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Dense-core vesicles (DCVs) are regulated secretory organelles found in many types of neurons. In neurons of the hippocampus, their cargo includes proteins that mediate several pivotal processes, including differentiation and synaptic plasticity. Motivated by interest in DCV distribution and its impact on cargo action, we have used fluorescence microscopy and statistical analysis to develop a quantitative model of the subcellular organization of DCVs in hippocampal neurons that are spontaneously active (their most prevalent state). We also have tested the functionally motivated hypothesis that these organelles are synaptically enriched. Variance-to-mean ratio, frequency distribution, and Moran's autocorrelation analyses reveal that DCV distribution along shafts, and within synapses, follows Poisson statistics, establishing that stochastically dictated organization sustains cargo function. Occupancy in boutons exceeds that at nearby extrasynaptic axonal sites by approximately threefold, revealing significant local presynaptic enrichment. Widespread stochastic organization is consistent with the emerging functional importance of synaptically and extrasynaptically localized DCVs. Presynaptic enrichment is consistent with the established importance of protecting presynaptic sites from depletion of DCV cargo. These results enhance understanding of the link between DCV organization and mechanisms of cargo action, and they reinforce the emerging theme that randomness is a prevalent aspect of synaptic organization and composition., (Copyright © 2016 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

Detection of fluorescence provides the foundation for many widely utilized and rapidly advancing microscopy techniques employed in modern biological and medical applications. Strengths of fluorescence include its sensitivity, specificity, and compatibility with live imaging. Unfortunately, conventional forms of fluorescence microscopy suffer from one major weakness, diffraction-limited resolution in the imaging plane, which hampers studies of structures with dimensions smaller than ~250 nm. Recently, this limitation has been overcome with the introduction of super-resolution fluorescence microscopy techniques, such as photoactivated localization microscopy (PALM). Unlike its conventional counterparts, PALM can produce images with a lateral resolution of tens of nanometers. It is thus now possible to use fluorescence, with its myriad strengths, to elucidate a spectrum of previously inaccessible attributes of cellular structure and organization. Unfortunately, PALM is not trivial to implement, and successful strategies often must be tailored to the type of system under study. In this article, we show how to implement single-color PALM studies of vesicular structures in fixed, cultured neurons. PALM is ideally suited to the study of vesicles, which have dimensions that typically range from ~50-250 nm. Key steps in our approach include labeling neurons with photoconvertible (green to red) chimeras of vesicle cargo, collecting sparsely sampled raw images with a super-resolution microscopy system, and processing the raw images to produce a high-resolution PALM image. We also demonstrate the efficacy of our approach by presenting exceptionally well-resolved images of dense-core vesicles (DCVs) in cultured hippocampal neurons, which refute the hypothesis that extrasynaptic trafficking of DCVs is mediated largely by DCV clusters.

Dense-core granules (DCGs) are organelles found in neuroendocrine cells and neurons that house, transport, and release a number of important peptides and proteins. In neurons, DCG cargo can include the secreted neuromodulatory proteins tissue plasminogen activator (tPA) and/or brain-derived neurotrophic factor (BDNF), which play a key role in modulating synaptic efficacy in the hippocampus. This function has spurred interest in DCGs that localize to synaptic contacts between hippocampal neurons, and several studies recently have established that DCGs localize to, and undergo regulated exocytosis from, postsynaptic sites. To complement this work, we have studied presynaptically localized DCGs in hippocampal neurons, which are much more poorly understood than their postsynaptic analogs. Moreover, to enhance relevance, we visualized DCGs via fluorescence labeling of exogenous and endogenous tPA and BDNF. Using single-particle tracking, we determined trajectories of more than 150 presynaptically localized DCGs. These trajectories reveal that mobility of DCGs in presynaptic boutons is highly hindered and that storage is long-lived. We also computed mean-squared displacement curves, which can be used to elucidate mechanisms of transport. Over shorter time windows, most curves are linear, demonstrating that DCG transport in boutons is driven predominantly by diffusion. The remaining curves plateau with time, consistent with motion constrained by a submicron-sized corral. These results have relevance to recent models of presynaptic organization and to recent hypotheses about DCG cargo function. The results also provide estimates for transit times to the presynaptic plasma membrane that are consistent with measured times for onset of neurotrophin release from synaptically localized DCGs., (Copyright © 2011 Wiley Periodicals, Inc.)

Recent data suggest that tissue plasminogen activator (tPA) influences long-term plasticity at hippocampal synapses by converting plasminogen into plasmin, which then generates mature brain-derived neurotrophic factor (mBDNF) from its precursor, proBDNF. Motivated by this hypothesis, we used fluorescent chimeras, expressed in hippocampal neurons, to elucidate (1) mechanisms underlying plasminogen secretion from hippocampal neurons, (2) if tPA, plasminogen, and proBDNF are copackaged and cotransported in hippocampal neurons, especially within dendritic spines, and (3) mechanisms mediating the transport of these neuromodulators to sites of release. We find that plasminogen chimeras traffic through the regulated secretory pathway of hippocampal neurons in dense-core granules (DCGs) and that tPA, plasminogen, and proBDNF chimeras are extensively copackaged in DCGs throughout hippocampal neurons. We also find that 80% of spines that contain DCGs contain chimeras of these neuromodulators in the same DCG. Finally, we demonstrate, for the first time, that neuromodulators undergo cotransport along dendrites in rapidly mobile DCGs, indicating that neuromodulators can be efficiently recruited into active spines. These results support the hypothesis that tPA mediates synaptic activation of BDNF by demonstrating that tPA, plasminogen, and proBDNF colocalize in DCGs in spines, where these neuromodulators can undergo activity-dependent release and then interact and/or mediate changes that influence synaptic efficacy. The results also raise the possibility that frequency-dependent changes in extents of neuromodulator release from DCGs influence the direction of plasticity at hippocampal synapses by altering the relative proportions of two proteins, mBDNF and proBDNF, that exert opposing effects on synaptic efficacy.

Tissue plasminogen activator (tPA) has been implicated in a variety of important cellular functions, including learning-related synaptic plasticity and potentiating N-methyl-D-aspartate (NMDA) receptor-dependent signaling. These findings suggest that tPA may localize to, and undergo activity-dependent secretion from, synapses; however, conclusive data supporting these hypotheses have remained elusive. To elucidate these issues, we studied the distribution, dynamics, and depolarization-induced secretion of tPA in hippocampal neurons, using fluorescent chimeras of tPA. We found that tPA resides in dense-core granules (DCGs) that traffic to postsynaptic dendritic spines and that can remain in spines for extended periods. We also found that depolarization induced by high potassium levels elicits a slow, partial exocytotic release of tPA from DCGs in spines that is dependent on extracellular Ca(+2) concentrations. This slow, partial release demonstrates that exocytosis occurs via a mechanism, such as fuse-pinch-linger, that allows partial release and reuse of DCG cargo and suggests a mechanism that hippocampal neurons may rely upon to avoid depleting tPA at active synapses. Our results also demonstrate release of tPA at a site that facilitates interaction with NMDA-type glutamate receptors, and they provide direct confirmation of fundamental hypotheses about tPA localization and release that bear on its neuromodulatory functions, for example, in learning and memory.

Neurons and related cell types often contain two major classes of neurosecretory vesicles, synaptic vesicles (SVs) and dense-core granules (DCGs), which store and release distinct cargo. SVs store and release classic neurotransmitters, which facilitate propagation of action potentials across the synaptic cleft, whereas DCGs transport, store, and release hormones, proteins, and neuropeptides, which facilitate neuronal survival, synaptic transmission, and learning. Over the past few years, there has been a major surge in our understanding of many of the key molecular mechanisms underlying cargo release from SVs and DCGs. This surge has been driven largely by the use of fluorescence microscopy (especially total internal reflection fluorescence microscopy) to visualize SVs or DCGs in living cells. This review highlights some of the recent insights into cargo release from neurosecretory vesicles provided by fluorescence microscopy, with emphasis on DCGs.

Dense-core granules (DCGs) are organelles found in specialized secretory cells, including neuroendocrine cells and neurons. Neuronal DCGs facilitate many critical processes, including the transport and secretion of proteins involved in learning, and yet their transport and exocytosis are poorly understood. We have used wide-field and total internal reflection fluorescence microscopy, in conjunction with transport theory, to visualize the transport and exocytosis of DCGs containing a tissue plasminogen activator-green fluorescent protein hybrid in cell bodies, neurites, and growth cones of developing hippocampal neurons and to quantify the roles that diffusion, directed motion, and immobility play in these processes. Our results demonstrate that shorter-ranged transport of DCGs near sites of exocytosis in hippocampal neurons and neuroendocrine cells differs markedly. Specifically, the immobile fraction of DCGs within growth cones and near the plasma membrane of hippocampal neurons is small and relatively unaltered by actin disruption, unlike in neuroendocrine cells. Moreover, transport of DCGs in these domains of hippocampal neurons is unusually heterogeneous, being significantly rapid and directed as well as slow and diffusive. Our results also demonstrate that exocytosis is preceded by substantial movement and heterogeneous transport; this movement may facilitate delivery of DCG cargo in hippocampal neurons, given the relatively low abundance of neuronal DCGs. In addition, the extensive mobility of DCGs in hippocampal neurons argues strongly against the hypothesis that cortical actin is a major barrier to membrane-proximal DCGs in these cells. Instead, our results suggest that extended release of DCG cargo from hippocampal neurons arises from heterogeneity in DCG mobility.

The difficulty of deriving binding ligands to targets identified by genomic sequencing has led to a bottleneck in genomic research. By inserting diverse antibody binding loops into four of the exposed loops at one end of green fluorescent protein (GFP), we have mimicked the natural antibody binding footprint to create robust binding ligands that combine the advantages of antibodies (high affinity and specificity) with those of GFP (intrinsic fluorescence, high stability, expression and solubility). These 'fluorobodies' have been used effectively in enzyme-linked immunosorbent assays (ELISAs), flow cytometry, immuno-fluorescence, arrays and gel shift assays, and show affinities as high as antibodies. Furthermore, the intrinsic fluorescence of fluorobodies correlates with binding activity, allowing the rapid determination of functionality, concentration and affinity. These properties render them especially suitable for the high-throughput genomic scale selections required in proteomics, as well as in diagnostics, target validation and drug development.

Neuronal calcium sensor-1 (NCS-1) and its non-mammalian homologue, frequenin, have been implicated in a spectrum of cellular processes, including regulation of stimulated exocytosis of synaptic vesicles and secretory granules (SGs) in neurons and neuroendocrine cells and regulation of phosphatidylinositol 4-kinase beta activity in yeast. However, apart from these intriguing putative functions, NCS-1 and frequenin are relatively poorly understood. Here, the distribution, dynamics and function of NCS-1 were studied using PC12 cells that stably express NCS-1-EYFP (NCS-1 fused to enhanced yellow fluorescent protein) or that stably overexpress NCS-1. Fluorescence and electron microscopies show that NCS-1-EYFP is absent from SGs but is present on small clear organelles, some of which are just below the plasma membrane. Total internal reflection fluorescence microscopy shows that NCS-1-EYFP is associated with synaptic-like microvesicles (SLMVs) in growth cones. Overexpression studies show that NCS-1 enhances exocytosis of synaptotagmin-labeled regulated secretory organelles (RSOs) under basal conditions and during stimulation by UTP. Significantly, these studies implicate NCS-1 in the enhancement of both basal and stimulated phosphoinositide-dependent exocytosis of RSOs in PC12 cells, and they show that NCS-1 is distributed strategically to interact with putative targets on the plasma membrane and on SLMVs. These studies also reveal that SLMVs undergo both fast directed motion and highly hindered diffusive motion in growth cones, suggesting that cytoskeletal constituents can both facilitate and hinder SLMV motion. These results also reveal interesting similarities and differences between transport organelles in differentiated neuroendocrine cells and neurons.

Vesicle recycling through exocytosis and endocytosis is mediated by a coordinated cascade of protein-protein interactions. Previously, exocytosis and endocytosis were studied separately so that the coupling between them was understood only indirectly. We focused on the coupling of these processes by observing the secretory vesicle marker synaptobrevin and the endocytotic vesicle marker dynamin I tagged with green and red fluorescent proteins under an evanescent wave microscope in pheochromocytoma cells. In control cells, many synaptobrevin-expressing vesicles were found as fluorescent spots near the plasma membrane. Upon electrical stimulation, many of these vesicles showed an exocytotic response as a transient increase in fluorescence intensity followed by their disappearance. In contrast, fluorescent dynamin appeared as clusters increasing slowly in number upon stimulation. The clusters of fluorescent dynamin moved around beneath the plasma membrane for a significant distance. Simultaneous observations of green fluorescent dynamin and red fluorescent synaptobrevin indicated that more than 70% of the exocytotic responses of synaptobrevin had no immediate dynamin counterpart at the same site. From these findings it was concluded that dynamin-mediated recycling is not directly coupled to exocytosis but rather completed by a scanning movement of dynamin for the sites of invaginating membrane destined to endocytosis.

Secretory granules containing a hybrid protein consisting of the regulated secretory protein tissue plasminogen activator and an enhanced form of green fluorescent protein were tracked at high spatial resolution in growth cones of differentiated PC12 cells. Tracking shows that granules, unlike synaptic vesicles, generally are mobile in growth cones. Quantitative analysis of trajectories generated by granules revealed two dominant modes of motion: diffusive and directed. Diffusive motion was observed primarily in central and peripheral parts of growth cones, where most granules diffused two to four orders of magnitude more slowly than comparably sized spheres in dilute solution. Directed motion was observed primarily in proximal parts of growth cones, where a subset of granules underwent rapid, directed motion at average speeds comparable to those observed for granules in neurites. This high-resolution view of the dynamics of secretory granules in growth cones provides insight into granule organization and release at nerve terminals. In particular, the mobility of granules suggests that granules, unlike synaptic vesicles, are not tethered stably to cytoskeletal structures in nerve terminals. Moreover, the slow diffusive nature of this mobility suggests that secretory responses involving centrally distributed granules in growth cones will occur slowly, on a time scale of minutes or longer.

A hybrid protein, tPA/GFP, consisting of rat tissue plasminogen activator (tPA) and green fluorescent protein (GFP) was expressed in PC12 cells and used to study the distribution, secretory behavior, and dynamics of secretory granules containing tPA in living cells with a neuronal phenotype. High-resolution images demonstrate that tPA/GFP has a growth cone-biased distribution in differentiated cells and that tPA/GFP is transported in granules of the regulated secretory pathway that colocalize with granules containing secretogranin II. Time-lapse images of secretion reveal that secretagogues induce substantial loss of cellular tPA/GFP fluorescence, most importantly from growth cones. Time-lapse images of the axonal transport of granules containing tPA/GFP reveal a surprising complexity to granule dynamics. Some granules undergo canonical fast axonal transport; others move somewhat more slowly, especially in highly fluorescent neurites. Most strikingly, granules traffic bidirectionally along neurites to an extent that depends on granule accumulation, and individual granules can reverse their direction of motion. The retrograde component of this bidirectional transport may help to maintain cellular homeostasis by transporting excess tPA/GFP back toward the cell body. The results presented here provide a novel view of the axonal transport of secretory granules. In addition, the results suggest that tPA is targeted for regulated secretion from growth cones of differentiated cells, strategically positioning tPA to degrade extracellular barriers or to activate other barrier-degrading proteases during axonal elongation.

Translational dynamics of chromatin in interphase nuclei of living Swiss 3T3 and HeLa cells was studied using fluorescence microscopy and fluorescence recovery after photobleaching. Chromatin was fluorescently labeled using dihydroethidium, a membrane-permeant derivative of ethidium bromide. After labeling, a laser was used to bleach small (approximately 0.4 microm radius) spots in the heterochromatin and euchromatin of cells of both types. These spots were observed to persist for >1 h, implying that interphase chromatin is immobile over distance scales >/=0.4 microm. Over very short times (<1 s), a partial fluorescence recovery within the spots was observed. This partial recovery is attributed to independent dye motion, based on comparison with results obtained using ethidium homodimer-1, which binds essentially irreversibly to nucleic acids. The immobility observed here is consistent with chromosome confinement to domains in interphase nuclei. This immobility may reflect motion-impeding steric interactions that arise in the highly concentrated nuclear milieu or outright attachment of the chromatin to underlying nuclear substructures, such as nucleoli, the nuclear lamina, or the nuclear matrix.

The wavelength dependence of the incoherent point spread function in a wide-field microscope was investigated experimentally. Dispersion in the sample and optics can lead to significant changes in the point spread function as wavelength is varied over the range commonly used in fluorescence microscopy. For a given sample, optical conditions can generally be optimized to produce a point spread function largely free of spherical aberration at a given wavelength. Unfortunately, deviations in wavelength from this value will result in spherically aberrated point spread functions. Therefore, when multiple fluorophores are used to localize different components in the same sample, the image of the distribution of at least one of the fluorophores will be spherically aberrated. This aberration causes a loss of intensity and resolution, thereby complicating the localization and analysis of multiple components in a multi-wavelength image. We show that optimal resolution can be restored to a spherically aberrated image by constrained, iterative deconvolution, as long as the spherical aberration in the point spread function used for deconvolution matches the aberration in the image reasonably well. The success of this method is essentially independent of the initial degree of spherical aberration in the image. Deconvolution of many biological images can be achieved by collecting a small library of spherically aberrated and unaberrated point spread functions, and then choosing a point spread function appropriate for deconvolving each image. The co-localization and relative intensities of multiple components can then be accurately studied in a multi-wavelength image.

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.

The increasing experimental use of total internal reflection/fluorescence photobleaching recovery has motivated a theoretical study of the spatial intensity profiles generated by two interfering evanescent waves. The interference patterns generated by evanescent waves differ considerably from those generated by plane waves in a homogenous medium because evanescent waves are not transverse and because the evanescent propagation number depends on the incidence angle of the totally internally reflected light. The periodicity and contrast of the evanescent interference patterns under various conditions are calculated; these parameters depend on the intensities, polarizations, and incidence angles of the two incident beams, as well as the refractive indices of the two media that form the planar interface where total internal reflection occurs. The derived intensity profiles are used to develop expressions for the shapes of fluorescence photobleaching recovery curves when evanescent interference patterns are used for fluorescence excitation and bleaching. The calculations also suggest that colliding beam experiments may confirm theoretically predicted evanescent field polarizations.

The coupling between molecular diffusion and the structure and function of the rat liver mitochondrial matrix was explored using fluorescence anisotropy techniques and electron microscopy. The results confirm that matrix ultrastructure and the concentration of matrix protein are influenced by the respiratory state of mitochondria and the osmolarity of the external medium. At physiological osmolarity, a fluorescent metabolite-sized probe was found to diffuse slowly in the mitochondrial matrix but not to be completely immobile. In addition, significant differences in diffusion rates were found to exist between different mitochondrial respiratory states, with the slowest diffusion occurring in states with the highest matrix protein concentration. These data support the concept of a matrix structure in which diffusion is considerably hindered due to limited probe-accessible water and further suggest that volume-dependent regulation of matrix protein packing may modulate metabolite diffusion and, in turn, mitochondrial metabolism.

Polarized fluorescence recovery after photobleaching (pFRAP) was used to monitor the effects that condensation, i.e. compaction and aggregation, have on the (microseconds and ms) internal dynamics of chromatin in intact nuclei. When divalent cations were present with physiological (approximately 90 mM) monovalent salt the chromatin was found to exist in a compact and aggregated state which was characterized by rotational immobilization over timescales that range from 10 microseconds to 40 milliseconds. This immobilization is attributed to suppression of internal dynamics by intermolecular interactions. When the divalent cations were removed, the compact fibers no longer aggregated and were free to reorient with a characteristic decay time of about 1.2 milliseconds. It is shown that this millisecond relaxation could represent rigid rotation of topologically independent structural domains. Dilution of the monovalent salt induced a gradual change in the structural state of the chromatin that was manifest as a dramatic increase in internal flexibility. At the lowest salt concentration studied (11 mM-monovalent salt) the chromatin reorients in fewer than ten microseconds. These changes in flexibility are continuous with salt concentration, indicating that there are no well-defined endpoints to structural transitions and that the microsecond-millisecond internal dynamics of chromatin are a sensitive measure of structure. Measurements made on nuclei from cells that are either transcriptionally quiescent or active indicate that the dynamics mirrors biological activity.

Interparticle interactions are incorporated into the theoretical description of the initial amplitude, G(0), of the normalized fluorescence correlation spectroscopy autocorrelation function. Measurements of particle number, aggregate size, and interaction-dependent diffusion are then analyzed in the context of this generalized theory. It is shown that the neglect of interactions can introduce order-of-magnitude errors into estimates of particle number and aggregate size. It is also shown that measurement of G(0) provides an essentially unique method for testing the validity of theories of interaction-dependent membrane protein diffusion.

Polarized fluorescence recovery after photobleaching (pFRAP) has been used to study the internal dynamics of relatively long DNA molecules embedded in gels that range in concentration from 1% to 5% agarose. The data indicate that, even in very congested gels, rapid internal relaxation of DNA is largely unhindered; however, interactions with gel matrices apparently do perturb the larger amplitude, more slowly (microseconds to milliseconds) relaxing internal motions of large DNAs. The relationship between this work and recent studies which indicate that internal motions of DNA play an important role in the separation achieved with pulsed-field gel electrophoresis techniques is discussed. The polarized photobleaching technique is also analyzed in some detail. In particular, it is shown that "reversible" photobleaching phenomena are probably related to depletion of the ground state by intersystem crossing to the triplet state.

We have conducted a polarized fluorescence photobleaching recovery (FPR) study of the rotational dynamics of ethidium azide labeled DNA. Polarized photobleaching experiments provide data on microsecond and millisecond molecular reorientation that complement the information available from nanosecond fluorescence depolarization studies. In polarized FPR experiments an anisotropic angular concentration of fluorophore is created by bleaching dye molecules in a preferred orientation with a short, intense pulse of polarized light. The sample is then weakly illuminated, and the temporal variation in the emitted fluorescence is monitored. The fluorescence signal will systematically change as molecules undergo post-bleach reorientation and the angular distribution of dye tends toward isotropy. We have observed that the time dependence of our microsecond FPR curves is also determined in part by nonrotational phenomena. To isolate the reorientational recovery we conduct our FPR experiments in two modes (called parallel and perpendicular) that differ only in the polarization of the bleaching light. A quotient function, R(t), is constructed from the data obtained in these two modes; the variation with time of this new quantity is governed solely by processes that are sensitive to the polarization of the incident light (e.g., molecular rotation). It is found experimentally that R(t) remains constant, as expected, for rotationally restricted DNA systems despite a temporal recovery in the parallel and perpendicular FPR curves. We also follow the dynamics of solutions of phage lambda DNA as revealed in the temporal dependence of R(t). This DNA system rotationally relaxes after approximately 100 microseconds and the dye/DNA complex reorients substantially during the 10-microseconds bleach period. Our FPR data are interpreted in terms of dynamic models of DNA motion.

The generalized Stokes-Einstein equation is used, together with the two-dimensional pressure equation, to analyze mutual diffusion in concentrated membrane systems. These equations can be used to investigate the role that both direct and hydrodynamic interactions play in determining diffusive behavior. Here only direct interactions are explicitly incorporated into the theory at high densities; however, both direct and hydrodynamic interactions are analyzed for some dilute solutions. We look at diffusion in the presence of weak attractions, soft repulsions, and hard-core repulsions. It is found that, at low densities, attractions retard mutual diffusion while repulsions enhance it. Mechanistically, attractions tend to tether particles together and oppose the dissipation of gradients or fluctuations in concentration, while repulsions provide a driving force that pushes particles apart. At higher concentrations, changes in the structure of the fluid enhance mutual diffusion even in the presence of attractions. It is shown that the theoretical description of postelectrophoresis relaxation and fluorescence correlation spectroscopy experiments must be modified if interacting systems are studied. The effects of interactions on mutual diffusion coefficients have probably already been seen in postelectrophoresis relaxation experiments.

A two-dimensional version of the generalized Smoluchowski equation is used to analyze the time (or distance) dependent self diffusion of interacting membrane proteins in concentrated membrane systems. This equation provides a well established starting point for descriptions of the diffusion of particles that interact through both direct and hydrodynamic forces; in this initial work only the effects of direct interactions are explicitly considered. Data describing diffusion in the presence of hard-core repulsions, soft repulsions, and soft repulsions with weak attractions are presented. The effect that interactions have on the self-diffusion coefficient of a real protein molecule from mouse liver gap junctions is also calculated. The results indicate that self diffusion is always inhibited by direct interactions; this observation is interpreted in terms of the caging that will exist at finite protein concentration. It is also noted that, over small distance scales, the diffusion coefficient is determined entirely by the very strong Brownian forces; therefore, as a function of displacement the self-diffusion coefficient decays (rapidly) from its value at infinite dilution to its steady-state interaction-averaged value. The steady-state self-diffusion coefficient describes motion over distance scales that range from approximately 10 nm to cellular dimensions and is the quantity measured in fluorescence recovery after photobleaching experiments. The short-ranged behavior of the diffusion coefficient is important on the interparticle-distance scale and may therefore influence the rate at which nearest-neighbor collisional processes take place. The hard-disk theoretical results presented here are in excellent agreement with lattice Monte-Carlo results obtained by other workers. The concentration dependence of experimentally measured diffusion coefficients of antibody-hapten complexes bound to the membrane surface is consistent with that predicted by the theory. The variation in experimental diffusion coefficients of integral membrane proteins is greater than that predicted by the theory, and may also reflect protein-induced perturbations in membrane viscosity.

Self diffusion and mutual diffusion in two-dimensional membrane systems are analyzed. It is shown that interprotein interactions can produce markedly different density-dependent changes in the diffusion coefficients describing these two processes; the qualitative differences are illustrated by using a theoretical formalism valid for dilute solutions. Results are obtained for three analytical potentials: hard-core repulsions, soft repulsions, and soft repulsions with weak attractions. Self diffusion is inhibited by all three interactions. In contrast, mutual diffusion is inhibited by attractions but is enhanced by repulsions. It is shown that such interaction-dependent differences in self diffusion and mutual diffusion could underlie, among other things, the disparity in protein diffusion coefficients extracted from fluorescence recovery after photobleaching and postelectrophoresis relaxation data.