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arxiv: 2508.02509 · v3 · submitted 2025-08-04 · ⚛️ physics.chem-ph

Quantitative and Predictive Folding Models from Limited Single-Molecule Data Using Simulation-Based Inference

Lars Dingeldein , Aaron Lyons , Pilar Cossio , Michael Woodside , Roberto Covino This is my paper

Pith reviewed 2026-05-19 00:52 UTC · model grok-4.3

classification ⚛️ physics.chem-ph
keywords simulation-based inferencesingle-molecule force spectroscopybiomolecular foldingfree energy landscapeDNA hairpinriboswitch aptamerBayesian inferencepredictive modeling
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The pith

Simulation-based inference extracts accurate folding landscapes and dynamics from a single two-second trajectory.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents a framework that combines physics-based simulations with deep learning to build quantitative models of how biomolecules fold. It demonstrates that a single short experimental trace from single-molecule force spectroscopy can yield the full free energy landscape and kinetic rates for a DNA hairpin, matching results from conventional methods that need far longer recordings. The same approach resolves a more complex landscape with four states in a riboswitch aptamer. Because the method is Bayesian, it returns uncertainty estimates for every inferred quantity, including diffusion constants and linker properties, without separate calibration experiments. The resulting models are predictive: they generate new simulated traces that match the original data in both equilibrium populations and transition rates.

Core claim

We introduce a simulation-based inference framework that integrates physics-based modeling with deep learning to derive quantitative folding models from minimal SMFS data. Applied to constant-force measurements, this method reconstructs the free energy landscape and folding dynamics of a DNA hairpin from a single two-second experimental trajectory, yielding results consistent with deconvolution methods that require substantially larger datasets. The framework extends to a riboswitch aptamer, resolving a landscape with four metastable states from one trajectory, while Bayesian inference quantifies uncertainties in parameters such as diffusion coefficients without separate calibrations.

What carries the argument

A neural network trained via simulation-based inference on synthetic trajectories generated from a physics-based model of the molecule, linkers, and instrument noise; the network inverts observed data to infer the underlying free-energy profile, diffusion coefficient, and experimental parameters.

If this is right

  • The inferred models generate new trajectories that match experimental thermodynamics and kinetics without further fitting.
  • Uncertainties on all parameters, including diffusion coefficients and linker stiffness, are obtained directly from the data.
  • The method works for systems with multiple metastable states and tertiary contacts from a single short recording.
  • Quantitative models become feasible for biomolecular systems where collecting large datasets is impractical.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The framework could be adapted to other single-molecule modalities such as fluorescence or optical tweezers that share similar noise and artifact characteristics.
  • Short-trajectory inference opens the possibility of tracking folding changes in response to varying conditions within one continuous experiment rather than averaging many separate runs.
  • Because the approach separates the physical model from the inference step, it could be extended to include additional molecular degrees of freedom once faster simulation engines become available.

Load-bearing premise

The physics-based simulation model used to generate training data accurately captures all relevant instrumental noise, linker artifacts, and stochastic dynamics of the real experimental system.

What would settle it

If simulated trajectories drawn from the inferred parameters fail to reproduce the observed folding rates, equilibrium occupancies, or transition statistics in a new, independent experimental recording of the same molecule, the reconstruction would be shown to be inaccurate.

Figures

Figures reproduced from arXiv: 2508.02509 by Aaron Lyons, Lars Dingeldein, Michael Woodside, Pilar Cossio, Roberto Covino.

Figure 1
Figure 1. Figure 1: Framework for analyzing single-molecule force spectroscopy data using simulation-based inference. The process [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Free energy profile reconstruction. (A) Experi [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Diffusion coefficients and linker stiffness estimates. [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Predictive check using simulations with best [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
read the original abstract

The study of biomolecular folding has been greatly advanced by single-molecule force spectroscopy (SMFS), which enables the observation of the dynamics of individual molecules. However, extracting quantitative models of fundamental properties such as folding landscapes from SMFS data is very challenging due to instrumental noise, linker artifacts, and the inherent stochasticity of the process, often requiring extensive datasets and complex calibration. Here, we introduce a framework based on simulation-based inference (SBI) that overcomes these limitations by integrating physics-based modeling with deep learning. We first apply this framework to analyze constant-force measurements of a DNA hairpin. From a single experimental trajectory of only two seconds, we successfully reconstruct the hairpin's free energy landscape and folding dynamics, obtaining results in close agreement with established deconvolution methods that require 10-100 times more data. Furthermore, we demonstrate the generality of our approach by applying it to a riboswitch aptamer featuring multiple states and tertiary contacts, resolving the profile of a landscape featuring four metastable states from a single trajectory. The Bayesian nature of this approach robustly quantifies uncertainties for all inferred parameters, including diffusion coefficients and linker stiffness, without needing independent measurements of instrument properties. The inferred models are predictive, generating simulated trajectories that quantitatively reproduce experimental thermodynamics and kinetics. The ability to derive statistically robust models from minimal datasets is crucial for investigating complex biomolecular systems where extensive data collection is impractical, paving the way for novel applications of SMFS.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces a simulation-based inference (SBI) framework integrating physics-based modeling with deep learning to derive quantitative and predictive models of biomolecular folding from limited single-molecule force spectroscopy (SMFS) data. For a DNA hairpin, it reconstructs the free energy landscape and folding dynamics from a single 2-second experimental trajectory, claiming close agreement with established deconvolution methods that require 10-100 times more data. The approach is extended to a riboswitch aptamer with four metastable states and tertiary contacts. The Bayesian procedure quantifies uncertainties in parameters including diffusion coefficients and linker stiffness without independent calibrations, and the inferred models generate simulated trajectories that reproduce experimental thermodynamics and kinetics.

Significance. If the central results hold, the work has substantial significance for single-molecule biophysics. It directly addresses the practical barrier of extensive data requirements in SMFS by enabling landscape and kinetic reconstruction from minimal trajectories, which is especially valuable for complex or low-abundance systems. The built-in uncertainty quantification for instrumental and physical parameters, combined with demonstrated predictive power of the inferred models, represents a methodological strength. The generality shown on the multi-state riboswitch further broadens potential impact.

major comments (2)
  1. [Abstract] Abstract: the claim of 'close agreement' with established deconvolution methods is stated without any quantitative metrics (e.g., RMSD between landscapes, overlap of rate distributions, or statistical tests), error bars, or explicit validation details. This absence makes it impossible to evaluate whether the 10-100× data reduction is quantitatively supported or merely qualitative.
  2. [Methods] The physics-based simulator used to train the SBI network is load-bearing for the headline result. The abstract asserts that the posterior quantifies uncertainties in diffusion coefficients and linker stiffness 'without needing independent measurements,' yet this holds only if the forward model already encodes the correct functional forms and ranges for all relevant noise, filtering, and linker effects. No section provides explicit validation of the simulator against independent controls or known benchmark trajectories.
minor comments (2)
  1. Add a dedicated table or figure panel that directly compares key extracted quantities (barrier heights, well depths, folding/unfolding rates) between the SBI posterior and the reference deconvolution results, including uncertainties.
  2. Clarify the precise architecture and training procedure of the inference network (e.g., number of simulations, summary statistics used, network depth) so that the method can be reproduced from the text alone.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their positive assessment of the significance of our work and for the constructive major comments. We address each point below and describe the revisions we will implement.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim of 'close agreement' with established deconvolution methods is stated without any quantitative metrics (e.g., RMSD between landscapes, overlap of rate distributions, or statistical tests), error bars, or explicit validation details. This absence makes it impossible to evaluate whether the 10-100× data reduction is quantitatively supported or merely qualitative.

    Authors: We agree that quantitative metrics would strengthen the abstract and enable a more rigorous assessment of the data-reduction claim. In the revised manuscript we will add explicit metrics, including the RMSD between the SBI-inferred free-energy landscape and the reference landscape from established deconvolution, an overlap coefficient for the rate distributions, and posterior-derived error bars. We will also add a sentence directing readers to the relevant main-text and supplementary figures that contain the full validation details. revision: yes

  2. Referee: [Methods] The physics-based simulator used to train the SBI network is load-bearing for the headline result. The abstract asserts that the posterior quantifies uncertainties in diffusion coefficients and linker stiffness 'without needing independent measurements,' yet this holds only if the forward model already encodes the correct functional forms and ranges for all relevant noise, filtering, and linker effects. No section provides explicit validation of the simulator against independent controls or known benchmark trajectories.

    Authors: We appreciate the referee’s emphasis on forward-model validation. The simulator is built from established SMFS physical models (worm-like-chain linkers, trap dynamics, and additive noise) whose functional forms are standard in the literature. The current manuscript already shows that trajectories generated from the inferred posterior reproduce experimental thermodynamics and kinetics, providing indirect support. Nevertheless, we agree that a dedicated validation subsection would increase transparency. In the revision we will add a supplementary section and figure that compares simulator outputs against both analytical benchmark cases and independent experimental controls for the DNA-hairpin system, thereby confirming that the chosen functional forms and parameter ranges adequately capture the dominant effects. revision: yes

Circularity Check

0 steps flagged

No significant circularity; SBI inference is self-contained against external benchmarks

full rationale

The paper's core procedure trains a neural network on trajectories generated from an independent physics-based simulator (incorporating force, linkers, and diffusion) and then applies the trained network to infer parameters and landscapes from a single experimental trace. This chain does not reduce to self-definition or fitted-input-as-prediction because the simulator is constructed from first-principles models of the instrument and molecule rather than being tuned to the target trace itself. Results are explicitly cross-checked against established deconvolution methods that operate on 10-100 times more data, supplying an external benchmark. No load-bearing self-citations, uniqueness theorems, or ansatzes imported from prior author work are invoked to force the outcome. Posterior predictive checks (simulated trajectories reproducing observed thermodynamics and kinetics) constitute standard validation rather than tautological reproduction of inputs.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The method rests on the assumption that the chosen physics-based model class is sufficient to generate realistic simulated trajectories for training the inference network; no new entities are introduced.

free parameters (2)
  • diffusion coefficients
    Inferred jointly with landscape parameters from the data without separate calibration
  • linker stiffness
    Inferred jointly with landscape parameters from the data without separate calibration
axioms (1)
  • domain assumption The simulation model accurately reproduces instrumental noise and linker effects present in real SMFS experiments
    Required for the trained network to map experimental data to correct physical parameters

pith-pipeline@v0.9.0 · 5799 in / 1215 out tokens · 51839 ms · 2026-05-19T00:52:57.813360+00:00 · methodology

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Reference graph

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