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Articles by Erwin Frey
Protein pattern morphology and dynamics emerging from effective interfacial tension - Nature Physics
Abstract For cellular functions such as division and polarization, protein pattern formation driven by NTPase cycles is a central spatial control strategy. Operating far from equilibrium, no general theory links microscopic reaction networks and parameters to the pattern type and dynamics in these protein systems. Here we discover a generic mechanism giving rise to an effective interfacial tension organizing the macroscopic structure of non-equilibrium steady-state patterns.
Robust and resource-optimal dynamic pattern formation of Min proteins in vivo - Nature Physics
Abstract The Min protein system prevents abnormal cell division in bacteria by forming oscillatory patterns between cell poles. However, predicting the protein concentrations at which oscillations start and whether cells can maintain them under physiological perturbations remains challenging. Here we show that dynamic pattern formation is robust across a wide range of Min protein levels and variations in the growth physiology using genetically engineered Escherichia coli strains.
Light-induced cortical excitability reveals programmable shape dynamics in starfish oocytes - Nature Physics
Abstract Chemo-mechanical waves play a key role in force generation and long-range signal transmission in cells that dynamically change shape, for example, during cell division or morphogenesis. Reconstituting and controlling such chemically controlled cell deformations is a crucial but unsolved challenge for the development of synthetic cells.
Basic interactions responsible for thymus function explain convoluted medulla shape
Abstract The thymus is one of the most important organs of the immune system. It is responsible for both the production of T cells and the prevention of their autoimmunity. It comprises two types of tissue: the cortex, where nascent T cells (thymocytes) are generated; and the medulla, embedded within the cortex, where autoreactive thymocytes are eliminated through negative selection.
Dimensionality reduction in bulk-boundary reaction-diffusion systems
Intracellular protein patterns regulate many vital cellular functions, such as the processing of spatiotemporal information or the control of shape deformations. To do so, pattern-forming systems can be sensitive to the cell geometry by means of coupling the protein dynamics on the cell membrane to dynamics in the cytosol.
Supramolecular Assemblies in Active Motor-Filament Systems: Micelles, Bilayers, and Foams
Popular Summary Active matter systems, in which individual elements evade thermal equilibrium by consuming energy at a local scale, can self-organize into large-scale patterns. A fundamental question in the field is to understand how the interactions between individual constituents are linked to the collective behavior of the system. Here, we consider mixtures of active filaments (such as microtubules) and motor proteins.
Design Principles for Fast and Efficient Self-Assembly Processes
synopsis Shape Matters in Self-Assembly Published 3 April 2024 A theoretical study of self-assembly finds that hexagon-shaped building blocks can form large structures faster than triangular or square blocks. See more in Physics Click to Expand Popular Summary In biology and nanotechnology, tiny building blocks can quickly and robustly come together to form complex structures.
Coarsening and wavelength selection far from equilibrium: A unifying framework based on singular perturbation theory
Intracellular protein patterns are described by (nearly) mass-conserving reaction–diffusion systems. While these patterns initially form out of a homogeneous steady state due to the well-understood Turing instability, no general theory exists for the dynamics of fully nonlinear patterns. We develop a unifying theory for nonlinear wavelength-selection dynamics in (nearly) mass-conserving two-component reaction–diffusion systems independent of the specific mathematical model chosen.
Periodic temporal environmental variations induce coexistence in resource competition models
Natural ecosystems, in particular on the microbial scale, are inhabited by a large number of species. The population size of each species is affected by interactions of individuals with each other and by spatial and temporal changes in environmental conditions, such as resource abundance. Here, we use a generic population dynamics model to study how, and under what conditions, a periodic temporal environmental variation can alter an ecosystem's composition and biodiversity.
Hierarchical defect-induced condensation in active nematics
Hierarchical defect-induced condensation in active nematics† Topological defects play a central role in the formation and organization of various biological systems. Historically, such nonequilibrium defects have been mainly studied in the context of homogeneous active nematics. Phase-separated systems, in turn, are known to form dense and dynamic nematic bands, but typically lack topological defects.
Geometry-induced patterns through mechanochemical coupling
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.
Mechanochemical feedback loop drives persistent motion of liposomes - Nature Physics
Abstract Achieving autonomous motion is a central objective in designing artificial cells that mimic biological cells in form and function. Cellular motion often involves complex multiprotein machineries, which are challenging to reconstitute in vitro. Here we achieve persistent motion of cell-sized liposomes. These small artificial vesicles are driven by a direct mechanochemical feedback loop between the MinD and MinE protein systems of Escherichia coli and the liposome membrane.
Polarity and chirality control of an active fluid by passive nematic defects - Nature Materials
Abstract Much like passive materials, active systems can be affected by the presence of imperfections in their microscopic order, called defects, that influence macroscopic properties. This suggests the possibility to steer collective patterns by introducing and controlling defects in an active system. Here we show that a self-assembled, passive nematic is ideally suited to control the pattern formation process of an active fluid.
A hierarchy of protein patterns robustly decodes cell shape information
Abstract Many cellular processes, such as cell division1,2,3, cell motility4, wound healing5 and tissue folding6,7, rely on the precise positioning of proteins on the membrane. Such protein patterns emerge from a combination of protein interactions, transport, conformational state changes and chemical reactions at the molecular level8.
Topological Phase Transition in Coupled Rock-Paper-Scissors Cycles
Abstract A hallmark of topological phases is the occurrence of topologically protected modes at the system’s boundary. Here, we find topological phases in the antisymmetric Lotka-Volterra equation (ALVE). The ALVE is a nonlinear dynamical system and describes, for example, the evolutionary dynamics of a rock-paper-scissors cycle. On a one-dimensional chain of rock-paper-scissor cycles, topological phases become manifest as robust polarization states.
Pattern-induced local symmetry breaking in active-matter systems
Significance Propelled agents that align their orientations upon collisions can give rise to macroscopic order. Depending on the details of the agents’ collisions, this ordering process can lead to spatiotemporal patterns, including traveling polar waves and nematic lanes. Recent experiments suggest that such patterns can also coexist and dynamically interconvert. Here we propose a general mechanism for such a phenomenology, which is based on patterned-induced local symmetry breaking.
Geometric cues stabilise long-axis polarisation of PAR protein patterns in C. elegans
Abstract In the Caenorhabditis elegans zygote, PAR protein patterns, driven by mutual anatagonism, determine the anterior-posterior axis and facilitate the redistribution of proteins for the first cell division. Yet, the factors that determine the selection of the polarity axis remain unclear. We present a reaction-diffusion model in realistic cell geometry, based on biomolecular reactions and accounting for the coupling between membrane and cytosolic dynamics.
A mechanistic view of collective filament motion in active nematic networks
Moritz Striebel † Author Footnotes † M.S. and I.R.G. contributed equally to this work. Moritz Striebel Footnotes † M.S. and I.R.G. contributed equally to this work. Affiliations Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, München, Germany Search for articles by this author Isabella R. Graf † Author Footnotes † M.S. and I.R.G. contributed equally to this work. Isabella R.
Evolutionary games of condensates in coupled birth-death processes
Abstract Condensation phenomena arise through a collective behaviour of particles. They are observed in both classical and quantum systems, ranging from the formation of traffic jams in mass transport models to the macroscopic occupation of the energetic ground state in ultra-cold bosonic gases (Bose–Einstein condensation). Recently, it has been shown that a driven and dissipative system of bosons may form multiple condensates.
Can a flux-based mechanism explain protein cluster positioning in a three-dimensional cell geometry?
Matthias Kober 2 Author Footnotes 2 These two authors contributed equally Matthias Kober Footnotes 2 These two authors contributed equally Affiliations Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, Theresienstraße 37, D-80333 Munich, Germany Search for articles by this author Silke Bergeler 2 Author Footnotes 2 These two authors contributed equally Silke Bergeler Footnotes 2 These two authors...
Crowding and pausing strongly affect dynamics of kinesin-1 motors along microtubules
Molecular motors of the kinesin-1 family move in a directed and processive fashion along microtubules (MTs). It is generally accepted that steric hindrance of motors leads to crowding effects; however, little is known about the specific interactions involved. We employ an agent-based lattice gas model to study the impact of interactions which enhance the detachment of motors from crowded filaments on their collective dynamics.
Disentangling entanglements in biopolymer solutions
To learn how the polymers first entangle and then disentangle, i.e., how topological constraints emerge and are released, we studied the dynamics of individual (tracer) polymers in an entangled polymer solution; see Supplementary Movie 1.
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