Mean square displacement analysis of single-particle trajectories with localization error: Brownian motion in an isotropic medium

Imaging Minimal Bacteria at the Nanoscale: a Reliable and Versatile Process to Perform Single-Molecule Localization Microscopy in Mycoplasmas

Mycoplasmas are the smallest free-living organisms. These bacteria are important models for both fundamental and synthetic biology, owing to their highly reduced genomes. They are also relevant in the medical and veterinary fields, as they are pathogenic to both humans and most livestock species. Mycoplasma cells have minute sizes, often in the 300- to 800-nm range. As these dimensions are close to the diffraction limit of visible light, fluorescence imaging in mycoplasmas is often poorly informative. Recently developed superresolution imaging techniques can break this diffraction limit, improving the imaging resolution by an order of magnitude and offering a new nanoscale vision of the organization of these bacteria. These techniques have, however, not been applied to mycoplasmas before. Here, we describe an efficient and reliable protocol to perform single-molecule localization microscopy (SMLM) imaging in mycoplasmas. We provide a polyvalent transposon-based system to express the photoconvertible fluorescent protein mEos3.2, enabling photo-activated localization microscopy (PALM) in most Mycoplasma species. We also describe the application of direct stochastic optical reconstruction microscopy (dSTORM). We showcase the potential of these techniques by studying the subcellular localization of two proteins of interest. Our work highlights the benefits of state-of-the-art microscopy techniques for mycoplasmology and provides an incentive to further the development of SMLM strategies to study these organisms in the future.

IMPORTANCE Mycoplasmas are important models in biology, as well as highly problematic pathogens in the medical and veterinary fields. The very small sizes of these bacteria, well below a micron, limits the usefulness of traditional fluorescence imaging methods, as their resolution limit is similar to the dimensions of the cells. Here, to bypass this issue, we established a set of state-of-the-art superresolution microscopy techniques in a wide range of Mycoplasma species. We describe two strategies: PALM, based on the expression of a specific photoconvertible fluorescent protein, and dSTORM, based on fluorophore-coupled antibody labeling. With these methods, we successfully performed single-molecule imaging of proteins of interest at the surface of the cells and in the cytoplasm, at lateral resolutions well below 50 nm. Our work paves the way toward a better understanding of mycoplasma biology through imaging of subcellular structures at the nanometer scale.

Microrheology of Pseudomonas aeruginosa biofilms grown in wound beds

A new technique was used to measure the viscoelasticity of in vivo Pseudomonas aeruginosa biofilms. This was done through ex vivo microrheology measurements of in vivo biofilms excised from mouse wound beds. To our knowledge, this is the first time that the mechanics of in vivo biofilms have been measured. In vivo results are then compared to typical in vitro measurements. Biofilms grown in vivo are more relatively elastic than those grown in a wound-like medium in vitro but exhibited similar compliance. Using various genetically mutated P. aeruginosa strains, it is observed that the contributions of the exopolysaccharides Pel, Psl, and alginate to biofilm viscoelasticity were different for the biofilms grown in vitro and in vivo. In vitro experiments with collagen containing medium suggest this likely arises from the incorporation of host material, most notably collagen, into the matrix of the biofilm when it is grown in vivo. Taken together with earlier studies that examined the in vitro effects of collagen on mechanical properties, we conclude that collagen may, in some cases, be the dominant contributor to biofilm viscoelasticity in vivo.

Biotropic liquid crystal phase transformations in cellulose-producing bacterial communities

Biological functionality is often enabled by a fascinating variety of physical phenomena that emerge from orientational order of building blocks, a defining property of nematic liquid crystals that is also pervasive in nature. Out-of-equilibrium, "living" analogs of these technological materials are found in biological embodiments ranging from myelin sheath of neurons to extracellular matrices of bacterial biofilms and cuticles of beetles. However, physical underpinnings behind manifestations of orientational order in biological systems often remain unexplored. For example, while nematiclike birefringent domains of biofilms are found in many bacterial systems, the physics behind their formation is rarely known. Here, using cellulose-synthesizing Acetobacter xylinum bacteria, we reveal how biological activity leads to orientational ordering in fluid and gel analogs of these soft matter systems, both in water and on solid agar, with a topological defect found between the domains. Furthermore, the nutrient feeding direction plays a role like that of rubbing of confining surfaces in conventional liquid crystals, turning polydomain organization within the biofilms into a birefringent monocrystal-like order of both the extracellular matrix and the rod-like bacteria within it. We probe evolution of scalar orientational order parameters of cellulose nanofibers and bacteria associated with fluid-gel and isotropic-nematic transformations, showing how highly ordered active nematic fluids and gels evolve with time during biological-activity-driven, disorder-order transformation. With fluid and soft-gel nematics observed in a certain range of biological activity, this mesophase-exhibiting system is dubbed "biotropic," analogously to thermotropic nematics that exhibit solely orientational order within a temperature range, promising technological and fundamental-science applications.

Precision size and refractive index analysis of weakly scattering nanoparticles in polydispersions

Characterization of the size and material properties of particles in liquid suspensions is in very high demand, for example, in the analysis of colloidal samples or of bodily fluids such as urine or blood plasma. However, existing methods are limited in their ability to decipher the constituents of realistic samples. Here we introduce iNTA as a new method that combines interferometric detection of scattering with nanoparticle tracking analysis to reach unprecedented sensitivity and precision in determining the size and refractive index distributions of nanoparticles in suspensions. After benchmarking iNTA with samples of colloidal gold, we present its remarkable ability to resolve the constituents of various multicomponent and polydisperse samples of known origin. Furthermore, we showcase the method by elucidating the refractive index and size distributions of extracellular vesicles from Leishmania parasites and human urine. The current performance of iNTA already enables advances in several important applications, but we also discuss possible improvements.

Controlled delivery of quantum dots using microelectrophoresis technique: Intracellular behavior and preservation of cell viability

The use of synthetic nanomaterials as contrast agents, sensors, and drug delivery vehicles in biological research primarily requires effective approaches for intracellular delivery. Recently, the well-accepted microelectrophoresis technique has been reported to exhibit the ability to deliver nanomaterials, quantum dots (QDs) as an example, into live cells, but information about cell viability and intracellular fate of delivered nanomaterials is yet to be provided. Here we show that cell viability following microelectrophoresis of QDs is strongly correlated with the amount of delivered QDs, which can be finely controlled by tuning the ejection duration to maintain long-term cell survival. We reveal that microelectrophoretic delivered QDs distribute homogeneously and present pure Brownian diffusion inside the cytoplasm without endosomal entrapment, having great potential for the study of dynamic intracellular events. We validate that microelectrophoresis is a powerful technique for the effective intracellular delivery of QDs and potentially various functional nanomaterials in biological research.

Resolving the subtle details of human DNA alkyltransferase lesion search and repair mechanism by single-molecule studies

We directly visualize DNA translocation and lesion recognition by the O⁶-alkylguanine DNA alkyltransferase (AGT). Our data show bidirectional movement of AGT monomers and clusters on undamaged DNA that depended on Zn²⁺ occupancy of AGT. A role of cooperative AGT clusters in enhancing lesion search efficiencies by AGT has previously been proposed. Surprisingly, our data show no enhancement of DNA translocation speed by AGT cluster formation, suggesting that AGT clusters may serve a different role in AGT function. Our data support preferential cluster formation by AGT at alkyl lesions, suggesting a role of these clusters in stabilizing lesion-bound complexes. From our data, we derive a new model for the lesion search and repair mechanism of AGT.

The O⁶-alkylguanine DNA alkyltransferase (AGT) is an important DNA repair protein. AGT repairs highly mutagenic and cytotoxic alkylguanine lesions that result from metabolic products but are also deliberately introduced during chemotherapy, making a better understanding of the working mechanism of AGT essential. To investigate lesion interactions by AGT, we present a protocol to insert a single alkylguanine lesion at a well-defined position in long DNA substrates for single-molecule fluorescence microscopy coupled with dual-trap optical tweezers. Our studies address the longstanding enigma in the field of how monomeric AGT complexes at alkyl lesions seen in crystal structures can be reconciled with AGT clusters on DNA at high protein concentrations that have been observed from atomic force microscopy (AFM) and biochemical studies. A role of AGT clusters in enhancing lesion search efficiencies by AGT has previously been proposed. Surprisingly, our data show no enhancement of DNA translocation speed by AGT cluster formation, suggesting that AGT clusters may serve a different role in AGT function. Interestingly, a possible role of these clusters is indicated by preferential cluster formation at alkyl lesions in our studies. From our data, we derive a model for the lesion search and repair mechanism of AGT.

Single-virus assay reveals membrane determinants and mechanistic features of Sendai virus binding

Sendai virus (SeV, formally murine respirovirus) is a membrane-enveloped, negative-sense RNA virus in the Paramyxoviridae family and is closely related to human parainfluenza viruses. SeV has long been utilized as a model paramyxovirus and has recently gained attention as a viral vector candidate for both laboratory and clinical applications. To infect host cells, SeV must first bind to sialic acid glycolipid or glycoprotein receptors on the host cell surface via its hemagglutinin-neuraminidase (HN) protein. Receptor binding induces a conformational change in HN, which allosterically triggers the viral fusion (F) protein to catalyze membrane fusion. While it is known that SeV binds to α2,3-linked sialic acid receptors, and there has been some study into the chemical requirements of those receptors, key mechanistic features of SeV binding remain unknown, in part because traditional approaches often convolve binding and fusion. Here, we develop and employ a fluorescence microscopy-based assay to observe SeV binding to supported lipid bilayers (SLBs) at the single-particle level, which easily disentangles binding from fusion. Using this assay, we investigate mechanistic questions of SeV binding. We identify chemical structural features of ganglioside receptors that influence viral binding and demonstrate that binding is cooperative with respect to receptor density. We measure the characteristic decay time of unbinding and provide evidence supporting a "rolling" mechanism of viral mobility following receptor binding. We also study the dependence of binding on target cholesterol concentration. Interestingly, we find that although SeV binding shows striking parallels in cooperative binding with a prior report of Influenza A virus, it does not demonstrate a similar sensitivity to cholesterol concentration and receptor nanocluster formation.

Evolutionary divergence of anaphase spindle mechanics in nematode embryos constrained by antagonistic pulling and viscous forces

Cellular functions like cell division are remarkably conserved across phyla. However the evolutionary principles of cellular organization that drive it are less well explored. Thus, an essential question remains: to what extent cellular parameters evolve without altering the basic function they sustain? Here we have observed 6 different nematode species for which the mitotic spindle is positioned asymmetrically during the first embryonic division. Whereas the C. elegans spindle undergoes oscillations during its displacement, the spindle elongates without oscillations in other species. We asked which evolutionary changes in biophysical parameters could explain differences in spindle motion while maintaining a constant output. Using laser microsurgery of the spindle we revealed that all species are subjected to cortical pulling forces, of varying magnitudes. Using a viscoelastic model to fit the recoil trajectories and with an independent measurement of cytoplasmic viscosity, we extracted the values of cytoplasmic drag, cortical pulling forces and spindle elasticity for all species. We found large variations in cytoplasmic viscosity whereas cortical pulling forces and elasticity were often more constrained. In agreement with previous simulations, we found that increased viscosity correlates with decreased oscillation speeds across species. However, the absence of oscillations despite low viscosity in some species, can only be explained by smaller pulling forces. Consequently, we find that spindle mobility across the species analyzed here is characterized by a tradeoff between cytoplasmic viscosity and pulling forces normalized by the size of the embryo. Our work provides a framework for understanding mechanical constraints on evolutionary diversification of spindle mobility.

Four-color single-molecule imaging with engineered tags resolves the molecular architecture of signaling complexes in the plasma membrane

Localization and tracking of individual receptors by single-molecule imaging opens unique possibilities to unravel the assembly and dynamics of signaling complexes in the plasma membrane. We present a comprehensive workflow for imaging and analyzing receptor diffusion and interaction in live cells at single molecule level with up to four colors. Two engineered, monomeric GFP variants, which are orthogonally recognized by anti-GFP nanobodies, are employed for efficient and selective labeling of target proteins in the plasma membrane with photostable fluorescence dyes. This labeling technique enables us to quantitatively resolve the stoichiometry and dynamics of the interferon-γ (IFNγ) receptor signaling complex in the plasma membrane of living cells by multicolor single-molecule imaging. Based on versatile spatial and spatiotemporal correlation analyses, we identify ligand-induced receptor homo- and heterodimerization. Multicolor single-molecule co-tracking and quantitative single-molecule Förster resonance energy transfer moreover reveals transient assembly of IFNγ receptor heterotetramers and confirms its structural architecture.

ATP-responsive biomolecular condensates tune bacterial kinase signaling

Biomolecular condensates formed via liquid-liquid phase separation enable spatial and temporal organization of enzyme activity. Phase separation in many eukaryotic condensates has been shown to be responsive to intracellular adenosine triphosphate (ATP) levels, although the consequences of these mechanisms for enzymes sequestered within the condensates are unknown. Here, we show that ATP depletion promotes phase separation in bacterial condensates composed of intrinsically disordered proteins. Enhanced phase separation promotes the sequestration and activity of a client kinase enabling robust signaling and maintenance of viability under the stress posed by nutrient scarcity. We propose that a diverse repertoire of condensates can serve as control knobs to tune enzyme sequestration and reactivity in response to the metabolic state of bacterial cells.

Self-healing behavior of recycled asphalt prepared by residue oil of straw liquefaction based on molecular dynamics simulation

In order to accurately describe the self-healing behavior of recycled asphalt prepared by residue oil of straw liquefaction (ROSL), five ROSL contents of 2%, 4%, 6%, 10%, and 15% were added to the aged asphalt to represent the recycled asphalt and are denoted as ROSL-2, ROSL-4, ROSL-6, ROSL-10, and ROSL-15, respectively. Molecular simulation was used to simulate the healing behavior of nano cracks. A three-layer system was established in which the two sides are asphalt molecules and the middle is a 30 Å vacuum layer. The vacuum layer represented the internal nano cracks in the asphalt. The results show that the disappearance of cracks during the self-healing process was the result of the combined effect of model volume compression and asphalt molecule stretching. Self-healing is mainly affected by the van der Waals forces between the molecules. The self-healing rate of recycled asphalt is closely related to the content of ROSL, the higher the ROSL content, the greater the diffusion coefficient, which is more conducive to asphalt self-healing. However, as the time for ROSL-10 and ROSL-15 to reach the equilibrium distribution of relative concentration and density stability is basically the same, and the diffusion coefficient of ROSL-10 is basically the same as that of virgin asphalt, the optimal content of the ROSL is recommended to be 10%.

Impact of neurite alignment on organelle motion

Intracellular transport is pivotal for cell growth and survival. Malfunctions in this process have been associated with devastating neurodegenerative diseases, highlighting the need for a deeper understanding of the mechanisms involved. Here, we use an experimental methodology that leads neurites of differentiated PC12 cells into either one of two configurations: a one-dimensional configuration, where the neurites align along lines, or a two-dimensional configuration, where the neurites adopt a random orientation and shape on a flat substrate. We subsequently monitored the motion of functional organelles, the lysosomes, inside the neurites. Implementing a time-resolved analysis of the mean-squared displacement, we quantitatively characterized distinct motion modes of the lysosomes. Our results indicate that neurite alignment gives rise to faster diffusive and super-diffusive lysosomal motion than the situation in which the neurites are randomly oriented. After inducing lysosome swelling through an osmotic challenge by sucrose, we confirmed the predicted slowdown in diffusive mobility. Surprisingly, we found that the swelling-induced mobility change affected each of the (sub-/super-)diffusive motion modes differently and depended on the alignment configuration of the neurites. Our findings imply that intracellular transport is significantly and robustly dependent on cell morphology, which might in part be controlled by the extracellular matrix.

Thermodynamics, static properties and transport behaviour of fluids with competing interactions

Competing interaction fluids have become ideal model systems to study a large number of phenomena, for example, the formation of intermediate range order structures, condensed phases not seen in fluids driven by purely attractive or repulsive forces, the onset of particle aggregation under in- and out-of-equilibrium conditions, which results in the birth of reversible and irreversible aggregates or clusters whose topology and morphology depend additionally on the thermodynamic constrictions, and a particle dynamics that has a strong influence on the transport behaviour and rheological properties of the fluid. In this contribution, we study a system of particles interacting through a potential composed by a continuous succession of a short-ranged square-well (SW), an intermediate-ranged square-shoulder and a long-ranged SW. This potential model is chosen to systematically analyse the contribution of every component of the interaction potential on the phase behaviour, the microstructure, the morphology of the resulting aggregates and the transport phenomena of fluids described by competing interactions. Our results indicate that the inclusion of a barrier and a second well leads to new and interesting effects, which in addition result in variations of the physical properties associated to the competition among interactions.

Recapitulation of cell-like KRAS4b membrane dynamics on complex biomimetic membranes

Understanding the spatiotemporal distribution and dynamics of RAS on the plasma membrane (PM) is the key for elucidating the molecular mechanisms of the RAS signaling pathway. Single particle tracking (SPT) experiments show that in cells, KRAS diffuses in at least three interchanging states on the cellular PM; however, KRAS remains monomeric and always shows homogeneous diffusion on artificial membranes. Here, we show for the first time on a supported lipid bilayer composed of heterogeneous lipid components that we can recapitulate the three-state diffusion of KRAS seen in cells. The use of a biologically relevant eight-lipid system opens a new frontier in the biophysical studies of RAS and other membrane associated proteins on a biomimetic system that recapitulates the complexity of a cellular PM.

•

KRAS4b shows homogeneous diffusion on simple 2-lipids bilayer

•

KRAS4b shows a cell-like, three-state diffusion on a complex 8-lipid bilayer

•

Phase separation in lipids favors the multi-state diffusion of KRAS4b

•

The complex lipid composition favors RAS nanoclustering irrespective of nucleotide state

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...

Simultaneous, Single-Particle Measurements of Size and Loading Give Insights into the Structure of Drug-Delivery Nanoparticles

Nanoparticles are a promising solution for delivery of a wide range of medicines and vaccines. Optimizing their design depends on being able to resolve, understand, and predict biophysical and therapeutic properties, as a function of design parameters. While existing tools have made great progress, gaps in understanding remain because of the inability to make detailed measurements of multiple correlated properties. Typically, an average measurement is made across a heterogeneous population, obscuring potentially important information. In this work, we develop and apply a method for characterizing nanoparticles with single-particle resolution. We use convex lens-induced confinement (CLiC) microscopy to isolate and quantify the diffusive trajectories and fluorescent intensities of individual nanoparticles trapped in microwells for long times. First, we benchmark detailed measurements of fluorescent polystyrene nanoparticles against prior data to validate our approach. Second, we apply our method to investigate the size and loading properties of lipid nanoparticle (LNP) vehicles containing silencing RNA (siRNA), as a function of lipid formulation, solution pH, and drug-loading. By taking a comprehensive look at the correlation between the intensity and size measurements, we gain insights into LNP structure and how the siRNA is distributed in the LNP. Beyond introducing an analytic for size and loading, this work allows for future studies of dynamics with single-particle resolution, such as LNP fusion and drug-release kinetics. The prime contribution of this work is to better understand the connections between microscopic and macroscopic properties of drug-delivery vehicles, enabling and accelerating their discovery and development.

Study of the Fabrication Technology of Hybrid Microfluidic Biochips for Label-Free Detection of Proteins

A study of the peculiarities and a comparative analysis of the technologies used for the fabrication of elements of novel hybrid microfluidic biochips for express biomedical analysis have been carried out. The biochips were designed with an incorporated microfluidic system, which enabled an accumulation of the target compounds in a biological fluid to be achieved, thus increasing the biochip system's sensitivity and even implementing a label-free design of the detection unit. The multilevel process of manufacturing a microfluidic system of a given topology for label-free fluorometric detection of protein structures is presented. The technological process included the chemical modification of the working surface of glass substrates by silanization using (3-aminopropyl) trimethoxysilane (APTMS), formation of the microchannels, for which SU-8 technologies and a last generation dry film photoresist were studied and compared. The solid-state phosphor layers were deposited using three methods: drop application; airbrushing; and mechanical spraying onto the adhesive surface. The processes of sealing the system, installing input ports, and packaging using micro-assembly technologies are described. The technological process has been optimized and the biochip was implemented and tested. The presented system can be used to design novel high-performance diagnostic tools that implement the function of express detection of protein markers of diseases and create low-power multimodal, highly intelligent portable analytical decision-making systems in medicine.

Fast 3D imaging of giant unilamellar vesicles using reflected light-sheet microscopy with single molecule sensitivity

Observation of highly dynamic processes inside living cells at the single molecule level is key for a better understanding of biological systems. However, imaging of single molecules in living cells is usually limited by the spatial and temporal resolution, photobleaching and the signal-to-background ratio. To overcome these limitations, light-sheet microscopes with thin selective plane illumination, for example, in a reflected geometry with a high numerical aperture imaging objective, have been developed. Here, we developed a reflected light-sheet microscope with active optics for fast, high contrast, two-colour acquisition of z -stacks. We demonstrate fast volume scanning by imaging a two-colour giant unilamellar vesicle (GUV) hemisphere. In addition, the high contrast enabled the imaging and tracking of single lipids in the GUV cap. The enhanced reflected scanning light-sheet microscope enables fast 3D scanning of artificial membrane systems and potentially live cells with single-molecule sensitivity and thereby could provide quantitative and molecular insight into the operation of cells.

Diffusion State Transitions in Single-Particle Trajectories of MET Receptor Tyrosine Kinase Measured in Live Cells

Single-particle tracking enables the analysis of the dynamics of biomolecules in living cells with nanometer spatial and millisecond temporal resolution. This technique reports on the mobility of membrane proteins and is sensitive to the molecular state of a biomolecule and to interactions with other biomolecules. Trajectories describe the mobility of single particles over time and provide information such as the diffusion coefficient and diffusion state. Changes in particle dynamics within single trajectories lead to segmentation, which allows to extract information on transitions of functional states of a biomolecule. Here, mean-squared displacement analysis is developed to classify trajectory segments into immobile, confined diffusing, and freely diffusing states, and to extract the occurrence of transitions between these modes. We applied this analysis to single-particle tracking data of the membrane receptor MET in live cells and analyzed state transitions in single trajectories of the un-activated receptor and the receptor bound to the ligand internalin B. We found that internalin B-bound MET shows an enhancement of transitions from freely and confined diffusing states into the immobile state as compared to un-activated MET. Confined diffusion acts as an intermediate state between immobile and free, as this state is most likely to change the diffusion state in the following segment. This analysis can be readily applied to single-particle tracking data of other membrane receptors and intracellular proteins under various conditions and contribute to the understanding of molecular states and signaling pathways.

Tracking Brownian motion in three dimensions and characterization of individual nanoparticles using a fiber-based high-finesse microcavity

The dynamics of nanosystems in solution contain a wealth of information with relevance for diverse fields ranging from materials science to biology and biomedical applications. When nanosystems are marked with fluorophores or strong scatterers, it is possible to track their position and reveal internal motion with high spatial and temporal resolution. However, markers can be toxic, expensive, or change the object’s intrinsic properties. Here, we simultaneously measure dispersive frequency shifts of three transverse modes of a high-finesse microcavity to obtain the three-dimensional path of unlabeled SiO₂ nanospheres with 300 μs temporal and down to 8 nm spatial resolution. This allows us to quantitatively determine properties such as the polarizability, hydrodynamic radius, and effective refractive index. The fiber-based cavity is integrated in a direct-laser-written microfluidic device that enables the precise control of the fluid with ultra-small sample volumes. Our approach enables quantitative nanomaterial characterization and the analysis of biomolecular motion at high bandwidth.

Tracking of nanoparticle dynamics in solution often require labelling. Here, the authors use a high-finesse microcavity and simultaneously measure dispersive frequency shifts of three transverse modes, demonstrating 3D tracking of unlabelled single nanospheres, and quantitatively determine their physical properties.

Objective comparison of methods to decode anomalous diffusion

Deviations from Brownian motion leading to anomalous diffusion are found in transport dynamics from quantum physics to life sciences. The characterization of anomalous diffusion from the measurement of an individual trajectory is a challenging task, which traditionally relies on calculating the trajectory mean squared displacement. However, this approach breaks down for cases of practical interest, e.g., short or noisy trajectories, heterogeneous behaviour, or non-ergodic processes. Recently, several new approaches have been proposed, mostly building on the ongoing machine-learning revolution. To perform an objective comparison of methods, we gathered the community and organized an open competition, the Anomalous Diffusion challenge (AnDi). Participating teams applied their algorithms to a commonly-defined dataset including diverse conditions. Although no single method performed best across all scenarios, machine-learning-based approaches achieved superior performance for all tasks. The discussion of the challenge results provides practical advice for users and a benchmark for developers.

Precise measurements of chromatin diffusion dynamics by modeling using Gaussian processes

The spatiotemporal organization of chromatin influences many nuclear processes: from chromosome segregation to transcriptional regulation. To get a deeper understanding of these processes, it is essential to go beyond static viewpoints of chromosome structures, to accurately characterize chromatin's diffusion properties. We present GP-FBM: a computational framework based on Gaussian processes and fractional Brownian motion to extract diffusion properties from stochastic trajectories of labeled chromatin loci. GP-FBM uses higher-order temporal correlations present in the data, therefore, outperforming existing methods. Furthermore, GP-FBM allows to interpolate incomplete trajectories and account for substrate movement when two or more particles are present. Using our method, we show that average chromatin diffusion properties are surprisingly similar in interphase and mitosis in mouse embryonic stem cells. We observe surprising heterogeneity in local chromatin dynamics, correlating with potential regulatory activity. We also present GP-Tool, a user-friendly graphical interface to facilitate usage of GP-FBM by the research community.

Neurotransmitter signaling regulates distinct phases of multimodal human interneuron migration

Inhibitory GABAergic interneurons migrate over long distances from their extracortical origin into the developing cortex. In humans, this process is uniquely slow and prolonged, and it is unclear whether guidance cues unique to humans govern the various phases of this complex developmental process. Here, we use fused cerebral organoids to identify key roles of neurotransmitter signaling pathways in guiding the migratory behavior of human cortical interneurons. We use scRNAseq to reveal expression of GABA, glutamate, glycine, and serotonin receptors along distinct maturation trajectories across interneuron migration. We develop an image analysis software package, TrackPal, to simultaneously assess 48 parameters for entire migration tracks of individual cells. By chemical screening, we show that different modes of interneuron migration depend on distinct neurotransmitter signaling pathways, linking transcriptional maturation of interneurons with their migratory behavior. Altogether, our study provides a comprehensive quantitative analysis of human interneuron migration and its functional modulation by neurotransmitter signaling.

Heterogeneity of cell membrane structure studied by single molecule tracking

Heterogeneity in cell membrane structure, typified by microdomains with different biophysical and biochemical properties, is thought to impact on a variety of cell functions. Integral membrane proteins act as nanometre-sized probes of the lipid environment and their thermally-driven movements can be used to report local variations in membrane properties. In the current study, we have used total internal reflection fluorescence microscopy (TIRFM) combined with super-resolution tracking of multiple individual molecules, in order to create high-resolution maps of local membrane viscosity. We used a quadrat sampling method and show how statistical tests for membrane heterogeneity can be conducted by analysing the paths of many molecules that pass through the same unit area of membrane. We describe experiments performed on cultured primary cells, stable cell lines and ex vivo tissue slices using a variety of membrane proteins, under different imaging conditions. In some cell types, we find no evidence for heterogeneity in mobility across the plasma membrane, but in others we find statistically significant differences with some regions of membrane showing significantly higher viscosity than others.

We use total internal reflection fluorescence microscopy combined with super-resolution tracking of multiple individual molecules, in order to create high-resolution maps of local membrane viscosity.

Untying the Gordian KNOT: Unbiased Single Particle Tracking Using Point Clouds and Adaptive Motion Analysis

Achieving mechanistic understanding of transport in complex environments such as inside cells or at polymer interfaces is challenging. We need better ways to image transport in 3-D and better single particle tracking algorithms to determine transport that are not systemically biased toward any classical motion model. Here we present an unbiased single particle tracking algorithm: Knowing Nothing Outside Tracking (KNOT). KNOT uses point clouds provided by iterative deconvolution to educate individual particle localizations and link particle positions between frames to achieve 2-D and 3-D tracking. Information from prior point clouds fuels an independent adaptive motion model for each particle to avoid global models that could introduce biases. KNOT competes with or surpasses other 2-D methods from the 2012 particle tracking challenge while accurately tracking adsorption dynamics of proteins on polymer surfaces and early endosome transport in live cells in 3-D. We apply KNOT to study 3-D endosome transport to reveal new physical insight into locally directed and diffusive transport in live cells. Our analysis demonstrates better accuracy in classifying local motion and its direction compared to previous methods, revealing intricate intracellular transport heterogeneities.

Fast Leaps between Millisecond Confinements Govern Ase1 Diffusion along Microtubules

Diffusion is the most fundamental mode of protein translocation within cells. Confined diffusion of proteins along the electrostatic potential constituted by the surface of microtubules, although modeled meticulously in molecular dynamics simulations, has not been experimentally observed in real-time. Here, interferometric scattering microscopy is used to directly visualize the movement of the microtubule-associated protein Ase1 along the microtubule surface at nanometer and microsecond resolution. Millisecond confinements of Ase1 and fast leaps between these positions of dwelling preferentially occurring along the microtubule protofilaments are resolved, revealing Ase1's mode of diffusive translocation along the microtubule's periodic surface. The derived interaction potential closely matches the tubulin-dimer periodicity and the distribution of the electrostatic potential on the microtubule lattice. It is anticipated that mapping the interaction landscapes for different proteins on microtubules, finding plausible energetic barriers of different positioning and heights, can provide valuable insights into regulating the dynamics of essential cytoskeletal processes, such as intracellular cargo trafficking, cell division, and morphogenesis, all of which rely on diffusive translocation of proteins along microtubules.

An overview of diffusion models for intracellular dynamics analysis

We present an overview of diffusion models commonly used for quantifying the dynamics of intracellular particles (e.g. biomolecules) inside eukaryotic living cells. It is established that inference on the modes of mobility of molecules is central in cell biology since it reflects interactions between structures and determines functions of biomolecules in the cell. In that context, Brownian motion is a key component in short distance transportation (e.g. connectivity for signal transduction). Another dynamical process that has been heavily studied in the past decade is the motor-mediated transport (e.g. dynein, kinesin and myosin) of molecules. Primarily supported by actin filament and microtubule network, it ensures spatial organization and temporal synchronization in the intracellular mechanisms and structures. Nevertheless, the complexity of internal structures and molecular processes in the living cell influence the molecular dynamics and prevent the systematic application of pure Brownian or directed motion modeling. On the one hand, cytoskeleton density will hinder the free displacement of the particle, a phenomenon called subdiffusion. On the other hand, the cytoskeleton elasticity combined with thermal bending can contribute a phenomenon called superdiffusion. This paper discusses the basics of diffusion modes observed in eukariotic cells, by introducing the essential properties of these processes. Applications of diffusion models include protein trafficking and transport and membrane diffusion.

Multiscale Investigation of the Diffusion Mechanism within the Solid-Electrolyte Interface Layer: Coupling Quantum Mechanics, Molecular Dynamics, and Macroscale Mathematical Modeling

The solid-electrolyte interface (SEI) layer has a critical role in Li-ion batteries' (LIBs) life span. The SEI layer, even in modern commercial LIBs, is responsible for more than 50% of capacity loss. Due to the inherent complexity in studying the SEI layer, many aspects of its performance and characteristics, including diffusion mechanisms in this layer, are unknown. As a result, most mathematical models use a constant value of the diffusion coefficient, instead of a variable formulation, to predict LIBs' properties and performance such as capacity fading and the SEI growth rate. In this work, by employing a multiscale investigation using a combination of quantum mechanics, molecular dynamics, and macroscale mathematical modeling, some equations are presented to evaluate the energy barrier against diffusion and the diffusion coefficient in different crystal structures in the inner section of the SEI layer. The equations are evaluated as a function of temperature and concentration and can be used to study the diffusion mechanism in the SEI layer. They can also be integrated with other mathematical models of LIBs to increase the accuracy of the latter.

EM-based algorithms for single particle tracking of Ornstein-Uhlenbeck motion from sCMOS camera data

Single particle tracking plays an important role in studying physical and kinetic properties of biomolecules. In this work, we introduce the application of Expectation Maximization (EM) based algorithms for solving localization and parameter estimation problems in SPT using data captured from scientific complementary metal-oxide semiconductor (sCMOS) camera sensors. Two representative methods are considered for generating the filtered and smoothed distributions needed by EM: Sequential Monte Carlo - EM, and Unscented - EM. The SMC method uses particle filtering and particle smoothing to handle general distributions, while the U scheme reduces the computational burden through the use of an unscented Kalman Filter and an unscented Rauch-Tung Striebel Smoother. We also investigate the influence of the number of images in the dataset on the final estimates through intensive simulations as well as the computational efficiency of the two methods.

Kinetic Analysis of Acanthamoeba castellanii Infected with Giant Viruses Quantitatively Revealed Process of Morphological and Behavioral Changes in Host Cells

Most virus-infected cells show morphological and behavioral changes, which are called cytopathic effects. Acanthamoeba castellanii, an abundant, free-living protozoan, serves as a laboratory host for some viruses of the phylum Nucleocytoviricota-the giant viruses. Many of these viruses cause cell rounding in the later stages of infection in the host cells. Here, we show the changes that lead to cell rounding in the host cells through time-lapse microscopy and image analysis. Time-lapse movies of A. castellanii cells infected with Mimivirus shirakomae, kyotovirus, medusavirus, or Pandoravirus japonicus were generated using a phase-contrast microscope. We updated our phase-contrast-based kinetic analysis algorithm for amoebae (PKA3) and used it to analyze these time-lapse movies. Image analysis revealed that the process leading to cell rounding varies among the giant viruses; for example, M. shirakomae infection did not cause changes for some time after the infection, kyotovirus infection caused an early decrease in the number of cells with typical morphologies, and medusavirus and P. japonicus infection frequently led to the formation of intercellular bridges and rotational behavior of host cells. These results suggest that in the case of giant viruses, the putative reactions of host cells against infection and the putative strategies of virus spread are diverse. IMPORTANCE Quantitative analysis of the infection process is important for a better understanding of viral infection strategies and virus-host interactions. Here, an image analysis of the phase-contrast time-lapse movies displayed quantitative differences in the process of cytopathic effects due to the four giant viruses in Acanthamoeba castellanii, which were previously unclear. It was revealed that medusavirus and Pandoravirus japonicus infection led to the formation of a significant number of elongated particles related to intercellular bridges, emphasizing the importance of research on the interaction of viruses with host cell nuclear function. Mimivirus shirakomae infection did not cause any changes in the host cells initially, so it is thought that the infected cells can actively move and spread over a wider area, emphasizing the importance of observation in a wider area and analysis of infection efficiency. These results suggest that a kinetic analysis using the phase-contrast-based kinetic analysis algorithm for amoebae (PKA3) reveals the infection strategies of each giant virus.

Three-dimensional localization refinement and motion model parameter estimation for confined single particle tracking under low-light conditions

Confined diffusion is an important model for describing the motion of biological macromolecules moving in the crowded, three-dimensional environment of the cell. In this work we build upon the technique known as sequential Monte Carlo - expectation maximization (SMC-EM) to simultaneously localize the particle and estimate the motion model parameters from single particle tracking data. We extend SMC-EM to handle the double-helix point spread function (DH-PSF) for encoding the three-dimensional position of the particle in the two-dimensional image plane of the camera. SMC-EM can handle a wide range of camera models and here we assume the data was acquired using a scientific CMOS (sCMOS) camera. The sensitivity and speed of these cameras make them well suited for SPT, though the pixel-dependent nature of the camera noise presents a challenge for analysis. We focus on the low signal setting and compare our method through simulation to more standard approaches that use the paradigm of localize-then-estimate. To localize the particle under the standard paradigm, we use both a Gaussian fit and a maximum likelihood estimator (MLE) that accounts for both the DH-PSF and the pixel-dependent noise of the camera. Model estimation is then carried out either by fitting the model to the mean squared displacement (MSD) curve, or through an optimal estimation approach. Our results indicate that in the low signal regime, the SMC-EM approach outperforms the other methods while at higher signal-to-background levels, SMC-EM and the MLE-based methods perform equally well and both are significantly better than fitting to the MSD. In addition our results indicate that at smaller confinement lengths where the nonlinearities dominate the motion model, the SMC-EM approach is superior to the alternative approaches.

Two-dimensional Brownian motion of anisotropic dimers

We study the two-dimensional motion of colloidal dimers by single-particle tracking and compare the experimental observations obtained by bright-field microscopy to theoretical predictions for anisotropic diffusion. The comparison is based on the mean-square displacements in the laboratory and particle frame as well as generalizations of the self-intermediate scattering functions, which provide insights into the rotational dynamics of the dimer. The diffusional anisotropy leads to a measurable translational-rotational coupling that becomes most prominent by aligning the coordinate system with the initial orientation of the particles. In particular, we find a splitting of the time-dependent diffusion coefficients parallel and perpendicular to the long axis of the dimer which decays over the orientational relaxation time. Deviations of the self-intermediate scattering functions from pure exponential relaxation are small but can be resolved experimentally. The theoretical predictions and experimental results agree quantitatively.

TRAIT2D: a Software for Quantitative Analysis of Single Particle Diffusion Data

Single particle tracking (SPT) is one of the most widely used tools in optical microscopy to evaluate particle mobility in a variety of situations, including cellular and model membrane dynamics. Recent technological developments, such as Interferometric Scattering microscopy, have allowed recording of long, uninterrupted single particle trajectories at kilohertz framerates. The resulting data, where particles are continuously detected and do not displace much between observations, thereby do not require complex linking algorithms. Moreover, while these measurements offer more details into the short-term diffusion behaviour of the tracked particles, they are also subject to the influence of localisation uncertainties, which are often underestimated by conventional analysis pipelines. we thus developed a Python library, under the name of TRAIT2D (Tracking Analysis Toolbox - 2D version), in order to track particle diffusion at high sampling rates, and analyse the resulting trajectories with an innovative approach. The data analysis pipeline introduced is more localisation-uncertainty aware, and also selects the most appropriate diffusion model for the data provided on a statistical basis. A trajectory simulation platform also allows the user to handily generate trajectories and even synthetic time-lapses to test alternative tracking algorithms and data analysis approaches. A high degree of customisation for the analysis pipeline, for example with the introduction of different diffusion modes, is possible from the source code. Finally, the presence of graphical user interfaces lowers the access barrier for users with little to no programming experience.

TRAIT2D: a Software for Quantitative Analysis of Single Particle Diffusion Data

Single particle tracking (SPT) is one of the most widely used tools in optical microscopy to evaluate particle mobility in a variety of situations, including cellular and model membrane dynamics. Recent technological developments, such as Interferometric Scattering microscopy, have allowed recording of long, uninterrupted single particle trajectories at kilohertz framerates. The resulting data, where particles are continuously detected and do not displace much between observations, thereby do not require complex linking algorithms. Moreover, while these measurements offer more details into the short-term diffusion behaviour of the tracked particles, they are also subject to the influence of localisation uncertainties, which are often underestimated by conventional analysis pipelines. we thus developed a Python library, under the name of TRAIT2D (Tracking Analysis Toolbox - 2D version), in order to track particle diffusion at high sampling rates, and analyse the resulting trajectories with an innovative approach. The data analysis pipeline introduced is more localisation-uncertainty aware, and also selects the most appropriate diffusion model for the data provided on a statistical basis. A trajectory simulation platform also allows the user to handily generate trajectories and even synthetic time-lapses to test alternative tracking algorithms and data analysis approaches. A high degree of customisation for the analysis pipeline, for example with the introduction of different diffusion modes, is possible from the source code. Finally, the presence of graphical user interfaces lowers the access barrier for users with little to no programming experience.

Multipoint Lock-and-Key Assembly of Particles with Anisotropic Dents toward Modeling Rigid Macromolecules in a Colloidal Scale

Multipoint lock-and-key particle assembly, consisting of lock particles with multiple anisotropic dents and rod-shaped particles as key particles, is developed for colloidal modeling application. The lock particles were connected with each other at a key particle as their joint in the presence of depletants, forming rigid colloidal molecules imitating rigid polymers (e.g., polymers containing aromatic rings and intramolecular hydrogen bonds). A single-particle level observation was conducted to visualize the colloidal polymerization of the particle assembly. Motion trajectories of the lock particles observed by optical microscopy indicated that the particle diffusivity was dramatically lowered when the lock particle connected with another one, suggesting that particle diffusion was suppressed by particle assembly formation. Because the kinetic and regioselectivity of colloidal polymerization are assumed to be analogous to those at the atomic scale, the proposed lock-and-key assembly can be a promising colloidal model for atomic-scale polymers associated with their micro-Brownian motion.

Stent strut streamlining and thickness reduction promote endothelialization

Stent thrombosis (ST) carries a high risk of myocardial infarction and death. Lack of endothelial coverage is an important prognostic indicator of ST after stenting. While stent strut thickness is a critical factor in ST, a mechanistic understanding of its effect is limited and the role of haemodynamics is unclear. Endothelialization was tested using a wound-healing assay and five different stent strut models ranging in height between 50 and 150 µm for circular arc (CA) and rectangular (RT) geometries and a control without struts. Under static conditions, all stent strut surfaces were completely endothelialized. Reversing pulsatile disturbed flow caused full endothelialization, except for the stent strut surfaces of the 100 and 150 µm RT geometries, while fully antegrade pulsatile undisturbed flow with a higher mean wall shear stress caused only the control and the 50 µm CA geometries to be fully endothelialized. Modest streamlining and decrease in height of the stent struts improved endothelial coverage of the peri-strut and stent strut surfaces in a haemodynamics dependent manner. This study highlights the impact of the stent strut height (thickness) and geometry (shape) on the local haemodynamics, modulating reendothelialization after stenting, an important factor in reducing the risk of stent thrombosis.

Tracking single particles for hours via continuous DNA-mediated fluorophore exchange

Monitoring biomolecules in single-particle tracking experiments is typically achieved by employing fixed organic dyes or fluorescent fusion proteins linked to a target of interest. However, photobleaching typically limits observation times to merely a few seconds, restricting downstream statistical analysis and observation of rare biological events. Here, we overcome this inherent limitation via continuous fluorophore exchange using DNA-PAINT, where fluorescently-labeled oligonucleotides reversibly bind to a single-stranded DNA handle attached to the target molecule. Such versatile and facile labeling allows uninterrupted monitoring of single molecules for extended durations. We demonstrate the power of our approach by observing DNA origami on membranes for tens of minutes, providing perspectives for investigating cellular processes on physiologically relevant timescales.

The length of single-particle tracking experiments are limited due to photobleaching. Here the authors achieve long-term single-particle tracking with continuous fluorophore exchange in DNA-PAINT and use this to observe DNA origami on lipid bilayers for tens of minutes.

Classification of particle trajectories in living cells: Machine learning versus statistical testing hypothesis for fractional anomalous diffusion

Single-particle tracking (SPT) has become a popular tool to study the intracellular transport of molecules in living cells. Inferring the character of their dynamics is important, because it determines the organization and functions of the cells. For this reason, one of the first steps in the analysis of SPT data is the identification of the diffusion type of the observed particles. The most popular method to identify the class of a trajectory is based on the mean-square displacement (MSD). However, due to its known limitations, several other approaches have been already proposed. With the recent advances in algorithms and the developments of modern hardware, the classification attempts rooted in machine learning (ML) are of particular interest. In this work, we adopt two ML ensemble algorithms, i.e., random forest and gradient boosting, to the problem of trajectory classification. We present a new set of features used to transform the raw trajectories data into input vectors required by the classifiers. The resulting models are then applied to real data for G protein-coupled receptors and G proteins. The classification results are compared to recent statistical methods going beyond MSD.

Time-averaged mean squared displacement ratio test for Gaussian processes with unknown diffusion coefficient

The time-averaged mean squared displacement (TAMSD) is one of the most common statistics used for the analysis of anomalous diffusion processes. Anomalous diffusion is manifested by non-linear (mostly power-law) characteristics of the process in contrast to normal diffusion where linear characteristics are expected. One can distinguish between sub- and super-diffusive processes. We consider Gaussian anomalous diffusion models and propose a new approach used for their testing. This approach is based on the TAMSD ratio statistic for different time lags. Similar to the TAMSD, this statistic exhibits a specific behavior in the anomalous diffusion regime. Through its structure, it is independent of the diffusion coefficient, which, in general, does not influence anomalous diffusion behavior. Thus, the TAMSD ratio-based approach does not require preliminary knowledge of the diffusion coefficient's value, in contrast to the TAMSD-approach, where this value is crucial in the testing procedure. Based on the quadratic form representation of the TAMSD ratio, we calculate its main characteristics and propose a step-by-step testing procedure that can be applied for any Gaussian process. For the anomalous diffusion model used here, namely, the fractional Brownian motion, we demonstrate the effectiveness of the proposed methodology. We show that the new approach outperforms the TAMSD-based one, especially for small sample sizes. Finally, the methodology is applied to the real data from the financial market.

Flagellated Janus particles for multimodal actuation and transport

Catalytic Janus particles rely on chemical decomposition to self-propel and have displayed enormous potential for targeted drug delivery and cellular penetration. Catalytic propulsion mechanisms are limiting, however, with fuel requirements and specialized fluid properties being necessary to achieve propulsion. We have improved the dynamic propulsion of catalytic Janus particles by functionalizing flagellar filaments to one of their hemispheres. Flagellated Janus particles, torqued by rotating magnetic fields, swim along their rotation axis using the explicit chirality and flexibility of flagella, mimicking flagellar rotation of live bacteria. Depending on the working fluid, flagellated Janus particles can propel using either catalytic or swimming propulsion. We demonstrate experimentally that flagellated Janus particles behave predictably under the two actuation modes and can precisely follow trajectories under closed-loop feedback control. Flagellated Janus particles were demonstrated to swim in both Newtonian and shear-thickening fluids. These are the first Janus particles developed that can be propelled interchangeably between catalytic and flagellar swimming propulsion, allowing two distinct propulsion mechanisms for future use within in vivo operations.

Effect of collagen and EPS components on the viscoelasticity of Pseudomonas aeruginosa biofilms

Pseudomonas aeruginosa is an opportunistic pathogen that causes thousands of deaths every year in part due to its ability to form biofilms composed of bacteria embedded in a matrix of self-secreted extracellular polysaccharides (EPS), e-DNA, and proteins. In chronic wounds, biofilms are exposed to the host extracellular matrix, of which collagen is a major component. How bacterial EPS interacts with host collagen and whether this interaction affects biofilm viscoelasticity is not well understood. Since physical disruption of biofilms is often used in their removal, knowledge of collagen's effects on biofilm viscoelasticity may enable new treatment strategies that are better tuned to biofilms growing in host environments. In this work, biofilms are grown in the presence of different concentrations of collagen that mimic in vivo conditions. In order to explore collagen's interaction with EPS, nine strains of P. aeruginosa with different patterns of EPS production were used to grow biofilms. Particle tracking microrheology was used to characterize the mechanical development of biofilms over two days. Collagen is found to decrease biofilm compliance and increase relative elasticity regardless of the EPS present in the system. However, this effect is minimized when biofilms overproduce EPS. Collagen appears to become a de facto component of the EPS, through binding to bacteria or physical entanglement.

Apoptosis-inducing anti-HER2 agents operate through oligomerization-induced receptor immobilization

Overexpression of the receptor tyrosine kinase HER2 plays a critical role in the development of various tumors. Biparatopic designed ankyrin repeat proteins (bipDARPins) potently induce apoptosis in HER2-addicted breast cancer cell lines. Here, we have investigated how the spatiotemporal receptor organization at the cell surface is modulated by these agents and is distinguished from other molecules, which do not elicit apoptosis. Binding of conventional antibodies is accompanied by moderate reduction of receptor mobility, in agreement with HER2 being dimerized by the bivalent IgG. In contrast, the most potent apoptosis-inducing bipDARPins lead to a dramatic arrest of HER2. Dual-color single-molecule tracking revealed that the HER2 "lockdown" by these bipDARPins is caused by the formation of HER2-DARPin oligomer chains, which are trapped in nanoscopic membrane domains. Our findings establish that efficient neutralization of receptor tyrosine kinase signaling can be achieved through intermolecular bipDARPin crosslinking alone, resulting in inactivated, locked-down bipDARPin-HER2 complexes.

Maximum likelihood estimates of diffusion coefficients from single-particle tracking experiments

Single-molecule localization microscopy allows practitioners to locate and track labeled molecules in biological systems. When extracting diffusion coefficients from the resulting trajectories, it is common practice to perform a linear fit on mean-squared-displacement curves. However, this strategy is suboptimal and prone to errors. Recently, it was shown that the increments between the observed positions provide a good estimate for the diffusion coefficient, and their statistics are well-suited for likelihood-based analysis methods. Here, we revisit the problem of extracting diffusion coefficients from single-particle tracking experiments subject to static noise and dynamic motion blur using the principle of maximum likelihood. Taking advantage of an efficient real-space formulation, we extend the model to mixtures of subpopulations differing in their diffusion coefficients, which we estimate with the help of the expectation-maximization algorithm. This formulation naturally leads to a probabilistic assignment of trajectories to subpopulations. We employ the theory to analyze experimental tracking data that cannot be explained with a single diffusion coefficient. We test how well a dataset conforms to the assumptions of a diffusion model and determine the optimal number of subpopulations with the help of a quality factor of known analytical distribution. To facilitate use by practitioners, we provide a fast open-source implementation of the theory for the efficient analysis of multiple trajectories in arbitrary dimensions simultaneously.

Discriminating Gaussian processes via quadratic form statistics

Gaussian processes are powerful tools for modeling and predicting various numerical data. Hence, checking their quality of fit becomes a vital issue. In this article, we introduce a testing methodology for general Gaussian processes based on a quadratic form statistic. We illustrate the methodology on three statistical tests recently introduced in the literature, which are based on the sample autocovariance function, time average mean-squared displacement, and detrended moving average statistics. We compare the usefulness of the tests by taking into consideration three very important Gaussian processes: the fractional Brownian motion, which is self-similar with stationary increments (SSSIs), scaled Brownian motion, which is self-similar with independent increments (SSIIs), and the Ornstein-Uhlenbeck (OU) process, which is stationary. We show that the considered statistics' ability to distinguish between these Gaussian processes is high, and we identify the best performing tests for different scenarios. We also find that there is no omnibus quadratic form test; however, the detrended moving average test seems to be the first choice in distinguishing between same processes with different parameters. We also show that the detrended moving average method outperforms the Cholesky method. Based on the previous findings, we introduce a novel procedure of discriminating between Gaussian SSSI, SSII, and stationary processes. Finally, we illustrate the proposed procedure by applying it to real-world data, namely, the daily EURUSD currency exchange rates, and show that the data can be modeled by the OU process.

Detection of Anomalous Diffusion with Deep Residual Networks

Identification of the diffusion type of molecules in living cells is crucial to deduct their driving forces and hence to get insight into the characteristics of the cells. In this paper, deep residual networks have been used to classify the trajectories of molecules. We started from the well known ResNet architecture, developed for image classification, and carried out a series of numerical experiments to adapt it to detection of diffusion modes. We managed to find a model that has a better accuracy than the initial network, but contains only a small fraction of its parameters. The reduced size significantly shortened the training time of the model. Moreover, the resulting network has less tendency to overfitting and generalizes better to unseen data.

Expectation maximization based framework for joint localization and parameter estimation in single particle tracking from segmented images

Single Particle Tracking (SPT) is a well known class of tools for studying the dynamics of biological macromolecules moving inside living cells. In this paper, we focus on the problem of localization and parameter estimation given a sequence of segmented images. In the standard paradigm, the location of the emitter inside each frame of a sequence of camera images is estimated using, for example, Gaussian fitting (GF), and these locations are linked to provide an estimate of the trajectory. Trajectories are then analyzed by using Mean Square Displacement (MSD) or Maximum Likelihood Estimation (MLE) techniques to determine motion parameters such as diffusion coefficients. However, the problems of localization and parameter estimation are clearly coupled. Motivated by this, we have created an Expectation Maximization (EM) based framework for simultaneous localization and parameter estimation. We demonstrate this framework through two representative methods, namely, Sequential Monte Carlo combined with Expectation Maximization (SMC-EM) and Unscented Kalman Filter combined with Expectation Maximization (U-EM). Using diffusion in two-dimensions as a prototypical example, we conduct quantitative investigations on localization and parameter estimation performance across a wide range of signal to background ratios and diffusion coefficients and compare our methods to the standard techniques based on GF-MSD/MLE. To demonstrate the flexibility of the EM based framework, we do comparisons using two different camera models, an ideal camera with Poisson distributed shot noise but no readout noise, and a camera with both shot noise and the pixel-dependent readout noise that is common to scientific complementary metal-oxide semiconductor (sCMOS) camera. Our results indicate our EM based methods outperform the standard techniques, especially at low signal levels. While U-EM and SMC-EM have similar accuracy, U-EM is significantly more computationally efficient, though the use of the Unscented Kalman Filter limits U-EM to lower diffusion rates.