Erwin Frey

Ludwig-Maximilians-Universität in Munich | LMU · Department of Physics

Emergent cooperative functionality in active matter systems plays a crucial role in various applications of active swarms, ranging from pollutant foraging and collective threat detection to tissue embolization. In nature, animals like bats and whales use acoustic signals to communicate and enhance their evolutionary competitiveness. Here, we show t...

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...

Auto-chemotaxis, the directed movement of cells along gradients in chemicals they secrete, is central to the formation of complex spatiotemporal patterns in biological systems. Since the introduction of the Keller-Segel model, numerous variants have been analyzed, revealing phenomena such as coarsening of aggregates, stable aggregate sizes, and spa...

For cellular functions like 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. We discover a generic mechanism giving rise to an effective interfacial...

Chemotaxis allows single cells to self-organize at the population level, as classically described by Keller-Segel models. We show that chemotactic aggregation can be understood using a generalized Maxwell construction based on the balance of density fluxes and reactive turnover. This formulation implies that aggregates generically undergo coarsenin...

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. Recent studies demonstrat...

The self-organization of proteins into enriched compartments and the formation of complex patterns are crucial processes for life on the cellular level. Liquid-liquid phase separation is one mechanism for forming such enriched compartments. When phase-separating proteins are membrane-bound and locally disturb it, the mechanical response of the memb...

The general epidemic process (GEP), also known as susceptible-infected-recovered model, provides a minimal model of how an epidemic spreads within a population of susceptible individuals who acquire permanent immunization upon recovery. This model exhibits a second-order absorbing state phase transition, commonly studied assuming immobile healthy i...

Chemo-mechanical waves on active deformable surfaces are a key component for many vital cellular functions. In particular, these waves play a major role in force generation and long-range signal transmission in cells that dynamically change shape, as encountered during cell division or morphogenesis. Reconstituting and controlling such chemically c...

Active matter systems evade the constraints of thermal equilibrium, leading to the emergence of intriguing collective behavior. A paradigmatic example is given by motor-filament mixtures, where the motion of motor proteins drives alignment and sliding interactions between filaments and their self-organization into macroscopic structures. After defi...

We address how the interplay between the finite availability and carrying capacity of particles at different parts of a spatially extended system can control the steady state currents and density profiles in the one-dimensional current-carrying lanes connecting the different parts of the system. To study this, we set up a minimal model consisting o...

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. Th...

The synthesis of life from non-living matter has captivated scientists for centuries. It is a grand challenge aimed at unraveling the fundamental principles of life and leveraging its unique features, such as resilience, sustainability, and the ability to evolve. Synthetic life holds immense potential in biotechnology, medicine, and materials scien...

Self-assembly is a fundamental concept in biology and of significant interest to nanotechnology. Significant progress has been made in characterizing and controlling the properties of the resulting structures, both experimentally and theoretically. However, much less is known about kinetic constraints and determinants of dynamical properties like t...

Active matter systems evade the constraints of thermal equilibrium, leading to the emergence of intriguing collective behavior. A paradigmatic example is given by motor-filament mixtures, where the motion of motor proteins drives alignment and sliding interactions between filaments and their self-organization into macroscopic structures. After defi...

The general epidemic process (GEP), also known as susceptible-infected-recovered model (SIR), describes how an epidemic spreads within a population of susceptible individuals who acquire permanent immunization upon recovery. This model exhibits a second-order absorbing state phase transition, commonly studied assuming immobile healthy individuals....

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. Th...

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-selecti...

In this in silico study, we show that phase-separated active nematics form −1/2 defects, contrary to the current paradigm. We also observe and characterize lateral arc-like structures separating from nematic bands and moving in transverse direction.

How can a self-organized cellular function evolve, adapt to perturbations, and acquire new sub-functions? To make progress in answering these basic questions of evolutionary cell biology, we analyze, as a concrete example, the cell polarity machinery of Saccharomyces cerevisiae . This cellular module exhibits an intriguing resilience: it remains op...

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 ho...

While the role of local interactions in nonequilibrium phase transitions is well studied, a fundamental understanding of the effects of long-range interactions is lacking. We study the critical dynamics of reproducing agents subject to autochemotactic interactions and limited resources. A renormalization group analysis reveals distinct scaling regi...

The Min system in Escherichia coli plays a crucial role in cellular reproduction by preventing minicell formation through pole-to-pole oscillations. Despite extensive research, predicting the onset of Min protein concentrations for oscillation and understanding the system’s robustness under physiological perturbations remains challenging. Our study...

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. In thi...

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...

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...

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 feedb...

The Min proteins constitute the best-studied model system for pattern formation in cell biology. We theoretically predict and experimentally show that the propagation direction of in vitro Min protein patterns can be controlled by a hydrodynamic flow of the bulk solution. We find downstream propagation of Min wave patterns for low MinE:MinD concent...

Enzyme-enriched condensates can organize the spatial distribution of their substrates by catalyzing non-equilibrium reactions. Conversely, an inhomogeneous substrate distribution induces enzyme fluxes through substrate-enzyme interactions. We find that condensates move towards the center of a confining domain when this feedback is weak. Above a fee...

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...

Cytoskeletal networks form complex intracellular structures. Here we investigate a minimal model for filament-motor mixtures in which motors act as depolymerases and thereby regulate filament length. Combining agent-based simulations and hydrodynamic equations, we show that resource-limited length regulation drives the formation of filament cluster...

The emergence of collective motion among interacting, self-propelled agents is a central paradigm in non-equilibrium physics. Examples of such active matter range from swimming bacteria and cytoskeletal motility assays to synthetic self-propelled colloids and swarming microrobots. Remarkably, the aggregation capabilities of many of these systems re...

Active matter encompasses systems whose individual constituents irreversibly dissipate energy to exert self-propelling forces on their environment. From molecular motors to bacteria, from crawling cells to large animals, active entities are found at all scales in the biological world. Over the past twenty years, scientists have managed to engineer...

For the emergence of life, the abiotic synthesis of RNA from its monomers is a central step. We found that in alkaline, drying conditions in bulk and at heated air‐water interfaces, 2′,3′‐cyclic nucleotides oligomerised without additional catalyst, forming up to 10‐mers within a day. The oligomerisation proceeded at a pH range of 7–12, at temperatu...

While the role of local interactions in nonequilibrium phase transitions is well studied, a fundamental understanding of the effects of long-range interactions is lacking. We study the critical dynamics of reproducing agents subject to auto-chemotactic interactions and limited resources. A renormalization group analysis reveals distinct scaling reg...

Self-organized pattern formation is vital for many biological processes. Reaction–diffusion models have advanced our understanding of how biological systems develop spatial structures, starting from homogeneity. However, biological processes inherently involve multiple spatial and temporal scales and transition from one pattern to another over time...

The emergence of collective motion among interacting, self-propelled agents is a central paradigm in non-equilibrium physics. Examples of such active matter range from swimming bacteria and cytoskeletal motility assays to synthetic self-propelled colloids and swarming microrobots. Remarkably, the aggregation capabilities of many of these systems re...

For the emergence of life, the abiotic synthesis of RNA from its monomers is a central step. We found alkaline, uncatalysed drying conditions in bulk and at heated air-water interfaces where 2´,3´-cyclic nucleotides polymerised, forming up to 10-mers within a day. The polymerisation proceeded at a pH range of 7-12 at temperatures between 40-80 °C a...

Proteins control many vital functions in living cells, such as cell growth and cell division. Reliable coordination of these functions requires the spatial and temporal organization of proteins inside cells, which encodes information about the cell’s geometry and the cell-cycle stage. The study of such protein patterns has long focused around forma...

Intracellular protein patterns regulate a variety of vital cellular processes such as cell division and motility, which often involve dynamic changes of cell shape. 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 seve...

For the emergence of life, the abiotic synthesis of RNA from its monomers is a central challenge. We found alkaline drying conditions in bulk and at heated air-water interfaces where 2 ́,3 ́-cyclic nucleotides reacted to form copolymers up to 10-mers. The polymerisation proceeded at a pH range of 7-12, temperatures between 40-80 °C and was enhanced...

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 wavelength-selection dynamic...

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 ho...

The diffusive epidemic process is a paradigmatic example of an absorbing state phase transition in which healthy and infected individuals spread with different diffusion constants. Using stochastic activity spreading simulations in combination with finite-size scaling analyses we reveal two qualitatively different processes that characterize the cr...

Proteins control many vital functions in living cells, such as cell growth and cell division. Reliable coordination of these functions requires the spatial and temporal organizaton of proteins inside cells, which encodes information about the cell's geometry and the cell-cycle stage. Such protein patterns arise from protein transport and reaction k...

Significance An important limiting factor for self-assembly processes is the time it takes to assemble large structures with high yield. While equilibrium self-assembly systems slowly relax toward a state of minimal free energy, nonequilibrium systems offer various ways to control assembly processes and to optimize their time efficiency. We show th...

We theoretically predict and experimentally show that the propagation direction of in vitro Min protein patterns can be controlled by a hydrodynamic flow of the bulk solution. We find downstream propagation of Min wave patterns relative to the bulk flow direction for low MinE:MinD concentration ratios, but upstream propagation for large MinE:MinD r...

Programmable nano-bio interfaces driven by tuneable vertically configured nanostructures have recently emerged as a powerful tool for cellular manipulations and interrogations. Such interfaces have strong potential for ground-breaking advances, particularly in cellular nanobiotechnology and mechanobiology. However, the opaque nature of many nanostr...

Self-organized pattern formation is vital for many biological processes. Mathematical modeling using reaction-diffusion models has advanced our understanding of how biological systems develop spatial structures, starting from homogeneity. However, biological processes inherently involve multiple spatial and temporal scales and transition from one p...

Evolutionary games between species are known to lead to intriguing spatiotemporal patterns in systems of diffusing agents. However, the role of interspecies interactions is hardly studied when agents are (self-)propelled, as is the case in many biological systems. Here, we combine aspects from active matter and evolutionary game theory and study a...

Organ development involves complex shape transformations driven by active mechanical stresses that sculpt the growing tissue1,2. Epithelial gland morphogenesis is a prominent example where cylindrical branches transform into spherical alveoli during growth3–5. Here we show that this shape transformation is induced by a local change from anisotropic...

The spatiotemporal organization of bacterial cells is crucial for the active segregation of replicating chromosomes. In several species, including Caulobacter crescentus, the ATPase ParA binds to DNA and forms a gradient along the long cell axis. The ParB partition complex on the newly replicated chromosome translocates up this ParA gradient, there...

Cytoskeletal networks form complex intracellular structures. Here we investigate a minimal model for filament-motor mixtures in which motors act as depolymerases and thereby regulate filament length. Combining agent-based simulations and hydrodynamic equations, we show that resource-limited length regulation drives the formation of filament cluster...

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,...

Self-organisation of Min proteins is responsible for the spatial control of cell division in Escherichia coli , and has been studied both in vivo and in vitro. Intriguingly, the protein patterns observed in these settings differ qualitatively and quantitatively. This puzzling dichotomy has not been resolved to date. Using reconstituted proteins in...

The diffusive epidemic process is a paradigmatic example of an absorbing state phase transition in which healthy and infected individuals spread with different diffusion constants. Using stochastic activity spreading simulations in combination with finite-size scaling analyses we reveal two qualitatively different processes that characterize the cr...

Many cellular processes, such as cell division1–3, 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. Recent experimental and...

Evolutionary games between species are known to lead to intriguing spatio-temporal patterns in systems of diffusing agent. However, the role of inter-species interactions is hardly studied when agents are (self-)propelled, as is the case in many biological systems. Here, we combine aspects from active-matter and evolutionary game theory and study a...

Division site selection is a vital process to ensure generation of viable offspring. In many rod-shaped bacteria, a dynamic protein system, termed the Min system, acts as a central regulator of division site placement. The Min system is best studied in Escherichia coli, where it shows a remarkable oscillation from pole to pole with a time-averaged...

Time efficiency of self-assembly is crucial for many biological processes. Moreover, with the advances of nanotechnology, time efficiency in artificial self-assembly becomes ever more important. While structural determinants and the final assembly yield are increasingly well understood, kinetic aspects concerning the time efficiency, however, remai...