Widening the criteria for emergence of Turing patterns

conditions for Turing and wave instabilities in reaction-diffusion systems

Necessary and sufficient conditions are provided for a diffusion-driven instability of a stable equilibrium of a reaction-diffusion system with n components and diagonal diffusion matrix. These can be either Turing or wave instabilities. Known necessary and sufficient conditions are reproduced for there to exist diffusion rates that cause a Turing bifurcation of a stable homogeneous state in the absence of diffusion. The method of proof here though, which is based on study of dispersion relations in the contrasting limits in which the wavenumber tends to zero and to [Formula: see text], gives a constructive method for choosing diffusion constants. The results are illustrated on a 3-component FitzHugh-Nagumo-like model proposed to study excitable wavetrains, and for two different coupled Brusselator systems with 4-components.

Turing patterns by supramolecular self-assembly of a single salphen building block

In the 1950s, Alan Turing showed that concerted reactions and diffusion of activating and inhibiting chemical species can autonomously generate patterns without previous positional information, thus providing a chemical basis for morphogenesis in Nature. However, access to these patterns from only one molecular component that contained all the necessary information to execute agonistic and antagonistic signaling is so far an elusive goal, since two or more participants with different diffusivities are a must. Here, we report on a single-molecule system that generates Turing patterns arrested in the solid state, where supramolecular interactions are used instead of chemical reactions, whereas diffusional differences arise from heterogeneously populated self-assembled products. We employ a family of hydroxylated organic salphen building blocks based on a bis-Schiff-base scaffold with portions responsible for either activation or inhibition of assemblies at different hierarchies through purely supramolecular reactions, only depending upon the solvent dielectric constant and evaporation as fuel.

Progressive Changes in Brain Regional Homogeneity Induced by Electroconvulsive Therapy Among Patients With Schizophrenia

OBJECTIVES

Electroconvulsive therapy (ECT) has significant effects on improving psychotic symptoms in schizophrenia (SZ), but the changes of brain function induced by it are unclear. The purpose of the study was to explore progressive ECT-induced changes in regional homogeneity (ReHo) at multiple time points before, during, and after a course of ECT.

METHODS

The 27 in-patients with SZ (SZ group) who met the recruitment criteria accepted clinical evaluations and resting-state functional magnetic resonance imaging scans before the first ECT (pre-ECT), after the first ECT (ECT1), and after the eighth ECT (ECT8), all conducted within 10 to 12 hours. Forty-three healthy controls (HCs; HC group) who matched well with the patients for age, sex, and years of education were recruited. For Positive and Negative Syndrome Scale (PANSS) and ReHo, progressive changes were examined.

RESULTS

Pair-wise comparisons of patient pre-ECT, ECT1, and ECT8 ReHo values with HC ReHo values revealed that ECT normalized the ReHo values in bilateral superior occipital gyrus (SOG), right lingual gyrus (LG), left medial prefrontal cortex. Furthermore, improved ReHo in bilateral SOG and right LG appeared after the first ECT application. The ReHo values in right middle occipital gyrus, right middle temporal gyrus, and right inferior parietal lobule were not significantly altered by ECT. The total PANSS score was lower even after the first ECT application (mean ΔPANSSECT1, 11.7%; range, 2%-32.8%) and markedly reduced after the eighth application (mean ΔPANSSECT8, 86.3%; range, 72.5%-97.9%).

CONCLUSIONS

The antipsychotic effects of ECT may be achieved through regulating synchronization of some regions such as bilateral SOG, right LG, and left medial prefrontal cortex. Furthermore, the enhanced synchronizations also take place in other regions.

Robust controlled formation of Turing patterns in three-component systems

Over the past few decades, formation of Turing patterns in reaction-diffusion systems has been shown to be the underlying process in several examples of biological morphogenesis, confirming Alan Turing's hypothesis, put forward in 1952. However, theoretical studies suggest that Turing patterns formation via classical "short-range activation and long-range inhibition" concept in general can happen within only narrow parameter ranges. This feature seemingly contradicts the accuracy and reproducibility of biological morphogenesis given the stochasticity of biochemical processes and the influence of environmental perturbations. Moreover, it represents a major hurdle to synthetic engineering of Turing patterns. In this work it is shown that this problem can be overcome in some systems under certain sets of interactions between their elements, one of which is immobile and therefore corresponding to a cell-autonomous factor. In such systems Turing patterns formation can be guaranteed by a simple universal control under any values of kinetic parameters and diffusion coefficients of mobile elements. This concept is illustrated by analysis and simulations of a specific three-component system, characterized in absence of diffusion by a presence of codimension two pitchfork-Hopf bifurcation.