Dynamic analysis of a diffusing particle in a trapping potential

Deep learning-based size prediction for optical trapped nanoparticles and extracellular vesicles from limited bandwidth camera detection

Due to its ability to record position, intensity, and intensity distribution information, camera-based monitoring of nanoparticles in optical traps can enable multi-parametric morpho-optical characterization at the single-particle level. However, blurring due to the relatively long (10s of microsecond) integration times and aliasing from the resulting limited temporal bandwidth affect the detected particle position when considering nanoparticles in traps with strong stiffness, leading to inaccurate size predictions. Here, we propose a ResNet-based method for accurate size characterization of trapped nanoparticles, which is trained by considering only simulated time series data of nanoparticles' constrained Brownian motion. Experiments prove the method outperforms state-of-art sizing algorithms such as adjusted Lorentzian fitting or CNN-based networks on both standard nanoparticles and extracellular vesicles (EVs), as well as maintains good accuracy even when measurement times are relatively short (<1s per particle). On samples of clinical EVs, our network demonstrates a well-generalized ability to accurately determine the EV size distribution, as confirmed by comparison with gold-standard nanoparticle tracking analysis (NTA). Furthermore, by combining the sizing network with still frame images from high-speed video, the camera-based optical tweezers have the unique capacity to quantify both the size and refractive index of bio-nanoparticles at the single-particle level. These experiments prove the proposed sizing network as an ideal path for predicting the morphological heterogeneity of bio-nanoparticles in optical potential trapping-related measurements.

Forecasting COVID-19 Severity by Intelligent Optical Fingerprinting of Blood Samples

Forecasting COVID-19 disease severity is key to supporting clinical decision making and assisting resource allocation, particularly in intensive care units (ICUs). Here, we investigated the utility of time- and frequency-related features of the backscattered signal of serum patient samples to predict COVID-19 disease severity immediately after diagnosis. ICU admission was the primary outcome used to define disease severity. We developed a stacking ensemble machine learning model including the backscattered signal features (optical fingerprint), patient comorbidities, and age (AUROC = 0.80), which significantly outperformed the predictive value of clinical and laboratory variables available at hospital admission (AUROC = 0.71). The information derived from patient optical fingerprints was not strongly correlated with any clinical/laboratory variable, suggesting that optical fingerprinting brings unique information for COVID-19 severity risk assessment. Optical fingerprinting is a label-free, real-time, and low-cost technology that can be easily integrated as a front-line tool to facilitate the triage and clinical management of COVID-19 patients.

Anomalous nanoparticle surface diffusion in LCTEM is revealed by deep learning-assisted analysis

The motion of nanoparticles near surfaces is of fundamental importance in physics, biology, and chemistry. Liquid cell transmission electron microscopy (LCTEM) is a promising technique for studying motion of nanoparticles with high spatial resolution. Yet, the lack of understanding of how the electron beam of the microscope affects the particle motion has held back advancement in using LCTEM for in situ single nanoparticle and macromolecule tracking at interfaces. Here, we experimentally studied the motion of a model system of gold nanoparticles dispersed in water and moving adjacent to the silicon nitride membrane of a commercial LC in a broad range of electron beam dose rates. We find that the nanoparticles exhibit anomalous diffusive behavior modulated by the electron beam dose rate. We characterized the anomalous diffusion of nanoparticles in LCTEM using a convolutional deep neural-network model and canonical statistical tests. The results demonstrate that the nanoparticle motion is governed by fractional Brownian motion at low dose rates, resembling diffusion in a viscoelastic medium, and continuous-time random walk at high dose rates, resembling diffusion on an energy landscape with pinning sites. Both behaviors can be explained by the presence of silanol molecular species on the surface of the silicon nitride membrane and the ionic species in solution formed by radiolysis of water in presence of the electron beam.

Chromatin Viscoelasticity Measured by Local Dynamic Analysis

The nucleus in eukaryotic cells is a crowded environment that consists of genetic code along the DNA, together with a condensed solution of proteins, RNA, and other molecules. It is subjected to highly dynamic processes, including cell division, transcription, and DNA repair. In addition, the genome in the nucleus is subjected to external forces applied by the cytoplasmic skeleton and neighboring cells, as well as to internal nuclear forces. These forces oppose the need to maintain the genome order, which may be compensated by the internal nuclear viscoelastic properties that can restrain these forces. The structural and mechanical properties of chromatin inside the nucleus are still not fully clear; however, their importance for the proper functioning of the cells is unquestionable. Different approaches have been developed for this aim, ranging from directly measuring the dynamic and elastic properties of chromatin to studying the interactions of chromatin with the surrounding envelope and nuclear bodies. Although the elasticity of naked DNA in vitro is well characterized, the elasticity of chromatin in live cells is more complex and is still not fully understood. Here, we studied the elastic properties of chromatin by dynamic measurements in live cells, followed by viscoelastic modeling. We measured the trajectories of single chromatin loci, centromeres, and telomeres in live cells and analyzed their dynamics using the Langevin formalism. We assumed that the overall effect of the chromatin network forces can be modeled for each locus by a local harmonic potential and calculated the effective force constant. In addition, we assumed that this harmonic force results from the chromatin network formed by the internal polymer structure together with cross-links formed by the protein complex. We show that lamin A has the greatest effect on chromatin viscoelasticity and that its removal leads to a significant reduction in the local harmonic force.

Temporally Anticorrelated Subdiffusion in Water Nanofilms on Silica Suggests Near-Surface Viscoelasticity

Single-molecule tracking was used to probe the local rheology of interfacial water. Fluorescent rhodamine molecules were tracked on silica surfaces as a function of ambient relative humidity, which controlled the thickness of condensed water nanofilms. At low humidity, the molecules exhibited confined diffusion in the vicinity of isolated adsorption sites characterized by a broad distribution of binding stiffness constants; subsequent chemical or physical surface passivation selectively eliminated stiffer binding sites. At increased humidity, molecularly thin water films condensed, permitting near-surface transport of rhodamine molecules. Motion was subdiffusive, with an anomalous exponent increasing with the nanofilm thickness. Molecular trajectories were temporally anticorrelated, ergodic, but also featured transient binding and intermittent diffusion. Statistical modeling demonstrated that this complex motion in water nanofilms had the characteristics of fractional Brownian motion combined with a continuous-time random walk. This was consistent with diffusion within viscoelastic nanofilms, suggesting persistent molecular structuring in the vicinity of the silica surface.

iLoF: An intelligent Lab on Fiber Approach for Human Cancer Single-Cell Type Identification

With the advent of personalized medicine, there is a movement to develop "smaller" and "smarter" microdevices that are able to distinguish similar cancer subtypes. Tumor cells display major differences when compared to their natural counterparts, due to alterations in fundamental cellular processes such as glycosylation. Glycans are involved in tumor cell biology and they have been considered to be suitable cancer biomarkers. Thus, more selective cancer screening assays can be developed through the detection of specific altered glycans on the surface of circulating cancer cells. Currently, this is only possible through time-consuming assays. In this work, we propose the "intelligent" Lab on Fiber (iLoF) device, that has a high-resolution, and which is a fast and portable method for tumor single-cell type identification and isolation. We apply an Artificial Intelligence approach to the back-scattered signal arising from a trapped cell by a micro-lensed optical fiber. As a proof of concept, we show that iLoF is able to discriminate two human cancer cell models sharing the same genetic background but displaying a different surface glycosylation profile with an accuracy above 90% and a speed rate of 2.3 seconds. We envision the incorporation of the iLoF in an easy-to-operate microchip for cancer identification, which would allow further biological characterization of the captured circulating live cells.

Measuring the Conformation and Persistence Length of Single-Stranded DNA Using a DNA Origami Structure

Measuring the mechanical properties of single-stranded DNA (ssDNA) is a challenge that has been addressed by different methods lately. The short persistence length, fragile structure, and the appearance of stem loops complicate the measurement, and this leads to a large variability in the measured values. Here we describe an innovative method based on DNA origami for studying the biophysical properties of ssDNA. By synthesizing a DNA origami structure that consists of two rigid rods with an ssDNA segment between them, we developed a method to characterize the effective persistence length of a random-sequence ssDNA while allowing the formation of stem loops. We imaged the structure with an atomic force microscope (AFM); the rigid rods provide a means for the exact identification of the ssDNA ends. This leads to an accurate determination of the end-to-end distance of each ssDNA segment, and by fitting the measured distribution to the ideal chain polymer model we measured an effective persistence length of 1.98 ± 0.72 nm. This method enables one to measure short or long strands of ssDNA, and it can cope with the formation of stem loops that are often formed along ssDNA. We envision that this method can be used for measuring stem loops for determining the effect of repetitive nucleotide sequences and environmental conditions on the mechanical properties of ssDNA and the effect of interacting proteins with ssDNA. We further noted that the method can be extended to nanoprobes for measuring the interactions of specific DNA sequences, because the DNA origami rods (or similar structures) can hold multiple fluorescent probes that can be easily detected.

Time averages and their statistical variation for the Ornstein-Uhlenbeck process: Role of initial particle distributions and relaxation to stationarity

How ergodic is diffusion under harmonic confinements? How strongly do ensemble- and time-averaged displacements differ for a thermally-agitated particle performing confined motion for different initial conditions? We here study these questions for the generic Ornstein-Uhlenbeck (OU) process and derive the analytical expressions for the second and fourth moment. These quantifiers are particularly relevant for the increasing number of single-particle tracking experiments using optical traps. For a fixed starting position, we discuss the definitions underlying the ensemble averages. We also quantify effects of equilibrium and nonequilibrium initial particle distributions onto the relaxation properties and emerging nonequivalence of the ensemble- and time-averaged displacements (even in the limit of long trajectories). We derive analytical expressions for the ergodicity breaking parameter quantifying the amplitude scatter of individual time-averaged trajectories, both for equilibrium and out-of-equilibrium initial particle positions, in the entire range of lag times. Our analytical predictions are in excellent agreement with results of computer simulations of the Langevin equation in a parabolic potential. We also examine the validity of the Einstein relation for the ensemble- and time-averaged moments of the OU-particle. Some physical systems, in which the relaxation and nonergodic features we unveiled may be observable, are discussed.

The role of near-wall drag effects in the dynamics of tethered DNA under shear flow

We utilized single-molecule tethered particle motion (TPM) tracking, optimized for studying the behavior of short (0.922 μm) dsDNA molecules under shear flow conditions, in the proximity of a wall (surface). These experiments track the individual trajectories through a gold nanobead (40 nm in radius), attached to the loose end of the DNA molecules. Under such circumstances, local interactions with the wall become more pronounced, manifested through hydrodynamic interactions. To elucidate the mechanical mechanism that affects the statistics of the molecular trajectories of the tethered molecules, we estimate the resting diffusion coefficient of our system. Using this value and our measured data, we calculate the orthogonal distance of the extended DNA molecules from the surface. This calculation considers the hydrodynamic drag effect that emerges from the proximity of the molecule to the surface, using the Faxén correction factors. Our finding enables the construction of a scenario according to which the tension along the chain builds up with the applied shear force, driving the loose end of the DNA molecule away from the wall. With the extension from the wall, the characteristic times of the system decrease by three orders of magnitude, while the drag coefficients decay to a plateau value that indicates that the molecule still experiences hydrodynamic effects due to its proximity to the wall.

Tethered Particle Motion: An Easy Technique for Probing DNA Topology and Interactions with Transcription Factors

Tethered Particle Motion (TPM) is a versatile in vitro technique for monitoring the conformations a linear macromolecule, such as DNA, can exhibit. The technique involves monitoring the diffusive motion of a particle anchored to a fixed point via the macromolecule of interest, which acts as a tether. In this chapter, we provide an overview of TPM, review the fundamental principles that determine the accuracy with which effective tether lengths can be used to distinguish different tether conformations, present software tools that assist in capturing and analyzing TPM data, and provide a protocol which uses TPM to characterize lac repressor-induced DNA looping. Critical to any TPM assay is the understanding of the timescale over which the diffusive motion of the particle must be observed to accurately distinguish tether conformations. Approximating the tether as a Hookean spring, we show how to estimate the diffusion timescale and discuss how it relates to the confidence with which tether conformations can be distinguished. Applying those estimates to a lac repressor titration assay, we describe how to perform a TPM experiment. We also provide graphically driven software which can be used to speed up data collection and analysis. Lastly, we detail how TPM data from the titration assay can be used to calculate relevant molecular descriptors such as the J factor for DNA looping and lac repressor-operator dissociation constants. While the included protocol is geared toward studying DNA looping, the technique, fundamental principles, and analytical methods are more general and can be adapted to a wide variety of molecular systems.

Fast Diffusion of Long Guest Rods in a Lamellar Phase of Short Host Particles

We investigate the dynamic behavior of long guest rodlike particles immersed in liquid crystalline phases formed by shorter host rods, tracking both guest and host particles by fluorescence microscopy. Counterintuitively, we evidence that long rods diffuse faster than short rods forming the one-dimensional ordered smectic-A phase. This results from the larger and noncommensurate size of the guest particles as compared to the wavelength of the energy landscape set by the lamellar stack of liquid slabs. The long guest particles are also shown to be still mobile in the crystalline smectic-B phase, as they generate their own voids in the adjacent layers.

Simultaneous Characterization of Nanoparticle Size and Particle-Surface Interactions with Three-Dimensional Nanophotonic Force Microscopy

The behavior of a nanoparticle in solution depends strongly on the particle's physical and chemical characteristics, most notably the particle size and the surface properties. Accurately characterizing these properties is critical for quality control in a wide variety of industries. To understand a complex and polydisperse nanoparticle suspension, however, ensemble averaging is not sufficient, and there is a great need for direct measurements of size and surface properties at the individual nanoparticle level. In this work, we present an analysis technique for simultaneous characterization of particle-surface interactions and size using near-field light scattering and verify it using Brownian-dynamics simulations. Using a nanophotonic waveguide, single particles can be stably held near the waveguide's surface by strongly localized optical forces. By tracking the dynamic 3D motion of the particle under the influence of these forces using an optical microscope, it is possible to extract the particle-surface interaction forces, as well as to estimate the size and refractive index of the nanoparticle. Because of the strong light-scattering signal, this method is viable for high-throughput characterization of particles as small as 100 nm in only a few seconds each.

Dynamics of an optically confined nanoparticle diffusing normal to a surface

Here we measure the hindered diffusion of an optically confined nanoparticle in the direction normal to a surface, and we use this to determine the particle-surface interaction profile in terms of the absolute height. These studies are performed using the evanescent field of an optically excited single-mode silicon nitride waveguide, where the particle is confined in a height-dependent potential energy well generated from the balance of optical gradient and surface forces. Using a high-speed cmos camera, we demonstrate the ability to capture the short time-scale diffusion dominated motion for 800-nm-diam polystyrene particles, with measurement times of only a few seconds per particle. Using established theory, we show how this information can be used to estimate the equilibrium separation of the particle from the surface. As this measurement can be made simultaneously with equilibrium statistical mechanical measurements of the particle-surface interaction energy landscape, we demonstrate the ability to determine these in terms of the absolute rather than relative separation height. This enables the comparison of potential energy landscapes of particle-surface interactions measured under different experimental conditions, enhancing the utility of this technique.

Simple method to measure and analyze the fluctuations of a small particle in biopolymer solutions

We developed a simple method to investigate the motion of a small particle in biopolymer solutions. Using optical tweezers with low stiffness, a trapped probe particle fluctuates widely for a long time along the light axis, which reflects the rheological properties of the surrounding environment. We present a convenient technique for three-dimensional position tracking and the analysis focused on the distribution of particle positions and its variance in a given time interval. It allows us to obtain useful information about the dynamics of a small particle in a wide range from a free diffusive motion to a constrained motion with statistical significance. We applied this method to investigate the dynamics in collagen and DNA solutions; it was found that a collagen solution behaves as a simple viscous liquid and a DNA solution has apparent elasticity due to the slow relaxation of the configuration of molecules.

Small Crowders Slow Down Kinesin-1 Stepping by Hindering Motor Domain Diffusion

The dimeric motor protein kinesin-1 moves processively along microtubules against forces of up to 7 pN. However, the mechanism of force generation is still debated. Here, we point to the crucial importance of diffusion of the tethered motor domain for the stepping of kinesin-1: small crowders stop the motor at a viscosity of 5 mPa·s-corresponding to a hydrodynamic load in the sub-fN (~10^{-4} pN) range-whereas large crowders have no impact even at viscosities above 100 mPa·s. This indicates that the scale-dependent, effective viscosity experienced by the tethered motor domain is a key factor determining kinesin's functionality. Our results emphasize the role of diffusion in the kinesin-1 stepping mechanism and the general importance of the viscosity scaling paradigm in nanomechanics.

Analysis of Single Locus Trajectories for Extracting In Vivo Chromatin Tethering Interactions

Is it possible to extract tethering forces applied on chromatin from the statistics of a single locus trajectories imaged in vivo? Chromatin fragments interact with many partners such as the nuclear membrane, other chromosomes or nuclear bodies, but the resulting forces cannot be directly measured in vivo. However, they impact chromatin dynamics and should be reflected in particular in the motion of a single locus. We present here a method based on polymer models and statistics of single trajectories to extract the force characteristics and in particular when they are generated by the gradient of a quadratic potential well. Using numerical simulations of a Rouse polymer and live cell imaging of the MAT-locus located on the yeast Saccharomyces cerevisiae chromosome III, we recover the amplitude and the distance between the observed and the interacting monomer. To conclude, the confined trajectories we observed in vivo reflect local interaction on chromatin.

Enhanced tethered-particle motion analysis reveals viscous effects

Tethered-particle motion experiments do not require expensive or technically complex hardware, and increasing numbers of researchers are adopting this methodology to investigate the topological effects of agents that act on the tethering polymer or the characteristics of the polymer itself. These investigations depend on accurate measurement and interpretation of changes in the effective length of the tethering polymer (often DNA). However, the bead size, tether length, and buffer affect the confined diffusion of the bead in this experimental system. To evaluate the effects of these factors, improved measurements to calibrate the two-dimensional range of motion (excursion) versus DNA length were carried out. Microspheres of 160 or 240 nm in radius were tethered by DNA molecules ranging from 225 to 3477 basepairs in length in aqueous buffers containing 100 mM potassium glutamate and 8 mM MgCl2 or 10 mM Tris-HCl and 200 mM KCl, with or without 0.5% Tween added to the buffer, and the motion was recorded. Different buffers altered the excursion of beads on identical DNA tethers. Buffer with only 10 mM NaCl and >5 mM magnesium greatly reduced excursion. Glycerol added to increase viscosity slowed confined diffusion of the tethered beads but did not change excursion. The confined-diffusion coefficients for all tethered beads were smaller than those expected for freely diffusing beads and decreased for shorter tethers. Tethered-particle motion is a sensitive framework for diffusion experiments in which small beads on long leashes most closely resemble freely diffusing, untethered beads.

Tethered particle analysis of supercoiled circular DNA using peptide nucleic acid handles

This protocol describes how to monitor individual naturally supercoiled circular DNA plasmids bound via peptide nucleic acid (PNA) handles between a bead and a surface. The protocol was developed for single-molecule investigation of the dynamics of supercoiled DNA, and it allows the investigation of both the dynamics of the molecule itself and of its interactions with a regulatory protein. Two bis-PNA clamps designed to bind with extremely high affinity to predetermined homopurine sequence sites in supercoiled DNA are prepared: one conjugated with digoxigenin for attachment to an anti-digoxigenin-coated glass cover slide, and one conjugated with biotin for attachment to a submicron-sized streptavidin-coated polystyrene bead. Plasmids are constructed, purified and incubated with the PNA handles. The dynamics of the construct is analyzed by tracking the tethered bead using video microscopy: less supercoiling results in more movement, and more supercoiling results in less movement. In contrast to other single-molecule methodologies, the current methodology allows for studying DNA in its naturally supercoiled state with constant linking number and constant writhe. The protocol has potential for use in studying the influence of supercoils on the dynamics of DNA and its associated proteins, e.g., topoisomerase. The procedure takes ~4 weeks.

Multiple LacI-mediated loops revealed by Bayesian statistics and tethered particle motion

The bacterial transcription factor LacI loops DNA by binding to two separate locations on the DNA simultaneously. Despite being one of the best-studied model systems for transcriptional regulation, the number and conformations of loop structures accessible to LacI remain unclear, though the importance of multiple coexisting loops has been implicated in interactions between LacI and other cellular regulators of gene expression. To probe this issue, we have developed a new analysis method for tethered particle motion, a versatile and commonly used in vitro single-molecule technique. Our method, vbTPM, performs variational Bayesian inference in hidden Markov models. It learns the number of distinct states (i.e. DNA–protein conformations) directly from tethered particle motion data with better resolution than existing methods, while easily correcting for common experimental artifacts. Studying short (roughly 100 bp) LacI-mediated loops, we provide evidence for three distinct loop structures, more than previously reported in single-molecule studies. Moreover, our results confirm that changes in LacI conformation and DNA-binding topology both contribute to the repertoire of LacI-mediated loops formed in vitro, and provide qualitatively new input for models of looping and transcriptional regulation. We expect vbTPM to be broadly useful for probing complex protein–nucleic acid interactions.

Reaction-diffusion theory in the presence of an attractive harmonic potential

Problems involving the capture of a moving entity by a trap occur in a variety of physical situations, the moving entity being an electron, an excitation, an atom, a molecule, a biological object such as a receptor cluster, a cell, or even an animal such as a mouse carrying an epidemic. Theoretical considerations have almost always assumed that the particle motion is translationally invariant. We study here the case when that assumption is relaxed, in that the particle is additionally subjected to a harmonic potential. This tethering to a center modifies the reaction-diffusion phenomenon. Using a Smoluchowski equation to describe the system, we carry out a study which is explicit in one dimension but can be easily extended for arbitrary dimensions. Interesting features emerge depending on the relative location of the trap, the attractive center, and the initial placement of the diffusing particle.