Restricted diffusion in biophysical systems: Theory

Theoretical results are presented on measurements of restricted diffusion in biophysical systems by the pulsed gradient spin echo nuclear magnetic resonance (PGSENMR) technique. A Fokker-Planck equation is developed to describe restricted diffusion, and it is shown that only two basic types of penetrable diffusion barriers exist, those in which the diffusing particles are partially excluded from the barrier region because of an increased free energy, and those in which the diffusing particles are not excluded but experience increased viscosity in the region. The Fokker-Planck equation is used to obtain expressions for the spin echo amplitude in PGSENMR experiments, and it is shown that for restricted diffusion the average diffusion coefficient measured in these experiments over short intervals is larger than that measured over long intervals. The possibility of distinguishing between the two types of barriers is considered. The experimental parameters required for intracellular restricted diffusion measurements are discussed, and it is shown that the interpretation of PGSENMR results in animal tissues should include the possibility of penetrable barriers rather than just the impenetrable barriers of previous PGSENMR calculations.     

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.     

Septin-dependent compartmentalization of the endoplasmic reticulum during yeast polarized growth

Polarized cells frequently use diffusion barriers to separate plasma membrane domains. It is unknown whether diffusion barriers also compartmentalize intracellular organelles. We used photobleaching techniques to characterize protein diffusion in the yeast endoplasmic reticulum (ER). Although a soluble protein diffused rapidly throughout the ER lumen, diffusion of ER membrane proteins was restricted at the bud neck. Ultrastructural studies and fluorescence microscopy revealed the presence of a ring of smooth ER at the bud neck. This ER domain and the restriction of diffusion for ER membrane proteins through the bud neck depended on septin function. The membrane-associated protein Bud6 localized to the bud neck in a septin-dependent manner and was required to restrict the diffusion of ER membrane proteins. Our results indicate that Bud6 acts downstream of septins to assemble a fence in the ER membrane at the bud neck. Thus, in polarized yeast cells, diffusion barriers compartmentalize the ER and the plasma membrane along parallel lines.     

Intracellular diffusion restrictions in isolated cardiomyocytes from rainbow trout

Background  

Restriction of intracellular diffusion of adenine nucleotides has been studied intensively on adult rat cardiomyocytes. However, their cause and role in vivo is still uncertain. Intracellular membrane structures have been suggested to play a role. We therefore chose to study cardiomyocytes from rainbow trout (Oncorhynchus mykiss), which are thinner and have fewer intracellular membrane structures than adult rat cardiomyocytes. Previous studies suggest that trout permeabilized cardiac fibers also have diffusion restrictions. However, results from fibers may be affected by incomplete separation of the cells. This is avoided when studying permeabilized, isolated cardiomyocytes. The aim of this study was to verify the existence of diffusion restrictions in trout cardiomyocytes by comparing ADP-kinetics of mitochondrial respiration in permeabilized fibers, permeabilized cardiomyocytes and isolated mitochondria from rainbow trout heart. Experiments were performed at 10, 15 and 20°C in the absence and presence of creatine.     

ADP Compartmentation Analysis Reveals Coupling between Pyruvate Kinase and ATPases in Heart Muscle

Cardiomyocytes have intracellular diffusion restrictions, which spatially compartmentalize ADP and ATP. However, the models that predict diffusion restrictions have used data sets generated in rat heart permeabilized fibers, where diffusion distances may be heterogeneous. This is avoided by using isolated, permeabilized cardiomyocytes. The aim of this work was to analyze the intracellular diffusion of ATP and ADP in rat permeabilized cardiomyocytes. To do this, we measured respiration rate, ATPase rate, and ADP concentration in the surrounding solution. The data were analyzed using mathematical models that reflect different levels of cell compartmentalization. In agreement with previous studies, we found significant diffusion restriction by the mitochondrial outer membrane and confirmed a functional coupling between mitochondria and a fraction of ATPases in the cell. In addition, our experimental data show that considerable activity of endogenous pyruvate kinase (PK) remains in the cardiomyocytes after permeabilization. A fraction of ATPases were inactive without ATP feedback by this endogenous PK. When analyzing the data, we were able to reproduce the measurements only with the mathematical models that include a tight coupling between the fraction of endogenous PK and ATPases. To our knowledge, this is the first time such a strong coupling of PK to ATPases has been demonstrated in permeabilized cardiomyocytes.     

Permeabilized rat cardiomyocyte response demonstrates intracellular origin of diffusion obstacles

Intracellular diffusion restrictions for ADP and other molecules have been predicted earlier based on experiments on permeabilized fibers or cardiomyocytes. However, it is possible that the effective diffusion distance is larger than the cell dimensions due to clumping of cells and incomplete separation of cells in fiber preparations. The aim of this work was to check whether diffusion restrictions exist inside rat cardiomyocytes or are caused by large effective diffusion distance. For that, we determined the response of oxidative phosphorylation (OxPhos) to exogenous ADP and ATP stimulation in permeabilized rat cardiomyocytes using fluorescence microscopy. The state of OxPhos was monitored via NADH and flavoprotein autofluorescence. By varying the ADP or ATP concentration in flow chamber, we determined that OxPhos has a low affinity in cardiomyocytes. The experiments were repeated in a fluorometer on cardiomyocyte suspensions leading to similar autofluorescence changes induced by ADP as recorded under the microscope. ATP stimulated OxPhos more in a fluorometer than under the microscope, which was attributed to accumulation of ADP in fluorometer chamber. By calculating the flow profile around the cell in the microscope chamber and comparing model solutions to measured data, we demonstrate that intracellular structures impose significant diffusion obstacles in rat cardiomyocytes.     

Multiple diffusion mechanisms due to nanostructuring in crowded environments

One of the key questions regarding intracellular diffusion is how the environment affects molecular mobility. Mostly, intracellular diffusion has been described as hindered, and the physical reasons for this behavior are: immobile barriers, molecular crowding, and binding interactions with immobile or mobile molecules. Using results from multi-photon fluorescence correlation spectroscopy, we describe how immobile barriers and crowding agents affect translational mobility. To study the hindrance produced by immobile barriers, we used sol-gels (silica nanostructures) that consist of a continuous solid phase and aqueous phase in which fluorescently tagged molecules diffuse. In the case of molecular crowding, translational mobility was assessed in increasing concentrations of 500 kDa dextran solutions. Diffusion of fluorescent tracers in both sol-gels and dextran solutions shows clear evidence of anomalous subdiffusion. In addition, data from the autocorrelation function were analyzed using the maximum entropy method as adapted to fluorescence correlation spectroscopy data and compared with the standard model that incorporates anomalous diffusion. The maximum entropy method revealed evidence of different diffusion mechanisms that had not been revealed using the anomalous diffusion model. These mechanisms likely correspond to nanostructuring in crowded environments and to the relative dimensions of the crowding agent with respect to the tracer molecule. Analysis with the maximum entropy method also revealed information about the degree of heterogeneity in the environment as reported by the behavior of diffusive molecules.     

Mitochondrial respiratory control can compensate for intracellular O(2) gradients in cardiomyocytes at low PO(2)

In isolated single cardiomyocytes with moderately elevated mitochondrial respiration, direct evidence for intracellular radial gradients of oxygen concentration was obtained by subcellular spectrophotometry of myoglobin (Mb). When oxygen consumption was increased by carbonyl cyanide m-chlorophenylhydrazone (CCCP) during superfusion of cells with 4% oxygen, PO(2) at the cell core dropped to 2.3 mmHg, whereas Mb near the plasma membrane was almost fully saturated with oxygen. Subcellular NADH fluorometry demonstrated corresponding intracellular heterogeneities of NADH, indicating suppression of mitochondrial oxidative metabolism due to relatively slow intracellular oxygen diffusion. When oxygen consumption was increased by electrical pacing in 2% oxygen, radial oxygen gradients of similar magnitude were demonstrated (cell core PO(2) = 2.6 mmHg). However, an increase in NADH fluorescence at the cell core was not detected. Because CCCP abolished mitochondrial respiratory control while it was intact in electrically paced cardiomyocytes, we conclude that mitochondria with intact respiratory control can sustain electron transfer with reduced oxygen supply. Thus mitochondrial intrinsic regulation can compensate for relatively slow oxygen diffusion within cardiomyocytes.     

Hydrocortisone has a protective effect on CyclosporinA-induced cardiotoxicity

CyclosporinA (CsA) is an immunosuppressive drug which induces severe adverse effects such as cardiotoxicity and nephrotoxicity. In several therapeutic protocols CsA is used in association with corticosteroids to obtain better therapeutic results. Recently, our studies showed that CsA increases blood pressure while inhibit Nitric Oxide (NO) production in vivo. In this study we evaluated in rat cardiomyocytes the effects of CsA, used alone or in association with Hydrocortisone (HY), on intracellular calcium concentration, NO production and lipid peroxidation (MDA level). Our results demonstrated that CsA increased intracellular calcium and such effect was dose-dependent. HY used alone, slightly decreased intracellular calcium, while dramatically reduced CsA-induced calcium fluxes. CsA (3.2 microM) increased lipid peroxidation and this effect was blunted by HY. Both CsA and HY inhibited NO production in rat cardiomyocytes acting on this pathway synergically. Our results demonstrated that in rat cardiomyocytes, CsA toxicity is due to a calcium overload, which in turn induce lipid peroxidation and determines oxidative stress-induced cell injury. Treatment with HY effectively inhibits CsA-induced toxicity, decreasing lipid peroxidation as well as calcium intracellular concentration. Our findings seem to suggest that glucocorticoids may be effective in reducing CsA-induced cardiotoxicity at concentrations which are consistent with current therapeutic doses.     

Mechanisms of cytosolic targeting of matrix metalloproteinase-2

Matrix metalloproteinase-2 (MMP-2) is best understood for its biological actions outside the cell. However, MMP-2 also localizes to intracellular compartments and the cytosol where it has several substrates, including troponin I (TnI). Despite a growing list of cytosolic substrates, we currently do not know the mechanism(s) that give rise to the equilibrium between intracellular and secreted MMP-2 moieties. Therefore, we explored how cells achieve the unique distribution of this protease. Our data show that endogenous MMP-2 targets inefficiently to the endoplasmic reticulum (ER) and shows significant amounts in the cytosol. Transfection of canonical MMP-2 essentially reproduces this targeting pattern, suggesting it is the quality of the MMP-2 signal sequence that predominantly determines MMP-2 targeting. However, we also found that human cardiomyocytes express an MMP-2 splice variant which entirely lacks the signal sequence. Like the fraction of ER-excluded, full-length MMP-2, this variant MMP-2 is restricted to the cytosol and specifically enhances TnI cleavage upon hypoxia-reoxygenation injury in cardiomyocytes. Together, our findings describe for the first time a set of mechanisms that cells utilize to equilibrate MMP-2 both in the extracellular milieu and intracellular, cytosolic locations. Our results also suggest approaches to specifically investigate the overlooked intracellular biology of MMP-2.     

The effects of CGRP on calcium transients of dedifferentiating cultured adult rat cardiomyocytes compared to non-cultured adult cardiomyocytes: possible protective and deleterious results in cardiac function

CGRP has potent cardiovascular effects but its role in heart failure is unclear. Effects of CGRP on calcium concentrations in fresh adult rat cardiomyocytes, cultured adult cardiomyocytes and neonatal cardiomyocytes were determined by real time fluorescence spectrophotometry. Treatment of cultured adult cardiomyocytes with CGRP resulted in a rapid cessation of beating and a reduction in intracellular calcium. Similar results were obtained in cultured neonatal myocytes. However, rod-shaped adult cardiomyocytes revealed a number of responses; (a) non-beating cells began to beat with increased intracellular calcium; (b) spontaneously beating cells exhibited increased intracellular calcium content and a faster beating rate or (c), myocytes increased their beating rate and became arrhythmic, suggesting that CGRP action on cultured dedifferentiated adult and neonatal myocytes depletes intracellular calcium, whereas in the rod-shaped mature myocytes calcium is retained, pointing to a different mode of action for CGRP on developing and dedifferentiating cardiomyocytes, compared to fully developed cardiomyocytes.     

Cation diffusion in cartilage measured by pulsed field gradient NMR

In this study, the pulsed field gradient (PFG) nuclear magnetic resonance (NMR) technique was used for the investigation of (1) concentration and compression effects on cation self-diffusion, and (2) restricted diffusion of cations in cartilage. Since physiologically relevant cations like Na+ are difficult to investigate owing to their very short relaxation times, the cations tetramethylammonium (TMA) and tetraethylammonium (TEA) were employed for diffusion studies in samples of explanted cartilage. Results indicated that the diffusion of monovalent cations shows strong similarities to observations already made in studies of the diffusion of water in cartilage: with increasing compression, i.e. decreasing water content, the diffusion coefficient of the cation decreases concomitantly. The diffusion coefficients also showed a decrease with increasing cation concentrations, basically reflecting the corresponding decrease in the water content. Both results could be explained by the well-established model of Mackie and Meares. This, together with the similarity of the diffusion coefficient D in cartilage relative to free solution (about 50%) for both cations, is consistent with the view that the water content and not the charge is the most important determinant of the intratissue diffusivity of monovalent cations. Diffusion studies with increasing observation times showed strong evidence of restricted diffusion, allowing the estimation of the geometry of barriers within cartilage.     

Studies of mitochondrial respiration in muscle cells in situ: Use and misuse of experimental evidence in mathematical modelling

Applications of permeabilized cell and skinned fiber techniques in combination with methods of mathematical modelling for studies of mitochondrial function in the cell are critically evaluated. Mathematical models may be useful tools for explaining biological phenomena, but only if they are selected by fitting the computing results with real experimental data. Confocal microscopy has been used in experiments with permeabilized cardiomyocytes and myocardial fibers to determine the maximal diffusion distance from medium to the core of cells, which is shown not to exceed 8-10 microm. This is a principal index for correctly explaining high apparent Km for exogenous ADP (200-300 microM) in regulation of mitochondrial respiration in oxidative muscle cells in situ. The best fitting of the results of in silico studies may be achieved by using of the compartmentalized energy transfer model. From these results, it may be concluded that in cardiac muscle cells the mitochondria and ATPases are organized into intracellular energetic units (ICEUs) separated from the bulk phase of cytoplasm by some barriers which limit the diffusion of adenine nucleotides. In contrast, alternative models based on the concept of the cell as homogenous system do not explain the observed experimental phenomena and have led to misleading conclusions. The various sources of experimental and conceptual errors are analyzed.     

Specific limitations for intracellular diffusion of ADP in cardiomyocytes

Isolated cardiomyocytes and bundles of cardiac fibers were studied after lysis of their sarcolemma by saponin (40-50 micrograms/ml). 60-70% of cardiomyocytes were rod-like and Ca2(+)-tolerant. The kinetics of stimulation of oxidative phosphorylation by ADP and creatine via the mitochondrial creatine kinase reaction: MgATP + creatine----MgADP + phosphocreatine, was investigated after perforation of sarcolemma. The criterion for sarcolemmal perforation was an almost complete (80-100%) leakage of lactate dehydrogenase. It was shown that the Km values for ADP during stimulation of oxidative phosphorylation in cardiomyocytes are 250 +/- 39 microM (264 +/- 57 microM in cardiac bundles) which exceeds by one order of magnitude the Km value for ADP in isolated mitochondria (18 +/- 5 microM). On the contrary, Km for creatine is the same for all preparations studied (6-6.9 mM). The data obtained suggest the absence of diffusion difficulties for creatine inside the cells. In contrast, intracellular diffusion of ADP is restricted, most probably, dye to its binding to intracellular structures. These data emphasize the crucial role of the creatine kinase system in energy transfer processes. In the presence of 25 mM creatine Km for ADP is decreased to 36 +/- 6 mM due to a manyfold use of ADP in the coupled creatine kinase-oxidative phosphorylation reaction occurring in mitochondria.     

Understanding morphogen gradients: a problem of dispersion and containment

Protein morphogens are instructive signals that regulate growth and patterning of tissues and organs. They form long-range, dynamic gradients by moving from regions of high concentration (producing cells) to regions of low concentration (the adjacent, nonproducing developmental field). Since morphogen activity must be limited to the adjacent target field, we want to understand both how signaling proteins move and how their dispersion is restricted. We consider the variety of settings for long-range morphogen systems in Drosophila. In the early embryo, morphogens appear to disperse by free diffusion, and impermeable membranes physically constrain them. However, at later stages, containment is achieved without physical barriers. We argue that in the absence of constraining barriers, gradient-generating dispersion of morphogens cannot be achieved by passive diffusion and that other mechanisms for distribution must be considered.     

Modeling of spatial metabolite distributions in the cardiac sarcomere

Although a high ATP diffusion rate implies homogeneous distribution of the principal energetic currency in the cytosol, local diffusion barriers represented by macromolecular structures can render ATP concentrations to be inhomogeneous. A method is presented here that provides apparent diffusion coefficient values in local intracellular regions and allows the estimation of spatial metabolite distribution. The apparent local diffusion coefficient for ATP in cardiac myofibrils was determined from the analysis of diffusion-dependent rightward shift of the substrate dependence for actomyosin ATPase activity using the reaction-diffusion model, which accounted for the properties of phosphotransfer reactions. This functional analysis, which took into account the local diffusional ATP delivery to the active sites, provided an apparent value that was three orders of magnitude lower than that defined by direct methods for the cytosol. The low value of the diffusion coefficient was shown to define unusual properties of the intracellular space in working heart, where small reductions in ATP levels in the surrounding cytosol result in a large drop in [ATP] inside myofibrils. This drop is critical for vital cellular functions, and the analysis presented here defines its physical basis. The diffusion barriers thus defined explain the coexistence of pathological energy deficit with almost normal average ATP levels.     

Mitochondria-cytoskeleton interaction: distribution of β-tubulins in cardiomyocytes and HL-1 cells

Mitochondria-cytoskeleton interactions were analyzed in adult rat cardiomyocytes and in cancerous non-beating HL-1 cells of cardiac phenotype. We show that in adult cardiomyocytes βII-tubulin is associated with mitochondrial outer membrane (MOM). βI-tubulin demonstrates diffused intracellular distribution, βIII-tubulin is colocalized with Z-lines and βIV-tubulin forms microtubular network. HL-1 cells are characterized by the absence of βII-tubulin, by the presence of bundles of filamentous βIV-tubulin and diffusely distributed βI- and βIII-tubulins. Mitochondrial isoform of creatine kinase (MtCK), highly expressed in cardiomyocytes, is absent in HL-1 cells. Our results show that high apparent K(m) for exogenous ADP in regulation of respiration and high expression of MtCK both correlate with the expression of βII-tubulin. The absence of βII-tubulin isotype in isolated mitochondria and in HL-1 cells results in increased apparent affinity of oxidative phosphorylation for exogenous ADP. This observation is consistent with the assumption that the binding of βII-tubulin to mitochondria limits ADP/ATP diffusion through voltage-dependent anion channel of MOM and thus shifts energy transfer via the phosphocreatine pathway. On the other hand, absence of both βII-tubulin and MtCK in HL-1 cells can be associated with their more glycolysis-dependent energy metabolism which is typical for cancer cells (Warburg effect).     

The spermatid plasma membrane comes of age

Spermiogenesis affords a unique opportunity to examine the formation of plasma membrane domains. Recent attempts to chart the life cycles of well-characterized integral plasma membrane proteins during spermiogenesis have suggested that spermatids are at least as adept as epithelial cells or neurons at establishing their plasma membrane domains. They appear to expand upon the standard recipe involving concurrent domain-specific protein targeting and diffusion barriers by using a combination of intracellular storage within the secretory pathway, developmentally-regulated delivery to provisional plasma membrane domains, large-scale redistributions of diffusion barriers and integral plasma membrane proteins, and the shedding of an entire plasma membrane domain.     

Effect of cytoskeletal geometry on intracellular diffusion.

A method is presented for determining the retardation of diffusion of particles inside cells owing to cytoskeletal barriers. The cytoskeletal meshwork is treated as a repeating periodic two-dimensional or three-dimensional lattice composed of elements of given size, shape, and spacing. We derive an analytic expression for the diffusion coefficient relative to that of the cytosol. This expression is evaluated by solving numerically an appropriate boundary-value problem for the Laplace equation. For the two-dimensional case, e.g., diffusion in a membrane, the results are quantitatively similar to those obtained by Saxton (1987. Biophys. J. 52:989-997) using Monte Carlo methods. The three-dimensional results are quantitatively similar to experimental results reported by Luby-Phelps et al. (1987. Proc. Natl. Acad. Sci. USA. 84:4910-4913) for the diffusion of dextran and Ficoll particles in Swiss 3T3 cells. By accounting for geometrical factors, these results allow one to assess the relative contributions of geometrical hindrance and of binding to the cytoskeletal lattice from measurements of intracellular diffusion coefficients of proteins.