Tracer diffusion through F-actin: effect of filament length and cross-linking.

We have determined diffusion coefficients for small (50- to 70-nm diameter) fluorescein-thiocarbamoyl-labeled Ficoll tracers through F-actin as a function of filament length and cross-linking. fx45 was used to regulate filament length and avidin/biotinylated actin or ABP-280 was used to prepare cross-linked actin gels. We found that tracer diffusion was generally independent of filament length in agreement with theoretical predictions for diffusion through solutions of rods. However, in some experiments diffusion was slower through short (< or = 1.0 micron) filaments, although this result was not consistently reproducible. Measured diffusion coefficients through unregulated F-actin and filaments of lengths > 1.0 micron were more rapid than predicted by theory for tracer diffusion through rigid, random networks, which was consistent with some degree of actin bundling. Avidin-induced cross-linking of biotinylated F-actin did not affect diffusion through unregulated F-actin, but in cases where diffusion was slower through short filaments this cross-linking method resulted in enhanced tracer diffusion rates indistinguishable from unregulated F-actin. This finding, in conjunction with increased turbidity of 1.0-micron filaments upon avidin cross-linking, indicated that this cross-linking method induces F-actin bundling. By contrast, ABP-280 cross-linking retarded diffusion through unregulated F-actin and decreased turbidity. Tracer diffusion under these conditions was well approximated by the diffusion theory. Both cross-linking procedures resulted in gel formation as determined by falling ball viscometry. These results demonstrate that network microscopic geometry is dependent on the cross-linking method, although both methods markedly increase F-actin macroscopic viscosity.     

Protein diffusion in mammalian cell cytoplasm

We introduce a new method for mesoscopic modeling of protein diffusion in an entire cell. This method is based on the construction of a three-dimensional digital model cell from confocal microscopy data. The model cell is segmented into the cytoplasm, nucleus, plasma membrane, and nuclear envelope, in which environment protein motion is modeled by fully numerical mesoscopic methods. Finer cellular structures that cannot be resolved with the imaging technique, which significantly affect protein motion, are accounted for in this method by assigning an effective, position-dependent porosity to the cell. This porosity can also be determined by confocal microscopy using the equilibrium distribution of a non-binding fluorescent protein. Distinction can now be made within this method between diffusion in the liquid phase of the cell (cytosol/nucleosol) and the cytoplasm/nucleoplasm. Here we applied the method to analyze fluorescence recovery after photobleach (FRAP) experiments in which the diffusion coefficient of a freely-diffusing model protein was determined for two different cell lines, and to explain the clear difference typically observed between conventional FRAP results and those of fluorescence correlation spectroscopy (FCS). A large difference was found in the FRAP experiments between diffusion in the cytoplasm/nucleoplasm and in the cytosol/nucleosol, for all of which the diffusion coefficients were determined. The cytosol results were found to be in very good agreement with those by FCS.     

Plant mitochondria move on F-actin, but their positioning in the cortical cytoplasm depends on both F-actin and microtubules

Mitochondrion movement and positioning was studied in elongating cultured cells of tobacco (Nicotiana tabacum L.), containing mitochondria-localized green fluorescent protein. In these cells mitochondria are either actively moving in strands of cytoplasm transversing or bordering the vacuole, or immobile positioned in the cortical layer of cytoplasm. Depletion of the cell's ATP stock with the uncoupling agent DNP shows that the movement is much more energy demanding than the positioning. The active movement is F-actin based. It is inhibited by the actin filament disrupting drug latrunculin B, the myosin ATPase inhibitor 2,3-butanedione 2-monoxime and the sulphydryl-modifying agent N-ethylmaleimide. The microtubule disrupting drug oryzalin did not affect the movement of mitochondria itself, but it slightly stimulated the recruitment of cytoplasmic strands, along which mitochondria travel. The immobile mitochondria are often positioned along parallel lines, transverse or oblique to the cell axis, in the cortical cytoplasm of elongated cells. This positioning is mainly microtubule based. After complete disruption of the F-actin, the mitochondria parked themselves into conspicuous parallel arrays transverse or oblique to the cell axis or clustered around chloroplasts and around patches and strands of endoplasmic reticulum. Oryzalin inhibited all positioning of the mitochondria in parallel arrays.     

Normal modes as refinement parameters for the F-actin model.

The slow normal modes of G-actin were used as structural parameters to refine the F-actin model against 8-A resolution x-ray fiber diffraction data. The slowest frequency normal modes of G-actin pertain to collective rearrangements of domains, motions that are characterized by correlation lengths on the order of the resolution of the fiber diffraction data. Using a small number of normal mode degrees of freedom (< or = 12) improved the fit to the data significantly. The refined model of F-actin shows that the nucleotide binding cleft has narrowed and that the DNase I binding loop has twisted to a lower radius, consistent with other refinement techniques and electron microscopy data. The methodology of a normal mode refinement is described, and the results, as applied to actin, are detailed.     

Reduced diffusion of charge-modified, conformationally intact anionic Ficoll relative to neutral Ficoll across the rat glomerular filtration barrier in vivo

The glomerular filtration barrier (GFB) is commonly conceived as a negatively charged sieve to proteins. Recent studies, however, indicate that glomerular charge effects are small for anionic, carboxymethylated (CM) dextran vs. neutral dextran. Furthermore, two studies assessing the glomerular sieving coefficients (θ) for negative CM-Ficoll vs. native Ficoll have demonstrated an increased glomerular permeability for CM-Ficoll (Asgeirsson D, Venturoli D, Rippe B, Rippe C. Am J Physiol Renal Physiol 291: F1083-F1089, 2006; Guimar?es M, Nikolovski J, Pratt L, Greive K, Comper W. Am Physiol Renal Physiol 285: F1118-F1124, 2003.). The CM-Ficoll used, however, showed a larger Stokes-Einstein radius (a(e)) than neutral Ficoll, and it was proposed that the introduction of negative charges in the Ficoll molecule had made it more flexible and permeable. Recently, a negative FITC-labeled CM-Ficoll (CMI-Ficoll) was produced with a conformation identical to that of neutral FITC-Ficoll. Using these probes, we determined their θ:s in anesthetized Wistar rats (259 ± 2.5 g). After blood access had been achieved, the left ureter was cannulated for urine sampling. Either polysaccharide was infused (iv) together with a filtration marker, and urine and plasma were collected. Assessment of θ FITC-Ficoll was achieved by high-performance size-exclusion chromatography (HPSEC). CMI-Ficoll and native Ficoll had identical elugrams on the HPSEC. Diffusion of anionic Ficoll was significantly reduced compared with that of neutral Ficoll across the GFB for molecules of a(e) ～20-35 ?, while there were no charge effects for Ficoll of a(e) = 35-80 ?. The data are consistent with a charge effect present in "small pores," but not in "large pores," of the GFB and mimicked those obtained for anionic membranes in vitro for the same probes.     

Analysis of rhodamine and fluorescein-labeled F-actin diffusion in vitro by fluorescence photobleaching recovery.

Properties of filamentous acetamidofluorescein-labeled actin and acetamidotetramethylrhodamine-labeled actin (AF and ATR-actin, respectively) were examined to resolve discrepancies in the reported translational diffusion coefficients of F-actin measured in vitro by FPR and other techniques. Using falling-ball viscometry and two independent versions of fluorescence photobleaching recovery (FPR), the present data indicate that several factors are responsible for these discrepancies. Gel filtration chromatography profoundly affects the viscosity of actin solutions and filament diffusion coefficients. ATR-actin and, to a lesser degree, AF-actin show a reduction in viscosity in proportion to the fraction labeled, presumably due to filament shortening. Actin filaments containing AF-actin or ATR-actin are susceptible to photoinduced damage, including a covalent cross-linking of actin protomers within filaments and an apparent cleavage of filaments detected by a decrease of the measured viscosity and an increase in the measured filament diffusion coefficients. Quantum yields of the two photoinduced effects are quite different. Multiple cross-links are produced relative to each photobleaching event, whereas less than 1% filament cleavage occurs. Substantial differences in the filament diffusion coefficients measured by FPR are also the result of differences in illumination geometry and sampling time. However, under controlled conditions, FPR can be used as a quantitative tool for measuring the hydrodynamic properties of actin filaments. Incremented filament shortening caused by photoinduced cleavage or incremental addition of filament capping proteins produces a continuous and approximately linear increase of filament diffusion coefficients, indicating that filaments are not associated in solution. Our results indicate that actin filaments exhibit low mobilities and it is inferred that actin filaments formed in vitro by column-purified actin, under standard conditions, are much longer than has conventionally been presumed.     

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.     

Toward a multi-membrane model for potassium conduction in squid giant axon.

Possible physical mechanisms are considered which come close to a quantitative explanation for features of the potassium admittance magnitude. At 1–30 Hz there is an elevation of [Y] and positive phase above that obtained from the Hodgkin-Huxley model. Moreover there appears to be a slight negative phase for lower frequencies. An additional important feature for model fitting is the movement of the middle zero-phase crossing to the left with depolarization. Two general classes of subsystems are discussed. (1) Extracellular: potassium accumulation, barriers to diffusion near or adjacent to the excitable membrane, diffusion with volume flow, bulklimited diffusion through the Schwann cell layer and adsorption or absorption by the Schwann cells; (2) processes intrinsic to the excitable membrane: cyclic steady state, co-operative, inactivating and second order. A generalized potassium inactivation is treated in detail which provides fairly quantitative fits to transmembrane transfer data with a voltage-dependent inactivation time constant ranging between 40 and 100 ms. However, potassium accumulation coupled with hypothesized sorptive effects of the greater membrane, particularly the Schwann cell layer, also provide reasonable fits. Based on lack of experimental evidence for an inactivation, the choice is made for a multicompartment model. When an HH membrane element is combined with accumulation-depletion in an extracellular space and with a bulk limited or surface limited diffusion through the Schwann cells good agreement is obtained with measured admittance.     

Free diffusion coefficient of ionic calcium in cytoplasm

The free diffusion coefficient of ionic Ca was measured in isolated samples of Myxicola axoplasm by following the migration of 45Ca. When precautions were taken to minimize the sequestration and chelation of 45Ca (i.e., using inhibitors, energy deprivation, and saturation of Ca chelation sites), a diffusion coefficient of 5.3 x 10(-6) cm2 s-1 was measured. The diffusion coefficient was not appreciably changed by lowering free calcium from 100 microM to approximately 10 microM or by increasing the diffusion time from ten to twenty minutes. In untreated cytoplasm taken directly from the giant axon of Myxicola, the migration of Ca was more complex and could not be described by a single diffusion coefficient. This result is interpreted to suggest that bulk movement of Ca-buffers may occur in untreated Myxicola axoplasm, a system that contains few microtubules.     

Heterogeneous anomalous diffusion of a virus in the cytoplasm of a living cell

The infection pathway of a virus in the cytoplasm of a living cell is studied from the viewpoint of diffusion theory, based on a phenomenon observed by single-molecule imaging. The cytoplasm plays the role of a medium for stochastic motion of a virus contained in an endosome as well as a free virus. It is experimentally known that the exponent of anomalous diffusion fluctuates in localized areas of the cytoplasm. Here, generalizing the fractional kinetic theory, such fluctuations are described in terms of the exponent locally distributed over the cytoplasm and a theoretical proposition is presented for its statistical form. The proposed fluctuations may be examined in an experiment of heterogeneous diffusion in the infection pathway.     

F-actin, a model polymer for semiflexible chains in dilute, semidilute, and liquid crystalline solutions.

Single actin filaments were analyzed in solutions ranging from dilute (0.2 microgram/ml), where filaments interact only with solvent, to concentrations (4.0 mg/ml) at which F-actin forms a nematic phase. A persistence length of approximately 1.8 microns and an average length of approximately 22 microns (Kaufmann et al., 1992) identify actin as a model for studying the dynamics of semiflexible polymers. In dilute solutions the filaments exhibit thermal bending undulations in addition to diffusive motion. At higher semidilute concentrations (1.4 mg/ml) three-dimensional reconstructions of confocal images of fluorescently labeled filaments in a matrix of unlabeled F-actin reveal steric interactions between filaments, which account for the viscoelastic behavior of these solutions. The restricted undulations of these labeled chains reveal the virtual tube formed around a filament by the surrounding actin. The average tube diameter <a> scales with monomer concentration c as <a> varies; is directly proportional to c-(0.5 +/- 0.15). The diffusion of filaments in semidilute solutions (c = (0.1-2.0) mg/ml) is dominated by diffusion along the filament contour (reptation), and constraint release by remodeling of the surrounding filaments is rare. The self-diffusion coefficient D parallel along the tube decreases linearly with the chain length for semidilute solutions. For concentrations > 2.5 mg/ml a transition occurs from an isotropic entangled phase to a coexistence between isotropic and nematic domains. Analysis of the molecular motions of filaments suggests that the filaments in the aligned domains are in thermal equilibrium and that the diffusion coefficient parallel to the director D parallel is nearly independent of filament length. We also report the novel direct observation of u-shaped defects, called hairpins, in the nematic domains.     

Local migration of myosin in F-actin plus ATP solution on the boundary of a diffusion cell.

The diffusion phenomena of myosin (myosin A, H-meromyosin or subfragment-1) in F-actin plus ATP solutions were investigated. The upper part of the diffusion cell was filled with F-actin plus ATP, and the lower part was filled with F-actin, ATP, and myosin, then both parts were brought into contact so that a boundary of the two solutions was formed and the diffusion of myosin in F-actin plus ATP solutions started. The diffusion pattern was observed with a schlieren lens system. When almost all the ATP in the lower part of the cell had been consumed by actomyosin, a hyper-sharp schlieren pattern appeared near the boundary. On analyzing this pattern, it was found that a local fast migration of proteins was occurring. Simple Brownian motion of myosin molecules could not explain the hyper-sharp phenomenon. This phenomenon occurred in ther pesence of Mg2+ or Ca2+, but very little in the presence of EDTA. Although it is well known that the superprecipitation of myosin B suspension occurs only at physiological ionic strength, this phenomenon occurred over a relatively wide range of ionic strengths. The molecular mechanism of this phenomenon is discussed in relation to the basic mechanism of the interaction between myosin and F-actin.     

Toward a comprehensive model for induced endoreduplication

Both the biological significance and the molecular mechanism of endoreduplication (END) have been debated for a long time by cytogeneticists and researchers into cell cycle enzymology and dynamics alike. Mainly due to the fact that a wide variety of agents have been reported as able to induce endoreduplication and the diversity of cell types where it has been described, until now no clear or unique mechanism of induction of this phenomenon, rare in animals but otherwise quite common in plants, has been proposed. DNA topoisomerase II (topo II), plays a major role in mitotic chromosome segregation after DNA replication. The classical topo II poisons act by stabilizing the enzyme in the so-called cleavable complex and result in DNA damage as well as END, while the true catalytic inhibitors, which are not cleavable-complex-stabilizers, do induce END without concomitant DNA and chromosome damage. Taking into account these observations on the induction of END by drugs that interfere with topo II, together with our recently obtained evidence that the nature of DNA plays an important role for chromosome segregation [Cortes, F., Pastor, N., Mateos, S., Dominguez, I., 2003. The nature of DNA plays a role in chromosome segregation: endoreduplication in halogen-substituted chromosomes. DNA Repair 2, 719-726.], a straightforward model is proposed in which the different mechanisms leading to induced END are considered.     

Rotational diffusion of TEMPONE in the cytoplasm of Chinese hamster lung cells.

The correlation time for rotational diffusion (tau R) of 2,2,6,6-tetramethyl-4-piperidone-N-oxide (TEMPONE) in Chinese hamster lung (V79) cells has been measured. For these cells in an isosmotic solution at 20 degrees C, tau R = 4.18 X 10(-11) s, approximately 3.6 times greater than tau R = 1.17 X 10(-11) s in water. The relationship between tau R and viscosity was investigated in a number of glycerol-water (0-50%) and sucrose-water (20-40%) solutions and a constant Stokes-Einstein volume of 44 A3 was found for TEMPONE in solutions of less than 20% glycerol and sucrose. This gives an average shear viscosity (for rotation of a small molecule) of 0.038 poise for the cytoplasm. When nonsecular terms were used in the calculation of tau R, the activation energies for rotation of TEMPONE in the above solutions correlated well with the activation energies for shear viscosity. The viscosity increases as the cell is shrunk in hypertonic solutions. It also increases with decreasing temperature with an activation energy of 3.7 kcal/mol, about the same as the activation energy for the viscosity of pure water. The rotational correlation times were carefully calculated considering inhomogeneous line broadening, non-Lorentzian line shapes, the need for accurate tensor values and nonsecular terms.     

Van Gieson's picrofuchsin. The staining mechanisms for collagen and cytoplasm,and an examination of the dye diffusion rate model of differential staining

The staining mechanism of van Gieson's picrofuchsin was studied by use of simple protein model systems and tissue sections, and by spectrophotometry and dialysis experiments. At the endpoint of the staining reaction (equilibrium) cytoplasm is yellow. Dye dilution experiments demonstrated that the highest affinity in the tissue section — picrofuchsin system is between binding sites in cytoplasmic protein and acid fuchsin. Nevertheless sections that were first stained in acid fuchsin (AcF) and then in picrofuchsin ended up with cytoplasm stained yellow. It was concluded that differences in the dye diffusion rates and differences in the permeability of tissue components cannot be invoked to explain the differential staining result. Model experiments with dissolved proteins demonstrated a positive relationship between protein concentration and uptake of picric acid (PA) from picrofuchsin. From this and experiments with additives (sodium dodecylsulphate, urea etc.) and organic solvents, it is proposed that coagulant interchain cross-linking at the high protein concentration of the cytoplasm masks potential dye-binding sites. This affects high affinity dyes with multiple binding sites more than small dyes, and so puts AcF at a disadvantage compared to PA. Staining of non-collagen proteins is mainly by hydrophobic bonding, involving ionic attractions, apolar bonds, and release of water. This mode of binding is relatively strong, decreases swelling and leads to slow dye exchange. Dye binding to collagen is mostly by hydrogen bonds, but in aqueous dye solvent nonpolar residues and charged residues may also participate. This structure remains relatively open during and after dye-binding, and the bound dye ions are therefore easily exchanged for other dye ions. Address at which the main part of the investigation was carried out     

p-NN''-phenylenebismaleimide, a specific cross-linking agent for F-actin.

Covalent cross-links can be inserted between the subunits of F-actin by using p-NN'-phenylenebismaleimide. Cross-linking reaches its maximum value when one molecule of reagent has reacted with each actin subunit. p-NN'-Phenylenebismaleimide reacts initially with a cysteine residue on one subunit, the slower cross-linking reaction involving a lysine residue on a neighbouring subunit. Hydrolysis of the actin-bound reagent limits the extent of cross-linking. Quantitative analysis of the amounts of cross-linked oligomers seen on polyacrylamide gels containing sodium dodecyl sulphate suggests that neither the binding of the reagent to actin nor the formation of cross-links introduces strain into the structure. The cross-links do not join together different F-actin filaments, and evidence is presented that suggests that the cross-links join subunits of the same long-pitched helix.