On Traveling Wave Fronts in a Bacterial Growth Model with Density-Dependent Diffusion and Chemotaxis

Bacterial colonies often generate patterns that are characterized by fingerlike projections growing out of the propagating front. In this paper, we analyze the traveling wave fronts in bacterial growth model that accounts for chemotactic movement as well as random motion in density-dependent diffusion. Specifically, the existence of traveling wave solutions to model equations is examined by means of methods of local linear and nonlinear analysis, and numerical simulations. The occurrence is shown of both sharp and smooth traveling wave fronts.     

Self-organized patterns and traffic flow in Colonies of organisms: from bacteria and social insects to vertebrates

Flocks of birds and schools of fish are familiar examples of spatial patterns formed by living organisms. In contrast to the patterns on the skins of, say, zebras and giraffes, the patterns of our interest are transient although different patterns change over different timescales. The aesthetic beauty of these patterns has attracted the attention of poets and philosophers for centuries. Scientists from various disciplines, however, are in search of common underlying principles that give rise to the transient patterns in colonies of organisms. Such patterns are observed not only in colonies of organisms as simple as single-cell bacteria, but also in social insects like ants and termites. They are also observed in colonies of vertebrates as complex as birds and fish, and in human societies. In recent years, physicists have utilized the framework of statistical physics to understand these patterns. In this article, we present an overview emphasizing the common trends that rely on theoretical modeling of these systems using the so-called agent-based Lagrangian approach.     

Cooperative self-organization of microorganisms

In nature, microorganisms must often cope with hostile environmental conditions. To do so they have developed sophisticated cooperative behaviour and intricate communication capabilities, such as: direct cell-cell physical interactions via extra-membrane polymers, collective production of extracellular 'wetting' fluid for movement on hard surfaces, long range chemical signalling such as quorum sensing and chemotactic (bias of movement according to gradient of chemical agent) signalling, collective activation and deactivation of genes and even exchange of genetic material. Utilizing these capabilities, the colonies develop complex spatio-temporal patterns in response to adverse growth conditions. We present a wealth of beautiful patterns formed during colony development of various microorganisms and for different environmental conditions. Invoking ideas from pattern formation in non-living systems and using 'generic' modelling we are able to reveal novel survival strategies which account for the salient features of the evolved patterns. Using the models, we demonstrate how communication leads to self-organization via cooperative behaviour of the cells. In this regard, pattern formation in microorganisms can be viewed as the result of the exchange of information between the micro-level (the individual cells) and the macro-level (the colony). As such, a full understanding of bacterial behaviour must focus simultaneously on individual cell responses and overall colony organization.     

Characterizing and modeling an electoral campaign in the context of Twitter: 2011 Spanish Presidential election as a case study

Transmitting messages in the most efficient way as possible has always been one of politicians' main concerns during electoral processes. Due to the rapidly growing number of users, online social networks have become ideal platforms for politicians to interact with their potential voters. Exploiting the available potential of these tools to maximize their influence over voters is one of politicians' actual challenges. To step in this direction, we have analyzed the user activity in the online social network Twitter, during the 2011 Spanish Presidential electoral process, and found that such activity is correlated with the election results. We introduce a new measure to study political sentiment in Twitter, which we call the relative support. We have also characterized user behavior by analyzing the structural and dynamical patterns of the complex networks emergent from the mention and retweet networks. Our results suggest that the collective attention is driven by a very small fraction of users. Furthermore, we have analyzed the interactions taking place among politicians, observing a lack of debate. Finally, we develop a network growth model to reproduce the interactions taking place among politicians.     

Modeling of spatiotemporal patterns in bacterial colonies

A diffusion-reaction model for the growth of bacterial colonies is presented. The often observed cooperative behavior developed by bacteria which increases their motility in adverse growth conditions is here introduced as a nonlinear diffusion term. The presence of this mechanism depends on a response which can present hysteresis. By changing only the concentrations of agar and initial nutrient, numerical integration of the proposed model reproduces the different patterns shown by Bacillus subtilis OG-01.     

Kinetic and hydrodynamic models of chemotactic aggregation

We derive general kinetic and hydrodynamic models of chemotactic aggregation that describe certain features of the morphogenesis of biological colonies (like bacteria, amoebae, endothelial cells or social insects). Starting from a stochastic model defined in terms of N coupled Langevin equations, we derive a nonlinear mean-field Fokker-Planck equation governing the evolution of the distribution function of the system in phase space. By taking the successive moments of this kinetic equation and using a local thermodynamic equilibrium condition, we derive a set of hydrodynamic equations involving a damping term. In the limit of small frictions, we obtain a hyperbolic model describing the formation of network patterns (filaments) and in the limit of strong frictions we obtain a parabolic model which is a generalization of the standard Keller-Segel model describing the formation of clusters (clumps). Our approach connects and generalizes several models introduced in the chemotactic literature. We discuss the analogy between bacterial colonies and self-gravitating systems and between the chemotactic collapse and the gravitational collapse (Jeans instability). We also show that the basic equations of chemotaxis are similar to nonlinear mean-field Fokker-Planck equations so that a notion of effective generalized thermodynamics can be developed.     

Lubricating bacteria model for branching growth of bacterial colonies

Various bacterial strains (e.g., strains belonging to the genera Bacillus, Paenibacillus, Serratia, and Salmonella) exhibit colonial branching patterns during growth on poor semisolid substrates. These patterns reflect the bacterial cooperative self-organization. A central part of the cooperation is the collective formation of a lubricant on top of the agar which enables the bacteria to swim. Hence it provides the colony means to advance towards the food. One method of modeling the colonial development is via coupled reaction-diffusion equations which describe the time evolution of the bacterial density and the concentrations of the relevant chemical fields. This idea has been pursued by a number of groups. Here we present an additional model which specifically includes an evolution equation for the lubricant excreted by the bacteria. We show that when the diffusion of the fluid is governed by a nonlinear diffusion coefficient, branching patterns evolve. We study the effect of the rates of emission and decomposition of the lubricant fluid on the observed patterns. The results are compared with experimental observations. We also include fields of chemotactic agents and food chemotaxis and conclude that these features are needed in order to explain the observations.     

Texture transitions in the liquid crystalline alkyloxybenzoic acid 6OBAC

The 4,n-alkyloxybenzoic acid 6OBAC has a very rich variety of crystalline structures and two nematic sub-phases, characterised by different textures. It is a material belonging to a family of liquid crystals formed by hydrogen bonded molecules, the 4,n-alkyloxybenzoic acids (n indicates the homologue number). The homologues with 7?≤?n?≤?13 display both smectic C and N phases. In spite of the absence of a smectic phase, 6OBAC exhibits two sub-phases with different textures, as it happens in other materials of the homologue series which possess the smectic phase. This is the first material that exhibits a texture transition in a nematic phase directly originating from a crystal phase. Here we present the results of an image processing assisted optical investigation to characterise the textures and the transitions between textures. This processing is necessary to discriminate between crystal modifications and nematic sub-phases.     

Hierarchy in social organization

We find that area and population distributions of nations follow an inverse power-law, as is known for cities, but with a different exponent. To interpret this result, we develop a growth model based on the geometrical properties of partitioning of the plane. The substantial agreement between the model and the actual nation distributions motivates the hypothesis that the distribution of aggregates of organisms is related to land partitioning. To test this hypothesis we follow the development of bacterial colonies of Escherichia coli, which, compared to humans, are on a completely different level of complexity. We find that the distributions of E. coli colonies follow an inverse power law with exponent similar to that of nations.     

Synchronization in multicell systems exhibiting dynamic plasticity

Collective behaviour in multicell systems arises from exchange of chemicals/ signals between cells and may be different from their intrinsic behaviour. These chemicals are products of regulated networks of biochemical pathways that underlie cellular functions, and can exhibit a variety of dynamics arising from the non-linearity of the reaction processes. We have addressed the emergent synchronization properties of a ring of cells, diffusively coupled by the end product of an intracellular model biochemical pathway exhibiting non-robust birhythmic behaviour. The aim is to examine the role of intercellular interaction in stabilizing the non-robust dynamics in the emergent collective behaviour in the ring of cells. We show that, irrespective of the inherent frequencies of individual cells, depending on the coupling strength, the collective behaviour does synchronize to only one type of oscillations above a threshold number of cells. Using two perturbation analyses, we also show that this emergent synchronized dynamical state is fairly robust under external perturbations. Thus, the inherent plasticity in the oscillatory phenotypes in these model cells may get suppressed to exhibit collective dynamics of a single type in a multicell system, but environmental influences can sometimes expose this underlying plasticity in its collective dynamics.      

Multiscale Information Propagation in Emergent Functional Networks

Complex biological systems consist of large numbers of interconnected units, characterized by emergent properties such as collective computation. In spite of all the progress in the last decade, we still lack a deep understanding of how these properties arise from the coupling between the structure and dynamics. Here, we introduce the multiscale emergent functional state, which can be represented as a network where links encode the flow exchange between the nodes, calculated using diffusion processes on top of the network. We analyze the emergent functional state to study the distribution of the flow among components of 92 fungal networks, identifying their functional modules at different scales and, more importantly, demonstrating the importance of functional modules for the information content of networks, quantified in terms of network spectral entropy. Our results suggest that the topological complexity of fungal networks guarantees the existence of functional modules at different scales keeping the information entropy, and functional diversity, high.     

Comments on the use of network structures to analyse commercial companies’ evolution and their impact on economic behaviour

Network analysis studies the development of the social structure of relationships around a group or an institutional body, and how it affects beliefs and behaviours. Causal constraints require a special and deeper attention to the social structure. The purpose of this paper is to give a new approach to the idea that this reality should be primarily conceived and investigated from the perspective of the properties of relations between and within units, instead of the properties of these units themselves. The relationship may refer to the exchange of products, labour, information and money. By mapping these relationships, network analysis can help to uncover the emergent and informal communication patterns of commercial companies that may be compared to the formal communication structures. These emergent patterns can be used to explain institutional and individuals’ behaviours. Network analysis techniques focus on the communication structure of an organization that can be subdivided and handled with different approaches. Structural features that can be analysed through the use of network analysis techniques are, for example, the (formal and informal) communication patterns in an organization or the identification of specific groups within an organization. Special attention may be given to specific aspects of communication patterns.     

Attractor-Specific and Common Expression Values in Random Boolean Network Models (with a Preliminary Look at Single-Cell Data)

Random Boolean Networks (RBNs for short) are strongly simplified models of gene regulatory networks (GRNs), which have also been widely studied as abstract models of complex systems and have been used to simulate different phenomena. We define the “common sea” (CS) as the set of nodes that take the same value in all the attractors of a given network realization, and the “specific part” (SP) as the set of all the other nodes, and we study their properties in different ensembles, generated with different parameter values. Both the CS and of the SP can be composed of one or more weakly connected components, which are emergent intermediate-level structures. We show that the study of these sets provides very important information about the behavior of the model. The distribution of distances between attractors is also examined. Moreover, we show how the notion of a “common sea” of genes can be used to analyze data from single-cell experiments.     

The evolution of chemical patterns in reactive liquids,driven by hydrodynamic instabilities

We summarize our activity in unveiling a very wide phenomenon: When a chemical reaction takes place at a liquid interface, spectacular patterns of product form (see Plate 1). The pattern formation phenomenon is general, and is observed in reactions between liquids separated by a membrane, in liquids subjected to gaseous reactants, and in photoreactive liquids. We have demonstrated the phenomenon on over 100 different reactions of all types, thus discovering what we believe to be one of the widest macroscopic pattern formation processes known to chemistry. As can be seen in the accompanying pictures, the richness, beauty, and variations in types of patterns can be breathtaking. Two important aspects of these patterns are noted: First, the patterns are true far-from-equilibrium structures, which are maintained only as long as reactants are available, or only as long as light energy is supplied to the system; and second, the chemical products that form the patterns are not precipitates, but are entirely soluble in the liquid in which they form. Thus, if the containers in which the patterns form are shaken or stirred, a homogeneous solution results. Our research of this phenomenon concentrated on three main aspects. The first one was phenomenological. Here we explored the scope and generality of the phenomenon, motivated both by the aesthetic appeal of the phenomenon, and by the puzzle of how is it that such a wide-scope, experimentally simple phenomenon, has by and large, escaped the attention of the scientific community.The second aspect was devoted to the understanding of the underlying general mechanism. Of the many mechanisms we analyzed and tested, some very complex, others quite trivial, the one that fits the majority of the physical and chemical observations is the following: By performing a reaction through a liquid interface, a concentration gradient of the product forms near the interface. We have shown that in many cases, these gradients lead to hydrodynamic instabilities, which then break nonlinearly into a pattern which onsets slow convections. In other words, we found that these patterns mark the route along which a chemical instability relaxes. The third aspect of our research was theoretical. Here we concentrated in depth on one of the reactions (the Fe(+2)/Fe(+3) photoredox reaction), determined all its important physical parameters, and modeled its behavior theoretically. Our model, which was based on the instability buildup described above, was solved numerically, and its results compared with computerized image analysis of the evolving patterns; very good agreement between theory and experiment, was obtained. (c) 1995 American Institute of Physics.     

Magnetic van der Waals materials: Synthesis,structure, magnetism,and their potential applications

As the family of magnetic materials is rapidly growing, two-dimensional (2D) van der Waals (vdW) magnets have attracted increasing attention as a platform to explore fundamental physical problems of magnetism and their potential applications. This paper reviews the recent progress on emergent vdW magnetic compounds and their potential applications in devices. First, we summarize the current vdW magnetic materials and their synthetic methods. Then, we focus on their structure and the modulation of magnetic properties by analyzing the representative vdW magnetic materials with different magnetic structures. In addition, we pay attention to the heterostructures of vdW magnetic materials, which are expected to produce revolutionary applications of magnetism-related devices. To motivate the researchers in this area, we finally provide the challenges and outlook on 2D vdW magnetism.     

Bacterial cell wall material properties determine E. coli resistance to sonolysis

The applications of bacterial sonolysis in industrial settings are plagued by the lack of the knowledge of the exact mechanism of action of sonication on bacterial cells, variable effectiveness of cavitation on bacteria, and inconsistent data of its efficiency. In this study we have systematically changed material properties of E. coli cells to probe the effect of different cell wall layers on bacterial resistance to ultrasonic irradiation (20 kHz, output power 6,73 W, horn type, 3 mm probe tip diameter, 1 ml sample volume). We have determined the rates of sonolysis decay for bacteria with compromised major capsular polymers, disrupted outer membrane, compromised peptidoglycan layer, spheroplasts, giant spheroplasts, and in bacteria with different cell physiology. The non-growing bacteria were 5-fold more resistant to sonolysis than growing bacteria. The most important bacterial cell wall structure that determined the outcome during sonication was peptidoglycan. If peptidoglycan was remodelled, weakened, or absent the cavitation was very efficient. Cells with removed peptidoglycan had sonolysis resistance equal to lipid vesicles and were extremely sensitive to sonolysis. The results suggest that bacterial physiological state as well as cell wall architecture are major determinants that influence the outcome of bacterial sonolysis.     

Parallel Detection of Multiple Transitional Spectral Patterns Using Optical Spectrogram Scope

In measurement of ultrafast phenomena caused by several photochemical reactions, multiple transitional spectral patterns contained in a signal pulse are directly associated with different interactions, allowing us to identify individual interactions from these patterns. We propose a new method by which we can detect multiple transitional spectral patterns contained in a signal pulse in parallel using optical spectrogram scope (OSS). In the experimental demonstration, we used an arrayed filter composed of matched filters recording three kinds of transitional spectral patterns in the OSS system, and we directly detected two different patterns contained in a signal pulse in parallel.     

Emergent organization of oscillator clusters in coupled self-regulatory chaotic maps

Here we introduce a model of parametrically coupled chaotic maps on a one-dimensional lattice. In this model, each element has its internal self-regulatory dynamics, whereby at fixed intervals of time the nonlinearity parameter at each site is adjusted by feedback from its past evolution. Additionally, the maps are coupled sequentially and unidirectionally, to their nearest neighbor, through the difference of their parametric variations. Interestingly we find that this model asymptotically yields clusters of superstable oscillators with different periods. We observe that the sizes of these oscillator clusters have a power-law distribution. Moreover, we find that the transient dynamics gives rise to a 1/f power spectrum. All these characteristics indicate self-organization and emergent scaling behavior in this system. We also interpret the power-law characteristics of the proposed system from an ecological point of view.