Stain-Free Approach to Determine and Monitor Cell Heath Using Supervised and Unsupervised Image-Based Deep Learning.

Cell-based medicinal products (CBMPs) are a growing class of therapeutics that promise new treatments for complex and rare diseases. Given the inherent complexity of the whole human cells comprising CBMPs, there is a need for robust and fast analytical methods for characterization, process monitoring, and quality control (QC) testing during their manufacture. Existing techniques to evaluate and monitor cell quality typically constitute labor-intensive, expensive, and highly specific staining assays. In this work, we combine image-based deep learning with flow imaging microscopy (FIM) to predict cell health metrics using cellular morphology "fingerprints" extracted from images of unstained Jurkat cells (immortalized human T-lymphocyte cells). A supervised (i.e., algorithm trained with human-generated labels for images) fingerprinting algorithm, trained on images of unstained healthy and dead cells, provides a robust stain-free, non-invasive, and non-destructive method for determining cell viability. Results from the stain-free method are in good agreement with traditional stain-based cytometric viability measurements. Additionally, when trained with images of healthy cells, dead cells and cells undergoing chemically induced apoptosis, the supervised fingerprinting algorithm is able to distinguish between the three cell states, and the results are independent of specific treatments or signaling pathways. We then show that an unsupervised variational autoencoder (VAE) algorithm trained on the same images, but without human-generated labels, is able to distinguish between samples of healthy, dead and apoptotic cells along with cellular debris based on learned morphological features and without human input. With this, we demonstrate that VAEs are a powerful exploratory technique that can be used as a process monitoring analytical tool.

Features in Backgrounds of Microscopy Images Introduce Biases in Machine Learning Analyses.

Subvisible particles may be encountered throughout the processing of therapeutic protein formulations. Flow imaging microscopy (FIM) and backgrounded membrane imaging (BMI) are techniques commonly used to record digital images of these particles, which may be analyzed to provide particle size distributions, concentrations, and identities. Although both techniques record digital images of particles within a sample, FIM analyzes particles suspended in flowing liquids, whereas BMI records images of dry particles after collection by filtration onto a membrane. This study compared the performance of convolutional neural networks (CNNs) in classifying images of subvisible particles recorded by both imaging techniques. Initially, CNNs trained on BMI images appeared to provide higher classification accuracies than those trained on FIM images. However, attribution analyses showed that classification predictions from CNNs trained on BMI images relied on features contributed by the membrane background, whereas predictions from CNNs trained on FIM features were based largely on features of the particles. Segmenting images to minimize the contributions from image backgrounds reduced the apparent accuracy of CNNs trained on BMI images but caused minimal reduction in the accuracy of CNNs trained on FIM images. Thus, the seemingly superior classification accuracy of CNNs trained on BMI images compared to FIM images was an artifact caused by subtle features in the backgrounds of BMI images. Our findings emphasize the importance of examining machine learning algorithms for image analysis with attribution methods to ensure the robustness of trained models and to mitigate potential influence of artifacts within training data sets.

Supervised and unsupervised machine learning approaches for monitoring subvisible particles within an aluminum-salt adjuvanted vaccine formulation.

Suspensions of protein antigens adsorbed to aluminum-salt adjuvants are used in many vaccines and require mixing during vial filling operations to prevent sedimentation. However, the mixing of vaccine formulations may generate undesirable particles that are difficult to detect against the background of suspended adjuvant particles. We simulated the mixing of a suspension containing a protein antigen adsorbed to an aluminum-salt adjuvant using a recirculating peristaltic pump and used flow imaging microscopy to record images of particles within the pumped suspensions. Supervised convolutional neural networks (CNNs) were used to analyze the images and create "fingerprints" of particle morphology distributions, allowing detection of new particles generated during pumping. These results were compared to those obtained from an unsupervised machine learning algorithm relying on variational autoencoders (VAEs) that were also used to detect new particles generated during pumping. Analyses of images conducted by applying both supervised CNNs and VAEs found that rates of generation of new particles were higher in aluminum-salt adjuvant suspensions containing protein antigen than placebo suspensions containing only adjuvant. Finally, front-face fluorescence measurements of the vaccine suspensions indicated changes in solvent exposure of tryptophan residues in the protein that occurred concomitantly with new particle generation during pumping.

Motion of VAPB molecules reveals ER-mitochondria contact site subdomains.

To coordinate cellular physiology, eukaryotic cells rely on the rapid exchange of molecules at specialized organelle-organelle contact sites1,2. Endoplasmic reticulum-mitochondrial contact sites (ERMCSs) are particularly vital communication hubs, playing key roles in the exchange of signalling molecules, lipids and metabolites3,4. ERMCSs are maintained by interactions between complementary tethering molecules on the surface of each organelle5,6. However, due to the extreme sensitivity of these membrane interfaces to experimental perturbation7,8, a clear understanding of their nanoscale organization and regulation is still lacking. Here we combine three-dimensional electron microscopy with high-speed molecular tracking of a model organelle tether, Vesicle-associated membrane protein (VAMP)-associated protein B (VAPB), to map the structure and diffusion landscape of ERMCSs. We uncovered dynamic subdomains within VAPB contact sites that correlate with ER membrane curvature and undergo rapid remodelling. We show that VAPB molecules enter and leave ERMCSs within seconds, despite the contact site itself remaining stable over much longer time scales. This metastability allows ERMCSs to remodel with changes in the physiological environment to accommodate metabolic needs of the cell. An amyotrophic lateral sclerosis-associated mutation in VAPB perturbs these subdomains, likely impairing their remodelling capacity and resulting in impaired interorganelle communication. These results establish high-speed single-molecule imaging as a new tool for mapping the structure of contact site interfaces and reveal that the diffusion landscape of VAPB at contact sites is a crucial component of ERMCS homeostasis.

Interfacial Adsorption Controls Particle Formation in Antibody Formulations Subjected to Extensional Flows and Hydrodynamic Shear.

During their manufacturing and delivery to patients, therapeutic proteins are commonly exposed to various interfaces and to hydrodynamic shear forces. Although adsorption of proteins to solid-liquid interfaces is known to foster formation of protein aggregates and particles, the impact of shear remains controversial, in part because of experimental challenges in separating the effects of shear from those caused by simultaneous exposure to interfaces. Extensional flows (occurring when solutions flow through sudden contractions) exert localized elongational forces that have been suspected to be damaging to proteins. In this work, we measured aggregation and particle formation in formulations of polyclonal and monoclonal antibodies subjected to extensional flow, high shear (105 s-1) and exposure to stainless-steel/water interfaces. Modification of the surface charge at the stainless steel/water interface changed protein adsorption characteristics without altering shear profiles, enabling shear and interfacial interactions to be separated. Even under conditions where antibodies were subjected to high hydrodynamic shear and extensional flow, production of subvisible particles could be inhibited by modifying the stainless-steel surface charge to minimize antibody adsorption. Digital images of particles recorded by flow imaging microscopy (FIM) and analyzed with machine learning algorithms were consistent with a particle formation mechanism by which antibodies adsorb and aggregate at the stainless-steel/water interface and subsequently form particles when shear displaces the interfacial aggregates, transporting them into the bulk solution. Topographical differences measured using atomic force microscopy (AFM) supported the proposed mechanism by showing reduced levels of protein adsorption on surface-charge-modified stainless-steel.

Machine learning approaches to root cause analysis, characterization, and monitoring of subvisible particles in monoclonal antibody formulations.

Processing stresses on therapeutic proteins may cause formation of subvisible particles. Different stress mechanisms generate particle populations with characteristic morphological "fingerprints," and machine learning techniques like convolutional neural networks (CNNs) allow classification of microscopy images of these particles according to known stresses at their root cause. Using CNNs to classify novel particle types not included during network training may lead to inaccurate classification, however, using CNNs to monitor the presence of particulate matter not explicitly used in training could serve as a useful process analytical technology. We used CNNs to classify and identify the root cause of particles generated by subjecting three monoclonal antibodies (mAbs) to various common manufacturing stresses. We probed the generality of particles generated by stressing different mAbs in different formulations and showed that CNN analyses were sensitive not only to the applied stress, but also the buffer conditions and the particular mAb that generated particle populations. Thus, models trained on images of particles created with one mAb and buffer system may not provide accurate root cause analysis when applied to particles generated by other mAb and buffer systems. A lever-rule analysis of CNN-derived fingerprints was used to characterize the composition of mixtures of particle types. Finally, we monitored the temporal evolution of CNN-derived fingerprints when novel populations of particles, which were not included during training, were generated by pumping mAb solutions through a peristaltic pump.

Machine Learning Analysis Provides Insight into Mechanisms of Protein Particle Formation Inside Containers During Mechanical Agitation.

Container choice can influence particle generation within protein formulations. Incompatibility between proteins and containers can manifest as increased particle concentrations, shifts in particle size distributions and changes in particle morphology distributions. In this study, flow imaging microscopy (FIM) combined with machine learning-based goodness-of-fit hypothesis testing algorithms were used in accelerated stability studies to investigate the impact of containers on particle formation. Containers in four major container categories subdivided into eleven container types were filled with monoclonal antibody formulations and agitated with and without headspace, producing subvisible particles. Digital images of the particles were recorded using flow imaging microscopy and analyzed with machine learning algorithms. Particle morphology distributions depended on container category and type, revealing differences that would not have been obvious by analysis of particle concentrations or container surface characteristics alone. Additionally, the algorithm was used to compare morphologies of particles generated in containers against those generated using isolated stresses at air-liquid and container-air-liquid interfaces. These comparisons showed that the morphology distributions of particles formed during agitation most closely resemble distributions that result from exposure of proteins to moving triple interface lines at points where container-air-liquid interfaces intersect. The approach described here can be used to identify dominant causes of particle generation due to protein-container interactions.

Combining Machine Learning and Backgrounded Membrane Imaging: A Case Study in Comparing and Classifying Different Types of Biopharmaceutically Relevant Particles.

This study investigates how backgrounded membrane imaging (BMI) can be used in combination with convolutional neural networks (CNNs) in order to quantitatively and qualitatively study subvisible particles in both protein biopharmaceuticals and samples containing synthetic model particles. BMI requires low sample volumes and avoids many technical complications associated with imaging particles in solution, e.g., air bubble interference, low refractive index contrast between solution and particles of interest, etc. Hence, BMI is an attractive technique for characterizing particles at various stages of drug product development. However, to date, the morphological information encoded in brightfield BMI images has scarcely been utilized. Here we show that CNN based methods can be useful in extracting morphological information from (label-free) brightfield BMI particle images. Images of particles from biopharmaceutical products and from laboratory prepared samples were analyzed with two types of CNN based approaches: traditional supervised classifiers and a recently proposed fingerprinting analysis method. We demonstrate that the CNN based methods are able to efficiently leverage BMI data to distinguish between particles comprised of different proteins, various fatty acids (representing polysorbate degradation related particles), and protein surrogates (NIST ETFE reference material) only based on BMI images. The utility of using the fingerprinting method for comparing morphological differences and similarities of particles formed in distinct drug products and/or laboratory prepared samples is further demonstrated and discussed through three case studies.

Testing Precision Limits of Neural Network-Based Quality Control Metrics in High-Throughput Digital Microscopy.

OBJECTIVE: Digital microscopy is used to monitor particulates such as protein aggregates within biopharmaceutical products. The images that result encode a wealth of information that is underutilized in pharmaceutical process monitoring. For example, images of particles in protein drug products typically are analyzed only to obtain particle counts and size distributions, even though the images also reflect particle characteristics such as shape and refractive index. Multiple groups have demonstrated that convolutional neural networks (CNNs) can extract information from images of protein aggregates allowing assignment of the likely stress at the "root-cause" of aggregation. A practical limitation of previous CNN-based approaches is that the potential aggregation-inducing stresses must be known a priori, disallowing identification of particles produced by unknown stresses. METHODS: We demonstrate an expanded CNN analysis of flow imaging microscopy (FIM) images incorporating judiciously chosen particle standards within a recently proposed "fingerprinting algorithm" (Biotechnol. & Bioeng. (2020) 117:3322) that allows detection of particles formed by unknown root-causes. We focus on ethylene tetrafluoroethylene (ETFE) microparticles as standard surrogates for protein aggregates. We quantify the sensitivity of the new algorithm to experimental parameters such as microscope focus and solution refractive index changes, and explore how FIM sample noise affects statistical testing procedures. RESULTS & CONCLUSIONS: Applied to real-world microscopy images of protein aggregates, the algorithm reproducibly detects complex, distinguishing "textural features" of particles that are not easily described by standard morphological measurements. This offers promise for quality control applications and for detecting shifts in protein aggregate populations due to stresses resulting from unknown process upsets.

Enhanced Diffusive Transport in Fluctuating Porous Media.

Mass transport within porous structures is a ubiquitous process in biological, geological, and technological systems. Despite the importance of these phenomena, there is no comprehensive theory that describes the complex and diverse transport behavior within porous environments. While the porous matrix itself is generally considered a static and passive participant, many porous environments are in fact dynamic, with fluctuating walls, pores that open and close, and dynamically changing cross-links. While diffusion has been measured in fluctuating structures, notably in model biological systems, it is rarely possible to isolate the effect of fluctuations because of the absence of control experiments involving an identical static counterpart, and it is generally impossible to observe the dynamics of the structure. Here we present a direct comparison of the diffusion of nanoparticles of various sizes within a trackable, fluctuating porous matrix and a geometrically equivalent static matrix, in conditions spanning a range of regimes from obstructed to highly confined. The experimental system comprised a close-packed layer of colloidal spheres that were either immobilized to a planar surface or allowed to fluctuate locally, within the space defined by their nearest neighbors. Interestingly, the effective long-time diffusion coefficient was approximately 35-65% greater in the fluctuating porous matrix than in the static one (depending on the size of the nanoparticle probes), regardless of the geometric regime. This was explained by considering the enhancing effects of matrix fluctuations on the short-time diffusion coefficient and cooperative "gate-opening" motions of matrix particles and nanoparticle probes.

Machine Learning and Accelerated Stress Approaches to Differentiate Potential Causes of Aggregation in Polyclonal Antibody Formulations During Shipping.

Therapeutic proteins are among the most widely prescribed medications, with wide distribution and complex supply chains. Shipping exposes protein formulations to stresses that can trigger aggregation, although the exact mechanism(s) responsible for aggregation are unknown. To better understand how shipping causes aggregation, we compared populations of aggregates that were formed in a polyclonal antibody formulation during live shipping studies to populations observed in accelerated stability studies designed to mimic both the sporadic high g-force and continuous low g-force stresses encountered during shipping. Additionally, we compared the effects on aggregation levels generated in two types of secondary packaging, one of which was designed to mitigate the effects of large g-force stresses. Aggregation was quantified using fluorescence intensity of 4,4'-dianilino-1,1'-binaphthyl-5,5'-disulfonic acid (bis-ANS) dye, size exclusion high performance liquid chromatography (SECHPLC), and flow imaging microscopy (FIM). FIM was also combined with machine learning methods to analyze particle morphology distributions. These comparisons revealed that the morphology distributions of aggregates formed during live shipping resemble distributions that result from low g-force events, but not those observed following high g-force events, suggesting that low g-force stresses play a predominant role in shipping-induced aggregation.

Hydrogel Coatings on Container Surfaces Reduce Protein Aggregation Caused by Mechanical Stress and Cavitation.

This work reports the ability of hydrogel coatings to protect therapeutic proteins from cavitation-induced aggregation caused by mechanical stress. Here, we show that polyacrylamide hydrogel coatings on container surfaces suppress mechanical shock-induced cavitation and the associated aggregation of intravenous immunoglobulin (IVIg). First, crosslinked polyacrylamide hydrogels were grown on the surfaces of borosilicate glass vials. Treatment with ultrasound showed that these hydrogel surfaces suppressed cavitation events to levels below those found for unfunctionalized borosilicate glass. Next, IVIg solutions were loaded into these vials and subjected to tumbling, horizontal shaking, and drop testing. Aggregation was quantified by bisANS fluorescence staining and particle counting by flow imaging microscopy (FIM). In all cases, the presence of polyacrylamide hydrogels on the vial surfaces reduced the amount of IVIg aggregation and the number of particulates. In addition, the polyacrylamide appeared to have a protective effect that prevented additional aggregates from forming at extended tumbling times. Finally, drop test studies showed that the polyacrylamide coatings suppressed detectable cavitation. This work reveals how even a simple hydrogel vial coating can have a profound effect on stabilizing protein therapeutics.

Statistical Inference of Transport Mechanisms and Long Time Scale Behavior from Time Series of Solute Trajectories in Nanostructured Membranes.

Appropriate time series modeling of complex diffusion in soft matter systems on the microsecond time scale can provide a path toward inferring transport mechanisms and predicting bulk properties characteristic of much longer time scales. In this work we apply nonparametric Bayesian time series analysis, more specifically the sticky hierarchical Dirichlet process autoregressive hidden Markov model (HDP-AR-HMM) to solute center-of-mass trajectories generated from long molecular dynamics (MD) simulations in a cross-linked inverted hexagonal phase lyotropic liquid crystal (LLC) membrane in order to automatically detect a variety of solute dynamical modes. We can better understand the mechanisms controlling these dynamical modes by grouping the states identified by the HDP-AR-HMM into clusters based on multiple metrics aimed at distinguishing solute behavior based on their fluctuations, dwell times in each state, and positions within the inhomogeneous membrane structure. We analyze predominant clusters in order to relate their dynamical parameters to physical interactions between solutes and the membrane. Along with parameters of individual states, the HDP-AR-HMM simultaneously infers a transition matrix which allows us to stochastically propagate solute behavior from all of the independent trajectories onto arbitrary length time scales while still preserving the qualitative behavior characteristic of the MD trajectories. This affords a direct connection to important macroscopic observables used to characterize performance like solute flux and selectivity. This work provides a promising way to simultaneously identify transport mechanisms in nanoporous materials and project complex diffusive behavior on long time scales. Our enhanced understanding of the diverse range of solute behavior allows us to hypothesize design changes to LLC monomers aimed toward controlling the rates of solute passage, thus improving the selective performance of LLC membranes.

Machine learning and statistical analyses for extracting and characterizing "fingerprints" of antibody aggregation at container interfaces from flow microscopy images.

Therapeutic proteins are exposed to numerous stresses during their manufacture, shipping, storage and administration to patients, causing them to aggregate and form particles through a variety of different mechanisms. These varied mechanisms generate particle populations with characteristic morphologies, creating "fingerprints" that are reflected in images recorded using flow imaging microscopy. Particle population fingerprints in test samples can be extracted and compared against those of particles produced under baseline conditions using an algorithm that combines machine learning tools such as convolutional neural networks with statistical tools such as nonparametric density estimation and Rosenblatt transform-based goodness-of-fit hypothesis testing. This analysis provides a quantitative method with user-specified type 1 error rates to determine whether the mechanisms that produce particles in test samples differ from particle formation mechanisms operative under baseline conditions. As a demonstration, this algorithm was used to compare particles within intravenous immunoglobulin formulations that were exposed to freeze-thawing and shaking stresses within a variety of different containers. This analysis revealed that seemingly subtle differences in containers (e.g., glass vials from different manufacturers) generated distinguishable particle populations after the stresses were applied. This algorithm can be used to assess the impact of process and formulation changes on aggregation-related product instabilities.

Deep Convolutional Neural Network Analysis of Flow Imaging Microscopy Data to Classify Subvisible Particles in Protein Formulations.

Flow-imaging microscopy (FIM) is commonly used to characterize subvisible particles in therapeutic protein formulations. Although pharmaceutical companies often collect large repositories of FIM images of protein therapeutic products, current state-of-the-art methods for analyzing these images rely on low-dimensional lists of "morphological features" to characterize particles that ignore much of the information encoded in the existing image databases. Deep convolutional neural networks (sometimes referred to as "CNNs or ConvNets") have demonstrated the ability to extract predictive information from raw macroscopic image data without requiring the selection or specification of "morphological features" in a variety of tasks. However, the inherent heterogeneity of protein therapeutics and optical phenomena associated with subvisible FIM particle measurements introduces new challenges regarding the application of ConvNets to FIM image analysis. We demonstrate a supervised learning technique leveraging ConvNets to extract information from raw images in order to predict the process conditions or stress states (freeze-thawing, mechanical shaking, etc.) that produced a variety of different protein particles. We demonstrate that our new classifier, in combination with a "data pooling" strategy, can nearly perfectly differentiate between protein formulations in a variety of scenarios of relevance to protein therapeutics quality control and process monitoring using as few as 20 particles imaged via FIM.

Motion blur filtering: A statistical approach for extracting confinement forces and diffusivity from a single blurred trajectory.

Single particle tracking (SPT) can aid in understanding a variety of complex spatiotemporal processes. However, quantifying diffusivity and confinement forces from individual live cell trajectories is complicated by inter- and intratrajectory kinetic heterogeneity, thermal fluctuations, and (experimentally resolvable) statistical temporal dependence inherent to the underlying molecule's time correlated confined dynamics experienced in the cell. The problem is further complicated by experimental artifacts such as localization uncertainty and motion blur. The latter is caused by the tagged molecule emitting photons at different spatial positions during the exposure time of a single frame. The aforementioned experimental artifacts induce spurious time correlations in measured SPT time series that obscure the information of interest (e.g., confinement forces and diffusivity). We develop a maximum likelihood estimation (MLE) technique that decouples the above noise sources and systematically treats temporal correlation via time series methods. This ultimately permits a reliable algorithm for extracting diffusivity and effective forces in confined or unconfined environments. We illustrate how our approach avoids complications inherent to mean square displacement or autocorrelation techniques. Our algorithm modifies the established Kalman filter (which does not handle motion blur artifacts) to provide a likelihood based time series estimation procedure. The result extends A. J. Berglund's motion blur model [Phys. Rev. E 82, 011917 (2010)PLEEE81539-375510.1103/PhysRevE.82.011917] to handle confined dynamics. The approach can also systematically utilize (possibly time dependent) localization uncertainty estimates afforded by image analysis if available. This technique, which explicitly treats confinement and motion blur within a time domain MLE framework, uses an exact likelihood (time domain methods facilitate analyzing nonstationary signals). Our estimator is demonstrated to be consistent over a wide range of exposure times (5 to 100 ms), diffusion coefficients (1×10^{-3} to 1µm^{2}/s), and confinement widths (100 nm to 2µm). We demonstrate that neglecting motion blur or confinement can substantially bias estimation of kinetic parameters of interest to researchers. The technique also permits one to check statistical model assumptions against measured individual trajectories without "ground truth." The ability to reliably and consistently extract motion parameters in trajectories exhibiting confined and/or non-stationary dynamics, without exposure time artifacts corrupting estimates, is expected to aid in directly comparing trajectories obtained from different experiments or imaging modalities. A Python implementation is provided (open-source code will be maintained on GitHub; see also the Supplemental Material with this paper).

Inferring Latent States and Refining Force Estimates via Hierarchical Dirichlet Process Modeling in Single Particle Tracking Experiments.

Understanding the basis for intracellular motion is critical as the field moves toward a deeper understanding of the relation between Brownian forces, molecular crowding, and anisotropic (or isotropic) energetic forcing. Effective forces and other parameters used to summarize molecular motion change over time in live cells due to latent state changes, e.g., changes induced by dynamic micro-environments, photobleaching, and other heterogeneity inherent in biological processes. This study discusses limitations in currently popular analysis methods (e.g., mean square displacement-based analyses) and how new techniques can be used to systematically analyze Single Particle Tracking (SPT) data experiencing abrupt state changes in time or space. The approach is to track GFP tagged chromatids in metaphase in live yeast cells and quantitatively probe the effective forces resulting from dynamic interactions that reflect the sum of a number of physical phenomena. State changes can be induced by various sources including: microtubule dynamics exerting force through the centromere, thermal polymer fluctuations, and DNA-based molecular machines including polymerases and protein exchange complexes such as chaperones and chromatin remodeling complexes. Simulations aiming to show the relevance of the approach to more general SPT data analyses are also studied. Refined force estimates are obtained by adopting and modifying a nonparametric Bayesian modeling technique, the Hierarchical Dirichlet Process Switching Linear Dynamical System (HDP-SLDS), for SPT applications. The HDP-SLDS method shows promise in systematically identifying dynamical regime changes induced by unobserved state changes when the number of underlying states is unknown in advance (a common problem in SPT applications). We expand on the relevance of the HDP-SLDS approach, review the relevant background of Hierarchical Dirichlet Processes, show how to map discrete time HDP-SLDS models to classic SPT models, and discuss limitations of the approach. In addition, we demonstrate new computational techniques for tuning hyperparameters and for checking the statistical consistency of model assumptions directly against individual experimental trajectories; the techniques circumvent the need for "ground-truth" and/or subjective information.

Correction: Calderon, C.P. Data-Driven Techniques for Detecting Dynamical State Changes in Noisily Measured 3D Single-Molecule Trajectories. Molecules 19, 18381-18398.

The author wishes to make the following corrections to paper [1] (doi:10.3390/molecules 191118381, website: http://www.mdpi.com/1420-3049/19/11/18381):

Data-driven techniques for detecting dynamical state changes in noisily measured 3D single-molecule trajectories.

Optical microscopes and nanoscale probes (AFM, optical tweezers, etc.) afford researchers tools capable of quantitatively exploring how molecules interact with one another in live cells. The analysis of in vivo single-molecule experimental data faces numerous challenges due to the complex, crowded, and time changing environments associated with live cells. Fluctuations and spatially varying systematic forces experienced by molecules change over time; these changes are obscured by "measurement noise" introduced by the experimental probe monitoring the system. In this article, we demonstrate how the Hierarchical Dirichlet Process Switching Linear Dynamical System (HDP-SLDS) of Fox et al. [IEEE Transactions on Signal Processing 59] can be used to detect both subtle and abrupt state changes in time series containing "thermal" and "measurement" noise. The approach accounts for temporal dependencies induced by random and "systematic overdamped" forces. The technique does not require one to subjectively select the number of "hidden states" underlying a trajectory in an a priori fashion. The number of hidden states is simultaneously inferred along with change points and parameters characterizing molecular motion in a data-driven fashion. We use large scale simulations to study and compare the new approach to state-of-the-art Hidden Markov Modeling techniques. Simulations mimicking single particle tracking (SPT) experiments are the focus of this study.

Robust hypothesis tests for detecting statistical evidence of two-dimensional and three-dimensional interactions in single-molecule measurements.

Experimental advances have improved the two- (2D) and three-dimensional (3D) spatial resolution that can be extracted from in vivo single-molecule measurements. This enables researchers to quantitatively infer the magnitude and directionality of forces experienced by biomolecules in their native environment. Situations where such force information is relevant range from mitosis to directed transport of protein cargo along cytoskeletal structures. Models commonly applied to quantify single-molecule dynamics assume that effective forces and velocity in the x,y (or x,y,z) directions are statistically independent, but this assumption is physically unrealistic in many situations. We present a hypothesis testing approach capable of determining if there is evidence of statistical dependence between positional coordinates in experimentally measured trajectories; if the hypothesis of independence between spatial coordinates is rejected, then a new model accounting for 2D (3D) interactions can and should be considered. Our hypothesis testing technique is robust, meaning it can detect interactions, even if the noise statistics are not well captured by the model. The approach is demonstrated on control simulations and on experimental data (directed transport of intraflagellar transport protein 88 homolog in the primary cilium).