Resolving mixed mechanisms of protein subdiffusion at the T cell plasma membrane

Left-right Myosin-Is, Myosin1C, and Myosin1D exhibit distinct single molecule behaviors on the plasma membrane of Drosophila macrophages

Left-right (LR) asymmetry is crucial for animal development, particularly in Drosophila where LR-asymmetric morphogenesis of organs hinges on cellular-level chirality, termed cell chirality. In this species, two class I myosins, Myosin1D (Myo1D), and Myosin1C (Myo1C), respectively determine dextral (wild type) and sinistral (mirror image) cell chirality. Previous studies demonstrated Myo1D's ability to propel F-actin in leftward circles during in vitro gliding assays, suggesting its mechanochemical role in defining dextral chirality. Conversely, Myo1C propels F-actin without exhibiting LR-directional preference in this assay, suggesting at other properties governing sinistral chirality. Given the interaction of Myo1D and Myo1C with the membrane, we hypothesized that differences in their membrane behaviors might be critical in dictating their dextral or sinistral activities. In this study, employing single-molecule imaging analyses, we investigated the dynamic behaviors of Myo1D and Myo1C on the plasma membrane. Our findings revealed that Myo1C exhibits a significantly greater proportion of slow-diffusing population compared to Myo1D. Importantly, this characteristic was contingent upon both head and tail domains of Myo1C. The distinct diffusion patterns of Myo1D and Myo1C did not exert mutual influence on each other. This divergence in membrane diffusion between Myo1D and Myo1C may be crucial for dictating cell and organ chirality.

Simulation study on the effect of polydisperse nanoparticles on polymer diffusion in crowded environments

The diffusion of polymer chains in a crowded environment with large and small immobile, attractive nanoparticles (NPs) is studied using Langevin dynamics simulations. For orderly distributed NPs on the simple cubic lattice, our results show that the diffusion of polymer chains is dependent on the NP-NP distance or lattice distance d. At low d where NPs are placed closely, subdiffusion occurs at a sufficiently high polydispersity of NPs, PD. Both the apparent diffusion coefficient and subdiffusion exponent of polymer chains decrease with increasing PD, attributed to the adsorption of polymers on NP clusters formed by larger NPs. At large d, normal diffusion is always observed, and the diffusion coefficient increases with increasing PD. The reason is that, at high PD, the difference between single large NP adsorption and double large NP adsorption is reduced, which increases the exchange of a polymer between the two adsorption states. Finally, the impact of size polydispersity of NPs on the diffusion of polymer chains in a crowded environment with randomly distributed NPs is also investigated. The results show that the position disorder of NPs enhances the subdiffusion of the system.

Burst of hopping trafficking correlated reversible dynamic interactions between lipid droplets and mitochondria under starvation

Dynamic membrane contacts between lipid droplets (LDs) and mitochondria play key roles in lipid metabolism and energy homeostasis. Understanding the dynamics of LDs under energy stimulation is thereby crucial to disclosing the metabolic mechanism. Here, the reversible interactions between LDs and mitochondria are tracked in real-time using a robust LDs-specific fluorescent probe (LDs-Tags). Through tracking the dynamics of LDs at the single-particle level, spatiotemporal heterogeneity is revealed. LDs in starved cells communicate and integrate their activities (i.e., lipid exchange) through a membrane contact site-mediated mechanism. Thus the diffusion is intermittently alternated between active and confined states. Statistical analysis shows that the translocation of LDs in response to starvation stress is non-Gaussian, and obeys nonergodic-like behavior. These results provide deep understanding of the anomalous diffusion of LDs in living cells, and also afford guidance for rationally designing efficient transporter.

Transition between Different Diffusion Modes of Individual Lipids during the Membrane-Specific Action of As-CATH4 Peptides

The cell membrane permeabilization ability of immune defense antimicrobial peptides (AMPs) is widely applied in biomedicine. Although the mechanisms of peptide-membrane interactions have been widely investigated, analyses at the molecular level are still lacking. Herein, the membrane-specific action of a native AMP, As-CATH4, is investigated using a single-lipid tracking method in combination with live cell and model membrane assays conducted at different scales. The peptide-membrane interaction process is characterized by analyzing single-lipid diffusion behaviors. As-CATH4 exhibits potent antimicrobial activity through bacterial membrane permeabilization, with moderate cytotoxicity against mammalian cells. In-plane diffusion analyses of individual lipids show that the lipid molecules exhibit non-Gaussian and heterogeneous diffusion behaviors in both pristine and peptide-treated membranes, which can be decomposed into two Gaussian subgroups corresponding to normal- and slow-diffusive lipids. Assessment of the temporal evolution of these two diffusion modes of lipids reveal that the peptide action states of As-CATH4 include surface binding, transmembrane defect formation, and dynamic equilibrium. The action mechanisms of As-CATH4 at varying concentrations and against different membranes are distinguished. This work resolves the simultaneous mixed diffusion mechanisms of single lipids in biomimetic cell membranes, especially during dynamic membrane permeabilization by AMPs.

Non-Gaussian Diffusion of Individual Lipids Unveils the Unique Peptide-Membrane Interaction Dynamics

The dynamics of protein (or peptide)-membrane interactions plays a central role in cellular functions; however, the underlying mechanisms remain unclear. Herein, through analyzing the diffusion of individual lipids in a bilayer membrane during the membrane actions of typical peptides (e.g., pore-forming peptide melittin and cell-penetrating peptide TAT) at varying concentrations, the spatial heterogeneity as well as temporal dynamics of lipid motions were investigated which showed close correlation with the peptide action mechanism. Specifically, the spatial heterogeneity of lipid diffusion was characterized by the non-Gaussianity of lipid trajectories, which was further decomposed into two basic diffusion modes; moreover, the temporal evolution of the Gaussian fitting parameters provided quantitative information on the varying metastable interaction states between peptides and the membrane (e.g., peptide landing, membrane insertion, and equilibrium). Generally, this work gives an insight into the correlation between single-lipid diffusion and function-realization of membrane-active peptides.

Extracting, quantifying, and comparing dynamical and biomechanical properties of living matter through single particle tracking

A panoply of new tools for tracking single particles and molecules has led to an explosion of experimental data, leading to novel insights into physical properties of living matter governing cellular development and function, health and disease. In this Perspective, we present tools to investigate the dynamics and mechanics of living systems from the molecular to cellular scale via single-particle techniques. In particular, we focus on methods to measure, interpret, and analyse complex data sets that are associated with forces, materials properties, transport, and emergent organisation phenomena within biological and soft-matter systems. Current approaches, challenges, and existing solutions in the associated fields are outlined in order to support the growing community of researchers at the interface of physics and the life sciences. Each section focuses not only on the general physical principles and the potential for understanding living matter, but also on details of practical data extraction and analysis, discussing limitations, interpretation, and comparison across different experimental realisations and theoretical frameworks. Particularly relevant results are introduced as examples. While this Perspective describes living matter from a physical perspective, highlighting experimental and theoretical physics techniques relevant for such systems, it is also meant to serve as a solid starting point for researchers in the life sciences interested in the implementation of biophysical methods.

mGluR5 is transiently confined in perisynaptic nanodomains to shape synaptic function

The unique perisynaptic distribution of postsynaptic metabotropic glutamate receptors (mGluRs) at excitatory synapses is predicted to directly shape synaptic function, but mechanistic insight into how this distribution is regulated and impacts synaptic signaling is lacking. We used live-cell and super-resolution imaging approaches, and developed molecular tools to resolve and acutely manipulate the dynamic nanoscale distribution of mGluR5. Here we show that mGluR5 is dynamically organized in perisynaptic nanodomains that localize close to, but not in the synapse. The C-terminal domain of mGluR5 critically controlled perisynaptic confinement and prevented synaptic entry. We developed an inducible interaction system to overcome synaptic exclusion of mGluR5 and investigate the impact on synaptic function. We found that mGluR5 recruitment to the synapse acutely increased synaptic calcium responses. Altogether, we propose that transient confinement of mGluR5 in perisynaptic nanodomains allows flexible modulation of synaptic function.

Time-averaging and nonergodicity of reset geometric Brownian motion with drift

How do near-bankruptcy events in the past affect the dynamics of stock-market prices in the future? Specifically, what are the long-time properties of a time-local exponential growth of stock-market prices under the influence of stochastically occurring economic crashes? Here, we derive the ensemble- and time-averaged properties of the respective "economic" or geometric Brownian motion (GBM) with a nonzero drift exposed to a Poissonian constant-rate price-restarting process of "resetting." We examine-based both on thorough analytical calculations and on findings from systematic stochastic computer simulations-the general situation of reset GBM with a nonzero [positive] drift and for all special cases emerging for varying parameters of drift, volatility, and reset rate in the model. We derive and summarize all short- and long-time dependencies for the mean-squared displacement (MSD), the variance, and the mean time-averaged MSD (TAMSD) of the process of Poisson-reset GBM under the conditions of both rare and frequent resetting. We consider three main regions of model parameters and categorize the crossovers between different functional behaviors of the statistical quantifiers of this process. The analytical relations are fully supported by the results of computer simulations. In particular, we obtain that Poisson-reset GBM is a nonergodic stochastic process, with generally MSD(Δ)≠TAMSD(Δ) and Variance(Δ)≠TAMSD(Δ) at short lag times Δ and for long trajectory lengths T. We investigate the behavior of the ergodicity-breaking parameter in each of the three regions of parameters and examine its dependence on the rate of reset at Δ/T≪1. Applications of these theoretical results to the analysis of prices of reset-containing options are pertinent.

Heterogeneous nanoscopic lipid diffusion in the live cell membrane and its dependency on cholesterol

Cholesterol plays a unique role in the regulation of membrane organization and dynamics by modulating the membrane phase transition at the nanoscale. Unfortunately, due to their small sizes and dynamic nature, the effects of cholesterol-mediated membrane nanodomains on membrane dynamics remain elusive. Here, using ultrahigh-speed single-molecule tracking with advanced optical microscope techniques, we investigate the diffusive motion of single phospholipids in the live cell plasma membrane at the nanoscale and its dependency on the cholesterol concentration. We find that both saturated and unsaturated phospholipids undergo anomalous subdiffusion on the length scale of 10-100 nm. The diffusion characteristics exhibit considerable variations in space and in time, indicating that the nanoscopic lipid diffusion is highly heterogeneous. Importantly, through the statistical analysis, apparent dual-mobility subdiffusion is observed from the mixed diffusion behaviors. The measured subdiffusion agrees well with the hop diffusion model that represents a diffuser moving in a compartmentalized membrane created by the cytoskeleton meshwork. Cholesterol depletion diminishes the lipid mobility with an apparently smaller compartment size and a stronger confinement strength. Similar results are measured with temperature reduction, suggesting that the more heterogeneous and restricted diffusion is connected to the nanoscopic membrane phase transition. Our conclusion supports the model that cholesterol depletion induces the formation of gel-phase, solid-like membrane nanodomains. These nanodomains undergo restricted diffusion and act as diffusion obstacles to the membrane molecules that are excluded from the nanodomains. This work provides the experimental evidence that the nanoscopic lipid diffusion in the cell plasma membrane is heterogeneous and sensitive to the cholesterol concentration and temperature, shedding new light on the regulation mechanisms of nanoscopic membrane dynamics.

Two GPSes in a Ball: Deciphering the Endosomal Tug-of-War Using Plasmonic Dark-Field STORM

Live video recording of intracellular material transport is a promising means of deciphering the fascinating underlying mechanisms driving life at the molecular level. Such technology holds the key to realizing real-time observation at appropriate resolutions in three-dimensional (3D) space within living cells. Here, we report an optical microscopic method for probing endosomal dynamics with proper spatiotemporal resolution within 3D space in live cells: plasmonic dark-field STORM (pdf-STORM). We first confirmed that pdf-STORM has a spatial resolution comparable to that of scanning electron microscopy. Additionally, by observing two optical probes within a single organelle, we were able to track rotational movements and demonstrate the feasibility of using pdf-STORM to observe the angular displacements of an endosome during a "tug-of-war" over an extended period. Finally, we show various biophysical parameters of the hitherto unelucidated dynamics of endosomes-angular displacement is discontinuous and y-axis movement predominates and follows a long-tail distribution.

Precise Detection and Visualization of Nanoscale Temporal Confinement in Single-Molecule Tracking Analysis

The plasma membrane consists of a diverse mixture of molecules that dynamically assemble into a highly non-random organization. The formation of nanoscale domains in the membrane is of particular interest as these domains underlie critical cellular functions. Single-molecule tracking is a powerful method to detect and quantify molecular motion at high temporal and spatial resolution and has therefore been instrumental in understanding mechanisms that underlie membrane organization. In single-molecule trajectories, regions of temporal confinement can be determined that might reveal interesting biophysical interactions important for domain formation. However, analytical methods for the detection of temporal confinement in single-molecule trajectories depend on a variety of parameters that heavily depend on experimental factors and the influence of these factors on the performance of confinement detection are not well understood. Here, we present elaborate confinement analyses on simulated random walks and trajectories that display transient confined behavior to optimize the parameters for different experimental conditions. Furthermore, we demonstrate a heatmap visualization tool that allows spatial mapping of confinement hotspots relative to subcellular markers. Using these optimized tools, we reliably detected subdiffusive behavior of different membrane components and observed differences in the confinement behavior of two types of glutamate receptors in neurons. This study will help in further understanding the dynamic behavior of the complex membrane and its role in cellular functioning.

Role of ergodicity, aging, and Gaussianity in resolving the origins of biomolecule subdiffusion

The internal motions of biomolecules are essential to their function. Although biological macromolecules conventionally show subdiffusive dynamics, only recently has subdiffusion been associated with non-ergodicity. These findings have stimulated new questions in biophysics and statistical mechanics. Is non-ergodic subdiffusion a general strategy shared by biomolecules? What underlying mechanisms are responsible for it? Here, we performed extensive molecular dynamics (MD) simulations to characterize the internal dynamics of six different biomolecules, ranging from single or double-stranded DNA, a single domain protein (KRAS), two globular proteins (PGK and SHP2), to an intrinsically disordered protein (SNAP-25). We found that the subdiffusive behavior of these biomolecules falls into two classes. The internal motion of the first three cases is ergodic subdiffusion and can be interpreted by fractional Brownian motion (FBM), while the latter three cases involve non-ergodic subdiffusion and can be modeled by mixed origins of continuous-time random walk (CTRW) and FBM.

Effect of biphosphate salt on dipalmitoylphosphatidylcholine bilayer deformation by Tat polypeptide

Translocation of positively charged cell penetrating peptides (CPP) through cell membrane is important in drug delivery. Here we report all-atom molecular dynamics simulations to investigate how a biphosphate salt in a solvent affects the interaction of a CPP, HIV-1 Tat peptide with model dipalmitoylphosphatidylcholine (DPPC) lipid bilayer. Tat peptide has a large number of basic arginines and a couple of polar glutamines. We observe that in absence of salt, the basic residues of the polypeptide get localized in the vicinity of the membrane without altering the bilayer properties much; polypeptide induce local thinning of the bilayer membrane at the area of localization. In presence of biphosphate salt, the basic residues, dressed by the biphosphate ions, are repelled by the phosphate head groups of the lipid molecules. However, polar glutamine prefers to stay in the vicinity of the bilayer. This leads to larger local bilayer thickness at the contact point by the polar residue and non-uniform bilayer thickness profile. The thickness deformation of bilayer structure disappears upon mutating the polar residue, suggesting importance of the polar residue in bilayer deformation. Our studies point to control bilayer deformation by appropriate peptide sequence and solvent conditions.

Subsynaptic mobility of presynaptic mGluR types is differentially regulated by intra- and extracellular interactions

Presynaptic metabotropic glutamate receptors (mGluRs) are essential for the control of synaptic transmission. However, how the subsynaptic dynamics of these receptors is controlled and contributes to synaptic signaling remain poorly understood quantitatively. Particularly, since the affinity of individual mGluR subtypes for glutamate differs considerably, the activation of mGluR subtypes critically depends on their precise subsynaptic distribution. Here, using superresolution microscopy and single-molecule tracking, we unravel novel molecular mechanisms that control the nanoscale distribution and mobility of presynaptic mGluRs in hippocampal neurons. We demonstrate that the high-affinity group II receptor mGluR2 localizes diffusely along the axon, and is highly mobile, while the low-affinity group III receptor mGluR7 is stably anchored at the active zone. We demonstrate that intracellular interactions modulate surface diffusion of mGluR2, while immobilization of mGluR7 at the active zone relies on its extracellular domain. Receptor activation or increases in synaptic activity do not alter the surface mobility of presynaptic mGluRs. Finally, computational modeling of presynaptic mGluR activity revealed that this particular nanoscale arrangement directly impacts their ability to modulate neurotransmitter release. Altogether, this study demonstrates that distinct mechanisms control surface mobility of presynaptic mGluRs to contribute differentially to glutamatergic synaptic transmission.

Experimental evidence for long-distance electrodynamic intermolecular forces

Both classical and quantum electrodynamics predict the existence of dipole-dipole long-range electrodynamic intermolecular forces; however, these have never been hitherto experimentally observed. The discovery of completely new and unanticipated forces acting between biomolecules could have considerable impact on our understanding of the dynamics and functioning of the molecular machines at work in living organisms. Here, using two independent experiments, on the basis of different physical effects detected by fluorescence correlation spectroscopy and terahertz spectroscopy, respectively, we demonstrate experimentally the activation of resonant electrodynamic intermolecular forces. This is an unprecedented experimental proof of principle of a physical phenomenon that, having been observed for biomacromolecules and with long-range action (up to 1000 Å), could be of importance for biology. In addition to thermal fluctuations that drive molecular motion randomly, these resonant (and thus selective) electrodynamic forces may contribute to molecular encounters in the crowded cellular space.

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.

Anomalous diffusion, aging, and nonergodicity of scaled Brownian motion with fractional Gaussian noise: overview of related experimental observations and models

How does a systematic time-dependence of the diffusion coefficient $D (t)$ affect the ergodic and statistical characteristics of fractional Brownian motion (FBM)? Here, we examine how the behavior of the...

Non-ergodicity of a globular protein extending beyond its functional timescale

Internal motions of folded proteins have been assumed to be ergodic, i.e., that the dynamics of a single protein molecule averaged over a very long time resembles that of an ensemble. Here, by performing single-molecule fluorescence resonance energy transfer (smFRET) experiments and molecular dynamics (MD) simulations of a multi-domain globular protein, cytoplasmic protein-tyrosine phosphatase (SHP2), we demonstrate that the functional inter-domain motion is observationally non-ergodic over the time spans 10⁻¹² to 10⁻⁷ s and 10⁻¹ to 10² s. The difference between observational non-ergodicity and simple non-convergence is discussed. In comparison, a single-strand DNA of similar size behaves ergodically with an energy landscape resembling a one-dimensional linear chain. The observed non-ergodicity results from the hierarchical connectivity of the high-dimensional energy landscape of the protein molecule. As the characteristic time for the protein to conduct its dephosphorylation function is ∼10 s, our findings suggest that, due to the non-ergodicity, individual, seemingly identical protein molecules can be dynamically and functionally different.

Internal motions of folded proteins have been assumed to be ergodic, i.e., that the dynamics of a single protein molecule averaged over a very long time resembles that of an ensemble.

A deep learning-based approach to model anomalous diffusion of membrane proteins: the case of the nicotinic acetylcholine receptor

We present a concatenated deep-learning multiple neural network system for the analysis of single-molecule trajectories. We apply this machine learning-based analysis to characterize the translational diffusion of the nicotinic acetylcholine receptor at the plasma membrane, experimentally interrogated using superresolution optical microscopy. The receptor protein displays a heterogeneous diffusion behavior that goes beyond the ensemble level, with individual trajectories exhibiting more than one diffusive state, requiring the optimization of the neural networks through a hyperparameter analysis for different numbers of steps and durations, especially for short trajectories (<50 steps) where the accuracy of the models is most sensitive to localization errors. We next use the statistical models to test for Brownian, continuous-time random walk and fractional Brownian motion, and introduce and implement an additional, two-state model combining Brownian walks and obstructed diffusion mechanisms, enabling us to partition the two-state trajectories into segments, each of which is independently subjected to multiple analysis. The concatenated multi-network system evaluates and selects those physical models that most accurately describe the receptor's translational diffusion. We show that the two-state Brownian-obstructed diffusion model can account for the experimentally observed anomalous diffusion (mostly subdiffusive) of the population and the heterogeneous single-molecule behavior, accurately describing the majority (72.5 to 88.7% for α-bungarotoxin-labeled receptor and between 73.5 and 90.3% for antibody-labeled molecules) of the experimentally observed trajectories, with only ~15% of the trajectories fitting to the fractional Brownian motion model.

Time averaging and emerging nonergodicity upon resetting of fractional Brownian motion and heterogeneous diffusion processes

How different are the results of constant-rate resetting of anomalous-diffusion processes in terms of their ensemble-averaged versus time-averaged mean-squared displacements (MSDs versus TAMSDs) and how does stochastic resetting impact nonergodicity? We examine, both analytically and by simulations, the implications of resetting on the MSD- and TAMSD-based spreading dynamics of particles executing fractional Brownian motion (FBM) with a long-time memory, heterogeneous diffusion processes (HDPs) with a power-law space-dependent diffusivity D(x)=D_{0}|x|^{γ} and their "combined" process of HDP-FBM. We find, inter alia, that the resetting dynamics of originally ergodic FBM for superdiffusive Hurst exponents develops disparities in scaling and magnitudes of the MSDs and mean TAMSDs indicating weak ergodicity breaking. For subdiffusive HDPs we also quantify the nonequivalence of the MSD and TAMSD and observe a new trimodal form of the probability density function. For reset FBM, HDPs and HDP-FBM we compute analytically and verify by simulations the short-time MSD and TAMSD asymptotes and long-time plateaus reminiscent of those for processes under confinement. We show that certain characteristics of these reset processes are functionally similar despite a different stochastic nature of their nonreset variants. Importantly, we discover nonmonotonicity of the ergodicity-breaking parameter EB as a function of the resetting rate r. For all reset processes studied we unveil a pronounced resetting-induced nonergodicity with a maximum of EB at intermediate r and EB∼(1/r)-decay at large r. Alongside the emerging MSD-versus-TAMSD disparity, this r-dependence of EB can be an experimentally testable prediction. We conclude by discussing some implications to experimental systems featuring resetting dynamics.

Pontryagin Maximum Principle for Distributed-Order Fractional Systems

We consider distributed-order non-local fractional optimal control problems with controls taking values on a closed set and prove a strong necessary optimality condition of Pontryagin type. The possibility that admissible controls are subject to pointwise constraints is new and requires more sophisticated techniques to include a maximality condition. We start by proving results on continuity of solutions due to needle-like control perturbations. Then, we derive a differentiability result on the state solutions with respect to the perturbed trajectories. We end by stating and proving the Pontryagin maximum principle for distributed-order fractional optimal control problems, illustrating its applicability with an example.

Spectral Analysis of ATP-Dependent Mechanical Vibrations in T Cells

Mechanical vibrations affect multiple cell properties, including its diffusivity, entropy, internal content organization, and thus-function. Here, we used Differential Interference Contrast (DIC), confocal, and Total Internal Reflection Fluorescence (TIRF) microscopies to study mechanical vibrations in live (Jurkat) T cells. Vibrations were measured via the motion of intracellular particles and plasma membrane. These vibrations depend on adenosine triphosphate (ATP) consumption and on Myosin II activity. We then used spectral analysis of these vibrations to distinguish the effects of thermal agitation, ATP-dependent mechanical work and cytoskeletal visco-elasticity. Parameters of spectral analyses could be related to mean square displacement (MSD) analyses with specific advantages in characterizing intracellular mechanical work. We identified two spectral ranges where mechanical work dominated vibrations of intracellular components: 0-3 Hz for intracellular particles and the plasma-membrane, and 100-150 Hz for the plasma-membrane. The 0-3 Hz vibrations of the cell membrane that we measured in an experimental model of immune synapse (IS) are expected to affect the IS formation and function in effector cells. It may also facilitate immunological escape of extensively vibrating malignant cells.

Cell surface-localized imaging and sensing

Systematically dissecting the molecular basis of the cell surface as well as its related biological activities is considered as one of the most cutting-edge fields in fundamental sciences. The advent of various advanced cell imaging techniques allows us to gain a glimpse of how the cell surface is structured and coordinated with other cellular components to respond to intracellular signals and environmental stimuli. Nowadays, cell surface-related studies have entered a new era featured by a redirected aim of not just understanding but artificially manipulating/remodeling the cell surface properties. To meet this goal, biologists and chemists are intensely engaged in developing more maneuverable cell surface labeling strategies by exploiting the cell's intrinsic biosynthetic machinery or direct chemical/physical binding methods for imaging, sensing, and biomedical applications. In this review, we summarize the recent advances that focus on the visualization of various cell surface structures/dynamics and accurate monitoring of the microenvironment of the cell surface. Future challenges and opportunities in these fields are discussed, and the importance of cell surface-based studies is highlighted.

Characterising the diffusion of biological nanoparticles on fluid and cross-linked membranes

Tracing the motion of macromolecules, viruses, and nanoparticles adsorbed onto cell membranes is currently the most direct way of probing the complex dynamic interactions behind vital biological processes, including cell signalling, trafficking, and viral infection. The resulting trajectories are usually consistent with some type of anomalous diffusion, but the molecular origins behind the observed anomalous behaviour are usually not obvious. Here we use coarse-grained molecular dynamics simulations to help identify the physical mechanisms that can give rise to experimentally observed trajectories of nanoscopic objects moving on biological membranes. We find that diffusion on membranes of high fluidities typically results in normal diffusion of the adsorbed nanoparticle, irrespective of the concentration of receptors, receptor clustering, or multivalent interactions between the particle and membrane receptors. Gel-like membranes on the other hand result in anomalous diffusion of the particle, which becomes more pronounced at higher receptor concentrations. This anomalous diffusion is characterised by local particle trapping in the regions of high receptor concentrations and fast hopping between such regions. The normal diffusion is recovered in the limit where the gel membrane is saturated with receptors. We conclude that hindered receptor diffusivity can be a common reason behind the observed anomalous diffusion of viruses, vesicles, and nanoparticles adsorbed on cell and model membranes. Our results enable direct comparison with experiments and offer a new route for interpreting motility experiments on cell membranes.

Tracer Diffusion in Tightly-Meshed Homogeneous Polymer Networks: A Brownian Dynamics Simulation Study

We report Brownian dynamics simulations of tracer diffusion in regularly crosslinked polymer networks in order to elucidate the transport of a tracer particle in polymer networks. The average mesh size of homogeneous polymer networks is varied by assuming different degrees of crosslinking or swelling, and the size of a tracer particle is comparable to the average mesh size. Simulation results show subdiffusion of a tracer particle at intermediate time scales and normal diffusion at long times. In particular, the duration of subdiffusion is significantly prolonged as the average mesh size decreases with increasing degree of crosslinking, for which long-time diffusion occurs via the hopping processes of a tracer particle after undergoing rattling motions within a cage of the network mesh for an extended period of time. On the other hand, the cage dynamics and hopping process are less pronounced as the mesh size decreases with increasing polymer volume fractions. The interpretation is provided in terms of fluctuations in network mesh size: at higher polymer volume fractions, the network fluctuations are large enough to allow for collective, structural changes of network meshes, so that a tracer particle can escape from the cage, whereas, at lower volume fractions, the fluctuations are so small that a tracer particle remains trapped within the cage for a significant period of time before making infrequent jumps out of the cage. This work suggests that fluctuation in mesh size, as well as average mesh size itself, plays an important role in determining the dynamics of molecules and nanoparticles that are embedded in tightly meshed polymer networks.

Diffusion of DNA-Binding Species in the Nucleus: A Transient Anomalous Subdiffusion Model

Single-particle tracking experiments have measured escape times of DNA-binding species diffusing in living cells: CRISPR-Cas9, TetR, and LacI. The observed distribution is a truncated power law. Working backward from the experimental results, the observed distribution appears inconsistent with a Gaussian distribution of binding energies. Working forward, the observed distribution leads to transient anomalous subdiffusion, in which diffusion is anomalous at short times and normal at long times, here only mildly anomalous. Monte Carlo simulations are used to characterize the time-dependent diffusion coefficient D(t) in terms of the anomalous exponent α, the crossover time tcross, and the limits D(0) and D(∞) and to relate these quantities to the escape time distribution. The simplest interpretations identify the escape time as the actual binding time to DNA or the period of one-dimensional diffusion on DNA in the standard model combining one-dimensional and three-dimensional search, but a more complicated interpretation may be required. The model has several implications for cell biophysics. 1) The initial anomalous regime represents the search of the DNA-binding species for its target DNA sequence. 2) Non-target DNA sites have a significant effect on search kinetics. False positives in bioinformatic searches of the genome are potentially rate-determining in vivo. For simple binding, the search would be speeded if false-positive sequences were eliminated from the genome. 3) Both binding and obstruction affect diffusion. Obstruction ought to be measured directly, using as the primary probe the DNA-binding species with the binding site inactivated and eGFP as a calibration standard among laboratories and cell types. 4) Overexpression of the DNA-binding species reduces anomalous subdiffusion because the deepest binding sites are occupied and unavailable. 5) The model provides a coarse-grained phenomenological description of diffusion of a DNA-binding species, useful in larger-scale modeling of kinetics, FCS, and FRAP.

Quenched and annealed disorder mechanisms in comb models with fractional operators

Recent experimental findings on anomalous diffusion have demanded novel models that combine annealed (temporal) and quenched (spatial or static) disorder mechanisms. The comb model is a simplified description of diffusion on percolation clusters, where the comblike structure mimics quenched disorder mechanisms and yields a subdiffusive regime. Here we extend the comb model to simultaneously account for quenched and annealed disorder mechanisms. To do so, we replace usual derivatives in the comb diffusion equation by different fractional time-derivative operators and the conventional comblike structure by a generalized fractal structure. Our hybrid comb models thus represent a diffusion where different comblike structures describe different quenched disorder mechanisms, and the fractional operators account for various annealed disorder mechanisms. We find exact solutions for the diffusion propagator and mean square displacement in terms of different memory kernels used for defining the fractional operators. Among other findings, we show that these models describe crossovers from subdiffusion to Brownian or confined diffusions, situations emerging in empirical results. These results reveal the critical role of interactions between geometrical restrictions and memory effects on modeling anomalous diffusion.

Increased Confinement and Polydispersity of STIM1 and Orai1 after Ca2+ Store Depletion

STIM1 (a Ca²⁺ sensor in the endoplasmic reticulum (ER) membrane) and Orai1 (a pore-forming subunit of the Ca²⁺-release-activated calcium channel in the plasma membrane) diffuse in the ER membrane and plasma membrane, respectively. Upon depletion of Ca²⁺ stores in the ER, STIM1 translocates to the ER-plasma membrane junction and binds Orai1 to trigger store-operated Ca²⁺ entry. However, the motion of STIM1 and Orai1 during this process and its roles to Ca²⁺ entry is poorly understood. Here, we report real-time tracking of single STIM1 and Orai1 particles in the ER membrane and plasma membrane in living cells before and after Ca²⁺ store depletion. We found that the motion of single STIM1 and Orai1 particles exhibits anomalous diffusion both before and after store depletion, and their mobility-measured by the radius of gyration of the trajectories, mean-square displacement, and generalized diffusion coefficient-decreases drastically after store depletion. We also found that the measured displacement distribution is non-Gaussian, and the non-Gaussian parameter drastically increases after store depletion. Detailed analyses and simulations revealed that single STIM1 and Orai1 particles are confined in the compartmentalized membrane both before and after store depletion, and the changes in the motion after store depletion are explained by increased confinement and polydispersity of STIM1-Orai1 complexes formed at the ER-plasma membrane junctions. Further simulations showed that this increase in the confinement and polydispersity after store depletion localizes a rapid increase of Ca²⁺ influx, which can facilitate the rapid activation of local Ca²⁺ signaling pathways and the efficient replenishing of Ca²⁺ store in the ER in store-operated Ca²⁺ entry.

ATP-Dependent Diffusion Entropy and Homogeneity in Living Cells

Intracellular dynamics is highly complex, and includes diffusion of poly-dispersed objects in a non-homogeneous, out-of-equilibrium medium. Assuming non-equilibrium steady-state, we developed a framework that relates non-equilibrium fluctuations to diffusion, and generalized entropy in cells. We employed imaging of live Jurkat T cells, and showed that active cells have higher diffusion parameters (K_α and α) and entropy relative to the same cells after ATP depletion. K_α and α were related in ATP-depleted cells while this relation was not apparent in untreated cells, probably due to non-equilibrium applied work. Next we evaluated the effect of intracellular diffusion and entropy on the cell content homogeneity, which was displayed by the extent of its liquid–liquid phase separation (LLPS). Correlations between intracellular diffusion parameters, entropy and cell homogeneity could be demonstrated only in active cells while these correlations disappeared after ATP depletion. We conclude that non-equilibrium contributions to diffusivity and entropy by ATP-dependent mechanical work allow cells to control their content homogeneity and LLPS state. Such understanding may enable better intervention in extreme LLPS conditions associated with various cell malignancies and degenerative diseases.

Transport dynamics of complex fluids

Thermal motion in complex fluids is a complicated stochastic process but ubiquitously exhibits initial ballistic, intermediate subdiffusive, and long-time diffusive motion, unless interrupted. Despite its relevance to numerous dynamical processes of interest in modern science, a unified, quantitative understanding of thermal motion in complex fluids remains a challenging problem. Here, we present a transport equation and its solutions, which yield a unified quantitative explanation of the mean-square displacement (MSD), the non-Gaussian parameter (NGP), and the displacement distribution of complex fluids. In our approach, the environment-coupled diffusion kernel and its time correlation function (TCF) are the essential quantities that determine transport dynamics and characterize mobility fluctuation of complex fluids; their time profiles are directly extractable from a model-free analysis of the MSD and NGP or, with greater computational expense, from the two-point and four-point velocity autocorrelation functions. We construct a general, explicit model of the diffusion kernel, comprising one unbound-mode and multiple bound-mode components, which provides an excellent approximate description of transport dynamics of various complex fluidic systems such as supercooled water, colloidal beads diffusing on lipid tubes, and dense hard disk fluid. We also introduce the concepts of intrinsic disorder and extrinsic disorder that have distinct effects on transport dynamics and different dependencies on temperature and density. This work presents an unexplored direction for quantitative understanding of transport and transport-coupled processes in complex disordered media.

Non-Gaussian, non-ergodic, and non-Fickian diffusion of tracers in mucin hydrogels

Native mucus is polymer-based soft-matter material of paramount biological importance. How non-Gaussian and non-ergodic is the diffusive spreading of pathogens in mucus? We study the passive, thermally driven motion of micron-sized tracers in hydrogels of mucins, the main polymeric component of mucus. We report the results of the Bayesian analysis for ranking several diffusion models for a set of tracer trajectories [C. E. Wagner et al., Biomacromolecules, 2017, 18, 3654]. The models with "diffusing diffusivity", fractional and standard Brownian motion are used. The likelihood functions and evidences of each model are computed, ranking the significance of each model for individual traces. We find that viscoelastic anomalous diffusion is often most probable, followed by Brownian motion, while the model with a diffusing diffusion coefficient is only realised rarely. Our analysis also clarifies the distribution of time-averaged displacements, correlations of scaling exponents and diffusion coefficients, and the degree of non-Gaussianity of displacements at varying pH levels. Weak ergodicity breaking is also quantified. We conclude that-consistent with the original study-diffusion of tracers in the mucin gels is most non-Gaussian and non-ergodic at low pH that corresponds to the most heterogeneous networks. Using the Bayesian approach with the nested-sampling algorithm, together with the quantitative analysis of multiple statistical measures, we report new insights into possible physical mechanisms of diffusion in mucin gels.

Controlling Anomalous Diffusion in Lipid Membranes

Diffusion in cell membranes is not just simple two-dimensional Brownian motion but typically depends on the timescale of the observation. The physical origins of this anomalous subdiffusion are unresolved, and model systems capable of quantitative and reproducible control of membrane diffusion have been recognized as a key experimental bottleneck. Here, we control anomalous diffusion using supported lipid bilayers containing lipids derivatized with polyethylene glycol (PEG) headgroups. Bilayers with specific excluded area fractions are formed by control of PEG lipid mole fraction. These bilayers exhibit a switch in diffusive behavior, becoming anomalous as bilayer continuity is disrupted. Using a combination of single-molecule fluorescence and interferometric imaging, we measure the anomalous behavior in this model over four orders of magnitude in time. Diffusion in these bilayers is well described by a power-law dependence of the mean-square displacement with observation time. Anomaleity in this system can be tailored by simply controlling the mole fraction of PEG lipid, producing bilayers with diffusion parameters similar to those observed for anomalous diffusion in biological membranes.

Plant lipids: Key players of plasma membrane organization and function

The plasma membrane (PM) is the biological membrane that separates the interior of all cells from the outside. The PM is constituted of a huge diversity of proteins and lipids. In this review, we will update the diversity of molecular species of lipids found in plant PM. We will further discuss how lipids govern global properties of the plant PM, explaining that plant lipids are unevenly distributed and are able to organize PM in domains. From that observation, it emerges a complex picture showing a spatial and multiscale segregation of PM components. Finally, we will discuss how lipids are key players in the function of PM in plants, with a particular focus on plant-microbe interaction, transport and hormone signaling, abiotic stress responses, plasmodesmata function. The last chapter is dedicated to the methods that the plant membrane biology community needs to develop to get a comprehensive understanding of membrane organization in plants.

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.

Biased continuous-time random walks for ordinary and equilibrium cases: facilitation of diffusion, ergodicity breaking and ageing

We examine renewal processes with power-law waiting time distributions (WTDs) and non-zero drift via computing analytically and by computer simulations their ensemble and time averaged spreading characteristics. All possible values of the scaling exponent α are considered for the WTD ψ(t) ∼ 1/t1+α. We treat continuous-time random walks (CTRWs) with 0 < α < 1 for which the mean waiting time diverges, and investigate the behaviour of the process for both ordinary and equilibrium CTRWs for 1 < α < 2 and α > 2. We demonstrate that in the presence of a drift CTRWs with α < 1 are ageing and non-ergodic in the sense of the non-equivalence of their ensemble and time averaged displacement characteristics in the limit of lag times much shorter than the trajectory length. In the sense of the equivalence of ensemble and time averages, CTRW processes with 1 < α < 2 are ergodic for the equilibrium and non-ergodic for the ordinary situation. Lastly, CTRW renewal processes with α > 2-both for the equilibrium and ordinary situation-are always ergodic. For the situations 1 < α < 2 and α > 2 the variance of the diffusion process, however, depends on the initial ensemble. For biased CTRWs with α > 1 we also investigate the behaviour of the ergodicity breaking parameter. In addition, we demonstrate that for biased CTRWs the Einstein relation is valid on the level of the ensemble and time averaged displacements, in the entire range of the WTD exponent α.

Cholesterol modulates acetylcholine receptor diffusion by tuning confinement sojourns and nanocluster stability

Translational motion of neurotransmitter receptors is key for determining receptor number at the synapse and hence, synaptic efficacy. We combine live-cell STORM superresolution microscopy of nicotinic acetylcholine receptor (nAChR) with single-particle tracking, mean-squared displacement (MSD), turning angle, ergodicity, and clustering analyses to characterize the lateral motion of individual molecules and their collective behaviour. nAChR diffusion is highly heterogeneous: subdiffusive, Brownian and, less frequently, superdiffusive. At the single-track level, free walks are transiently interrupted by ms-long confinement sojourns occurring in nanodomains of ~36 nm radius. Cholesterol modulates the time and the area spent in confinement. Turning angle analysis reveals anticorrelated steps with time-lag dependence, in good agreement with the permeable fence model. At the ensemble level, nanocluster assembly occurs in second-long bursts separated by periods of cluster disassembly. Thus, millisecond-long confinement sojourns and second-long reversible nanoclustering with similar cholesterol sensitivities affect all trajectories; the proportion of the two regimes determines the resulting macroscopic motional mode and breadth of heterogeneity in the ensemble population.

Non-Gaussianity, population heterogeneity, and transient superdiffusion in the spreading dynamics of amoeboid cells

What is the underlying diffusion process governing the spreading dynamics and search strategies employed by amoeboid cells?