Complex pattern formation in reaction diffusion systems with spatially-varying parameters

Spontaneous pattern formation in reaction–diffusion systems on a spatially homogeneous domain has been well studied. However, in embryonic development and elsewhere, pattern formation often takes place on a spatially heterogeneous background. We explore the effects of spatially varying parameters on pattern formation in one and two dimensions using the Gierer–Meinhardt reaction–diffusion model. We investigate the effect of the wavelength of a pre-pattern and demonstrate a novel form of moving pattern. We find that spatially heterogeneous parameters can both increase the range and complexity of possible patterns and enhance the robustness of pattern selection

Speed of reaction diffusion in embryogenesis

Reaction diffusion systems have been proposed as mechanisms for patterning during many stages of embryonic development. While much attention has been focused on the study of the steady state patterns formed and the robustness of pattern selection, much less is known about the time scales required for pattern formation. Studies of gradient formation by the diffusion of a single morphogen from a localized source have shown that patterning can occur on realistic time scales over distances of a millimeter or less. Reaction diffusion has the potential to give rise to patterns on a faster time scale, since all points in the domain can act as sources of morphogen. However, the speed at which patterning can occur has hitherto not been explored in depth. In this paper, we investigate this issue in specific reaction diffusion models and address the question of whether patterning via reaction diffusion is fast enough to be applicable to morphogenesis

Pattern formation by lateral inhibition with feedback: a mathematical model of Delta-Notch intercellular signalling

In many developing tissues, adjacent cells diverge in character so as to create a fine-grained pattern of cells in contrasting states of differentiation. It has been proposed that such patterns can be generated through lateral inhibition—a type cells–cell interaction whereby a cell that adopts a particular fate inhibits its immediate neighbours from doing likewise. Lateral inhibition is well documented in flies, worms and vertebrates. In all of these organisms, the transmembrane proteins Notch and Delta (or their homologues) have been identified as mediators of the interaction—Notch as receptor, Delta as its ligand on adjacent cells. However, it is not clear under precisely what conditions the Delta-Notch mechanism of lateral inhibition can generate the observed types of pattern, or indeed whether this mechanism is capable of generating such patterns by itself. Here we construct and analyse a simple and general mathematical model of such contact-mediated lateral inhibition. In accordance with experimental data, the model postulates that receipt of inhibition (i.e. activation of Notch) diminishes the ability to deliver inhibition (i.e. to produce active Delta). This gives rise to a feedback loop that can amplify differences between adjacent cells. We investigate the pattern-forming potential and temporal behavior of this model both analytically and through numerical simulation. Inhomogeneities are self-amplifying and develop without need of any other machinery, provided the feedback is sufficiently strong. For a wide range of initial and boundary conditions, the model generates fine-grained patterns similar to those observed in living systems

A model of primitive streak initiation in the chick embryo

Initiation of the primitive streak in avian embryos provides a well-studied example of a pattern-forming event that displays a striking capacity for regulation. The mechanisms underlying the regulative properties are, however, poorly understood and are not easily accounted for by traditional models of pattern formation, such as reaction–diffusion models. In this paper, we propose a new activator–inhibitor model for streak initiation. We show that the model is consistent with experimental observations, both in its pattern-forming properties and in its ability to form these patterns on the correct time-scales for biologically realistic parameter values. A key component of the model is a travelling wave of inhibition. We present a mathematical analysis of the speed of such waves in both diffusive and juxtacrine relay systems. We use the streak initiation model to make testable predictions. By varying parameters of the model, two very different types of patterning can be obtained, suggesting that our model may be applicable to other processes in addition to streak initiation

Human Amniocytes Are Receptive to Chemically Induced Reprogramming to Pluripotency

Restoring pluripotency using chemical compounds alone would be a major step forward in developing clinical-grade pluripotent stem cells, but this has not yet been reported in human cells. We previously demonstrated that VPA_ AFS cells, human amniocytes cultivated with valproic acid (VPA) acquired functional pluripotency while remaining distinct from human embryonic stem cells (hESCs), questioning the relationship between the modulation of cell fate and molecular regulation of the pluripotency network. Here, we used single-cell analysis and functional assays to reveal that VPA treatment resulted in a homogeneous population of self-renewing non-transformed cells that fulfill the hallmarks of pluripotency, i.e., a short G1 phase, a dependence on glycolytic metabolism, expression of epigenetic modifications on histones 3 and 4, and reactivation of endogenous OCT4 and downstream targets at a lower level than that observed in hESCs. Mechanistic insights into the process of VPA-induced reprogramming revealed that it was dependent on OCT4 promoter activation, which was achieved independently of the PI3K (phosphatidylinositol 3-kinase)/ AKT/ mTOR (mammalian target of rapamycin) pathway or GSK3 beta inhibition but was concomitant with the presence of acetylated histones H3K9 and H3K56, which promote pluripotency. Our data identify, for the first time, the pluripotent transcriptional and molecular signature and metabolic status of human chemically induced pluripotent stem cells

Weighted network modules

The inclusion of link weights into the analysis of network properties allows a deeper insight into the (often overlapping) modular structure of real-world webs. We introduce a clustering algorithm (CPMw, Clique Percolation Method with weights) for weighted networks based on the concept of percolating k-cliques with high enough intensity. The algorithm allows overlaps between the modules. First, we give detailed analytical and numerical results about the critical point of weighted k-clique percolation on (weighted) Erdos-Renyi graphs. Then, for a scientist collaboration web and a stock correlation graph we compute three-link weight correlations and with the CPMw the weighted modules. After reshuffling link weights in both networks and computing the same quantities for the randomised control graphs as well, we show that groups of 3 or more strong links prefer to cluster together in both original graphs.Comment: 19 pages, 7 figure

Complete Genome Sequences of Paenibacillus Larvae Phages BN12, Dragolir, Kiel007, Leyra, Likha, Pagassa, PBL1c, and Tadhana

We present here the complete genomes of eight phages that infect Paenibacillus larvae, the causative agent of American foulbrood in honeybees. Phage PBL1c was originally isolated in 1984 from a P. larvae lysogen, while the remaining phages were isolated in 2014 from bee debris, honeycomb, and lysogens from three states in the USA

Gene expression time delays & Turing pattern formation systems

The incorporation of time delays can greatly affect the behaviour of partial differential equations and dynamical systems. In addition, there is evidence that time delays in gene expression due to transcription and translation play an important role in the dynamics of cellular systems. In this paper, we investigate the effects of incorporating gene expression time delays into a one-dimensional putative reaction diffusion pattern formation mechanism on both stationary domains and domains with spatially uniform exponential growth. While oscillatory behaviour is rare, we find that the time taken to initiate and stabilise patterns increases dramatically as the time delay is increased. In addition, we observe that on rapidly growing domains the time delay can induce a failure of the Turing instability which cannot be predicted by a naive linear analysis of the underlying equations about the homogeneous steady state. The dramatic lag in the induction of patterning, or even its complete absence on occasions, highlights the importance of considering explicit gene expression time delays in models for cellular reaction diffusion patterning