Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2611.08354

Kinetic models of a K channel with 2 stage voltage sensor activation and an opening step

S. R. Vaccaro
View original source ↗Read source document ↗Export metadata ↓

Abstract

The activation of a K channel with 2 voltage sensors and a separate opening step may be described by a 4 state kinetic equation. If $k_{o}$ and $k_{c}$ are the opening and closing rates, and $α$ and $β$ are the voltage sensor rates such that $k_{o}$ $\ggα,k_{c}\ggβ$ and $k_{o}$ $\gg k_{c}$, the kinetic equation may be reduced to a 3 state model where the effective backward rate from the activated-open state is $2βk_{c}/(k_{o}+k_{c})$. However, if a K channel voltage sensor activates in 2 stages, and there is a separate opening step, the occupation probabilities of the states of the channel satisfy a 10 state kinetic equation. When the time constants of the characteristic equation for each voltage sensor differ by an order of magnitude, and $k_{o}$ $\gg k_{c}$, the open state probability is proportional to $n^{2}$, where $n$ satisfies a rate equation, and the derived rates have a similar voltage dependence to the rates $α_{n}$ and $β_{n}$ from voltage clamp data.

Explore related subjects

q-bio.BM

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

S. R. Vaccaro. 2026-11-05. Kinetic models of a K channel with 2 stage voltage sensor activation and an opening step. https://arxiv.org/abs/2611.08354

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Protein B-factor modeling with local magnitude

Topological magnitude characterizes the effective size and spatial organization of metric spaces, offering a geometric approach with potential applications in molecular biology and materials science. Previous work has demonstrated its utility in modeling protein flexibility from structure, but global magnitude weighting requires dense linear systems whose computational cost increases with protein size. We introduce a local magnitude representation that retains residue-level structural information through nearest-neighbor environments. The construction is well posed and geometrically invariant, with central weighting distinguished from scalar neighborhood magnitude. Across 364 proteins, the mean within-protein fitting Pearson correlation coefficient (PCC) increases from 0.725 for global magnitude to 0.728 for local magnitude. Blind-prediction experiments on 345 proteins combine each representation with identical auxiliary descriptors and evaluate random forests and gradient boosting under three validation protocols. Local features improve the primary PCC in all six model--protocol comparisons, with a maximum absolute increase of 0.008 in protein-level ten-fold gradient boosting. For a fixed feature bank, local factorization costs $O(Nk^3)$ compared with $O(N^3)$ for global factorization, where $N$ is the number of C$_α$ atoms and $k$ the neighborhood size. Timing measurements show a computational advantage of local magnitude on large structures. Within the tested single-seed configuration and distinct global and local scale banks, these results support local magnitude as a compact representation that preserves useful B-factor information while reducing feature-extraction costs for large proteins.

q-bio.BM↗
arXiv2026

Predicting protein structures at any folding stage from sequence

Protein structure prediction has largely focused on native conformations, leaving the continuum of unfolded states, folding intermediates, and native structures difficult to access. We present FoldScape, a sequence-conditioned deep learning framework for generating protein conformational ensembles at specified folding fractions $Q$. Trained on approximately one million conformations from 10,000 protein sequences, FoldScape combines coarse-grained folding and all-atom mechanical-unfolding trajectories. It reconstructs three-dimensional $C_α$ chains through hierarchical sliding-window regressions of inter-residue distances, chain-level assembly, and a rectified-flow decoder. By conditioning on folding progress, FoldScape generates conformations from unfolded states through intermediates to native-state structures without protein-specific molecular dynamics at inference. In matched-sample comparisons, FoldScape achieves median conformational-space coverage of 0.989, 0.722, and 0.877 along radius of gyration, fraction of native contacts $Q$, and secondary-structure fraction, respectively, versus 0.05, 0.05, and 0.10 for seed-varied AlphaFold 3 ensembles. Coverage advantages are consistent across the evaluated proteins and robust to binning choices. Reconstruction accuracy remains approximately stable across the evaluated stages of a folding trajectory, and stride-one crop-and-superpose inference extends predictions to chains several times longer than the single-pass limit. Analyses of mechanical-unfolding trajectories show residue-resolved pathways, reproducible extension-conditioned observables across pulling velocities, and geometrically coherent segments in partially unfolded chains. FoldScape extends sequence-based structure prediction beyond a single folded endpoint to controllable conformational-ensemble generation across protein folding.

q-bio.BM↗
arXiv2026

Discrete Backbone Elasticity and Curvature-Dependent Torsion Statistics in Proteins

Coarse-grained models of protein conformational dynamics use $\mathrm{C}_α$ geometry to describe the probabilities of regular helices, ordered turns and disordered conformations. To test how much of this order arises from local chain elasticity, we connect discrete Hasimoto frame transport to neighboring bending mismatch, deriving a curvature-product torsion interaction and a six-parameter generalized von Mises density. Fitted on 194 chains from the ATLAS molecular dynamics database and tested on 1744 sequence-nonredundant proteins, this baseline reduces negative log-density loss from 1.490 to 1.160 nats, torsion-sign error from 12.26 to 2.15 percentage points, and helix-fraction error from 21.84 to 10.41 points. Ablations and circular-moment projections against reference generative models motivate extensions to anisotropic stiffness and two partition-function-weighted elastic states, further lowering test loss to 0.790 nats and helix error to 1.65 points. The fixed hierarchy also improves predictions across 72 trajectories of peptides $\mathrm{Fs}$ and $(\mathrm{AAQAA})_3$ and miniprotein $\mathrm{HP35}$ spanning varied starting conformations and force fields. Remaining angular errors in these trajectories are associated with atomic context at shared bends, as bend-matched peptide frames adopt opposite torsion signs with distinct hydrogen-bond patterns and a proline-containing $\mathrm{HP35}$ turn remains at negative torsion. Introducing a bilinearly coupled $\mathrm{C}_α$--$\mathrm{N}$ orientation angle largely reparameterizes the existing bend-dependent harmonics, with an empirical $L^2$ Gram projection placing 96.7\% to 99.6\% of its added coefficient-function squared norm within the original six-function span. These results link discrete Hasimoto elasticity to statistical backbone potentials and clarify the scope and limits of local $\mathrm{C}_α$ geometry.

q-bio.BM↗