Anomalous protein diffusion in living cells as seen by fluorescence correlation spectroscopy

Quantifying biomolecular organisation in membranes with brightness-transit statistics

Cells crucially rely on the interactions of biomolecules at their plasma membrane to maintain homeostasis. Yet, a methodology to systematically quantify biomolecular organisation, measuring diffusion dynamics and oligomerisation, represents an unmet need. Here, we introduce the brightness-transit statistics (BTS) method based on fluorescence fluctuation spectroscopy and combine information from brightness and transit times to elucidate biomolecular diffusion and oligomerisation in both cell-free in vitro and in vitro systems incorporating living cells. We validate our approach in silico with computer simulations and experimentally using oligomerisation of EGFP tethered to supported lipid bilayers. We apply our pipeline to study the oligomerisation of CD40 ectodomain in vitro and endogenous CD40 on primary B cells. While we find a potential for CD40 to oligomerize in a concentration or ligand depended manner, we do not observe mobile oligomers on B cells. The BTS method combines sensitive analysis, quantification, and intuitive visualisation of dynamic biomolecular organisation.

Diffusion and Oligomerization States of the Muscarinic M1 Receptor in Live Cells─The Impact of Ligands and Membrane Disruptors

G protein-coupled receptors (GPCRs) are a major gateway to cellular signaling, which respond to ligands binding at extracellular sites through allosteric conformational changes that modulate their interactions with G proteins and arrestins at intracellular sites. High-resolution structures in different ligand states, together with spectroscopic studies and molecular dynamics simulations, have revealed a rich conformational landscape of GPCRs. However, their supramolecular structure and spatiotemporal distribution is also thought to play a significant role in receptor activation and signaling bias within the native cell membrane environment. Here, we applied single-molecule fluorescence techniques, including single-particle tracking, single-molecule photobleaching, and fluorescence correlation spectroscopy, to characterize the diffusion and oligomerization behavior of the muscarinic M1 receptor (M1R) in live cells. Control samples included the monomeric protein CD86 and fixed cells, and experiments performed in the presence of different orthosteric M1R ligands and of several compounds known to change the fluidity and organization of the lipid bilayer. M1 receptors exhibit Brownian diffusion characterized by three diffusion constants: confined/immobile (∼0.01 μm2/s), slow (∼0.04 μm2/s), and fast (∼0.14 μm2/s), whose populations were found to be modulated by both orthosteric ligands and membrane disruptors. The lipid raft disruptor C6 ceramide led to significant changes for CD86, while the diffusion of M1R remained unchanged, indicating that M1 receptors do not partition in lipid rafts. The extent of receptor oligomerization was found to be promoted by increasing the level of expression and the binding of orthosteric ligands; in particular, the agonist carbachol elicited a large increase in the fraction of M1R oligomers. This study provides new insights into the balance between conformational and environmental factors that define the movement and oligomerization states of GPCRs in live cells under close-to-native conditions.

Influence of Cigarette Aerosol in Alpha-Synuclein Oligomerization and Cell Viability in SH-SY5Y: Implications for Parkinson's Disease

Although cigarette aerosol exposure is associated with various adverse health issues, its impact on Parkinson's disease (PD) remains elusive. Here, we investigated the effect of cigarette aerosol extract (CAE) on SH-SY5Y cells for the first time, both with and without α-synuclein (α-Syn) overexpression. We found that α-Syn aggravates CAE-induced cell death, oxidative stress, and mitochondrial dysfunction. Fluorescence cross-correlation spectroscopy (FCCS) revealed a dual distribution of α-Syn within the cells, with homogeneous regions indicative of monomeric α-Syn and punctated regions, suggesting the formation of oligomers. Moreover, we observed colocalization of α-Syn oligomers with lysosomes along with a reduction in autophagy activity. These findings suggest that α-Syn overexpression exacerbates CAE-induced intracellular cytotoxicity, mitochondrial dysfunction, and autophagy dysregulation, leading to elevated cell mortality. Our findings provide new insights into the pathogenic mechanisms linking exposure to cigarette aerosols with neurodegenerative diseases.

Coherent light scattering from cellular dynamics in living tissues

This review examines the biological physics of intracellular transport probed by the coherent optics of dynamic light scattering from optically thick living tissues. Cells and their constituents are in constant motion, composed of a broad range of speeds spanning many orders of magnitude that reflect the wide array of functions and mechanisms that maintain cellular health. From the organelle scale of tens of nanometers and upward in size, the motion inside living tissue is actively driven rather than thermal, propelled by the hydrolysis of bioenergetic molecules and the forces of molecular motors. Active transport can mimic the random walks of thermal Brownian motion, but mean-squared displacements are far from thermal equilibrium and can display anomalous diffusion through Lévy or fractional Brownian walks. Despite the average isotropic three-dimensional environment of cells and tissues, active cellular or intracellular transport of single light-scattering objects is often pseudo-one-dimensional, for instance as organelle displacement persists along cytoskeletal tracks or as membranes displace along the normal to cell surfaces, albeit isotropically oriented in three dimensions. Coherent light scattering is a natural tool to characterize such tissue dynamics because persistent directed transport induces Doppler shifts in the scattered light. The many frequency-shifted partial waves from the complex and dynamic media interfere to produce dynamic speckle that reveals tissue-scale processes through speckle contrast imaging and fluctuation spectroscopy. Low-coherence interferometry, dynamic optical coherence tomography, diffusing-wave spectroscopy, diffuse-correlation spectroscopy, differential dynamic microscopy and digital holography offer coherent detection methods that shed light on intracellular processes. In health-care applications, altered states of cellular health and disease display altered cellular motions that imprint on the statistical fluctuations of the scattered light. For instance, the efficacy of medical therapeutics can be monitored by measuring the changes they induce in the Doppler spectra of livingex vivocancer biopsies.

Anomalous diffusion, non-Gaussianity, nonergodicity, and confinement in stochastic-scaled Brownian motion with diffusing diffusivity dynamics

Scaled Brownian motions (SBMs) with power-law time-dependent diffusivity have been used to describe various types of anomalous diffusion yet Gaussian observed in granular gases kinetics, turbulent diffusion, and molecules mobility in cells, to name a few. However, some of these systems may exhibit non-Gaussian behavior which can be described by SBM with diffusing diffusivity (DD-SBM). Here, we numerically investigate both free and confined DD-SBM models characterized by fixed or stochastic scaling exponent of time-dependent diffusivity. The effects of distributed scaling exponent, random diffusivity, and confinement are considered. Different regimes of ultraslow diffusion, subdiffusion, normal diffusion, and superdiffusion are observed. In addition, weak ergodic and non-Gaussian behaviors are also detected. These results provide insights into diffusion in time-fluctuating diffusivity landscapes with potential applications to time-dependent temperature systems spreading in heterogeneous environments.

Heterogeneous anomalous transport in cellular and molecular biology

It is well established that a wide variety of phenomena in cellular and molecular biology involve anomalous transport e.g. the statistics for the motility of cells and molecules are fractional and do not conform to the archetypes of simple diffusion or ballistic transport. Recent research demonstrates that anomalous transport is in many cases heterogeneous in both time and space. Thus single anomalous exponents and single generalised diffusion coefficients are unable to satisfactorily describe many crucial phenomena in cellular and molecular biology. We consider advances in the field ofheterogeneous anomalous transport(HAT) highlighting: experimental techniques (single molecule methods, microscopy, image analysis, fluorescence correlation spectroscopy, inelastic neutron scattering, and nuclear magnetic resonance), theoretical tools for data analysis (robust statistical methods such as first passage probabilities, survival analysis, different varieties of mean square displacements, etc), analytic theory and generative theoretical models based on simulations. Special emphasis is made on high throughput analysis techniques based on machine learning and neural networks. Furthermore, we consider anomalous transport in the context of microrheology and the heterogeneous viscoelasticity of complex fluids. HAT in the wavefronts of reaction-diffusion systems is also considered since it plays an important role in morphogenesis and signalling. In addition, we present specific examples from cellular biology including embryonic cells, leucocytes, cancer cells, bacterial cells, bacterial biofilms, and eukaryotic microorganisms. Case studies from molecular biology include DNA, membranes, endosomal transport, endoplasmic reticula, mucins, globular proteins, and amyloids.

Fractional and scaled Brownian motion on the sphere: The effects of long-time correlations on navigation strategies

We analyze fractional Brownian motion and scaled Brownian motion on the two-dimensional sphere S^{2}. We find that the intrinsic long-time correlations that characterize fractional Brownian motion collude with the specific dynamics (navigation strategies) carried out on the surface giving rise to rich transport properties. We focus our study on two classes of navigation strategies: one induced by a specific set of coordinates chosen for S^{2} (we have chosen the spherical ones in the present analysis), for which we find that contrary to what occurs in the absence of such long-time correlations, nonequilibrium stationary distributions are attained. These results resemble those reported in confined flat spaces in one and two dimensions [Guggenberger et al. New J. Phys. 21, 022002 (2019)1367-263010.1088/1367-2630/ab075f; Vojta et al. Phys. Rev. E 102, 032108 (2020)2470-004510.1103/PhysRevE.102.032108]; however, in the case analyzed here, there are no boundaries that affect the motion on the sphere. In contrast, when the navigation strategy chosen corresponds to a frame of reference moving with the particle (a Frenet-Serret reference system), then the equilibrium distribution on the sphere is recovered in the long-time limit. For both navigation strategies, the relaxation times toward the stationary distribution depend on the particular value of the Hurst parameter. We also show that on S^{2}, scaled Brownian motion, distinguished by a time-dependent diffusion coefficient with a power-scaling, is independent of the navigation strategy finding a good agreement between the analytical calculations obtained from the solution of a time-dependent diffusion equation on S^{2}, and the numerical results obtained from our numerical method to generate ensemble of trajectories.

Effects of crowding on the diffusivity of membrane adhered particles

The lateral diffusion of cell membrane inclusions, such as integral membrane proteins and bound receptors, drives critical biological processes, including the formation of complexes, cell-cell signaling, and membrane trafficking. These diffusive processes are complicated by how concentrated, or "crowded", the inclusions are, which can occupy between 30-50% of the area fraction of the membrane. In this work, we elucidate the effects of increasing concentration of model membrane inclusions in a free-standing artificial cell membrane on inclusion diffusivity and the apparent viscosity of the membrane. By multiple particle tracking of fluorescent microparticles covalently tethered to the bilayer, we show the transition from expected Brownian dynamics, which accurately measure the membrane viscosity, to subdiffusive behavior with decreased diffusion coefficient as the particle area fraction increases from 1% to around 30%, approaching physiological levels of crowding. At high crowding, the onset of non-Gaussian behavior is observed. Using hydrodynamic models relating the 2D diffusion coefficient to the viscosity of a membrane, we determine the apparent viscosity of the bilayer from the particle diffusivity and show an increase in the apparent membrane viscosity with increasing particle area fraction. However, the scaling of this increase is in contrast with the behavior of monolayer inclusion diffusion and bulk suspension rheology. These results demonstrate that physiological levels of model membrane crowding nontrivially alter the dynamics and apparent viscosity of the system, which has implications for understanding membrane protein interactions and particle-membrane transport processes.

Critical Assessment of Condensate Boundaries in Dual-Color Single Particle Tracking

Biomolecular condensates are membraneless cellular compartments generated by phase separation that regulate a broad variety of cellular functions by enriching some biomolecules while excluding others. Live-cell single particle tracking of individual fluorophore-labeled condensate components has provided insights into a condensate's mesoscopic organization and biological functions, such as revealing the recruitment, translation, and decay of RNAs within ribonucleoprotein (RNP) granules. Specifically, during dual-color tracking, one imaging channel provides a time series of individual biomolecule locations, while the other channel monitors the location of the condensate relative to these molecules. Therefore, an accurate assessment of a condensate's boundary is critical for combined live-cell single particle-condensate tracking. Despite its importance, a quantitative benchmarking and objective comparison of the various available boundary detection methods is missing due to the lack of an absolute ground truth for condensate images. Here, we use synthetic data of defined ground truth to generate noise-overlaid images of condensates with realistic phase separation parameters to benchmark the most commonly used methods for condensate boundary detection, including an emerging machine-learning method. We find that it is critical to carefully choose an optimal boundary detection method for a given dataset to obtain accurate measurements of single particle-condensate interactions. The criteria proposed in this study to guide the selection of an optimal boundary detection method can be broadly applied to imaging-based studies of condensates.

Fluorescence correlation spectroscopy based insights into diffusion in electrochemical energy systems

Fluorescence Correlation Spectroscopy, a commonly used technique for measuring diffusion of biomolecules and tracer dyes in different solvents, is employed to characterise the local transport properties in battery electrolytes. Diffusion of ions, a major limiting factor in battery capacity and charging rates, depends on the local interactions and structuredness of the electrolytic species. Structuredness in the electrolyte results from typical solvation behaviour of diffusing ions/molecules leading to long-range interactions. In this work, we have used FCS to measure tracer diffusion of Coumarin 343 in a mixture of Ethylene Carbonate (EC) and Dimethyl Carbonate (DMC), commonly used as electrolyte solvent in Li-ion batteries. The measured diffusion is found to depend on lithium-ion concentrations. It is found that the addition of LiPF6 to an EC-DMC equimolar mixture slows down tracer diffusion significantly. Indeed, the bulk viscosity of the electrolyte added with LiPF6 salt varies with salt concentration. However, the change in bulk viscosity (global behaviour) at high ion concentrations does not match the one inferred from applying Stoke-Einstein's relation to the diffusion data (local behaviour). This indicates that the homogeneity of the electrolyte does not extend spatially to molecular scales around the diffusing tracer molecule. Measurements made on coin cells prepared with different concentrations of LiPF6 show battery performance limited at higher concentrations, characterized by specific capacity loss at faster charging cycles. This limitation is directly related to the local behaviour of the electrolyte as quantified by measurements of tracer diffusion, which slows down, which remarkably outweighs the advantage of high carrier densities.

Change in the Oligomeric State of α-Synuclein Variants in Living Cells

The accumulation of β-sheet-rich α-synuclein (α-Syn) protein in human brain cells is a pathological hallmark of Parkinson's disease (PD). Moreover, it has been reported that familial PD mutations (A30P, E46K, H50Q, G51D, and A53T) accumulate at an accelerated rate both in vivo and in vitro. In addition, accumulations of various C-terminal α-Syn truncations, such as C-terminal-truncated N103 α-synuclein (N103), were found in an aggregated form in the brain tissue of PD patients. Fluorescent protein-tagged wild-type α-Syn, A30P, E46K, H50Q, G51D, A53T, and N103 were transfected into HEK293T and SHSY5Y cells, and their diffusion behaviors were investigated with a custom-built fluorescence microscope system. Based on our experimental results, the oligomerization of α-Syn is a time-dependent process in both HEK293T and SHSY5Y cells, and the oligomer state approaches a plateau after 48 h of transfection. The change in the oligomeric state of E46K, H50Q, and G51D exhibited a similar trend to the wild type at a lower concentration but became intense at a higher concentration. A53T and N103 possess smaller diffusion coefficients than wild-type α-synuclein and other family PD mutations, indicating that these two mutants could form higher oligomeric states or stronger interactions in HEK293T and SHSY5Y cells. In contrast, the smallest oligomer and the lowest intracellular interaction among all investigated α-Syn variants were found for A30P. These phenomena indicated the presence of different pathogeneses among familial PD mutants and C-terminal α-Syn truncations.

Z-α1-antitrypsin polymers impose molecular filtration in the endoplasmic reticulum after undergoing phase transition to a solid state

Misfolding of secretory proteins in the endoplasmic reticulum (ER) features in many human diseases. In α1-antitrypsin deficiency, the pathogenic Z variant aberrantly assembles into polymers in the hepatocyte ER, leading to cirrhosis. We show that α1-antitrypsin polymers undergo a liquid:solid phase transition, forming a protein matrix that retards mobility of ER proteins by size-dependent molecular filtration. The Z-α1-antitrypsin phase transition is promoted during ER stress by an ATF6-mediated unfolded protein response. Furthermore, the ER chaperone calreticulin promotes Z-α1-antitrypsin solidification and increases protein matrix stiffness. Single-particle tracking reveals that solidification initiates in cells with normal ER morphology, previously assumed to represent a healthy pool. We show that Z-α1-antitrypsin-induced hypersensitivity to ER stress can be explained by immobilization of ER chaperones within the polymer matrix. This previously unidentified mechanism of ER dysfunction provides a template for understanding a diverse group of related proteinopathies and identifies ER chaperones as potential therapeutic targets.

Fractional Diffusion with Geometric Constraints: Application to Signal Decay in Magnetic Resonance Imaging (MRI)

We investigate diffusion in three dimensions on a comb-like structure in which the particles move freely in a plane, but, out of this plane, are constrained to move only in the perpendicular direction. This model is an extension of the two-dimensional version of the comb model, which allows diffusion along the backbone when the particles are not in the branches. We also consider memory effects, which may be handled with different fractional derivative operators involving singular and non-singular kernels. We find exact solutions for the particle distributions in this model that display normal and anomalous diffusion regimes when the mean-squared displacement is determined. As an application, we use this model to fit the anisotropic diffusion of water along and across the axons in the optic nerve using magnetic resonance imaging. The results for the observed diffusion times (8 to 30 milliseconds) show an anomalous diffusion both along and across the fibers.

First-passage statistics of colloids on fractals: Theory and experimental realization

In nature and technology, particle dynamics frequently occur in complex environments, for example in restricted geometries or crowded media. These dynamics have often been modeled invoking a fractal structure of the medium although the fractal structure was only indirectly inferred through the dynamics. Moreover, systematic studies have not yet been performed. Here, colloidal particles moving in a laser speckle pattern are used as a model system. In this case, the experimental observations can be reliably traced to the fractal structure of the underlying medium with an adjustable fractal dimension. First-passage time statistics reveal that the particles explore the speckle in a self-similar, fractal manner at least over four decades in time and on length scales up to 20 times the particle radius. The requirements for fractal diffusion to be applicable are laid out, and methods to extract the fractal dimension are established.

Rapid ensemble measurement of protein diffusion and probe blinking dynamics in cells

We present a fluorescence fluctuation image correlation analysis method that can rapidly and simultaneously measure the diffusion coefficient, photoblinking rates, and fraction of diffusing particles of fluorescent molecules in cells. Unlike other image correlation techniques, we demonstrated that our method could be applied irrespective of a nonuniformly distributed, immobile blinking fluorophore population. This allows us to measure blinking and transport dynamics in complex cell morphologies, a benefit for a range of super-resolution fluorescence imaging approaches that rely on probe emission blinking. Furthermore, we showed that our technique could be applied without directly accounting for photobleaching. We successfully employed our technique on several simulations with realistic EMCCD noise and photobleaching models, as well as on Dronpa-C12-labeled β-actin in living NIH/3T3 and HeLa cells. We found that the diffusion coefficients measured using our method were consistent with previous literature values. We further found that photoblinking rates measured in the live HeLa cells varied as expected with changing excitation power.

Diffusion in Heterogenous Media and Sorption—Desorption Processes

We investigate particle diffusion in a heterogeneous medium limited by a surface where sorption–desorption processes are governed by a kinetic equation. We consider that the dynamics of the particles present in the medium are governed by a diffusion equation with a spatial dependence on the diffusion coefficient, i.e., K(x) = D|x|−η, with −1 < η and D = const, respectively. This system is analyzed in a semi-infinity region, i.e., the system is defined in the interval [0,∞) for an arbitrary initial condition. The solutions are obtained and display anomalous spreading, that is, the dynamics may be viewed as anomalous diffusion, which in turn is related, and hence, the model can be directly applied to several complex systems ranging from biological fluids to electrolytic cells.

Dynamic Cellular Cartography: Mapping the Local Determinants of Oligodendrocyte Transcription Factor 2 (OLIG2) Function in Live Cells Using Massively Parallel Fluorescence Correlation Spectroscopy Integrated with Fluorescence Lifetime Imaging Microscopy (mpFCS/FLIM)

Compartmentalization and integration of molecular processes through diffusion are basic mechanisms through which cells perform biological functions. To characterize these mechanisms in live cells, quantitative and ultrasensitive analytical methods with high spatial and temporal resolution are needed. Here, we present quantitative scanning-free confocal microscopy with single-molecule sensitivity, high temporal resolution (∼10 μs/frame), and fluorescence lifetime imaging capacity, developed by integrating massively parallel fluorescence correlation spectroscopy with fluorescence lifetime imaging microscopy (mpFCS/FLIM); we validate the method, use it to map in live cell location-specific variations in the concentration, diffusion, homodimerization, DNA binding, and local environment of the oligodendrocyte transcription factor 2 fused with the enhanced Green Fluorescent Protein (OLIG2-eGFP), and characterize the effects of an allosteric inhibitor of OLIG2 dimerization on these determinants of OLIG2 function. In particular, we show that cytoplasmic OLIG2-eGFP is largely monomeric and freely diffusing, with the fraction of freely diffusing OLIG2-eGFP molecules being f_D,free^cyt = (0.75 ± 0.10) and the diffusion time τ_D,free^cyt = (0.5 ± 0.3) ms. In contrast, OLIG2-eGFP homodimers are abundant in the cell nucleus, constituting ∼25% of the nuclear pool, some f_D,bound^nuc = (0.65 ± 0.10) of nuclear OLIG2-eGFP is bound to chromatin DNA, whereas freely moving OLIG2-eGFP molecules diffuse at the same rate as those in the cytoplasm, as evident from the lateral diffusion times τ_D,free^nuc = τ_D,free^cyt = (0.5 ± 0.3) ms. OLIG2-eGFP interactions with chromatin DNA, revealed through their influence on the apparent diffusion behavior of OLIG2-eGFP, τ_D,bound^nuc (850 ± 500) ms, are characterized by an apparent dissociation constant K_d,app^OLIG2-DNA = (45 ± 30) nM. The apparent dissociation constant of OLIG2-eGFP homodimers was estimated to be K_d,app^{(OLIG2-eGFP)2} ≈ 560 nM. The allosteric inhibitor of OLIG2 dimerization, compound NSC 50467, neither affects OLIG2-eGFP properties in the cytoplasm nor does it alter the overall cytoplasmic environment. In contrast, it significantly impedes OLIG2-eGFP homodimerization in the cell nucleus, increasing five-fold the apparent dissociation constant, K_{d,app,NSC50467}^{(OLIG2-eGFP)2} ≈ 3 μM, thus reducing homodimer levels to below 7% and effectively abolishing OLIG2-eGFP specific binding to chromatin DNA. The mpFCS/FLIM methodology has a myriad of applications in biomedical research and pharmaceutical industry. For example, it is indispensable for understanding how biological functions emerge through the dynamic integration of location-specific molecular processes and invaluable for drug development, as it allows us to quantitatively characterize the interactions of drugs with drug targets in live cells.

Effects of the curvature gradient on the distribution and diffusion of colloids confined to surfaces

The properties and behavior of colloids confined to move on curved surfaces offer a fertile ground for analysis since the geometric constraints induce specific features that are not available in flat spaces. Given their pertinence for biological and physicochemical processes, both with potential useful applications, the development of the concepts and methodology necessary for a deeper understanding of these unconventional systems is indeed an essential pursuit. The present study discusses a general and rigorous algorithm for the implementation of Brownian dynamics simulations that solves underlying difficulties and shortcomings inherent to conventional first-order schemes. Still based on the Ermak-McCammon recipe, our approach complements it with the higher-order geodesical projections of the elementary jumps generated on the associated tangent plane. This strategy, which warrants the locally isotropic propagation of non-interacting particles, is tested with a model system of colloidal particles interacting through a screened Coulomb potential while confined to move on ellipsoidal surfaces. This allows us to measure the effects prompted by the curvature gradient on the static and dynamic properties of this system. The varying curvature thus induces energetically favorable configurations in which the particles maximize their Euclidean distancing by crowding the regions with the largest Gaussian curvature, while withdrawing from those with the lowest. In turn, these inhomogeneous distributions provoke the anisotropic self-diffusion of the confined colloids, which is examined by exploiting the pertinent geodesic radial coordinates. The proficient methods under consideration thus allows dealing with the rich and remarkable new phenomena generated by any distinctive surface geometry.

Emergent Biosensing Technologies Based on Fluorescence Spectroscopy and Surface Plasmon Resonance

The purpose of this work is to provide an exhaustive overview of the emerging biosensor technologies for the detection of analytes of interest for food, environment, security, and health. Over the years, biosensors have acquired increasing importance in a wide range of applications due to synergistic studies of various scientific disciplines, determining their great commercial potential and revealing how nanotechnology and biotechnology can be strictly connected. In the present scenario, biosensors have increased their detection limit and sensitivity unthinkable until a few years ago. The most widely used biosensors are optical-based devices such as surface plasmon resonance (SPR)-based biosensors and fluorescence-based biosensors. Here, we will review them by highlighting how the progress in their design and development could impact our daily life.

Testing of Multifractional Brownian Motion

Fractional Brownian motion (FBM) is a generalization of the classical Brownian motion. Most of its statistical properties are characterized by the self-similarity (Hurst) index 0<H<1. In nature one often observes changes in the dynamics of a system over time. For example, this is true in single-particle tracking experiments where a transient behavior is revealed. The stationarity of increments of FBM restricts substantially its applicability to model such phenomena. Several generalizations of FBM have been proposed in the literature. One of these is called multifractional Brownian motion (MFBM) where the Hurst index becomes a function of time. In this paper, we introduce a rigorous statistical test on MFBM based on its covariance function. We consider three examples of the functions of the Hurst parameter: linear, logistic, and periodic. We study the power of the test for alternatives being MFBMs with different linear, logistic, and periodic Hurst exponent functions by utilizing Monte Carlo simulations. We also analyze mean-squared displacement (MSD) for the three cases of MFBM by comparing the ensemble average MSD and ensemble average time average MSD, which is related to the notion of ergodicity breaking. We believe that the presented results will be helpful in the analysis of various anomalous diffusion phenomena.

Anomalous diffusion and nonergodicity for heterogeneous diffusion processes with fractional Gaussian noise

Heterogeneous diffusion processes (HDPs) feature a space-dependent diffusivity of the form D(x)=D_{0}|x|^{α}. Such processes yield anomalous diffusion and weak ergodicity breaking, the asymptotic disparity between ensemble and time averaged observables, such as the mean-squared displacement. Fractional Brownian motion (FBM) with its long-range correlated yet Gaussian increments gives rise to anomalous and ergodic diffusion. Here, we study a combined model of HDPs and FBM to describe the particle dynamics in complex systems with position-dependent diffusivity driven by fractional Gaussian noise. This type of motion is, inter alia, relevant for tracer-particle diffusion in biological cells or heterogeneous complex fluids. We show that the long-time scaling behavior predicted theoretically and by simulations for the ensemble- and time-averaged mean-squared displacements couple the scaling exponents α of HDPs and the Hurst exponent H of FBM in a characteristic way. Our analysis of the simulated data in terms of the rescaled variable y∼|x|^{1/(2/(2-α))}/t^{H} coupling particle position x and time t yields a simple, Gaussian probability density function (PDF), P_{HDP-FBM}(y)=e^{-y^{2}}/sqrt[π]. Its universal shape agrees well with theoretical predictions for both uni- and bimodal PDF distributions.

Variations in Plasma Membrane Topography Can Explain Heterogenous Diffusion Coefficients Obtained by Fluorescence Correlation Spectroscopy

Fluorescence correlation spectroscopy (FCS) is frequently used to study diffusion in cell membranes, primarily the plasma membrane. The diffusion coefficients reported in the plasma membrane of the same cell type and even within single cells typically display a large spread. We have investigated whether this spread can be explained by variations in membrane topography throughout the cell surface, that changes the amount of membrane in the FCS focal volume at different locations. Using FCS, we found that diffusion of the membrane dye DiI in the apical plasma membrane was consistently faster above the nucleus than above the cytoplasm. Using live cell scanning ion conductance microscopy (SICM) to obtain a topography map of the cell surface, we demonstrate that cell surface roughness is unevenly distributed with the plasma membrane above the nucleus being the smoothest, suggesting that the difference in diffusion observed in FCS is related to membrane topography. FCS modeled on simulated diffusion in cell surfaces obtained by SICM was consistent with the FCS data from live cells and demonstrated that topography variations can cause the appearance of anomalous diffusion in FCS measurements. Furthermore, we found that variations in the amount of the membrane marker DiD, a proxy for the membrane, but not the transmembrane protein TCRζ or the lipid-anchored protein Lck, in the FCS focal volume were related to variations in diffusion times at different positions in the plasma membrane. This relationship was seen at different positions both at the apical cell and basal cell sides. We conclude that it is crucial to consider variations in topography in the interpretation of FCS results from membranes.

Fractional diffusion on the human proteome as an alternative to the multi-organ damage of SARS-CoV-2

The coronavirus 2019 (COVID-19) respiratory disease is caused by the novel coronavirus SARS-CoV-2 (severe acute respiratory syndrome coronavirus 2), which uses the enzyme ACE2 to enter human cells. This disease is characterized by important damage at a multi-organ level, partially due to the abundant expression of ACE2 in practically all human tissues. However, not every organ in which ACE2 is abundant is affected by SARS-CoV-2, which suggests the existence of other multi-organ routes for transmitting the perturbations produced by the virus. We consider here diffusive processes through the protein-protein interaction (PPI) network of proteins targeted by SARS-CoV-2 as an alternative route. We found a subdiffusive regime that allows the propagation of virus perturbations through the PPI network at a significant rate. By following the main subdiffusive routes across the PPI network, we identify proteins mainly expressed in the heart, cerebral cortex, thymus, testis, lymph node, kidney, among others of the organs reported to be affected by COVID-19.

Lévy walk dynamics in an external harmonic potential

Lévy walks (LWs) are spatiotemporally coupled random-walk processes describing superdiffusive heat conduction in solids, propagation of light in disordered optical materials, motion of molecular motors in living cells, or motion of animals, humans, robots, and viruses. We here investigate a key feature of LWs-their response to an external harmonic potential. In this generic setting for confined motion we demonstrate that LWs equilibrate exponentially and may assume a bimodal stationary distribution. We also show that the stationary distribution has a horizontal slope next to a reflecting boundary placed at the origin, in contrast to correlated superdiffusive processes. Our results generalize LWs to confining forces and settle some longstanding puzzles around LWs.

Diffusive transport of nanoscale objects through cell membranes: a computational perspective

Diffusion is an essential and fundamental means of transport of substances on cell membranes, and the dynamics of biomembranes plays a crucial role in the regulation of numerous cellular processes. The understanding of the complex mechanisms and the nature of particle diffusion have a bearing on establishing guidelines for the design of efficient transport materials and unique therapeutic approaches. Herein, this review article highlights the most recent advances in investigating diffusion dynamics of nanoscale objects on biological membranes, focusing on the approaches of tailored computer simulations and theoretical analysis. Due to the presence of the complicated and heterogeneous environment on native cell membranes, the diffusive transport behaviors of nanoparticles exhibit unique and variable characteristics. The general aspects and basic theories of normal diffusion and anomalous diffusion have been introduced. In addition, the influence of a series of external and internal factors on the diffusion behaviors is discussed, including particle size, membrane curvature, particle-membrane interactions or particle-inclusion, and the crowding degree of membranes. Finally, we seek to identify open problems in the existing experimental, simulation, and theoretical research studies, and to propose challenges for future development.

Understanding biochemical processes in the presence of sub-diffusive behavior of biomolecules in solution and living cells

In order to maintain cellular function, biomolecules like protein, DNA, and RNAs have to diffuse to the target spaces within the cell. Changes in the cytosolic microenvironment or in the nucleus during the fulfillment of these cellular processes affect their mobility, folding, and stability thereby impacting the transient or stable interactions with their adjacent neighbors in the organized and dynamic cellular interior. Using classical Brownian motion to elucidate the diffusion behavior of these biomolecules is hard considering their complex nature. The understanding of biomolecular diffusion inside cells still remains elusive due to the lack of a proper model that can be extrapolated to these cases. In this review, we have comprehensively addressed the progresses in this field, laying emphasis on the different aspects of anomalous diffusion in the different biochemical reactions in cell interior. These experiment-based models help to explain the diffusion behavior of biomolecules in the cytosolic and nuclear microenvironment. Moreover, since understanding of biochemical reactions within living cellular system is our main focus, we coupled the experimental observations with the concept of sub-diffusion from in vitro to in vivo condition. We believe that the pairing between the understanding of complex behavior and structure-function paradigm of biological molecules would take us forward by one step in order to solve the puzzle around diseases caused by cellular dysfunction.

A simulation algorithm for Brownian dynamics on complex curved surfaces

Brownian dynamics of colloidal particles on complex curved surfaces has found important applications in diverse physical, chemical, and biological processes. However, most Brownian dynamics simulation algorithms focus on relatively simple curved surfaces that can be analytically parameterized. In this work, we develop an algorithm to enable Brownian dynamics simulation on extremely complex curved surfaces. We approximate complex curved surfaces with triangle mesh surfaces and employ a novel scheme to perform particle simulation on these triangle mesh surfaces. Our algorithm computes forces and velocities of particles in global coordinates but updates their positions in local coordinates, which combines the strengths from both global and local simulation schemes. We benchmark the proposed algorithm with theory and then simulate Brownian dynamics of both single and multiple particles on torus and knot surfaces. The results show that our method captures well diffusion, transport, and crystallization of colloidal particles on complex surfaces with nontrivial topology. This study offers an efficient strategy for elucidating the impact of curvature, geometry, and topology on particle dynamics and microstructure formation in complex environments.

Tracking Single Molecules in Biomembranes: Is Seeing Always Believing?

The spatial organization of molecules in cell membranes and their dynamic interactions play a central role in regulating cell functions. Single-particle tracking (SPT), a technique in which single molecules are imaged and tracked in real time, has led to breakthrough discoveries regarding these spatiotemporal complexities of cell membranes. There are, however, emerging concerns about factors that might produce misleading interpretations of SPT results. Here, we briefly review the application of SPT to understanding the nanoscale heterogeneities of plasma membranes, with a focus on the unique challenges, pitfalls, and limitations that confront the use of nanoparticles as imaging probes for tracking the dynamics of single molecules in cell membranes.

IL-2 receptors preassemble and signal in the ER/Golgi causing resistance to antiproliferative anti-IL-2Rα therapies

Interleukin-2 (IL-2) and IL-15 play pivotal roles in T cell activation, apoptosis, and survival, and are implicated in leukemias and autoimmune diseases. Their heterotrimeric receptors share their β- and γ_c-chains, but have distinct α-chains. Anti-IL-2Rα (daclizumab) therapy targeting cell surface-expressed receptor subunits to inhibit T cell proliferation has only brought limited success in adult T cell leukemia/lymphoma (ATL) and in multiple sclerosis. We asked whether IL-2R subunits could already preassemble and signal efficiently in the endoplasmic reticulum (ER) and the Golgi. A combination of daclizumab and anti-IL-2 efficiently blocked IL-2-induced proliferation of IL-2-dependent wild-type (WT) ATL cells but not cells transfected with IL-2, suggesting that in IL-2-producing cells signaling may already take place before receptors reach the cell surface. In the Golgi fraction isolated from IL-2-producing ATL cells, we detected by Western blot phosphorylated Jak1, Jak3, and a phosphotyrosine signal attributed to the γ_c-chain, which occurred at much lower levels in the Golgi of WT ATL cells. We expressed EGFP- and mCherry-tagged receptor chains in HeLa cells to study their assembly along the secretory pathway. Confocal microscopy, Förster resonance energy transfer, and imaging fluorescence cross-correlation spectroscopy analysis revealed partial colocalization and molecular association of IL-2 (and IL-15) receptor chains in the ER/Golgi, which became more complete in the plasma membrane, further confirming our hypothesis. Our results define a paradigm of intracellular autocrine signaling and may explain resistance to antagonistic antibody therapies targeting receptors at the cell surface.

Self-diffusion of a highly concentrated monoclonal antibody by fluorescence correlation spectroscopy: insight into protein-protein interactions and self-association

The dynamic behavior of monoclonal antibodies (mAbs) at high concentration provides insight into protein microstructure and protein-protein interactions (PPI) that influence solution viscosity and protein stability. At high concentration, interpretation of the collective-diffusion coefficient Dc, as determined by dynamic light scattering (DLS), is highly challenging given the complex hydrodynamics and PPI at close spacings. In contrast, self-diffusion of a tracer particle by Brownian motion is simpler to understand. Herein, we develop fluorescence correlation spectroscopy (FCS) for the measurement of the long-time self-diffusion of mAb2 over a wide range of concentrations and viscosities in multiple co-solute formulations with varying PPI. The normalized self-diffusion coefficient D0/Ds (equal to the microscopic relative viscosity ηeff/η0) was found to be smaller than η/η0. Smaller ratios of the microscopic to macroscopic viscosity (ηeff/η) are attributed to a combination of weaker PPI and less self-association. The interaction parameters extracted from fits of D0/Ds with a length scale dependent viscosity model agree with previous measurements of PPI by SLS and SAXS. Trends in the degree of self-association, estimated from ηeff/η with a microviscosity model, are consistent with oligomer sizes measured by SLS. Finally, measurements of collective diffusion and osmotic compressibility were combined with FCS data to demonstrate that the changes in self-diffusion between formulations are due primarily to changes in the protein-protein friction in these systems, and not to protein-solvent friction. Thus, FCS is a robust and accessible technique for measuring mAb self-diffusion, and, by extension, microviscosity, PPI and self-association that govern mAb solution dynamics.

Dynamics of proteins confined in non-ionic bicontinuous microemulsions: a FCS study

In our present work we present an approach which allows one to confine proteins in structurally nearly identical bicontinuous microemulsions with systematically decreasing water domain size. It is shown that sub-diffusive behaviour occurs already at water domain sizes below 13 nm. However, above 13 nm normal diffusion is seen. Moreover, we compare protein diffusion in microemulsions to the transport of a much smaller fluorescent dye.

Anomalous dynamics of the endoplasmic reticulum network

Large portions of the endoplasmic reticulum (ER) in eukaryotic cells are organized as dynamic networks whose segments are connected by three-way junctions. Here we show that ER junctions move subdiffusively with signatures of fractional Brownian motion and a strong dependence on the cytoskeleton's integrity: The time-averaged mean square displacement scales as 〈r^{2}(τ)〉_{t}∼τ^{α} with α≈0.5 in untreated cells and α≈0.3 when disrupting microtubules, with successive steps being anticorrelated in both cases. We explain our observations by considering ER junctions to move like monomers in (semi)flexible polymer segments immersed in a viscoelastic environment. We also report that ER networks have a nontrivial fractal dimension d_{f}≈1.6 on mesoscopic scales and we provide evidence that the organelle's dynamics is governed by fractons.

Fluorescence Correlation Spectroscopy Reveals Efficient Cytosolic Delivery of Protein Cargo by Cell-Permeant Miniature Proteins

New methods for delivering proteins into the cytosol of mammalian cells are being reported at a rapid pace. Differentiating between these methods in a quantitative manner is difficult, however, as most assays for evaluating cytosolic protein delivery are qualitative and indirect and thus often misleading. Here we make use of fluorescence correlation spectroscopy (FCS) to determine with precision and accuracy the relative efficiencies with which seven different previously reported "cell-penetrating peptides" (CPPs) transport a model protein cargo-the self-labeling enzyme SNAP-tag-beyond endosomal membranes and into the cytosol. Using FCS, we discovered that the miniature protein ZF5.3 is an exceptional vehicle for delivering SNAP-tag to the cytosol. When delivered by ZF5.3, SNAP-tag can achieve a cytosolic concentration as high as 250 nM, generally at least 2-fold and as much as 6-fold higher than any other CPP evaluated. Additionally, we show that ZF5.3 can be fused to a second enzyme cargo-the engineered peroxidase APEX2-and reliably delivers the active enzyme to the cell interior. As FCS allows one to realistically assess the relative merits of protein transduction domains, we anticipate that it will greatly accelerate the identification, evaluation, and optimization of strategies to deliver large, intact proteins to intracellular locales.

Urea-mediated anomalous diffusion in supported lipid bilayers

Diffusion in biological membranes is seldom simply Brownian motion; instead, the rate of diffusion is dependent on the time scale of observation and so is often described as anomalous. In order to help better understand this phenomenon, model systems are needed where the anomalous diffusion of the lipid bilayer can be tuned and quantified. We recently demonstrated one such model by controlling the excluded area fraction in supported lipid bilayers (SLBs) through the incorporation of lipids derivatized with polyethylene glycol. Here, we extend this work, using urea to induce anomalous diffusion in SLBs. By tuning incubation time and urea concentration, we produce bilayers that exhibit anomalous behaviour on the same scale as that observed in biological membranes.

Time-Resolved Laurdan Fluorescence Reveals Insights into Membrane Viscosity and Hydration Levels

Membrane viscosity and hydration levels characterize the biophysical properties of biological membranes and are reflected in the rate and extent of solvent relaxation, respectively, of environmentally sensitive fluorophores such as Laurdan. Here, we first developed a method for a time-resolved general polarization (GP) analysis with fluorescence-lifetime imaging microscopy that captures both the extent and rate of Laurdan solvent relaxation. We then conducted time-resolved GP measurements with Laurdan-stained model membranes and cell membranes. These measurements revealed that cholesterol levels in lipid vesicles altered membrane hydration and viscosity, whereas curvature had little effect on either parameter. We also applied the method to the plasma membrane of live cells using a supercritical angle fluorescence objective, to our knowledge the first time fluorescence-lifetime imaging microscopy images were generated with supercritical angle fluorescence. Here, we found that local variations in membrane cholesterol most likely account for the heterogeneity of Laurdan lifetime in plasma membrane. In conclusion, time-resolved GP measurements provide additional insights into the biophysical properties of membranes.

Ligand-Induced Coupling between Oligomers of the M2 Receptor and the Gi1 Protein in Live Cells

Uncertainty over the mechanism of signaling via G protein-coupled receptors (GPCRs) relates in part to questions regarding their supramolecular structure. GPCRs and heterotrimeric G proteins are known to couple as monomers under various conditions. Many GPCRs form oligomers under many of the same conditions, however, and the biological role of those complexes is unclear. We have used dual-color fluorescence correlation spectroscopy to identify oligomers of the M₂ muscarinic receptor and of G_i1 in purified preparations and live Chinese hamster ovary cells. Measurements on differently tagged receptors (i.e., eGFP-M₂ and mCherry-M₂) and G proteins (i.e., eGFP-Gα_i1β₁γ₂ and mCherry-Gα_i1β₁γ₂) detected significant cross-correlations between the two fluorophores in each case, both in detergent micelles and in live cells, indicating that both the receptor and G_i1 can exist as homo-oligomers. Oligomerization of differently tagged G_i1 decreased upon the activation of co-expressed wild-type M₂ receptor by an agonist. Measurements on a tagged M₂ receptor (M₂-mCherry) and eGFP-Gα_i1β₁γ₂ co-expressed in live cells detected cross-correlations only in the presence of an agonist, which therefore promoted coupling of the receptor and the G protein. The effect of the agonist was retained when a fluorophore-tagged receptor lacking the orthosteric site (i.e., M₂(D103A)-mCherry) was co-expressed with the wild-type receptor and eGFP-Gα_i1β₁γ₂, indicating that the ligand acted via an oligomeric receptor. Our results point to a model in which an agonist promotes transient coupling of otherwise independent oligomers of the M₂ receptor on the one hand and of G_i1 on the other and that an activated complex leads to a reduction in the oligomeric size of the G protein. They suggest that GPCR-mediated signaling proceeds, at least in part, via oligomers.

Strong disorder leads to scale invariance in complex biological systems

Despite the innate complexity of the cell, emergent scale-invariant behavior is observed in many biological systems. We investigate one example of this phenomenon: the dynamics of large complexes in the bacterial cytoplasm. The observed dynamics of these complexes is scale invariant in three measures of dynamics: mean-squared displacement (MSD), velocity autocorrelation function, and the step-size distribution. To investigate the physical mechanism for this emergent scale invariance, we explore minimal models in which mobility is modeled as diffusion on a rough free-energy landscape in one dimension. We discover that all three scale-invariant characteristics emerge generically in the strong disorder limit. (Strong disorder is defined by the divergence of the ensemble-averaged hop time between lattice sites.) In particular, we demonstrate how the scale invariance of the relative step-size distribution can be understood from the perspective of extreme-value theory in statistics (EVT). We show that the Gumbel scale parameter is simply related to the MSD scaling parameter. The EVT mechanism of scale invariance is expected to be generic to strongly disordered systems and therefore a powerful tool for the analysis of other systems in biology and beyond.

Out of the Randomness: Correlating Noise in Biological Systems

The study of the dynamics of biological systems requires one to follow relaxation processes in time with micron-size spatial resolution. This need has led to the development of different fluorescence correlation techniques with high spatial resolution and a tremendous (from nanoseconds to seconds) temporal dynamic range. Spatiotemporal information can be obtained even on complex dynamic processes whose time evolution is not forecast by simple Brownian diffusion. Our discussion of the most recent applications of image correlation spectroscopy to the study of anomalous sub- or superdiffusion suggests that this field still requires the development of multidimensional image analyses based on analytical models or numerical simulations. We focus in particular on the framework of spatiotemporal image correlation spectroscopy and examine the critical steps in getting information on anomalous diffusive processes from the correlation maps. We point out how a dual space-time correlative analysis, in both the direct and the Fourier space, can provide quantitative information on superdiffusional processes when these are analyzed through an empirical model based on intermittent active dynamics. We believe that this dual space-time analysis, potentially amenable to mathematical treatment and to the exact fit of experimental data, could be extended to include the rich phenomenology of subdiffusive processes, thereby quantifying relevant parameters for the various motivating biological problems of interest.

Random Motion of Chromatin Is Influenced by Lamin A Interconnections

Using fluorescence correlation spectroscopy in single-plane illumination microscopy, we investigated the dynamics of chromatin in interphase mouse adult fibroblast cell nuclei under the influence of the intermediate filament protein lamin A. We find that 1) lamin A-eGFP and histone H2A-mRFP show significant comobility, indicating that their motions are clearly interconnected in the nucleus, and 2) that the random motion of histones H2A within the chromatin network is subdiffusive, i.e., the effective diffusion coefficient decreases for slow timescales. Knocking out lamin A changes the diffusion back to normal. Thus, lamin A influences the dynamics of the entire chromatin network. Our conclusion is that lamin A plays a central role in determining the viscoelasticity of the chromatin network and helping to maintain local ordering of interphase chromosomes.

Spatiotemporal Fluctuation Analysis of Molecular Diffusion Laws in Live-Cell Membranes

A present challenge of membrane biophysics is deciphering the dynamic behavior of molecules, such as lipids and proteins, within the natural environment of a living-cell membrane. Here, a fluorescence fluctuation-based approach will be described, which makes it possible to probe the "diffusion law" of molecules directly from imaging, in the form of a mean square displacement vs time-delay plot (iMSD), with no need for interpretative models. Of note, the presented approach does not require extraction of the molecular trajectories nor the use of bright fluorophores. Conversely, it can be used at high fluorophore density and with relatively dim fluorophores, such as GFP-tagged molecules transiently expressed within cells. The ability of this approach to resolve average molecular dynamic properties well below the diffraction limit will be discussed. Overall, this novel approach is proposed as a powerful tool for the determination of kinetic and thermodynamic parameters over wide spatial and temporal scales.

The Diverse Range of Possible Cell Membrane Interactions with Substrates: Drug Delivery, Interfaces and Mobility

The cell membrane has gained significant attention as a platform for the development of bio-inspired nanodevices due to its immune-evasive functionalities and copious bio-analogs. This review will examine several uses of cell membranes such as (i) therapeutic delivery carriers with or without substrates (i.e., nanoparticles and artificial polymers) that have enhanced efficiency regarding copious cargo loading and controlled release, (ii) exploiting nano-bio interfaces in membrane-coated particles from the macro- to the nanoscales, which would help resolve the biomedical issues involved in biological interfacing in the body, and (iii) its effects on the mobility of bio-moieties such as lipids and/or proteins in cell membranes, as discussed from a biophysical perspective. We anticipate that this review will influence both the development of novel anti-phagocytic delivery cargo and address biophysical problems in soft and complex cell membrane.

The imaging FCS diffusion law in the presence of multiple diffusive modes

The cellular plasma membrane is the barrier over which cells exchange materials and communicate with their surroundings, and thus plays the central role in cellular sensing and metabolism. Therefore, the investigation of plasma membrane organization and dynamics is required for understanding of cellular functions. The plasma membrane is a heterogeneous matrix. The presence of structures such as lipid and protein domains and the cytoskeleton meshwork poses a hindrance to the free diffusion of membrane associated biomolecules. However, these domains and the cytoskeleton meshwork barriers are below the optical diffraction limit with potentially short lifetimes and are not easily detected even in super-resolution microscopy. Therefore, dynamic measurements are often used to indirectly prove the existence of domains and barriers by analyzing the mode of diffusion of probe molecules. One of these tools is the Fluorescence Correlation Spectroscopy (FCS) diffusion law. The FCS diffusion law is a plot of diffusion time (τ_d) versus observation area. For at least three different diffusive modes - free, domain confined, and meshwork hindered hop diffusion - the expected plots have been characterized, typically by its y-intercept (τ₀) when fit with a linear model, and have been verified in many cases. However, a description of τ₀ has only been given for pure diffusive modes. But in many experimental cases it is not evident that a protein will undergo only one kind of diffusion, and thus the interpretation of the τ₀ value is problematic. Here, we therefore address the question about the absolute value of τ₀ in the case of complex diffusive modes, i.e. when either one molecule is domain confined and cytoskeleton hindered or when two molecules exhibit different diffusive behavior at the same position in a sample. In addition, we investigate how τ₀ changes when the diffusive mode of a probe alters upon disruption of domains or the cytoskeleton by drug treatments. By a combination of experimental studies and simulations, we show that τ₀ is not influenced equally by the different diffusive modes as typically found in cellular environments, and that it is the relative change of τ₀ rather than its absolute value that provides information on the mode of diffusion.

Tetramethylpyrazine-Loaded Hydrogels: Preparation, Penetration Through a Subcutaneous-Mucous-Membrane Model, and a Molecular Dynamics Simulation

Tetramethylpyrazine (TMP) was extracted from Ligusticum chuanxiong hort. The compound is known to have a variety of medicinal functions; in particular, it is used for the treatment of cerebral ischemic diseases. TMP-loaded hydrogels offer an excellent preparation with the capacity to bypass the blood-brain barrier, allowing treatment of the brain through intranasal administration. We prepared TMP-loaded hydrogels using carbomer 940 and evaluated the release of TMP from the hydrogel. We determined the release rate using Franz-type diffusion cell experiments with a subcutaneous-mucous-membrane model and also by a molecular dynamics (MD) simulation. In general, the former method was more complicated than the latter was. The dynamic behavior of TMP release from the hydrogel was revealed by analysis of the mean square displacement of the trajectory in the MD simulation. The coefficient of TMP diffusion from the hydrogel was calculated at different temperatures (277, 298, and 310 K) by using MD software. The results showed that the coefficient of diffusion increased with an increase in temperature. This trend was observed both experimentally and in the MD simulation. Therefore, the MD simulation was a complementary method to verify the experimental data.

Quantifying non-ergodicity of anomalous diffusion with higher order moments

Anomalous diffusion is being discovered in a fast growing number of systems. The exact nature of this anomalous diffusion provides important information on the physical laws governing the studied system. One of the central properties analysed for finite particle motion time series is the intrinsic variability of the apparent diffusivity, typically quantified by the ergodicity breaking parameter EB. Here we demonstrate that frequently EB is insufficient to provide a meaningful measure for the observed variability of the data. Instead, important additional information is provided by the higher order moments entering by the skewness and kurtosis. We analyse these quantities for three popular anomalous diffusion models. In particular, we find that even for the Gaussian fractional Brownian motion a significant skewness in the results of physical measurements occurs and needs to be taken into account. Interestingly, the kurtosis and skewness may also provide sensitive estimates of the anomalous diffusion exponent underlying the data. We also derive a new result for the EB parameter of fractional Brownian motion valid for the whole range of the anomalous diffusion parameter. Our results are important for the analysis of anomalous diffusion but also provide new insights into the theory of anomalous stochastic processes.

Structural and dynamic inhomogeneities induced by curvature gradients in elliptic colloidal halos of paramagnetic particles

Paramagnetic colloidal particles distributed along an ellipse are used as a model system to study the effects of curvature gradients on the structure and dynamics of colloids in curved manifolds. Unlike what happens for circular and spherical systems, in the present case, the equilibrium one-particle distribution function displays inhomogeneities due to the changing curvature along the ellipse. The ensuing effects on the two-body correlations are also analyzed, leading to the observation of anisotropic and long-ranged effects. Another noticeable consequence is the slowing down of the self-diffusion of these particles, which for large eccentricities may induce metastable states; this is evaluated by means of the time-dependent self-distribution.

Nonscaling displacement distributions as may be seen in fluorescence correlation spectroscopy

A continuous time random walk (CTRW) model with waiting times following the Lévy-stable distribution with exponential cutoff in equilibrium is a simple theoretical model giving rise to normal, yet non-Gaussian, diffusion. The distribution of the particles' displacements is explicitly time dependent and does not scale. Since fluorescent correlation spectroscopy (FCS) is often used to investigate diffusion processes, we discuss the influence of this lack of scaling on the possible outcome of the FCS measurements and calculate the FCS autocorrelation curves for such equilibrated CTRWs. The results show that although the deviations from Gaussian behavior may be detected when analyzing the short- and long-time asymptotic behavior of the corresponding curves, their bodies are still perfectly fitted by the fit forms used for normal diffusion. The diffusion coefficients obtained from the fits may however differ considerably from the true tracer diffusion coefficients as describing the time dependence of the mean squared displacement.

Disentangling Random Motion and Flow in a Complex Medium

We describe a technique for deconvolving the stochastic motion of particles from large-scale fluid flow in a dynamic environment such as that found in living cells. The method leverages the separation of timescales to subtract out the persistent component of motion from single-particle trajectories. The mean-squared displacement of the resulting trajectories is rescaled so as to enable robust extraction of the diffusion coefficient and subdiffusive scaling exponent of the stochastic motion. We demonstrate the applicability of the method for characterizing both diffusive and fractional Brownian motion overlaid by flow and analytically calculate the accuracy of the method in different parameter regimes. This technique is employed to analyze the motion of lysosomes in motile neutrophil-like cells, showing that the cytoplasm of these cells behaves as a viscous fluid at the timescales examined.