Formation Of Fractal Clusters Research Articles

Protein compactness and interaction valency define the architecture of a biomolecular condensate across scales.

Non-membrane-bound biomolecular condensates have been proposed to represent an important mode of subcellular organization in diverse biological settings. However, the fundamental principles governing the spatial organization and dynamics of condensates at the atomistic level remain unclear. The Saccharomyces cerevisiae Lge1 protein is required for histone H2B ubiquitination and its N-terminal intrinsically disordered fragment (Lge11-80) undergoes robust phase separation. This study connects single- and multi-chain all-atom molecular dynamics simulations of Lge11-80 with the in vitro behavior of Lge11-80 condensates. Analysis of modeled protein-protein interactions elucidates the key determinants of Lge11-80 condensate formation and links configurational entropy, valency, and compactness of proteins inside the condensates. A newly derived analytical formalism, related to colloid fractal cluster formation, describes condensate architecture across length scales as a function of protein valency and compactness. In particular, the formalism provides an atomistically resolved model of Lge11-80 condensates on the scale of hundreds of nanometers starting from individual protein conformers captured in simulations. The simulation-derived fractal dimensions of condensates of Lge11-80 and its mutants agree with their in vitro morphologies. The presented framework enables a multiscale description of biomolecular condensates and embeds their study in a wider context of colloid self-organization.

Modification of the RLA model for presenting a cluster system of a composite material with a fractal filler structure

The paper proposes a modification of the diffusion-limited aggregation model to study the properties of a cluster system. A computational experiment to determine the mutual influence of the sticking probability and the volume concentration of particles on the formation of fractal clusters in a cluster system was carried out in accordance with the second-order orthogonal central compositional plan (OCCP). As a result of a computational experiment in accordance with the OCCP, an equation was obtained for the dependence of the mass fractal dimension of clusters on the volume of particle concentration and the probability of adhesion of diffusing particles and cluster particles in the adhesion zone. This dependence was obtained in a range of volume concentration of particles from 2 to 5 % and the probability of adhesion of diffusing particles and particles of clusters in the adhesion zone from 0.2 to 1.

Modeling the process of formation of fractal structures in thin films

This paper presents the results of modeling the features of the formation of fractal structures in thin films of tin dioxide SnO2 obtained by the sol-gel method. The process of hydrolysis of tin tetrachloride SnCl4 leads to the formation of tin acid Sn(OH)4, which has a gel-like structure. Unstable tin acid decomposes to form water and tin dioxide. The formation of cluster structures is considered depending on the “competition” of these two processes. The nonlinear evolution of sol-gel stochastic processes leads to a fractal structure of the film clusters. The peculiarities of the formation of fractal clusters and the morphology of a thin film are estimated depending on the control (technological) parameters.

Ultrasonication Study for Suspending Single-Walled Carbon Nanotubes in Water

A systematic calorimetry-based technique was developed to standardize single-walled carbon nanotube (SWNT) dispersion protocol. Simple calorimetric experiments were performed to benchmark the performance of the ultra-dismembrator. Temperature profiles for the sonication period were utilized to estimate energy input to the system. Energy loss profile was generated for the ultradismembrator in use and a calibration relationship was formulated that could standardize the sonication process. The standardized protocol was used to prepare aqueous SWNT suspensions-sonicating SWNTs in a varied range of input energy (18-100 kJ) in water. SWNT mass fractions suspended for each energy input was accurately measured and the suspended SWNT samples were characterized for morphology, surface potential, cluster size and structure, and chemical functionality using high resolution transmission electron microscopy (HRTEM), electrophoresis, dynamic and static light scattering (DLS/SLS), and Raman spectroscopy. The study demonstrated that suspended mass of SWNTs increased up to 18 kJ of energy input with no further increase upon continued energy input. The physicochemical properties showed similar trend for energy input. The aggregate cluster size, surface potential behavior, as well as the Raman defect properties plateaued after the initial energy input. The significant changes observed were limited to morphological properties, i.e., shorter length, debundled, and sharp edged SWNTs and fractal cluster formation (lower D(f)) with increased input energy.

An event-driven algorithm for fractal cluster formation

A new cluster based event-driven algorithm is developed to simulate the formation of clusters in a two-dimensional gas: particles move freely until they collide and “stick” together irreversibly. These clusters aggregate into bigger structures in an isotropic (random) way, forming fractal structures whose fractal dimension depends on the initial density of the system.

Application of Asymmetric Flow-Field Flow Fractionation to the Characterization of Colloidal Dispersions Undergoing Aggregation

The characterization of complex colloidal dispersions is a relevant and challenging problem in colloidal science. In this work, we show how asymmetric flow-field flow fractionation (AF4) coupled to static light scattering can be used for this purpose. As an example of complex colloidal dispersions, we have chosen two systems undergoing aggregation. The first one is a conventional polystyrene latex undergoing reaction-limited aggregation, which leads to the formation of fractal clusters with well-known structure. The second one is a dispersion of elastomeric colloidal particles made of a polymer with a low glass transition temperature, which undergoes coalescence upon aggregation. Samples are withdrawn during aggregation at fixed times, fractionated with AF4 using a two-angle static light scattering unit as a detector. We have shown that from the analysis of the ratio between the intensities of the scattered light at the two angles the cluster size distribution can be recovered, without any need for calibration based on standard elution times, provided that the geometry and scattering properties of particles and clusters are known. The nonfractionated samples have been characterized also by conventional static and dynamic light scattering to determine their average radius of gyration and hydrodynamic radius. The size distribution of coalescing particles has been investigated also through image analysis of cryo-scanning electron microscopy (SEM) pictures. The average radius of gyration and the average hydrodynamic radius of the nonfractionated samples have been calculated and successfully compared to the values obtained from the size distributions measured by AF4. In addition, the data obtained are also in good agreement with calculations made with population balance equations.

Some topics in the kinetics of protein aggregation

Preliminary results are presented for the kinetics of phase separation in three distinct models of protein aggregation. The first is a model of the formation of spherical microcrystals of insulin via an initial formation of fractal clusters of insulin. The results of our Brownian dynamics study of this model are in qualitative agreement with a recent experimental study [1] of microcrystal formation from aqueous mixtures of insulin. A second work involves a theory for the formation of metastable bundles of sickle hemoglobin from fibers, based on a recent generic theory of bundle formation [2]. We also discuss a model for the microscopic formation of these fibers. Finally, we discuss preliminary results for the kinetics of cluster formation for a six patch model of protein crystallization.

The replacement reaction controlling the fractal assembly of copper nanoparticles

In this paper we describe a fractal assembly of copper nanoparticles on different substratesby controlling the chemical replacement reaction. Through calculation, we found that the‘fractal dimensions’ of copper dendrites synthesized by us were about 1.832, which agreedwell with the ‘fractal dimensions’ of natural fern leaves (fractal dimension, 1.826),suggesting that the fern fractal model was useful to describe the self-assembly of our coppernanoparticles during the chemical replacement reaction process. These results will bebeneficial for the understanding of the role that highly nonequilibrium conditions play inthe formation of fractal clusters as well as the self-assembly mystique of metallicnanoparticles in nonequilibrium conditions and also helpful in the future assembly ofcomplicated nanoarchitectures of metallic nanoparticles for potential applications.

Phase transitions in fractal clusters in the presence of electric fields

It is shown that if the size distribution of the nuclei formed during phase transition is a fractal cluster, then the spatial distribution of the electric field in the cluster is highly inhomogeneous. Electric field is accumulated in small scales, and its strength grows according to the power law from larger scales to smaller scales. When the dielectric permeability of the nuclei is much larger than that of the surrounding medium, the electric field grows as $E\ensuremath{\propto}{3}^{k},$ where k is a number of the nucleus in the fractal cluster with the sizes ${a}_{1}\ensuremath{\gg}{a}_{2}\ensuremath{\gg}{a}_{3}\ensuremath{\gg}\ensuremath{\cdots}\ensuremath{\gg}{a}_{k}.$ We determined the work of formation of the nuclei in the fractal cluster taking into account the change of the configuration of electric field E. It is demonstrated that the formation of fractal clusters leads to the dynamics of a phase transition with bifurcations, whereby the growth of a nucleus causes the formation of the new nuclei.

Enhanced backscattering of light by aggregation of particles in an absorbing and dense colloidal suspension

The angular intensity profile of the enhanced backscattering of light (EBL) is investigated experimentally with regard to the spatial distribution of particles suspended in a disordered, dense and absorbing medium. Particle aggregation is induced by adding NaCl solution to a colloidal suspension of polystyrene latex particles. We show experimentally that a decay slope of the peak intensity profile decreases suddenly at a certain concentration of NaCl due to the formation of fractal clusters. Such behaviour is shown to be independent of absorption. The dimension of the medium defined as a measure of the particle distribution is estimated by applying the EBL decay slope to the empirical formulae obtained in the previous study by Ishii et al (Ishii?K, Iwai?T and Asakura?T 1997 Opt. Rev. 4 643). As a result, we confirm that the EBL is applicable to the in situ monitoring of the aggregation process of particles without dilution of the suspension or degradation of accuracy by changes in absorption.

Anomalous infra-red absorption of nanocermets in the percolation range

We present a two-dimensional simulation of the optical absorption of gold granular films, using a real space renormalization procedure. This numerical effective-medium theory takes into account the actual morphology of the films. Results are compared both with experimental measurements and with other theoretical predictions asserting that the optical properties around the percolation threshold cannot be described by an effective dielectric function. Nevertheless, we obtain a good agreement between simulations and experimental data, whatever the morphology and the concentration. It is concluded on both theoretical and experimental arguments that the IR absorption can be attributed to classical surface plasmon modes, generally situated in the visible spectral range for spheroidal inclusions, broadened here towards higher wavelengths due to the formation of fractal clusters of various sizes and shapes.

Fractal clusters and self-propagating high-temperature synthesis in thin Al/Ge films

Fractal clusters in amorphous thin films are examples of growth models. The main models are the Witten-Sander model and its modifications. It is believed that fractal patterns are formed in the course of the crystallization of an amorphous phase. It is shown that self-propagating high-temperature synthesis can be initiated in an Al/Ge film system and fractal patterns are formed in the reaction products. It is conjectured that the transition of an amorphous phase to a crystalline phase does not play a substantial role in the appearance of such patterns, while the formation of fractal clusters is determined by self-propagating high-temperature synthesis.

Infrared Absorption of Nanocermets Close to the Percolation Threshold

We present a two dimensional simulation of the optical absorption of gold granular films, using a real space renormalization procedure. This numerical effective medium theory takes into account the actual morphology of the films. The results are compared both with experimental measurements and with other theoretical predictions asserting that the optical properties around the percolation threshold cannot be described by an effective dielectric function. Nevertheless, we obtain good agreement between the simulations and the experimental data, whatever the morphology and the concentration. It is concluded that the IR absorption can be attributed to the classical surface plasmon modes, generally situated in the visible spectral range for spheroidal inclusions, broadened here towards higher wavelengths due to the formation of fractal clusters of various sizes.

Formation of Fractal Clusters of Colloidal Copper Hydrous Oxides

AbstractThe fractal dimensions of colloidal particles of copper hydrous oxides in the presence of natural occurring anionic exopolymers are reported from measurements using both small‐angle X‐ray‐ and static light scattering techniques. The power law decay of the structure factor [S(k) ∼ k −D] of colloidal copper hydrous oxides dispersions can be explained in terms of fractal geometry. D is found to be 2.15 ± 0.05 for Cu(OH)2, and for colloidal Cu2O·x H2O aggregates a value of 1.75 ± 0.07 was determined.

Molecular interactions in crystallizing lysozyme solutions studied by photon correlation spectroscopy

The concentration dependence of the diffusion coefficient of particles suspended in solution depends primarily on the occupied volume fraction and on repulsive and attractive forces. This dependency is expressed by the interaction parameter that can be assessed experimentally by light scattering measurements. In the present work we have determined the interaction parameter for the diffusion coefficient of hen egg white lysozyme under nonstationary crystallization conditions. The hydrated lysozyme monomer has a free-particle diffusion coefficient D 0 = 102 ± 4 μm 2 s -1 that corresponds to a hydrodynamic radius a = 2.09 nm. It also bears a net charge of +6.4 and has a Hamaker constant, A H = 7.7 k B T, for the crystallization conditions employed. At an intermediate degree of screening, Van der Waals forces become dominant, and the behavior of λ can be correlated with the onset of fractal cluster formation. The latter is employed as a useful index for predicting the fate of the lysozyme solution under examination.

Dielectric Study of Fractal Clusters Formed by Aqueous Nanodroplets in Apolar Media

AbstractDielectric investigations of fractal cluster formation near the percolation threshold were carried out on water‐in‐oil microemulsions consisting of water, Aerosol OT, and isooctane. Temperature‐dependent dielectric relaxation measurements in the frequency range 100 kHz to 1 GHz reveal the formation of fractal clusters as the percolation threshold is approached. The degree of ramification of the fractal clusters is phenomenologically characterized by a swelling factor. A repeated application of Bruggeman's unsymmetrical effective‐medium theory yields an internally consistent first‐order approximation which describes satisfactorily the characteristic features of the experimental results.

Formation of Fractal Clusters and Networks by Irreversible Diffusion-Limited Aggregation

A model for diffusion-controlled aggregation in which growing clusters as well as individual particles are mobile has been investigated. Two versions of the model in which the cluster diffusion coefficient is either size independent or inversely proportional to number of particles (mass) give very similar results. In the limit of low concentration and large system size both models lead to structures with a fractal (Hausdorff) dimensionality of about 1.45-1.5 in two-dimensional lattice-based simulations.