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1. Unraveling multi-state molecular dynamics in single-molecule FRET experiments. I. Theory of FRET-lines

   https://doi.org/10.1063/5.0089134  

   Barth, Anders ; Opanasyuk, Oleg ; Peulen, Thomas-Otavio ; Felekyan, Suren ; Kalinin, Stanislav ; Sanabria, Hugo ; Seidel, Claus A. ( April 2022 , The Journal of Chemical Physics)

   Conformational dynamics of biomolecules are of fundamental importance for their function. Single-molecule studies of Förster Resonance Energy Transfer (smFRET) between a tethered donor and acceptor dye pair are a powerful tool to investigate the structure and dynamics of labeled molecules. However, capturing and quantifying conformational dynamics in intensity-based smFRET experiments remains challenging when the dynamics occur on the sub-millisecond timescale. The method of multiparameter fluorescence detection addresses this challenge by simultaneously registering fluorescence intensities and lifetimes of the donor and acceptor. Together, two FRET observables, the donor fluorescence lifetime τ D and the intensity-based FRET efficiency E, inform on the width of the FRET efficiency distribution as a characteristic fingerprint for conformational dynamics. We present a general framework for analyzing dynamics that relates average fluorescence lifetimes and intensities in two-dimensional burst frequency histograms. We present parametric relations of these observables for interpreting the location of FRET populations in E–τ D diagrams, called FRET-lines. To facilitate the analysis of complex exchange equilibria, FRET-lines serve as reference curves for a graphical interpretation of experimental data to (i) identify conformational states, (ii) resolve their dynamic connectivity, (iii) compare different kinetic models, and (iv) infer polymer properties of unfolded or intrinsically disordered proteins. For a simplified graphical analysis of complex kinetic networks, we derive a moment-based representation of the experimental data that decouples the motion of the fluorescence labels from the conformational dynamics of the biomolecule. Importantly, FRET-lines facilitate exploring complex dynamic models via easily computed experimental observables. We provide extensive computational tools to facilitate applying FRET-lines. 

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2. A Comprehensive Perturbative Formalism for Phase Mixing in Perturbed Disks. II. Phase Spirals in an Inhomogeneous Disk Galaxy with a Nonresponsive Dark Matter Halo

   https://doi.org/10.3847/1538-4357/acd641  

   Banik, Uddipan ; van den Bosch, Frank C. ; Weinberg, Martin D. ( July 2023 , The Astrophysical Journal)

   We develop a linear perturbative formalism to compute the response of an inhomogeneous stellar disk embedded in a nonresponsive dark matter (DM) halo to various perturbations like bars, spiral arms, and encounters with satellite galaxies. Without self-gravity to reinforce it, the response of a Fourier mode phase mixes away due to an intrinsic spread in the vertical (Ω_z), radial (Ω_r), and azimuthal (Ω_ϕ) frequencies, triggering local phase-space spirals. The detailed galactic potential dictates the shape of phase spirals: phase mixing occurs more slowly and thus phase spirals are more loosely wound in the outer disk and in the presence of an ambient DM halo. Collisional diffusion due to scattering of stars by structures like giant molecular clouds causes superexponential damping of the phase spiral amplitude. Thez–v_zphase spiral is one-armed (two-armed) for vertically antisymmetric (symmetric) bending (breathing) modes. Only transient perturbations with timescales (τ_P) comparable to the vertical oscillation period (τ_z∼ 1/Ω_z) can trigger vertical phase spirals. Each (n,l,m) mode of the response to impulsive (τ_P<τ= 1/(nΩ_z+lΩ_r+mΩ_ϕ)) perturbations is power-law (∼τ_P/τ) suppressed, but that to adiabatic (τ_P>τ) perturbations is exponentially weak ($\sim \exp \left[-{\left({\tau }_{\mathrm{P}}/\tau \right)}^{\alpha }\right]$) except for resonant (τ→ ∞ ) modes. Slower (τ_P>τ_z) perturbations, e.g., distant encounters with satellite galaxies, induce stronger bending modes. Sagittarius (Sgr) dominates the solar neighborhood response of the Milky Way (MW) disk to satellite encounters. Thus, if the Gaia phase spiral was triggered by a MW satellite, Sgr is the leading contender. However, the survival of the phase spiral against collisional damping necessitates an impact ∼0.6–0.7 Gyr ago.

    

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3. Electron Heating in 2D Particle-in-cell Simulations of Quasi-perpendicular Low-beta Shocks

   https://doi.org/10.3847/1538-4357/ad1f69  

   Tran, Aaron ; Sironi, Lorenzo ( April 2024 , The Astrophysical Journal)

   We measure the thermal electron energization in 1D and 2D particle-in-cell simulations of quasi-perpendicular, low-beta (β_p= 0.25) collisionless ion–electron shocks with mass ratiom_i/m_e= 200, fast Mach number${\mathcal{M}}_{\mathrm{ms}}=1$–4, and upstream magnetic field angleθ_Bn= 55°–85° from the shock normal$\hat{\mathit{n}}$. It is known that shock electron heating is described by an ambipolar,B-parallel electric potential jump, Δϕ_∥, that scales roughly linearly with the electron temperature jump. Our simulations have$\mathrm{\Delta }{\varphi }_{\parallel }/(0.5m_{\mathrm{i}}{u_{\mathrm{sh}}}^2)\sim 0.1$–0.2 in units of the pre-shock ions’ bulk kinetic energy, in agreement with prior measurements and simulations. Different ways to measureϕ_∥, including the use of de Hoffmann–Teller frame fields, agree to tens-of-percent accuracy. Neglecting off-diagonal electron pressure tensor terms can lead to a systematic underestimate ofϕ_∥in our low-β_pshocks. We further focus on twoθ_Bn= 65° shocks: a${\mathcal{M}}_{\mathrm{s}}=4$(${\mathcal{M}}_{\mathrm{A}}=1.8$) case with a long, 30d_iprecursor of whistler waves along$\hat{\mathit{n}}$, and a${\mathcal{M}}_{\mathrm{s}}=7$(${\mathcal{M}}_{\mathrm{A}}=3.2$) case with a shorter, 5d_iprecursor of whistlers oblique to both$\hat{\mathit{n}}$andB;d_iis the ion skin depth. Within the precursors,ϕ_∥has a secular rise toward the shock along multiple whistler wavelengths and also has localized spikes within magnetic troughs. In a 1D simulation of the${\mathcal{M}}_{\mathrm{s}}=4$,θ_Bn= 65° case,ϕ_∥shows a weak dependence on the electron plasma-to-cyclotron frequency ratioω_pe/Ω_ce, andϕ_∥decreases by a factor of 2 asm_i/m_eis raised to the true proton–electron value of 1836.

    

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4. Examining the role of acceptor molecule structure in self-assembled bilayers: surface loading, stability, energy transfer, and upconverted emission

   https://doi.org/10.1039/C8CP03628D  

   Zhou, Yan ; Ayad, Suliman ; Ruchlin, Cory ; Posey, Victoria ; Hill, Sean P. ; Wu, Qiang ; Hanson, Kenneth ( January 2018 , Physical Chemistry Chemical Physics)

   Self-assembly of sensitizer and acceptor molecules has recently emerged as a promising strategy to facilitate and harness photon upconversion via triplet–triplet annihilation (TTA-UC). In addition to the energetic requirements, the structure and relative orientation of these molecules can have a strong influence on TTA-UC rates and efficiency. Here we report the synthesis of five different acceptor molecules composed of an anthracene core functionalized with 9,10- or 2,6-phenyl, methyl, or directly bound phosphonic acid groups and their incorporation into self-assembled bilayers on a ZrO 2 surface. All five films facilitate green-to-blue photon upconversion with Φ uc as high as 0.0023. The efficiency of TTA, and not triplet energy transfer, fluorescence, or losses via FRET, was primarily responsible for dictating the Φ uc emission. Even for molecules having similar photophysical properties, variation in the position of the phosphonic acid resulted in dramatically different Φ TTA , I th values, γ TTA , and D . Interestingly, we observed a strong linear correlation between Φ TTA and the I th value but the cause of this relationship, if any, is unclear. 

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5. Inverse Lidov-Kozai resonance for an outer test particle due to an eccentric perturber

   https://doi.org/10.1051/0004-6361/201935220  

   de Elía, G. C. ; Zanardi, M. ; Dugaro, A. ; Naoz, S. ( July 2019 , Astronomy & Astrophysics)

   Aims. We analyze the behavior of the argument of pericenter ω 2 of an outer particle in the elliptical restricted three-body problem, focusing on the ω 2 resonance or inverse Lidov-Kozai resonance. Methods. First, we calculated the contribution of the terms of quadrupole, octupole, and hexadecapolar order of the secular approximation of the potential to the outer particle’s ω 2 precession rate (d ω 2 ∕d τ ). Then, we derived analytical criteria that determine the vanishing of the ω 2 quadrupole precession rate (d ω 2 /d τ ) quad for different values of the inner perturber’s eccentricity e 1 . Finally, we used such analytical considerations and described the behavior of ω 2 of outer particles extracted from N-body simulations developed in a previous work. Results. Our analytical study indicates that the values of the inclination i 2 and the ascending node longitude Ω 2 associated with the outer particle that vanish (d ω 2 /d τ ) quad strongly depend on the eccentricity e 1 of the inner perturber. In fact, if e 1 < 0.25 (>0.40825), (d ω 2 /d τ ) quad is only vanished for particles whose Ω 2 circulates (librates). For e 1 between 0.25 and 0.40825, (d ω 2 /d τ ) quad can be vanished for any particle for a suitable selection of pairs (Ω 2 , i 2 ). Our analysis of the N-body simulations shows that the inverse Lidov-Kozai resonance is possible for small, moderate, and high values of e 1 . Moreover, such a resonance produces distinctive features in the evolution of a particle in the (Ω 2 , i 2 ) plane. In fact, if ω 2 librates and Ω 2 circulates, the extremes of i 2 at Ω 2 = 90° and 270° do not reach the same value, while if ω 2 and Ω 2 librate, the evolutionary trajectory of the particle in the (Ω 2 , i 2 ) plane shows evidence of an asymmetry with respect to i 2 = 90°. The evolution of ω 2 associated with the outer particles of the N-body simulations can be very well explained by the analytical criteria derived in our investigation. 

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