The Genetic Control of the Compound Leaf Patterning in Medicago truncatula

Simple and compound which are the two basic types of leaves are distinguished by the pattern of the distribution of blades on the petiole. Compared to simple leaves comprising a single blade, compound leaves have multiple blade units and exhibit more complex and diverse patterns of organ organization, and the molecular mechanisms underlying their pattern formation are receiving more and more attention in recent years. Studies in model legume Medicago truncatula have led to an improved understanding of the genetic control of the compound leaf patterning. This review is an attempt to summarize the current knowledge about the compound leaf morphogenesis of M. truncatula, with a focus on the molecular mechanisms involved in pattern formation. It also includes some comparisons of the molecular mechanisms between leaf morphogenesis of different model species and offers useful information for the molecular design of legume crops.

Approximated Gene Expression Trajectories (AGETs) for Gene Regulatory Network Inference on Cell Tracks

The study of pattern formation has benefited from reverse-engineering gene regulatory network (GRN) structure from spatio-temporal quantitative gene expression data. Traditional approaches omit tissue morphogenesis, hence focusing on systems where the timescales of pattern formation and morphogenesis can be separated. In such systems, pattern forms as an emergent property of the underlying GRN. This is not the case in many animal patterning systems, where patterning and morphogenesis are simultaneous. To address pattern formation in these systems we need to adapt our methodologies to explicitly accommodate cell movements and tissue shape changes. In this work we present a novel framework to reverse-engineer GRNs underlying pattern formation in tissues experiencing morphogenetic changes and cell rearrangements. By combination of quantitative data from live and fixed embryos we approximate gene expression trajectories (AGETs) in single cells and use a subset to reverse-engineer candidate GRNs using a Markov Chain Monte Carlo approach. GRN fit is assessed by simulating on cell tracks (live-modelling) and comparing the output to quantitative data-sets. This framework outputs candidate GRNs that recapitulate pattern formation at the level of the tissue and the single cell. To our knowledge, this inference methodology is the first to integrate cell movements and gene expression data, making it possible to reverse-engineer GRNs patterning tissues undergoing morphogenetic changes.

Physical realization of complex dynamical pattern formation in magnetic active feedback rings

We report the clean experimental realization of cubic-quintic complex Ginzburg-Landau physics in a single driven, damped system. Four numerically predicted categories of complex dynamical behavior and pattern formation are identified for bright and dark solitary waves propagating around an active magnetic thin film-based feedback ring: (1) periodic breathing; (2) complex recurrence; (3) spontaneous spatial shifting; and (4) intermittency. These nontransient, long lifetime behaviors are observed in self-generated microwave spin wave envelopes circulating within a dispersive, nonlinear yttrium iron garnet waveguide. The waveguide is operated in a ring geometry in which the net losses are directly compensated for via linear amplification on each round trip (of the order of 100~ns). These behaviors exhibit periods ranging from tens to thousands of round trip times (of the order of $\mu$s) and are stable for 1000s of periods (of the order of~ms). We present 10 observations of these dynamical behaviors which span the experimentally accessible ranges of attractive cubic nonlinearity, dispersion, and external field strength that support the self-generation of backward volume spin waves in a four-wave-mixing dominant regime. Three-wave splitting is not explicitly forbidden and is treated as an additional source of nonlinear losses. All observed behaviors are robust over wide parameter regimes, making them promising for technological applications. We present ten experimental observations which span all categories of dynamical behavior previously theoretically predicted to be observable. This represents a complete experimental verification of the cubic-quintic complex Ginzburg-Landau equation as a model for the study of fundamental, complex nonlinear dynamics for driven, damped waves evolving in nonlinear, dispersive systems. The reported dynamical pattern formation of self-generated dark solitary waves in attractive nonlinearity without external sources or potentials, however, is entirely novel and is presented for both the periodic breather and complex recurrence behaviors.

The effect of landscape fragmentation on Turing-pattern formation

<abstract><p>Diffusion-driven instability and Turing pattern formation are a well-known mechanism by which the local interaction of species, combined with random spatial movement, can generate stable patterns of population densities in the absence of spatial heterogeneity of the underlying medium. Some examples of such patterns exist in ecological interactions between predator and prey, but the conditions required for these patterns are not easily satisfied in ecological systems. At the same time, most ecological systems exist in heterogeneous landscapes, and landscape heterogeneity can affect species interactions and individual movement behavior. In this work, we explore whether and how landscape heterogeneity might facilitate Turing pattern formation in predator–prey interactions. We formulate reaction-diffusion equations for two interacting species on an infinite patchy landscape, consisting of two types of periodically alternating patches. Population dynamics and movement behavior differ between patch types, and individuals may have a preference for one of the two habitat types. We apply homogenization theory to derive an appropriately averaged model, to which we apply stability analysis for Turing patterns. We then study three scenarios in detail and find mechanisms by which diffusion-driven instabilities may arise even if the local interaction and movement rates do not indicate it.</p></abstract>

Cyclic Tension Induced Pattern Formation on [001] Single-Crystal Aluminum Foil

Cyclic tension of (100)[001]-oriented single-crystal aluminum foils with the frequency 5 Hz forms a tweed pattern. Its period is several microns and increases by a factor of 1.5 in the temperature range 233–363 K. A model is proposed for structural relaxation of the medium on spatial and time meso- and macroscales under cyclic loading. Conditions under which a steady pattern forms are found based on the analysis of kinetic equations. The number of bands in the steady pattern is found to be related to the strain rate. The process activation energy is determined.