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Abstract Multiplexed, real-time fluorescence detection at the single-molecule level can reveal the stoichiometry, dynamics and interactions of multiple molecular species in mixtures and other complex samples. However, fluorescence-based sensing is typically limited to the detection of just 3–4 colours at a time due to low signal-to-noise ratio, high spectral overlap and the need to maintain the chemical compatibility of dyes. Here we engineered a palette of several dozen composite fluorescent labels, called FRETfluors, for multiplexed spectroscopic measurements at the single-molecule level. FRETfluors are compact nanostructures constructed from three chemical components (DNA, Cy3 and Cy5) with tunable spectroscopic properties due to variations in geometry, fluorophore attachment chemistry and DNA sequence. We demonstrate FRETfluor labelling and detection for low-concentration (<100 fM) mixtures of mRNA, dsDNA and proteins using an anti-Brownian electrokinetic trap. In addition to identifying the unique spectroscopic signature of each FRETfluor, this trap differentiates FRETfluors attached to a target from unbound FRETfluors, enabling wash-free sensing. Although usually considered an undesirable complication of fluorescence, here the inherent sensitivity of fluorophores to the local physicochemical environment provides a new design axis complementary to changing the FRET efficiency. As a result, the number of distinguishable FRETfluor labels can be combinatorically increased while chemical compatibility is maintained, expanding prospects for spectroscopic multiplexing at the single-molecule level using a minimal set of chemical building blocks. 

Single-molecule Förster resonance energy transfer (smFRET) is an experimental methodology to track the real-time dynamics of molecules using fluorescent probes to follow one or more intramolecular distances. These distances provide a low-dimensional representation of the full atomistic dynamics. Under mild technical conditions, Takens’ Delay Embedding Theorem guarantees that the full three-dimensional atomistic dynamics of a system are diffeomorphic (i.e., related by a smooth and invertible transformation) to a time-delayed embedding of one or more scalar observables. Appealing to these theoretical guarantees, we employ manifold learning, artificial neural networks, and statistical mechanics to learn from molecular simulation training data the a priori unknown transformation between the atomic coordinates and delay-embedded intramolecular distances accessible to smFRET. This learned transformation may then be used to reconstruct atomistic coordinates from smFRET time series data. We term this approach Single-molecule TAkens Reconstruction (STAR). We have previously applied STAR to reconstruct molecular configurations of a C24H50 polymer chain and the mini-protein Chignolin with accuracies better than 0.2 nm from simulated smFRET data under noise free and high time resolution conditions. In the present work, we investigate the role of signal-to-noise ratio, data volume, and time resolution in simulated smFRET data to assess the performance of STAR under conditions more representative of experimental realities. We show that STAR can reconstruct the Chignolin and Villin mini-proteins to accuracies of 0.12 and 0.42 nm, respectively, and place bounds on these conditions for accurate reconstructions. These results demonstrate that it is possible to reconstruct dynamical trajectories of protein folding from time series in noisy, time binned, experimentally measurable observables and lay the foundations for the application of STAR to real experimental data. 

Hepatitis B (HBV) is one of the most common infectious diseases, with a worldwide annual incidence of over 250 million people. About one-third of the cases are in China. While China made significant efforts to implement a nationwide HBV vaccination program for newborns, a significant number of susceptible adults and teens remain. In this paper, we analyze a game-theoretical model of HBV dynamics that incorporates government-provided vaccination at birth coupled with voluntary vaccinations of susceptible adults and teens. We show that the optimal voluntary vaccination brings the disease incidence to very low levels. This result is robust and, in particular, due to a high HBV treatment cost, essentially independent from the vaccine cost.