scholarly journals Fission Yeast Polarization: Modeling Cdc42 Oscillations, Symmetry Breaking, and Zones of Activation and Inhibition

Cells ◽  
2020 ◽  
Vol 9 (8) ◽  
pp. 1769 ◽  
Author(s):  
Bita Khalili ◽  
Hailey D. Lovelace ◽  
David M. Rutkowski ◽  
Danielle Holz ◽  
Dimitrios Vavylonis
Keyword(s):  
Fission Yeast ◽  
Model Organism ◽  
Reaction Diffusion ◽  
Small Gtpases ◽  
Membrane Diffusion ◽  
Gtpase Activating Proteins ◽  
Reaction Diffusion Model ◽  
Membrane Bound ◽  
Negative Feedbacks ◽  
Positive And Negative Feedbacks

Cells polarize for growth, motion, or mating through regulation of membrane-bound small GTPases between active GTP-bound and inactive GDP-bound forms. Activators (GEFs, GTP exchange factors) and inhibitors (GAPs, GTPase activating proteins) provide positive and negative feedbacks. We show that a reaction–diffusion model on a curved surface accounts for key features of polarization of model organism fission yeast. The model implements Cdc42 membrane diffusion using measured values for diffusion coefficients and dissociation rates and assumes a limiting GEF pool (proteins Gef1 and Scd1), as in prior models for budding yeast. The model includes two types of GAPs, one representing tip-localized GAPs, such as Rga3; and one representing side-localized GAPs, such as Rga4 and Rga6, that we assume switch between fast and slow diffusing states. After adjustment of unknown rate constants, the model reproduces active Cdc42 zones at cell tips and the pattern of GEF and GAP localization at cell tips and sides. The model reproduces observed tip-to-tip oscillations with periods of the order of several minutes, as well as asymmetric to symmetric oscillations transitions (corresponding to NETO “new end take off”), assuming the limiting GEF amount increases with cell size.

scholarly journals Studies of Turing pattern formation in zebrafish skin

2021 ◽  
Vol 379 (2213) ◽  
Author(s):  
Shigeru Kondo ◽  
Masakatsu Watanabe ◽  
Seita Miyazawa
Keyword(s):  
Pattern Formation ◽  
Diffusion Mechanism ◽  
Model Organism ◽  
Reaction Diffusion ◽  
Cell Interactions ◽  
Pigment Cells ◽  
Turing Pattern ◽  
Reaction Diffusion Model ◽  
Experimental Findings ◽  
Cell Cell

Skin patterns are the first example of the existence of Turing patterns in living organisms. Extensive research on zebrafish, a model organism with stripes on its skin, has revealed the principles of pattern formation at the molecular and cellular levels. Surprisingly, although the networks of cell–cell interactions have been observed to satisfy the ‘short-range activation and long-range inhibition’ prerequisites for Turing pattern formation, numerous individual reactions were not envisioned based on the classical reaction–diffusion model. For example, in real skin, it is not an alteration in concentrations of chemicals, but autonomous migration and proliferation of pigment cells that establish patterns, and cell–cell interactions are mediated via direct contact through cell protrusions. Therefore, the classical reaction–diffusion mechanism cannot be used as it is for modelling skin pattern formation. Various studies are underway to adapt mathematical models to the experimental findings on research into skin patterns, and the purpose of this review is to organize and present them. These novel theoretical methods could be applied to autonomous pattern formation phenomena other than skin patterns. This article is part of the theme issue ‘Recent progress and open frontiers in Turing's theory of morphogenesis’.

Characterization of the activation of small GTPases by their GEFs on membranes using artificial membrane tethering

2017 ◽  
Vol 474 (7) ◽  
pp. 1259-1272 ◽  
Author(s):  
François Peurois ◽  
Simon Veyron ◽  
Yann Ferrandez ◽  
Ilham Ladid ◽  
Sarah Benabdi ◽  
...  
Keyword(s):  
Small Gtpases ◽  
Small Gtpase ◽  
Nucleotide Exchange ◽  
Guanine Nucleotide Exchange ◽  
Nucleotide Exchange Factors ◽  
Gtpase Activating Proteins ◽  
Membrane Tethering ◽  
Quantitative Understanding ◽  
Membrane Bound ◽  
Histidine Tag

Active, GTP-bound small GTPases need to be attached to membranes by post-translational lipid modifications in order to process and propagate information in cells. However, generating and manipulating lipidated GTPases has remained difficult, which has limited our quantitative understanding of their activation by guanine nucleotide exchange factors (GEFs) and their termination by GTPase-activating proteins. Here, we replaced the lipid modification by a histidine tag in 11 full-length, human small GTPases belonging to the Arf, Rho and Rab families, which allowed to tether them to nickel–lipid-containing membranes and characterize the kinetics of their activation by GEFs. Remarkably, this strategy uncovered large effects of membranes on the efficiency and/or specificity in all systems studied. Notably, it recapitulated the release of autoinhibition of Arf1, Arf3, Arf4, Arf5 and Arf6 GTPases by membranes and revealed that all isoforms are efficiently activated by two GEFs with different regulatory regimes, ARNO and Brag2. It demonstrated that membranes stimulate the GEF activity of Trio toward RhoG by ∼30 fold and Rac1 by ∼10 fold, and uncovered a previously unknown broader specificity toward RhoA and Cdc42 that was undetectable in solution. Finally, it demonstrated that the exceptional affinity of the bacterial RabGEF DrrA for the phosphoinositide PI(4)P delimits the activation of Rab1 to the immediate vicinity of the membrane-bound GEF. Our study thus validates the histidine-tag strategy as a potent and simple means to mimic small GTPase lipidation, which opens a variety of applications to uncover regulations brought about by membranes.

scholarly journals A new analyzing technique for nonlinear time fractional Cauchy reaction-diffusion model equations

2020 ◽  
Vol 19 ◽  
pp. 103462 ◽  
Author(s):  
Hijaz Ahmad ◽  
Tufail A. Khan ◽  
Imtiaz Ahmad ◽  
Predrag S. Stanimirović ◽  
Yu-Ming Chu
Keyword(s):  
Diffusion Model ◽  
Reaction Diffusion ◽  
Reaction Diffusion Model ◽  
Model Equations

Conditions for the local and global asymptotic stability of the time–fractional Degn–Harrison system

2020 ◽  
Vol 21 (7-8) ◽  
pp. 749-759
Author(s):  
Rachida Mezhoud ◽  
Khaled Saoudi ◽  
Abderrahmane Zaraï ◽  
Salem Abdelmalek
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Lyapunov Method ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Linearization Method ◽  
Direct Lyapunov Method ◽  
Fractional Systems ◽  
Reaction Diffusion Model ◽  
Theoretical Results

AbstractFractional calculus has been shown to improve the dynamics of differential system models and provide a better understanding of their dynamics. This paper considers the time–fractional version of the Degn–Harrison reaction–diffusion model. Sufficient conditions are established for the local and global asymptotic stability of the model by means of invariant rectangles, the fundamental stability theory of fractional systems, the linearization method, and the direct Lyapunov method. Numerical simulation results are used to illustrate the theoretical results.

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