A universal dimensionality function for the fractal dimensions of Laplacian growth

Network efficiency of spatial systems with fractal morphology: a geometric graphs approach

The functional features of spatial networks depend upon a non-trivial relationship between the topological and physical structure. Here, we explore that relationship for spatial networks with radial symmetry and disordered fractal morphology. Under a geometric graphs approach, we quantify the effectiveness of the exchange of information in the system from center to perimeter and over the entire network structure. We mainly consider two paradigmatic models of disordered fractal formation, the Ballistic Aggregation and Diffusion-Limited Aggregation models, and complementary, the Viscek and Hexaflake fractals, and Kagome and Hexagonal lattices. First, we show that complex tree morphologies provide important advantages over regular configurations, such as an invariant structural cost for different fractal dimensions. Furthermore, although these systems are known to be scale-free in space, they have bounded degree distributions for different values of an euclidean connectivity parameter and, therefore, do not represent ordinary scale-free networks. Finally, compared to regular structures, fractal trees are fragile and overall inefficient as expected, however, we show that this efficiency can become similar to that of a robust hexagonal lattice, at a similar cost, by just considering a very short euclidean connectivity beyond first neighbors.

Aqueous habitats and carbon inputs shape the microscale geography and interaction ranges of soil bacteria

Earth's diverse soil microbiomes host bacteria within dynamic and fragmented aqueous habitats that occupy complex pore spaces and restrict the spatial range of ecological interactions. Yet, the spatial distributions of bacterial cells in soil communities remain underexplored. Here, we propose a modelling framework representing submillimeter-scale distributions of soil bacteria based on physical constraints supported by individual-based model results and direct observations. The spatial distribution of bacterial cell clusters modulates various metabolic interactions and soil microbiome functioning. Dry soils with long diffusion times limit localized interactions of the sparse communities. Frequently wet soils enable long-range trophic interactions between dense cell clusters through connected aqueous pathways. Biomes with high carbon inputs promote large and dense cell clusters where anoxic microsites form even in aerated soils. Micro-geographic considerations of difficult-to-observe microbial processes can improve the interpretation of data from bulk soil samples.

The growth simulation of pine-needle like structure with diffusion-limited aggregation and oriented attachment

A growth model combined with diffusion-limited aggregation (DLA) and oriented attachment (OA) is developed for deducing quantitative understanding of the growth process of pine-needle like structures. We define the completely random parameters for describing the realistic Brownian motion in DLA. The results indicate that the cluster by DLA changes from random branches to regular needles by the introduction of OA. And the cluster of DLA and OA has a fractal dimensionality of about 1.0 during the whole growth process. The maximum length of needels (L max) depends on the number of particles (N p). They satisfy the relation L max = aN p b (a and b are constant) over the whole range. The model has also been used to describe the formation of needles on a line, plane and sphere. The growth of needles has obvious steric hindrance from the outer needles. In particular, only one needle grows in the later period in the plane.

Heparin promotes rapid fibrillation of the basic Parathyroid Hormone at physiological pH

In acidic secretory granules of mammalian cells, peptide hormones including the parathyroid hormone (PTH) are presumably stored in the form of functional amyloid fibrils. Mature PTH, however, is considerably positively charged in acidic environments, a condition known to impede unassisted self-aggregation into fibrils. Here, we studied the role of the polyanion heparin on promoting fibril formation of PTH. Employing ITC, CD spectroscopy, NMR, SAXS and fluorescence-based assays we could demonstrate that heparin binds PTH with submicromolar affinity and facilitates its conversion into fibrillar seeds, enabling rapid formation of amyloid fibrils under acidic conditions. In absence of heparin, PTH remained in a soluble monomeric state. We suspect that heparin-like surfaces are required in vivo to convert PTH efficiently into fibrillar deposits.