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

Stolerman, Lucas M.; Getz, Michael; Smith, Stefan G. Llewellyn; Holst, Michael; Rangamani, Padmini

doi:10.1101/736165

Cited by 5 publications

(5 citation statements)

References 53 publications

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“…The roles of spatial localization and membrane-cytosol crosstalk of these biochemical interactions and the role of dendritic spine morphology in these processes are not well-known. The bulk-surface coupling between the cytosol and the synaptic membrane is likely a crucial mediator of AMPAR density [45,[60][61][62]. Additionally, surface diffusion is also an important parameter for governing the receptor dynamics [63][64][65][66].…”

Section: • Role Of Traffickingmentioning

confidence: 99%

Spatiotemporal modeling reveals geometric dependence of AMPAR dynamics on dendritic spine morphology

Bell

Lee

Rangamani

2022

Preprint

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The modification of neural circuits depends on the strengthening and weakening of synaptic connections. Synaptic strength is often correlated to the density of the ionotropic, glutamateric receptors, AMPAR, (α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptor) at the postsynaptic density (PSD). While AMPAR density is known to change based on complex biological signaling cascades, the effect of geometric factors such as dendritic spine shape, size, and curvature remain poorly understood. In this work, we developed a deterministic, spatiotemporal model to study the dynamics of AMPAR during long term potentiation (LTP). This model includes a minimal set of biochemical events that represent the upstream signaling events, trafficking of AMPAR to and from the PSD, lateral diffusion in the plane of the spine membrane, and the presence of an extrasynaptic AMPAR pool. Using idealized and realistic spine geometries, we show that the dynamics and increase of bound AMPAR at the PSD depends on a combination of endo- and exocytosis, membrane diffusion, availability of free AMPAR, and intracellular signaling interactions. We also found non-monotonic relationships between spine volume and change in AMPAR at the PSD, suggesting that spines restrict changes in AMPAR to optimize resources and prevent runaway potentiation.

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Section: • Role Of Traffickingmentioning

confidence: 99%

Spatiotemporal modeling reveals geometric dependence of AMPAR dynamics on dendritic spine morphology

Bell

Lee

Rangamani

2022

Preprint

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“…( [43], [9], [32], [31], [36]), and for certain specific biological applications, including cell polarization and Cdc42 protein pattern formation (cf. [4], [41], [42], [46], [38]).…”

Section: Introductionmentioning

confidence: 99%

The Emergence of Spatial Patterns for Compartmental Reaction Kinetics Coupled by Two Bulk Diffusing Species with Comparable Diffusivities

Pelz¹,

Ward²

2023

Preprint

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Originating from the pioneering study of Alan Turing, the bifurcation analysis predicting spatial pattern formation from a spatially uniform state for diffusing morphogens or chemical species that interact through nonlinear reactions is a central problem in many chemical and biological systems. From a mathematical viewpoint, one key challenge with this theory for two component systems is that stable spatial patterns can typically only occur from a spatially uniform state when a slowly diffusing "activator" species reacts with a much faster diffusing "inhibitor" species. However, from a modeling perspective, this large diffusivity ratio requirement for pattern formation is often unrealistic in biological settings since different molecules tend to diffuse with similar rates in extracellular spaces. As a result, one key long-standing question is how to robustly obtain pattern formation in the biologically realistic case where the time scales for diffusion of the interacting species are comparable. For a coupled 1-D bulk-compartment theoretical model, we investigate the emergence of spatial patterns for the scenario where two bulk diffusing species with comparable diffusivities are coupled to nonlinear reactions that occur only in localized "compartments", such as on the boundaries of a 1-D domain. The exchange between the bulk medium and the spatially localized compartments is modeled by a Robin boundary condition with certain binding rates. As regulated by these binding rates, we show for various specific nonlinearities that our 1-D coupled PDE-ODE model admits symmetry-breaking bifurcations, leading to linearly stable asymmetric steady-state patterns, even when the bulk diffusing species have equal diffusivities. Depending on the form of the nonlinear kinetics, oscillatory instabilities can also be triggered. Moreover, the analysis is extended to treat a periodic chain of compartments.

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“…( [48], [11], [36], [35], [40]), and for some specific biological applications (cf. [6], [46], [47], [52], [42]).…”

Section: Introductionmentioning

confidence: 99%

Symmetry-Breaking Bifurcations for Compartmental Reaction Kinetics Coupled by Two Bulk Diffusing Species with Comparable Diffusivities in 2-D

Pelz¹,

Ward²

2023

Preprint

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For a 2-D coupled PDE-ODE bulk-cell model, we investigate symmetry-breaking bifurcations that can emerge when two bulk diffusing species are coupled to two-component nonlinear intracellular reactions that are restricted to occur only within a disjoint collection of small circular compartments, or "cells", of a common small radius that are confined in a bounded 2-D domain. Outside of the union of these cells, the two bulk species with comparable diffusivities and bulk degradation rates diffuse and globally couple the spatially segregated intracellular reactions through Robin boundary conditions across the cell boundaries, which depend on certain membrane reaction rates. In the singular limit of a small common cell radius, we construct steady-state solutions for the bulk-cell model and formulate a nonlinear matrix eigenvalue problem that determines the linear stability properties of the steady-states. For a certain spatial arrangement of cells for which the steady-state and linear stability analysis become highly tractable, we construct a symmetric steady-state solution where the steady-states of the intracellular species are the same for each cell. As regulated by the ratio of the membrane reaction rates on the cell boundaries, we show for various specific prototypical intracellular reactions, and for a specific twocell arrangement, that our 2-D coupled PDE-ODE model admits symmetry-breaking bifurcations from this symmetric steady-state, leading to linearly stable asymmetric patterns, even when the bulk diffusing species have comparable or possibly equal diffusivities. Overall, our analysis shows that symmetry-breaking bifurcations can occur without the large diffusivity ratio requirement for the bulk diffusing species as is well-known from a Turing stability analysis applied to a spatially uniform steady-state for typical two-component activator-inhibitor systems. Instead, for our theoretical compartmental-reaction diffusion bulk-cell model, our analysis shows that the emergence of stable asymmetric steady-states can be controlled by the ratio of the membrane reaction rates for the two species. Bifurcation theoretic results for symmetric and asymmetric steady-state patterns obtained from our asymptotic theory are confirmed with full numerical PDE simulations.

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

Cited by 5 publications

References 53 publications

Spatiotemporal modeling reveals geometric dependence of AMPAR dynamics on dendritic spine morphology

Spatiotemporal modeling reveals geometric dependence of AMPAR dynamics on dendritic spine morphology

The Emergence of Spatial Patterns for Compartmental Reaction Kinetics Coupled by Two Bulk Diffusing Species with Comparable Diffusivities

Symmetry-Breaking Bifurcations for Compartmental Reaction Kinetics Coupled by Two Bulk Diffusing Species with Comparable Diffusivities in 2-D

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