Concentration correlation spectroscopy: a new biophysical probe based on occupation number fluctuations

VenusA206 Dimers Behave Coherently at Room Temperature

Fluorescent proteins (FPs) have revolutionized cell biology by allowing genetic tagging of specific proteins inside living cells. In conjunction with Förster's resonance energy transfer (FRET) measurements, FP-tagged proteins can be used to study protein-protein interactions and estimate distances between tagged proteins. FRET is mediated by weak Coulombic dipole-dipole coupling of donor and acceptor fluorophores that behave independently, with energy hopping discretely and incoherently between fluorophores. Stronger dipole-dipole coupling can mediate excitonic coupling in which excitation energy is distributed near instantaneously between coherently interacting excited states that behave as a single quantum entity. The interpretation of FP energy transfer measurements to estimate separation often assumes that donors and acceptors are very weakly coupled and therefore use a FRET mechanism. This assumption is considered reasonable as close fluorophore proximity, typically associated with strong excitonic coupling, is limited by the FP β-barrel structure. Furthermore, physiological temperatures promote rapid vibrational dephasing associated with a rapid decoherence of fluorophore-excited states. Recently, FP dephasing times that are 50 times slower than traditional organic fluorophores have been measured, raising the possibility that evolution has shaped FPs to allow stronger than expected coupling under physiological conditions. In this study, we test if excitonic coupling between FPs is possible at physiological temperatures. FRET and excitonic coupling can be distinguished by monitoring spectral changes associated with fluorophore dimerization. The weak coupling mediating FRET should not cause a change in fluorophore absorption, whereas strong excitonic coupling causes Davydov splitting. Circular dichroism spectroscopy revealed Davydov splitting when the yellow FP Venus_A206 dimerizes, and a novel approach combining photon antibunching and fluorescence correlation spectroscopy was used to confirm that the two fluorophores in a Venus_A206 homodimer behave as a single-photon emitter. We conclude that excitonic coupling between Venus_A206 fluorophores is possible at physiological temperatures.

Auto-FPFA: An Automated Microscope for Characterizing Genetically Encoded Biosensors

Genetically encoded biosensors function by linking structural change in a protein construct, typically tagged with one or more fluorescent proteins, to changes in a biological parameter of interest (such as calcium concentration, pH, phosphorylation-state, etc.). Typically, the structural change triggered by alterations in the bio-parameter is monitored as a change in either fluorescent intensity, or lifetime. Potentially, other photo-physical properties of fluorophores, such as fluorescence anisotropy, molecular brightness, concentration, and lateral and/or rotational diffusion could also be used. Furthermore, while it is likely that multiple photo-physical attributes of a biosensor might be altered as a function of the bio-parameter, standard measurements monitor only a single photo-physical trait. This limits how biosensors are designed, as well as the accuracy and interpretation of biosensor measurements. Here we describe the design and construction of an automated multimodal-microscope. This system can autonomously analyze 96 samples in a micro-titer dish and for each sample simultaneously measure intensity (photon count), fluorescence lifetime, time-resolved anisotropy, molecular brightness, lateral diffusion time, and concentration. We characterize the accuracy and precision of this instrument, and then demonstrate its utility by characterizing three types of genetically encoded calcium sensors as well as a negative control.

Kinetics of biochemical sensing by single cells and populations of cells

We investigate the collective stationary sensing using N communicative cells, which involves surface receptors, diffusive signaling molecules, and cell-cell communication messengers. We restrict the scenarios to the signal-to-noise ratios (SNRs) for both strong communication and extrinsic noise only. We modified a previous model [Bialek and Setayeshgar, Proc. Natl. Acad. Sci. USA 102, 10040 (2005)PNASA60027-842410.1073/pnas.0504321102] to eliminate the singularities in the fluctuation correlations by considering a uniform receptor distribution over the surface of each cell with a finite radius a. The modified model enables a simple and rigorous mathematical treatment of the collective sensing phenomenon. We then derive the scaling of the SNR for both juxtacrine and autocrine cases in all dimensions. For the optimal locations of the cells in the autocrine case, we find identical scaling for both two and three dimensions.

A Novel Method of Determining the Functional Effects of a Minor Genetic Modification of a Protein

Contraction of muscles results from the ATP-coupled cyclic interactions of the myosin cross-bridges with actin filaments. Macroscopic parameters of contraction, such as maximum tension, speed of shortening, or ATPase activity, are unlikely to reveal differences between the wild-type and mutated (MUT) proteins when the level of transgenic protein expression is low. This is because macroscopic measurements are made on whole organs containing trillions of actin and myosin molecules. An average of the information collected from such a large assembly is bound to conceal any differences imposed by a small fraction of MUT molecules. To circumvent the averaging problem, the measurements were done on isolated ventricular myofibril (MF) in which thin filaments were sparsely labeled with a fluorescent dye. We isolated a single MF from a ventricle, oriented it vertically (to be able measure the orientation), and labeled 1 in 100,000 actin monomers with a fluorescent dye. We observed the fluorescence from a small confocal volume containing approximately three actin molecules. During the contraction of a ventricle actin constantly changes orientation (i.e., the transition moment of rigidly attached fluorophore fluctuates in time) because it is repetitively being "kicked" by myosin cross-bridges. An autocorrelation functions (ACFs) of these fluctuations are remarkably sensitive to the mutation of myosin. We examined the effects of Alanine to Threonine (A13T) mutation in the myosin regulatory light chain shown by population studies to cause hypertrophic cardiomyopathy. This is an appropriate example, because mutation is expressed at only 10% in the ventricles of transgenic mice. ACFs were either "Standard" (Std) (decaying monotonically in time) or "Non-standard" (NStd) (decaying irregularly). The sparse labeling of actin also allowed the measurement of the spatial distribution of actin molecules. Such distribution reflects the interaction of actin with myosin cross-bridges and is also remarkably sensitive to myosin mutation. The result showed that the A13T mutation caused 9% ACFs and 9% of spatial distributions of actin to be NStd, while the remaining 91% were Std, suggesting that the NStd performances were executed by the MUT myosin heads and that the Std performances were executed by non-MUT myosin heads. We conclude that the method explored in this study is a sensitive and valid test of the properties of low prevalence mutations in sarcomeric proteins.

Effect of a myosin regulatory light chain mutation K104E on actin-myosin interactions

Familial hypertrophic cardiomyopathy (FHC) is the most common cause of sudden cardiac death in young individuals. Molecular mechanisms underlying this disorder are largely unknown; this study aims at revealing how disruptions in actin-myosin interactions can play a role in this disorder. Cross-bridge (XB) kinetics and the degree of order were examined in contracting myofibrils from the ex vivo left ventricles of transgenic (Tg) mice expressing FHC regulatory light chain (RLC) mutation K104E. Because the degree of order and the kinetics are best studied when an individual XB makes a significant contribution to the overall signal, the number of observed XBs in an ex vivo ventricle was minimized to ∼20. Autofluorescence and photobleaching were minimized by labeling the myosin lever arm with a relatively long-lived red-emitting dye containing a chromophore system encapsulated in a cyclic macromolecule. Mutated XBs were significantly better ordered during steady-state contraction and during rigor, but the mutation had no effect on the degree of order in relaxed myofibrils. The K104E mutation increased the rate of XB binding to thin filaments and the rate of execution of the power stroke. The stopped-flow experiments revealed a significantly faster observed dissociation rate in Tg-K104E vs. Tg-wild-type (WT) myosin and a smaller second-order ATP-binding rate for the K104E compared with WT myosin. Collectively, our data indicate that the mutation-induced changes in the interaction of myosin with actin during the contraction-relaxation cycle may contribute to altered contractility and the development of FHC.

The spatial distribution of actin and mechanical cycle of myosin are different in right and left ventricles of healthy mouse hearts

The contraction of the right ventricle (RV) expels blood into the pulmonary circulation, and the contraction of the left ventricle (LV) pumps blood into the systemic circulation through the aorta. The respective afterloads imposed on the LV and RV by aortic and pulmonary artery pressures create very different mechanical requirements for the two ventricles. Indeed, differences have been observed in the contractile performance between left and right ventricular myocytes in dilated cardiomyopathy, in congestive heart failure, and in energy usage and speed of contraction at light loads in healthy hearts. In spite of these functional differences, it is commonly believed that the right and left ventricular muscles are identical because there were no differences in stress development, twitch duration, work performance, or power among the RV and LV in dogs. This report shows that on a mesoscopic scale [when only a few molecules are studied (here three to six molecules of actin) in ex vivo ventricular myofibrils], the two ventricles in rigor differ in the degree of orientational disorder of actin within in filaments and during contraction in the kinetics of the cross-bridge cycle.

Measuring protein dynamics in live cells: protocols and practical considerations for fluorescence fluctuation microscopy

Quantitative analysis of protein complex stoichiometries and mobilities are critical for elucidating the mechanisms that regulate cellular pathways. Fluorescence fluctuation spectroscopy (FFS) techniques can measure protein dynamics, such as diffusion coefficients and formation of complexes, with extraordinary precision and sensitivity. Complete calibration and characterization of the microscope instrument is necessary in order to avoid artifacts during data acquisition and to capitalize on the full capabilities of FFS techniques. We provide an overview of the theory behind FFS techniques, discuss calibration procedures, provide protocols, and give practical considerations for performing FFS experiments. One important parameter recovered from FFS measurements is the relative molecular brightness that can correlate with oligomerization. Three methods for measuring molecular brightness (fluorescence correlation spectroscopy, photon-counting histogram, and number and brightness analysis) recover similar values when measuring samples under ideal conditions in vitro. However, examples are given illustrating that these different methods used for calculating molecular brightness of fluorescent molecules in cells are not always equivalent. Methods relying on spot measurements are more prone to bleaching and movement artifacts that can lead to underestimation of brightness values. We advocate for the use of multiple FFS techniques to study molecular brightnesses to overcome and compliment limitations of individual techniques.

Phosphorylation of myosin regulatory light chain has minimal effect on kinetics and distribution of orientations of cross bridges of rabbit skeletal muscle

Force production in muscle results from ATP-driven cyclic interactions of myosin with actin. A myosin cross bridge consists of a globular head domain, containing actin and ATP-binding sites, and a neck domain with the associated light chain 1 (LC1) and the regulatory light chain (RLC). The actin polymer serves as a "rail" over which myosin translates. Phosphorylation of the RLC is thought to play a significant role in the regulation of muscle relaxation by increasing the degree of skeletal cross-bridge disorder and increasing muscle ATPase activity. The effect of phosphorylation on skeletal cross-bridge kinetics and the distribution of orientations during steady-state contraction of rabbit muscle is investigated here. Because the kinetics and orientation of an assembly of cross bridges (XBs) can only be studied when an individual XB makes a significant contribution to the overall signal, the number of observed XBs was minimized to ∼20 by limiting the detection volume and concentration of fluorescent XBs. The autofluorescence and photobleaching from an ex vivo sample was reduced by choosing a dye that was excited in the red and observed in the far red. The interference from scattering was eliminated by gating the signal. These techniques decrease large uncertainties associated with determination of the effect of phosphorylation on a few molecules ex vivo with millisecond time resolution. In spite of the remaining uncertainties, we conclude that the state of phosphorylation of RLC had no effect on the rate of dissociation of cross bridges from thin filaments, on the rate of myosin head binding to thin filaments, and on the rate of power stroke. On the other hand, phosphorylation slightly increased the degree of disorder of active cross bridges.

Imaging large cohorts of single ion channels and their activity

As calcium is the most important signaling molecule in neurons and secretory cells, amongst many other cell types, it follows that an understanding of calcium channels and their regulation of exocytosis is of vital importance. Calcium imaging using calcium dyes such as Fluo3, or FRET-based dyes that have been used widely has provided invaluable information, which combined with modeling has estimated the subtypes of channels responsible for triggering the exocytotic machinery as well as inferences about the relative distances away from vesicle fusion sites these molecules adopt. Importantly, new super-resolution microscopy techniques, combined with novel Ca(2+) indicators and imaginative imaging approaches can now define directly the nano-scale locations of very large cohorts of single channel molecules in relation to single vesicles. With combinations of these techniques the activity of individual channels can be visualized and quantified using novel Ca(2+) indicators. Fluorescently labeled specific channel toxins can also be used to localize endogenous assembled channel tetramers. Fluorescence lifetime imaging microscopy and other single-photon-resolution spectroscopic approaches offer the possibility to quantify protein-protein interactions between populations of channels and the SNARE protein machinery for the first time. Together with simultaneous electrophysiology, this battery of quantitative imaging techniques has the potential to provide unprecedented detail describing the locations, dynamic behaviors, interactions, and conductance activities of many thousands of channel molecules and vesicles in living cells.

Comparison of orientation and rotational motion of skeletal muscle cross-bridges containing phosphorylated and dephosphorylated myosin regulatory light chain

Calcium binding to thin filaments is a major element controlling active force generation in striated muscles. Recent evidence suggests that processes other than Ca(2+) binding, such as phosphorylation of myosin regulatory light chain (RLC) also controls contraction of vertebrate striated muscle (Cooke, R. (2011) Biophys. Rev. 3, 33-45). Electron paramagnetic resonance (EPR) studies using nucleotide analog spin label probes showed that dephosphorylated myosin heads are highly ordered in the relaxed fibers and have very low ATPase activity. This ordered structure of myosin cross-bridges disappears with the phosphorylation of RLC (Stewart, M. (2010) Proc. Natl. Acad. Sci. U.S.A. 107, 430-435). The slower ATPase activity in the dephosporylated moiety has been defined as a new super-relaxed state (SRX). It can be observed in both skeletal and cardiac muscle fibers (Hooijman, P., Stewart, M. A., and Cooke, R. (2011) Biophys. J. 100, 1969-1976). Given the importance of the finding that suggests a novel pathway of regulation of skeletal muscle, we aim to examine the effects of phosphorylation on cross-bridge orientation and rotational motion. We find that: (i) relaxed cross-bridges, but not active ones, are statistically better ordered in muscle where the RLC is dephosporylated compared with phosphorylated RLC; (ii) relaxed phosphorylated and dephosphorylated cross-bridges rotate equally slowly; and (iii) active phosphorylated cross-bridges rotate considerably faster than dephosphorylated ones during isometric contraction but the duty cycle remained the same, suggesting that both phosphorylated and dephosphorylated muscles develop the same isometric tension at full Ca(2+) saturation. A simple theory was developed to account for this fact.

Molecular brightness analysis reveals phosphatidylinositol 4-Kinase IIβ association with clathrin-coated vesicles in living cells

Mammalian cells express two classes of phosphatidylinositol 4-kinase (PI4K), designated as Types II and III, that phosphorylate phosphatidylinositol to generate PI4P. A number of studies have indicated that these enzymes are important for Golgi trafficking and both early and late stages of endocytosis. In this study, we focus on PI4KIIβ, a protein that is evenly distributed between membrane and soluble fractions, and is believed to participate in stimulus-dependent phosphoinositide signaling. Using molecular brightness analysis, we found that EGFP-tagged PI4KIIβ exists as two distinct species in the cytoplasm: a soluble monomer and a high-order complex enriched with multiple copies of PI4KIIβ. This observation was confirmed by an autocorrelation analysis that identified two species with distinct mobilities. We further demonstrate that the high-order complex enriched with PI4KIIβ is sensitive to inhibition of palmitoylation, indicating that it is associated with membranes, very likely vesicles. Indeed, we show that the high-order PI4KIIβ complex is sensitive to expression of dynamin 2 (K44A), a dominant-negative inhibitor of endocytosis. Using dual-color heterospecies partition analysis, we directly detected that PI4KIIβ comoves with clathrin light chain on vesicles. This analysis allows us to isolate the comobile species in the presence of strong background contribution from the monomeric pool of PI4KIIβ. Our results strongly suggest that PI4KIIβ is involved in an early stage of endocytosis and is associated with clathrin-coated vesicles. Moreover, we establish molecular brightness as a powerful tool for characterizing cellular cytosolic vesicles that are otherwise difficult to characterize by other techniques.

Fluorescence polarization and fluctuation analysis monitors subunit proximity, stoichiometry, and protein complex hydrodynamics

Förster resonance energy transfer (FRET) microscopy is frequently used to study protein interactions and conformational changes in living cells. The utility of FRET is limited by false positive and negative signals. To overcome these limitations we have developed Fluorescence Polarization and Fluctuation Analysis (FPFA), a hybrid single-molecule based method combining time-resolved fluorescence anisotropy (homo-FRET) and fluorescence correlation spectroscopy. Using FPFA, homo-FRET (a 1–10 nm proximity gauge), brightness (a measure of the number of fluorescent subunits in a complex), and correlation time (an attribute sensitive to the mass and shape of a protein complex) can be simultaneously measured. These measurements together rigorously constrain the interpretation of FRET signals. Venus based control-constructs were used to validate FPFA. The utility of FPFA was demonstrated by measuring in living cells the number of subunits in the α-isoform of Venus-tagged calcium-calmodulin dependent protein kinase-II (CaMKIIα) holoenzyme. Brightness analysis revealed that the holoenzyme has, on average, 11.9±1.2 subunit, but values ranged from 10–14 in individual cells. Homo-FRET analysis simultaneously detected that catalytic domains were arranged as dimers in the dodecameric holoenzyme, and this paired organization was confirmed by quantitative hetero-FRET analysis. In freshly prepared cell homogenates FPFA detected only 10.2±1.3 subunits in the holoenzyme with values ranging from 9–12. Despite the reduction in subunit number, catalytic domains were still arranged as pairs in homogenates. Thus, FPFA suggests that while the absolute number of subunits in an auto-inhibited holoenzyme might vary from cell to cell, the organization of catalytic domains into pairs is preserved.

Scanning image correlation spectroscopy

Molecular interactions are at the origin of life. How molecules get at different locations in the cell and how they locate their partners is a major and partially unresolved question in biology that is paramount to signaling. Spatio-temporal correlations of fluctuating fluorescently tagged molecules reveal how they move, interact, and bind in the different cellular compartments. Methods based on fluctuations represent a remarkable technical advancement in biological imaging. Here we discuss image analysis methods based on spatial and temporal correlation of fluctuations, raster image correlation spectroscopy, number and brightness, and spatial cross-correlations that give us information about how individual molecules move in cells and interact with partners at the single molecule level. These methods can be implemented with a standard laser scanning microscope and produce a cellular level spatio-temporal map of molecular interactions.

Quantification of receptor targeting aptamer binding characteristics using single-molecule spectroscopy

This experimental design presents a single molecule approach based on fluorescence correlation spectroscopy (FCS) for the quantification of outer membrane proteins which are receptors to an aptamer specifically designed to target the surface receptors of live Salmonella typhimurium. By using correlation analysis, we also show that it is possible to determine the associated binding kinetics of these aptamers on live single cells. Aptamers are specific oligonucleotides designed to recognize conserved sequences that bind to receptors with high affinity, and therefore can be integrated into selective biosensor platforms. In our experiments, aptamers were constructed to bind to outer membrane proteins of S. typhimurium and were assessed for specificity against Escherichia coli. By fluorescently labeling aptamer probes and applying FCS, we were able to study the diffusion dynamics of bound and unbound aptamers and compare them to determine the dissociation constants and receptor densities of the bacteria for each aptamer at single molecule sensitivity. The dissociation constants for these aptamer probes calculated from autocorrelation data were 0.1285 and 0.3772 nM and the respective receptor densities were 42.27 receptors per µm(2) and 49.82 receptors per µm(2). This study provides ample evidence that the number of surface receptors is sufficient for binding and that both aptamers have a high-binding affinity and can therefore be used in detection processes. The methods developed here are unique and can be generalized to examine surface binding kinetics and receptor quantification in live bacteria at single molecule sensitivity levels. The impact of this study is broad because our approach can provide a methodology for biosensor construction and calculation of live single cell receptor-ligand kinetics in a variety of environmental and biological applications.

Lessons in fluctuation correlation spectroscopy

Molecular diffusion and transport processes are fundamental in physical, chemical, and biological systems. Current approaches to measuring molecular transport in cells and tissues based on perturbation methods, e.g., fluorescence recovery after photobleaching, are invasive; single-point fluctuation correlation methods are local; and single-particle tracking requires the observation of isolated particles for relatively long periods of time. We discuss here the detection of molecular transport by exploiting spatiotemporal correlations measured among points at large distances (>1 μm). We illustrate the evolution of the conceptual framework that started with single-point fluorescence fluctuation analysis based on the transit of fluorescent molecules through a small volume of illumination. This idea has evolved to include the measurement of fluctuations at many locations in the sample using microscopy imaging methods. Image fluctuation analysis has become a rich and powerful technique that can be used to extract information about the spatial distribution of molecular concentration and transport in cells and tissues.

Fluorescence correlation spectroscopy and fluorescence cross-correlation spectroscopy

This article focuses on methods based on fluctuation correlation spectroscopy to determine the formation of protein complexes in living cells. We present the principles of the fluctuation method applied to cells. We discuss the novelty and the promises of this approach. The emphasis is in the discussion of the underlying statistical assumptions of the image correlation spectroscopy analysis rather than in reviewing applications of the method. Although one example of the application of the fluctuation method is given, this article also contains simulations that are better suited to illustrate and support the basic assumptions of the method.

Dynamics and function of compact nucleosome arrays

The packaging of eukaryotic DNA into chromatin sterically occludes polymerases, recombinases and repair enzymes. How chromatin structure changes to allow their actions is unknown. We constructed defined fluorescently labeled trinucleosome arrays, allowing analysis of chromatin conformational dynamics via fluorescence resonance energy transfer (FRET). The arrays undergo reversible Mg2+-dependent folding similar to that of longer arrays studied previously. We define two intermediate conformational states in the reversible folding of the nucleosome arrays and characterize the microscopic rate constants. Nucleosome arrays are highly dynamic even when compact, undergoing conformational fluctuations on timescales in the second to microsecond range. Compact states of the arrays allow binding to DNA within the central nucleosome via site exposure. Protein binding can also drive decompaction of the arrays. Thus, our results reveal multiple modes by which spontaneous chromatin fiber dynamics allow for the invasion and action of DNA-processing protein complexes.

Mapping the number of molecules and brightness in the laser scanning microscope

We describe a technique based on moment-analysis for the measurement of the average number of molecules and brightness in each pixel in fluorescence microscopy images. The average brightness of the particle is obtained from the ratio of the variance to the average intensity at each pixel. To obtain the average number of fluctuating particles, we divide the average intensity at one pixel by the brightness. This analysis can be used in a wide range of concentrations. In cells, the intensity at any given pixel may be due to bright immobile structures, dim fast diffusing particles, and to autofluorescence or scattering. The total variance is given by the variance of each of the above components in addition to the variance due to detector noise. Assuming that all sources of variance are independent, the total variance is the sum of the variances of the individual components. The variance due to the particles fluctuating in the observation volume is proportional to the square of the particle brightness while the variance of the immobile fraction, the autofluorescence, scattering, and that of the detector is proportional to the intensity of these components. Only the fluctuations that depend on the square of the brightness (the mobile particles) will have a ratio of the variance to the intensity >1. Furthermore, changing the fluorescence intensity by increasing the illumination power, distinguishes between these possible contributions. We show maps of molecular brightness and number of cell migration proteins obtained using a two-photon scanning microscope operating with a photon-counting detector. These brightness maps reveal binding dynamics at the focal adhesions with pixel resolution and provide a picture of the binding and unbinding process in which dim molecules attach to the adhesions or large molecular aggregates dissociate from adhesion.

Open-system nonequilibrium steady state: statistical thermodynamics, fluctuations, and chemical oscillations

Gibbsian equilibrium statistical thermodynamics is the theoretical foundation for isothermal, closed chemical, and biochemical reaction systems. This theory, however, is not applicable to most biochemical reactions in living cells, which exhibit a range of interesting phenomena such as free energy transduction, temporal and spatial complexity, and kinetic proofreading. In this article, a nonequilibrium statistical thermodynamic theory based on stochastic kinetics is introduced, mainly through a series of examples: single-molecule enzyme kinetics, nonlinear chemical oscillation, molecular motor, biochemical switch, and specificity amplification. The case studies illustrate an emerging theory for the isothermal nonequilibrium steady state of open systems.

Fluctuations and membrane heterogeneity

Biological membranes contain many specialized domains, ranging from tens of nanometers to several microns in size and characterized by different concentrations and compositions of protein. Because these domains influence membrane function, considerable attention has focused on understanding their origin. Here it is shown that number fluctuations and nonspecific interprotein interactions can lead to considerable heterogeneity in the distribution of membrane proteins, and to an associated submicron-scale domain structure. Number fluctuations were analyzed by modeling the membrane as a two-dimensional fluid containing interacting protein solutes. The characteristic size and lifetime of a domain in which one would expect to observe a fluctuation of specified magnitude was calculated; snapshots showing fluctuation-induced heterogeneity were generated by Monte Carlo simulation. Domain size was found to depend on the nature of the interprotein force (e.g., attractive or repulsive) and on the average protein concentration. Domain size was largest at low protein concentrations and in the presence of attractive interprotein forces, and was smallest at high protein concentrations and in the presence of repulsive interprotein forces. Domain lifetime was found to depend on domain size and on the diffusion coefficient of the proteins. In a 'typical' membrane containing 5-nm proteins with diffusion coefficient 10(-10) cm(2)/s at a density of 1000 proteins/microm(2), a 30% fluctuation will yield domains characterized by a 2-fold difference in local concentration; these domains persist over a distance of about 100 nm and have a lifetime of about 0.25 s. These results can be used to analyze the domain structure commonly observed in electron micrographs, and have implications for both number fluctuation and Monte Carlo studies of the distribution and dynamics of membrane proteins.

COMMENTARY ON THE PLEASURES OF SOLVING IMPOSSIBLE PROBLEMS OF EXPERIMENTAL PHYSIOLOGY

This commentary presents a series of examples of "impossible experimental problems" that we have encountered over the years in addressing various challenging questions in physiology. We aim to show how stimulating the challenges of physiology can be and demonstrate how our naive invocation of methods from disparate fields of science and engineering has led to delightful resolutions of physiological challenges that were utterly new to this intrepid interdisciplinary researcher.

Structural analysis of sterol distributions in the plasma membrane of living cells

Although plasma membrane (PM) cholesterol-rich and -poor domains have been isolated by subcellular fractionation, the real-time arrangement of cholesterol in such domains in living cells is still unclear. Therefore, dehydroergosterol (DHE), a naturally occurring fluorescent sterol, was incorporated into cultured L-cell fibroblasts. Two PM markers, the enhanced cyan fluorescent protein (ECFP-Mem) and 3'-dioctadecyloxacarbocyanine perchlorate [DiOC(18)(3)], were used to distinguish DHE localized at the PM of living cells. Spatial enrichment of DHE in the PM of living cells was visualized in real time by multiphoton laser scanning microscopy (MPLSM). Quantitative models and image-processing techniques were developed for statistical analysis of the distribution of DHE within the PM. The PM was resolved from the cytoplasm in a two-step process, and a smooth trajectory reference of the PM was refined by statistical regression and moments-based techniques. Thus, DHE intensities over the PM were measured following the major DHE intensity distributions. Spatial distributions of DHE within the PM were examined by a statistical inference technique, complete spatial randomness (CSR). For PM regions densely populated with DHE, the distributions of DHE exhibited statistical arrangements that were not spatial random (i.e., homogeneous Poisson process) or regular but, instead, exhibited strong cluster patterns. In effect, real-time MPLSM imaging data for the first time demonstrated that sterol enrichment occurred in clustered regions in the PM, consistent with the existence of cholesterol-rich domains in the plasma membrane of living cells.

Quick tour of fluorescence correlation spectroscopy from its inception

Fluorescence correlation spectroscopy (FCS) was originally developed in the early 1970s as a way to measure the kinetics of chemical reactions under zero perturbation conditions. At its inception, the measurement was difficult due to experimental limitations and was primarily used during the 1970s and 1980s to characterize diffusion. More recently, as a result of technological advances, FCS measurements have become easier and more versatile. In addition to measurements of diffusion both in solution and in cells, FCS is now also used to measure not only chemical reaction kinetics but also extents of molecular aggregation, the dynamics of photophysical processes, conformational fluctuations, molecular interactions in solution and in cells, and has even found application as a pharmaceutical screening method. From its inception to the present, the contributions of Webb and his coworkers have had a central and defining role in the development and applications of FCS.

Analyzing protein-protein interactions in cell membranes

Interactions among membrane proteins regulate numerous cellular processes, including cell growth, cell differentiation and apoptosis. We need to understand which proteins interact, where they interact and to which extent they interact. This article describes a set of novel approaches to measure, on the surface of living cells, the number of clusters of proteins, the number of proteins per cluster, the number of clusters or membrane domains that contain pairs of interacting proteins and the fraction of one protein species that interacts with another protein within these domains. These data can then be interpreted in terms of the function of the protein-protein interactions.

Isolation of bright aggregate fluctuations in a multipopulation image correlation spectroscopy system using intensity subtraction

Image correlation spectroscopy allows sensitive measurement of the spatial distribution and aggregation state of fluorescent membrane macro molecules. When studying a single population system (i.e., aggregates of similar brightness), an accurate measure can be made of the aggregate number per observation area, but this measurement becomes much more complex in a distributed population system (i.e., bright and faint aggregates). This article describes an alternate solution that involves extraction of the bright aggregate population information. This novel development for image correlation spectroscopy, termed intensity subtraction analysis, uses sequential uniform intensity subtraction from raw confocal images. Sequential intensity subtraction results in loss of faint aggregate fluctuations that are smaller in magnitude than fluctuations due to the brightest aggregates. The resulting image has correlatable fluctuations originating from only the brightest population, permitting quantification of this population's distribution and further cross-correlation measurements. The feasibility of this technique is demonstrated using fluorescent microsphere images and biological samples. The technique is further used to examine the spatial distribution of a plasma-membrane-labeled fluorescent synthetic ganglioside, and to cross-correlate this probe with various membrane markers. The evidence provided demonstrates that bright aggregates of the fluorescent ganglioside are associated with clathrin-coated pits, membrane microvilli, and detergent-resistant membranes.

Single-molecule enzymology: stochastic Michaelis-Menten kinetics

We provide a stochastic analysis of single-molecule enzymatic reactions that follow Michaelis-Menten kinetics. We show that this system can exhibit oscillatory behavior in the non-equilibrium steady-state at appropriate substrate concentrations. The stochastic model includes both enzyme dynamics and substrate turnover kinetics. The relationship between the probability of substrate survival and the time-correlation of enzyme conformation trajectories is discussed. Deterministic kinetics at large substrate concentrations are obtained as a limit of the stochastic model. We suggest that in addition to fluctuating enzyme conformation, the stochastic nature of substrate concentration fluctuations is another possible source of the complex behavior of single-molecule enzyme kinetics.

Concentration fluctuations in a mesoscopic oscillating chemical reaction system

Under sustained pumping, kinetics of macroscopic nonlinear biochemical reaction systems far from equilibrium either can be in a stationary steady state or can execute sustained oscillations about a fixed mean. For a system of two dynamic species X and Y, the concentrations n(x) and n(y) will be constant or will repetitively trace a closed loop in the (n(x), n(y)) phase plane, respectively. We study a mesoscopic system with n(x) and n(y) very small; hence the occurrence of random fluctuations modifies the deterministic behavior and the law of mass action is replaced by a stochastic model. We show that n(x) and n(y) execute cyclic random walks in the (n(x), n(y)) plane whether or not the deterministic kinetics for the corresponding macroscopic system represents a steady or an oscillating state. Probability distributions and correlation functions for n(x)(t) and n(y)(t) show quantitative but not qualitative differences between states that would appear as either oscillating or steady in the corresponding macroscopic systems. A diffusion-like equation for probability P(n(x), n(y), t) is obtained for the two-dimensional Brownian motion in the (n(x), n(y)) phase plane. In the limit of large n(x), n(y), the deterministic nonlinear kinetics derived from mass action is recovered. The nature of large fluctuations in an oscillating nonequilibrium system and the conceptual difference between "thermal stochasticity" and "temporal complexity" are clarified by this analysis. This result is relevant to fluorescence correlation spectroscopy and metabolic reaction networks.

Fluorescence correlation spectroscopy: inception, biophysical experimentations, and prospectus

Fluorescence correlation spectroscopy examines the chemical and the photophysical dynamics of dilute molecular solutions by measurement of the dynamic optical fluctuations of the fluorescence of a few molecules, even averaging less than one molecule at a time, in open focal volumes that are usually less than a femtoliter (<10(-18) m(3)). It applies the same principles of statistical thermodynamics as does quasi-elastic light scattering. Molecular interactions, conformational changes, chemical reactions, and photophysical dynamics that are not ordinarily detectable by quasi-elastic light scattering can be analyzed by fluorescence correlation spectroscopy in cases in which molecular fluorescence changes in the dynamic range 10(-7)-10(2) s.

Response tuning in bacterial chemotaxis

Chemotaxis of enteric bacteria in spatial gradients toward a source of chemoattractant is accomplished by increases in the length of swimming runs up the gradient. Biochemical components of the intracellular signal pathway have been identified, but mechanisms for achieving the high response sensitivity remain unknown. Binding of attractant ligand to its receptor inactivates a receptor-associated histidine kinase, CheA, which phosphorylates the signal protein CheY. The reduction in phospho-CheY, CheY-P, levels prolongs swimming runs. Here, the stimulus-response relation has been determined by measurement of excitation responses mediated by the Tar receptor to defined concentration jumps of the attractant, aspartate, administered within milliseconds by photolysis of a photolabile precursor. The bacteria responded to <1% changes in Tar occupancy when adapted to aspartate over concentrations spanning three orders of magnitude. Response amplitudes increased approximately logarithmically with stimulus strength, extending responsiveness over a greater stimulus range. The extent and form of this relation indicates that, in contrast to mechanisms for adaptive recovery, excitation signal generation involves amplification based on cooperative interactions. These interactions could entail inactivation of multiple receptor-CheA signaling complexes and/or simultaneous activation of CheY-P dephosphorylation.

Quantitative study of polymer conformation and dynamics by single-particle tracking

We present a new method for analyzing the dynamics of conformational fluctuations of individual flexible polymer molecules. In single-particle tracking (SPT), one end of the polymer molecule is tethered to an immobile substratum. A microsphere attached to the other end serves as an optical marker. The conformational fluctuations of the polymer molecule can be measured by optical microscopy via the motion of the microsphere. The bead-and-spring theory for polymer dynamics is further developed to account for the microsphere, and together the measurement and the theory yield quantitative information about molecular conformations and dynamics under nonperturbing conditions. Applying the method to measurements carried out on DNA molecules provides information complementary to recent studies of single DNA molecules under extensional force. Combining high precision measurements with the theoretical analysis presented here creates a powerful tool for studying conformational dynamics of biological and synthetic macromolecules at the single-molecule level.

Fluorescence correlation spectroscopy: diagnostics for sparse molecules

The robust glow of molecular fluorescence renders even sparse molecules detectable and susceptible to analysis for concentration, mobility, chemistry, and photophysics. Correlation spectroscopy, a statistical-physics-based tool, gleans quantitative information from the spontaneously fluctuating fluorescence signals obtained from small molecular ensembles. This analytical power is available for studying molecules present at minuscule concentrations in liquid solutions (less than one nanomolar), or even on the surfaces of living cells at less than one macromolecule per square micrometer. Indeed, routines are becoming common to detect, locate, and examine individual molecules under favorable conditions.

Kinetic investigations by fluorescence correlation spectroscopy: the analytical and diagnostic potential of diffusion studies

This review demonstrates the large analytical and diagnostic potential of fluorescence correlation spectroscopy applied to freely diffusing biomolecules in solution. All applications discussed here in detail are based on changes in the diffusion characteristics of fluorescenctly labeled complementary strands of nucleic acids when they associate. However, the principle of the measurement can be extended to many different reactions with characteristic association times between several minutes up to several hours. If the reaction significantly affects the diffusion constants of at least one partner, single-color auto-correlation analysis is sufficient to extract kinetic parameters. If the observed binding process has only a moderate effect on diffusion coefficients, the detection selectivity and sensitivity can be improved by dual-color cross-correlation analysis. Finally, we show that diffusional analysis on the single-molecule level even opens up diagnostic applications, such as the detection of minute amounts of infectious agents like HIV-1 viruses in blood.

Conductivity noise in transmembrane ion channels due to ion concentration fluctuations via diffusion

A Green's function approach is developed from first principles to evaluate the power spectral density of conductance fluctuations caused by ion concentration fluctuations via diffusion in an electrolyte system. This is applied to simple geometric models of transmembrane ion channels to obtain an estimate of the magnitude of ion concentration fluctuation noise in the channel current. Pure polypeptide alamethicin forms stable ion channels with multiple conductance states in artificial phospholipid bilayers isolated onto tips of micropipettes with gigaohm seals. In the single-channel current recorded by voltage-clamp techniques, excess noise was found after the background instrumental noise and the intrinsic Johnson and shot noises were removed. The noise que to ion concentration fluctuations via diffusion was isolated by the dependence of the excess current noise on buffer ion concentration. The magnitude of the concentration fluctuation noise derived from experimental data lies within limits estimated using our simple geometric channel models. Variation of the noise magnitude for alamethicin channels in various conductance states agrees with theoretical prediction.

Motion of actin filaments in the presence of myosin heads and ATP

We measured, by fluorescence correlation spectroscopy, the motion of actin filaments in solution during hydrolysis of ATP by acto-heavy meromyosin (acto-HMM). The method relies on the fact that the intensity of fluorescence fluctuates as fluorescently labeled actin filaments enter and leave a small sample volume. The rapidity of these number fluctuations is characterized by the autocorrelation function, which decays to 0 in time that is related to the average velocity of translation of filaments. The time of decay of the autocorrelation function of bare actin filaments in solution was 10.59 +/- 0.85 s. Strongly bound (rigor) heads slowed down the diffusion. Direct observation of filaments under an optical microscope showed that addition of HMM did not change the average length or flexibility of actin filaments, suggesting that the decrease in diffusion was not due to a HMM-induced change in the shape of filaments. Rather, slowing down of translational motion was caused by an increase in the volume of the diffusing complex. Surprisingly, the addition of ATP to acto-HMM accelerated the motion of actin filaments. The acceleration was the greatest at the low molar ratios of HMM:actin. Direct observation of filaments under an optical microscope showed that in the presence of ATP the average length of filaments did not change and that the filaments became stiffer, suggesting that acceleration of diffusion was not due to an ATP-induced increase in flexibility of filaments. These results show that some of the energy of splitting of ATP is impaired to actin filaments and suggest that 0.06 +/- 0.02 of HMM interferes with the diffusion of actin filaments during hydrolysis of ATP.

Studies on the structure of actin gels using time correlation spectroscopy of fluorescent beads

Fluorescence correlation spectroscopy (FCS) has been used to measure the diffusion of fluorescently labeled beads in solutions of polymerized actin or buffer. The results, obtained at actin concentrations of 1 mg/ml, show that small beads (0.09 micron in diameter) diffuse nearly as rapidly in the actin gel as in buffer, whereas the largest beads tested (0.5 micron in diameter) are immobilized. Measured autocorrelation times for motions of beads with intermediate sizes show that the diffusion is retarded (relative to buffer) and that the time behavior cannot be represented as a single diffusive process. In addition to the retarded diffusion observed over distances > 1 micron, 0.23-micron beads also show a faster motion over smaller distances. Based on the measured rate of this faster motion, we estimate that the beads may be constrained within a cage approximately 0.67 micron on a side, equal to a filament length of approximately 250 subunits. Fluorescence correlation spectroscopy measurements made in the same small spot (radius of 1.4 microns) of the gel vary over time. From the variations of both the autocorrelation functions and the mean fluorescence, we conclude that, corresponding to a spatial scale of 1.4 microns, the actin gel is a dynamic structure with slow rearrangement of the gel occurring over periods of 20-50 s at 21-22 degrees C. This rearrangement may result from local reorganization of the actin matrix. Data for the retardation of beads by the actin gel are consistent with a detailed theory of the diffusion of particles through solutions of rigid rods that have longitudinal diffusion coefficients much less than that of the particles (Ogston, A. G., B. N. Preston, and J. D. Wells. 1973. Proc. R. Soc. Lond. A. 333:297-316).

Velocity of movement of actin filaments in in vitro motility assay. Measured by fluorescence correlation spectroscopy

We have measured the velocity of actin filaments in in vitro motility assay by fluorescence correlation spectroscopy. In this method, one measures fluctuations in the number of filaments in an open sample volume. The number of filaments was calculated from measurements of fluorescence of rhodamine-phalloidin bound to F-actin. Sample volume was defined by a diaphragm placed in front of the photomultiplier. Fluctuations arise when actin filaments enter and leave the sample volume due to translations driven by mechanochemical interactions with myosin heads which are immobilized on a glass surface. The average velocity of the translation of filaments determined by the correlation method, (Vc), was equal to the diameter of the diaphragm divided by the half-time of the relaxation of fluctuations. The average number of moving filaments determined by correlation method, (Nc), was inversely proportional to the relative fluctuations. By the fluctuation method it was possible to determine the average velocity of over 800 moving filaments in less than 4 min. There was good agreement between (Vc) and (Nc) and the average velocity and the average number of moving filaments determined manually. To be able to apply correlation measurements to an experimental problem, neither (Vc) nor (Nc) must depend on the position of observation of filaments. We first confirmed that this was indeed the case. We then applied the method to investigate the dependence of motility on the ATPase activity of myosin heads. ATPase activity was varied by mixing intact heads with heads which were labeled with different thiol reagents. It was found that the motion was drastically influenced by the reagent used for modification. When the reagent was N-ethyl-maleimide, 1.5% modification was sufficient to completely inhibit the motion. When the reagent was 5-iodoacetamidofluorescein, motion declined hyperbolically with the fraction of modified heads.