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The purposes of this study were: (a) to measure the translational mobility of a small solute in cell cytoplasm; (b) to define quantitatively the factors that determine solute translation; and (c) to compare and contrast solute rotation and translation. A small fluorescent probe, 2,7-bis-(2-carboxyethyl)-5-(and 6-)-carboxyfluorescein (BCECF), was introduced into the cytoplasm of Swiss 3T3 fibroblasts. BCECF translation was measured by fluorescence recovery after photo-bleaching; rotation was measured by Fourier transform polarization microscopy. Diffusion coefficients relative to those in water (D/D0) were determined by comparing mobility in cytoplasm with mobility in standard solutions of known viscosity. At isosmotic cell volume, the relative diffusion coefficients for BCECF translation and rotation in cytoplasm were 0.27 +/- 0.01 (SEM, n = 24, 23 degrees C) and 0.78 +/- 0.03 (n = 4), respectively. As cell volume increased from 0.33 to 2 times isosmotic volume, the relative translational diffusion coefficient increased from 0.047 to 0.32, while the relative rotational diffusion coefficient remained constant. The factors determining BCECF translation were evaluated by comparing rotation and translation in cytoplasm, and in artificial solutions containing dextrans (mobile barriers) and agarose gels (immobile barriers). It was concluded that the hindrance of BCECF translation in cytoplasm could be quantitatively attributed to three independent factors: (a) fluid-phase cytoplasmic viscosity is 28% greater than the viscosity of water (factor 1 = 0.78); (b) 19% of BCECF is transiently bound to intracellular components of low mobility (factor 2 = 0.81); and most importantly, (c) translation of unbound BCECF is hindered 2.5-fold by collisions with cell solids comprising 13% of isosmotic cell volume (factor 3 = 0.40). The product of the 3 factors is 0.25 +/- 0.03, in good agreement with the measured D/D0 of 0.27 +/- 0.01. These results provide the first measurement of the translational mobility of a small solute in cell cytoplasm and define quantitatively the factors that slow solute translation.

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.

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.

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.

Analytical and numerical models were developed to describe fluorescence resonance energy transfer (RET) in crowded biological membranes. It was assumed that fluorescent donors were linked to membrane proteins and that acceptors were linked to membrane lipids. No restrictions were placed on the location of the donor within the protein or the partitioning of acceptors between the two leaflets of the bilayer; however, acceptors were excluded from the area occupied by proteins. Analytical equations were derived that give the average quantum yield of a donor at low protein concentrations. Monte Carlo simulations were used to generate protein and lipid distributions that were linked numerically with RET equations to determine the average quantum yield and the distribution of donor fluorescence lifetimes at high protein concentrations, up to 50% area fraction. The Monte Carlo results show such crowding always reduces the quantum yield, probably because crowding increases acceptor concentrations near donor-bearing proteins; the magnitude of the reduction increases monotonically with protein concentration. The Monte Carlo results also show that the distribution of fluorescence lifetimes can differ markedly, even for systems possessing the same average lifetime. The dependence of energy transfer on acceptor concentration, protein radius, donor position within the protein, and the fraction of acceptors in each leaflet was also examined. The model and results are directly applicable to the analysis of RET data obtained from biological membranes; their application should result in a more complete and accurate determination of the structures of membrane components.

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.

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.

We have studied the relationship between interprotein forces and the lateral distribution of proteins in disordered mouse liver gap junctions. Data on protein positions are obtained from freeze-fracture electron micrographs. Short-ranged correlations in observed positions are characteristic of interacting particles in a fluid state. An analysis derived from statistical mechanics allows the determination of the magnitude and functional form of interprotein forces. We find that jap junction proteins are mutually repulsive, in a manner consistent with electrostatics and excluded volume. This dictates that long-ranged protein aggregation into jap junction plaques cannot arise solely from interparticle interactions. An alternative is the balance of lateral pressures between the junction and the surrounding glycocalyx. This idea is quantified into a model. Junctional pressure arises from protein-protein interactions and is computed from a pressure equation based on the force and a radial distribution function describing order. The pressure from the glycocalyx is assumed to arise from mixing, electrostatic, and elastic interactions of sugar residues, and is described with terms from Flory-Krigbaum and McMillan-Mayer theories. The results of this modeling are in reasonable agreement with available experimental data.

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.

Treatment for a patient with a severe Class II malocclusion, maxillary anterior protrusion, left maxillary posterior overeruption with resultant loss of intermaxillary space, and an undesirable plane of occlusion has been presented. Through the combined approaches of oral surgery and restorative dentistry, the patient was successfully treated without the loss of multiple posterior teeth.

We consider the lateral distribution of intrinsic membrane proteins from the viewpoint of the statistical-mechanical theory of liquids. We connect the information in freeze-fracture electron micrographs--positions of proteins but not lipids or aqueous species--to a well developed theory of liquid mixtures. An algorithm, based on the Born-Green-Yvon integral equation, is presented for deducing forces between proteins from correlations among protein positions that are observed in micrographs. The algorithm is tested on simulated micrographs, obtained by Monte-Carlo methods, where forces between proteins are known analytically. We conclude that valid estimates of such forces, both attractions and repulsions, can be obtained from the positions of a few thousand proteins.

In gap junctions, identical membrane proteins are linked up in pairs (dyads) that bridge the extracellular space between two apposed cell membranes. Typically, several thousand of these dyads are aggregated in the plane of the membranes and form a junctional plaque with a distinct boundary. The question thus arises as to what maintains the dyads in an aggregated state. From a statistical mechanical analysis of the positions of dyads in a freeze-fracture electron micrograph, we report here that the aggregates are not maintained by an attractive force between pairs of dyads, but probably by the minimization of the repulsive force between apposed membranes. On the basis of this analysis we present a model for the structure of mature gap junctions as well as certain aspects of the formation and disassembly of gap junctions.

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.