3D Dune Skeleton Model as a Coupled Dynamical System of 2D Cross-Sections

To analyze theoretically the stability of the shape and the migration process of transverse dunes and barchans, we propose a {\it skeleton model} of 3D dunes described with coupled dynamics of 2D cross-sections. First, 2D cross-sections of a 3D dune parallel to the wind direction are extracted as elements of a skeleton of the 3D dune, hence, the dynamics of each and interaction between them is considered. This model simply describes the essential dynamics of 3D dunes as a system of coupled ordinary differential equations. Using the model we study the stability of the shape of 3D transversal dunes and their deformation to barchans depending on the amount of available sand in the dune field, sand flow in parallel and perpendicular to wind direction.Comment: 6 pages, 6 figures, lette

Collision dynamics of two barchan dunes simulated by a simple model

The collision processes of two crescentic dunes called barchans are systematically studied using a simple computer simulation model. The simulated processes, coalescence, ejection and reorganization, qualitatively correspond to those observed in a water tank experiment. Moreover we found the realized types of collision depend both on the mass ratio and on the lateral distance between barchans under initial conditions. A simple set of differential equations to describe the collision of one-dimensional (1D) dunes is introduced.Comment: 4 pages, 5 figures : To be published in Journal of the Physical Society of Japa

microRNA input into a neural ultradian oscillator controls emergence and timing of alternative cell states.

© 2014 Macmillan Publishers LimitedThis is an open access article that is freely available in ORE or from the publisher's web site. Please cite the published version.Progenitor maintenance, timed differentiation and the potential to enter quiescence are three fundamental processes that underlie the development of any organ system. In the nervous system, progenitor cells show short-period oscillations in the expression of the transcriptional repressor Hes1, while neurons and quiescent progenitors show stable low and high levels of Hes1, respectively. Here we use experimental data to develop a mathematical model of the double-negative interaction between Hes1 and a microRNA, miR-9, with the aim of understanding how cells transition from one state to another. We show that the input of miR-9 into the Hes1 oscillator tunes its oscillatory dynamics, and endows the system with bistability and the ability to measure time to differentiation. Our results suggest that a relatively simple and widespread network of cross-repressive interactions provides a unifying framework for progenitor maintenance, the timing of differentiation and the emergence of alternative cell states.Wellcome Trus

Designing attractive models via automated identification of chaotic and oscillatory dynamical regimes

Chaos and oscillations continue to capture the interest of both the scientific and public domains. Yet despite the importance of these qualitative features, most attempts at constructing mathematical models of such phenomena have taken an indirect, quantitative approach, for example, by fitting models to a finite number of data points. Here we develop a qualitative inference framework that allows us to both reverse-engineer and design systems exhibiting these and other dynamical behaviours by directly specifying the desired characteristics of the underlying dynamical attractor. This change in perspective from quantitative to qualitative dynamics, provides fundamental and new insights into the properties of dynamical systems

The mechanisms of boronate ester formation and fluorescent turn-on in ortho-aminomethylphenylboronic acids

ortho-Aminomethylphenylboronic acids are used in receptors for carbohydrates and various other compounds containing vicinal diols. The presence of the o-aminomethyl group enhances the affinity towards diols at neutral pH, and the manner in which this group plays this role has been a topic of debate. Further, the aminomethyl group is believed to be involved in the turn-on of the emission properties of appended fluorophores upon diol binding. In this treatise, a uniform picture emerges for the role of this group: it primarily acts as an electron-withdrawing group that lowers the pK(a) of the neighbouring boronic acid thereby facilitating diol binding at neutral pH. The amine appears to play no role in the modulation of the fluorescence of appended fluorophores in the protic-solvent-inserted form of the boronic acid/boronate ester. Instead, fluorescence turn-on can be consistently tied to vibrational-coupled excited-state relaxation (a loose-bolt effect). Overall, this Review unifies and discusses the existing data as of 2019 whilst also highlighting why o-aminomethyl groups are so widely used, and the role they play in carbohydrate sensing using phenylboronic acids

Stochastic loss and gain of symmetric divisions in the C. elegans epidermis perturbs robustness of stem cell number

Biological systems are subject to inherent stochasticity. Nevertheless, development is remarkably robust, ensuring the consistency of key phenotypic traits such as correct cell numbers in a certain tissue. It is currently unclear which genes modulate phenotypic variability, what their relationship is to core components of developmental gene networks, and what is the developmental basis of variable phenotypes. Here, we start addressing these questions using the robust number of Caenorhabditis elegans epidermal stem cells, known as seam cells, as a readout. We employ genetics, cell lineage tracing, and single molecule imaging to show that mutations in lin-22, a Hes-related basic helix-loop-helix (bHLH) transcription factor, increase seam cell number variability. We show that the increase in phenotypic variability is due to stochastic conversion of normally symmetric cell divisions to asymmetric and vice versa during development, which affect the terminal seam cell number in opposing directions. We demonstrate that LIN-22 acts within the epidermal gene network to antagonise the Wnt signalling pathway. However, lin-22 mutants exhibit cell-to-cell variability in Wnt pathway activation, which correlates with and may drive phenotypic variability. Our study demonstrates the feasibility to study phenotypic trait variance in tractable model organisms using unbiased mutagenesis screens

Numerical study of short-term afterimages and associate properties in foveal vision.

A cellular model of the primate retina has been developed. Unlike existing models, it incorporates spatial non-uniformities, such as the random arrangement of L and M cones, and the radial dilation with eccentricity. Based on a population of ganglion cell activities, colour-image representation is modelled with the luminance and the R-G opponent channels. The developed model reproduces experimentally known properties in temporal and spatial vision. Furthermore, spatio-temporally coupled properties such as transition from positive to negative phases in an afterimage, are recapped. In colour vision, the model can explain the insensitivity in our colour perception to the L/M cone ratio

A numerical study of red-green colour opponent properties in the primate retina.

It remains an important question whether neural function is mediated entirely by its tailored circuitry. A persistent debate in retinal colour vision is whether the centre and the surround of a ganglion cell receptive field receive dominant inputs either from L or M cones in an antagonistic manner (the selective wiring model) or mixed inputs (the mixed wiring model). Despite many anatomical, physiological and psychophysical experiments, a decisive conclusion has not been reached. An in-depth examination of what the pure mixed wiring mechanisms predicts is therefore important. These two models make different predictions both for the fovea and for the peripheral retina. Recently, a dynamic cellular model of the primate fovea was developed [Momiji et al. (2006) Vis. Res., 46, 365-381]. Unlike earlier models, it explicitly incorporates spatial non-uniformities, such as the random arrangement of L and M cones. Here, a related model is developed for the peripheral retina by incorporating anatomically reasonable degrees of convergence between cones, bipolar cells and ganglion cells. These two models, in which selective wiring mechanisms are absent, are applied to describe both foveal and peripheral colour vision. In numerical simulations, peripheral ganglion cells are less colour sensitive than foveal counterparts, but none-the-less display comparative sensitivities. Furthermore, peripheral colour sensitivity increases with temporal frequency, relative to foveal sensitivity. These results are congruent with recent physiological experiments

Numerical study of short-term afterimages and associate properties in foveal vision.

A cellular model of the primate retina has been developed. Unlike existing models, it incorporates spatial non-uniformities, such as the random arrangement of L and M cones, and the radial dilation with eccentricity. Based on a population of ganglion cell activities, colour-image representation is modelled with the luminance and the R-G opponent channels. The developed model reproduces experimentally known properties in temporal and spatial vision. Furthermore, spatio-temporally coupled properties such as transition from positive to negative phases in an afterimage, are recapped. In colour vision, the model can explain the insensitivity in our colour perception to the L/M cone ratio

A stochastic transcriptional switch model for single cell imaging data

Gene expression is made up of inherently stochastic processes within single cells and can be modeled through stochastic reaction networks (SRNs). In particular, SRNs capture the features of intrinsic variability arising from intracellular biochemical processes. We extend current models for gene expression to allow the transcriptional process within an SRN to follow a random step or switch function which may be estimated using reversible jump Markov chain Monte Carlo (MCMC). This stochastic switch model provides a generic framework to capture many different dynamic features observed in single cell gene expression. Inference for such SRNs is challenging due to the intractability of the transition densities. We derive a model-specific birth-death approximation and study its use for inference in comparison with the linear noise approximation where both approximations are considered within the unifying framework of state-space models. The methodology is applied to synthetic as well as experimental single cell imaging data measuring expression of the human prolactin gene in pituitary cells