2023
1
Geometry-induced patterns through mechanochemical coupling Open access
Laeschkir Würthner*; Andriy Goychuk*; Erwin Frey
* Equal contribution
In: Physical Review E, vol. 108, no. 1, pp. 014404, 2023, ISSN: 2470-0045, 2470-0053.
Biological Self-OrganizationCell MembraneDifferential EquationsFinite-Element MethodPattern FormationPhase Space MethodsProtein Interaction NetworksProtein-Membrane Interactions
@article{wurthner_geometry-induced_2023,
title = {Geometry-induced patterns through mechanochemical coupling},
author = {Laeschkir Würthner and Andriy Goychuk and Erwin Frey},
doi = {10.1103/PhysRevE.108.014404},
issn = {2470-0045, 2470-0053},
year = {2023},
date = {2023-07-01},
urldate = {2023-07-01},
journal = {Physical Review E},
volume = {108},
number = {1},
pages = {014404},
abstract = {Intracellular protein patterns regulate a variety of vital cellular processes such as cell division and motility, which often involve dynamic cell-shape changes. These changes in cell shape may in turn affect the dynamics of pattern-forming proteins, hence leading to an intricate feedback loop between cell shape and chemical dynamics. While several computational studies have examined the rich resulting dynamics, the underlying mechanisms are not yet fully understood. To elucidate some of these mechanisms, we explore a conceptual model for cell polarity on a dynamic one-dimensional manifold. Using concepts from differential geometry, we derive the equations governing mass-conserving reaction–diffusion systems on time-evolving manifolds. Analyzing these equations mathematically, we show that dynamic shape changes of the membrane can induce pattern-forming instabilities in parts of the membrane, which we refer to as regional instabilities. Deformations of the local membrane geometry can also (regionally) suppress pattern formation and spatially shift already existing patterns. We explain our findings by applying and generalizing the local equilibria theory of mass-conserving reaction–diffusion systems. This allows us to determine a simple onset criterion for geometry-induced pattern-forming instabilities, which is linked to the phase-space structure of the reaction–diffusion system. The feedback loop between membrane shape deformations and reaction–diffusion dynamics then leads to a surprisingly rich phenomenology of patterns, including oscillations, traveling waves, and standing waves, even if these patterns do not occur in systems with a fixed membrane shape. Our paper reveals that the local conformation of the membrane geometry acts as an important dynamical control parameter for pattern formation in mass-conserving reaction-diffusion systems.},
keywords = {Biological Self-Organization, Cell Membrane, Differential Equations, Finite-Element Method, Pattern Formation, Phase Space Methods, Protein Interaction Networks, Protein-Membrane Interactions},
pubstate = {published},
tppubtype = {article}
}
Intracellular protein patterns regulate a variety of vital cellular processes such as cell division and motility, which often involve dynamic cell-shape changes. These changes in cell shape may in turn affect the dynamics of pattern-forming proteins, hence leading to an intricate feedback loop between cell shape and chemical dynamics. While several computational studies have examined the rich resulting dynamics, the underlying mechanisms are not yet fully understood. To elucidate some of these mechanisms, we explore a conceptual model for cell polarity on a dynamic one-dimensional manifold. Using concepts from differential geometry, we derive the equations governing mass-conserving reaction–diffusion systems on time-evolving manifolds. Analyzing these equations mathematically, we show that dynamic shape changes of the membrane can induce pattern-forming instabilities in parts of the membrane, which we refer to as regional instabilities. Deformations of the local membrane geometry can also (regionally) suppress pattern formation and spatially shift already existing patterns. We explain our findings by applying and generalizing the local equilibria theory of mass-conserving reaction–diffusion systems. This allows us to determine a simple onset criterion for geometry-induced pattern-forming instabilities, which is linked to the phase-space structure of the reaction–diffusion system. The feedback loop between membrane shape deformations and reaction–diffusion dynamics then leads to a surprisingly rich phenomenology of patterns, including oscillations, traveling waves, and standing waves, even if these patterns do not occur in systems with a fixed membrane shape. Our paper reveals that the local conformation of the membrane geometry acts as an important dynamical control parameter for pattern formation in mass-conserving reaction-diffusion systems.