scholarly journals The proneural wave in the Drosophila optic lobe is driven by an excitable reaction-diffusion mechanism

eLife ◽  
2019 ◽  
Vol 8 ◽  
Author(s):  
David J Jörg ◽  
Elizabeth E Caygill ◽  
Anna E Hakes ◽  
Esteban G Contreras ◽  
Andrea H Brand ◽  
...  
Keyword(s):  
Visual Processing ◽  
Optic Lobe ◽  
Diffusion Mechanism ◽  
Growth Factor Receptor ◽  
Reaction Diffusion ◽  
Travelling Wave ◽  
Proneural Gene ◽  
Spatiotemporal Information ◽  
Drosophila Brain ◽  
Living Organisms

In living organisms, self-organised waves of signalling activity propagate spatiotemporal information within tissues. During the development of the largest component of the visual processing centre of the Drosophila brain, a travelling wave of proneural gene expression initiates neurogenesis in the larval optic lobe primordium and drives the sequential transition of neuroepithelial cells into neuroblasts. Here, we propose that this ‘proneural wave’ is driven by an excitable reaction-diffusion system involving epidermal growth factor receptor (EGFR) signalling interacting with the proneural gene l’sc. Within this framework, a propagating transition zone emerges from molecular feedback and diffusion. Ectopic activation of EGFR signalling in clones within the neuroepithelium demonstrates that a transition wave can be excited anywhere in the tissue by inducing signalling activity, consistent with a key prediction of the model. Our model illuminates the physical and molecular underpinnings of proneural wave progression and suggests a generic mechanism for regulating the sequential differentiation of tissues.

scholarly journals Author response: The proneural wave in the Drosophila optic lobe is driven by an excitable reaction-diffusion mechanism

2019 ◽  
Author(s):  
David J Jörg ◽  
Elizabeth E Caygill ◽  
Anna E Hakes ◽  
Esteban G Contreras ◽  
Andrea H Brand ◽  
...  
Keyword(s):  
Optic Lobe ◽  
Diffusion Mechanism ◽  
Reaction Diffusion ◽  
Author Response

scholarly journals A Laplace transform finite difference scheme for the Fisher-KPP equation

2021 ◽  
Vol 15 ◽  
pp. 174830262199958
Author(s):  
Colin L Defreitas ◽  
Steve J Kane
Keyword(s):  
Finite Difference ◽  
Laplace Transform ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Finite Difference Methods ◽  
Reaction Diffusion ◽  
Numerical Approach ◽  
Travelling Wave ◽  
Reaction Diffusion Equation ◽  
Kpp Equation

This paper proposes a numerical approach to the solution of the Fisher-KPP reaction-diffusion equation in which the space variable is developed using a purely finite difference scheme and the time development is obtained using a hybrid Laplace Transform Finite Difference Method (LTFDM). The travelling wave solutions usually associated with the Fisher-KPP equation are, in general, not deemed suitable for treatment using Fourier or Laplace transform numerical methods. However, we were able to obtain accurate results when some degree of time discretisation is inbuilt into the process. While this means that the advantage of using the Laplace transform to obtain solutions for any time t is not fully exploited, the method does allow for considerably larger time steps than is otherwise possible for finite-difference methods.

scholarly journals Travelling colourful patterns in self-organized cellulose-based liquid crystalline structures

2021 ◽  
Vol 2 (1) ◽  
Author(s):  
Pedro E. S. Silva ◽  
Ricardo Chagas ◽  
Susete N. Fernandes ◽  
Pawel Pieranski ◽  
Robin L. B. Selinger ◽  
...  
Keyword(s):  
Simple Model ◽  
Temporal Variation ◽  
Liquid Crystalline ◽  
Diffusion Mechanism ◽  
Reaction Diffusion ◽  
Self Organization ◽  
Spatial And Temporal Variation ◽  
Living Matter ◽  
Equilibrium Conditions ◽  
Self Organized

AbstractCellulose-based systems are useful for many applications. However, the issue of self-organization under non-equilibrium conditions, which is ubiquitous in living matter, has scarcely been addressed in cellulose-based materials. Here, we show that quasi-2D preparations of a lyotropic cellulose-based cholesteric mesophase display travelling colourful patterns, which are generated by a chemical reaction-diffusion mechanism being simultaneous with the evaporation of solvents at the boundaries. These patterns involve spatial and temporal variation in the amplitude and sign of the helix´s pitch. We propose a simple model, based on a reaction-diffusion mechanism, which simulates the observed spatiotemporal colour behaviour.

Reaction-Diffusion Modeling of Photopolymerization During Femtosecond Projection Two-Photon Lithography

2021 ◽  
Author(s):  
Rushil Pingali ◽  
Sourabh K. Saha
Keyword(s):  
Diffusion Mechanism ◽  
Chemical Properties ◽  
Reaction Diffusion ◽  
Element Model ◽  
Polymerization Process ◽  
Layer By Layer ◽  
Length Scales ◽  
Two Photon ◽  
Reaction Diffusion Model ◽  
Direct Laser

Abstract Two-photon lithography (TPL) is a polymerization-based direct laser writing process that is capable of fabricating arbitrarily complex three-dimensional (3D) structures with submicron features. Traditional TPL techniques have limited scalability due to the slow point-by-point serial writing scheme. The femtosecond projection TPL (FP-TPL) technique increases printing rate by a thousand times by enabling layer-by-layer parallelization. However, parallelization alters the time and the length scales of the underlying polymerization process. It is therefore challenging to apply the models of serial TPL to accurately predict process outcome during FP-TPL. To solve this problem, we have generated a finite element model of the polymerization process on the time and length scales relevant to FP-TPL. The model is based on the reaction-diffusion mechanism that underlies polymerization. We have applied this model to predict the geometry of nanowires printed under a variety of conditions and compared these predictions against empirical data. Our model accurately predicts the nanowire widths. However, accuracy of aspect ratio prediction is hindered by uncertain values of the chemical properties of the photopolymer. Nevertheless, our results demonstrate that the reaction-diffusion model can accurately capture the effect of controllable parameters on FP-TPL process outcome and can therefore be used for process control and optimization.

scholarly journals Reaction Diffusion and Chemotaxis for Decentralized Gathering on FPGAs

2009 ◽  
Vol 2009 ◽  
pp. 1-15 ◽  
Author(s):  
Bernard Girau ◽  
César Torres-Huitzil ◽  
Nikolaos Vlassopoulos ◽  
José Hugo Barrón-Zambrano
Keyword(s):  
Large Scale ◽  
Complex Dynamics ◽  
Diffusion Mechanism ◽  
Reaction Diffusion ◽  
Fpga Implementation ◽  
Cellular Slime Mold ◽  
Reaction Diffusion Model ◽  
Cellular Slime ◽  
Computational Resources ◽  
Embedded Implementation

We consider here the feasibility of gathering multiple computational resources by means of decentralized and simple local rules. We study such decentralized gathering by means of a stochastic model inspired from biology: the aggregation of theDictyostelium discoideumcellular slime mold. The environment transmits information according to a reaction-diffusion mechanism and the agents move by following excitation fronts. Despite its simplicity this model exhibits interesting properties of self-organization and robustness to obstacles. We first describe the FPGA implementation of the environment alone, to perform large scale and rapid simulations of the complex dynamics of this reaction-diffusion model. Then we describe the FPGA implementation of the environment together with the agents, to study the major challenges that must be solved when designing a fast embedded implementation of the decentralized gathering model. We analyze the results according to the different goals of these hardware implementations.

scholarly journals FKPP equation with impulses on unbounded domain

2017 ◽  
Vol 1 ◽  
pp. 1 ◽  
Author(s):  
Valaire Yatat ◽  
Yves Dumont
Keyword(s):  
Travelling Waves ◽  
Reaction Diffusion ◽  
Bare Soil ◽  
Travelling Wave ◽  
Reaction Diffusion Equations ◽  
Spreading Speed ◽  
Systems Dynamics ◽  
Travelling Wave Solutions ◽  
Minimal Speed ◽  
Wave Solutions

This paper deals with the problem of travelling wave solutions in a scalar impulsive FKPP-like equation. It is a first step of a more general study that aims to address existence of travelling wave solutions for systems of impulsive reaction-diffusion equations that model ecological systems dynamics such as fire-prone savannas. Using results on scalar recursion equations, we show existence of populated vs. extinction travelling waves invasion and compute an explicit expression of their spreading speed (characterized as the minimal speed of such travelling waves). In particular, we find that the spreading speed explicitly depends on the time between two successive impulses. In addition, we carry out a comparison with the case of time-continuous events. We also show that depending on the time between two successive impulses, the spreading speed with pulse events could be lower, equal or greater than the spreading speed in the case of time-continuous events. Finally, we apply our results to a model of fire-prone grasslands and show that pulse fires event may slow down the grassland vs. bare soil invasion speed.

scholarly journals Neuralized regulates a travelling wave of Epithelium-to-Neural Stem Cell morphogenesis in Drosophila

2020 ◽  
Author(s):  
Chloé Shard ◽  
Juan Luna-Escalante ◽  
François Schweisguth
Keyword(s):  
Stem Cells ◽  
Ubiquitin Ligase ◽  
Epithelial To Mesenchymal Transition ◽  
Optic Lobe ◽  
E3 Ubiquitin Ligase ◽  
Tissue Level ◽  
Travelling Wave ◽  
Cell Morphogenesis ◽  
Apical Constriction ◽  
Mesenchymal Transition

AbstractMany tissues are produced during development by specialized progenitor cells emanating from epithelia via an Epithelial-to-Mesenchymal Transition (EMT). Most studies have so far focused on cases involving single or isolated groups of cells. Here we describe an EMT-like process that requires tissue level coordination. This EMT-like process occurs along a continuous front in the Drosophila optic lobe neuroepithelium to produce neural stem cells (NSCs). We find that emerging NSCs remain epithelial and apically constrict before dividing asymmetrically to produce neurons. Apical constriction is associated with contractile myosin pulses and requires the E3 ubiquitin ligase Neuralized and RhoGEF3. Neuralized down-regulates the apical protein Crumbs via its interaction with Stardust. Disrupting the regulation of Crumbs by Neuralized led to defects in apical constriction and junctional myosin accumulation, and to imprecision in the integration of emerging NSCs into the transition front. Neuralized therefore appears to mechanically couple NSC fate acquisition with cell-cell rearrangement to promote smooth progression of the differentiation front.

scholarly journals Allee dynamics: growth, extinction and range expansion

2017 ◽  
Author(s):  
I Bose ◽  
M Pal ◽  
C Karmakar
Keyword(s):  
Population Density ◽  
Range Expansion ◽  
Population Biology ◽  
Allee Effect ◽  
Additive Noise ◽  
Finite Population ◽  
Reaction Diffusion ◽  
Travelling Wave ◽  
One Dimension ◽  
Negative Growth

AbstractIn population biology, the Allee dynamics refer to negative growth rates below a critical population density. In this Letter, we study a reaction-diffusion (RD) model of population growth and dispersion in one dimension, which incorporates the Allee effect in both the growth and mortality rates. In the absence of diffusion, the bifurcation diagram displays regions of both finite population density and zero population density, i.e., extinction. The early signatures of the transition to extinction at a bifurcation point are computed in the presence of additive noise. For the full RD model, the existence of travelling wave solutions of the population density is demonstrated. The parameter regimes in which the travelling wave advances (range expansion) and retreats are identified. In the weak Allee regime, the transition from the pushed to the pulled wave is shown as a function of the mortality rate constant. The results obtained are in agreement with the recent experimental observations on budding yeast populations.

scholarly journals Effect of FMRFamide on voltage-dependent currents in identified centrifugal neurons of the optic lobe of the cuttlefish, Sepia officinalis

2020 ◽  
Author(s):  
Abdesslam Chrachri
Keyword(s):  
Visual Processing ◽  
Calcium Current ◽  
Optic Lobe ◽  
Low Voltage ◽  
Sodium Current ◽  
Calcium Currents ◽  
Delayed Rectifier ◽  
Outward Currents ◽  
Voltage Dependent ◽  
Inward Currents

AbstractWhole-cell patch-clamp recordings from identified centrifugal neurons of the optic lobe in a slice preparation allowed the characterization of five voltage-dependent currents; two outward and three inward currents. The outward currents were; the 4-aminopyridine-sensitive transient potassium or A-current (IA), the TEA-sensitive sustained current or delayed rectifier (IK). The inward currents were; the tetrodotoxin-sensitive transient current or sodium current (INa). The second is the cobalt- and cadmium-sensitive sustained current which is enhanced by barium and blocked by the dihydropyridine antagonist, nifedipine suggesting that it could be the L-type calcium current (ICaL). Finally, another transient inward current, also carried by calcium, but unlike the L-type, this current is activated at more negative potentials and resembles the low-voltage-activated or T-type calcium current (ICaT) of other preparations.Application of the neuropeptide FMRFamide caused a significant attenuation to the peak amplitude of both sodium and sustained calcium currents without any apparent effect on the transient calcium current. Furthermore, FMRFamide also caused a reduction of both outward currents in these centrifugal neurons. The fact that FMRFamide reduced the magnitude of four of five characterized currents could suggest that this neuropeptide may act as a strong inhibitory agent on these neurons.SummaryFMRFamide modulate the ionic currents in identified centrifugal neurons in the optic lobe of cuttlefish: thus, FMRFamide could play a key role in visual processing of these animals.

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