Diffusion Of Single Molecules Research Articles

Fundamental Limits in Measuring the Anisotropic Rotational Diffusion of Single Molecules.

Many biophysical techniques, such as single-molecule fluorescence correlation spectroscopy, Förster resonance energy transfer, and fluorescence anisotropy, measure the translation and rotation of biomolecules to quantify molecular processes at the nanoscale. These methods often simplify data analysis by assuming isotropic rotational diffusion, e.g., that molecules wobble within a circular cone. This simplification ignores the anisotropy present in many biological contexts that may cause molecules to exhibit different degrees of diffusion in different directions. Here, we loosen this assumption and establish a theoretical framework for describing and measuring anisotropic rotational diffusion using fluorescence imaging. We show that anisotropic wobble is directly quantified by the eigenvalues of a 3-by-3 positive-semidefinite Hermitian matrix M consisting of the second-order moments of a molecule's transition dipole μ. This formalism enables us to model the influence of unavoidable shot noise using a Hermitian perturbation matrix E; the eigenvalues of E directly bound errors in measurements of wobble via Weyl's inequality. Quantifying various perturbations E reveals that anisotropic wobble measurements are generally more sensitive to errors compared to quantifying isotropic wobble. Moreover, severe shot noise can induce negative eigenvalues in estimates of M, thereby causing the anisotropic wobble measurement to fail. Our analysis, using Fisher information, shows that techniques with worse orientation measurement sensitivity experience stronger perturbations E and require larger signal to background ratios to measure anisotropic rotational diffusion accurately. Our work provides deep insights for improving the state of the art in imaging the orientations and anisotropic rotational diffusion of single molecules.

Heterogeneity in condensates regulates intra-condensate diffusion of RNA single molecules

Heterogeneity in condensates regulates intra-condensate diffusion of RNA single molecules

Inferring pointwise diffusion properties of single trajectories with deep learning

To characterize the mechanisms governing the diffusion of particles in biological scenarios, it is essential to accurately determine their diffusive properties. To do so, we propose a machine-learning method to characterize diffusion processes with time-dependent properties at the experimental time resolution. Our approach operates at the single-trajectory level predicting the properties of interest, such as the diffusion coefficient or the anomalous diffusion exponent, at every time step of the trajectory. In this way, changes in the diffusive properties occurring along the trajectory emerge naturally in the prediction and thus allow the characterization without any prior knowledge or assumption about the system. We first benchmark the method on synthetic trajectories simulated under several conditions. We show that our approach can successfully characterize both abrupt and continuous changes in the diffusion coefficient or the anomalous diffusion exponent. Finally, we leverage the method to analyze experiments of single-molecule diffusion of two membrane proteins in living cells: the pathogen-recognition receptor DC-SIGN and the integrin α5β1. The analysis allows us to characterize physical parameters and diffusive states with unprecedented accuracy, shedding new light on the underlying mechanisms.

Comparing radical diffusion crossover phenomena in alkanes and alcohols

We applied electron spin resonance (ESR) to study tracer diffusivities of a nitroxide radical at various temperatures in the normal alkanes (octane to tridecane) and alcohols (methanol to 1-octanol). We studied and compared radical diffusivities in these liquids because their molecules are similar, but alcohols exhibit heterogeneous structures due to the hydrogen bonding of hydroxyl groups, which is absent in alkanes. The crossover temperature behavior of radical diffusivities was found in all liquids by relating radical diffusivities and solvent self-diffusivities. This finding evidences the transformation from a single-molecule diffusion process into a collective process upon temperature lowering. However, the crossover behavior strongly differs in alcohols and alkanes, indicating that the heterogeneous structure of alcohols affects the radical diffusion crossover.

Interfacial diffusion of single polyethylene oxide molecules: the consistency between fluorescence correlation spectroscopy and single molecule fluorescence tracking

高分子表界面的扩散运动在决定体系流变学性质、界面化学反应速率、相分离及其动力学、生物功能与信号传导等发挥着关键作用，因而，有效、准确测量表界面处单个高分子的扩散运动具有十分重要的意义. 本文以荧光关联光谱、单分子荧光轨迹追踪技术为手段，以吸附于固液界面的聚乙二醇（PEO）分子为模型体系，对上述两种研究方法进行了详细的比较. 结果表明，虽然两种方法原理不同，覆盖的时间窗口不同，测量空间范围不同，但是在合适的测量时间窗口内，对理想界面（水/硅烷化单晶薄膜的界面）处的PEO单分子扩散运动测量，获得了一致的扩散系数结果，表明了两种研究方法对于理想界面处单分子扩散测量的准确性与可靠性.

Reversible Live-Cell Labeling with Retro-engineered HaloTags Enables Long-Term High- and Super-Resolution Imaging.

Self-labeling enzymes (SLE) such as the HaloTag have emerged as powerful tools in high and super-resolution fluorescence microscopy. Newly developed fluorogenic SLE substrates enable imaging in the presence of excess dye. To exploit this feature for reversible labeling, we engineered two variants of HaloTag7 with restored dehalogenase activity. Kinetic studies in vitro showed different turnover kinetics for reHaloTagS (≈0.006 s-1 ) and reHaloTagF (≈0.055 s-1 ). Imaging by confocal and stimulated emission depletion microscopy yielded 3-5-time enhanced photostability of reHaloTag labeling. Prominently, single molecule imaging with reHaloTags enabled controlled and stable labeling density over extended time periods. By combination with structured illumination, simultaneous visualization of single molecule diffusion and organellar dynamics was achieved. These applications highlight the potential of reHaloTag labeling for pushing the limits of advanced fluorescence microscopy techniques.

PDK1:PKCα heterodimer association-dissociation dynamics in single-molecule diffusion tracks on a target membrane

Previous studies have documented the formation of a heterodimer between the two protein kinases PDK1 and PKCα on a lipid bilayer containing their target lipids. This work investigates the association-dissociation kinetics of this PDK1:PKCα heterodimer. The approach monitors the two-dimensional diffusion of single, membrane-associated PDK1 molecules for diffusivity changes as PKCα molecules bind and unbind. In the absence of PKCα, a membrane-associated PDK1 molecule exhibits high diffusivity (or large diffusion constant, D) because its membrane-contacting PH domain binds the target PIP3 lipid headgroup with little bilayer penetration, yielding minimal frictional drag against the bilayer. In contrast, membrane-associated PKCα contacts the bilayer via its C1A, C1B, and C2 domains, which each bind at least one target lipid with significant bilayer insertion, yielding a large frictional drag and low diffusivity. The present findings reveal that individual fluor-PDK1 molecules freely diffusing on the membrane surface undergo reversible switching between distinct high and low diffusivity states, corresponding to the PDK1 monomer and the PDK1:PKCα heterodimer, respectively. The observed single-molecule diffusion trajectories are converted to step length time courses, then subjected to two-state, hidden Markov modeling and dwell time analysis. The findings reveal that both the PDK1 monomer state and the PDK1:PKCα heterodimer state decay via simple exponential kinetics, yielding estimates of rate constants for state switching in both directions. Notably, the PDK1:PKCα heterodimer has been shown to competitively inhibit PDK1 phosphoactivation of AKT1, and is believed to play a tumor suppressor role by limiting excess activation of the highly oncogenic PDK1/AKT1/mTOR pathway. Thus, the present elucidation of the PDK1:PKCα association-dissociation kinetics has important biological and medical implications. More broadly, the findings illustrate the power of single-molecule diffusion measurements to reveal the kinetics of association-dissociation events in membrane signaling reactions that yield a large change in diffusive mobility.

Abstract IA019: Ectopic levels of low-complexity domain interactions repress endogenous oncogenic transcription

Abstract Mammalian transcription factors (TFs) ubiquitously contain intrinsically disordered low-complexity domains (LCDs) that perform transactivation functions. Recent studies have shown that dynamic, multivalent, and selective interactions between TF LCDs play an essential role in transactivation, but how such interactions mediate gene transcription remains unclear. It has been proposed that liquid-liquid phase separation (LLPS) of TFs driven by extensive LCD-LCD interactions is the mechanism underlying transactivation. Here, we investigate how tuning the level and localization of LCD-LCD interactions in vivo affects transcription of endogenous human genes. By quantitative single-cell imaging, we reveal that efficient gene activation by the oncogenic TF EWS/FLI1 requires narrow optimum of LCD-LCD interactions at its target genes associated with GGAA microsatellites. Increasing LCD-LCD interactions toward putative LLPS represses transcription of these genes in Ewing sarcoma cells. Likewise, ectopically creating LCD-LCD interactions to sequester EWS/FLI1 into a well-documented LLPS compartment, the nucleolus, represses EWS/FLI1 -driven transcription and inhibits malignant transformation of Ewing sarcoma. In addition, using live-cell single-molecule imaging, we show that a TF diffuses significantly more slowly in the nucleolus than in the nucleoplasm, demonstrating an important impact of LLPS on TF dynamic behaviors and single-molecule diffusion measurement as an effective approach to diagnose LLPS in vivo. Our findings show how altering the balance of LCD-LCD interactions can influence transcriptional regulation and suggest a potential therapeutic strategy for targeting disease-causing TFs. Citation Format: Shasha Chong. Ectopic levels of low-complexity domain interactions repress endogenous oncogenic transcription. [abstract]. In: Proceedings of the AACR Special Conference: Cancer Epigenomics; 2022 Oct 6-8; Washington, DC. Philadelphia (PA): AACR; Cancer Res 2022;82(23 Suppl_2):Abstract nr IA019.

Radical Diffusion Crossover Phenomenon in Glass-Forming Liquids.

We studied the diffusivities of a nitroxide radical at various temperatures in six glass-forming molecular liquids by electron spin resonance. By comparing the radical diffusivities and solvent self-diffusivities, we found that the radical diffusivities are lower than the self-diffusivities at high temperatures and approach them at low temperatures in all liquids. This crossover behavior was considered as evidence that a single-molecule diffusion process transforms into a collective process with temperature lowering. The crossover phenomenon was analyzed by a novel, simple diffusion model, combining collective and single-molecule diffusion processes, and it was compared to the Arrhenius crossover phenomenon. The obtained results suggest that future studies of tracer diffusion could contribute to a better understanding of diffusion mechanisms in glass-forming liquids. The proposed diffusion model could be used to study the crossover phenomena of tracer diffusion measured by other techniques, and it could serve as a base for developing more advanced models.

Scanning Tunneling Microscopy Reveals Surface Diffusion of Single Double-Decker Phthalocyanine Molecules at the Solution/Solid Interface

Scanning Tunneling Microscopy Reveals Surface Diffusion of Single Double-Decker Phthalocyanine Molecules at the Solution/Solid Interface

SFCS provides a window to bio-molecular organization

Nano-scale molecular interactions of proteins and lipids at the plasma membrane of cells drive cellular reorganisation and initiation of signalling in countless biological scenarios. We need to visualise the underlying dynamic bio-molecular organisation to better understand how large-scale morphological changes and cellular interactions evolve and are regulated. Fluorescence fluctuation spectroscopy (FFS) approaches represent a uniquely suited set of tools offering a window into single molecule diffusion, transport, and oligomerisation events.

Unravelling Channel Structure–Diffusivity Relationships in Zeolite ZSM‐5 at the Single‐Molecule Level

AbstractThe development of improved zeolite materials for applications in separation and catalysis requires understanding of mass transport. Herein, diffusion of single molecules is tracked in the straight and sinusoidal channels of the industrially relevant ZSM‐5 zeolites using a combination of single‐molecule localization microscopy and uniformly oriented zeolite thin films. Distinct motion behaviors are observed in zeolite channels with the same geometry, suggesting heterogeneous guest–host interactions. Quantification of the diffusion heterogeneities in the sinusoidal and straight channels suggests that the geometry of zeolite channels dictates the mobility and motion behavior of the guest molecules, resulting in diffusion anisotropy. The study of hierarchical zeolites shows that the addition of secondary pore networks primarily enhances the diffusivity of sinusoidal zeolite channels, and thus alleviating the diffusion limitations of microporous zeolites.

Unravelling Channel Structure-Diffusivity Relationships in Zeolite ZSM-5 at the Single-Molecule Level.

The development of improved zeolite materials for applications in separation and catalysis requires understanding of mass transport. Herein, diffusion of single molecules is tracked in the straight and sinusoidal channels of the industrially relevant ZSM‐5 zeolites using a combination of single‐molecule localization microscopy and uniformly oriented zeolite thin films. Distinct motion behaviors are observed in zeolite channels with the same geometry, suggesting heterogeneous guest–host interactions. Quantification of the diffusion heterogeneities in the sinusoidal and straight channels suggests that the geometry of zeolite channels dictates the mobility and motion behavior of the guest molecules, resulting in diffusion anisotropy. The study of hierarchical zeolites shows that the addition of secondary pore networks primarily enhances the diffusivity of sinusoidal zeolite channels, and thus alleviating the diffusion limitations of microporous zeolites.

Optical Imaging and Tracking of Single Molecules in Ultrahigh Vacuum

Molecule-surface interaction is key to many physical and chemical processes at interfaces. Here, we show that the dynamics of single molecules on a surface under ultrahigh vacuum can be resolved using fluorescence imaging. By adapting oil-immersion microscopy to a thin vacuum window, we measure the adsorption, translational and rotational diffusion of single perylene molecules on a fused silica surface with high spatial and temporal resolution. Time-dependent measurements of the fluorescence signal allow us to deduce two characteristic decay time scales, which can be explained through a simplified model involving two adsorption states and five energy levels. The system presented in this work combines fluorescence imaging with essential ingredients for surface science and promises a platform for probing molecule-surface interactions in highly defined conditions.

The dynamic face of lipid membranes.

Cell membranes - primarily composed of lipids, sterols, and proteins - form a dynamic interface between living cells and their environment. They act as a mechanical barrier around the cell while selectively facilitating material transport, signal transduction, and various other functions necessary for the cell viability. The complex functionality of cell membranes and the hierarchical motions and responses they exhibit demand a thorough understanding of the origin of different membrane dynamics and how they are influenced by molecular additives and environmental cues. These dynamic modes include single-molecule diffusion, thermal fluctuations, and large-scale membrane deformations, to name a few. This review highlights advances in investigating structure-driven dynamics associated with model cell membranes, with a particular focus on insights gained from neutron scattering and spectroscopy experiments. We discuss the uniqueness of neutron contrast variation and its remarkable potential in probing selective membrane structure and dynamics on spatial and temporal scales over which key biological functions occur. We also present a summary of current and future opportunities in synergistic combinations of neutron scattering with molecular dynamics (MD) simulations to gain further understanding of the molecular mechanisms underlying complex membrane functions.

100th Anniversary of Macromolecular Science Viewpoint: Enabling Advances in Fluorescence Microscopy Techniques.

In the past few decades there has been a revolution in the field of optical microscopy with emerging capabilities such as super-resolution and single-molecule fluorescence techniques. Combined with the classical advantages of fluorescence imaging, such as chemical labeling specificity, and noninvasive sample preparation and imaging, these methods have enabled significant advances in our polymer community. This Viewpoint discusses several of these capabilities and how they can uniquely offer information where other characterization techniques are limited. Several examples are highlighted that demonstrate the ability of fluorescence microscopy to understand key questions in polymer science such as single-molecule diffusion and orientation, 3D nanostructural morphology, and interfacial and multicomponent dynamics. Finally, we briefly discuss opportunities for further advances in techniques that may allow them to make an even greater contribution in polymer science.

Lateral diffusion of single polymer molecules at interfaces between water and oil.

Lateral diffusion of polymer molecules at the interfaces between immiscible oil and water is investigated at the single molecular level. The interfaces between water and alkanes are chosen as the model systems and polyethylene oxide (PEO) is the model polymer. Fluorescence correlation spectroscopy is used to measure the interfacial diffusion of fluorescence-labeled PEO with its molecular weight ranging over more than an order of magnitude. It is discovered that the interfacial diffusion coefficient scales with the molecular weight by the exponent of −0.5. Detailed analysis shows that the PEO chain takes an ideal two-dimensional random coil conformation at these fluidic interfaces and the bigger contribution from water's hydrodynamic friction is discovered.

Analysis of the Diffusivity Change from Single-Molecule Trajectories on Living Cells.

With the wide application of live-cell single-molecule imaging and tracking of biomolecules at work, deriving diffusion state changes of individual molecules is of particular interest as these changes reflect molecular oligomerization or interaction with other cellular components and thus correlate with functional changes. We have developed a Rayleigh mixture distribution-based hidden Markov model method to analyze time-lapse diffusivity change of single molecules, especially membrane proteins, with unknown dynamic states in living cells. With this method, the diffusion parameters, including diffusion state number, state transition probability, diffusion coefficient, and state mixture ratio, can be extracted from the single-molecule diffusion trajectories accurately via easy computation. The validity of our method has been demonstrated with not only experiments on synthetic trajectories but also single-molecule fluorescence imaging data of two typical membrane receptors. Our method offers a new analytical tool for the investigation of molecular interaction kinetics at the single-molecule level.

Structural state recognition facilitates tip tracking of EB1 at growing microtubule ends

The microtubule binding protein EB1 specifically targets the growing ends of microtubules in cells, where EB1 facilitates the interactions of cellular proteins with microtubule plus-ends. Microtubule end targeting of EB1 has been attributed to high-affinity binding of EB1 to GTP-tubulin that is present at growing microtubule ends. However, our 3D single-molecule diffusion simulations predicted a ~ 6000% increase in EB1 arrivals to open, tapered microtubule tip structures relative to closed lattice conformations. Using quantitative fluorescence, single-molecule, and electron microscopy experiments, we found that the binding of EB1 onto opened, structurally disrupted microtubules was dramatically increased relative to closed, intact microtubules, regardless of hydrolysis state. Correspondingly, in cells, the blunting of growing microtubule plus-ends by Vinblastine was correlated with reduced EB1 targeting. Together, our results suggest that microtubule structural recognition, based on a fundamental diffusion-limited binding model, facilitates the tip tracking of EB1 at growing microtubule ends.

Adsorption, diffusion, and limited dissociation of a single water molecule on the α-Pu2O3 (1 1 1) surface

We have investigated the adsorption, diffusion and dissociation of single water molecule on the α-Pu2O3 (1 1 1) surface using DFT + U approach. We show that, with very low absorption energies, the H2O molecule prefers to be absorbed at the surface oxygen vacancies. We futher reveal that the electrons transferred from the H2O molecule to the surface Pu atom mostly belong to the O atom in H2O. We also find that diffusion energy barriers are very low, indicating that the adsorbed H2O molecules are easy to diffuse. The trajectories obtained from ab initio molecular dynamics (AIMD) and the dissociation barrier calculated using nudged elastic band (NEB) methods both show that the absorbed H2O prefers to dissociate into hydrogen atom and hydroxyl group, other than into hydrogen molecule and oxygen atom. The present work suggests that the absorbed H2O easily diffuses but dissociates limitedly on the the α-Pu2O3 (1 1 1) surface.