-
The Journal of Chemical Physics Aug 2023Most biological processes in living cells rely on interactions between proteins. Live-cell compatible approaches that can quantify to what extent a given protein... (Review)
Review
Most biological processes in living cells rely on interactions between proteins. Live-cell compatible approaches that can quantify to what extent a given protein participates in homo- and hetero-oligomeric complexes of different size and subunit composition are therefore critical to advance our understanding of how cellular physiology is governed by these molecular interactions. Biomolecular complex formation changes the diffusion coefficient of constituent proteins, and these changes can be measured using fluorescence microscopy-based approaches, such as single-molecule tracking, fluorescence correlation spectroscopy, and fluorescence recovery after photobleaching. In this review, we focus on the use of single-molecule tracking to identify, resolve, and quantify the presence of freely-diffusing proteins and protein complexes in living cells. We compare and contrast different data analysis methods that are currently employed in the field and discuss experimental designs that can aid the interpretation of the obtained results. Comparisons of diffusion rates for different proteins and protein complexes in intracellular aqueous environments reported in the recent literature reveal a clear and systematic deviation from the Stokes-Einstein diffusion theory. While a complete and quantitative theoretical explanation of why such deviations manifest is missing, the available data suggest the possibility of weighing freely-diffusing proteins and protein complexes in living cells by measuring their diffusion coefficients. Mapping individual diffusive states to protein complexes of defined molecular weight, subunit stoichiometry, and structure promises to provide key new insights into how protein-protein interactions regulate protein conformational, translational, and rotational dynamics, and ultimately protein function.
Topics: Single Molecule Imaging; Diffusion; Microscopy, Fluorescence; Photobleaching; Protein Conformation
PubMed: 37589409
DOI: 10.1063/5.0155638 -
European Biophysics Journal : EBJ Apr 2018Lateral movement of a molecule in a biomembrane containing small compartments (0.23-μm diameter) and large ones (0.75 μm) is analyzed using a fractal description of...
Lateral movement of a molecule in a biomembrane containing small compartments (0.23-μm diameter) and large ones (0.75 μm) is analyzed using a fractal description of its walk. The early time dependence of the mean square displacement varies from linear due to the contribution of ballistic motion. In small compartments, walking molecules do not have sufficient time or space to develop an asymptotic relation and the diffusion coefficient deduced from the experimental records is lower than that measured without restrictions. The model makes it possible to deduce the molecule step parameters, namely the step length and time, from data concerning confined and unrestricted diffusion coefficients. This is also possible using experimental results for sub-diffusive transport. The transition from normal to anomalous diffusion does not affect the molecule step parameters. The experimental literature data on molecular trajectories recorded at a high time resolution appear to confirm the modeled value of the mean free path length of DOPE for Brownian and anomalous diffusion. Although the step length and time give the proper values of diffusion coefficient, the DOPE speed calculated as their quotient is several orders of magnitude lower than the thermal speed. This is interpreted as a result of intermolecular interactions, as confirmed by lateral diffusion of other molecules in different membranes. The molecule step parameters are then utilized to analyze the problem of multiple visits in small compartments. The modeling of the diffusion exponent results in a smooth transition to normal diffusion on entering a large compartment, as observed in experiments.
Topics: Cell Membrane; Diffusion; Fractals; Models, Biological; Movement
PubMed: 29094176
DOI: 10.1007/s00249-017-1264-0 -
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 -
Analytical Chemistry Apr 2020Measuring the translational diffusion of proteins under physiological conditions can be very informative, especially when multiple diffusing species can be...
Measuring the translational diffusion of proteins under physiological conditions can be very informative, especially when multiple diffusing species can be distinguished. Diffusion NMR or diffusion-ordered spectroscopy (DOSY) is widely used to study molecular diffusion, where protons are used as probes, which can be further edited by the proton-attached heteronuclei to provide additional resolution. For example, the combination of the backbone amide protons (H) to measure diffusion with the well-resolved H/N correlations has afforded high-resolution DOSY experiments. However, significant amide-water proton exchange at physiological temperature and pH can affect the accuracy of diffusion data or cause complete loss of DOSY signals. Although aliphatic protons do not exchange with water protons, and thus are potential probes to measure diffusion rates, H/C correlations are often in spectral overlap or masked by the water signal, which hampers the use of these correlations. In this report, a method was developed that separates the nuclei used for diffusion (α protons, H) and those used for detection (H/N and C'/N correlations). This approach enables high-resolution diffusion measurements of polypeptides in a mixture of biomolecules, thereby providing a powerful tool to investigate coexisting species under physiologically relevant conditions.
Topics: Diffusion; Nuclear Magnetic Resonance, Biomolecular; Proteins
PubMed: 32163276
DOI: 10.1021/acs.analchem.9b05453 -
Proceedings of the National Academy of... May 2019We develop a detailed description of protein translational and rotational diffusion in concentrated solution on the basis of all-atom molecular dynamics simulations in...
We develop a detailed description of protein translational and rotational diffusion in concentrated solution on the basis of all-atom molecular dynamics simulations in explicit solvent. Our systems contain up to 540 fully flexible proteins with 3.6 million atoms. In concentrated protein solutions (100 mg/mL and higher), the proteins ubiquitin and lysozyme, as well as the protein domains third IgG-binding domain of protein G and villin headpiece, diffuse not as isolated particles, but as members of transient clusters between which they constantly exchange. A dynamic cluster model nearly quantitatively explains the increase in viscosity and the decrease in protein diffusivity with protein volume fraction, which both exceed the predictions from widely used colloid models. The Stokes-Einstein relations for translational and rotational diffusion remain valid, but the effective hydrodynamic radius grows linearly with protein volume fraction. This increase follows the observed increase in cluster size and explains the more dramatic slowdown of protein rotation compared with translation. Baxter's sticky-sphere model of colloidal suspensions captures the concentration dependence of cluster size, viscosity, and rotational and translational diffusion. The consistency between simulations and experiments for a diverse set of soluble globular proteins indicates that the cluster model applies broadly to concentrated protein solutions, with equilibrium dissociation constants for nonspecific protein-protein binding in the K ≈ 10-mM regime.
Topics: Colloids; Diffusion; Hydrodynamics; Molecular Dynamics Simulation; Proteins; Viscosity
PubMed: 31036655
DOI: 10.1073/pnas.1817564116 -
Biophysical Journal Aug 2008Complex diffusive dynamics are often observed when one is investigating the mobility of macromolecules in living cells and other complex environments, yet the underlying...
Complex diffusive dynamics are often observed when one is investigating the mobility of macromolecules in living cells and other complex environments, yet the underlying physical or chemical causes of anomalous diffusion are often not fully understood and are thus a topic of ongoing research interest. Theoretical models capturing anomalous dynamics are widely used to analyze mobility data from fluorescence correlation spectroscopy and other experimental measurements, yet there is significant confusion regarding these models because published versions are not entirely consistent and in some cases do not appear to satisfy the diffusion equation. Further confusion is introduced through variations in how fitting parameters are reported. A clear definition of fitting parameters and their physical significance is essential for accurate interpretation of experimental data and comparison of results from different studies acquired under varied experimental conditions. This article aims to clarify the physical meaning of the time-dependent diffusion coefficients associated with commonly used fitting models to facilitate their use for investigating the underlying causes of anomalous diffusion. We discuss a propagator for anomalous diffusion that captures the power law dependence of the mean-square displacement and can be shown to rigorously satisfy the extended diffusion equation provided one correctly defines the time-dependent diffusion coefficient. We also clarify explicitly the relation between the time-dependent diffusion coefficient and fitting parameters in fluorescence correlation spectroscopy.
Topics: Biopolymers; Computer Simulation; Diffusion; Models, Biological; Models, Chemical; Models, Molecular
PubMed: 18487294
DOI: 10.1529/biophysj.107.121608 -
European Biophysics Journal : EBJ Jul 2020A computational methodology to simulate the diffusion of ions from point sources (e.g., ion channels) is described. The outlined approach computes the ion concentration...
A computational methodology to simulate the diffusion of ions from point sources (e.g., ion channels) is described. The outlined approach computes the ion concentration from a cluster of many ion channels at pre-specified locations as a function of time using the theory of propagation integrals. How the channels' open/closed states evolve in time does not need to be known at the start of the simulation, but can be updated on-the-fly as the simulation goes along. The technique uses analytic formulas for the solutions of the diffusion equation for three common geometries: (1) ions diffusing from a membrane (planar symmetry); (2) ions diffusing into a narrow cleft for effective two-dimensional diffusion (cylindrical symmetry); and (3) ions diffusing into open space like the cytosol (spherical symmetry). Because these formulas are exact solutions valid for arbitrarily long timesteps, no spatial or time discretizations are necessary. The only discrete locations are where the ion concentration is computed, and the only discrete timesteps are when the channels' open/closed states are updated. Beyond pure diffusion, the technique is generalized to the Excess Buffer Approximation of ion chelation to give an analytic solution of this approximation of the full reaction/diffusion system. Both the pure diffusion and the diffusion/buffering algorithms scale linearly with the number of channels and the number of ion concentration locations.
Topics: Cell Membrane; Computer Simulation; Diffusion; Ion Channels; Models, Biological
PubMed: 32488299
DOI: 10.1007/s00249-020-01438-9 -
Biophysical Journal Jul 2008The immunological synapse is a stable intercellular structure that specializes in substance and signal transfer from one immune cell to another. Its formation is...
The immunological synapse is a stable intercellular structure that specializes in substance and signal transfer from one immune cell to another. Its formation is regulated in part by the diffusion of adhesion and signaling molecules into, and their binding of countermolecules in the contact area. The stability of immunological synapses allows receptor-ligand interactions to approximate chemical equilibrium despite other dynamic aspects. We have developed a mathematical model that describes the coupled reaction-diffusion process in an established immunological synapse. In this study, we extend a previously described contact area fluorescence recovery after photobleaching (FRAP) experiment to test the validity of the model. The receptor binding activity and lateral mobility of fluorescently labeled, lipid-anchored ligands in the bilayer resulted in their accumulation, as revealed by a much higher fluorescence intensity inside the contact area than outside. After complete photobleaching of the synapse, fluorescence recovery requires ligands to dissociate and rebind, and to diffuse in and out of the contact area. Such a FRAP time course consequently provides information on reaction and diffusion, which can be extracted by fitting the model solution to the data. Surprisingly, reverse rates in the two-dimensional contact area were at least 100-fold slower than in three-dimensional solution. As previously reported in immunological synapses, a significant nonrecoverable fraction of fluorescence was observed with one of two systems studied, suggesting some ligands either dissociated or diffused much more slowly compared with other ligands in the same synapse. The combined theory and experiment thus provides a new method for in situ measurements of kinetic rates, diffusion coefficients, and nonrecoverable fractions of interacting molecules in immunological synapses and other stable cell-bilayer junctions.
Topics: Binding Sites; Computer Simulation; Diffusion; Fluorescence Recovery After Photobleaching; Kinetics; Models, Biological; Models, Chemical; Protein Binding; Protein Interaction Mapping; Proteins
PubMed: 18390627
DOI: 10.1529/biophysj.107.114447 -
Journal of Biophotonics Feb 2018Quantitative measurements of intravascular microscopic dynamics, such as absolute blood flow velocity, shear stress and the diffusion coefficient of red blood cells...
Quantitative measurements of intravascular microscopic dynamics, such as absolute blood flow velocity, shear stress and the diffusion coefficient of red blood cells (RBCs), are fundamental in understanding the blood flow behavior within the microcirculation, and for understanding why diffuse correlation spectroscopy (DCS) measurements of blood flow are dominantly sensitive to the diffusive motion of RBCs. Dynamic light scattering-optical coherence tomography (DLS-OCT) takes the advantages of using DLS to measure particle flow and diffusion within an OCT resolution-constrained three-dimensional volume, enabling the simultaneous measurements of absolute RBC velocity and diffusion coefficient with high spatial resolution. In this work, we applied DLS-OCT to measure both RBC velocity and the shear-induced diffusion coefficient within penetrating venules of the somatosensory cortex of anesthetized mice. Blood flow laminar profile measurements indicate a blunted laminar flow profile and the degree of blunting decreases with increasing vessel diameter. The measured shear-induced diffusion coefficient was proportional to the flow shear rate with a magnitude of ~0.1 to 0.5 × 10 mm . These results provide important experimental support for the recent theoretical explanation for why DCS is dominantly sensitive to RBC diffusive motion.
Topics: Algorithms; Animals; Biomechanical Phenomena; Diffusion; Dynamic Light Scattering; Erythrocytes; Female; Mechanical Phenomena; Mice; Tomography, Optical Coherence
PubMed: 28700129
DOI: 10.1002/jbio.201700070 -
Biophysical Journal Jun 2021From nutrient uptake to chemoreception to synaptic transmission, many systems in cell biology depend on molecules diffusing and binding to membrane receptors....
From nutrient uptake to chemoreception to synaptic transmission, many systems in cell biology depend on molecules diffusing and binding to membrane receptors. Mathematical analysis of such systems often neglects the fact that receptors process molecules at finite kinetic rates. A key example is the celebrated formula of Berg and Purcell for the rate that cell surface receptors capture extracellular molecules. Indeed, this influential result is only valid if receptors transport molecules through the cell wall at a rate much faster than molecules arrive at receptors. From a mathematical perspective, ignoring receptor kinetics is convenient because it makes the diffusing molecules independent. In contrast, including receptor kinetics introduces correlations between the diffusing molecules because, for example, bound receptors may be temporarily blocked from binding additional molecules. In this work, we present a modeling framework for coupling bulk diffusion to surface receptors with finite kinetic rates. The framework uses boundary homogenization to couple the diffusion equation to nonlinear ordinary differential equations on the boundary. We use this framework to derive an explicit formula for the cellular uptake rate and show that the analysis of Berg and Purcell significantly overestimates uptake in some typical biophysical scenarios. We confirm our analysis by numerical simulations of a many-particle stochastic system.
Topics: Diffusion; Kinetics; Ligands; Models, Biological; Receptors, Cell Surface
PubMed: 33794148
DOI: 10.1016/j.bpj.2021.03.021