scholarly journals Analysis and asymptotic reduction of a bulk-surface reaction-diffusion model of Gierer-Meinhardt type

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Jan-Phillip Bäcker ◽  
Matthias Röger
Keyword(s):  
Surface Reaction ◽  
Lateral Diffusion ◽  
Reaction Diffusion ◽  
Reaction Diffusion Model ◽  
Bulk Surface ◽  
Parabolic Pde ◽  
Surface System ◽  
Arbitrary Space ◽  
Asymptotic Reduction ◽  
Uniformly Bounded

<p style='text-indent:20px;'>We consider a Gierer-Meinhardt system on a surface coupled with a parabolic PDE in the bulk, the domain confined by this surface. Such a model was recently proposed and analyzed for two-dimensional bulk domains by Gomez, Ward and Wei (<i>SIAM J. Appl. Dyn. Syst. 18</i>, 2019). We prove the well-posedness of the bulk-surface system in arbitrary space dimensions and show that solutions remain uniformly bounded in parabolic Hölder spaces for all times. The cytosolic diffusion is typically much larger than the lateral diffusion on the membrane. This motivates to a corresponding asymptotic reduction, which consists of a nonlocal system on the membrane. We prove the convergence of solutions of the full system towards unique solutions of the reduction.</p>

scholarly journals A bulk-surface reaction-diffusion system for cell polarization

2020 ◽  
Vol 22 (1) ◽  
pp. 85-117
Author(s):  
Barbara Niethammer ◽  
Matthias Röger ◽  
Juan Velázquez
Keyword(s):  
Surface Reaction ◽  
Reaction Diffusion ◽  
Cell Polarization ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Bulk Surface

scholarly journals Stability Analysis of a Bulk-Surface Reaction Model for Membrane-Protein Clustering

2019 ◽  
Author(s):  
Lucas M. Stolerman ◽  
Michael Getz ◽  
Stefan G. Llewellyn Smith ◽  
Michael Holst ◽  
Padmini Rangamani
Keyword(s):  
Lateral Diffusion ◽  
Reaction Diffusion ◽  
Protein Aggregates ◽  
Reaction Model ◽  
Surface Distribution ◽  
Protein Protein Interaction ◽  
Receptor Complexes ◽  
Protein Clustering ◽  
Threshold Phenomenon ◽  
Reaction Diffusion Model

ABSTRACTProtein aggregation on the plasma membrane (PM) is of critical importance to many cellular processes such as cell adhesion, endocytosis, fibrillar conformation, and vesicle transport. Lateral diffusion of protein aggregates or clusters on the surface of the PM plays an important role in governing their heterogeneous surface distribution. However, the stability behavior of the surface distribution of protein aggregates remains poorly understood. Therefore, understanding the spatial patterns that can emerge on the PM solely through protein-protein interaction, lateral diffusion, and feedback is an important step towards a complete description of the mechanisms behind protein clustering on the cell surface. In this work, we investigate the pattern formation of a reaction-diffusion model that describes the dynamics of a system of ligand-receptor complexes. The purely diffusive ligand in the cytosol can bind receptors in the PM, and the resultant ligand-receptor complexes not only diffuse laterally but can also form clusters resulting in different oligomers. Finally, the largest oligomers recruit ligands from the cytosol in a positive feedback. From a methodological viewpoint, we provide theoretical estimates for diffusion-driven instabilities of the protein aggregates based on the Turing mechanism. Our main result is a threshold phenomenon, in which a sufficiently high recruitment of ligands promotes the input of new monomeric components and consequently drives the formation of a single-patch spatially heterogeneous steady-state.

scholarly journals Stability analysis and simulations of coupled bulk-surface reaction–diffusion systems

2015 ◽  
Vol 471 (2175) ◽  
pp. 20140546 ◽  
Author(s):  
Anotida Madzvamuse ◽  
Andy H. W. Chung ◽  
Chandrasekhar Venkataraman
Keyword(s):  
Surface Reaction ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Reaction Diffusion Equations ◽  
Diffusion System ◽  
Diffusion Equations ◽  
Surface Dynamics ◽  
Bulk Reaction ◽  
Bulk Surface ◽  
Type Boundary

In this article, we formulate new models for coupled systems of bulk-surface reaction–diffusion equations on stationary volumes. The bulk reaction–diffusion equations are coupled to the surface reaction–diffusion equations through linear Robin-type boundary conditions. We then state and prove the necessary conditions for diffusion-driven instability for the coupled system. Owing to the nature of the coupling between bulk and surface dynamics, we are able to decouple the stability analysis of the bulk and surface dynamics. Under a suitable choice of model parameter values, the bulk reaction–diffusion system can induce patterning on the surface independent of whether the surface reaction–diffusion system produces or not, patterning. On the other hand, the surface reaction–diffusion system cannot generate patterns everywhere in the bulk in the absence of patterning from the bulk reaction–diffusion system. For this case, patterns can be induced only in regions close to the surface membrane. Various numerical experiments are presented to support our theoretical findings. Our most revealing numerical result is that, Robin-type boundary conditions seem to introduce a boundary layer coupling the bulk and surface dynamics.

Modeling the Electrical Double Layer to Understand the Reaction Environment in a CO2 Electrocatalytic System

2019 ◽  
Author(s):  
Divya Bohra ◽  
Jehanzeb Chaudhry ◽  
Thomas Burdyny ◽  
Evgeny Pidko ◽  
wilson smith
Keyword(s):  
Electric Field ◽  
Double Layer ◽  
Electrical Double Layer ◽  
Surface Reaction ◽  
Catalyst Surface ◽  
Local Reaction ◽  
Reaction Diffusion ◽  
Alkali Metal Cations ◽  
Applied Potential ◽  
Critical Aspect

<p>The environment of a CO<sub>2</sub> electroreduction (CO<sub>2</sub>ER) catalyst is intimately coupled with the surface reaction energetics and is therefore a critical aspect of the overall system performance. The immediate reaction environment of the electrocatalyst constitutes the electrical double layer (EDL) which extends a few nanometers into the electrolyte and screens the surface charge density. In this study, we resolve the species concentrations and potential profiles in the EDL of a CO<sub>2</sub>ER system by self-consistently solving the migration, diffusion and reaction phenomena using the generalized modified Poisson-Nernst-Planck (GMPNP) equations which include the effect of volume exclusion due to the solvated size of solution species. We demonstrate that the concentration of solvated cations builds at the outer Helmholtz plane (OHP) with increasing applied potential until the steric limit is reached. The formation of the EDL is expected to have important consequences for the transport of the CO<sub>2</sub> molecule to the catalyst surface. The electric field in the EDL diminishes the pH in the first 5 nm from the OHP, with an accumulation of protons and a concomitant depletion of hydroxide ions. This is a considerable departure from the results obtained using reaction-diffusion models where migration is ignored. Finally, we use the GMPNP model to compare the nature of the EDL for different alkali metal cations to show the effect of solvated size and polarization of water on the resultant electric field. Our results establish the significance of the EDL and electrostatic forces in defining the local reaction environment of CO<sub>2</sub> electrocatalysts.</p>

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