Kinetics of cellular uptake of viruses and nanoparticles via clathrin-mediated endocytosis.

Several viruses exploit clathrin-mediated endocytosis to gain entry into host cells. This process is also used extensively in biomedical applications to deliver nanoparticles (NPs) to diseased cells. The internalization of these nano-objects is controlled by the assembly of a clathrin-containing protein coat on the cytoplasmic side of the plasma membrane, which drives the invagination of the membrane and the formation of a cargo-containing endocytic vesicle. Current theoretical models of receptor-mediated endocytosis of viruses and NPs do not explicitly take coat assembly into consideration. In this paper we study cellular uptake of viruses and NPs with a focus on coat assembly. We characterize the internalization process by the mean time between the binding of a particle to the membrane and its entry into the cell. Using a coarse-grained model which maps the stochastic dynamics of coat formation onto a one-dimensional random walk, we derive an analytical formula for this quantity. A study of the dependence of the mean internalization time on NP size shows that there is an upper bound above which this time becomes extremely large, and an optimal size at which it attains a minimum. Our estimates of these sizes compare well with experimental data. We also study the sensitivity of the obtained results on coat parameters to identify factors which significantly affect the internalization kinetics.

Hemoglobinopathic erythrocytes affect the intraerythrocytic multiplication of Plasmodium falciparum in vitro.

BACKGROUND: The mechanisms by which α-thalassemia and sickle cell traits confer protection from severe Plasmodium falciparum malaria are not yet fully elucidated. We hypothesized that hemoglobinopathic erythrocytes reduce the intraerythrocytic multiplication of P. falciparum, potentially delaying the development of life-threatening parasite densities until parasite clearing immunity is achieved. METHODS: We developed a novel in vitro assay to quantify the number of merozoites released from an individual schizont, termed the "intraerythrocytic multiplication factor" (IMF). RESULTS: P. falciparum (3D7 line) schizonts produce variable numbers of merozoites in all erythrocyte types tested, with median IMFs of 27, 27, 29, 23, and 23 in control, HbAS, HbSS, and α- and ß-thalassemia trait erythrocytes, respectively. IMF correlated strongly (r(2) = 0.97; P < .001) with mean corpuscular hemoglobin concentration, and varied significantly with mean corpuscular volume and hemoglobin content. Reduction of IMFs in thalassemia trait erythrocytes was confirmed using clinical parasite isolates with different IMFs. Mathematical modeling of the effect of IMF on malaria progression indicates that the lower IMF in thalassemia trait erythrocytes limits parasite density and anemia severity over the first 2 weeks of parasite replication. CONCLUSIONS: P. falciparum IMF, a parasite heritable virulence trait, correlates with erythrocyte indices and is reduced in thalassemia trait erythrocytes. Parasite IMF should be examined in other low-indices erythrocytes.

Multiwell stiffness assay for the study of cell responsiveness to cytotoxic drugs.

It is now well understood that the cell microenvironment, including the surrounding matrix, profoundly affects cell fate. This is especially true for solid tumors where, for example, matrix stiffness is believed to be an important factor in tumorogenesis. Our hypothesis is that since matrix stiffness affects cell fate, it may also be important in drug resistance. To test this hypothesis, we designed and built a multiwell polyacrylamide (PA) gel-based stiffness assay, in which the gels were coated with collagen in order to facilitate cell attachment and proliferation. This PA-based assay was used to examine the effect of stiffness on cultured cell responsiveness to cytotoxic drugs. In particular, we tested multiple cancer cell lines and their susceptibility to paclitaxel, a microtubule-targeting agent. By assessing cell proliferation, morphology, and the IC50 of the drug, we were able to establish that the stiffness affects responsiveness to cytotoxic drugs in a cell-dependent manner.

Unraveling protein-protein interactions in clathrin assemblies via atomic force spectroscopy.

Atomic force microscopy (AFM), single molecule force spectroscopy (SMFS), and single particle force spectroscopy (SPFS) are used to characterize intermolecular interactions and domain structures of clathrin triskelia and clathrin-coated vesicles (CCVs). The latter are involved in receptor-mediated endocytosis (RME) and other trafficking pathways. Here, we subject individual triskelia, bovine-brain CCVs, and reconstituted clathrin-AP180 coats to AFM-SMFS and AFM-SPFS pulling experiments and apply novel analytics to extract force-extension relations from very large data sets. The spectroscopic fingerprints of these samples differ markedly, providing important new information about the mechanism of CCV uncoating. For individual triskelia, SMFS reveals a series of events associated with heavy chain alpha-helix hairpin unfolding, as well as cooperative unraveling of several hairpin domains. SPFS of clathrin assemblies exposes weaker clathrin-clathrin interactions that are indicative of inter-leg association essential for RME and intracellular trafficking. Clathrin-AP180 coats are energetically easier to unravel than the coats of CCVs, with a non-trivial dependence on force-loading rate.

Micellization model for the polymerization of clathrin baskets.

A thermodynamic model is used to investigate the conditions under which clathrin triskelions form polyhedral baskets. The analysis, which is similar to classical methods used to study micelle formation, relates clathrin basket energetics to system parameters linked to triskelial rigidity, the natural curvature of an isolated triskelion, and interactions between triskelial legs in the assembled polyhedra. Mathematical theory predicts that a minimal ("critical") clathrin concentration, C(C), needs to be surpassed in order for basket polymerization to occur, and indicates how C(C), and the amount of polymerized material, depend on the chosen parameters. Analytical expressions are obtained to indicate how changes in the parameters affect the sizes of the polyhedra which arise when the total clathrin concentration exceeds C(C). A continuum analytic approximation then is used to produce numerical results that illustrate the derived dependences.

Critical point for membrane bilayer formation.

Unilamellar liposomes often are employed in investigations of lipid-protein interactions and the delivery of drugs in therapies for disease. Also, related lipid-containing nanoparticles have been developed as elements of a new class of mRNA vaccines. We show that only unilamellar films form in equilibrium lipid dispersions, at temperature values {T*} that depend on the identities of the lipids (e.g., T* ≈ 29 °C for DMPC). Thermodynamic analysis confirms that films at air-water surfaces can be used to monitor the properties of the lipid vesicles that form in the dispersion. When T > T*, critical exponents describing film properties as T approaches T* are µ ≈ 1.4 and ν ≈ 0.7, which are close to values for the interfacial tension and the correlation length of density fluctuations at fluid interfaces. These results, and observations that within the bilayer the lateral diffusion of fluorescent lipid probes demonstrates increases at T*, suggest that unilamellar vesicles at T* are a transition state between two different multilamellar structures. We generalize the thermodynamic arguments to explain the linkage between lipid structures in the surface and bulk dispersion within more complex samples, showing that dispersions containing total lipid extracts of cell membranes have properties similar to those in dispersions containing single lipids. Information from various independent studies indicates that T* noted for bilayer membranes of a population of cells is identical to the temperature at which the growth or gestation of the cells occurs in vivo. Examples include whole-cell lipid extracts obtained from bacteria, and poikilothermic and homeothermic animals.

Stochastic model of clathrin-coated pit assembly.

In recent years, fluorescence microscopy has enabled researchers to observe the dynamics of clathrin-coated pit (CCP) assembly in real time. The assembly dynamics of CCPs shows striking heterogeneity. Some CCPs are long-lived (productive CCPs); they bind cargo and grow in size to form clathrin-coated vesicles. In contrast, other CCPs (abortive CCPs) are relatively short-lived and disassemble well before reaching vesicle size. Within both populations there is significant variance in CCP lifetime. We propose a stochastic biophysical model that links these observations with the energetics of CCPs and kinetics of their assembly. We show that without cargo, CCP assembly faces a high energy barrier that is difficult to overcome. As a consequence, CCPs without cargo are almost always abortive. We suggest a mechanism by which cargo binding stabilizes CCPs and facilitates their growth. The lifetime distribution of abortive pits calculated from our model agrees well with published experimental data. We also estimate the lifetimes of productive CCPs and show that the stochastic nature of CCP assembly plays a crucial role in causing their observed wide distribution.

Hindered diffusion in polymeric solutions studied by fluorescence correlation spectroscopy.

Diffusion of molecules in the crowded and charged interior of the cell has long been of interest for understanding cellular processes. Here, we introduce a model system of hindered diffusion that includes both crowding and binding. In particular, we obtained the diffusivity of the positively charged protein, ribonuclease A (RNase), in solutions of dextrans of various charges (binding) and concentrations (crowding), as well as combinations of both, in a buffer of physiological ionic strength. Using fluorescence correlation spectroscopy, we observed that the diffusivity of RNase was unaffected by the presence of positively charged or neutral dextrans in the dilute regime but was affected by crowding at higher polymer concentrations. Conversely, protein diffusivity was significantly reduced by negatively charged dextrans, even at 0.4 µM (0.02% w/v) dextran. The diffusivity of RNase decreased with increasing concentrations of negative dextran, and the amount of bound RNase increased until it reached a plateau of ∼80% bound RNase. High salt concentrations were used to establish the electrostatic nature of the binding. Binding of RNase to the negatively charged dextrans was further confirmed by ultrafiltration.

Nematic order in small systems: measuring the elastic and wall-anchoring constants in vibrofluidized granular rods.

We investigate nematic order in vibrated granular rods confined to a small quasi-2D container less than 10 rod lengths in diameter. As rod density ρ increases, patterning shifts from bipolar to uniform alignment. We find that a continuum liquid crystal free energy functional captures key patterning features down to almost the particle size. By fitting theory to experiments, we estimate the relative values of bend and splay elastic constants and wall anchoring. We find that splay is softer than bend for all ρ and rod lengths tested, while the ratio of the average elastic constant to wall anchoring increases with ρ.

Depletion forces drive polymer-like self-assembly in vibrofluidized granular materials.

Ranging from nano- to granular-scales, control of particle assembly can be achieved by limiting the available free space, for example by increasing the concentration of particles ("crowding") or through their restriction to 2D environments. It is unclear, however, if self-assembly principles governing thermally-equilibrated molecules can also apply to mechanically-excited macroscopic particles in non-equilibrium steady-state. Here we show that low densities of vibrofluidized steel rods, when crowded by high densities of spheres and confined to quasi-2D planes, can self-assemble into linear polymer-like structures. Our 2D Monte Carlo simulations show similar finite sized aggregates in thermally equilibrated binary mixtures. Using theory and simulations, we demonstrate how depletion interactions create oriented "binding" forces between rigid rods to form these "living polymers." Unlike rod-sphere mixtures in 3D that can demonstrate well-defined equilibrium phases, our mixtures confined to 2D lack these transitions because lower dimensionality favors the formation of linear aggregates, thus suppressing a true phase transition. The qualitative and quantitative agreement between equilibrium and granular patterning for these mixtures suggests that entropy maximization is the determining driving force for bundling. Furthermore, this study uncovers a previously unknown patterning behavior at both the granular and nanoscales, and may provide insights into the role of crowding at interfaces in molecular assembly.

Movements of HIV-virions in human cervical mucus.

Time-resolved confocal microscopy and fluorescence correlation spectroscopy were used to examine the movements of fluorescently labeled HIV-virions (approximately 100 nm) added to samples of human cervical mucus. Particle-tracking analysis indicates that the motion of most virions is decreased 200-fold compared to that in aqueous solution and is not driven by typical diffusion. Rather, the time-dependence of their ensemble-averaged mean-square displacements is proportional to tau(alpha) + v(2)tau(2), describing a combination of anomalous diffusion (alpha approximately 0.3) and flow-like behavior, with tau being the lag time. We attribute the flow-like behavior to slowly relaxing mucus matrix that follows mechanical perturbations such as stretching and twisting of the sample. Further analysis of the tracks and displacements of individual virions indicates differences in the local movements among the virions, including constrained motion and infrequent jumps, perhaps due to abrupt changes in matrix structure. Changes in the microenvironments due to slow structural changes may facilitate movement of the virions, allowing them to reach the epithelial layer.

Clathrin triskelia show evidence of molecular flexibility.

The clathrin triskelion, which is a three-legged pinwheel-shaped heteropolymer, is a major component in the protein coats of certain post-Golgi and endocytic vesicles. At low pH, or at physiological pH in the presence of assembly proteins, triskelia will self-assemble to form a closed clathrin cage, or "basket". Recent static light scattering and dynamic light scattering studies of triskelia in solution showed that an individual triskelion has an intrinsic pucker similar to, but differing from, that inferred from a high resolution cryoEM structure of a triskelion in a clathrin basket. We extend the earlier solution studies by performing small-angle neutron scattering (SANS) experiments on isolated triskelia, allowing us to examine a higher q range than that probed by static light scattering. Results of the SANS measurements are consistent with the light scattering measurements, but show a shoulder in the scattering function at intermediate q values (0.016 A(-1)), just beyond the Guinier regime. This feature can be accounted for by Brownian dynamics simulations based on flexible bead-spring models of a triskelion, which generate time-averaged scattering functions. Calculated scattering profiles are in good agreement with the experimental SANS profiles when the persistence length of the assumed semiflexible triskelion is close to that previously estimated from the analysis of electron micrographs.

Endocytosis: curvature to the ENTH degree.

Recent work has shown that the protein epsin 1 induces highly curved lipidic structures when added with clathrin to appropriate lipid mixtures. This property may be a critical factor in the 'curvature stress cycle' of membrane trafficking.

Modeling neutrophil migration in dynamic chemoattractant gradients: assessing the role of exosomes during signal relay.

Migrating cells often exhibit signal relay, a process in which cells migrating in response to a chemotactic gradient release a secondary chemoattractant to enhance directional migration. In neutrophils, signal relay toward the primary chemoattractant N--formylmethionyl-leucyl-phenylalanine (fMLP) is mediated by leukotriene B4 (LTB4). Recent evidence suggests that the release of LTB4 from cells occurs through packaging in exosomes. Here we present a mathematical model of neutrophil signal relay that focuses on LTB4 and its exosome-mediated secretion. We describe neutrophil chemotaxis in response to a combination of a defined gradient of fMLP and an evolving gradient of LTB4, generated by cells in response to fMLP. Our model enables us to determine the gradient of LTB4 arising either through directed secretion from cells or through time-varying release from exosomes. We predict that the secondary release of LTB4 increases recruitment range and show that the exosomes provide a time delay mechanism that regulates the development of LTB4 gradients. Additionally, we show that under decaying primary gradients, secondary gradients are more stable when secreted through exosomes as compared with direct secretion. Our chemotactic model, calibrated from observed responses of cells to gradients, thereby provides insight into chemotactic signal relay in neutrophils during inflammation.

Electrolysis induces gradients and domain orientation in agarose gels.

We have used small-angle light-scattering (SALS), microscopy, and measurements to study structural changes produced in unbuffered agarose gels as ions migrate under applied electric fields (3-20 V/cm). Anisotropic, bowtielike, light-scattering patterns were observed, whose development occurred more quickly at higher fields. The horizontal lobes were more pronounced at higher polymer concentration. Analysis of the SALS data with a simple model of scattering from anisotropic rods in an electric field is consistent with anisotropic rodlike domains on the order of 10-15 microm in length, which align perpendicular to the electric field. The anisotropic domains in the gel reach almost the same level of orientation, regardless of the field strength. Microscope imaging revealed anisotropic domains on the same length scale, also aligned perpendicular to the field. Profiles of pH variation across the gel, measured by video photography, indicate that the anisotropic patterns appear when the H+ and OH- ions, migrating in opposite directions, meet. Calculations of pH profiles using a model based on electrodiffusion reproduce several features of measured pH profiles, including the power-law dependence on the electric field of the time at which the oppositely charged fronts meet. Ions migrating from both ends of the gel produce pH changes that are correlated with macroscopic shrinking and orientation of the gel.

Imaging and tracking HIV viruses in human cervical mucus.

We describe a systematic approach to image, track, and quantify the movements of HIV viruses embedded in human cervical mucus. The underlying motivation for this study is that, in HIV-infected adults, women account for more than half of all new cases and most of these women acquire the infection through heterosexual contact. The endocervix is believed to be a susceptible site for HIV entry. Cervical mucus, which coats the endocervix, should play a protective role against the viruses. Thus, we developed a methodology to apply time-resolved confocal microscopy to examine the motion of HIV viruses that were added to samples of untreated cervical mucus. From the images, we identified the viruses, tracked them over time, and calculated changes of the statistical mean-squared displacement (MSD) of each virus. Approximately half of tracked viruses appear constrained while the others show mobility with MSDs that are proportional to ??+?2?2, over time range ?, depicting a combination of anomalous diffusion (0

Zoetic polymers.

Conditions mediating the formation of biological polymers in situ are reviewed, and terminology suggested to differentiate polymers found in living cells from synthetic materials and polymers derived from biological sources that are modified or studied in a way that obscures their biological function. Methods currently used to characterize the mechanical properties of biopolymer networks in cells are briefly discussed.

Improving the design of the agarose spot assay for eukaryotic cell chemotaxis.

Migration of cells along gradients of effector molecules, i.e., chemotaxis, is necessary in immune response and is involved in development and cancer metastasis. The experimental assessment of chemotaxis thus is of high interest. The agarose spot assay is a simple tissue culture system used to analyze chemotaxis. Although direction sensing requires gradients to be sufficiently steep, how the chemical gradients developed in this assay change over time, and thus, under what conditions chemotaxis is plausible, has not yet been determined. Here, we use numerical solution of the diffusion equation to determine the chemoattractant gradient produced in the assay. Our analysis shows that, for the usual spot size, the lifetime of the assay is optimized if the chemoattractant concentration in the spot is initially 30 times the dissociation constant of the chemoattractant-receptor bond. This result holds regardless of the properties of the chemoattractant. With this initial concentration, the chemoattractant gradient falls to the minimum threshold for directional sensing at the same time that the concentration drops to the optimal level for detecting gradient direction. If a higher initial chemoattractant concentration is used, the useful lifetime of the assay is likely to be shortened because receptor saturation may decrease the cells' sensitivity to the gradient; lower initial concentrations would result in too little chemoattractant for the cells to detect. Moreover, chemoattractants with higher diffusion coefficients would sustain gradients for less time. Based on previous measurements of the diffusion coefficients of the chemoattractants EGF and CXCL12, we estimate that the assay will produce gradients that cells can sense for a duration of 10 h for EGF and 5 h for CXCL12. These gradient durations are comparable to what can be achieved with the Boyden chamber assay. The analysis presented in this work facilitates determination of suitable parameters for the assay, and can be used to assess whether observed cell motility is likely due to chemotaxis or chemokinesis.

Distributions of lifetime and maximum size of abortive clathrin-coated pits.

Clathrin-mediated endocytosis is a complex process through which eukaryotic cells internalize nutrients, antigens, growth factors, pathogens, etc. The process occurs via the formation of invaginations on the cell membrane, called clathrin-coated pits (CCPs). Over the years, much has been learned about the mechanism of CCP assembly, but a complete understanding of the assembly process still remains elusive. In recent years, using fluorescence microscopy, studies have been done to determine the statistical properties of CCP formation. In this paper, using a recently proposed coarse-grained, stochastic model of CCP assembly [Banerjee, Berezhkovskii, and Nossal, Biophys. J. 102, 2725 (2012)], we suggest new ways of analyzing such experimental data. To be more specific, we derive analytical expressions for the distribution of maximum size of abortive CCPs, and the probability density of their lifetimes. Our results show how these functions depend on the kinetic and energetic parameters characterizing the assembly process, and therefore could be useful in extracting information about the mechanism of CCP assembly from experimental data. We find excellent agreement between our analytical results and those obtained from kinetic Monte Carlo simulations of the assembly process.

Effects of multiple scattering on fluorescence correlation spectroscopy measurements of particles moving within optically dense media.

Fluorescence correlation spectroscopy (FCS) is increasingly being used to assess the movement of particles diffusing in complex, optically dense surroundings, in which case measurement conditions may complicate data interpretation. It is considered how a single-photon FCS measurement can be affected if the sample properties result in scattering of the incident light. FCS autocorrelation functions of Atto 488 dye molecules diffusing in solutions of polystyrene beads are measured, which acted as scatterers. Data indicated that a scattering-linked increase in the illuminated volume, as much as two fold, resulted in minimal increase in diffusivity. To analyze the illuminated beam profile, Monte-Carlo simulations were employed, which indicated a larger broadening of the beam along the axial than the radial directions, and a reduction of the incident intensity at the focal point. The broadening of the volume in the axial direction has only negligible effect on the measured diffusion time, since intensity fluctuations due to diffusion events in the radial direction are dominant in FCS measurements. Collectively, results indicate that multiple scattering does not result in FCS measurement artifacts and thus, when sufficient signal intensity is attainable, single-photon FCS can be a useful technique for measuring probe diffusivity in optically dense media.