Decoding Single Molecule Time Traces with Dynamic Disorder

Single molecule time trajectories of biomolecules provide glimpses into complex folding landscapes that are difficult to visualize using conventional ensemble measurements. Recent experiments and theoretical analyses have highlighted dynamic disorder in certain classes of biomolecules, whose dynamic pattern of conformational transitions is affected by slower transition dynamics of internal state hidden in a low dimensional projection. A systematic means to analyze such data is, however, currently not well developed. Here we report a new algorithm - Variational Bayes-double chain Markov model (VB-DCMM) - to analyze single molecule time trajectories that display dynamic disorder. The proposed analysis employing VB-DCMM allows us to detect the presence of dynamic disorder, if any, in each trajectory, identify the number of internal states, and estimate transition rates between the internal states as well as the rates of conformational transition within each internal state. Applying VB-DCMM algorithm to single molecule FRET data of H-DNA in 100 mM-Na$^+$ solution, followed by data clustering, we show that at least 6 kinetic paths linking 4 distinct internal states are required to correctly interpret the duplex-triplex transitions of H-DNA

Direct observation of the formation of DNA triplexes by single-molecule FRET measurements

In this report we investigated the effects of various biological and chemical factors (DNA sequence, pH, ions, and molecularity) on the formation of DNA triplexes through single-molecule FRET technique. Using this method, we determined how the third strand bound to a DNA duplex and how stable the triplex structure was under various conditions. From this study, we not only verified a variety of well-known features of DNA triplex but also discovered or experimentally supported several interesting behaviors: at neutral pH, a pyrimidine-motif triplex can be formed; the parallel arrangement was not only possible but also dominant over the antiparallel arrangement for a purine-motif triplex. We demonstrated that our method is a versatile analytical tool in studying structural aspects of nucleic acids, particularly non-classical DNA structures, and provides insights into physical mechanism of such structures. (C) 2012 Elsevier B. V. All rights reservedclos

DNA triplex folding: Moderate versus high salt conditions

Some specific sequences in duplex DNA can give rise to local formation of a triple helical DNA called triplex together with a separate strand. Recent single-molecule FRET experiments, performed on DNA strands designed to fold into a triplex, allow us to measure the folding and unfolding time distributions under neutral p H conditions. The average times of both processes are of the order of 1s. The folding time is moderately sensitive to salt concentration. The average unfolding time is found to be nearly constant. Interestingly, the distributions of the unfolding time revealed heterogeneous kinetics at moderate salt concentration (∼ 10 mM), but not at high salt (∼ 100 mM). We relate this salt dependence to different folding paths and folded states, which are governed by the (salt-dependent) stiffness of the third single-stranded donor sequence. Finally we comment on the formation of intramolecular triplex named H-DNA in a torsionally constrained duplex under physiological salt conditions, which mimics the in vivo situation of triplex folding

Sequence-dependent cost for Z-form shapes the torsion-driven B-Z transition via close interplay of Z-DNA and DNA bubble

Despite recent genome-wide investigations of functional DNA elements, the mechanistic details about their actions remain elusive. One intriguing possibility is that DNA sequences with special patterns play biological roles, adopting non-B-DNA conformations. Here we investigated dynamics of thymine-guanine (TG) repeats, microsatellite sequences and recurrently found in promoters, as well as cytosine-guanine (CG) repeats, best-known Z-DNA forming sequence, in the aspect of Z-DNA formation. We measured the energy barriers of the B-Z transition with those repeats and discovered the sequence-dependent penalty for Z-DNA generates distinctive thermodynamic and kinetic features in the torque-induced transition. Due to the higher torsional stress required for Z-form in TG repeats, a bubble could be induced more easily, suppressing Z-DNA induction, but facilitate the B-Z interconversion kinetically at the transition midpoint. Thus, the Z-form by TG repeats has advantages as a torsion buffer and bubble selector while the Z-form by CG repeats likely behaves as torsion absorber. Our statistical physics model supports quantitatively the populations of Z-DNA and reveals the pivotal roles of bubbles in state dynamics. All taken together, a quantitative picture for the transition was deduced within the close interplay among bubbles, plectonemes and Z-DNA.11Nsciescopu

Axial profiling of interferometric scattering enables an accurate determination of nanoparticle size

Interferometric scattering (iSCAT) microscopy has undergone significant development in recent years. It is a promising technique for imaging and tracking nanoscopic label-free objects with nanometer localization precision. The current iSCAT-based photometry technique allows quantitative estimation for the size of a nanoparticle by measuring iSCAT contrast and has been successfully applied to nano-objects smaller than the Rayleigh scattering limit. Here we provide an alternative method that overcomes such size limitations. We take into account the axial variation of iSCAT contrast and utilize a vectorial point spread function model to uncover the position of a scattering dipole and, consequently, the size of the scatterer, which is not limited to the Rayleigh limit. We found that our technique accurately measures the size of spherical dielectric nanoparticles in a purely optical and non-contact way. We also tested fluorescent nanodiamonds (fND) and obtained a reasonable estimate for the size of fND particles. Together with fluorescence measurement from fND, we observed a correlation between the fluorescent signal and the size of fND. Our results showed that the axial pattern of iSCAT contrast provides sufficient information for the size of spherical particles. Our method enables us to measure the size of nanoparticles from tens of nanometers and beyond the Rayleigh limit with nanometer precision, making a versatile all-optical nanometric technique. © 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement.11Nsciescopu

Long-term cargo tracking reveals intricate trafficking through active cytoskeletal networks in the crowded cellular environment

A eukaryotic cell is a microscopic world within which efficient material transport is essential. Yet, how a cell manages to deliver cellular cargos efficiently in a crowded environment remains poorly understood. Here, we used interferometric scattering microscopy to track unlabeled cargos in directional motion in a massively parallel fashion. Our label-free, cargo-tracing method revealed not only the dynamics of cargo transportation but also the fine architecture of the actively used cytoskeletal highways and the long-term evolution of the associated traffic at sub-diffraction resolution. Cargos frequently run into a blocked road or experience a traffic jam. Still, they have effective strategies to circumvent those problems: opting for an alternative mode of transport and moving together in tandem or migrating collectively. All taken together, a cell is an incredibly complex and busy space where the principle and practice of transportation intriguingly parallel those of our macroscopic world. © 2023, The Author(s).11Nsciescopu

Representative time traces of H-DNA at [Na⁺] = 100 mM and their analysis.

<p>(A) (i) Fluorescence signal and (ii) their FRET state. (iii) Internal states estimated for <i>K</i> = 1, 2, …, 5. Right panel shows <i>G</i>(<i>K</i>) (blue circle) where <i>K</i>_<i>obs</i> specifies the number of detected internal states in individual traces (blue). (B, C, D) Other representative time traces and their <i>G</i>(<i>K</i>) obtained under the same experimental condition.</p

Average accuracy of internal state detection as a function of <i>D</i>_conf, and <i>D</i>_int.

<p>To construct this diagram, we employed various synthetic data in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005286#pcbi.1005286.g004" target="_blank">Fig 4</a> (circle, two internal states (<i>K</i> = 2), two FRET states (<i>N</i> = 2)), <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005286#pcbi.1005286.s006" target="_blank">S5 Fig</a> (left triangle, <i>K</i> = 3, <i>N</i> = 2), and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005286#pcbi.1005286.s007" target="_blank">S6 Fig</a> (hexagon, <i>K</i> = 2, <i>N</i> = 3). The right triangle symbol denotes the result from the similar analysis shown in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005286#pcbi.1005286.s006" target="_blank">S5 Fig</a> with <i>K</i> = 3 but with smaller relative differences in the transition rates, <i>k</i>’s. Pentagon represents the result obtained with <i>K</i> = 4 and <i>N</i> = 2. (A) Color code denotes the accuracy of internal states predictions in terms of 〈<i>χ</i>〉, averaged over 100 traces for each condition. (B) The dashed lines corresponding to Δ = <i>D</i>_conf + 0.8<i>D</i>_int = 4, 5, … 9 are overlaid on the 2-D scatter plot of 〈<i>χ</i>〉(<i>D</i>_conf, <i>D</i>_int) calculated in (A).</p

Validation of VB-DCMM on synthetic data.

<p>(A) (i) A time trace of internal state generated with <i>γ</i>^(1)→(2)Δ<i>t</i> = γ^(2)→(1)Δ<i>t</i> = 0.001. (ii) An observable time trace generated based on the trace of internal state in (i) by using internal state-dependent parameters , , . (iii) An synthetic FRET data with Gaussian noise overlaid on the trace in (ii). (iv) Noised filtered FRET state by HMM (blue line). (v) Traces of internal state with different <i>K</i>, estimated using VB-DCMM on the noise-filtered FRET trace from (iv) (black line is the true internal state trace while red, orange, and blue are internal state estimated from the model with <i>K</i> = 1, 2, and 3, respectively. The indices of internal state were determined by comparing <b><i>B</i></b>^(<i>μ</i>) estimated for each internal state with <b><i>B</i></b>^{(<i>μ</i>),true} which is used to generate the synthetic data). (B) Estimated lower bound of the evidence function <i>F</i>(<i>K</i>) of DCMM models with <i>K</i> = 1, 2, and 3. (C) Accuracy of detecting internal states. The overlap function <i>χ</i> calculated for 100 synthetic FRET traces generated under the identical condition used for generating the trace of internal state shown in (A).</p

A rugged energy-landscape with hierarchical structure and an emergence of multiple time scales of transitions.

<p><i>τ</i>_<i>int</i> is the transition time between different superbasins of attraction whereas <i>τ</i>_<i>conf</i> is the time scale of conformational dynamics of molecule <i>within</i> each basin. Due to large difference in kinetic barriers (), <i>τ</i>_<i>int</i> ≫ <i>τ</i>_<i>conf</i>.</p