A Primer on the Bayesian Approach to High-Density Single-Molecule Trajectories Analysis

Confinement energy landscape classification reveals membrane receptor nano-organization mechanisms

The cell membrane organization has an essential functional role through the control of membrane receptor confinement in micro- or nanodomains. Several mechanisms have been proposed to account for these properties, although some features have remained controversial, notably the nature, size, and stability of cholesterol- and sphingolipid-rich domains or lipid rafts. Here, we probed the effective energy landscape acting on single-nanoparticle-labeled membrane receptors confined in raft nanodomains- epidermal growth factor receptor (EGFR), Clostridium perfringens ε-toxin receptor (CPεTR), and Clostridium septicum α-toxin receptor (CSαTR)-and compared it with hop-diffusing transferrin receptors. By establishing a new analysis pipeline combining Bayesian inference, decision trees, and clustering approaches, we systematically classified single-protein trajectories according to the type of effective confining energy landscape. This revealed the existence of only two distinct organization modalities: confinement in a quadratic energy landscape for EGFR, CPεTR, and CSαTR (A), and free diffusion in confinement domains resulting from the steric hindrance due to F-actin barriers for transferrin receptor (B). The further characterization of effective confinement energy landscapes by Bayesian inference revealed the role of interactions with the domain environment in cholesterol- and sphingolipid-rich domains with (EGFR) or without (CPεTR and CSαTR) interactions with F-actin to regulate the confinement energy depth. These two distinct mechanisms result in the same organization type (A). We revealed that the apparent domain sizes for these receptor trajectories resulted from Brownian exploration of the energy landscape in a steady-state-like regime at a common effective temperature, independently of the underlying molecular mechanisms. These results highlight that confinement domains may be adequately described as interaction hotspots rather than rafts with abrupt domain boundaries. Altogether, these results support a new model for functional receptor confinement in membrane nanodomains and pave the way to the constitution of an atlas of membrane protein organization.

Effect of local active fluctuations on structure and dynamics of flexible biopolymers

Active fluctuations play a significant role in the structure and dynamics of biopolymers (e.g. chromatin and cytoskeletal proteins) that are instrumental in the functioning of living cells. For a large range of experimentally accessible length and time scales, these polymers can be represented as flexible chains that are subjected to spatially and temporally varying fluctuating forces. In this work, we introduce a mathematical framework that correlates the spatial and temporal patterns of the fluctuations to different observables that describe the dynamics and conformations of the polymer. We demonstrate the power of this approach by analyzing the case of a point fluctuation on the polymer with an exponential decay of correlation in time with a finite time constant. Specifically, we identify the length and time scale over which the behavior of the polymer exhibits a significant departure from the behavior of a Rouse chain and the range of impact of the fluctuation along the chain. Furthermore, we show that the conformation of the polymer retains the memory of the active fluctuation from earlier times. Altogether, this work sets the basis for understanding and interpreting the role of spatio-temporal patterns of fluctuations in the dynamics, conformation, and functionality of biopolymers in living cells.

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.

Quantifying postsynaptic receptor dynamics: insights into synaptic function

The molecular composition of presynaptic and postsynaptic neuronal terminals is dynamic, and yet long-term stabilizations in postsynaptic responses are necessary for synaptic development and long-term plasticity. The need to reconcile these concepts is further complicated by learning- and memory-related plastic changes in the molecular make-up of synapses. Advances in single-particle tracking mean that we can now quantify the number and diffusive properties of specific synaptic molecules, while statistical thermodynamics provides a framework to analyse these molecular fluctuations. In this Review, we discuss the use of these approaches to gain quantitative descriptions of the processes underlying the turnover, long-term stability and plasticity of postsynaptic receptors and show how these can help us to understand the balance between local molecular turnover and synaptic structural identity and integrity.

TRamWAy: Mapping physical properties of individual biomolecule random motion in large scale single-particle tracking experiments

MOTIVATION

Single-molecule localization microscopy allows studying the dynamics of biomolecules in cells and resolving the biophysical properties of the molecules and their environment underlying cellular function. With the continuously growing amount of data produced by individual experiments, the computational cost of quantifying these properties is increasingly becoming the bottleneck of single molecule analysis. Mining these data require an integrated and efficient analysis toolbox.

RESULTS

We introduce TRamWAy, a modular Python library that features: 1. a conservative tracking procedure for localization data, 2. a range of sampling techniques for meshing the spatio-temporal support of the data, 3. computationally efficient solvers for inverse models, with the option of plugging in user-defined functions, 4. a collection of analysis tools and a simple web-based interface.

AVAILABILITY

TRamWAy is a Python library and can be installed with pip & conda. The source code is available at https://github.com/DecBayComp/TRamWAy.

MANUAL AND TUTORIALS

available online at https://tramway-tour.readthedocs.io.

DNA replication: In vitro single-molecule manipulation data analysis and models

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Data analysis allows to extract information from the noisy single-molecule data.

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Models provide insight in the underlying biochemical processes.

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Ligands can activate or inhibit DNA replication and DNA unwinding.

DNA replication is a key biochemical process of the cell cycle. In the last years, analysis of in vitro single-molecule DNA replication events has provided new information that cannot be obtained with ensembles studies. Here, we introduce crucial techniques for the proper analysis and modelling of DNA replication in vitro single-molecule manipulation data. Specifically, we review some of the main methods to analyze and model the real-time kinetics of the two main molecular motors of the replisome: DNA polymerase and DNA helicase. Our goal is to facilitate access to and understanding of these techniques to promotetheir use in the study of DNA replication at the single-molecule level. A proper analysis of single-molecule data is crucial to obtain a detailed picture of, among others, the kinetics rates, equilibrium contants and conformational changes of the system under study. The techniques presented here have been used or can be adapted to study the operation of other proteins involved in nucleic acids metabolism.

Bayesian Inference: The Comprehensive Approach to Analyzing Single-Molecule Experiments

Biophysics experiments performed at single-molecule resolution provide exceptional insight into the structural details and dynamic behavior of biological systems. However, extracting this information from the corresponding experimental data unequivocally requires applying a biophysical model. In this review, we discuss how to use probability theory to apply these models to single-molecule data. Many current single-molecule data analysis methods apply parts of probability theory, sometimes unknowingly, and thus miss out on the full set of benefits provided by this self-consistent framework. The full application of probability theory involves a process called Bayesian inference that fully accounts for the uncertainties inherent to single-molecule experiments. Additionally, using Bayesian inference provides a scientifically rigorous method of incorporating information from multiple experiments into a single analysis and finding the best biophysical model for an experiment without the risk of overfitting the data. These benefits make the Bayesian approach ideal for analyzing any type of single-molecule experiment.

Genuage: visualize and analyze multidimensional single-molecule point cloud data in virtual reality

Experimentally recorded point cloud data, such as those generated by single-molecule localization microscopy, are continuously increasing in size and dimension. Gaining an intuitive understanding and facilitating the analysis of such multidimensional data remains challenging. Here we report a new open-source software platform, Genuage, that enables the easy perception of, interaction with and analysis of multidimensional point clouds in virtual reality. Genuage is compatible with arbitrary multidimensional data extending beyond single-molecule localization microscopy.

SMAUG: Analyzing single-molecule tracks with nonparametric Bayesian statistics

Single-molecule fluorescence microscopy probes nanoscale, subcellular biology in real time. Existing methods for analyzing single-particle tracking data provide dynamical information, but can suffer from supervisory biases and high uncertainties. Here, we develop a method for the case of multiple interconverting species undergoing free diffusion and introduce a new approach to analyzing single-molecule trajectories: the Single-Molecule Analysis by Unsupervised Gibbs sampling (SMAUG) algorithm, which uses nonparametric Bayesian statistics to uncover the whole range of information contained within a single-particle trajectory dataset. Even in complex systems where multiple biological states lead to a number of observed mobility states, SMAUG provides the number of mobility states, the average diffusion coefficient of single molecules in that state, the fraction of single molecules in that state, the localization noise, and the probability of transitioning between two different states. In this paper, we provide the theoretical background for the SMAUG analysis and then we validate the method using realistic simulations of single-particle trajectory datasets as well as experiments on a controlled in vitro system. Finally, we demonstrate SMAUG on real experimental systems in both prokaryotes and eukaryotes to measure the motions of the regulatory protein TcpP in Vibrio cholerae and the dynamics of the B-cell receptor antigen response pathway in lymphocytes. Overall, SMAUG provides a mathematically rigorous approach to measuring the real-time dynamics of molecular interactions in living cells.

Errors in Energy Landscapes Measured with Particle Tracking

Tracking Brownian particles is often employed to map the energy landscape they explore. Such measurements have been exploited to study many biological processes and interactions in soft materials. Yet video tracking is irremediably contaminated by localization errors originating from two imaging artifacts: the "static" errors come from signal noise, and the "dynamic" errors arise from the motion blur due to finite frame-acquisition time. We show that these errors result in systematic and nontrivial biases in the measured energy landscapes. We derive a relationship between the true and the measured potential that elucidates, among other aberrations, the presence of false double-well minima in the apparent potentials reported in recent studies. We further assess several canonical trapping and pair-interaction potentials by using our analytically derived results and Brownian dynamics simulations. In particular, we show that the apparent spring stiffness of harmonic potentials (such as optical traps) is increased by dynamic errors but decreased by static errors. Our formula allows for the development of efficient corrections schemes, and we also present in this work a provisional method for reconstructing true potentials from the measured ones.

Monitoring HIV-1 Assembly in Living Cells: Insights from Dynamic and Single Molecule Microscopy

The HIV-1 assembly process is a multi-complex mechanism that takes place at the host cell plasma membrane. It requires a spatio-temporal coordination of events to end up with a full mature and infectious virus. The molecular mechanisms of HIV-1 assembly have been extensively studied during the past decades, in order to dissect the respective roles of the structural and non-structural viral proteins of the viral RNA genome and of some host cell factors. Nevertheless, the time course of HIV-1 assembly was observed in living cells only a decade ago. The very recent revolution of optical microscopy, combining high speed and high spatial resolution, in addition to improved fluorescent tags for proteins, now permits study of HIV-1 assembly at the single molecule level within living cells. In this review, after a short description of these new approaches, we will discuss how HIV-1 assembly at the cell plasma membrane has been revisited using advanced super resolution microscopy techniques and how it can bridge the study of viral assembly from the single molecule to the entire host cell.

Single molecule localisation microscopy reveals how HIV-1 Gag proteins sense membrane virus assembly sites in living host CD4 T cells

Monitoring virus assembly at the nanoscale in host cells remains a major challenge. Human immunodeficiency virus type 1 (HIV-1) components are addressed to the plasma membrane where they assemble to form spherical particles of 100 nm in diameter. Interestingly, HIV-1 Gag protein expression alone is sufficient to produce virus-like particles (VLPs) that resemble the immature virus. Here, we monitored VLP formation at the plasma membrane of host CD4+ T cells using a newly developed workflow allowing the analysis of long duration recordings of single-molecule Gag protein localisation and movement. Comparison of Gag assembling platforms in CD4+ T cells expressing wild type or assembly-defective Gag mutant proteins showed that VLP formation lasts roughly 15 minutes with an assembly time of 5 minutes. Trapping energy maps, built from membrane associated Gag protein movements, showed that one third of the assembling energy is due to direct Gag capsid-capsid interaction while the remaining two thirds require the nucleocapsid-RNA interactions. Finally, we show that the viral RNA genome does not increase the attraction of Gag at the membrane towards the assembling site but rather acts as a spatiotemporal coordinator of the membrane assembly process.

Variational Algorithms for Analyzing Noisy Multistate Diffusion Trajectories

Single-particle tracking offers a noninvasive high-resolution probe of biomolecular reactions inside living cells. However, efficient data analysis methods that correctly account for various noise sources are needed to realize the full quantitative potential of the method. We report algorithms for hidden Markov-based analysis of single-particle tracking data, which incorporate most sources of experimental noise, including heterogeneous localization errors and missing positions. Compared to previous implementations, the algorithms offer significant speedups, support for a wider range of inference methods, and a simple user interface. This will enable more advanced and exploratory quantitative analysis of single-particle tracking data.

Estimation of microscope drift using fluorescent nanodiamonds as fiducial markers

Fiducial markers are used to correct the microscope drift and should be photostable, be usable at multiple wavelengths and be compatible for multimodal imaging. Fiducial markers such as beads, gold nanoparticles, microfabricated patterns and organic fluorophores lack one or more of these criteria. Moreover, the localization accuracy and drift correction can be degraded by other fluorophores, instrument noise and artefacts due to image processing and tracking algorithms. Estimating mechanical drift by assuming Gaussian distributed noise is not suitable under these circumstances. Here we present a method that uses fluorescent nanodiamonds as fiducial markers and uses an improved maximum likelihood algorithm to estimate the drift with both accuracy and precision within the range 1.55-5.75 nm.

Nonergodic subdiffusion from transient interactions with heterogeneous partners

Spatiotemporal disorder has been recently associated to the occurrence of anomalous nonergodic diffusion of molecular components in biological systems, but the underlying microscopic mechanism is still unclear. We introduce a model in which a particle performs continuous Brownian motion with changes of diffusion coefficients induced by transient molecular interactions with diffusive binding partners. In spite of the exponential distribution of waiting times, the model shows subdiffusion and nonergodicity similar to the heavy-tailed continuous time random walk. The dependence of these properties on the density of binding partners is analyzed and discussed. Our work provides an experimentally testable microscopic model to investigate the nature of nonergodicity in disordered media.