Single-particle diffusional fingerprinting: A machine-learning framework for quantitative analysis of heterogeneous diffusion

Physics-informed deep learning for stochastic particle dynamics estimation

Single-particle tracking has enabled quantitative studies of complex systems, providing nanometer localization precision and millisecond temporal resolution in heterogeneous environments. However, at micro- or nanometer scales, probe dynamics become inherently stochastic due to Brownian motion and complex interactions, leading to varied diffusion behaviors. Typically, analysis of such trajectory data involves certain moving-window operation and assumes the existence of some pseudo-steady states, particularly when evaluating predefined parameters or specific types of diffusion modes. Here, we introduce the stochastic particle-informed neural network (SPINN), a physics-informed deep learning framework that integrates stochastic differential equations to model and infer particle diffusion dynamics. The SPINN autonomously explores parameter spaces and distinguishes between deterministic and stochastic components with single-frame resolution. Using the anomalous diffusion dataset, we validated SPINN's ability to reduce frame-to-frame variability while preserving key statistical correlations, allowing for accurate characterization of different stochastic processes. When applied to the diffusion of single gold nanorods in hydrogels, the SPINN revealed enhanced microrheological properties during hydrogel gelation and uncovered interfacial dynamics during dextran/tetra-PEG liquid-liquid phase separation. By improving the temporal resolution of stochastic dynamics, the SPINN facilitates the estimation and prediction of complex diffusion behaviors, offering insights into underlying physical mechanisms at mesoscopic scales.

Transcription dynamics and genome organization in the mammalian nucleus: Recent advances

Single-molecule tracking (SMT) has emerged as the dominant technology to investigate the dynamics of chromatin-transcription factor (TF) interactions. How long a TF needs to bind to a regulatory site to elicit a transcriptional response is a fundamentally important question. However, highly divergent estimates of TF binding have been presented in the literature, stemming from differences in photobleaching correction and data analysis. TF movement is often interpreted as specific or non-specific association with chromatin, yet the dynamic nature of the chromatin polymer is often overlooked. In this perspective, we highlight how recent SMT studies have reshaped our understanding of TF dynamics, chromatin mobility, and genome organization in the mammalian nucleus, focusing on the technical details and biological implications of these approaches. In a remarkable convergence of fixed and live-cell imaging, we show how super-resolution and SMT studies of chromatin have dovetailed to provide a convincing nanoscale view of genome organization.

Rapid Deployment of Antiviral Drugs Using Single-Virus Tracking and Machine Learning

The outbreak of emerging acute viral diseases urgently requires the acceleration of specialized antiviral drug development, thus widely adopting phenotypic screening as a strategy for drug repurposing in antiviral research. However, traditional phenotypic screening methods typically require several days of experimental cycles and lack visual confirmation of a drug's ability to inhibit viral infection. Here, we report a robust method that utilizes quantum-dot-based single-virus tracking and machine learning to generate unique single-virus infection fingerprint data from viral trajectories and detect the dynamic changes in viral movement following drug administration. Our findings demonstrated that this approach can successfully identify viral infection patterns at various infection phases and predict antiviral drug efficacy through machine learning within 90 min. This method provides valuable support for assessing the efficacy of antiviral drugs and offers promising applications for responding to future outbreaks of emerging viruses.

High-fidelity predictions of diffusion in the brain microenvironment

Multiple-particle tracking (MPT) is a microscopy technique capable of simultaneously tracking hundreds to thousands of nanoparticles in a biological sample and has been used extensively to characterize biological microenvironments, including the brain extracellular space (ECS). Machine learning techniques have been applied to MPT data sets to predict the diffusion mode of nanoparticle trajectories as well as more complex biological variables, such as biological age. In this study, we develop a machine learning pipeline to predict and investigate changes to the brain ECS due to injury using supervised classification and feature importance calculations. We first validate the pipeline on three related but distinct MPT data sets from the living brain ECS-age differences, region differences, and enzymatic degradation of ECS structure. We predict three ages with 86% accuracy, three regions with 90% accuracy, and healthy versus enzyme-treated tissue with 69% accuracy. Since injury across groups is normally compared with traditional statistical approaches, we first used linear mixed effects models to compare features between healthy control conditions and injury induced by two different oxygen glucose deprivation exposure times. We then used machine learning to predict injury state using MPT features. We show that the pipeline predicts between the healthy control, 0.5 h OGD treatment, and 1.5 h OGD treatment with 59% accuracy in the cortex and 66% in the striatum, and identifies nonlinear relationships between trajectory features that were not evident from traditional linear models. Our work demonstrates that machine learning applied to MPT data is effective across multiple experimental conditions and can find unique biologically relevant features of nanoparticle diffusion.

Single-particle rotational microrheology enables pathological staging of macrophage foaming and antiatherosclerotic studies

The formation of macrophage-derived foam cells has been recognized as the pathological hallmark of atherosclerotic diseases. However, the pathological evolution dynamics and underlying regulatory mechanisms remain largely unknown. Herein, we introduce a single-particle rotational microrheology method for pathological staging of macrophage foaming and antiatherosclerotic explorations by probing the dynamic changes of lysosomal viscous feature over the pathological evolution progression. The principle of this method involves continuous monitoring of out-of-plane rotation-caused scattering brightness fluctuations of the gold nanorod (AuNR) probe-based microrheometer and subsequent determination of rotational relaxation time to analyze the viscous feature in macrophage lysosomes. With this method, we demonstrated the lysosomal viscous feature as a robust pathological reporter and uncovered three distinct pathological stages underlying the evolution dynamics, which are highly correlated with a pathological stage-dependent activation of the NLRP3 inflammasome-involved positive feedback loop. We also validated the potential of this positive feedback loop as a promising therapeutic target and revealed the time window-dependent efficacy of NLRP3 inflammasome-targeted drugs against atherosclerotic diseases. To our knowledge, the pathological staging of macrophage foaming and the pathological stage-dependent activation of the NLRP3 inflammasome-involved positive feedback mechanism have not yet been reported. These findings provide insights into in-depth understanding of evolutionary features and regulatory mechanisms of macrophage foaming, which can benefit the analysis of effective therapeutical drugs as well as the time window of drug treatment against atherosclerotic diseases in preclinical studies.

Trajectory Analysis in Single-Particle Tracking: From Mean Squared Displacement to Machine Learning Approaches

Single-particle tracking is a powerful technique to investigate the motion of molecules or particles. Here, we review the methods for analyzing the reconstructed trajectories, a fundamental step for deciphering the underlying mechanisms driving the motion. First, we review the traditional analysis based on the mean squared displacement (MSD), highlighting the sometimes-neglected factors potentially affecting the accuracy of the results. We then report methods that exploit the distribution of parameters other than displacements, e.g., angles, velocities, and times and probabilities of reaching a target, discussing how they are more sensitive in characterizing heterogeneities and transient behaviors masked in the MSD analysis. Hidden Markov Models are also used for this purpose, and these allow for the identification of different states, their populations and the switching kinetics. Finally, we discuss a rapidly expanding field-trajectory analysis based on machine learning. Various approaches, from random forest to deep learning, are used to classify trajectory motions, which can be identified by motion models or by model-free sets of trajectory features, either previously defined or automatically identified by the algorithms. We also review free software available for some of the analysis methods. We emphasize that approaches based on a combination of the different methods, including classical statistics and machine learning, may be the way to obtain the most informative and accurate results.

Defect-Engineered Metal-Organic Frameworks as Nanocarriers for Pharmacotherapy: Insights into Intracellular Dynamics at The Single Particle Level

Nanoscale Metal-Organic Frameworks (nanoMOFs) are widely implemented in a host of assays involving drug delivery, biosensing catalysis, and bioimaging. However, the cell pathways and cell fate remain poorly understood. Here, a new fluorescent nanoMOF integrating ATTO 655 into surface defects of colloidal UiO-66 is synthesized, allowing to track the spatiotemporal localization of Single nanoMOF in live cells. Density functional theory reveals the stronger binding of ATTO 655 to the Zr6 cluster nodes compared with phosphate and Alendronate Sodium. Parallelized tracking of the spatiotemporal localization of thousands of nanoMOFs and analysis using machine learning platforms reveals whether nanoMOFs remain outside as well as their cellular internalization pathways. To quantitatively assess their colocalization with endo/lysosomal compartments, a colocalization proxy approach relying on the nanoMOF detection of particles in one channel to the signal in the corresponding endo/lysosomal compartments channel, considering signal versus local background intensity ratio and signal-to-noise ratio is developed. This strategy mitigates colocalization value inflation from high or low signal expression in endo/lysosomal compartments. The results accurately measure the nanoMOFs' colocalization from early to late endosomes and lysosomes and emphasize the importance of understanding their intracellular dynamics based on single-particle tracking for optimal and safe drug delivery.

Coarse-grained modeling and dynamics tracking of nanoparticles diffusion in human gut mucus

The gastrointestinal (GI) tract's mucus layer serves as a critical barrier and a mediator in drug nanoparticle delivery. The mucus layer's diverse molecular structures and spatial complexity complicates the mechanistic study of the diffusion dynamics of particulate materials. In response, we developed a bi-component coarse-grained mucus model, specifically tailored for the colorectal cancer environment, that contained the two most abundant glycoproteins in GI mucus: Muc2 and Muc5AC. This model demonstrated the effects of molecular composition and concentration on mucus pore size, a key determinant in the permeability of nanoparticles. Using this computational model, we investigated the diffusion rate of polyethylene glycol (PEG) coated nanoparticles, a widely used muco-penetrating nanoparticle. We validated our model with experimentally characterized mucus pore sizes and the diffusional coefficients of PEG-coated nanoparticles in the mucus collected from cultured human colorectal goblet cells. Machine learning fingerprints were then employed to provide a mechanistic understanding of nanoparticle diffusional behavior. We found that larger nanoparticles tended to be trapped in mucus over longer durations but exhibited more ballistic diffusion over shorter time spans. Through these discoveries, our model provides a promising platform to study pharmacokinetics in the GI mucus layer.

Mapping Extracellular Space Features of Viral Encephalitis to Evaluate the Proficiency of Anti-Viral Drugs

The extracellular space (ECS) is an important barrier against viral attack on brain cells, and dynamic changes in ECS microstructure characteristics are closely related to the progression of viral encephalitis in the brain and the efficacy of antiviral drugs. However, mapping the precise morphological and rheological features of the ECS in viral encephalitis is still challenging so far. Here, a robust approach is developed using single-particle diffusional fingerprinting of quantum dots combined with machine learning to map ECS features in the brain and predict the efficacy of antiviral encephalitis drugs. These results demonstrated that this approach can characterize the microrheology and geometry of the brain ECS at different stages of viral infection and identify subtle changes induced by different drug treatments. This approach provides a potential platform for drug proficiency assessment and is expected to offer a reliable basis for the clinical translation of drugs.

Disordered C-terminal domain drives spatiotemporal confinement of RNAPII to enhance search for chromatin targets

Efficient gene expression requires RNA polymerase II (RNAPII) to find chromatin targets precisely in space and time. How RNAPII manages this complex diffusive search in three-dimensional nuclear space remains largely unknown. The disordered carboxy-terminal domain (CTD) of RNAPII, which is essential for recruiting transcription-associated proteins, forms phase-separated droplets in vitro, hinting at a potential role in modulating RNAPII dynamics. In the present study, we use single-molecule tracking and spatiotemporal mapping in living yeast to show that the CTD is required for confining RNAPII diffusion within a subnuclear region enriched for active genes, but without apparent phase separation into condensates. Both Mediator and global chromatin organization are required for sustaining RNAPII confinement. Remarkably, truncating the CTD disrupts RNAPII spatial confinement, prolongs target search, diminishes chromatin binding, impairs pre-initiation complex formation and reduces transcription bursting. The present study illuminates the pivotal role of the CTD in driving spatiotemporal confinement of RNAPII for efficient gene expression.

Neonatal intestinal mucus barrier changes in response to maturity, inflammation, and sodium decanoate supplementation

The integrity of the intestinal mucus barrier is crucial for human health, as it serves as the body's first line of defense against pathogens. However, postnatal development of the mucus barrier and interactions between maturity and its ability to adapt to external challenges in neonatal infants remain unclear. In this study, we unveil a distinct developmental trajectory of the mucus barrier in preterm piglets, leading to enhanced mucus microstructure and reduced mucus diffusivity compared to term piglets. Notably, we found that necrotizing enterocolitis (NEC) is associated with increased mucus diffusivity of our large pathogen model compound, establishing a direct link between the NEC condition and the mucus barrier. Furthermore, we observed that addition of sodium decanoate had varying effects on mucus diffusivity depending on maturity and health state of the piglets. These findings demonstrate that regulatory mechanisms governing the neonatal mucosal barrier are highly complex and are influenced by age, maturity, and health conditions. Therefore, our results highlight the need for specific therapeutic strategies tailored to each neonatal period to ensure optimal gut health.

Deep Learning-Assisted Automated Multidimensional Single Particle Tracking in Living Cells

The translational and rotational dynamics of anisotropic optical nanoprobes revealed in single particle tracking (SPT) experiments offer molecular-level information about cellular activities. Here, we report an automated high-speed multidimensional SPT system integrated with a deep learning algorithm for tracking the 3D orientation of anisotropic gold nanoparticle probes in living cells with high localization precision (<10 nm) and temporal resolution (0.9 ms), overcoming the limitations of rotational tracking under low signal-to-noise ratio (S/N) conditions. This method can resolve the azimuth (0°-360°) and polar angles (0°-90°) with errors of less than 2° on the experimental and simulated data under S/N of ∼4. Even when the S/N approaches the limit of 1, this method still maintains better robustness and noise resistance than the conventional pattern matching methods. The usefulness of this multidimensional SPT system has been demonstrated with a study of the motions of cargos transported along the microtubules within living cells.

SEMORE: SEgmentation and MORphological fingErprinting by machine learning automates super-resolution data analysis

The morphology of protein assemblies impacts their behaviour and contributes to beneficial and aberrant cellular responses. While single-molecule localization microscopy provides the required spatial resolution to investigate these assemblies, the lack of universal robust analytical tools to extract and quantify underlying structures limits this powerful technique. Here we present SEMORE, a semi-automatic machine learning framework for universal, system- and input-dependent, analysis of super-resolution data. SEMORE implements a multi-layered density-based clustering module to dissect biological assemblies and a morphology fingerprinting module for quantification by multiple geometric and kinetics-based descriptors. We demonstrate SEMORE on simulations and diverse raw super-resolution data: time-resolved insulin aggregates, and published data of dSTORM imaging of nuclear pore complexes, fibroblast growth receptor 1, sptPALM of Syntaxin 1a and dynamic live-cell PALM of ryanodine receptors. SEMORE extracts and quantifies all protein assemblies, their temporal morphology evolution and provides quantitative insights, e.g. classification of heterogeneous insulin aggregation pathways and NPC geometry in minutes. SEMORE is a general analysis platform for super-resolution data, and being a time-aware framework can also support the rise of 4D super-resolution data.

Deep learning assisted single particle tracking for automated correlation between diffusion and function

Sub-cellular diffusion in living systems reflects cellular processes and interactions. Recent advances in optical microscopy allow the tracking of this nanoscale diffusion of individual objects with an unprecedented level of precision. However, the agnostic and automated extraction of functional information from the diffusion of molecules and organelles within the sub-cellular environment, is labor-intensive and poses a significant challenge. Here we introduce DeepSPT, a deep learning framework to interpret the diffusional 2D or 3D temporal behavior of objects in a rapid and efficient manner, agnostically. Demonstrating its versatility, we have applied DeepSPT to automated mapping of the early events of viral infections, identifying distinct types of endosomal organelles, and clathrin-coated pits and vesicles with up to 95% accuracy and within seconds instead of weeks. The fact that DeepSPT effectively extracts biological information from diffusion alone illustrates that besides structure, motion encodes function at the molecular and subcellular level.

Everything, everywhere, almost at once

A new platform that can follow the movement of individual proteins inside millions of cells in a single day will help contribute to existing knowledge of cell biology and identify new therapeutics.

Extract latent features of single-particle trajectories with historical experience learning

Single-particle tracking has enabled real-time, in situ quantitative studies of complex systems. However, inferring dynamic state changes from noisy and undersampling trajectories encounters challenges. Here, we introduce a data-driven method for extracting features of subtrajectories with historical experience learning (Deep-SEES), where a single-particle tracking analysis pipeline based on a self-supervised architecture automatically searches for the latent space, allowing effective segmentation of the underlying states from noisy trajectories without prior knowledge on the particle dynamics. We validated our method on a variety of noisy simulated and experimental data. Our results showed that the method can faithfully capture both stable states and their dynamic switch. In highly random systems, our method outperformed commonly used unsupervised methods in inferring motion states, which is important for understanding nanoparticles interacting with living cell membranes, active enzymes, and liquid-liquid phase separation. Self-generating latent features of trajectories could potentially improve the understanding, estimation, and prediction of many complex systems.

Deep learning assisted single particle tracking for automated correlation between diffusion and function

Sub-cellular diffusion in living systems reflects cellular processes and interactions. Recent advances in optical microscopy allow the tracking of this nanoscale diffusion of individual objects with an unprecedented level of precision. However, the agnostic and automated extraction of functional information from the diffusion of molecules and organelles within the sub-cellular environment, is labor-intensive and poses a significant challenge. Here we introduce DeepSPT, a deep learning framework to interpret the diffusional 2D or 3D temporal behavior of objects in a rapid and efficient manner, agnostically. Demonstrating its versatility, we have applied DeepSPT to automated mapping of the early events of viral infections, identifying distinct types of endosomal organelles, and clathrin-coated pits and vesicles with up to 95% accuracy and within seconds instead of weeks. The fact that DeepSPT effectively extracts biological information from diffusion alone indicates that besides structure, motion encodes function at the molecular and subcellular level.

Heterogeneous anomalous transport in cellular and molecular biology

It is well established that a wide variety of phenomena in cellular and molecular biology involve anomalous transport e.g. the statistics for the motility of cells and molecules are fractional and do not conform to the archetypes of simple diffusion or ballistic transport. Recent research demonstrates that anomalous transport is in many cases heterogeneous in both time and space. Thus single anomalous exponents and single generalised diffusion coefficients are unable to satisfactorily describe many crucial phenomena in cellular and molecular biology. We consider advances in the field ofheterogeneous anomalous transport(HAT) highlighting: experimental techniques (single molecule methods, microscopy, image analysis, fluorescence correlation spectroscopy, inelastic neutron scattering, and nuclear magnetic resonance), theoretical tools for data analysis (robust statistical methods such as first passage probabilities, survival analysis, different varieties of mean square displacements, etc), analytic theory and generative theoretical models based on simulations. Special emphasis is made on high throughput analysis techniques based on machine learning and neural networks. Furthermore, we consider anomalous transport in the context of microrheology and the heterogeneous viscoelasticity of complex fluids. HAT in the wavefronts of reaction-diffusion systems is also considered since it plays an important role in morphogenesis and signalling. In addition, we present specific examples from cellular biology including embryonic cells, leucocytes, cancer cells, bacterial cells, bacterial biofilms, and eukaryotic microorganisms. Case studies from molecular biology include DNA, membranes, endosomal transport, endoplasmic reticula, mucins, globular proteins, and amyloids.

Machine-Learning Solutions for the Analysis of Single-Particle Diffusion Trajectories

Single-particle traces of the diffusive motion of molecules, cells, or animals are by now routinely measured, similar to stochastic records of stock prices or weather data. Deciphering the stochastic mechanism behind the recorded dynamics is vital in understanding the observed systems. Typically, the task is to decipher the exact type of diffusion and/or to determine the system parameters. The tools used in this endeavor are currently being revolutionized by modern machine-learning techniques. In this Perspective we provide an overview of recently introduced methods in machine-learning for diffusive time series, most notably, those successfully competing in the anomalous diffusion challenge. As such methods are often criticized for their lack of interpretability, we focus on means to include uncertainty estimates and feature-based approaches, both improving interpretability and providing concrete insight into the learning process of the machine. We expand the discussion by examining predictions on different out-of-distribution data. We also comment on expected future developments.

Anomalous diffusion, nonergodicity, non-Gaussianity, and aging of fractional Brownian motion with nonlinear clocks

How do nonlinear clocks in time and/or space affect the fundamental properties of a stochastic process? Specifically, how precisely may ergodic processes such as fractional Brownian motion (FBM) acquire predictable nonergodic and aging features being subjected to such conditions? We address these questions in the current study. To describe different types of non-Brownian motion of particles-including power-law anomalous, ultraslow or logarithmic, as well as superfast or exponential diffusion-we here develop and analyze a generalized stochastic process of scaled-fractional Brownian motion (SFBM). The time- and space-SFBM processes are, respectively, constructed based on FBM running with nonlinear time and space clocks. The fundamental statistical characteristics such as non-Gaussianity of particle displacements, nonergodicity, as well as aging are quantified for time- and space-SFBM by selecting different clocks. The latter parametrize power-law anomalous, ultraslow, and superfast diffusion. The results of our computer simulations are fully consistent with the analytical predictions for several functional forms of clocks. We thoroughly examine the behaviors of the probability-density function, the mean-squared displacement, the time-averaged mean-squared displacement, as well as the aging factor. Our results are applicable for rationalizing the impact of nonlinear time and space properties superimposed onto the FBM-type dynamics. SFBM offers a general framework for a universal and more precise model-based description of anomalous, nonergodic, non-Gaussian, and aging diffusion in single-molecule-tracking observations.

Single-molecule tracking to determine the abundances and stoichiometries of freely-diffusing protein complexes in living cells: Past applications and future prospects

Most biological processes in living cells rely on interactions between proteins. Live-cell compatible approaches that can quantify to what extent a given protein participates in homo- and hetero-oligomeric complexes of different size and subunit composition are therefore critical to advance our understanding of how cellular physiology is governed by these molecular interactions. Biomolecular complex formation changes the diffusion coefficient of constituent proteins, and these changes can be measured using fluorescence microscopy-based approaches, such as single-molecule tracking, fluorescence correlation spectroscopy, and fluorescence recovery after photobleaching. In this review, we focus on the use of single-molecule tracking to identify, resolve, and quantify the presence of freely-diffusing proteins and protein complexes in living cells. We compare and contrast different data analysis methods that are currently employed in the field and discuss experimental designs that can aid the interpretation of the obtained results. Comparisons of diffusion rates for different proteins and protein complexes in intracellular aqueous environments reported in the recent literature reveal a clear and systematic deviation from the Stokes-Einstein diffusion theory. While a complete and quantitative theoretical explanation of why such deviations manifest is missing, the available data suggest the possibility of weighing freely-diffusing proteins and protein complexes in living cells by measuring their diffusion coefficients. Mapping individual diffusive states to protein complexes of defined molecular weight, subunit stoichiometry, and structure promises to provide key new insights into how protein-protein interactions regulate protein conformational, translational, and rotational dynamics, and ultimately protein function.

Realizing integration in structural biology: The 2022 ISBUC Annual Meeting

This meeting report presents the 2022 Annual Meeting of the cluster for Integrative Structural Biology at the University of Copenhagen (ISBUC) and discusses the cluster approach to interdisciplinary research management. This approach successfully facilitates cross-faculty and inter-departmental collaboration. Innovative integrative research collaborations ignited by ISBUC, as well as research presented at the meeting, are showcased.

Identification of nanoparticles as vesicular cargo via Airy scanning fluorescence microscopy and spatial statistics

Many biomedical applications of nanoparticles on the cellular level require a characterisation of their subcellular distribution. Depending on the nanoparticle and its preferred intracellular compartment, this may be a nontrivial task, and consequently, the available methodologies are constantly increasing. Here, we show that super-resolution microscopy in combination with spatial statistics (SMSS), comprising the pair correlation and the nearest neighbour function, is a powerful tool to identify spatial correlations between nanoparticles and moving vesicles. Furthermore, various types of motion like for example diffusive, active or Lévy flight transport can be distinguished within this concept via suitable statistical functions, which also contain information about the factors limiting the motion, as well as regarding characteristic length scales. The SMSS concept fills a methodological gap related to mobile intracellular nanoparticle hosts and its extension to further scenarios is straightforward. It is exemplified on MCF-7 cells after exposure to carbon nanodots, demonstrating that these particles are stored predominantly in the lysosomes.

Uncovering diffusive states of the yeast membrane protein, Pma1, and how labeling method can change diffusive behavior

We present and analyze video-microscopy-based single-particle-tracking measurements of the budding yeast (Saccharomyces cerevisiae) membrane protein, Pma1, fluorescently labeled either by direct fusion to the switchable fluorescent protein, mEos3.2, or by a novel, light-touch, labeling scheme, in which a 5 amino acid tag is directly fused to the C-terminus of Pma1, which then binds mEos3.2. The track diffusivity distributions of these two populations of single-particle tracks differ significantly, demonstrating that labeling method can be an important determinant of diffusive behavior. We also applied perturbation expectation maximization (pEMv2) (Koo and Mochrie in Phys Rev E 94(5):052412, 2016), which sorts trajectories into the statistically optimum number of diffusive states. For both TRAP-labeled Pma1 and Pma1-mEos3.2, pEMv2 sorts the tracks into two diffusive states: an essentially immobile state and a more mobile state. However, the mobile fraction of Pma1-mEos3.2 tracks is much smaller ([Formula: see text]) than the mobile fraction of TRAP-labeled Pma1 tracks ([Formula: see text]). In addition, the diffusivity of Pma1-mEos3.2's mobile state is several times smaller than the diffusivity of TRAP-labeled Pma1's mobile state. Thus, the two different labeling methods give rise to very different overall diffusive behaviors. To critically assess pEMv2's performance, we compare the diffusivity and covariance distributions of the experimental pEMv2-sorted populations to corresponding theoretical distributions, assuming that Pma1 displacements realize a Gaussian random process. The experiment-theory comparisons for both the TRAP-labeled Pma1 and Pma1-mEos3.2 reveal good agreement, bolstering the pEMv2 approach.

The Utility of Fluorescence Recovery after Photobleaching (FRAP) to Study the Plasma Membrane

The plasma membrane of mammalian cells is involved in a wide variety of cellular processes, including, but not limited to, endocytosis and exocytosis, adhesion and migration, and signaling. The regulation of these processes requires the plasma membrane to be highly organized and dynamic. Much of the plasma membrane organization exists at temporal and spatial scales that cannot be directly observed with fluorescence microscopy. Therefore, approaches that report on the membrane's physical parameters must often be utilized to infer membrane organization. As discussed here, diffusion measurements are one such approach that has allowed researchers to understand the subresolution organization of the plasma membrane. Fluorescence recovery after photobleaching (or FRAP) is the most widely accessible method for measuring diffusion in a living cell and has proven to be a powerful tool in cell biology research. Here, we discuss the theoretical underpinnings that allow diffusion measurements to be used in elucidating the organization of the plasma membrane. We also discuss the basic FRAP methodology and the mathematical approaches for deriving quantitative measurements from FRAP recovery curves. FRAP is one of many methods used to measure diffusion in live cell membranes; thus, we compare FRAP with two other popular methods: fluorescence correlation microscopy and single-particle tracking. Lastly, we discuss various plasma membrane organization models developed and tested using diffusion measurements.

Single-Particle Tracking of Thermomyces lanuginosus Lipase Reveals How Mutations in the Lid Region Remodel Its Diffusion

The function of most lipases is controlled by the lid, which undergoes conformational changes at a water–lipid interface to expose the active site, thus activating catalysis. Understanding how lid mutations affect lipases’ function is important for designing improved variants. Lipases’ function has been found to correlate with their diffusion on the substrate surface. Here, we used single-particle tracking (SPT), a powerful tool for deciphering enzymes’ diffusional behavior, to study Thermomyces lanuginosus lipase (TLL) variants with different lid structures in a laundry-like application condition. Thousands of parallelized recorded trajectories and hidden Markov modeling (HMM) analysis allowed us to extract three interconverting diffusional states and quantify their abundance, microscopic transition rates, and the energy barriers for sampling them. Combining those findings with ensemble measurements, we determined that the overall activity variation in the application condition is dependent on surface binding and lipase mobility when bound. Specifically, the L4 variant with a TLL-like lid and wild-type (WT) TLL displayed similar ensemble activity, but WT bound stronger to the surface than L4, while L4 had a higher diffusion coefficient and thus activity when bound to the surface. These mechanistic elements can only be de-convoluted by our combined assays. Our findings offer fresh perspectives on the development of the next iteration of enzyme-based detergent.

Machine-learning-powered extraction of molecular diffusivity from single-molecule images for super-resolution mapping

While critical to biological processes, molecular diffusion is difficult to quantify, and spatial mapping of local diffusivity is even more challenging. Here we report a machine-learning-enabled approach, pixels-to-diffusivity (Pix2D), to directly extract the diffusion coefficient D from single-molecule images, and consequently enable super-resolved D spatial mapping. Working with single-molecule images recorded at a fixed framerate under typical single-molecule localization microscopy (SMLM) conditions, Pix2D exploits the often undesired yet evident motion blur, i.e., the convolution of single-molecule motion trajectory during the frame recording time with the diffraction-limited point spread function (PSF) of the microscope. Whereas the stochastic nature of diffusion imprints diverse diffusion trajectories to different molecules diffusing at the same given D, we construct a convolutional neural network (CNN) model that takes a stack of single-molecule images as the input and evaluates a D-value as the output. We thus validate robust D evaluation and spatial mapping with simulated data, and with experimental data successfully characterize D differences for supported lipid bilayers of different compositions and resolve gel and fluidic phases at the nanoscale.

Dimensional Reduction for Single-Molecule Imaging of DNA and Nucleosome Condensation by Polyamines, HP1α and Ki-67

Macromolecules organize themselves into discrete membrane-less compartments. Mounting evidence has suggested that nucleosomes as well as DNA itself can undergo clustering or condensation to regulate genomic activity. Current in vitro condensation studies provide insight into the physical properties of condensates, such as surface tension and diffusion. However, methods that provide the resolution needed for complex kinetic studies of multicomponent condensation are desired. Here, we use a supported lipid bilayer platform in tandem with total internal reflection microscopy to observe the two-dimensional movement of DNA and nucleosomes at the single-molecule resolution. This dimensional reduction from three-dimensional studies allows us to observe the initial condensation events and dissolution of these early condensates in the presence of physiological condensing agents. Using polyamines, we observed that the initial condensation happens on a time scale of minutes while dissolution occurs within seconds upon charge inversion. Polyamine valency, DNA length, and GC content affect the threshold polyamine concentration for condensation. Protein-based nucleosome condensing agents, HP1α and Ki-67, have much lower threshold concentrations for condensation than charge-based condensing agents, with Ki-67 being the most effective, requiring as low as 100 pM for nucleosome condensation. In addition, we did not observe condensate dissolution even at the highest concentrations of HP1α and Ki-67 tested. We also introduce a two-color imaging scheme where nucleosomes of high density labeled in one color are used to demarcate condensate boundaries and identical nucleosomes of another color at low density can be tracked relative to the boundaries after Ki-67-mediated condensation. Our platform should enable the ultimate resolution of single molecules in condensation dynamics studies of chromatin components under defined physicochemical conditions.

Heterogeneous and Surface-Catalyzed Amyloid Aggregation Monitored by Spatially Resolved Fluorescence and Single Molecule Microscopy

Amyloid aggregation is associated with many diseases and may also occur in therapeutic protein formulations. Addition of co-solutes is a key strategy to modulate the stability of proteins in pharmaceutical formulations and select inhibitors for drug design in the context of diseases. However, the heterogeneous nature of this multicomponent system in terms of structures and mechanisms poses a number of challenges for the analysis of the chemical reaction. Using insulin as protein system and polysorbate 80 as co-solute, we combine a spatially resolved fluorescence approach with single molecule microscopy and machine learning methods to kinetically disentangle the different contributions from multiple species within a single aggregation experiment. We link the presence of interfaces to the degree of heterogeneity of the aggregation kinetics and retrieve the rate constants and underlying mechanisms for single aggregation events. Importantly, we report that the mechanism of inhibition of the self-assembly process depends on the details of the growth pathways of otherwise macroscopically identical species. This information can only be accessed by the analysis of single aggregate events, suggesting our method as a general tool for a comprehensive physicochemical characterization of self-assembly reactions.

Impact of Saccharomyces cerevisiae on the Field of Single-Molecule Biophysics

Cellular functions depend on the dynamic assembly of protein regulator complexes at specific cellular locations. Single Molecule Tracking (SMT) is a method of choice for the biochemical characterization of protein dynamics in vitro and in vivo. SMT follows individual molecules in live cells and provides direct information about their behavior. SMT was successfully applied to mammalian models. However, mammalian cells provide a complex environment where protein mobility depends on numerous factors that are difficult to control experimentally. Therefore, yeast cells, which are unicellular and well-studied with a small and completely sequenced genome, provide an attractive alternative for SMT. The simplicity of organization, ease of genetic manipulation, and tolerance to gene fusions all make yeast a great model for quantifying the kinetics of major enzymes, membrane proteins, and nuclear and cellular bodies. However, very few researchers apply SMT techniques to yeast. Our goal is to promote SMT in yeast to a wider research community. Our review serves a dual purpose. We explain how SMT is conducted in yeast cells, and we discuss the latest insights from yeast SMT while putting them in perspective with SMT of higher eukaryotes.

Physical and barrier changes in gastrointestinal mucus induced by the permeation enhancer sodium 8-[(2-hydroxybenzoyl)amino]octanoate (SNAC)

Drug delivery systems (DDS) for oral delivery of peptide drugs contain excipients that facilitate and enhance absorption. However, little knowledge exists on how DDS excipients such as permeation enhancers interact with the gastrointestinal mucus barrier. This study aimed to investigate interactions of the permeation enhancer sodium 8-[(2-hydroxybenzoyl)amino]octanoate (SNAC) with ex vivo porcine intestinal mucus (PIM), ex vivo porcine gastric mucus (PGM), as well as with in vitro biosimilar mucus (BM) by profiling their physical and barrier properties upon exposure to SNAC. Bulk mucus permeability studies using the peptides cyclosporine A and vancomycin, ovalbumin as a model protein, as well as fluorescein-isothiocyanate dextrans (FDs) of different molecular weights and different surface charges were conducted in parallel to mucus retention force studies using a texture analyzer, rheological studies, cryo-scanning electron microscopy (cryo-SEM), and single particle tracking of fluorescence-labelled nanoparticles to investigate the effects of the SNAC-mucus interaction. The exposure of SNAC to PIM increased the mucus retention force, storage modulus, viscosity, increased nanoparticle confinement within PIM as well as decreased the permeation of cyclosporine A and ovalbumin through PIM. Surprisingly, the viscosity of PGM and the permeation of cyclosporine A and ovalbumin through PGM was unaffected by the presence of SNAC, thus the effect of SNAC depended on the regional site that mucus was collected from. In the absence of SNAC, the permeation of different molecular weight and differently charged FDs through PIM was comparable to that through BM. However, while bulk permeation of neither of the FDs through PIM was affected by SNAC, the presence of SNAC decreased the permeation of FD4 and increased the permeation of FD150 kDa through BM. Additionally, and in contrast to observations in PIM, nanoparticle confinement within BM remained unaffected by the presence of SNAC. In conclusion, the present study showed that SNAC altered the physical and barrier properties of PIM, but not of PGM. The effects of SNAC in PIM were not observed in the BM in vitro model. Altogether, the study highlights the need for further understanding how permeation enhancers influence the mucus barrier and illustrates that the selected mucus model for such studies should be chosen with care.

Bayesian deep learning for error estimation in the analysis of anomalous diffusion

Modern single-particle-tracking techniques produce extensive time-series of diffusive motion in a wide variety of systems, from single-molecule motion in living-cells to movement ecology. The quest is to decipher the physical mechanisms encoded in the data and thus to better understand the probed systems. We here augment recently proposed machine-learning techniques for decoding anomalous-diffusion data to include an uncertainty estimate in addition to the predicted output. To avoid the Black-Box-Problem a Bayesian-Deep-Learning technique named Stochastic-Weight-Averaging-Gaussian is used to train models for both the classification of the diffusion model and the regression of the anomalous diffusion exponent of single-particle-trajectories. Evaluating their performance, we find that these models can achieve a well-calibrated error estimate while maintaining high prediction accuracies. In the analysis of the output uncertainty predictions we relate these to properties of the underlying diffusion models, thus providing insights into the learning process of the machine and the relevance of the output.

Deep learning in single-molecule imaging and analysis: recent advances and prospects

Single-molecule microscopy is advantageous in characterizing heterogeneous dynamics at the molecular level. However, there are several challenges that currently hinder the wide application of single molecule imaging in bio-chemical studies, including how to perform single-molecule measurements efficiently with minimal run-to-run variations, how to analyze weak single-molecule signals efficiently and accurately without the influence of human bias, and how to extract complete information about dynamics of interest from single-molecule data. As a new class of computer algorithms that simulate the human brain to extract data features, deep learning networks excel in task parallelism and model generalization, and are well-suited for handling nonlinear functions and extracting weak features, which provide a promising approach for single-molecule experiment automation and data processing. In this perspective, we will highlight recent advances in the application of deep learning to single-molecule studies, discuss how deep learning has been used to address the challenges in the field as well as the pitfalls of existing applications, and outline the directions for future development.

Direct observation of heterogeneous formation of amyloid spherulites in real-time by super-resolution microscopy

Protein misfolding in the form of fibrils or spherulites is involved in a spectrum of pathological abnormalities. Our current understanding of protein aggregation mechanisms has primarily relied on the use of spectrometric methods to determine the average growth rates and diffraction-limited microscopes with low temporal resolution to observe the large-scale morphologies of intermediates. We developed a REal-time kinetics via binding and Photobleaching LOcalization Microscopy (REPLOM) super-resolution method to directly observe and quantify the existence and abundance of diverse aggregate morphologies of human insulin, below the diffraction limit and extract their heterogeneous growth kinetics. Our results revealed that even the growth of microscopically identical aggregates, e.g., amyloid spherulites, may follow distinct pathways. Specifically, spherulites do not exclusively grow isotropically but, surprisingly, may also grow anisotropically, following similar pathways as reported for minerals and polymers. Combining our technique with machine learning approaches, we associated growth rates to specific morphological transitions and provided energy barriers and the energy landscape at the level of single aggregate morphology. Our unifying framework for the detection and analysis of spherulite growth can be extended to other self-assembled systems characterized by a high degree of heterogeneity, disentangling the broad spectrum of diverse morphologies at the single-molecule level.

Real-time super-resolution microscopy analysis reveals the growth kinetics, morphology, and abundance of human insulin amyloid spherulites with different growth pathways.

From Static to Dynamic: A Review on the Role of Mucus Heterogeneity in Particle and Microbial Transport

Mucus layers (McLs) are on the front line of the human defense system that protect us from foreign abiotic/biotic particles (e.g., airborne virus SARS-CoV-2) and lubricates our organs. Recently, the impact of McLs on human health (e.g., nutrient absorption and drug delivery) and diseases (e.g., infections and cancers) has been studied extensively, yet their mechanisms are still not fully understood due to their high variety among organs and individuals. We characterize these variances as the heterogeneity of McLs, which lies in the thickness, composition, and physiology, making the systematic research on the roles of McLs in human health and diseases very challenging. To advance mucosal organoids and develop effective drug delivery systems, a comprehensive understanding of McLs' heterogeneity and how it impacts mucus physiology is urgently needed. When the role of airway mucus in the penetration and transmission of coronavirus (CoV) is considered, this understanding may also enable a better explanation and prediction of the CoV's behavior. Hence, in this Review, we summarize the variances of McLs among organs, health conditions, and experimental settings as well as recent advances in experimental measurements, data analysis, and model development for simulations.

Anomalous diffusion, aging, and nonergodicity of scaled Brownian motion with fractional Gaussian noise: overview of related experimental observations and models

How does a systematic time-dependence of the diffusion coefficient $D (t)$ affect the ergodic and statistical characteristics of fractional Brownian motion (FBM)? Here, we examine how the behavior of the...