Biophysical Society Thematic Meeting | Tutzing 2026

Single-Molecule FRET: The Next 30 Years

Wednesday Speaker Abstracts

A PHOTON-BY-PHOTON LIKELIHOOD FOR CONTINUOUS FREE-ENERGY LANDSCAPES AND DIFFUSION COEFFICIENTS FROM SINGLE-MOLECULE FRET Lars Dingeldein 1,3 ; Roberto Covino 1,2 ; 1 Frankfurt Institute for Advanced Studies, Frankfurt am Main, Germany 2 Goethe University Frankfurt, Department for Computer Science, Frankfurt am Main, Germany 3 Goethe University Frankfurt, Department for Physics, Frankfurt am Main, Germany Single-molecule FRET probes the conformational dynamics of biomolecules by measuring the distance between two dyes. The experiment produces a stream of coloured photons, which is only an indirect readout of these dynamics. Recovering the underlying free-energy landscape and diffusion coefficient from a photon stream is a difficult inverse problem. Existing approaches address this problem by assuming a small number of discrete states, binning the photons, or sampling the hidden trajectories.Here we derive an exact likelihood for the recorded photon stream under a model in which the dye distance diffuses on a continuous free-energy landscape. It uses the raw inter-photon times and colours at full time resolution, and it analytically integrates out all hidden trajectories. The likelihood is differentiable, so automatic differentiation returns exact gradients with respect to all model parameters. This enables us to jointly infer the free energy landscape, the diffusion coefficient, and the photophysical parameters by gradient-based optimisation. On simulated data, we recover the true free-energy landscapes, including ones with a short-lived intermediate, together with the diffusion coefficients. Uncertainties follow from the curvature of the likelihood, which can be computed directly from the gradients. In addition to inference, we can use the same framework to guide the design of experimental acquisition settings. Before any data are recorded, we can evaluate on simulated data how much a particular acquisition setting reduces the uncertainty. Likelihood evaluation on the GPU is fast, and independent traces are processed in parallel, so a single fit converges in minutes and the approach scales to large datasets. The likelihood extends photon-by-photon analysis to continuous free-energy landscapes and diffusion coefficients. Fitting is fast, and uncertainties come from the same computation. This puts quantitative inference within reach of the smFRET community.

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