Complex Networks from Simple Rewrite Systems

Complex networks are all around us, and they can be generated by simple mechanisms. Understanding what kinds of networks can be produced by following simple rules is therefore of great importance. We investigate this issue by studying the dynamics of extremely simple systems where are `writer' moves around a network, and modifies it in a way that depends upon the writer's surroundings. Each vertex in the network has three edges incident upon it, which are colored red, blue and green. This edge coloring is done to provide a way for the writer to orient its movement. We explore the dynamics of a space of 3888 of these `colored trinet automata' systems. We find a large variety of behaviour, ranging from the very simple to the very complex. We also discover simple rules that generate forms which are remarkably similar to a wide range of natural objects. We study our systems using simulations (with appropriate visualization techniques) and analyze selected rules mathematically. We arrive at an empirical classification scheme which reveals a lot about the kinds of dynamics and networks that can be generated by these systems

Spectral and Dynamical Properties in Classes of Sparse Networks with Mesoscopic Inhomogeneities

We study structure, eigenvalue spectra and diffusion dynamics in a wide class of networks with subgraphs (modules) at mesoscopic scale. The networks are grown within the model with three parameters controlling the number of modules, their internal structure as scale-free and correlated subgraphs, and the topology of connecting network. Within the exhaustive spectral analysis for both the adjacency matrix and the normalized Laplacian matrix we identify the spectral properties which characterize the mesoscopic structure of sparse cyclic graphs and trees. The minimally connected nodes, clustering, and the average connectivity affect the central part of the spectrum. The number of distinct modules leads to an extra peak at the lower part of the Laplacian spectrum in cyclic graphs. Such a peak does not occur in the case of topologically distinct tree-subgraphs connected on a tree. Whereas the associated eigenvectors remain localized on the subgraphs both in trees and cyclic graphs. We also find a characteristic pattern of periodic localization along the chains on the tree for the eigenvector components associated with the largest eigenvalue equal 2 of the Laplacian. We corroborate the results with simulations of the random walk on several types of networks. Our results for the distribution of return-time of the walk to the origin (autocorrelator) agree well with recent analytical solution for trees, and it appear to be independent on their mesoscopic and global structure. For the cyclic graphs we find new results with twice larger stretching exponent of the tail of the distribution, which is virtually independent on the size of cycles. The modularity and clustering contribute to a power-law decay at short return times

Understanding Three Hydration-Dependent Transitions of Zwitterionic Carboxybetaine Hydrogel by Molecular Dynamics Simulations

In this work, molecular dynamics simulations were performed to study a carboxybetaine methacrylate (CBMA) hydrogel under various swelling states. The water content in this study ranged from 28% to 91% of the total weight of the hydrogel. Three transitions of the CBMA hydrogel were observed as the water content increased. The first transition occurs when the water content increases from 33% to 37%. The observed kink in the self-diffusion coefficient of water indicates that the hydration of the polymer network of the hydrogel is saturated; the further added water is in a less confined state. The second transition was found to be related to the physical cross-links of the polymer network. As the water content rises to above 62%, the lifetime of the physical cross-links decreases significantly. This abrupt change in the lifetime indicates that the transition represents the equilibrium swelling state of the hydrogel. Finally, the third transition was observed when the water content goes above 81%. The significant increases in the bond and angle energies of the polymer network indicate that the hydrogel reaches its upper limit swelling state at this transition. These results are comparable to previously published experimental studies of similar zwitterionic hydrogels

High compression strength single network hydrogels with pillar[5]arene junction points

The present study highlights a straightforward and versatile strategy for the synthesis of strong poly(2-isopropenyl-2-oxazoline) hydrogels with tunable properties by using a bifunctional macrocyclic pillar[5]arene host having two carboxylic acid groups as cross-linker. This new strategy provides access to materials with tailored properties from soft and flexible to rigid and strong. The mechanical properties and water uptake of the hydrogels could be effortlessly controlled during the synthesis step through variation of the cross-linker content and after cross-linking by guest-host interactions. The hydrogels displayed strongly enhanced mechanical properties (i.e., compression and tensile modulus, energy dissipation, stress at break and storage modulus) compared to their counterparts cross-linked with linear dicarboxylic acids. The remarkable properties of the pillar[5]arene cross-linked hydrogels were assigned to the transfer of the external stress to the rigid and bulky pillar[5]arene residues that contribute to the overall dimensional stability of the hydrogels and allow energy dissipation. Moreover, we demonstrate the applicability of these materials for water purification. The hydrogels showed high adsorption performance for phenols and dyes such as methylene blue and methyl red and they could be easily regenerated, by washing with an organic solvent for reuse

A mechanistic explanation linking adaptive mutation, niche change, and fitness advantage for the Wrinkly Spreader

Experimental evolution studies have investigated adaptive radiation in static liquid microcosms using the environmental bacterium Pseudomonas fluorescens SBW25. In evolving populations a novel adaptive mutant known as the Wrinkly Spreader arises within days having significant fitness advantage over the ancestral strain. A molecular investigation of the Wrinkly Spreader has provided a mechanistic explanation linking mutation with fitness improvement through the production of a cellulose-based biofilm at the air-liquid interface. Colonisation of this niche provides greater access to oxygen, allowing faster growth than that possible for non-biofilm—forming competitors located in the lower anoxic region of the microcosm. Cellulose is probably normally used for attachment to plant and soil aggregate surfaces and to provide protection in dehydrating conditions. However, the evolutionary innovation of the Wrinkly Spreader in static microcosms is the use of cellulose as the matrix of a robust biofilm, and is achieved through mutations that deregulate multiple diguanylate cyclases leading to the over-production of cyclic-di-GMP and the stimulation of cellulose expression. The mechanistic explanation of the Wrinkly Spreader success is an exemplar of the modern evolutionary synthesis, linking molecular biology with evolutionary ecology, and provides an insight into the phenomenal ability of bacteria to adapt to novel environments

The Third Dimension of Reading the Sugar Code by Lectins

Coding of biological information is not confined to nucleic acids and proteins. Endowed with the highest level of structural versatility among biomolecules, the glycan chains of cellular glycoconjugates are well-suited to generate molecular messages/signals in a minimum of space. The sequence and shape of oligosaccharides as well as spatial aspects of multivalent presentation are assumed to underlie the natural specificity/selectivity that cellular glycans have for endogenous lectins. In order to eventually unravel structure-activity profiles cyclic scaffolds have been used as platforms to produce glycoclusters and afford valuable tools. Using adhesion/growth-regulatory galectins and the pan-galectin ligand lactose as a model, emerging insights into the potential of cyclodextrins, cyclic peptides, calixarenes and glycophanes for this purpose are presented herein. The systematic testing of lectin panels with spatially defined ligand presentations can be considered as a biomimetic means to help clarify the mechanisms, which lead to the exquisite accuracy at which endogenous lectins select their physiological counterreceptors from the complexity of the cellular glycome

Superelastic and pH-Responsive Degradable Dendrimer Cryogels Prepared by Cryo-aza-Michael Addition Reaction

Dendrimers exhibit super atomistic features by virtue of their well-defined discrete quantized nanoscale structures. Here, we show that hyperbranched amine-terminated polyamidoamine (PAMAM) dendrimer G4.0 reacts with linear polyethylene glycol (PEG) diacrylate (575 g/mol) via the aza-Michael addition reaction at a subzero temperature (−20 °C), namely cryo-aza-Michael addition, to form a macroporous superelastic network, i.e., dendrimer cryogel. Dendrimer cryogels exhibit biologically relevant Young’s modulus, high compression elasticity and super resilience at ambient temperature. Furthermore, the dendrimer cryogels exhibit excellent rebound performance and do not show significant stress relaxation under cyclic deformation over a wide temperature range (−80 to 100 °C). The obtained dendrimer cryogels are stable at acidic pH but degrade quickly at physiological pH through self-triggered degradation. Taken together, dendrimer cryogels represent a new class of scaffolds with properties suitable for biomedical applications

Onset of rigidty in glasses: from random to self-organized networks

We review in this paper the signatures of a new elastic phase that is found in glasses with selected compositions. It is shown that in contrast with random networks, where rigidity percolates at a single threshold, networks that are able to self-organize to avoid stress will remain in an almost stress- free state during a compositional interval, an intermediate phase, that is bounded by a flexible phase and a stressed rigid phase. We report the experimental signatures and describe the theoretical efforts that have been accomplished to characterize the intermediate phase. We illustrate one of the methods used in more detail with the example of Group III chalcogenides and finally suggest further possible experimental signatures of self-organization.Comment: 27 pages, 6 figures, Proceedings of the Conference on Non-Crystalline Materials 10, to appear in Journal of Non-Crystalline Solid

Information Super-Diffusion on Structured Networks

We study diffusion of information packets on several classes of structured networks. Packets diffuse from a randomly chosen node to a specified destination in the network. As local transport rules we consider random diffusion and an improved local search method. Numerical simulations are performed in the regime of stationary workloads away from the jamming transition. We find that graph topology determines the properties of diffusion in a universal way, which is reflected by power-laws in the transit-time and velocity distributions of packets. With the use of multifractal scaling analysis and arguments of non-extensive statistics we find that these power-laws are compatible with super-diffusive traffic for random diffusion and for improved local search. We are able to quantify the role of network topology on overall transport efficiency. Further, we demonstrate the implications of improved transport rules and discuss the importance of matching (global) topology with (local) transport rules for the optimal function of networks. The presented model should be applicable to a wide range of phenomena ranging from Internet traffic to protein transport along the cytoskeleton in biological cells.Comment: 27 pages 7 figure

Getting Wrinkly Spreaders to demonstrate evolution in schools

Understanding evolution is crucial to modern biology,but most teachers would assume that practical demonstrations of evolution in school laboratories are unfeasible. However, perhaps they have not heard of ‘evolution in a test tube’ and how Wrinkly Spreaders can form the basis for both practical demonstrations of bacterial evolution and further work