Searcharxiv⌕ 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 predictors reliably identify native conformations, but do not describe the continuum connecting unfolded ensembles to folded states. Here we present FoldScape, a sequence-conditioned deep learning framework that generates C$α$ conformational ensembles at a specified folding fraction $Q$. FoldScape reconstructs three-dimensional chains through hierarchical, sliding-window regressions of one-dimensional inter-residue distances, followed by chain assembly and sampling with a rectified-flow decoder. It is trained on multi-scale coarse-grained folding trajectories and all-atom mechanical-unfolding trajectories. Across 20 human proteins (36-857 residues), at matched sample size, FoldScape covers about an order of magnitude more of the folding coordinate than seed-varied AlphaFold 3 ensembles, robustly across proteins, order parameters and binning choices. AlphaFold 3 better anchors the immediate native vicinity, which FoldScape does not reach, making the approaches complementary. FoldScape reconstruction accuracy remains approximately constant along $Q$, from collapsed coil to near-native globule, rather than deteriorating away from the native state. A stride-one crop-and-superpose scheme extends inference to chains several times longer than a single chain-level forward pass. We also show that training trajectories resolve mechanical unfolding at residue resolution, that elongation-conditioned ensembles exhibit reproducible continuous observables across pulling velocities, and that partially unfolded chains form geometrically coherent segments. FoldScape thus combines broad coverage of folding stages with stable reconstruction accuracy, without per-protein simulation.

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↗
arXiv2026

Automatic Generation of Novel Highly-Functional Molecular Sequences

While multiple methods now exist to generate functional sequence variants from existing annotated examples, it is unclear how well such methods can be used to generate sequences that exceed the functionality of those contained in the example set. Using two complete fitness landscapes, we quantify how effectively generative tools can search sequence space and find rare, novel, highly functional sequences, focusing on variational auto-encoders and information-theoretic methods. We find that an information-theoretic method that does not require training and runs significantly faster than standard Machine-Learning/Artificial Intelligence (ML/AI) methods also is significantly more effective in finding rare highly-functional sequences. We discuss the application of this novel method to discover rare polypeptides with anti-bacterial properties that are specific to bacterial, but not eukaryotic, cell membranes.

q-bio.BM↗