Surface-induced aggregation of ferritin. Kinetics of adsorption to a hydrophobic surface

The adsorption of ferritin from a water solution to a hydrophobic methylised quartz surface was studied by transmission electron microscopy, allowing direct examination of the iron core of the molecule without further preparation. The initial adsorption was seen to result in small clusters of molecules, the number of sites/cm(2) being concentration dependent. The adsorption process continued via cluster growth. The rate of adsorption increased and the process became mass transport limited. The clusters formed initially had low fractal dimensions (D approximately 1.0) and a coordination number, cn of 2.6-2.8, which increased with time. These clusters were abruptly restructured at a coordination number of 3.5, and the apparent rate of adsorption decreased during the reorganisation of the adsorbed layer. Finally, an equilibrium level was reached which was stable for at least 24 h. The distribution of ferritin molecules at equilibrium was in clusters with a fractal dimension of D = 1.14 +/- 0.16 and D= 1.33 +/- 0.08, respectively, for ferritin concentrations in the bulk of 10 and 100 microg/ml. Rinsing of adsorbed ferritin layers with buffered salt solution resulted in a rapid transient condensation of the clusters, but the net dissociation of protein was slow with the rate of dissociation being proportional to the logarithm of time. The condensed clusters were slowly restructured to linear polymers of ferritin molecules with a coordination number of 1.9 after 24 h of rinsing. The dissociation of protein molecules continued slowly for more than 3 days of rinsing. The results of the present study indicate that the rate of protein adsorption and desorption is strongly related to the supramolecular structure of the adsorbed protein film. Dense clusters of protein are not stable and this phenomenon may explain the formation of a dynamic equilibrium in spite of the fact that protein adsorption to a solid phase may appear to be practically irreversible.     

Nonlinear kinetics of ferritin adsorption.

The adsorption of ferritin at a methylized quartz surface was measured with off-null ellipsometry and transmission electron microscopy. An initial lag-phase was seen, followed by an accelerating adsorption leading to mass transport limitation of the reaction. The rate of adsorption then decreased at a surface concentration far below monolayer coverage, and a continuously decreasing rate of binding was seen. The slope of the binding rate was linear with the logarithm of time (fractal kinetics). The adsorbed ferritin molecules were distributed in clusters as seen by transmission electron microscopy. Clusters grown during the mass transport limited adsorption had crystalline structure at short range and low fractal dimensions (df = 0.89) over long range. Clusters grown during adsorption with fractal kinetics showed random structure at short range and a high fractal dimension df = 1.86 over all ranges. These findings indicate some new important mechanisms responsible for the complex kinetics of macromolecular reactions at solid-liquid interfaces. The results are discussed in relation to recently developed theories of self-organized criticality.     

Surface-induced aggregation of ferritin. Concentration dependence of adsorption onto a hydrophobic surface

The isotherm of ferritin adsorption onto a hydrophobic surface was studied by transmission electron microscopy. Adsorbed ferritin was found to be distributed in molecular clusters. The adsorption process was diffusion-rate-limited after 20 h adsorption time at bulk concentrations below 1 mg/1. The clusters formed during the diffusion-rate-limited adsorption had a fractal dimension D approximately 1.0 when averaged over all clusters. The pair distribution function g(r) showed an increased probability of finding nearest neighbours at distances less than 30 nm. The surface concentration of adsorbed ferritin was weakly dependent on the bulk concentration of ferritin in the range 10 mg/1-10 g/1 and the average number of nearest neighbour molecules was constant in this concentration range. The mass distribution of adsorbed ferritin c(r) had a fractal dimension D = 1.8 at a bulk concentration of 10 g/l and a surface concentration corresponding to theta = 0.45 +/- 0.05. The pair correlation function g(r) showed decreasing probability of finding nearest neighbour molecules over long distances as in percolating clusters. The results indicate that ferritin adsorbs strongly to the surface at low surface concentrations and weakly at high surface concentrations. The stability of ferritin adsorption was correlated to the average number of nearest neighbour molecules, indicating a possibility that desorption is a critical supramolecular phenomenon.     

Self-organization of local magnetoplasma structures in the upper layers of the solar convection zone

Self-organization and evolution of magnetoplasma structures in the upper layers of the solar convection zone are discussed as a process of diffuse aggregation of magnetic flux tubes. Equations describing the tube motion under the action of magnetic interaction forces, hydrodynamic forces, and random forces are written explicitly. The process of aggregation of magnetic flux tubes into magnetic flux clusters of different shapes and dimensions is simulated numerically. The obtained structures are compared with the observed morphological types of sunspot groups. The quantitative comparison with the observational data was performed by comparing the fractal dimensions of the photospheric magnetic structures observed in solar active regions with those of structures obtained in the numerical experiment. The model has the following free parameters: the numbers of magnetic flux tubes with opposite polarities on the considered area element (Nn and Ns), the average radius of the cross section of the magnetic flux tube (a), its effective length (l), the twist factor of the tube field (k), and the absolute value of the average velocity of chaotic tube displacements (d). Variations in these parameters in physically reasonable limits leads to the formation of structures (tube clusters of different morphological types) having different fractal dimensions. Using the NOAA 10488 active region, which appeared and developed into a complicated configuration near the central meridian, as an example, it is shown that good quantitative agreement between the fractal dimensions is achieved at the following parameters of the model: Nn = Ns = 250 ± 50; a = 150 ± 50 km; l ～ 5000 km, and d = 80 ± 10 m/s. These results do not contradict the observational data and theoretical estimates obtained in the framework of the Parker “spaghetti” model and provide new information on the physical processes resulting in the origin and evolution of local magnetic plasma structures in the near-photospheric layers of the solar convection zone.     

Lateral diffusion and aggregation. A Monte Carlo study.

Aggregation in a lipid bilayer is modeled as cluster-cluster aggregation on a square lattice. In the model, clusters carry out a random walk on the lattice, with a diffusion coefficient inversely proportional to mass. On contact, they adhere with a prescribed probability, rigidly and irreversibly. Monte Carlo calculations show that, as expected, rotational diffusion of the aggregating species is highly sensitive to the initial stages of aggregation. Lateral diffusion of an inert tracer obstructed by the aggregate is a sensitive probe of the later stages of aggregation. Cluster-cluster aggregates are much more effective barriers to lateral diffusion of an inert tracer than the same area fraction of random point obstacles is, but random point obstacles are more effective barriers than the same area fraction of compact obstacles. The effectiveness of aggregates as obstacles is discussed in terms of particle-particle correlation functions and fractal dimensions. Results are applicable to aggregation of membrane proteins, and at least qualitatively to aggregation of gel-phase lipid during lateral phase separation.     

A mathematical analysis using fractals for binding interactions of nuclear estrogen receptors occurring on biosensor surfaces

A mathematical approach using fractal concepts is presented for modeling the binding and dissociation interactions between analytes and nuclear estrogen receptors (ER) occurring on surface plasmon resonance biosensor chip surfaces. A kinetic knowledge of the binding interactions mediated by ER would help in better understanding the carcinogenicity of these steroidogenic compounds and assist in modulating these reactions. The fractal approach is applied to analyte-ER interaction data obtained from literature. Numerical values obtained for the binding and dissociation rate coefficients are linked to the degree of roughness or heterogeneity (fractal dimension, D(f)) present on the biosensor surface. For example, a single-fractal analysis is used to describe the binding and dissociation phases for the binding of estradiol and ERalpha in solution to clone 31 protein immobilized on a biosensor chip (C-S. Suen et al., 1998, J. Biol. Chem. 273(42), 27645-27653). The binding and the dissociation rate coefficients are 27.57 and 8.813, respectively, and the corresponding fractal dimensions are 1.986 and 2.268, respectively. In some examples dual-fractal models were employed to obtain a better fit of either the association or the dissociation phases or for both. Predictive relationships are developed for (a) the binding and the dissociation rate coefficients as a function of their respective fractal dimensions and (b) the ratio K(A) (= k/k(d)) as a function of the ratio of the fractal dimensions (D(f)/D(fd)). The analysis should provide further physical insights into the ER-mediated interactions occurring on biosensor and other surfaces.     

Redistribution of surface anionic sites on the luminal front of blood vessel endothelium after interaction with polycationic ligand

The ability of anionic groups on the luminal surface of blood vessels to redistribute by lateral migration under the influence of multivalent ligands was analyzed by electron microscopy, using cationized ferritin (CF). In vitro interaction of blood vessel segments with CF results in rapid aggregation of most anionic sites on the luminal fromt of the endothelium, followed by internalization or detachment of the CF patches, leaving most of the luminal surface devoid of anionic sites. Further incubation of such endothelial cells without CF results in regeneration of binding capacity for the polycationic label. Transport of CF, but not of native ferritin, across the endothelium by vesicle transport, followed by exocytosis of the interiorized CF clusters on the tissue front of the endothelium, was also observed. The possibility that such activities in the blood vessels in vivo may be associated with local changes in the normal distribution of the surface anionic sites as well as in accumulation of debris in the subendothelial layers of the vessels is suggested.     

Fractal Binding and Dissociation Kinetics of Heart-Related Compounds on Biosensor Surfaces

A fractal analysis is presented for the binding and dissociation of different heart-related compounds in solution to receptors immobilized on biosensor surfaces. The data analyzed include LCAT (lecithin cholesterol acyl transferase) concentrations in solution to egg white apoA-I rHDL immobilized on a biosensor chip surface (), native, mildly oxidized, and strongly oxidized LDL in solution to a heparin-modified Au-surface of a surface plasmon resonance (SPR) biosensor (), and TRITC-labeled HDL in solution to a bare optical fiber surface (). Single-and dual-fractal models were used to fit the data. Values of the binding and the dissociation rate coefficient(s), affinity values, and the fractal dimensions were obtained from the regression analysis provided by Corel Quattro Pro 8.0 (). The binding rate coefficients are quite sensitive to the degree of heterogeneity on the sensor chip surface. Predictive equations are developed for the binding rate coefficient as a function of the degree of heterogeneity present on the sensor chip surface and on the LCAT concentration in solution and for the affinity as a function of the ratio of fractal dimensions present in the binding and the dissociation phases. The analysis presented provided physical insights into these analyte-receptor reactions occurring on different biosensor surfaces.     

Initial attachment of baby hamster kidney cells to an epoxy substratum. Ultrastructural analysis

In the presence of serum-containing medium, BHK cells attached and spread during a 1-h period onto a 3-5 nm thick serum layer absorbed on the substratum surface. The closest approach of the plasma membrane to the serum layer was observed to be about 9nm, which was determined by tilting the sectioned cells in a goniometer holder. Bundles of microfilaments or other cytoplasmic specializations were not observed in association with the regions of close contact. However, in the space between the plasma membrane and the adsorbed serum layer, a diffusely stained material could be visualized after fixation/staining by the tannic acid-glutaraldehyde technique. This technique also permitted increased clarity of visualization of trilaminar appearance of the plasma membrane. The distribution and mobility of anionic sites on the surfaces of attached and spreading cells was determined by labeling with polycationic ferritin. We observed movement of polycationic ferritin into large clusters on the cell surface, collapse of cell surface microextensions, and endocytosis, all of which were similar to our previous findings utilizing cells in suspension. However, the absolute amount of ferritin bound to the upper cell surface was less than that previously observed when suspended cells were put under similar labeling conditions. Also, polycationic ferritin did not appear to penetrate between the lower cell surface and the substratum.     

Fractal binding and dissociation kinetics of heart-related compounds on biosensor surfaces

A fractal analysis is presented for the binding and dissociation of different heart-related compounds in solution to receptors immobilized on biosensor surfaces. The data analyzed include LCAT (lecithin cholesterol acyl transferase) concentrations in solution to egg white apoA-I rHDL immobilized on a biosensor chip surface (1), native, mildly oxidized, and strongly oxidized LDL in solution to a heparin-modified Au-surface of a surface plasmon resonance (SPR) biosensor (2), and TRITC-labeled HDL in solution to a bare optical fiber surface (3). Single-and dual-fractal models were used to fit the data. Values of the binding and the dissociation rate coefficient(s), affinity values, and the fractal dimensions were obtained from the regression analysis provided by Corel Quattro Pro 8.0 (4). The binding rate coefficients are quite sensitive to the degree of heterogeneity on the sensor chip surface. Predictive equations are developed for the binding rate coefficient as a function of the degree of heterogeneity present on the sensor chip surface and on the LCAT concentration in solution and for the affinity as a function of the ratio of fractal dimensions present in the binding and the dissociation phases. The analysis presented provided physical insights into these analyte-receptor reactions occurring on different biosensor surfaces.     

The Folch-Lees proteolipid induces phase coexistence and transverse reorganization of lateral domains in myelin monolayers

Solvent solubilized myelin membranes spread as monomolecular layers at the air-water interface show a heterogeneous pattern at all surface pressures. In order to asses the role of myelin protein and lipid components in the surface structuring we compared the topography, as seen by Brewster angle microscopy (BAM) and epifluorescence microscopy, of monolayers made from mixtures containing all myelin lipids (except gangliosides) and variable proportions of Folch-Lees proteolipid protein (PLP, the major protein component of myelin). The presence of the single PLP, in the absence of the other myelin proteins, can reproduce the surface pattern of the whole myelin extract films in a concentration-dependant manner. Moreover, a threshold mole fraction of PLP is necessary to induce the lipid-protein component reorganization leading to the appearance of a rigid (gray) phase, acting as a surface skeleton, at low surface pressures and of fractal clusters at high surface pressures. The average size of those clusters is also dependent on the PLP content in the monolayer and on the time elapsed from the moment of film spreading, as they apparently result from an irreversible lateral aggregation process. The transverse rearrangement of the monolayer occurring under compression was different in films with the highest and lowest PLP mole fractions tested.     

The Folch-Lees proteolipid induces phase coexistence and transverse reorganization of lateral domains in myelin monolayers

Solvent solubilized myelin membranes spread as monomolecular layers at the air-water interface show a heterogeneous pattern at all surface pressures. In order to asses the role of myelin protein and lipid components in the surface structuring we compared the topography, as seen by Brewster angle microscopy (BAM) and epifluorescence microscopy, of monolayers made from mixtures containing all myelin lipids (except gangliosides) and variable proportions of Folch-Lees proteolipid protein (PLP, the major protein component of myelin). The presence of the single PLP, in the absence of the other myelin proteins, can reproduce the surface pattern of the whole myelin extract films in a concentration-dependant manner. Moreover, a threshold mole fraction of PLP is necessary to induce the lipid-protein component reorganization leading to the appearance of a rigid (gray) phase, acting as a surface skeleton, at low surface pressures and of fractal clusters at high surface pressures. The average size of those clusters is also dependent on the PLP content in the monolayer and on the time elapsed from the moment of film spreading, as they apparently result from an irreversible lateral aggregation process. The transverse rearrangement of the monolayer occurring under compression was different in films with the highest and lowest PLP mole fractions tested.     

Self-similar colony morphogenesis by gram-negative rods as the experimental model of fractal growth by a cell population.

The ability to form a fractal colony was shown to be common among several species of the family Enterobacteriaceae. Bacterial spreading growth in a two-dimensional field of nutrient concentration was indicated to be important for this experimental self-similar morphogenesis. As a basic analogy, the diffusion-limited aggregation model was suggested. Fractal dimensions of colonies were mostly in the range of values from 1.7 to 1.8, similar to those of the two-dimensional diffusion-limited aggregation model. Bacterial characteristics and culture conditions inducing changes in fractal patterns and growth rates were identified. The contribution of the bacterial multicellular nature to fractal morphogenesis is discussed.     

Self-similar colony morphogenesis by gram-negative rods as the experimental model of fractal growth by a cell population.

The ability to form a fractal colony was shown to be common among several species of the family Enterobacteriaceae. Bacterial spreading growth in a two-dimensional field of nutrient concentration was indicated to be important for this experimental self-similar morphogenesis. As a basic analogy, the diffusion-limited aggregation model was suggested. Fractal dimensions of colonies were mostly in the range of values from 1.7 to 1.8, similar to those of the two-dimensional diffusion-limited aggregation model. Bacterial characteristics and culture conditions inducing changes in fractal patterns and growth rates were identified. The contribution of the bacterial multicellular nature to fractal morphogenesis is discussed.     

Modelling Viscous Fingering on a Parallel Computer

Diffusion limited aggregation (DLA) has proved very successful in modelling systems which display fractal characteristics, like viscous fingering. However, by nature, such simulations are very processor intensive, requiring large amounts of processor time even for relatively small models. We have performed simulations of viscous fingering on the NCUBE parallel computer which has hypercube architecture. We find that, as long as the number of processors used is much less than both the total number of walkers released and the overall dimensions of the model, the fractal dimensions obtained using serial and parallel algorithms give similar results whilst achieving a considerable speed-up in the parallel implementation. An average fractal dimension of 1.71 was obtained along with a speed-up of 106 (in the best case) and 83% efficiency using 128 processors.     

Resolution of diaminobenzidine for the detection of horseradish peroxidase on surfaces of cultured cells

The resolution of indirect immunoperoxidase methods for localizing antigens on the surface of plasma membranes of cultured cells was tested using dissociated monolayer cultures of ciliary ganglion neurons prelabeled with cationic ferritin. Clusters of ferritin were produced on the cell surface by warming the cells to 37 degrees C after the ferritin, rabbit anti-ferritin, and goat anti-rabbit immunoglobulin coupled to horseradish peroxidase had all been applied. Intense 3,3'-diaminobenzidine tetrahydrochloride (DAB) staining was limited to the regions immediately surrounding the ferritin clusters. The lateral spread of the DAB reaction product beyond the outer ferritin particles in each cluster averaged 54-81 nm in four experiments. A second type of increased density, coinciding with the thickness of the plasma membrane, was also seen. These stained plasma membranes extended 161-339 nm from the ferritin clusters.     

Heat aggregation studies of phycobilisomes, ferritin, insulin, and immunoglobulin by dynamic light scattering.

Dynamic laser light scattering studies on the heat aggregation behavior of phycobilisomes (PBS), ferritin, insulin, and immunoglobulin (IgG) in dilute aqueous solutions has been reported. Except for PBS, results are reported for heat aggregation trends in these proteins for three different pH environments (4.0, 7.5, 9.1). For PBS, studies were performed only in the neutral buffer medium (pH 7.5). The experiments were performed in the very dilute concentration regime (between 0.23 and 1.8 gL-1). For all these samples heat aggregation and dissociation trends were found to be linear with temperature. Upon temperature reversal (self-cooling), hysteresis-like behavior observed in insulin was found to be predominantly large at pH 7.5. PBS, ferritin, and IgG showed no such behavior at any of three pH values, and retraced their path of aggregation while dissociating on temperature reversal. Heat aggregation and dissociation processes in ferritin were found to be independent of pH. The IgG samples showed smooth aggregation tendency only up to 35 degrees C in the buffer media pH 4.0 and 9.1, whereas for pH 7.0 the same could be observed until 60 degrees C. Low polydispersity in the correlation spectra was observed in case of all these samples.     

Exploring landscape structure effect on termite territory size using a model approach

The foraging territory of the Formosan subterranean termite, Coptotermes formosanus Shiraki, was simulated by using a lattice model in order to study how landscape structure affects the foraging territory. Three kinds of landscape were generated on lattice space: ideal, random and fractal landscape. Each lattice cell had a value ranging from 0.0 to 1.0, interpreted as transition probability, P_trans, which represents spatially distributed property of the landscapes. The heterogeneity of the fractal landscape was characterized by a parameter, H, controlling aggregation of lattice cells with higher value of P_trans. Higher H values corresponded to higher aggregation levels. The model made use of minimized local rules based on empirical data that determines the development of the foraging territory. Additionally, seasonal cycle (summer and winter season), and obstacles which hinder the growth of the territory were incorporated in the model as environmental variables. Territory size was largest in the ideal landscape while it was larger in the random landscape than in the fractal landscape. As obstacle density increased, the territory size decreased. In the fractal landscape, the territory size increased, decreased, and increased again as H increased.     

Topology of asialoglycoprotein receptor in rat liver subcellular fractions: a ferritin immunoelectron microscopic study

Direct ferritin immunoelectron microscopy was used to visualize the asialoglycoprotein receptor in various rat liver subcellular fractions. The cytoplasmic surfaces of cytoplasmic organelles such as the rough and smooth microsomes, Golgi cisternae and lysosomes showed hardly any ferritin label exception for the slight labeling of secretory granules found mainly in the light Golgi fraction (GF1). Occasionally, however, open membrane sheet structures, smooth vesicular or tubular structures heavily labeled with ferritin, were present in all these subcellular fractions. These structures probably correspond to fragmented sinusoidal or lateral hepatocyte plasma membranes recovered to these subcellular fractions. When the limiting membranes of the secretion granules were partially broken by mechanical force, a number of ferritin particles frequently were seen attached in large clusters to the luminal surface of the membrane, the cytoplasmic surface of the corresponding domain being slightly labeled. These observations are strong evidence that the receptor protein is never translocated vertically throughout the intracellular transport from ER to plasma membrane via Golgi apparatus and from plasma membrane back to trans-Golgi elements and also in lysosomes, always exposing the major antigenic sites to the luminal or extracellular surface and the minor counterparts to the cytoplasmic surface of the membranes. The receptor protein also is suggested to be concentrated in clusters on the luminal surface of secretion granules when they form on the trans-side of the Golgi apparatus.     

Analyte-receptor binding on surface plasmon resonance biosensors: a fractal analysis of Cre-loxP interactions and the influence of Cl, O, and S on drug-liposome interactions

A fractal analysis of the association and dissociation (whereever applicable) of Cre-loxP interactions and drug-liposome interactions on a sensor chip surface is presented. In both of these cases a dual-fractal analysis is required to adequately describe the association kinetics. The dissociation kinetics for Cre-loxP interactions is adequately described by a single-fractal analysis. The dual-fractal analysis used to describe the association kinetics of Cre-loxP interactions is consistent with the original two-step mechanism presented using a surface plasmon resonance biosensor. Our analysis includes both diffusion and surface effects by introducing the fractal dimension which makes quantitative the degree of heterogeneity on the sensor chip surface. Affinities are provided. Only the association kinetics were analysed for drug-liposome interactions since the initial sections of the dissociation curves were too steep to obtain reasonable drug-liposome complex concentration values on the sensor chip with time. Attempts made to relate the association rate coefficients with the molecular weight of the drug were unsuccessful. On using desipramine and imipramine as "arbitrarily selected standards" or "references" (only C, H, and N atoms present), it was noticed from the data analysed that the inclusion of the O and S atoms in the drug leads to a decrease in the association rate coefficients, ka1 (or k1) and ka2 (or k2) (compared with the arbitrarily selected standards or references). Similarly, the addition of the Cl atom in the drug leads to an increase in the association rate coefficient (compared with the arbitrarily selected standards or references). More data needs to be analysed to determine whether this is true for other drugs also.