Decision making in social neurobiological systems modeled as transitions in dynamic pattern formation

Extant models of decision making in social neurobiological systems have typically explained task dynamics as characterized by transitions between two attractors. In this paper, we model a three-attractor task exemplified in a team sport context. The model showed that an attacker–defender dyadic system can be described by the angle x between a vector connecting the participants and the try line. This variable was proposed as an order parameter of the system and could be dynamically expressed by integrating a potential function. Empirical evidence has revealed that this kind of system has three stable attractors, with a potential function of the form V(x)=−k1x+k2ax2/2−bx4/4+x6/6, where k1 and k2 are two control parameters. Random fluctuations were also observed in system behavior, modeled as white noise εt, leading to the motion equation dx/dt = −dV/dx+Q0.5εt, where Q is the noise variance. The model successfully mirrored the behavioral dynamics of agents in a social neurobiological system, exemplified by interactions of players in a team sport.

Inherent structures of phase-separating binary mixtures: Nucleation, spinodal decomposition, and pattern formation

An energy landscape view of phase separation and nonideality in binary mixtures is developed by exploring their potential energy landscape (PEL) as functions of temperature and composition. We employ molecular dynamics simulations to study a model that promotes structure breaking in the solute-solvent parent binary liquid, at low temperatures. The PEL of the system captures the potential energy distribution of the inherent structures (IS) of the system and is obtained by removing the kinetic energy (including that of intermolecular vibrations). The broader distribution of the inherent structure energy for structure breaking liquid than that of the structure making liquid demonstrates the larger role of entropy in stabilizing the parent liquid of the structure breaking type of binary mixtures. At high temperature, although the parent structure of the structure breaking binary mixture is homogenous, the corresponding inherent structure is found to be always phase separated, with a density pattern that exhibits marked correlation with the energy of its inherent structure. Over a broad range of intermediate inherent structure energy, bicontinuous phase separation prevails with interpenetrating stripes as signatures of spinodal decomposition. At low inherent structure energy, the structure is largely phase separated with one interface where as at high inherent structure energy we find nucleation type growth. Interestingly, at low temperature, the average inherent structure energy (< EIS >) exhibits a drop with temperature which signals the onset of crystallization in one of the phases while the other remains in the liquid state. The nonideal composition dependence of viscosity is anticorrelated with average inherent structure energy.

Pattern-Formation During Self-organization in Three-Phase Eutectic Solidification

Eutectic growth is an interesting example for exploring the topic of pattern-formation in multi-phase systems, where the growth of the phases is coupled with the diffusive transport of one or more components in the melt. While in the case of binary alloys, the number of possibilities are limited (lamellae, rods, labyrinth etc.), their number rapidly increases with the number of components and phases. In this paper, we will investigate pattern formation during three-phase eutectic solidification using a state-of-the art phase-field method based on the grand-canonical density formulation. The major aim of the study is to highlight the role of two properties, which are the volume fraction of the solid phases and the solid-liquid interfacial energies, in the self-organization of the solid phases during directional growth. Thereafter, we will show representative phase-field simulations of a micro-structure in a real alloy (Ag-Al-Cu) using an asymmetric phase diagram as well as interfacial properties.

Pattern formation in thin films of polymer solutions: Theory and simulations

Self-assembly has been recognized as an efficient tool for generating a wide range of functional, chemically, or physically textured surfaces for applications in small scale devices. In this work, we investigate the stability of thin films of polymer solutions. For low concentrations of polymer in the solution, long length scale dewetting patterns are obtained with wavelength approximately few microns. Whereas, for concentrations above a critical value, bimodal dispersion curves are obtained with the dominant wavelength being up to two orders smaller than the usual dewetting length scale. We further show that the short wavelength corresponds to the phase separation in the film resulting in uniformly distributed high and low concentration regions. Interestingly, due to the solvent entropy, at very high concentration values of polymer, a re-entrant behaviour is observed with the dominant length scale now again corresponding to the dewetting wavelength. Thus, we show that the binary films of polymer solutions provide additional control parameters that can be utilized for generating functional textured surfaces for various applications. (C) 2016 AIP Publishing LLC.

New tools for self-organised pattern formation

Position-dependent gene expression is a critical aspect of the development and behaviour of multicellular organisms. It requires a complex series of interactions to occur between different cell types in addition to intracellular signalling cascades. We used Escherichia coli to study the properties of an artificial signalling system at the interface between two expanding cell populations. We genetically engineered one population to produce a diffusible acyl-homoserine lactone (AHL) signal, and another population to respond to it. Our experiments demonstrate how such a signal can be used to reproducibly generate simple visible patterns with high accuracy in swimming agar. The producing and responding cassettes of two such signalling systems can be linked to produce a symmetric interface for bidirectional communication that can be used to visualise molecular logic. Intracellular feedback between these two cassettes would then create a framework for self-organised patterning of higher complexity. Adapting the experiments of Basu et al. (Basu et al., 2005) using cell motility, rather than a differential response to AHL concentrations as a way to define zones of response, we noted how the interaction of sender and receiver cell populations on a swimming plate could lead to complex pattern formation. Equipping highly motile strains such as E. coli MC1000 with AHL-mediated auto-inducing systems based on Vibrio fischeri luxI/luxR and Pseudomonas aeruginosa lasI/lasR cassettes would allow the amplification of a response to an AHL signal and its propagation. We designed and synthesised codon-optimised auto-inducing luxI/R and lasI/R cassettes as optimal gene expression is crucial for the generation of robust patterns. We still have to complete and test the entire genetic circuitry, although by modelling the system we were able to demonstrate its feasibility. © 2007 The Institution of Engineering and Technology.

Pattern formation and spatial solitons in bistable liquid-crystal microcavities

We report on spatial pattern formation, and appearances of 'optical bullet holes' in single-mode microcavities that are filled with liquid-crystals, when pumped above the cavity resonance frequency. These phenomena only occur beyond the bistability threshold. ©2002 Optical Society of America.

Fractal Pattern Formation In Anodic Bonding Of Pyrex Glass/Al/Si

Anodic bonding of Pyrex glass/Al/Si is an important bonding technique in micro/nanoelectromechanical systems (MEMS/NEMS) industry. The anodic bonding of Pyrex 7740 glass/Aluminum film/Silicon is completed at the temperature from 300 degrees C to 375 degrees C with a bonding voltage between 150 V and 450 V. The fractal patterns are formed in the intermediate Al thin film. This pattern has the fractal dimension of the typical two-dimensional diffusion-limited aggregation (2D DLA) process, and the fractal dimension is around 1.7. The fractal patterns consist of Al and Si crystalline grains, and their occurrences are due to the limited diffusion, aggregation, and crystallization of Si and Al atoms in the intermediate Al layers. The formation of the fractal pattern is helpful to enhance the bonding strength between the Pyrex 7740 glass and the aluminum thin film coated on the crystal silicon substrates.

Role Of Convection Flow On The Pattern Formation In The Drying Process Of Colloidal Suspension

We study the macroscopic drying patterns of aqueous suspensions of colloidal silica spheres. It was found that convection strength can influence pattern formation. Uniformed films are obtained at weaker convection strength. In addition, we make clear that it is not reasonable to discuss individually the effect of temperature and humidity on the colloid self-assembly. The physical mechanism is that these factors have relationship with the evaporation rate, which can affect the convection strength.

Laser-induced wavy pattern formation in metal thin films

Laser-induced well-ordered and controllable wavy patterns are constructed in the deposited metal thin film. The micrometer-sized structure and orientation of the wavy patterns can be controlled via scanning a different size of rectangle laser spot on the films. Ordered patterns such as aligned, crossed, and whirled wave structures were designed over large areas. This patterning technique may find applications in both exploring the reliability and mechanical properties of thin films, and fabricating microfluidic devices. (C) 2004 American Institute of Physics.

A new dynamic model for study of dislocation pattern formation

Based on the principle given in nonlinear diffusion-reaction dynamics, a new dynamic model for dislocation patterning is proposed by introducing a relaxation time to the relation between dislocation density and dislocation flux. The so-called chemical potential like quantities, which appear in the model can be derived from variation principle for free energy functional of dislocated media, where the free energy density function is expressed in terms of not only the dislocation density itself but also their spatial gradients. The Linear stability analysis on the governing equations of a simple dislocation density shows that there exists an intrinsic wave number leading to bifurcation of space structure of dislocation density. At the same time, the numerical results also demonstrate the coexistence and transition between different dislocation patterns.

Pattern formation during Caenorhabditis Elegans vulval development

Pattern formation during animal development involves at least three processes: establishment of the competence of precursor cells to respond to intercellular signals, formation of a pattern of different cell fates adopted by precursor cells, and execution of the cell fate by generating a pattern of distinct descendants from precursor cells. I have analyzed the fundamental mechanisms of pattern formation by studying the development of Caenorhabditis elegans vulva.

In C. elegans, six multipotential vulval precursor cells (VPCs) are competent to respond to an inductive signal LIN-3 (EGF) mediated by LET- 23 (RTK) and a lateral signal via LIN-12 (Notch) to form a fixed pattern of 3°-3°-2°-1°-2°-3°. Results from expressing LIN-3 as a function of time in animals lacking endogenous LIN-3 indicate that both VPCs and VPC daughters are competent to respond to LIN-3. Although the daughters of VPCs specified to be 2° or 3° can be redirected to adopt the 1°fate, the decision to adopt the 1° fate is irreversible. Coupling of VPC competence to cell cycle progression reveals that VPC competence may be periodic during each cell cycle and involve LIN-39 (HOM-C). These mechanisms are essential to ensure a bias towards the 1° fate, while preventing an excessive response.

After adopting the 1° fate, the VPC executes its fate by dividing three rounds to form a fixed pattern of four inner vulF and four outer vulE descendants. These two types of descendants can be distinguished by a molecular marker zmp-1::GFP. A short-range signal from the anchor cell (AC), along with signaling between the inner and outer 1° VPC descendants and intrinsic polarity of 1° VPC daughters, patterns the 1° lineage. The Ras and the Wnt signaling pathways may be involved in these mechanisms.

The temporal expression pattern of egl-17::GFP, another marker ofthe 1° fate, correlates with three different steps of 1° fate execution: the commitment to the 1° fate, as well as later steps before and after establishment of the uterine-vulval connection. Six transcription factors, including LIN-1(ETS), LIN-39 (HOM-C), LIN-11(LIM), LIN-29 (zinc finger), COG-1 (homeobox) and EGL-38 (PAX2/5/8), are involved in different steps during 1° fate execution.

Nematic ordering pattern formation in the process of self-organization of microtubules in a gravitational field

Papaseit et al. (Proc. Nati. Acad. Sci. U.S.A. 97, 8364, 2000) showed the decisive role of gravity in the formation of patterns by assemblies of microtubules in vitro. By virtue of a functional scaling, the free energy for MT systems in a gravitational field was constructed. The influence of the gravitational field on MT's self-organization process, that can lead to the isotropic to nematic phase transition, is the focus of this paper. A coupling of a concentration gradient with orientational order characteristic of nernatic ordering pattern formation is the new feature emerging in the presence of gravity. The concentration range corresponding to a phase coexistence region increases with increasing g or NIT concentration. Gravity facilitates the isotropic to nernatic phase transition leading to a significantly broader transition region. The phase transition represents the interplay between the growth in the isotropic phase and the precipitation into the nematic phase. We also present and discuss the numerical results obtained for local NIT concentration change with the height of the vessel, order parameter and phase transition properties.

A gene cluster that regulates both heterocyst differentiation and pattern formation in Anabaena sp strain PCC 7120

Wild-type Anabaena sp. strain PCC 7120, a filamentous nitrogen-fixing cyanobacterium, produces single heterocysts at semi-regular intervals. asr0100 (patU5) and alr0101 (patU3) are homologous to the 5' and 3' portions of patU of Nostoc punctiforme. alr0099 (hetZ) overlaps the 5' end of patU5. hetZ, patU5 and patU3 were all upregulated, or expressed specifically, in proheterocysts and heterocysts. Mutants of hetZ showed delayed or no heterocyst differentiation. In contrast, a patU3 mutation produced a multiple contiguous heterocyst (Mch) phenotype and restored the formation of otherwise lost intercalary heterocysts in a patA background. Decreasing the expression of patU3 greatly increased the frequency of heterocysts in a mini-patS strain. Two promoter regions and two principal, corresponding transcripts were detected in the hetZ-patU5-patU3 region. Transcription of hetZ was upregulated in a hetZ mutant and downregulated in a patU3 mutant. When mutants hetZ::C.K2 and hetZ::Tn5-1087b were nitrogen-deprived, P-hetC-gfp was very weakly expressed, and in hetZ::Tn5-1087b, P-hetR-gfp was relatively strongly expressed in cells that had neither a regular pattern nor altered morphology. We conclude that the hetZ-patU5-patU3 cluster plays an important role in co-ordination of heterocyst differentiation and pattern formation. The presence of homologous clusters in filamentous genera without heterocysts is suggestive of a more general role.