AI 中文总结
本文提出一种逐光子可微似然，可从单分子FRET数据联合推断连续自由能景观、扩散系数等参数，该方法高效且支持不确定性评估，可扩展至大型数据集。
AI 中文摘要
单分子FRET通过测量两种染料间的距离来探测生物分子的构象动力学，该实验产生的是彩色光子流，而这仅是这些动力学的间接读出。从这类光子流中恢复自由能景观和扩散系数是一个困难的逆问题。现有方法假设存在少量离散状态、对光子进行分箱处理，或者计算成本高昂。本文在染料距离在连续自由能景观上扩散的模型下，推导了针对记录的光子流的精确似然。该似然使用全时间分辨率下的原始光子间时间和颜色，并解析积分所有隐藏轨迹。该似然是可微的，因此自动微分会返回关于所有模型参数的精确梯度，这让我们能够通过基于梯度的优化联合推断自由能景观、扩散系数和光物理参数。在模拟数据上，我们恢复了自由能景观，包括具有短寿命中间体的景观，以及扩散系数；不确定性来自似然的曲率，而该曲率可直接由相同的梯度计算得出。该框架还指导实验设计：在记录任何数据之前，我们可以评估给定采集设置会在多大程度上降低所得不确定性。在GPU上的评估速度很快，且独立轨迹可并行处理，因此单次拟合在几分钟内即可收敛，并可扩展到大型数据集。该似然将逐光子分析扩展到了连续自由能景观和扩散系数，让smFRET领域能够实现带不确定性的快速定量推断。
英文摘要
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 free-energy landscape and diffusion coefficient from such a photon stream is a difficult inverse problem. Existing approaches assume a small number of discrete states, bin the photons, or are computationally expensive. 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 analytically integrates out all hidden trajectories. The likelihood is differentiable, so automatic differentiation returns exact gradients with respect to all model parameters. This lets us jointly infer the free-energy landscape, the diffusion coefficient, and the photophysical parameters by gradient-based optimization. On simulated data, we recover free-energy landscapes, including ones with a short-lived intermediate, together with the diffusion coefficients. Uncertainties follow from the curvature of the likelihood, computed directly from the same gradients. The framework also guides experimental design. Before any data are recorded, we can evaluate how much a given acquisition setting reduces the resulting uncertainty. Evaluation on the GPU is fast, and independent traces are processed in parallel, so a single fit converges in minutes and scales to large datasets. The likelihood extends photon-by-photon analysis to continuous free-energy landscapes and diffusion coefficients, putting fast quantitative inference with uncertainties within reach of the smFRET community.
