Analysis of Glycerol-3H Transport in the Frog Oocyte by Extractive and Radioautographic Techniques

The efflux of glycerol-³H from mature R. pipiens oocytes was studied by extractive analysis and by quantitative radioautography using techniques suitable for diffusible solutes. Extractive analysis was used to determine the total cellular concentration of tracer, and radioautography, regional intracellular concentrations, at equilibrium and as a function of efflux time, t_E. The efflux was resolvable into four kinetic fractions: cytoplasmic fast and slow fractions, and nuclear fast and slow fractions. The fast fractions represent freely diffusible glycerol in the two compartments; the solvent space accessible to glycerol is unity in the nucleus (germinal vesicle), but only 0.73 in the cytoplasm. The efflux of both fast fractions from the cell is determined by the permeability of the cortical membrane, with neither the nuclear membrane nor diffusion in the cytoplasm detectably slowing the flux. The permeability at 13.6°C is 2.2 x 10^-5 cm/sec. The slow fractions leave the cell at about one-tenth the rate of the fast; the interpretation is that these fractions represent glycerol bound to impermeant cellular constituents. The size of these constituents is below the radioautographic resolution; in the cytoplasm, they appear not to be the yolk platelets. The extent of binding is about fourfold greater, per milliliter of compartment water, in the cytoplasm than in the germinal vesicle.     

Coarse-grained molecular simulation of diffusion and reaction kinetics in a crowded virtual cytoplasm

We present a general-purpose model for biomolecular simulations at the molecular level that incorporates stochasticity, spatial dependence, and volume exclusion, using diffusing and reacting particles with physical dimensions. To validate the model, we first established the formal relationship between the microscopic model parameters (timestep, move length, and reaction probabilities) and the macroscopic coefficients for diffusion and reaction rate. We then compared simulation results with Smoluchowski theory for diffusion-limited irreversible reactions and the best available approximation for diffusion-influenced reversible reactions. To simulate the volumetric effects of a crowded intracellular environment, we created a virtual cytoplasm composed of a heterogeneous population of particles diffusing at rates appropriate to their size. The particle-size distribution was estimated from the relative abundance, mass, and stoichiometries of protein complexes using an experimentally derived proteome catalog from Escherichia coli K12. Simulated diffusion constants exhibited anomalous behavior as a function of time and crowding. Although significant, the volumetric impact of crowding on diffusion cannot fully account for retarded protein mobility in vivo, suggesting that other biophysical factors are at play. The simulated effect of crowding on barnase-barstar dimerization, an experimentally characterized example of a bimolecular association reaction, reveals a biphasic time course, indicating that crowding exerts different effects over different timescales. These observations illustrate that quantitative realism in biosimulation will depend to some extent on mesoscale phenomena that are not currently well understood.     

A New Coarse-Grained Model for E. coli Cytoplasm: Accurate Calculation of the Diffusion Coefficient of Proteins and Observation of Anomalous Diffusion

A new coarse-grained model of the E. coli cytoplasm is developed by describing the proteins of the cytoplasm as flexible units consisting of one or more spheres that follow Brownian dynamics (BD), with hydrodynamic interactions (HI) accounted for by a mean-field approach. Extensive BD simulations were performed to calculate the diffusion coefficients of three different proteins in the cellular environment. The results are in close agreement with experimental or previously simulated values, where available. Control simulations without HI showed that use of HI is essential to obtain accurate diffusion coefficients. Anomalous diffusion inside the crowded cellular medium was investigated with Fractional Brownian motion analysis, and found to be present in this model. By running a series of control simulations in which various forces were removed systematically, it was found that repulsive interactions (volume exclusion) are the main cause for anomalous diffusion, with a secondary contribution from HI.     

Determinants of the translational mobility of a small solute in cell cytoplasm

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.     

Diffusion in Pseudomonas aeruginosa biofilms: a pulsed field gradient NMR study

A Pseudomonas aeruginosa biofilm is studied with pulsed field gradient echo nuclear magnetic resonance. Although not all spectral components are assigned yet, the experimental results show that a biofilm consists of components with very different diffusion coefficients. The various biofilm components that give motionally narrowed 1H NMR signals, can be grouped into five classes with diffusion coefficients, ranging from 2 x 10(-9) to 1 x 10(-13) m2 s-1. Investigation of the diffusion behavior of water in the biofilm shows three fractions with different diffusion coefficients. Besides the highly mobile bulk water at least two other fractions with much lower diffusion coefficients are detected. It is shown that one of the fractions with the low diffusion coefficient probably arises from intracellular water. Also for another component of the biofilm, glycerol, three fractions with diffusion coefficients that differ more than a factor ten are detected. Also a group of signals exists which result from practically immobile components.     

The Intracellular Mobility of Nuclear Import Receptors and NLS Cargoes

We have investigated classical nuclear localization sequence (NLS) mediated protein trafficking by measuring biomolecular dynamics within living cells using two-photon fluorescence correlation spectroscopy. By directly observing the behavior of specific molecules in their native cellular environment, it is possible to uncover functional details that are not apparent from traditional biochemical investigations or functional assays. We show that the intracellular mobility of NLS cargoes and their import receptor proteins, karyopherin-α and karyopherin-β, can be robustly measured and that quantitative comparison of intracellular diffusion coefficients provides new insights into nuclear transport mechanisms. Import cargo complexes are assembled throughout the cytoplasm, and their diffusion is slower than predicted by molecular weight due to specific interactions. Analysis of NLS cargo diffusion in the cytoplasm indicates that these interactions are likely disrupted by NLS cargo binding. Our results suggest that delivery of import receptors and NLS cargoes to nuclear pores may complement selective translocation through the pores as a functional mechanism for regulating transport of proteins into the nucleus.     

Defining the Subcellular Interface of Nanoparticles by Live-Cell Imaging

Understanding of nanoparticle-bio-interactions within living cells requires knowledge about the dynamic behavior of nanomaterials during their cellular uptake, intracellular traffic and mutual reactions with cell organelles. Here, we introduce a protocol of combined kinetic imaging techniques that enables investigation of exemplary fluorochrome-labelled nanoparticles concerning their intracellular fate. By time-lapse confocal microscopy we observe fast, dynamin-dependent uptake of polystyrene and silica nanoparticles via the cell membrane within seconds. Fluorescence recovery after photobleaching (FRAP) experiments reveal fast and complete exchange of the investigated nanoparticles at mitochondria, cytoplasmic vesicles or the nuclear envelope. Nuclear translocation is observed within minutes by free diffusion and active transport. Fluorescence correlation spectroscopy (FCS) and raster image correlation spectroscopy (RICS) indicate diffusion coefficients of polystyrene and silica nanoparticles in the nucleus and the cytoplasm that are consistent with particle motion in living cells based on diffusion. Determination of the apparent hydrodynamic radii by FCS and RICS shows that nanoparticles exert their cytoplasmic and nuclear effects mainly as mobile, monodisperse entities. Thus, a complete toolkit of fluorescence fluctuation microscopy is presented for the investigation of nanomaterial biophysics in subcellular microenvironments that contributes to develop a framework of intracellular nanoparticle delivery routes.     

Age-related quantitative changes in the organelles of rat neocerebellar Purkinje cells.

A quantitative study regarding the age-related changes occurring in the somatic organelles of the neocerebellar Purkinje cell is carried out, using female rats aged 2 to 24 months. Standard manual morphometric techniques are used to calculate the following parameters: somatic volume, volumetric fractions and absolute volumes of the intracellular structures as well as the membrane profile concentration, the membrane surface concentration and the mean surface of the rough endoplasmic reticulum cisternae per cell (RER-S). From a statistical point of view, all the cell components significantly modify their volumetric fractions (except the multivesicular bodies and nucleolus; the latter in relation to the nucleus) and their absolute volumes (except the mitochondria and the multivesicular bodies); the parameters regarding the reticulum are also modified during ageing. There is a linear trend between the age and either the somatic volume of the RER-S or the absolute volumes of the following structures: mitochondria, dense bodies, ground substance and total cytoplasm. A linear correlation is also observed between the cell volume and either the RER-S or the absolute volume of intracellular structures (the Golgi apparatus, the multivesicular bodies and nucleolus being excluded). Anatomophysiological considerations about the findings are discussed. The role of the ground substance as the major modulator of the volumetric plasticity of the Purkinje cell during ageing, is emphasized as a conclusion.     

Effects of organelle shape on fluorescence recovery after photobleaching

The determination of diffusion coefficients from fluorescence recovery data is often complicated by geometric constraints imposed by the complex shapes of intracellular compartments. To address this issue, diffusion of proteins in the lumen of the endoplasmic reticulum (ER) is studied using cell biological and computational methods. Fluorescence recovery after photobleaching (FRAP) experiments are performed in tissue culture cells expressing GFP-KDEL, a soluble, fluorescent protein, in the ER lumen. The three-dimensional (3D) shape of the ER is determined by confocal microscopy and computationally reconstructed. Within these ER geometries diffusion of solutes is simulated using the method of particle strength exchange. The simulations are compared to experimental FRAP curves of GFP-KDEL in the same ER region. Comparisons of simulations in the 3D ER shapes to simulations in open 3D space show that the constraints imposed by the spatial confinement result in two- to fourfold underestimation of the molecular diffusion constant in the ER if the geometry is not taken into account. Using the same molecular diffusion constant in different simulations, the observed speed of fluorescence recovery varies by a factor of 2.5, depending on the particular ER geometry and the location of the bleached area. Organelle shape considerably influences diffusive transport and must be taken into account when relating experimental photobleaching data to molecular diffusion coefficients. This novel methodology combines experimental FRAP curves with high accuracy computer simulations of diffusion in the same ER geometry to determine the molecular diffusion constant of the solute in the particular ER lumen.     

Diffusion anisotropy in collagen gels and tumors: the effect of fiber network orientation

The interstitial matrix is comprised of cross-linked collagen fibers, generally arranged in nonisotropic orientations. Spatial alignment of matrix components within the tissue can affect diffusion patterns of drugs. In this study, we developed a methodology for the calculation of diffusion coefficients of macromolecules and nanoparticles in collagenous tissues. The tissues are modeled as three-dimensional, stochastic, fiber networks with varying degrees of alignment. We employed a random walk approach to simulate diffusion and a Stokesian dynamics method to account for hydrodynamic hindrance. We performed our analysis for four different structures ranging from nearly isotropic to perfectly aligned. We showed that the overall diffusion coefficient is not affected by the orientation of the network. However, structural anisotropy results in diffusion anisotropy, which becomes more significant with increase in the degree of alignment, the size of the diffusing particle, and the fiber volume fraction. To test our model predictions we performed diffusion measurements in reconstituted collagen gels and tumor xenografts. We measured fiber alignment and diffusion with second harmonic generation and multiphoton fluorescent recovery after photobleaching techniques, respectively. The results showed for the first time in tumors that the structure and orientation of collagen fibers in the extracellular space leads to diffusion anisotropy.     

Superhelix density heterogeneity in closed circular intracellular PM2 DNA

Covalently closed intracellular DNA obtained from Pseudomonas BAL 31 20 min after infection with PM2 phage has been shown to be heterogeneous in superhelix density. Analytical band sedimentation, in the presence of low concentrations of ethidium bromide, has been carried out on fractions centripetal and centrifugal to the mode of a single band of closed circular DNA in a preparative propidium iodide–CsCl buoyant density gradient. Different average sedimentation rates, as well as different band shapes, have been observed for upper and lower fractions centrifuged at a dye concentration near the minimum in s° versus ethidium bromide concentration titrations performed on DNA from proximate intermediate fractions. Similar differences, although not as pronounced, have been obtained at a dye concentration corresponding to a point in the steep region of the titrations. Differential band sedimentation experiments performed on the same fractions have confirmed these results. Differential band sedimentation experiments on similarly fractionated mature PM2 I DNA (closed circular form) have shown slight differences in the relative sedimentation rates of upper and lower fractions at dye concentrations corresponding to the steep regions in the titrations. The same experiments, when performed on nicked circular DNA obtained from heating both the mature and intracellular fractions, showed no evidence of differences in sedimentation coefficients. Such results may indicate slight heterogeneity in the superhelix density of viral PM2 I DNA; however, the degree of this heterogeneity would be somewhat less than that of the intracellular DNA. The possibility that superhelix density heterogeneity may arise from displacement loops, which have been found at low levels in intracellular PM2 DNA, has been subjected to experimental tests. Unless such structures are originally present and removed by the isolation procedure, this possibility may be rejected.     

Confinement as a determinant of macromolecular structure and reactivity.

The confinement of macromolecules within enclosures or "pores" of comparable dimensions results in significant size- and shape-dependent alterations of macromolecular chemical potential and reactivity. Calculations of the magnitude of this effect for model particles of different shapes in model enclosures of different shapes were carried out using hard particle partition theory developed by Giddings et al. (J. Phys. Chem. 1968. 72:4397-4408). Results obtained indicate that the equilibrium constants of reactions, such as isomerization, self-association, and site binding, that result in significant change in macromolecular size, shape, and/or mobility may be altered within pores by as much as several orders of magnitude relative to the value in the unbounded or bulk phase. Confinement also produces a substantial size-dependent outward force on the walls of an enclosure. These results are likely to be important within the fluid phase of biological media, such as the cytoplasm of eukaryotic cells, containing significant volume fractions of large fibrous structures (e.g., the cytomatrix).     

An improved function for fitting sedimentation velocity data for low-molecular-weight solutes.

Many traditional approaches to the analysis of sedimentation velocity data work poorly with data for low-molecular-weight solutes, which have sedimentation boundaries that are severely broadened by diffusion. An approach that has previously had some success is to directly fit these broad boundaries to approximate solutions of the Lamm equation that directly account for the high diffusion. However, none of the available approximate solutions work well at times both early and late in the run, or give boundary shapes that are highly accurate, especially for species of molecular weight < 10,000. An improved fitting function has been developed to overcome some of these limitations. The new function adds two correction terms to the Fujita-MacCosham solution. The optimum coefficients for these new correction terms were determined by a least-squares approach. The accuracy and limitations of fitting with this new function were tested against synthetic data sets obtained by finite-element methods, for analysis of samples containing either single species or several noninteracting species. We also compare the strengths and weaknesses of this method of analysis, and its ability to work with noisy data, relative to recently developed time-derivative methodologies.     

Impact of osmotic stress on protein diffusion in Lactococcus lactis

We measured translational diffusion of proteins in the cytoplasm and plasma membrane of the Gram‐positive bacterium Lactococcus lactis and probed the effect of osmotic upshift. For cells in standard growth medium the diffusion coefficients for cytosolic proteins (27 and 582 kDa) and 12‐transmembrane helix membrane proteins are similar to those in Escherichia coli. The translational diffusion of GFP in L. lactis drops by two orders of magnitude when the medium osmolality is increased by ～ 1.9 Osm, and the decrease in mobility is partly reversed in the presence of osmoprotectants. We find a large spread in diffusion coefficients over the full population of cells but a smaller spread if only sister cells are compared. While in general the diffusion coefficients we measure under normal osmotic conditions in L. lactis are similar to those reported in E. coli, the decrease in translational diffusion upon osmotic challenge in L. lactis is smaller than in E. coli. An even more striking difference is that in L. lactis the GFP diffusion coefficient drops much more rapidly with volume than in E. coli. We discuss these findings in the light of differences in turgor, cell volume, crowding and cytoplasmic structure of Gram‐positive and Gram‐negative bacteria.     

Molecular mobility and nucleocytoplasmic flux in hepatoma cells

Fluorescence microphotolysis (photobleaching) was used to measure, in single polyethylene glycol-induced polykaryons of hepatoma tissue culture cells, nucleocytoplasmic flux and intracellular mobility for a series of dextrans ranging in molecular mass from 3 to 150 kD and for bovine serum albumin. For the dextrans, the cytoplasmic and the nucleoplasmic translational diffusion coefficients amounted to approximately 9 and approximately 15%, respectively, of the value in dilute buffer. The diffusion coefficients depended inversely on molecular radius, suggesting that diffusion was dominated by viscosity effects. By application of the Stokes-Einstein equation, cytoplasmic and nucleoplasmic viscosities were derived to be 6.6 and 8.1 cP, respectively, at 23 degrees C. Between 10 and 37 degrees C nucleoplasmic diffusion coefficients increased by approximately 45-85%, whereas cytoplasmic diffusion coefficients were virtually independent of temperature. In contrast to that of the dextrans, diffusion of bovine serum albumin was more restricted. In the cytoplasm the diffusion coefficient was approximately 1.5% of the value in dilute buffer; in the nucleus albumin was largely immobile. This indicated that albumin mobility is dominated by association with immobile cellular structures. Nucleocytoplasmic flux of dextrans depended inversely on molecular mass with an exclusion limit between 17 and 41 kD. This agrees with previous measurements on primary hepatocytes (Peters, R., 1984, EMBO [Eur. Mol. Biol. Organ.] J. 3:1831-1836), suggesting that in both cell types the nuclear envelope has properties of a molecular sieve with a functional pore radius of approximately 55 A.     

Study of the translational diffusion of macromolecules in beads of gel chromatography by the FRAP method

We measured the translational diffusion of fractions of dextrans labelled with fluorescein isothiocyanate, in Sephadex gel beads permeated by aqueous solutions of these molecules. The molecular weights of these fractions were between 5400 and 200,000 and measurements of their diffusion coefficients inside a gel bead (D) and in the free solution (D0), were performed using the fluorescence recovery after photobleaching method (FRAP). We also determined the coefficient of partitioning (Kav) of these fractions between the gel and the free solvent, with a new microfluorimetric method. We found that, for Sephadex G-50, G-75, G-100, G-150 and G-200 gels, Kav varied with the Stokes radius (rs) of the dextran molecules, in agreement with the formula of Laurent and Killander (J. Chromatogr. 14 (1964) 317). For Sephadex G-100, G-150 and G-200 gels, D/D0 varied with rs, according to the theory of Ogston et al. (Proc. R. Soc. Lond. 333 (1973) 297). In addition, these theories predict a relation linking D/D0 to Kav which was well verified. Our work is the first systematic study of the translational diffusion of macromolecules in a chromatography gel. These measurements should allow a better evaluation of the factors which influence the resolution in exclusion chromatography. In addition, the diffusion of macromolecules in gels may provide models for the diffusion of these molecules in the cytoplasm of living cells and in connective biological tissues.     

Measurement of grouped intracellular solute osmotic virial coefficients

Models of cellular osmotic behaviour depend on thermodynamic solution theories to calculate chemical potentials in the solutions inside and outside the cell. These solutions are generally thermodynamically non-ideal under cryobiological conditions. The molality-based Elliott et al. form of the multi-solute osmotic virial equation is a solution theory which has been demonstrated to provide accurate predictions in cryobiological solutions, accounting for the non-ideality of these solutions using solute-specific thermodynamic parameters called osmotic virial coefficients. However, this solution theory requires as inputs the exact concentration of every solute in the solution being modeled, which poses a problem for the cytoplasm, where such detailed information is rarely available. This problem can be overcome by using a grouped solute approach for modeling the cytoplasm, where all the non-permeating intracellular solutes are treated as a single non-permeating “grouped” intracellular solute. We have recently shown (Zielinski et al., J Physical Chemistry B, 2017) that such a grouped solute approach is theoretically valid when used with the Elliott et al. model, and Ross-Rodriguez et al. (Biopreservation and Biobanking, 2012) have previously developed a method for measuring the cell type-specific osmotic virial coefficients of the grouped intracellular solute. However, the Ross-Rodriguez et al. method suffers from a lack of precision, which—as we demonstrate in this work—can severely impact the accuracy of osmotic model predictions under certain conditions. Thus, we herein develop a novel method for measuring grouped intracellular solute osmotic virial coefficients which yields more precise values than the existing method and then apply this new method to measure these coefficients for human umbilical vein endothelial cells.     

Protein mobility and diffusive barriers in Escherichia coli: consequences of osmotic stress

The effect of osmotic stress on the intracellular diffusion of proteins in Escherichia coli was studied, using a pulsed version of fluorescence recovery after photo-bleaching, pulsed-FRAP. This method employs sequences of laser pulses which only partly bleach the fluorophores in a cell. Because the cell size and geometry are taken into account, pulsed-FRAP enables to measure diffusion in very small cells of different shapes. We found that upon an osmotic upshock from 0.15 to 0.6 Osm, imposed by NaCl or sorbitol, the apparent intracellular diffusion (D) of mobile green fluorescent protein (GFP) decreased from 3.2 to 0.4 microm(2) s(-1), whereas the membrane permeable glycerol had no effect. Exposing E. coli cells to higher osmolalities (> 0.6 Osm) led to compartmentalization of the GFP into discrete pools, from where the GFP could not escape. Although free diffusion through the cell was hindered, the mobility of GFP in these pools was still relatively high (D approximately 0.4 microm(2) s(-1)). The presence of osmoprotectants restored the effect of osmotic stress on the protein mobility and apparent compartmentalization. Also, lowering the osmolality from 0.6 Osm back to 0.15 Osm restored the mobility of GFP. The implications of these findings in terms of heterogeneities and diffusive barriers inside the cell are discussed.     

Two-photon fluorescence correlation spectroscopy: method and application to the intracellular environment.

We report on the application of two photon molecular excitation to fluorescence correlation spectroscopy. We demonstrate the first fluorescence correlation spectroscopy measurements of translational mobility in the cytoplasm of living cells. Two-photon excitation inherently excites small sample volumes in three dimensions, providing depth discrimination similar to confocal microscopy, without emission pinholes. We demonstrated accurate measurements of the diffusion constant, D, for particles of several different known sizes, in bulk solutions of different viscosity. We then showed measurements of translational diffusion for 7- and 15-nm radius latex beads in the cytoplasm of mouse fibroblast cells. We measured time-dependent diffusion coefficients. When first injected in the cells, the spheres moved from two to five times slower than in water, with average rates of 18 x 10(-8) cm2/s for the 7 nm and 5 x 10(-8) cm2/s for the 15 nm radius spheres. After a few hours, spheres stick to the cells, and the motion slows down 10 to 100 times.     

Anisotropic diffusion of fluorescently labeled ATP in rat cardiomyocytes determined by raster image correlation spectroscopy

A series of experimental data points to the existence of profound diffusion restrictions of ADP/ATP in rat cardiomyocytes. This assumption is required to explain the measurements of kinetics of respiration, sarcoplasmic reticulum loading with calcium, and kinetics of ATP-sensitive potassium channels. To be able to analyze and estimate the role of intracellular diffusion restrictions on bioenergetics, the intracellular diffusion coefficients of metabolites have to be determined. The aim of this work was to develop a practical method for determining diffusion coefficients in anisotropic medium and to estimate the overall diffusion coefficients of fluorescently labeled ATP in rat cardiomyocytes. For that, we have extended raster image correlation spectroscopy (RICS) protocols to be able to discriminate the anisotropy in the diffusion coefficient tensor. Using this extended protocol, we estimated diffusion coefficients of ATP labeled with the fluorescent conjugate Alexa Fluor 647 (Alexa-ATP). In the analysis, we assumed that the diffusion tensor can be described by two values: diffusion coefficient along the myofibril and that across it. The average diffusion coefficients found for Alexa-ATP were as follows: 83 +/- 14 microm(2)/s in the longitudinal and 52 +/- 16 microm(2)/s in the transverse directions (n = 8, mean +/- SD). Those values are approximately 2 (longitudinal) and approximately 3.5 (transverse) times smaller than the diffusion coefficient value estimated for the surrounding solution. Such uneven reduction of average diffusion coefficient leads to anisotropic diffusion in rat cardiomyocytes. Although the source for such anisotropy is uncertain, we speculate that it may be induced by the ordered pattern of intracellular structures in rat cardiomyocytes.