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.     

Computer simulation of surface-induced aggregation of ferritin.

Models are presented describing the transient mass-transport limited adsorption and cluster growth of ferritin at a solid surface. Computer simulations are carried out on a hexagonal lattice using a computer model that can be characterized as a two-dimensional stochastic cellular automaton allowing different rules regarding association, lateral interaction and dissociation to be incorporated in the model. The fractal dimensions of individual clusters were extracted from simulated aggregates and for similar rules found to be consistent with literature values on reversible diffusion-limited aggregation in two dimensions. The distribution of clusters versus free surface were shown to be affected by neighbor-dependent association probability. Low fractal dimension clusters were generated by a combination of strong lateral cohesion and neighbor-dependent dissociation to the bulk. By comparing computer simulated aggregation to experimental electron micrographs of adsorbed ferritin layers it is suggested that neighbor-dependent association, neighbor-dependent dissociation and lateral interactions are important factors in the complex dynamics of adsorbed protein layers.     

Diversity of the growth patterns of Bacillus subtilis colonies on agar plates

Abstract A Bacillus subtilis strain showed a variety of colony growth patterns on agar plates. The bacterium grew to a fractal colony through the diffusion-limited aggregation process, a round colony reminiscent of the Eden model, a colony with a straight and densely branched structure similar to the dence branching, morphology, a colony spreading without any openings, and a colony with concentric rings, on plates with various agar and nutrient concentrations. The microstructures of these colonies were also characteristic and dynamic. The patterns of these bacterial colonies were thought to grow in relation to the diffusion of nutrient in the agar plate.     

Glucose induced fractal colony pattern of Bacillus thuringiensis

Growing colonies of bacteria on the surface of thin agar plates exhibit fractal patterns as a result of nonlinear response to environmental conditions, such as nutrients, solidity of the agar medium and temperature. Here, we examine the effect of glucose on pattern formation by growing colonies of Bacillus thuringiensis isolate KPWP1. We also present the theoretical modeling of the colony growth of KPWP1 and the associated spatio-temporal patterns. Our experimental results are in excellent agreement with simulations based on a reaction-diffusion model that describes diffusion-limited aggregation and branching, in which individual cells move actively in the periphery, but become immotile in the inner regions of the growing colony. We obtain the Hausdorff fractal dimension of the colony patterns: D_H.Expt=1.1969 and D_{H, R.D.=}1.1965, for experiment and reaction-diffusion model, respectively. Results of our experiments and modeling clearly show how glucose at higher concentration can prove to be inhibitory for motility of growing colonies of B. thuringiensis cells on semisolid support and be responsible for changes in the growth pattern.     

Mechanochemical manipulation of hepatocyte aggregation can selectively induce or repress liver-specific function

Controlled activation of hepatocyte aggregation is critical to three-dimensional (3D) multicellular morphogenesis during native regeneration of liver as well as tissue reconstruction therapies. In this work, we quantify the stimulatory effects of two model hepatotrophic activators, epidermal growth factor (EGF) and hepatocyte growth factor (HGF), on the aggregation kinetics and liver-specific function of hepatocytes cultured on organotypic substrates with differing mechanical resistivity. Substrate-specific morphogenesis of cultured hepatocytes is induced on a tissue basement membrane extract, Matrigel, formulated at two distinct levels of mechanical compliance (storage modulus G', at oscillatory shear rate 1 rad/s, was 34 Pa for basal Matrigel and 118 Pa for crosslinked Matrigel). Overall, we report that growth factor stimulation selectively promotes the kinetics of aggregation in the form of two-dimensional corded aggregates on basal Matrigel and three-dimensional spheroidal aggregates on crosslinked Matrigel. Our analysis also indicates that costimulation with EGF and HGF (20 ng/mL each) cooperatively maximizes the kinetics of aggregation in a substrate-specific manner. In addition, we show that the role of growth factor stimulation on hepatocyte function is sensitively governed by the mechanical compliance of the substrate. In particular, on matrices with high compliance, costimulatory aggregation is shown to elicit a marked increase in albumin secretion rate, whereas on matrices with low compliance aggregation results in effective functional repression to basal, unstimulated levels. Thus, our studies highlight a novel interplay of physicochemical parameters of the culture microenvironment, leading to selective enhancement or repression of differentiated functions of hepatocytes, in concert with the activation of cellular morphogenesis.     

Aggregation kinetics of extended porphyrin and cyanine dye assemblies

The kinetics of J-aggregate formation has been studied for two chromophores, tetrakis-4-sulfonatophenylporphine in an acid medium and pseudoisocyanine on a polyvinylsulfonate template. The assembly processes differ both in their sensitivity to initiation protocols and in the reaction profiles they produce. The porphyrin's assembly kinetics, for example, displays an induction period unlike that of the cyanine dye. Two kinetic models are presented. For the porphyrin, an autocatalytic pathway in which the formation of an aggregation nucleus is rate-determining appears to be applicable; for the pseudoisocyanine dye, an equation derived for diffusion-limited aggregation of a fractal object satisfactorily fits the data. These models are shown to be useful for the analysis of kinetic data obtained for several biologically important aggregation processes.     

Kinetics of cold-set diffusion-limited aggregations of denatured whey protein isolate colloids

The CaCl2-induced cold-set aggregation kinetics of the denatured whey protein isolate (WPI) colloids has been investigated under dilute diffusion-limited cluster aggregation (DLCA) conditions, using small-angle light scattering. In particular, the structure factor, the scattered intensity at zero angle and the average radius of gyration have been measured for the aggregating system as a function of time. It is found that the fractal dimension of the clusters is df= 1.85, in the range typical of clusters aggregated under DLCA conditions. The aggregation kinetics in this transition region can be described by a power law relation in the initial stage of the aggregation, but the exponent of the power law is equal to 0.7, i.e., significantly larger than 1/df= 0.54, which is the typical value of the DLCA kinetics. Since it is found that the average gyration radius of the clusters has reached a value of 80 microm, leading to a cumulative volume fraction of clusters equal to 0.25, it is legitimate to expect that the process is in the region of transition from aggregation to gelation. This confirmed by the fact that, at the later stage of the aggregation, the growth of the average cluster size further accelerates with time and eventually becomes explosive, leading to gelation. The observed aggregation kinetics has been compared with that reported in the literature from DLCA Monte Carlo simulations, and a good agreement has been found with the data corresponding to the transition region from aggregation to gelation. Numerical simulations using the Smoluchowski kinetic model have also been carried out in order to support the experimental findings.     

Self-assembly of conjugated polymers and ds-oligonucleotides directed fractal-like aggregates

Highly ordered nanostructures between conjugated polymers and ds-oligonucleotides have been first fabricated by simply controlling the self-assembly processes, which shows a novel concept for fabricating fractal-like structures. The formation of polymer/DNA fractal-like aggregates is a diffusion-limited aggregation (DLA) process. The fractal dimension is independent of the polymer/DNA concentration but only related to the polymer/DNA charge ratio. More interestingly, the different fluorescent resonance energy transfer (FRET) behavior between the polymer and the DNA can be used to distinguish dsDNA from ssDNA.     

Arginine controls heat-induced cluster-cluster aggregation of lysozyme at around the isoelectric point

The process of protein aggregation has attracted a great deal of research attention, as aggregates are first of all a nuisance to preparation of high quality protein and secondly used as novel materials. In the latter case, the process of protein aggregation needs to be controlled. Here, we show how arginine (Arg) regulates the process of heat-induced protein aggregation. Dynamic light scattering and transmission electron microscopy revealed that heat-induced aggregation of lysozyme at around the isoelectric point occurred in a two-step process: formation of start aggregates, followed by further growth mediated by their sticking with diffusion-limited cluster-cluster aggregation. In the presence of Arg, the diffusion-limited regime changed to reaction-limited cluster-cluster aggregation. The data indicated that the solution additives that coexisted with proteins would affect the property of the formed product, such as morphology and mechanic strength.     

Microbial growth patterns described by fractal geometry.

Fractal geometry has made important contributions to understanding the growth of inorganic systems in such processes as aggregation, cluster formation, and dendritic growth. In biology, fractal geometry was previously applied to describe, for instance, the branching system in the lung airways and the backbone structure of proteins as well as their surface irregularity. This investigation applies the fractal concept to the growth patterns of two microbial species, Streptomyces griseus and Ashbya gossypii. It is a first example showing fractal aggregates in biological systems, with a cell as the smallest aggregating unit and the colony as an aggregate. We find that the global structure of sufficiently branched mycelia can be described by a fractal dimension, D, which increases during growth up to 1.5. D is therefore a new growth parameter. Two different box-counting methods (one applied to the whole mass of the mycelium and the other applied to the surface of the system) enable us to evaluate fractal dimensions for the aggregates in this analysis in the region of D = 1.3 to 2. Comparison of both box-counting methods shows that the mycelial structure changes during growth from a mass fractal to a surface fractal.     

Effect of salt addition on the fractal structure of aggregates formed by heating dilute BSA solutions

The fractal dimension, Df, of aggregates in a dilute BSA system with added salt was evaluated by static light scattering (SLS). A fractal structure was observed for the system with NaCl addition. The values of Df increased with increasing heating time and ionic strength. The values of Df were larger than those (Df = 1.8 or 2.1) predicted by the conventional cluster-cluster aggregation model, probably due to a "restructuring" of aggregates during the aggregation process. On the other hand, a fractal structure was not apparent for the system with added CaCl2.     

Protein folding stabilizing time measurement: a direct folding process and three-dimensional random walk simulation

Protein particles undergo Brownian motion and collisions in solution. The diffusive collisions may lead to aggregation. For proteins to fold successfully the process has to occur quickly and before significant collision takes place. The speed of protein folding was deduced by studying the correlation time of a lysozyme refolding process from autocorrelation function analysis of the mean collision time and aggregation/soluble ratio of protein. It is a measure of time before which an aggregate can be formed and also is the time measure for a protein to fold into a stable state. We report on the protein folding stabilizing time of a lysozyme system to be 25.5-27.5 micros (<+/-4%) between 295 and 279K via direct folding experimental studies, supported by a three-dimensional random walk simulation of diffusion-limited aggregation model. Aggregation is suppressed when the protein is folded to a stable form. Spontaneous folding and diffusion-limited aggregation are antagonistic in nature. Meanwhile, the resultant aggresome, suggested by Raman and mass spectroscopy, may be formed by cross-linkages of disulfide bonds and hydrophobic interactions.     

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.     

Aggregation of ligand-modified liposomes by specific interactions with proteins. I: Biotinylated liposomes and avidin

The aggregation of biotin-modified phospholipid vesicles (liposomes) induced by binding the protein avidin in solution is analyzed experimentally and theoretically. Avidin has four binding sites that can recognize biotin specifically, and is able to cross-link the liposomes to form large aggregates. The aggregation kinetics were followed using quasi-elastic light scattering (QLS) to measure the mean particle size, and by measuring the solution turbidity. The rate and extent of aggregation were determined as a function of vesicle concentration, protein concentration, and the biotin density on the surface of the liposomes. A model based on Smoluchowski kinetics, fractal concepts, and Rayleigh and Mie light scattering theory was developed to analyze the experimental observations. Small aggregates (<7800 A diameter) may be treated as globular; however, the fractal nature of larger particles must be taken into account. Parameters in the model are taken from molecular simulations, or fit to the experimental observations. The aggregation kinetics are primarily determined by the biotin density on the liposome surface, the stoichiometric ratio of avidin molecules to liposomes, and the liposome concentration. Good agreement is found between the model and the experimental results. (c) 1996 John Wiley & Sons, Inc.     

A New Preparation Method of Coenzyme A with Microorganisms

The structure of aggregates formed by heating dilute BSA solution was analyzed with the fractal concept using light scattering methods. BSA was dissolved in HEPES buffer of pH 7.0 and acetate buffer of pH 5.1 to 0.1% and 0.001% solutions, respectively, and heated at 95°C, varying the heating time t_a. The fractal dimension D_f of the aggregate in the solution was evaluated from static light scattering experiments. The polydispersity exponent τ and the average hydrodynamic radius <R_h> of the aggregates were calculated from dynamic light scattering experiments using master curves obtained by Klein et al. The values of D_f and τ of heat-induced aggregates of BSA at pH 7.0 were about 2.1 and 1.5, respectively, the values of which agreed with those predicted by the reaction-limited cluster–cluster aggregation (RLCCA) model. On the other hand, D_f of heat-induced aggregates at pH 5.1 was about 1.8, which agreed with that predicted by the diffusion-limited cluster–cluster aggregation (DLCCA) model. The dependence of <R_h> for the sample of pH 7.0 on t_a was similar to that of the polystyrene colloids reported previously.     

Gold nanoparticles decorated with oligo(ethylene glycol) thiols: kinetics of colloid aggregation driven by depletion forces

We have studied the kinetics of the phase-separation process of mixtures of colloid and protein in solutions by real-time UV-vis spectroscopy. Complementary small-angle X-ray scattering (SAXS) was employed to determine the structures involved. The colloids used are gold nanoparticles functionalized with protein resistant oligo(ethylene glycol) (OEG) thiol, HS(CH(2))(11)(OCH(2)CH(2))(6)OMe (EG6OMe). After mixing with protein solution above a critical concentration, c*, SAXS measurements show that a scattering maximum appears after a short induction time at q = 0.0322 A(-1), which increases its intensity with time but the peak position does not change with time, protein concentration and salt addition. The peak corresponds to the distance of the nearest neighbor in the aggregates. The upturn of scattering intensities in the low q-range developed with time indicating the formation of aggregates. No Bragg peaks corresponding to the formation of colloidal crystallites could be observed before the clusters dropped out from the solution. The growth kinetics of aggregates is followed in detail by real-time UV-vis spectroscopy, using the flocculation parameter defined as the integral of the absorption in the range of 600-800 nm wavelengths. At low salt addition (<0.5 M), a kinetic crossover from reaction-limited cluster aggregation (RLCA) to diffusion-limited cluster aggregation (DLCA) growth model is observed, and interpreted as being due to the effective repulsive interaction barrier between colloids within the depletion potential. Above 0.5 M NaCl, the surface charge of proteins is screened significantly, and the repulsive potential barrier disappeared, thus the growth kinetics can be described by a DLCA model only.     

Fractal Organization of Cultivated in vitro Spiculogenous Cells and Larval Spicules of the Sea Urchin Strongylocentrotus nudus

The morphological patterns of the cultivated cells of primary mesenchyme and the spicules of the larval skeleton of the sea urchin Strongylocentrotus nudus were quantified, and the value of their fractal dimensions (D) was determined with ImageJ 1.20s software. It was shown that during cytodifferentiation, the values of D in the fractal (fractional) dimension, which reflects the complex spatial organization of the spiculogenous mesenchyme elements in two-dimensional space, increase to values close to 1.7. The invertible treatment with cytochalasin, which destroys the system of the actin filaments, suppresses the normal control of biomineralization and causes a complex form of spicules, the fractal dimension of which varies within 1.5–1.6. Thus, the determination of the fractal dimension value serves as evidence of the fractional essence of the patterns studied, quantifies the spatially complex organization of cells and their assemblies during morphogenesis, and allows us to estimate the variation in the spicule morphology after cytochalasin treatment.     

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.     

Growth patterns of yeast colonies depending on nutrient supply

Common theories of microbial growth and physiology are formulated exclusively in terms of the isolated microorganisms – especially bacteria. This is, however, an inadmissible simplification because it is obvious that the organization of microbial populations and colonies follows certain general rules. Bacterial colonies are able to generate complex interfacial growth patterns similar to those observed during diffusion-limited growth processes in non-living systems. One reason for these patterns is assumed to be the ability of many bacteria to swarm in an active manner on a substrate surface. Therefore the models of bacterial colony growth incorporate “random walkers”, which move actively in response to a gradient in the concentration of nutrients and communicate with each other by means of a chemotactic feedback. A selected number of yeasts were tested with regard to their colony growth patterns depending on the medium parameters such as nutrient concentration. Growth patterns similar to those which were described in literature for bacteria were also found in these experiments. It concerns in particular growth types like compact growth, fractal growth and dense-branching growth. This result allows a hypothesis to be formulated, that – especially in the case of fractal growth patterns – wandering of cells on a substrate surface may be induced by uncontrolled “swimming” on a thin water film caused by the metabolic activity (e.g. respiration) of the cells on the surface of the agar. Furthermore it was found that an interplay between changes in the individual morphology of yeast cells and the morphology transitions takes place. Such growth patterns are known for Candida sp. which are able to form pseudomycel and blastospores.