practical test of the workflow: decoded intermediates can be relaxed, inserted into a realistic membrane/solvent environment, and propagated by MD. Together with the DOPE and Ramachandran analyses, this supports the use of the generated structures as atomistic starting models for more extensive simulations, mutation-specific tests, or enhanced-sampling campaigns.

Pore geometry reveals activation-gate widening without pore-specific supervision

While the learned manifold was implicitly regularized by the gating charge specific loss function component, no pore-specific term was included in the training objective. Pore geometry therefore provides an independent structural test of the decoded pathway. If the generated intermediates reproduce meaningful pore behavior, this behavior must emerge from structural correlations learned from the endpoint ensembles rather than from direct supervision of pore opening. We analyzed the decoded structures using HOLE radius profiles.

The clearest pore-related change was observed at the activation gate. Along the decoded pathway, the activation-gate minimum radius remained relatively narrow and nearly flat through the early intermediates, with values around 2.2–2.3 Å for interpolations 0–8, and then increased through the late intermediates, reaching approximately 4 Å (Figure 5A). Thus, the generated path does not behave as a simple linear dilation of the pore. Instead, it contains a gated transition in which activation-gate expansion occurs mainly in the late-intermediate/opening region of the decoded pathway.

This behavior is consistent with the general architecture of Kv channels, in which pore opening is controlled primarily by rearrangements near the intracellular S6 bundle-crossing gate, while the voltage sensor and pore are coupled through the S4-S5 linker/S6 interface (Long et al., 2005; Kalstrup and Blunck, 2018). It is also consistent with Kv7.1-specific studies showing that VSD activation and pore opening are separable but coupled processes, and that PIP2 is required for efficient coupling between voltage-sensor activation and pore opening (Wang et al., 2020; Taylor et al., 2020; Hou et al., 2020; Mandala and MacKinnon, 2023; Ma et al., 2022). In Kv7.1, the intermediate and activated VSD states can both support open states in the absence of KCNE1 (Taylor et al., 2020; Hou et al., 2020), whereas PIP2-free structures can have activated VSDs but closed pores (Mandala and MacKinnon, 2023).

Modulators reshape predicted Kv7.1 transition pathways

As a final modulatory-context control, we asked whether the same endpoint-trained workflow could detect structural remodeling imposed by the IKs environment. This analysis was motivated by previous MD models of the KCNQ1/KCNE1 complex showing that PIP2 is essential for VSD–pore coupling and that two PIP2 molecules per Kv7.1 monomer stabilize IKs state models more effectively than one PIP2 molecule per monomer. In those simulations, KCNE1 interacted with both PIP2-binding regions and formed a “tourniquet”-like electrostatic network around the cytoplasmic S6 region, providing a possible molecular explanation for suppression of intermediate-state pore opening in IKs (Deyawe et al., 2023).

We therefore trained and compared models derived from IKs simulations containing either one or two PIP2 molecules per Kv7.1 monomer. In these tests, PIP2 and KCNE1 were present in the source MD systems but were not included directly in the learned atom selection; the network saw only Kv7.1 channel-core coordinates. Thus, any separation between the one-PIP2 and two-PIP2 conditions reflects structural remodeling propagated from the modulatory environment into the Kv7.1 protein coordinates, rather than direct recognition of PIP2 or KCNE1 atoms. The resulting latent spaces showed distinct organization of the one-PIP2/monomer and two-PIP2/monomer datasets, and the generated paths followed different regions of the learned landscape (Figure 6A).

We next asked whether these IKs-derived transition paths differed in their residue-contact remodeling. The two-PIP2/monomer path showed reduced contact-count fluctuation and a larger number of contacts gained by the final interpolation frame. Contacts preferentially gained in the two-PIP2/monomer path mapped to canonical gating-associated regions, including VSD/S4, S4–S5 linker/S6-gate, and S5–pore/S6-gate interfaces. Thus, the two-PIP2 condition was associated with greater contact persistence and more coherent channel-core remodeling along the inferred transition path, rather than a nonspecific global increase in close contacts.

We interpret this analysis as a proof-of-principle extension rather than a complete mechanistic model of IKs gating. The result shows that the same endpoint-trained framework is sensitive to modulatory context: differences imposed by PIP2 stoichiometry and the KCNE1-containing IKs environment in the source MD ensembles were propagated into the Kv7.1 channel-core coordinates and produced distinguishable inferred pathways by learning indirect protein-coordinate consequences of the IKs/PIP2 environment. However, because KCNE1 and PIP2 atoms were not included explicitly in the coordinate representation used here, this analysis cannot resolve the full lipid/protein coupling mechanism. Instead, it demonstrates that the workflow can detect protein-coordinate consequences of modulatory context and motivates conditional or expanded models that include KCNE1, PIP2, and explicit lipid–protein contact descriptors.

In this work, we used Kv7.1/KCNQ1 as a structurally and mechanistically rich test case for physics-informed transition-path prediction. The central objective was not to redefine the established biology of Kv7.1 gating, but to ask whether a learning framework trained on limited endpoint molecular-dynamics ensembles could recover a conformational organization that is consistent with the voltage-sensor progression, pore remodeling, and recently resolved experimental landmarks. The results support this objective. A model trained only on resting/closed-like and activated/open-like ensembles organized the withheld intermediate/open ensemble in an interpretable region of the learned manifold, generated intermediate conformations with progressive voltage-sensor signatures, placed independent cryo-EM structures in biologically meaningful regions, and produced decoded structures that could be relaxed in an explicit membrane environment. Thus, the main contribution of this study is integrative: it establishes a route for converting sparse state-local simulations and structural snapshots into pathway-resolved, atomistic hypotheses for Kv7.1 gating.

A key result is that endpoint-local sampling was sufficient to learn an ordered Kv7.1 channel-core landscape. This is a demanding test because the model was not trained on a continuous transition trajectory, nor on the withheld IO ensemble. The learned pathway agrees with the emerging structural picture of Kv7.1 as a channel in which voltage-sensor position, pore opening, and PIP2-dependent coupling are related but separable. The model learned correlations between voltage-sensor progression, coupling-region organization, and pore-domain remodeling from the endpoint ensembles.

The decoded structures also appear practically useful as atomistic starting models. Their stereochemical quality metrics remained within a range suitable for follow-up simulations, and selected intermediates could be inserted into a membrane/solvent environment and propagated in short MD simulations without any observed structural instability. This point is important for positioning the method. The model can help generate plausible intermediate structures that are suitable for follow-up sampling. This is likely one of the strongest practical applications of the framework: producing pathway-informed starting conformations for enhanced sampling, mutation-specific simulations, or local mechanistic analysis in systems where spontaneous gating transitions are inaccessible on routine MD timescales.

The brief IKs/PIP2 analysis extends this point by showing that the framework is sensitive to modulatory context even when the modulators are not included explicitly in the learned coordinate representation. The separation between one- and two-PIP2-per-monomer conditions arose from protein-coordinate consequences of the modulatory environment. It demonstrates that the coordinates retain a detectable imprint of lipid and accessory-subunit modulation.

Several limitations should be made explicit. First, the generated pathway is conditioned by the endpoint ensembles, preprocessing choices, atom selection, loss function, and latent-space sampling procedure. It should therefore be interpreted as a preferred transition hypothesis under the current model, not as a unique physical pathway. Second, the model does not provide transition kinetics, free-energy barriers, or state probabilities. The learned energy-like landscape is useful for organizing conformations, but it is not equivalent to a rigorously sampled thermodynamic free-energy surface. Classical path-finding and enhanced-sampling methods remain complementary approaches (See Supplementary Material S7); in the present workflow, decoded intermediates are intended as rapidly generated starting structures or path anchors for such more expensive simulations. Third, the current coordinate representation omits lipids, PIP2, KCNE1, ions, water, and CaM. This choice made the full-channel learning problem tractable and allowed direct comparison across contexts, but it limits mechanistic interpretation of lipid binding, accessory-subunit contacts, and hydration or ion-permeation effects. Fourth, fixed-order coordinate autoencoders require careful chain matching for tetrameric proteins and may not naturally handle symmetry-related permutations. Finally, the short relaxation simulations used here test basic structural compatibility, but longer simulations and more extensive sampling will be required to evaluate the functional relevance of selected intermediates.

These limitations also define the next steps. One clear extension is to develop conditional models that compare diverse modulatory contexts explicitly, for example, by including PIP2 occupancy, KCNE subunit identity, ligand state, lipid-contact descriptors, or experimental state labels. A second direction is to integrate the current generator into an iterative simulation workflow, in which decoded intermediates are relaxed by MD, newly sampled conformations are added back into the training set, and the model is retrained until the path between endpoints becomes more densely populated and physically refined. A third direction is mutation-focused modeling. Many channel disease variants likely perturb local stability, voltage-sensor activation, electromechanical coupling, or pore opening in distinct ways. A pathway-generation framework could provide mutant-specific starting structures for downstream simulations, allowing variants to be examined not only as static structural perturbations but also as changes in the accessible activation pathway. Finally, broader benchmarking across alternative neural architectures and non-channel protein transitions will be important for separating what is specific to Kv7.1 gating from what is general to physics-informed protein transition modeling.

More broadly, the present implementation should be viewed as one member of a broader class of physics-informed generative strategies for protein conformational transitions. Recent advances in protein artificial intelligence have shifted attention from static structure prediction toward conformational ensembles, alternative states, and generative sampling of protein motions. In this context, the important feature of our framework is not only the specific autoencoder architecture used here, but the modular coupling between a generative coordinate model and interpretable loss terms. In preliminary architecture-switch tests within our in-house pipeline, the same composite loss formulation could also be coupled to adversarial generative models, producing intermediate structures of comparable qualitative utility. Similarly, tests with trainable weighting coefficients for the auxiliary loss terms suggested that the framework remains functional when these parameters are learned, although manually chosen physically motivated weights gave more stable behavior in the recent applications. These observations open multiple methodological directions beyond the specific application presented here.

Although the current study focuses on voltage-gated ion channels, the framework is not intrinsically restricted to channels. The gating-charge branch is channel-specific and was introduced to impose a physically meaningful direction on voltage-sensor progression. By contrast, the geometric reconstruction and molecular-mechanics components are broadly applicable to other protein families, while the gating-charge term could be quite easily exchanged to encode alternative system-specific biophysical descriptors. In this sense, the framework is not restricted to voltage-gated channels: channels provide a stringent and therapeutically relevant benchmark because of their size, membrane embedding, and experimentally distinguishable functional states, but the same modular strategy could be adapted to other protein-transition problems. At the same time, previous tests on non-channel conformational benchmarks, such as adenylate kinase open/closed transitions, suggest that the same pipeline can be adapted to more general protein transition problems.