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Biophysical Journal May 2019The trajectory of a single protein in the cytosol of a living cell contains information about its molecular interactions in its native environment. However, it has...
The trajectory of a single protein in the cytosol of a living cell contains information about its molecular interactions in its native environment. However, it has remained challenging to accurately resolve and characterize the diffusive states that can manifest in the cytosol using analytical approaches based on simplifying assumptions. Here, we show that multiple intracellular diffusive states can be successfully resolved if sufficient single-molecule trajectory information is available to generate well-sampled distributions of experimental measurements and if experimental biases are taken into account during data analysis. To address the inherent experimental biases in camera-based and MINFLUX-based single-molecule tracking, we use an empirical data analysis framework based on Monte Carlo simulations of confined Brownian motion. This framework is general and adaptable to arbitrary cell geometries and data acquisition parameters employed in two-dimensional or three-dimensional single-molecule tracking. We show that, in addition to determining the diffusion coefficients and populations of prevalent diffusive states, the timescales of diffusive state switching can be determined by stepwise increasing the time window of averaging over subsequent single-molecule displacements. Time-averaged diffusion analysis of single-molecule tracking data may thus provide quantitative insights into binding and unbinding reactions among rapidly diffusing molecules that are integral for cellular functions.
Topics: Computer Simulation; Cytoplasm; Cytosol; Diffusion; Kinetics; Monte Carlo Method; Single Molecule Imaging; Time Factors
PubMed: 31030884
DOI: 10.1016/j.bpj.2019.03.039 -
ELife Apr 2022In addition to diffusive signals, cells in tissue also communicate via long, thin cellular protrusions, such as airinemes in zebrafish. Before establishing...
In addition to diffusive signals, cells in tissue also communicate via long, thin cellular protrusions, such as airinemes in zebrafish. Before establishing communication, cellular protrusions must find their target cell. Here, we demonstrate that the shapes of airinemes in zebrafish are consistent with a finite persistent random walk model. The probability of contacting the target cell is maximized for a balance between ballistic search (straight) and diffusive search (highly curved, random). We find that the curvature of airinemes in zebrafish, extracted from live-cell microscopy, is approximately the same value as the optimum in the simple persistent random walk model. We also explore the ability of the target cell to infer direction of the airineme's source, finding that there is a theoretical trade-off between search optimality and directional information. This provides a framework to characterize the shape, and performance objectives, of non-canonical cellular protrusions in general.
Topics: Animals; Cell Surface Extensions; Diffusion; Zebrafish
PubMed: 35467525
DOI: 10.7554/eLife.75690 -
Single-molecule displacement mapping unveils nanoscale heterogeneities in intracellular diffusivity.Nature Methods May 2020Intracellular diffusion underlies vital cellular processes. However, it remains difficult to elucidate how an unbound protein diffuses inside the cell with good spatial...
Intracellular diffusion underlies vital cellular processes. However, it remains difficult to elucidate how an unbound protein diffuses inside the cell with good spatial resolution and sensitivity. Here we introduce single-molecule displacement/diffusivity mapping (SMdM), a super-resolution strategy that enables the nanoscale mapping of intracellular diffusivity through local statistics of the instantaneous displacements of freely diffusing single molecules. We thus show that the diffusion of an average-sized protein in the mammalian cytoplasm and nucleus is spatially heterogeneous at the nanoscale, and that variations in local diffusivity correlate with the ultrastructure of the actin cytoskeleton and the organization of the genome, respectively. SMdM of differently charged proteins further unveils that the possession of positive, but not negative, net charges drastically impedes diffusion, and that the rate is determined by the specific subcellular environments. We thus unveil rich heterogeneities and charge effects in intracellular diffusion at the nanoscale.
Topics: Cell Nucleus; Cells, Cultured; Cytoplasm; Diffusion; Humans; Image Interpretation, Computer-Assisted; Intracellular Space; Microscopy, Fluorescence; Models, Theoretical; Nanoparticles; Proteins; Single Molecule Imaging
PubMed: 32203387
DOI: 10.1038/s41592-020-0793-0 -
Proceedings of the National Academy of... Oct 2022Understanding the activated transport of penetrant or tracer atoms and molecules in condensed phases is a challenging problem in chemistry, materials science, physics,...
Understanding the activated transport of penetrant or tracer atoms and molecules in condensed phases is a challenging problem in chemistry, materials science, physics, and biophysics. Many angstrom- and nanometer-scale features enter due to the highly variable shape, size, interaction, and conformational flexibility of the penetrant and matrix species, leading to a dramatic diversity of penetrant dynamics. Based on a minimalist model of a spherical penetrant in equilibrated dense matrices of hard spheres, a recent microscopic theory that relates hopping transport to local structure has predicted a novel correlation between penetrant diffusivity and the matrix thermodynamic dimensionless compressibility, () (which also quantifies the amplitude of long wavelength density fluctuations), as a consequence of a fundamental statistical mechanical relationship between structure and thermodynamics. Moreover, the penetrant activation barrier is predicted to have a factorized/multiplicative form, scaling as the product of an inverse power law of () and a linear/logarithmic function of the penetrant-to-matrix size ratio. This implies an enormous reduction in chemical complexity that is verified based solely on experimental data for diverse classes of chemically complex penetrants dissolved in molecular and polymeric liquids over a wide range of temperatures down to the kinetic glass transition. The predicted corollary that the penetrant diffusion constant decreases exponentially with inverse temperature raised to an exponent determined solely by how () decreases with cooling is also verified experimentally. Our findings are relevant to fundamental questions in glassy dynamics, self-averaging of angstrom-scale chemical features, and applications such as membrane separations, barrier coatings, drug delivery, and self-healing.
Topics: Diffusion; Glass; Phase Transition; Physics; Thermodynamics
PubMed: 36194629
DOI: 10.1073/pnas.2210094119 -
Nature Communications Oct 2018Most biochemical reactions in living cells rely on diffusive search for target molecules or regions in a heterogeneous overcrowded cytoplasmic medium. Rapid...
Most biochemical reactions in living cells rely on diffusive search for target molecules or regions in a heterogeneous overcrowded cytoplasmic medium. Rapid rearrangements of the medium constantly change the effective diffusivity felt locally by a diffusing particle and thus impact the distribution of the first-passage time to a reaction event. Here, we investigate the effect of these dynamic spatiotemporal heterogeneities onto diffusion-limited reactions. We describe a general mathematical framework to translate many results for ordinary homogeneous Brownian motion to heterogeneous diffusion. In particular, we derive the probability density of the first-passage time to a reaction event and show how the dynamic disorder broadens the distribution and increases the likelihood of both short and long trajectories to reactive targets. While the disorder slows down reaction kinetics on average, its dynamic character is beneficial for a faster search and realization of an individual reaction event triggered by a single molecule.
Topics: Diffusion; Models, Theoretical; Time Factors
PubMed: 30353010
DOI: 10.1038/s41467-018-06610-6 -
Biophysical Journal Oct 2022Fluorescence recovery after photobleaching (FRAP) is a widely used biological experiment to study the kinetics of molecules that react and move randomly. Since the...
Fluorescence recovery after photobleaching (FRAP) is a widely used biological experiment to study the kinetics of molecules that react and move randomly. Since the development of FRAP in the 1970s, many reaction-diffusion models have been used to interpret FRAP data. However, intracellular molecules are widely observed to move by anomalous subdiffusion instead of normal diffusion. In this article, we extend a popular reaction-diffusion model of FRAP to the case of subdiffusion modeled by a fractional diffusion equation. By analyzing this reaction-subdiffusion model, we show that FRAP data are consistent with both diffusive and subdiffusive motion in many scenarios. We illustrate this general result by fitting our model to FRAP data from glucocorticoid receptors in a cell nucleus. We further show that the assumed model of molecular motion (normal diffusion or subdiffusion) strongly impacts the biological parameter values inferred from a given experimentally observed FRAP curve. We additionally analyze our model in three simplified parameter regimes and discuss parameter identifiability for varying subdiffusion exponents.
Topics: Fluorescence Recovery After Photobleaching; Receptors, Glucocorticoid; Diffusion; Kinetics; Motion
PubMed: 36127879
DOI: 10.1016/j.bpj.2022.09.015 -
Journal of the Royal Society, Interface Jul 2023Turing's mechanism is often invoked to explain periodic patterns in nature, although direct experimental support is scarce. Turing patterns form in reaction-diffusion...
Turing's mechanism is often invoked to explain periodic patterns in nature, although direct experimental support is scarce. Turing patterns form in reaction-diffusion systems when the activating species diffuse much slower than the inhibiting species, and the involved reactions are highly nonlinear. Such reactions can originate from cooperativity, whose physical interactions should also affect diffusion. We here take direct interactions into account and show that they strongly affect Turing patterns. We find that weak repulsion between the activator and inhibitor can substantially lower the required differential diffusivity and reaction nonlinearity. By contrast, strong interactions can induce phase separation, but the resulting length scale is still typically governed by the fundamental reaction-diffusion length scale. Taken together, our theory connects traditional Turing patterns with chemically active phase separation, thus describing a wider range of systems. Moreover, we demonstrate that even weak interactions affect patterns substantially, so they should be incorporated when modelling realistic systems.
Topics: Diffusion
PubMed: 37434500
DOI: 10.1098/rsif.2023.0244 -
Proceedings of the National Academy of... Aug 2021Single-particle tracking (SPT) is a key tool for quantitative analysis of dynamic biological processes and has provided unprecedented insights into a wide range of...
Single-particle tracking (SPT) is a key tool for quantitative analysis of dynamic biological processes and has provided unprecedented insights into a wide range of systems such as receptor localization, enzyme propulsion, bacteria motility, and drug nanocarrier delivery. The inherently complex diffusion in such biological systems can vary drastically both in time and across systems, consequently imposing considerable analytical challenges, and currently requires an a priori knowledge of the system. Here we introduce a method for SPT data analysis, processing, and classification, which we term "diffusional fingerprinting." This method allows for dissecting the features that underlie diffusional behavior and establishing molecular identity, regardless of the underlying diffusion type. The method operates by isolating 17 descriptive features for each observed motion trajectory and generating a diffusional map of all features for each type of particle. Precise classification of the diffusing particle identity is then obtained by training a simple logistic regression model. A linear discriminant analysis generates a feature ranking that outputs the main differences among diffusional features, providing key mechanistic insights. Fingerprinting operates by both training on and predicting experimental data, without the need for pretraining on simulated data. We found this approach to work across a wide range of simulated and experimentally diverse systems, such as tracked lipases on fat substrates, transcription factors diffusing in cells, and nanoparticles diffusing in mucus. This flexibility ultimately supports diffusional fingerprinting's utility as a universal paradigm for SPT diffusional analysis and prediction.
Topics: Computer Simulation; Diffusion; Image Interpretation, Computer-Assisted; Machine Learning; Movement; Particle Size; Single Molecule Imaging
PubMed: 34321355
DOI: 10.1073/pnas.2104624118 -
Nucleic Acids Research Mar 2018We reanalyze trajectories of hOGG1 repair proteins diffusing on DNA. A previous analysis of these trajectories with the popular mean-squared-displacement approach...
We reanalyze trajectories of hOGG1 repair proteins diffusing on DNA. A previous analysis of these trajectories with the popular mean-squared-displacement approach revealed only simple diffusion. Here, a new optimal estimator of diffusion coefficients reveals two-state kinetics of the protein. A simple, solvable model, in which the protein randomly switches between a loosely bound, highly mobile state and a tightly bound, less mobile state is the simplest possible dynamic model consistent with the data. It yields accurate estimates of hOGG1's (i) diffusivity in each state, uncorrupted by experimental errors arising from shot noise, motion blur and thermal fluctuations of the DNA; (ii) rates of switching between states and (iii) rate of detachment from the DNA. The protein spends roughly equal time in each state. It detaches only from the loosely bound state, with a rate that depends on pH and the salt concentration in solution, while its rates for switching between states are insensitive to both. The diffusivity in the loosely bound state depends primarily on pH and is three to ten times higher than in the tightly bound state. We propose and discuss some new experiments that take full advantage of the new tools of analysis presented here.
Topics: DNA; DNA Glycosylases; DNA-Binding Proteins; Diffusion; Humans; Kinetics; Models, Biological; Motion
PubMed: 29361033
DOI: 10.1093/nar/gky004 -
Proceedings of the National Academy of... Nov 2021Do some types of information spread faster, broader, or further than others? To understand how information diffusions differ, scholars compare structural properties of...
Do some types of information spread faster, broader, or further than others? To understand how information diffusions differ, scholars compare structural properties of the paths taken by content as it spreads through a network, studying so-called cascades. Commonly studied cascade properties include the reach, depth, breadth, and speed of propagation. Drawing conclusions from statistical differences in these properties can be challenging, as many properties are dependent. In this work, we demonstrate the essentiality of controlling for cascade sizes when studying structural differences between collections of cascades. We first revisit two datasets from notable recent studies of online diffusion that reported content-specific differences in cascade topology: an exhaustive corpus of Twitter cascades for verified true- or false-news content by Vosoughi et al. [S. Vosoughi, D. Roy, S. Aral. 359, 1146-1151 (2018)] and a comparison of Twitter cascades of videos, pictures, news, and petitions by Goel et al. [S. Goel, A. Anderson, J. Hofman, D. J. Watts. 62, 180-196 (2016)]. Using methods that control for joint cascade statistics, we find that for false- and true-news cascades, the reported structural differences can almost entirely be explained by false-news cascades being larger. For videos, images, news, and petitions, structural differences persist when controlling for size. Studying classical models of diffusion, we then give conditions under which differences in structural properties under different models do or do not reduce to differences in size. Our findings are consistent with the mechanisms underlying true- and false-news diffusion being quite similar, differing primarily in the basic infectiousness of their spreading process.
Topics: Communication; Diffusion; Humans; Information Dissemination; Social Media
PubMed: 34750252
DOI: 10.1073/pnas.2100786118