Measurement of the chemotaxis coefficient for human neutrophils in the under-agarose migration assay

Clinical and scientific investigations of leukocyte chemotaxis will be greatly aided by an ability to measure quantitative parameters characterizing the intrinsic random motility, chemokinetic, and chemotactic properties of cell populations responding to a given attractant. Quantities typically used at present, such as leading front distances, migrating cell numbers, etc., are unsatisfactory in this regard because their values are affected by many aspects of the assay system unrelated to cell behavioral properties. In this paper we demonstrate the measurement of cell migration parameters that do, in fact, characterize the intrinsic cell chemosensory movement responses using cell density profiles obtained in the linear under-agarose assay. These parameters are the random motility coefficient, mu, and the chemotaxis coefficient, chi, which appear in a theoretical expression for cell population migration. We propose a priori the dependence of chi on attractant concentration, based on an independent experimental correlation of individual cell orientation bias in an attractant gradient with a spatial difference in receptor occupancy. Our under-agarose population migration results are consistent with this proposition, allowing chemotaxis to be reliably characterized by a chemotactic sensitivity constant, chi 0, to which chi is directly proportional. Further, chi 0 has fundamental significance; it represents the reciprocal of the difference in number of bound receptors across cell dimensions required for directional orientation bias. In particular, for the system of human peripheral blood polymorphonuclear neutrophil leukocytes responding to FNLLP, we find that the chemotaxis coefficient is a function of attractant concentration, a following the expression: chi = chi 0NT0 f(a) S(a) Kd/(Kd + a)2 where Kd is the FNLLP-receptor equilibrium dissociation constant and NT0 is the total number of cell surface receptors for FNLLP. f(a) is the fraction of surface receptors remaining after down-regulation, and S(a) is the cell movement speed, both known functions of FNLLP concentration. We find that chi 0NT0 = 0.2 cm; according to a theoretical argument outlined in the Appendix this means that these cells exhibit 75% orientation toward higher attractant concentration when the absolute spatial difference in bound receptors is 0.0025NT0 over 10 micron. (For example, if NT0 = 50,000 this would correspond to a spatial difference of 125 bound receptors over 10 micron.) This result can be compared with estimates obtained from visual studies of individual neutrophils.     

A theory of measurement error and its implications for spatial and temporal gradient sensing during chemotaxis

Cells generally chemotax along a direction in which their receptor occupancy gradient—whether spatial or temporal—is maximum. Occupancy differentials are, however, often so small as to be masked by thermal noise; i.e., by fluctuations inherent in the stochastic nature of ligand binding. Such fluctuations therefore impose a fundamental limit on the sensitivity of a cell's ability to detect a chemoattractant gradient. In order to pursue the implications of this limit, fluctuation theories have been developed. The theories assume that the signal is some function of the receptor occupancy gradient, allow an estimate of the standard deviation abouts the mean signal, and permit an evaluation of, among other things, the extent to which a receptor defect can impair an effective response. Previous theories have assumed an equilibrated ligand-receptor interaction. In this paper we introduce a generalized definition of a signal caused by a receptor occupancy gradient that allows us to develop a non-equilibrium theory of thermal noise. We show that previous formulations are a special case of the current development. More specifically, we find the following.

1. Swimming cells subject to Brownian tumbling must generally average their signals over a very long time period to achieve a signal-to-noise ratio≤1. Spatial gradient detection is possible with ligand-receptor equilibrium constants<10³ M ^?1, but since such ligands are rare, theory predicts that tumbling cells will generally not detect gradients by measuring spatial occupancy differentials.These conclusions hold irrespective of whether chemical equilibrium is achieved.
2. For crawling cells not subject to Brownian tumbling, a range of affinities exists in which spatial or temporal gradient detection is possible. In general a spatial mechanism is more efficient for low affinity ligands (dissociation times <0.3s), whereas a temporal mechanism is more efficients for higherK. In this case the detection of gradients in slowly dissociating ligand will be facilitated if signal processing begins prior to chemical equilibration.
3. An important new parameter is indicated by the theory. The definitions of a temporal gradient signal is based on estimating and comparing average occupancy over two time intervals displaced by a timet ₁. The theory predicts an optimalt ₁, of order milliseconds, that leads to the shortest minimum averaging time.
4. Fort ₁ values at and longer than the optimum, and for all averaging times exceeding some minimum, the cell will detect a temporal signal.
5. For values oft ₁ at and near the optimum, if the averaging time becomes too long, the cell enters a region of insensitivity in which it can no longer respond.
6. Finally, as the interval between estimates of average occupancy decreases below the optimum, a critical value oft ₁ is reached at which the minimum averaging time undergoes an abrupt transition from a relatively short value to a value five orders of magnitude longer.

The molecular process(es) controllingt ₁ are at present unknown, nor has any attempt been made to identify them since the parameter has not been previously recognized. We speculate that the search for its molecular basis might uncover a highly sensitive control mechanism, with defects in this mechanism predicted to have a far more pronounced effect on the cells behavior than defects in receptor number or affinity.     

Consequences of chemosensory phenomena for leukocyte chemotactic orientation

The stochastic nature of cell surface receptor-ligand binding is known to limit the accuracy of detection of chemoattractant gradients by leukocytes (11, 12), thus limiting the orientation ability that is crucial to the chemotactic response in host defense. The probabilistic cell orientation model of Lauffenburger (11) is extended here to assess the consequences of recently discovered receptor phenomena: “down-regulation” of total surface receptor number, spatial asymmetry of surface receptors, and existence of a higher-affinity receptor subpopulation. In general, a reduction in orientation accuracy is predicted by inclusion of these phenomena. An orientation signal based on a simple model of chemosensory adaptation (i.e., a spatial difference inrelative receptor occupancy) is found to be functionally different from the signal suggested by an experimental correlation (i.e., a spatial difference inabsolute receptor occupancy). However, in the context of receptor “signal noise,” the signal based on adaptation yields predictions in better qualitative agreement with the experimental orientation data of Zigmond (10). From this cell orientation model we can estimate the effective timeaveraging period required for noise diminution to a level allowing orientation predictions to match observed levels. This time-averaging period presumably reflects the time constant for receptor signal transduction and locomotory response.     

Measuring Stepwise Binding of Thermally Fluctuating Particles to Cell Membranes without Fluorescence

Thermal motions enable a particle to probe the optimal interaction state when binding to a cell membrane. However, especially on the scale of microseconds and nanometers, position and orientation fluctuations are difficult to observe with common measurement technologies. Here, we show that it is possible to detect single binding events of immunoglobulin-G-coated polystyrene beads, which are held in an optical trap near the cell membrane of a macrophage. Changes in the spatial and temporal thermal fluctuations of the particle were measured interferometrically, and no fluorophore labeling was required. We demonstrate both by Brownian dynamic simulations and by experiments that sequential stepwise increases in the force constant of the bond between a bead and a cell of typically 20 pN/μm are clearly detectable. In addition, this technique provides estimates about binding rates and diffusion constants of membrane receptors. The simple approach of thermal noise tracking points out new strategies in understanding interactions between cells and particles, which are relevant for a large variety of processes, including phagocytosis, drug delivery, and the effects of small microplastics and particulates on cells.     

Consequences of chemosensory phenomena for leukocyte chemotactic orientation

The stochastic nature of cell surface receptor-ligand binding is known to limit the accuracy of detection of chemoattractant gradients by leukocytes, thus limiting the orientation ability that is crucial to the chemotactic response in host defense. The probabilistic cell orientation model of Lauffenburger is extended here to assess the consequences of recently discovered receptor phenomena: "down-regulation" of total surface receptor number, spatial asymmetry of surface receptors, and existence of a higher-affinity receptor subpopulation. In general, a reduction in orientation accuracy is predicted by inclusion of these phenomena. An orientation signal based on a simple model of chemosensory adaptation (i.e., a spatial difference in relative receptor occupancy) is found to be functionally different from the signal suggested by an experimental correlation (i.e., a spatial difference in absolute receptor occupancy). However, in the context of receptor "signal noise," the signal based on adaptation yields predictions in better qualitative agreement with the experimental orientation data of Zigmond. From this cell orientation model we can estimate the effective time-averaging period required for noise diminution to a level allowing orientation predictions to match observed levels. This time-averaging period presumably reflects the time constant for receptor signal transduction and locomotory response.     

A theory of measurement error and its implications for spatial and temporal gradient sensing during chemotaxis. II. The effects of non-equilibrated ligand binding

Cells generally chemotax along a direction in which their receptor occupancy gradient--whether spatial or temporal--is maximum. Occupancy differentials are, however, often so small as to be masked by thermal noise; i.e., by fluctuations inherent in the stochastic nature of ligand binding. Such fluctuations therefore impose a fundamental limit on the sensitivity of a cell's ability to detect a chemoattractant gradient. In order to pursue the implications of this limit, fluctuation theories have been developed. The theories assume that the signal is some function of the receptor occupancy gradient, allow an estimate of the standard deviation about the mean signal, and permit an evaluation of, among other things, the extent to which a receptor defect can impair an effective response. Previous theories have assumed an equilibrated ligand-receptor interaction. In this paper we introduce a generalized definition of a signal caused by a receptor occupancy gradient that allows us to develop a non-equilibrium theory of thermal noise. We show that previous formulations are a special case of the current development. More specifically, we find the following. Swimming cells subject to Brownian tumbling must generally average their signals over a very long time period to achieve a signal-to-noise ratio less than or equal to 1. Spatial gradient detection is possible with ligand-receptor equilibrium constants less than 10(3)M-1, but since such ligands are rare, theory predicts that tumbling cells will generally not detect gradients by measuring spatial occupancy differentials. These conclusions hold irrespective of whether chemical equilibrium is achieved. For crawling cells not subject to Brownian tumbling, a range of affinities exists in which spatial or temporal gradient detection is possible. In general a spatial mechanism is more efficient for low affinity ligands (dissociation times less than 0.3 s), whereas a temporal mechanism is more efficient for higher K. In this case the detection of gradients in slowly dissociating ligand will be facilitated if signal processing begins prior to chemical equilibration. An important new parameter is indicated by the theory. The definitions of a temporal gradient signal is based on estimating and comparing average occupancy over two time intervals displaced by a time t1. The theory predicts an optimal t1, of order milliseconds, that leads to the shortest minimum averaging time. For t1 values at and longer than the optimum, and for all averaging times exceeding some minimum, the cell will detect a temporal signal.(ABSTRACT TRUNCATED AT 400 WORDS)     

Using FCS to accurately measure protein concentration in the presence of noise and photobleaching

Quantitative cell biology requires precise and accurate concentration measurements, resolved both in space and time. Fluorescence correlation spectroscopy (FCS) has been held as a promising technique to perform such measurements because the fluorescence fluctuations it relies on are directly dependent on the absolute number of fluorophores in the detection volume. However, the most interesting applications are in cells, where autofluorescence and confinement result in strong background noise and important levels of photobleaching. Both noise and photobleaching introduce systematic bias in FCS concentration measurements and need to be corrected for. Here, we propose to make use of the photobleaching inevitably occurring in confined environments to perform series of FCS measurements at different fluorophore concentration, which we show allows a precise in situ measurement of both background noise and molecular brightness. Such a measurement can then be used as a calibration to transform confocal intensity images into concentration maps. The power of this approach is first illustrated with in vitro measurements using different dye solutions, then its applicability for in vivo measurements is demonstrated in Drosophila embryos for a model nuclear protein and for two morphogens, Bicoid and Capicua.     

Attenuation of current and voltage noise signals recorded from epithelia

Transepithelially recorded current and voltage fluctuations are filtered by the impedance of the electrical equivalent parameters of the preparation, in series or in parallel, with the noise source. Fluctuations in voltage and current are assumed to be caused by fluctuations in conductance of the apical membrane. In order to obtain an estimation of the intrinsic noise amplitudes, calculations are presented to correct the transepithelial fluctuations. The influence of different model parameters on the recorded noise spectra is investigated. It is shown that the shape of the transepithelially recorded noise spectra may differ from the intrinsic ones, e.g. “peaking” in the power spectra may be explained by the assumption of a positive (referred to cell inside) e.m.f. at the basolateral membrane or a polarization impedance in series with the epithelium. Furthermore it is demonstrated that the ratio of voltage to current noise power may differ from the squared magnitude of the impedance.     

The dynamics of a discrete geotropic sensor subject to rotation-induced gravity compensation

A clinostat achieves gravity compensation by providing circular rotation with uniform speed, about a horizontal axis. The dynamics of an assumed, discrete and free-moving subcellular gravity receptor, subject to clinostat rotation, is analyzed. The results imply that there is an optimum rotation rate; higher speeds result in circular motions with diameters more comparable to thermal noise fluctuations, but with greater linear velocities due to increasing centrifugal forces. An optimizing function is proposed. The nucleolus and mitochondrion is chosen as a gravity receptor for illustrating the use of this theory. The characteristics of their clinostat-induced motions are incorporated with experimental results on Avena plant shoots in an illustrative example.     

Biological chromodynamics: a general method for measuring protein occupancy across the genome by calibrating ChIP-seq

Sequencing DNA fragments associated with proteins following in vivo cross-linking with formaldehyde (known as ChIP-seq) has been used extensively to describe the distribution of proteins across genomes. It is not widely appreciated that this method merely estimates a protein''s distribution and cannot reveal changes in occupancy between samples. To do this, we tagged with the same epitope orthologous proteins in Saccharomyces cerevisiae and Candida glabrata, whose sequences have diverged to a degree that most DNA fragments longer than 50 bp are unique to just one species. By mixing defined numbers of C. glabrata cells (the calibration genome) with S. cerevisiae samples (the experimental genomes) prior to chromatin fragmentation and immunoprecipitation, it is possible to derive a quantitative measure of occupancy (the occupancy ratio – OR) that enables a comparison of occupancies not only within but also between genomes. We demonstrate for the first time that this ‘internal standard’ calibration method satisfies the sine qua non for quantifying ChIP-seq profiles, namely linearity over a wide range. Crucially, by employing functional tagged proteins, our calibration process describes a method that distinguishes genuine association within ChIP-seq profiles from background noise. Our method is applicable to any protein, not merely highly conserved ones, and obviates the need for the time consuming, expensive, and technically demanding quantification of ChIP using qPCR, which can only be performed on individual loci. As we demonstrate for the first time in this paper, calibrated ChIP-seq represents a major step towards documenting the quantitative distributions of proteins along chromosomes in different cell states, which we term biological chromodynamics.     

Current noise of a protein-selective biological nanopore

1/f current noise is ubiquitous in protein pores, porins, and channels. We have previously shown that a protein-selective biological nanopore with an external protein receptor can function as a 1/f noise generator when a high-affinity protein ligand is reversibly captured by the receptor. Here, we demonstrate that the binding affinity and concentration of the ligand are key determinants for the nature of current noise. For example, 1/f was absent when a protein ligand was reversibly captured at a much lower concentration than its equilibrium dissociation constant against the receptor. Furthermore, we also analyzed the composite current noise that resulted from mixtures of low-affinity and high-affinity ligands against the same receptor. This study highlights the significance of protein recognition events in the current noise fluctuations across biological membranes.     

Molecular Mechanism for Attractant Signaling to DHMA by E. coli Tsr

The attractant chemotaxis response of Escherichia coli to norepinephrine requires that it be converted to 3,4-dihydroxymandelic acid (DHMA) by the monoamine oxidase TynA and the aromatic aldehyde dehydrogenase FeaB. DHMA is sensed by the serine chemoreceptor Tsr, and the attractant response requires that at least one subunit of the periplasmic domain of the Tsr homodimer (pTsr) has an intact serine-binding site. DHMA that is generated in vivo by E. coli is expected to be a racemic mixture of the (R) and (S) enantiomers, so it has been unclear whether one or both chiral forms are active. Here, we used a combination of state-of-the-art tools in molecular docking and simulations, including an in-house simulation-based docking protocol, to investigate the binding properties of (R)-DHMA and (S)-DHMA to E. coli pTsr. Our studies computationally predicted that (R)-DHMA should promote a stronger attractant response than (S)-DHMA because of a consistently greater-magnitude piston-like pushdown of the pTsr α-helix 4 toward the membrane upon binding of (R)-DHMA than upon binding of (S)-DHMA. This displacement is caused primarily by interaction of DHMA with Tsr residue Thr156, which has been shown by genetic studies to be critical for the attractant response to L-serine and DHMA. These findings led us to separate the two chiral species and test their effectiveness as chemoattractants. Both the tethered cell and motility migration coefficient assays validated the prediction that (R)-DHMA is a stronger attractant than (S)-DHMA. Our study demonstrates that refined computational docking and simulation studies combined with experiments can be used to investigate situations in which subtle differences between ligands may lead to diverse chemotactic responses.     

A Novel Assay for Assessing Juxtamembrane and Transmembrane Domain Interactions Important for Receptor Heterodimerization

Understanding the basis of specificity in receptor homodimerization versus heterodimerization is essential in determining the role receptor plays in signal transduction. Specificity in each of the interfaces formed during signal transduction involves cooperative interactions between receptor extracellular, transmembrane (TM), and cytoplasmic domains. While methods exist for studying receptor heterodimerization in cell membranes, they are limited to either TM domains expressed in an inverted orientation or capture only heterodimerization in a single assay. To address this limitation, we have developed an assay (DN-AraTM) that enables simultaneous measurement of homodimerization and heterodimerization of type I receptor domains in their native orientation, including both soluble and TM domains. Using integrin α_IIb and RAGE (receptor for advanced glycation end products) as model type I receptor systems, we demonstrate both specificity and sensitivity of our approach, which will provide a novel tool to identify specific domain interactions that are important in regulating signal transduction.     

Stochastic Actin Polymerization and Steady Retrograde Flow Determine Growth Cone Advancement

Neuronal growth is an extremely complex yet reliable process that is directed by a dynamic lamellipodial structure at the tip of every growing neurite, called the growth cone. Lamellipodial edge fluctuations are controlled by the interplay between actin polymerization pushing the edge forward and molecular motor driven retrograde actin flow retracting the actin network. The leading edge switches randomly between extension and retraction processes. We identify switching of “on/off” states in actin polymerization as the main determinant of lamellipodial advancement. Our analysis of motility statistics allows for a prediction of growth direction. This was used in simulations explaining the amazing signal detection capabilities of neuronal growth by the experimentally found biased stochastic processes. Our measurements show that the intensity of stochastic fluctuations depend on changes in the underlying active intracellular processes and we find a power law η = a^∗x^α with exponent α = 2.63 ± 0.12 between noise intensity η and growth cone activity x, defined as the sum of protrusion and retraction velocity. Differences in the lamellipodial dynamics between primary neurons and a neuronal cell line further suggests that active processes tune the observed stochastic fluctuations. This hints at a possible role of noise intensity in determining signal detection sensitivity.     

Studies of bacterial chemotaxis in defined concentration gradients. A model for chemotaxis toward L-serine

The details of the chemotactic response of Salmonella typhimurium to gradients of L-serine have been examined in some detail. Two relatively macroscopic techniques have been employed to measure the bacterial response. These include measurements of the average velocity as the bacterial population moves toward attractants, and measurement of the upward-to-downward flux ratio, R, in the stable preformed attractant gradients. The dependence of the average velocity on gradient appears to be hyperbolic in nature, while the flux ratio depends linearly on the gradient. These data suggest a microscopic model for the dependence of bacterial behavior on the serine gradient. The model involves a linear dependence of the mean lifetime of a bacterial trajectory on the gradient for those bacteria moving toward higher attractant concentration. Those moving toward low concentrations of attractant do not change the mean duration of their trajectories, or the speed at which a given bacterium swims through the solution. This model generates the observed dependences of the average velocity and flux ratio on gradient. Interpretation of the experimental data suggests that a gradient which increases serine concentration by a factor of 2 in 10 mm is sufficient to double the average duration of a trajectory for a bacterium moving directly up the gradient. The concentration dependence of the chemotactic response to serine is more complicated. It suggests that more than one receptor of serine may be involved in determining chemotactic behavior to this attractant.     

Single-Cell E. coli Response to an Instantaneously Applied Chemotactic Signal

In response to an attractant or repellant, an Escherichia coli cell controls the rotational direction of its flagellar motor by a chemotaxis system. When an E. coli cell senses an attractant, a reduction in the intracellular concentration of a chemotaxis protein, phosphorylated CheY (CheY-P), induces counterclockwise (CCW) rotation of the flagellar motor, and this cellular response is thought to occur in several hundred milliseconds. Here, to measure the signaling process occurring inside a single E. coli cell, including the recognition of an attractant by a receptor cluster, the inactivation of histidine kinase CheA, and the diffusion of CheY and CheY-P molecules, we applied a serine stimulus by instantaneous photorelease from a caged compound and examined the cellular response at a temporal resolution of several hundred microseconds. We quantified the clockwise (CW) and CCW durations immediately after the photorelease of serine as the response time and the duration of the response, respectively. The results showed that the response time depended on the distance between the receptor and motor, indicating that the decreased CheY-P concentration induced by serine propagates through the cytoplasm from the receptor-kinase cluster toward the motor with a timing that is explained by the diffusion of CheY and CheY-P molecules. The response time included 240 ms for enzymatic reactions in addition to the time required for diffusion of the signaling molecule. The measured response time and duration of the response also revealed that the E. coli cell senses a similar serine concentration regardless of whether the serine concentration is increasing or decreasing. These detailed quantitative findings increase our understanding of the signal transduction process that occurs inside cells during bacterial chemotaxis.     

Direct Correlation between Motile Behavior and Protein Abundance in Single Cells

Understanding how stochastic molecular fluctuations affect cell behavior requires the quantification of both behavior and protein numbers in the same cells. Here, we combine automated microscopy with in situ hydrogel polymerization to measure single-cell protein expression after tracking swimming behavior. We characterized the distribution of non-genetic phenotypic diversity in Escherichia coli motility, which affects single-cell exploration. By expressing fluorescently tagged chemotaxis proteins (CheR and CheB) at different levels, we quantitatively mapped motile phenotype (tumble bias) to protein numbers using thousands of single-cell measurements. Our results disagreed with established models until we incorporated the role of CheB in receptor deamidation and the slow fluctuations in receptor methylation. Beyond refining models, our central finding is that changes in numbers of CheR and CheB affect the population mean tumble bias and its variance independently. Therefore, it is possible to adjust the degree of phenotypic diversity of a population by adjusting the global level of expression of CheR and CheB while keeping their ratio constant, which, as shown in previous studies, confers functional robustness to the system. Since genetic control of protein expression is heritable, our results suggest that non-genetic diversity in motile behavior is selectable, supporting earlier hypotheses that such diversity confers a selective advantage.     

Single-Cell E.?coli Response to an Instantaneously Applied Chemotactic Signal

In response to an attractant or repellant, an Escherichia coli cell controls the rotational direction of its flagellar motor by a chemotaxis system. When an E. coli cell senses an attractant, a reduction in the intracellular concentration of a chemotaxis protein, phosphorylated CheY (CheY-P), induces counterclockwise (CCW) rotation of the flagellar motor, and this cellular response is thought to occur in several hundred milliseconds. Here, to measure the signaling process occurring inside a single E. coli cell, including the recognition of an attractant by a receptor cluster, the inactivation of histidine kinase CheA, and the diffusion of CheY and CheY-P molecules, we applied a serine stimulus by instantaneous photorelease from a caged compound and examined the cellular response at a temporal resolution of several hundred microseconds. We quantified the clockwise (CW) and CCW durations immediately after the photorelease of serine as the response time and the duration of the response, respectively. The results showed that the response time depended on the distance between the receptor and motor, indicating that the decreased CheY-P concentration induced by serine propagates through the cytoplasm from the receptor-kinase cluster toward the motor with a timing that is explained by the diffusion of CheY and CheY-P molecules. The response time included 240 ms for enzymatic reactions in addition to the time required for diffusion of the signaling molecule. The measured response time and duration of the response also revealed that the E. coli cell senses a similar serine concentration regardless of whether the serine concentration is increasing or decreasing. These detailed quantitative findings increase our understanding of the signal transduction process that occurs inside cells during bacterial chemotaxis.     

Estimates of the local parameters of plasma density fluctuations by reflectometry measurements

The question is considered of how to estimate the parameters of local plasma density fluctuations from reflectometry measurements made by probing the plasma with an extraordinary electromagnetic wave. In the geometrical-optics approximation, a formula is derived that relates the fluctuation amplitude of the phase of the reflected signal to the amplitude of local plasma density fluctuations and the range of its applicability is considered. The spectral sensitivity of reflectometry measurements in a reflection region of finite dimensions to poloidal perturbations with wavenumbers k _⊥ ? k ₀ is estimated by the phase-screen method, and the expressions obtained are compared with the results of numerical simulations. Based on the relationships derived, an algorithm is proposed for recovering the amplitude of the local plasma density fluctuations from the fluctuations in the reflected reflectometer signal. The results obtained are compared with the results of the full-wave simulations of the reflection of microwaves from a turbulent plasma. Finally, an example is given of how to recover the data on the amplitude of the local plasma density fluctuations in the T-10 tokamak plasma.     

Four-Dimensional Spatial Nanometry of Single Particles in Living Cells Using Polarized Quantum Rods

Single particle tracking is widely used to study protein movement with high spatiotemporal resolution both in vitro and in cells. Quantum dots, which are semiconductor nanoparticles, have recently been employed in single particle tracking because of their intense and stable fluorescence. Although single particles inside cells have been tracked in three spatial dimensions (X, Y, Z), measurement of the angular orientation of a molecule being tracked would significantly enhance our understanding of the molecule’s function. In this study, we synthesized highly polarized, rod-shaped quantum dots (Qrods) and developed a coating method that optimizes the Qrods for biological imaging. We describe a Qrod-based single particle tracking technique that blends optical nanometry with nanomaterial science to simultaneously measure the three-dimensional and angular movements of molecules. Using Qrods, we spatially tracked a membrane receptor in living cells in four dimensions with precision close to the single-digit range in nanometers and degrees.