2024
6.
Andriy Goychuk; Leonardo Demarchi; Ivan Maryshev; Erwin Frey
Self-consistent sharp interface theory of active condensate dynamics Journal Article
In: Physical Review Research, vol. 6, no. 3, pp. 033082, 2024, ISSN: 2643-1564.
Abstract | Links | BibTeX | Tags: Biomolecular Dynamics, Enzymes, Liquid-Liquid Phase Transition, Nonequilibrium Systems, Pattern Formation, Protein-Protein Interactions, Traveling Waves
@article{goychuk_self-consistent_2024,
title = {Self-consistent sharp interface theory of active condensate dynamics},
author = {Andriy Goychuk and Leonardo Demarchi and Ivan Maryshev and Erwin Frey},
url = {https://link.aps.org/doi/10.1103/PhysRevResearch.6.033082},
doi = {10.1103/PhysRevResearch.6.033082},
issn = {2643-1564},
year = {2024},
date = {2024-07-01},
urldate = {2026-05-29},
journal = {Physical Review Research},
volume = {6},
number = {3},
pages = {033082},
abstract = {Biomolecular condensates help organize the cell cytoplasm and nucleoplasm into spatial compartments with different chemical compositions. A key feature of such compositional patterning is the local enrichment of enzymatically active biomolecules which, after transient binding via molecular interactions, catalyze reactions among their substrates. Thereby, biomolecular condensates provide a spatial template for nonuniform concentration profiles of substrates. In turn, the concentration profiles of substrates, and their molecular interactions with enzymes, drive enzyme fluxes which can enable novel nonequilibrium dynamics. To analyze this generic class of systems, with a current focus on self-propelled droplet motion, we here develop a self-consistent sharp interface theory. In our theory, we diverge from the usual bottom-up approach, which involves calculating the dynamics of concentration profiles based on a given chemical potential gradient. Instead, reminiscent of control theory, we take the reverse approach by deriving the chemical potential profile and enzyme fluxes required to maintain a desired condensate form and dynamics. The chemical potential profile and currents of enzymes come with a corresponding power dissipation rate, which allows us to derive a thermodynamic consistency criterion for the passive part of the system (here, reciprocal enzyme-enzyme interactions). As a first-use case of our theory, we study the role of reciprocal interactions, where the transport of substrates due to reactions and diffusion is, in part, compensated by redistribution due to molecular interactions. More generally, our theory applies to mass-conserved active matter systems with moving phase boundaries.},
keywords = {Biomolecular Dynamics, Enzymes, Liquid-Liquid Phase Transition, Nonequilibrium Systems, Pattern Formation, Protein-Protein Interactions, Traveling Waves},
pubstate = {published},
tppubtype = {article}
}
Biomolecular condensates help organize the cell cytoplasm and nucleoplasm into spatial compartments with different chemical compositions. A key feature of such compositional patterning is the local enrichment of enzymatically active biomolecules which, after transient binding via molecular interactions, catalyze reactions among their substrates. Thereby, biomolecular condensates provide a spatial template for nonuniform concentration profiles of substrates. In turn, the concentration profiles of substrates, and their molecular interactions with enzymes, drive enzyme fluxes which can enable novel nonequilibrium dynamics. To analyze this generic class of systems, with a current focus on self-propelled droplet motion, we here develop a self-consistent sharp interface theory. In our theory, we diverge from the usual bottom-up approach, which involves calculating the dynamics of concentration profiles based on a given chemical potential gradient. Instead, reminiscent of control theory, we take the reverse approach by deriving the chemical potential profile and enzyme fluxes required to maintain a desired condensate form and dynamics. The chemical potential profile and currents of enzymes come with a corresponding power dissipation rate, which allows us to derive a thermodynamic consistency criterion for the passive part of the system (here, reciprocal enzyme-enzyme interactions). As a first-use case of our theory, we study the role of reciprocal interactions, where the transport of substrates due to reactions and diffusion is, in part, compensated by redistribution due to molecular interactions. More generally, our theory applies to mass-conserved active matter systems with moving phase boundaries.
2023
5.
Laeschkir Würthner; Andriy Goychuk; Erwin Frey
Geometry-induced patterns through mechanochemical coupling Journal Article
In: Physical Review E, vol. 108, no. 1, pp. 014404, 2023, ISSN: 2470-0045, 2470-0053.
Abstract | Links | BibTeX | Tags: Biological Self-Organization, Cell Membrane, Differential Equations, Finite-Element Method, Pattern Formation, Phase Space Methods, Protein Interaction Networks, Protein-Membrane Interactions
@article{wurthner_geometry-induced_2023,
title = {Geometry-induced patterns through mechanochemical coupling},
author = {Laeschkir Würthner and Andriy Goychuk and Erwin Frey},
url = {https://link.aps.org/doi/10.1103/PhysRevE.108.014404},
doi = {10.1103/PhysRevE.108.014404},
issn = {2470-0045, 2470-0053},
year = {2023},
date = {2023-07-01},
urldate = {2026-05-29},
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.
4.
Leonardo Demarchi; Andriy Goychuk; Ivan Maryshev; Erwin Frey
Enzyme-Enriched Condensates Show Self-Propulsion, Positioning, and Coexistence Journal Article
In: Physical Review Letters, vol. 130, no. 12, pp. 128401, 2023, ISSN: 0031-9007, 1079-7114.
Abstract | Links | BibTeX | Tags: Analytical Theory, Biomolecular Dynamics, Enzymes, Liquid-Liquid Phase Transition, Nonequilibrium Systems, Pattern Formation, Protein-Protein Interactions, Simulation, Traveling Waves
@article{demarchi_enzyme-enriched_2023,
title = {Enzyme-Enriched Condensates Show Self-Propulsion, Positioning, and Coexistence},
author = {Leonardo Demarchi and Andriy Goychuk and Ivan Maryshev and Erwin Frey},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.130.128401},
doi = {10.1103/PhysRevLett.130.128401},
issn = {0031-9007, 1079-7114},
year = {2023},
date = {2023-03-01},
urldate = {2026-05-29},
journal = {Physical Review Letters},
volume = {130},
number = {12},
pages = {128401},
abstract = {Enzyme-enriched condensates can organize the spatial distribution of their substrates by catalyzing nonequilibrium reactions. Conversely, an inhomogeneous substrate distribution induces enzyme fluxes through substrate-enzyme interactions. We find that condensates move toward the center of a confining domain when this feedback is weak. Above a feedback threshold, they exhibit self-propulsion, leading to oscillatory dynamics. Moreover, catalysis-driven enzyme fluxes can lead to interrupted coarsening, resulting in equidistant condensate positioning, and to condensate division.},
keywords = {Analytical Theory, Biomolecular Dynamics, Enzymes, Liquid-Liquid Phase Transition, Nonequilibrium Systems, Pattern Formation, Protein-Protein Interactions, Simulation, Traveling Waves},
pubstate = {published},
tppubtype = {article}
}
Enzyme-enriched condensates can organize the spatial distribution of their substrates by catalyzing nonequilibrium reactions. Conversely, an inhomogeneous substrate distribution induces enzyme fluxes through substrate-enzyme interactions. We find that condensates move toward the center of a confining domain when this feedback is weak. Above a feedback threshold, they exhibit self-propulsion, leading to oscillatory dynamics. Moreover, catalysis-driven enzyme fluxes can lead to interrupted coarsening, resulting in equidistant condensate positioning, and to condensate division.
2021
3.
Beatrice Ramm; Andriy Goychuk; Alena Khmelinskaia; Philipp Blumhardt; Hiromune Eto; Kristina A. Ganzinger; Erwin Frey; Petra Schwille
A diffusiophoretic mechanism for ATP-driven transport without motor proteins Journal Article
In: Nature Physics, vol. 17, no. 7, pp. 850–858, 2021, ISSN: 1745-2473, 1745-2481.
Abstract | Links | BibTeX | Tags: Analytical Theory, Diffusiophoresis, Nonequilibrium Dynamics, Pattern Formation, Transport
@article{ramm_diffusiophoretic_2021,
title = {A diffusiophoretic mechanism for ATP-driven transport without motor proteins},
author = {Beatrice Ramm and Andriy Goychuk and Alena Khmelinskaia and Philipp Blumhardt and Hiromune Eto and Kristina A. Ganzinger and Erwin Frey and Petra Schwille},
url = {https://www.nature.com/articles/s41567-021-01213-3},
doi = {10.1038/s41567-021-01213-3},
issn = {1745-2473, 1745-2481},
year = {2021},
date = {2021-07-01},
urldate = {2026-05-29},
journal = {Nature Physics},
volume = {17},
number = {7},
pages = {850–858},
abstract = {The healthy growth and maintenance of a biological system depends on the precise spatial organization of molecules within the cell through the dissipation of energy. Reaction–diffusion mechanisms can facilitate this organization, as can directional cargo transport orchestrated by motor proteins, by relying on specific protein interactions. However, transport of material through the cell can also be achieved by active processes based on non-specific, purely physical mechanisms, a phenomenon that remains poorly explored. Here, using a combined experimental and theoretical approach, we discover and describe a hidden function of the Escherichia coli MinDE protein system: in addition to forming dynamic patterns, this system accomplishes the directional active transport of functionally unrelated cargo on membranes. Remarkably, this mechanism enables the sorting of diffusive objects according to their effective size, as evidenced using modular DNA origami–streptavidin nanostructures. We show that the diffusive fluxes of MinDE and non-specific cargo couple via density-dependent friction. This non-specific process constitutes a diffusiophoretic mechanism, as yet unknown in a cell biology setting. This nonlinear coupling between diffusive fluxes could represent a generic physical mechanism for establishing intracellular organization.},
keywords = {Analytical Theory, Diffusiophoresis, Nonequilibrium Dynamics, Pattern Formation, Transport},
pubstate = {published},
tppubtype = {article}
}
The healthy growth and maintenance of a biological system depends on the precise spatial organization of molecules within the cell through the dissipation of energy. Reaction–diffusion mechanisms can facilitate this organization, as can directional cargo transport orchestrated by motor proteins, by relying on specific protein interactions. However, transport of material through the cell can also be achieved by active processes based on non-specific, purely physical mechanisms, a phenomenon that remains poorly explored. Here, using a combined experimental and theoretical approach, we discover and describe a hidden function of the Escherichia coli MinDE protein system: in addition to forming dynamic patterns, this system accomplishes the directional active transport of functionally unrelated cargo on membranes. Remarkably, this mechanism enables the sorting of diffusive objects according to their effective size, as evidenced using modular DNA origami–streptavidin nanostructures. We show that the diffusive fluxes of MinDE and non-specific cargo couple via density-dependent friction. This non-specific process constitutes a diffusiophoretic mechanism, as yet unknown in a cell biology setting. This nonlinear coupling between diffusive fluxes could represent a generic physical mechanism for establishing intracellular organization.
2020
2.
Daniel Rüdiger; Kerstin Kick; Andriy Goychuk; Angelika M. Vollmar; Erwin Frey; Stefan Zahler
Cell-Based Strain Remodeling of a Nonfibrous Matrix as an Organizing Principle for Vasculogenesis Journal Article
In: Cell Reports, vol. 32, no. 6, pp. 108015, 2020, ISSN: 22111247.
Abstract | Links | BibTeX | Tags: Angiogenesis, Endothelial, Matrigel, Pattern Formation, Strain-Stiffening
@article{rudiger_cell-based_2020,
title = {Cell-Based Strain Remodeling of a Nonfibrous Matrix as an Organizing Principle for Vasculogenesis},
author = {Daniel Rüdiger and Kerstin Kick and Andriy Goychuk and Angelika M. Vollmar and Erwin Frey and Stefan Zahler},
url = {https://linkinghub.elsevier.com/retrieve/pii/S2211124720310007},
doi = {10.1016/j.celrep.2020.108015},
issn = {22111247},
year = {2020},
date = {2020-08-01},
urldate = {2026-05-29},
journal = {Cell Reports},
volume = {32},
number = {6},
pages = {108015},
abstract = {Endothelial tube formation on a reconstituted basement membrane (Matrigel) is a well-established in vitro model for studying the processes of angiogenesis and vasculogenesis. However, to date, the organizing principles that underlie the morphogenesis of this network and that shape the initial process of cells’ finding one another remain elusive. Here, we identify a mechanism that allows cells to form networks by mechanically reorganizing and stiffening their extracellular matrix, independent of chemical guidance cues. Interestingly, we find that this cellular self-organization strongly depends on the connectivity, plasticity, and topology of the surrounding matrix; cell contractility; and cell density. Cells rearrange the matrix and form bridges of matrix material that are stiffer than their surroundings, thus creating a durotactic track for the initiation of cell protrusions and cell-cell contacts. This contractility-based communication via strain stiffening and matrix rearrangement might be a general organizing principle during tissue development or regeneration.},
keywords = {Angiogenesis, Endothelial, Matrigel, Pattern Formation, Strain-Stiffening},
pubstate = {published},
tppubtype = {article}
}
Endothelial tube formation on a reconstituted basement membrane (Matrigel) is a well-established in vitro model for studying the processes of angiogenesis and vasculogenesis. However, to date, the organizing principles that underlie the morphogenesis of this network and that shape the initial process of cells’ finding one another remain elusive. Here, we identify a mechanism that allows cells to form networks by mechanically reorganizing and stiffening their extracellular matrix, independent of chemical guidance cues. Interestingly, we find that this cellular self-organization strongly depends on the connectivity, plasticity, and topology of the surrounding matrix; cell contractility; and cell density. Cells rearrange the matrix and form bridges of matrix material that are stiffer than their surroundings, thus creating a durotactic track for the initiation of cell protrusions and cell-cell contacts. This contractility-based communication via strain stiffening and matrix rearrangement might be a general organizing principle during tissue development or regeneration.
2019
1.
Andriy Goychuk; Erwin Frey
Protein Recruitment through Indirect Mechanochemical Interactions Journal Article
In: Physical Review Letters, vol. 123, no. 17, pp. 178101, 2019, ISSN: 0031-9007, 1079-7114.
Abstract | Links | BibTeX | Tags: Analytical Theory, Biomolecular Self-Assembly, Elastic Deformation, First Passage Problems, Mean Field Theory, Pattern Formation, Protein-Membrane Interactions, Protein-Protein Interactions
@article{goychuk_protein_2019,
title = {Protein Recruitment through Indirect Mechanochemical Interactions},
author = {Andriy Goychuk and Erwin Frey},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.123.178101},
doi = {10.1103/PhysRevLett.123.178101},
issn = {0031-9007, 1079-7114},
year = {2019},
date = {2019-10-01},
urldate = {2026-05-29},
journal = {Physical Review Letters},
volume = {123},
number = {17},
pages = {178101},
abstract = {Some of the key proteins essential for important cellular processes are capable of recruiting other proteins from the cytosol to phospholipid membranes. The physical basis for this cooperativity of binding is, surprisingly, still unclear. Here, we suggest a general feedback mechanism that explains cooperativity through mechanochemical coupling mediated by the mechanical properties of phospholipid membranes. Our theory predicts that protein recruitment, and therefore also protein pattern formation, involves membrane deformation and is strongly affected by membrane composition.},
keywords = {Analytical Theory, Biomolecular Self-Assembly, Elastic Deformation, First Passage Problems, Mean Field Theory, Pattern Formation, Protein-Membrane Interactions, Protein-Protein Interactions},
pubstate = {published},
tppubtype = {article}
}
Some of the key proteins essential for important cellular processes are capable of recruiting other proteins from the cytosol to phospholipid membranes. The physical basis for this cooperativity of binding is, surprisingly, still unclear. Here, we suggest a general feedback mechanism that explains cooperativity through mechanochemical coupling mediated by the mechanical properties of phospholipid membranes. Our theory predicts that protein recruitment, and therefore also protein pattern formation, involves membrane deformation and is strongly affected by membrane composition.