Human papillomavirus type 16 entry: retrograde cell surface transport along actin-rich protrusions

The lateral mobility of individual, incoming human papillomavirus type 16 pseudoviruses (PsV) bound to live HeLa cells was studied by single particle tracking using fluorescence video microscopy. The trajectories were computationally analyzed in terms of diffusion rate and mode of motion as described by the moment scaling spectrum. Four distinct modes of mobility were seen: confined movement in small zones (30-60 nm in diameter), confined movement with a slow drift, fast random motion with transient confinement, and linear, directed movement for long distances. The directed movement was most prominent on actin-rich cell protrusions such as filopodia or retraction fibres, where the rate was similar to that measured for actin retrograde flow. It was, moreover, sensitive to perturbants of actin retrograde flow such as cytochalasin D, jasplakinolide, and blebbistatin. We found that transport along actin protrusions significantly enhanced HPV-16 infection in sparse tissue culture, cells suggesting a role for in vivo infection of basal keratinocytes during wound healing.     

Identifying Transport Behavior of Single-Molecule Trajectories

Models of biological diffusion-reaction systems require accurate classification of the underlying diffusive dynamics (e.g., Fickian, subdiffusive, or superdiffusive). We use a renormalization group operator to identify the anomalous (non-Fickian) diffusion behavior from a short trajectory of a single molecule. The method provides quantitative information about the underlying stochastic process, including its anomalous scaling exponent. The classification algorithm is first validated on simulated trajectories of known scaling. Then it is applied to experimental trajectories of microspheres diffusing in cytoplasm, revealing heterogeneous diffusive dynamics. The simplicity and robustness of this classification algorithm makes it an effective tool for analysis of rare stochastic events that occur in complex biological systems.     

Classification of Dynamical Diffusion States in Single Molecule Tracking Microscopy

Single molecule tracking of membrane proteins by fluorescence microscopy is a promising method to investigate dynamic processes in live cells. Translating the trajectories of proteins to biological implications, such as protein interactions, requires the classification of protein motion within the trajectories. Spatial information of protein motion may reveal where the protein interacts with cellular structures, because binding of proteins to such structures often alters their diffusion speed. For dynamic diffusion systems, we provide an analytical framework to determine in which diffusion state a molecule is residing during the course of its trajectory. We compare different methods for the quantification of motion to utilize this framework for the classification of two diffusion states (two populations with different diffusion speed). We found that a gyration quantification method and a Bayesian statistics-based method are the most accurate in diffusion-state classification for realistic experimentally obtained datasets, of which the gyration method is much less computationally demanding. After classification of the diffusion, the lifetime of the states can be determined, and images of the diffusion states can be reconstructed at high resolution. Simulations validate these applications. We apply the classification and its applications to experimental data to demonstrate the potential of this approach to obtain further insights into the dynamics of cell membrane proteins.     

Classification of Dynamical Diffusion States in Single Molecule Tracking Microscopy

Single molecule tracking of membrane proteins by fluorescence microscopy is a promising method to investigate dynamic processes in live cells. Translating the trajectories of proteins to biological implications, such as protein interactions, requires the classification of protein motion within the trajectories. Spatial information of protein motion may reveal where the protein interacts with cellular structures, because binding of proteins to such structures often alters their diffusion speed. For dynamic diffusion systems, we provide an analytical framework to determine in which diffusion state a molecule is residing during the course of its trajectory. We compare different methods for the quantification of motion to utilize this framework for the classification of two diffusion states (two populations with different diffusion speed). We found that a gyration quantification method and a Bayesian statistics-based method are the most accurate in diffusion-state classification for realistic experimentally obtained datasets, of which the gyration method is much less computationally demanding. After classification of the diffusion, the lifetime of the states can be determined, and images of the diffusion states can be reconstructed at high resolution. Simulations validate these applications. We apply the classification and its applications to experimental data to demonstrate the potential of this approach to obtain further insights into the dynamics of cell membrane proteins.     

Reaction null-space filter: extracting reactionless synergies for optimal postural balance from motion capture data

This paper introduces the notion of a reactionless synergy: a postural variation for a specific motion pattern/strategy, whereby the movements of the segments do not alter the force/moment balance at the feet. Given an optimal initial posture in terms of stability, a reactionless synergy can ensure optimality throughout the entire movement. Reactionless synergies are derived via a dynamical model wherein the feet are regarded to be unfixed. Though in contrast with the conventional fixed-feet models, this approach has the advantage of exhibiting the reactions at the feet explicitly. The dynamical model also facilitates a joint-space decomposition scheme yielding two motion components: the reactionless synergy and an orthogonal complement responsible for the dynamical coupling between the feet and the support. Since the reactionless synergy provides the basis (a feedforward control component) for optimal balance control, it may play an important role when evaluating balance abnormalities or when assessing optimality in balance control. We show how to apply the proposed method for analysis of motion capture data obtained from three voluntary movement patterns in the sagittal plane: squat, sway, and forward bend.     

Oscillating focus of SopA associated with filamentous structure guides partitioning of F plasmid

The F plasmid is actively partitioned to daughter cells by the sopABC gene. To elucidate the partitioning mechanisms, we simultaneously analysed movements of the plasmid and the SopA ATPase in single living cells. SopA, which is a putative motor protein assembled densely near nucleoid borders and formed a single discrete focus associated with less dense filamentous distribution along the long axis of the cell. The dense SopA focus oscillates between cell poles. The direction of the plasmid motion switches as the SopA focus switches its position. The velocity of the plasmid motion stays constant while it oscillates moving towards the SopA focus. The low density filamentous distribution of SopA persisted throughout the SopA oscillation. The focus associated with filamentous distribution of SopA was also observed in a cell without nucleoid. The SopA filament may guide the movement of the plasmid as a railway track and lead it to cell quarters.     

Protein dynamics: Mössbauer spectroscopy on deoxymyoglobin crystals

Mössbauer absorption experiments on ⁵⁷Fe of deoxygenated myoglobin crystals and on K₄⁵⁷Fe(CN)₆ dissolved in the water of metmyoglobin crystals were performed over a large temperature range. At low temperatures the mean square displacements, 〈x²〉, of the iron indicate solid-like behaviour of the whole system, whereas at higher temperatures protein-specific modes of motion contribute to 〈x²>. The protein dynamics are correlated with the mobility of the water within the protein crystals. A Brownian oscillator is used to model the protein-specific modes of motion measured at the ⁵⁷Fe nucleus. Three modes are necessary for understanding the Mössbauer spectrum. Two of them correspond to an extremely overdamped Brownian oscillator. The third mode can be understood as quasi-free diffusion. Whereas the protein molecule is frozen in conformational substates in the low temperature regime, it reaches transition states with a finite probability in the high temperature regime. The surface water mediates a possible trigger mechanism that switches on protein dynamics within a narrow temperature interval. Results from Mössbauer spectroscopy and from X-ray structure analysis are compared.     

Motion segmentation method for hybrid characteristic on human motion

Motion segmentation and analysis are used to improve the process of classification of motion and information gathered on repetitive or periodic characteristic. The classification result is useful for ergonomic and postural safety analysis, since repetitive motion is known to be related to certain musculoskeletal disorders. Past studies mainly focused on motion segmentation on particular motion characteristic with certain prior knowledge on static or periodic property of motion, which narrowed method's applicability. This paper attempts to introduce a method to tackle human joint motion without having prior knowledge. The motion is segmented by a two-pass algorithm. Recursive least square (RLS) is firstly used to estimate possible segments on the input human-motion set. Further, period identification and extra segmentation process are applied to produce meaningful segments. Each of the result segments is modeled by a damped harmonic model, with frequency, amplitude and duration produced as parameters for ergonomic evaluation and other human factor studies such as task safety evaluation and sport analysis. Experiments show that the method can handle periodic, random and mixed characteristics on human motion, which can also be extended to the usage in repetitive motion in workflow and irregular periodic motion like sport movement.     

Anomalous versus Slowed-Down Brownian Diffusion in the Ligand-Binding Equilibrium

Measurements of protein motion in living cells and membranes consistently report transient anomalous diffusion (subdiffusion) that converges back to a Brownian motion with reduced diffusion coefficient at long times after the anomalous diffusion regime. Therefore, slowed-down Brownian motion could be considered the macroscopic limit of transient anomalous diffusion. On the other hand, membranes are also heterogeneous media in which Brownian motion may be locally slowed down due to variations in lipid composition. Here, we investigate whether both situations lead to a similar behavior for the reversible ligand-binding reaction in two dimensions. We compare the (long-time) equilibrium properties obtained with transient anomalous diffusion due to obstacle hindrance or power-law-distributed residence times (continuous-time random walks) to those obtained with space-dependent slowed-down Brownian motion. Using theoretical arguments and Monte Carlo simulations, we show that these three scenarios have distinctive effects on the apparent affinity of the reaction. Whereas continuous-time random walks decrease the apparent affinity of the reaction, locally slowed-down Brownian motion and local hindrance by obstacles both improve it. However, only in the case of slowed-down Brownian motion is the affinity maximal when the slowdown is restricted to a subregion of the available space. Hence, even at long times (equilibrium), these processes are different and exhibit irreconcilable behaviors when the area fraction of reduced mobility changes.     

Anomalous versus Slowed-Down Brownian Diffusion in the Ligand-Binding Equilibrium

Measurements of protein motion in living cells and membranes consistently report transient anomalous diffusion (subdiffusion) that converges back to a Brownian motion with reduced diffusion coefficient at long times after the anomalous diffusion regime. Therefore, slowed-down Brownian motion could be considered the macroscopic limit of transient anomalous diffusion. On the other hand, membranes are also heterogeneous media in which Brownian motion may be locally slowed down due to variations in lipid composition. Here, we investigate whether both situations lead to a similar behavior for the reversible ligand-binding reaction in two dimensions. We compare the (long-time) equilibrium properties obtained with transient anomalous diffusion due to obstacle hindrance or power-law-distributed residence times (continuous-time random walks) to those obtained with space-dependent slowed-down Brownian motion. Using theoretical arguments and Monte Carlo simulations, we show that these three scenarios have distinctive effects on the apparent affinity of the reaction. Whereas continuous-time random walks decrease the apparent affinity of the reaction, locally slowed-down Brownian motion and local hindrance by obstacles both improve it. However, only in the case of slowed-down Brownian motion is the affinity maximal when the slowdown is restricted to a subregion of the available space. Hence, even at long times (equilibrium), these processes are different and exhibit irreconcilable behaviors when the area fraction of reduced mobility changes.     

Study of polysaccharides by the fluorescence method. III. Chain length dependence of the micro-Brownian motion of amylose in an aqueous solution

The fluorescence polarization method was applied to the investigation of the micro-Brownian motion of amylose chains having a wide range of degree of polymerization (DP). We prepared two types of fluorescent conjugates of amylose: amylose conjugated with fluorescein randomly throughout the chain (F-amylose) and amylose conjugated locally on a terminal segment (t-F-amylose). The degree of fluorescence polarization of these conjugates was measured by changing the solvent viscosity at a constant temperature (25°C). The data obtained were analyzed by a Perrin-type equation to calculate the mean rotational relaxation time, 〈ρ〉. By examination of the plots of 〈ρ〉 vs DP, and by comparison of 〈ρ〉 with the theoretical rotational relaxation time of the whole molecule at a given DP, it was found that 〈ρ〉 mainly reflects the segmental motion of the amylose chain in the high-DP range. Thus, the fact that 〈ρ〉 for t-F-amylose is much smaller than that for F-amylose at a sufficiently high DP shows that a terminal segment undergoes a more rapid micro-Brownian motion than interior segments. In the low-DP range, we felt that the rotational diffusion of the whole molecule contributes significantly to the relaxation process. We also examined, for comparison, the segmental motion of dextran and pullulan in a similar manner and found that these segmental motions are more rapid than those of amylose. Based on the results obtained, the segmental mobility and conformation of the amylose molecule are discussed in relation to its chain length.     

Segmental conformational disorder and dynamics in the intrinsically disordered protein α-synuclein and its chain length dependence

Conformational ensembles of fully disordered natural polypeptides represent the starting point of protein refolding initiated by transfer to folding conditions. Thus, understanding the transient properties and dimensions of such peptides under folding conditions is a necessary step in the understanding of their subsequent folding behavior. Such ensembles can also undergo alternative folding and form amyloid structures, which are involved in many neurological degenerative diseases. Here, we performed a structural study of this initial state using time-resolved fluorescence resonance energy transfer analysis of a series of eight partially overlapping double-labeled chain segments of the N-terminal and NAC domains of the α-synuclein molecule. The distributions of end-to-end distance and segmental intramolecular diffusion coefficients were simultaneously determined for eight labeled chain segments. We used the coefficient of variation, C_v, as a measure of the conformational heterogeneity (i.e., structural disorder). With the exception of two segments, the C_vs were characteristic of a fully disordered state of the chain. Subtle deviations from this behavior at the segment labeled in the NAC domain and the segment at the N termini reflected subtle conformational bias that might be related to the initiation of transition to amyloid aggregates. The chain length dependence of the mean segmental end-to-end distance followed a power law as predicted by Flory, but the dependence was steeper than previously predicted, probably due to the contribution of the excluded volume effect, which is more dominant for shorter-chain segments. The observed intramolecular diffusion coefficients (< 10 to ∼ 25 ?²/ns) are only an order of magnitude lower than the common diffusion coefficients of low molecular weight probes. This diffusion coefficient increased with chain length, probably due to the cumulative contributions of minor bond rotations along the chain. These results gave us a reference both for characteristics of a natural unfolded polypeptide at the moment of initiation of folding and for detection of possible initiation sites of the amyloid transition.     

A theoretical study of the effects of RF fields in the vicinity of membranes

In this article the forces associated with the gradients of a radio frequency (RF) field at the boundary between fluids and cell membranes are calculated, and it is shown that they can be large enough to affect the particle motion by amounts that are on the same order of magnitude as the random diffusion motion when the energy imparted to the particles is a reasonable fraction of the thermal energy. The induced dipole moment is assumed to track the alternating RF so that the force exerted by the gradient is in a constant direction; and this in turn leads to a modification of the particle distribution, even when the energy added to the particle is very small. For RF fields of 45 V/m the energy acquired by an induced dipole moment is expected to be on the order of a micro electron volt and small compared to the average thermal energy.     

Analysis of kinetics in noisy systems: application to single molecule tethered particle motion

In the tethered particle motion method the length of a DNA molecule is monitored by measuring the range of diffusion of a microsphere tethered to the surface of a microscope coverslip through the DNA molecule itself. Looping of DNA (induced by binding of a specific protein) can be detected with this method and the kinetics of the looping/unlooping processes can be measured at the single molecule level. The microsphere's position variance represents the experimental variable reporting on the polymer length. Therefore, data windowing is required to obtain position variance from raw position data. Due to the characteristic diffusion time of the microsphere, the low-pass filtering required to attain a good signal/noise ratio (S/N) in the discrimination of looped versus unlooped state impacts significantly the measurement's time resolution. Here we present a method for measuring lifetimes based on half-amplitude thresholding and then correcting the kinetic measurements, taking into account low S/N (leading to false events) and limited time resolution (leading to missed events). This method allows an accurate and unbiased estimation of the kinetic parameters under investigation, independently of the choice of the window used for variance calculation, with potential applications to other single molecule measurements with low S/N.     

Analysis of transient behavior in complex trajectories: application to secretory vesicle dynamics

Analysis of trajectories of dynamical biological objects, such as breeding ants or cell organelles, is essential to reveal the interactions they develop with their environments. Many previous works used a global characterization based on parameters calculated for entire trajectories. In cases where transient behavior was detected, this usually concerned only a particular type, such as confinement or directed motion. However, these approaches are not appropriate in situations in which the tracked objects may display many different types of transient motion. We have developed a method to exhaustively analyze different kinds of transient behavior that the tracked objects may exhibit. The method discriminates stalled periods, constrained and directed motions from random dynamics by evaluating the diffusion coefficient, the mean-square displacement curvature, and the trajectory asymmetry along individual trajectories. To detect transient motions of various durations, these parameters are calculated along trajectories using a rolling analysis window whose width is variable. The method was applied to the study of secretory vesicle dynamics in the subplasmalemmal region of human carcinoid BON cells. Analysis of transitions between transient motion periods, combined with plausible assumptions about the origin of each motion type, leads to a model of dynamical subplasmalemmal organization.     

Vesicle mobility studied in cultured astrocytes

Astrocytes release many neuroactive substances, which are stored in membrane bound vesicles and may play a role in synapse modulation and in the coupling between neuronal activity and the local blood flow. However, the mobility of these vesicles in astrocytes has not been studied yet. We here used a fluorescently tagged proatrial natriuretic peptide to label single vesicles and dynamic microscopy to monitor their mobility. To track and analyze labeled vesicles, we employed a computer software. We found two modes of vesicle mobility, directional and non-directional. The mobility of non-directional vesicles is likely determined mainly by free diffusion. Only directional vesicles displayed a straight-line motion. The relationship of mean square displacement with time in directional vesicles resembled a quadratic function, indicating that in addition to free diffusion other mechanisms may contribute to vesicle movements in astrocytes, the biophysical properties of which are similar to those of neurons.     

Anomalous Diffusion Induced by Cristae Geometry in the Inner Mitochondrial Membrane

Diffusion of inner membrane proteins is a prerequisite for correct functionality of mitochondria. The complicated structure of tubular, vesicular or flat cristae and their small connections to the inner boundary membrane impose constraints on the mobility of proteins making their diffusion a very complicated process. Therefore we investigate the molecular transport along the main mitochondrial axis using highly accurate computational methods. Diffusion is modeled on a curvilinear surface reproducing the shape of mitochondrial inner membrane (IM). Monte Carlo simulations are carried out for topologies resembling both tubular and lamellar cristae, for a range of physiologically viable crista sizes and densities. Geometrical confinement induces up to several-fold reduction in apparent mobility. IM surface curvature per se generates transient anomalous diffusion (TAD), while finite and stable values of projected diffusion coefficients are recovered in a quasi-normal regime for short- and long-time limits. In both these cases, a simple area-scaling law is found sufficient to explain limiting diffusion coefficients for permeable cristae junctions, while asymmetric reduction of the junction permeability leads to strong but predictable variations in molecular motion rate. A geometry-based model is given as an illustration for the time-dependence of diffusivity when IM has tubular topology. Implications for experimental observations of diffusion along mitochondria using methods of optical microscopy are drawn out: a non-homogenous power law is proposed as a suitable approach to TAD. The data demonstrate that if not taken into account appropriately, geometrical effects lead to significant misinterpretation of molecular mobility measurements in cellular curvilinear membranes.