Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · q-bio/0612026

Dwell time symmetry in random walks and molecular motors

Martin Lindén·Mats Wallin
View original source ↗Read source document ↗Export metadata ↓

Abstract

The statistics of steps and dwell times in reversible molecular motors differ from those of cycle completion in enzyme kinetics. The reason is that a step is only one of several transitions in the mechanochemical cycle. As a result, theoretical results for cycle completion in enzyme kinetics do not apply to stepping data. To allow correct parameter estimation, and to guide data analysis and experiment design, a theoretical treatment is needed that takes this observation into account. In this paper, we model the distribution of dwell times and number of forward and backward steps using first passage processes, based on the assumption that forward and backward steps correspond to different directions of the same transition. We extend recent results for systems with a single cycle and consider the full dwell time distributions as well as models with multiple pathways, detectable substeps, and detachments. Our main results are a symmetry relation for the dwell time distributions in reversible motors, and a relation between certain relative step frequencies and the free energy per cycle. We demonstrate our results by analyzing recent stepping data for a bacterial flagellar motor, and discuss the implications for the efficiency and reversibility of the force-generating subunits. Key words: motor proteins; single molecule kinetics; enzyme kinetics; flagellar motor; Markov process; non-equilibrium fluctuations.

Explore related subjects

q-bio.BMcond-mat.stat-mechphysics.bio-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Martin Lindén, Mats Wallin. 2007-04-17. Dwell time symmetry in random walks and molecular motors. https://doi.org/10.1529/biophysj.106.103044

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

KEEP EXPLORING

Related papers

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↗
arXiv2026

Ablating Design Choices for Protein Ensemble Generators Across Structural Regimes

Generative models of protein conformational ensembles inherit much of their design from structure prediction for folded proteins. Ordered and disordered proteins, however, occupy distinct structural regimes, and we investigate how design choices hold up across them. Using a minimal C$α$ flow-matching model, we ablate choices of architecture, sequence conditioning, rigid-body alignment and training source, and evaluate each variant against experimental SAXS and NMR chemical-shift data partitioned into ordered, disordered, multi-domain and transitional proteins. Mixture-of-experts routing, a static pair representation and a disorder probe have no detectable effect, a smaller protein language model performs worse on ordered proteins but not on disordered ones, and alignment in the loss degrades agreement with SAXS. Replacing coarse-grained simulations of disordered proteins with fragment-assembled ensembles improves agreement with chemical shifts at a cost to SAXS, while an equal mixture of the two keeps most of the gain at a smaller cost. This points to the training data, rather than the architecture, as the main constraint.

q-bio.BM↗