arXiv subjects

Erwin Frey

Publications and source records attributed to Erwin Frey.

At least 91 records · Page 5Linked to original sources

arXiv2016

Active Curved Polymers form Vortex Patterns on Membranes

Recent in vitro experiments with FtsZ polymers show self-organization into different dynamic patterns, including structures reminiscent of the bacterial Z-ring. We model FtsZ polymers as active particles moving along chiral, circular paths by Brownian dynamics simulations and a Boltzmann approach. Our two conceptually different methods point to a generic phase behavior. At intermediate particle densities, we find self-organization into vortex structures including closed rings. Moreover, we show that the dynamics at the onset of pattern formation is described by a generalized complex Ginzburg-Landau equation.

cond-mat.soft↗

arXiv2016

Binary Mixtures of Particles with Different Diffusivities Demix

The influence of size differences, shape, mass and persistent motion on phase separation in binary mixtures has been intensively studied. Here we focus on the exclusive role of diffusivity differences in binary mixtures of equal-sized particles. We find an effective attraction between the less diffusive particles, which are essentially caged in the surrounding species with the higher diffusion constant. This effect leads to phase separation for systems above a critical size: A single close-packed cluster made up of the less diffusive species emerges. Experiments for testing of our predictions are outlined.

cond-mat.soft↗

arXiv2015

Non-selective evolution of growing populations

Non-selective effects, like genetic drift, are an important factor in modern conceptions of evolution, and have been extensively studied for constant population sizes. Here, we consider non-selective evolution in the case of growing populations that are of small size and have varying trait compositions (e.g. after a population bottleneck). We find that, in these conditions, populations never fixate to a trait, but tend to a random limit composition, and that the distribution of compositions 'freezes' to a steady state This final state is crucially influenced by the initial conditions. We obtain these findings from a combined theoretical and experimental approach, using multiple mixed subpopulations of two Pseudomonas putida strains in non-selective growth conditions as model system. The experimental results for the population dynamics match the theoretical predictions based on the Pólya urn model for all analyzed parameter regimes. In summary, we show that exponential growth stops genetic drift. This result contrasts with previous theoretical analyses of non-selective evolution (e.g. genetic drift), which investigated how traits spread and eventually take over populations (fixate). Moreover, our work highlights how deeply growth influences non-selective evolution, and how it plays a key role in maintaining genetic variability. Consequently, it is of particular importance in life-cycles models of periodically shrinking and expanding populations.

q-bio.PE↗

arXiv2015

The Emergence of Cooperation from a Single Mutant during Microbial Life-Cycles

Cooperative behavior is widespread in nature, even though cooperating individuals always run the risk to be exploited by free-riders. Population structure effectively promotes cooperation given that a threshold in the level of cooperation was already reached. However, the question how cooperation can emerge from a single mutant, which cannot rely on a benefit provided by other cooperators, is still puzzling. Here, we investigate this question for a well-defined but generic situation based on typical life-cycles of microbial populations where individuals regularly form new colonies followed by growth phases. We analyze two evolutionary mechanisms favoring cooperative behavior and study their strength depending on the inoculation size and the length of a life-cycle. In particular, we find that population bottlenecks followed by exponential growth phases strongly increase the survival and fixation probabilities of a single cooperator in a free-riding population.

q-bio.PE↗

arXiv2015

Emergence and Persistence of Collective Cell Migration on Small Circular Micropatterns

The spontaneous formation of vortices is a hallmark of collective cellular activity. Here, we study the onset and persistence of coherent angular motion (CAMo) as a function of the number of cells $N$ confined in circular micropatterns. We find that the persistence of CAMo increases with $N$ but exhibits a pronounced discontinuity accompanied by a geometric rearrangement of cells to a configuration containing a central cell. Computer simulations based on a generalized Potts model reproduce the emergence of vortex states and show in agreement with experiment that their stability depends on the interplay of spatial arrangement and internal polarization of neighboring cells. Hence, the distinct migrational states in finite size ensembles reveal significant insight into the local interaction rules guiding collective migration.

physics.bio-ph↗

arXiv2015

Traffic Dynamic Instability

Here we study a driven lattice gas model for microtubule depolymerizing molecular motors, where traffic jams of motors induce stochastic switching between microtubule growth and shrinkage. We term this phenomenon \enquote{traffic dynamic instability} because it is reminiscent of microtubule dynamic instability [T. Mitchison and M. Kirschner, Nature 312, 237 (1984)]. The intermittent dynamics of growth and shrinking emerges from the interplay between the arrival of motors at the microtubule tip, motor induced depolymerization, and motor detachment from the tip. The switching dynamics correlates with low and high motor density on the lattice. This leads to an effectively bistable particle density in the system. A refined domain wall theory predicts this transient appearance of different phases in the system. The theoretical results are supported by stochastic simulations.

cond-mat.stat-mech↗

arXiv2015

Evolutionary games of condensates in coupled birth-death processes

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. Which states become the condensates has, however, remained elusive thus far. The dynamics of this condensation are described by coupled birth-death processes, which also occur in evolutionary game theory. Here, we apply concepts from evolutionary game theory to explain the formation of multiple condensates in such driven-dissipative bosonic systems. We show that vanishing of relative entropy production determines their selection. The condensation proceeds exponentially fast, but the system never comes to rest. Instead, the occupation numbers of condensates may oscillate, as we demonstrate for a rock-paper-scissors game of condensates.

cond-mat.stat-mech↗

arXiv2015

How turbulence regulates biodiversity in systems with cyclic competition

Cyclic, nonhierarchical interactions among biological species represent a general mechanism by which ecosystems are able to maintain high levels of biodiversity. However, species coexistence is often possible only in spatially extended systems with a limited range of dispersal, whereas in well-mixed environments models for cyclic competition often lead to a loss of biodiversity. Here we consider the dispersal of biological species in a fluid environment, where mixing is achieved by a combination of advection and diffusion. In particular, we perform a detailed numerical analysis of a model composed of turbulent advection, diffusive transport, and cyclic interactions among biological species in two spatial dimensions and discuss the circumstances under which biodiversity is maintained when external environmental conditions, such as resource supply, are uniform in space. Cyclic interactions are represented by a model with three competitors, resembling the children's game of rock-paper-scissors, whereas the flow field is obtained from a direct numerical simulation of two-dimensional turbulence with hyperviscosity. It is shown that the space-averaged dynamics undergoes bifurcations as the relative strengths of advection and diffusion compared to biological interactions are varied.

q-bio.PE↗

arXiv2015

Quantifying protein diffusion and capture on filaments

The functional relevance of regulating proteins is often limited to specific binding sites such as the ends of microtubules or actin-filaments. A localization of proteins on these functional sites is of great importance. We present a quantitative theory for a diffusion and capture process, where proteins diffuse on a filament and stop diffusing when reaching the filament's end. It is found that end-association after one-dimensional diffusion is the main source for tip-localization of such proteins. As a consequence, diffusion and capture is highly efficient in enhancing the reaction velocity of enzymatic reactions, where proteins and filament ends are to each other as enzyme and substrate. We show that the reaction velocity can effectively be described within a Michaelis-Menten framework. Together one-dimensional diffusion and capture beats the (three-dimensional) Smoluchowski diffusion limit for the rate of protein association to filament ends.

physics.bio-ph↗

arXiv2014

Numerical treatment of the Boltzmann equation for self-propelled particle systems

Kinetic theories constitute one of the most promising tools to decipher the characteristic spatio-temporal dynamics in systems of actively propelled particles. In this context, the Boltzmann equation plays a pivotal role, since it provides a natural translation between a particle-level description of the system's dynamics and the corresponding hydrodynamic fields. Yet, the intricate mathematical structure of the Boltzmann equation substantially limits the progress toward a full understanding of this equation by solely analytical means. Here, we propose a general framework to numerically solve the Boltzmann equation for self-propelled particle systems in two spatial dimensions and with arbitrary boundary conditions. We discuss potential applications of this numerical framework to active matter systems, and use the algorithm to give a detailed analysis to a model system of self-propelled particles with polar interactions. In accordance with previous studies, we find that spatially homogeneous isotropic and broken symmetry states populate two distinct regions in parameter space, which are separated by a narrow region of spatially inhomogeneous, density-segregated moving patterns. We find clear evidence that these three regions in parameter space are connected by first order phase transitions, and that the transition between the spatially homogeneous isotropic and polar ordered phases bears striking similarities to liquid-gas phase transitions in equilibrium systems. Within the density segregated parameter regime, we find a novel stable limit-cycle solution of the Boltzmann equation, which consists of parallel lanes of polar clusters moving in opposite directions, so as to render the overall symmetry of the system's ordered state nematic, despite purely polar interactions on the level of single particles.

cond-mat.soft↗

arXiv2014

Periodic vs. intermittent adaptive cycles in quasispecies co-evolution

We study an abstract model for the co-evolution between mutating viruses and the adaptive immune system. In sequence space, these two populations are localized around transiently dominant strains. Delocalization or error thresholds exhibit a novel interdependence because immune response is conditional on the viral attack. An evolutionary chase is induced by stochastic fluctuations and can occur via periodic or intermittent cycles. Using simulations and stochastic analysis, we show how the transition between these two dynamic regimes depends on mutation rate, immune response, and population size.

q-bio.PE↗

arXiv2014

Specialization and Bet Hedging in Heterogeneous Populations

Phenotypic heterogeneity is a strategy commonly used by bacteria to rapidly adapt to changing environmental conditions. Here, we study the interplay between phenotypic heterogeneity and genetic diversity in spatially extended populations. By analyzing the spatio-temporal dynamics, we show that the level of mobility and the type of competition qualitatively influence the persistence of phenotypic heterogeneity. While direct competition generally promotes persistence of phenotypic heterogeneity, specialization dominates in models with indirect competition irrespective of the degree of mobility.

q-bio.PE↗

arXiv2014

Range Expansion of Heterogeneous Populations

Risk spreading in bacterial populations is generally regarded as a strategy to maximize survival. Here, we study its role during range expansion of a genetically diverse population where growth and motility are two alternative traits. We find that during the initial expansion phase fast growing cells do have a selective advantage. By contrast, asymptotically, generalists balancing motility and reproduction are evolutionarily most successful. These findings are rationalized by a set of coupled Fisher equations complemented by stochastic simulations.

q-bio.PE↗

arXiv2014

Molecular Mechanisms for Microtubule Length Regulation by Kinesin-8 and XMAP215 Proteins

The cytoskeleton is regulated by a plethora of enzymes that influence the stability and dynamics of cytoskeletal filaments. Molecular motors of the kinesin-8 protein family depolymerise microtubules in a length-dependent manner, and experimental and theoretical evidence suggest a role for kinesin-8 in the dynamic regulation of microtubules. However, so far the detailed molecular mechanisms how these molecular motors interact with the growing microtubule tip remain elusive. Here we investigate two interaction scenarios for kinesin-8 and the microtubule tip. We give a comprehensive analysis of regimes where length-regulation is possible and characterise how the stationary length depends on the biochemical rates and the bulk concentrations of the various proteins. For a neutral scenario, where microtubules grow irrespective of whether the microtubule tip is occupied by a molecular motor, length regulation is possible only for a narrow range of biochemical rates and limited to small polymerisation rates. In contrast, for an inhibition scenario, where the presence of a motor at the microtubule tip inhibits microtubule growth, the regime of length regulation is extremely broad and includes high growth rates. These results also apply to situations where polymerising enzymes, like XMAP215, and kinesin-8 mutually exclude each other from the microtubule tip. We also investigate the stochastic dynamics of the two scenarios. While for the neutral scenario length is tightly controlled, length dynamics is intermittent for the inhibition scenario and exhibits extended periods of microtubule growth and shrinkage, reminiscent of microtubule dynamic instability. On a broader perspective, the set of models established in this work quite generally suggests that mutual exclusion of molecules at the ends of cytoskeletal filaments is an important factor for filament dynamics and regulation.

q-bio.SC↗

arXiv2014

Chemical warfare and survival strategies in bacterial range expansions

Dispersal of species is a fundamental ecological process in the evolution and maintenance of biodiversity. Limited control over ecological parameters has hindered progress in understanding of what enables species to colonise new area, as well as the importance of inter-species interactions. Such control is necessary to construct reliable mathematical models of ecosystems. In our work, we studied dispersal in the context of bacterial range expansions and identified the major determinants of species coexistence for a bacterial model system of three Escherichia coli strains (toxin producing, sensitive, and resistant). Genetic engineering allowed us to tune strain growth rates and to design different ecological scenarios (cyclic and hierarchical). We found that coexistence of all strains depended on three strongly interdependent factors: composition of inoculum, relative strain growth rates, and effective toxin range. Robust agreement between our experiments and a thoroughly calibrated computational model enabled us to extrapolate these intricate interdependencies in terms of phenomenological biodiversity laws. Our mathematical analysis also suggested that cyclic dominance between strains is not a prerequisite for coexistence in competitive range expansions. Instead, robust three-strain coexistence required a balance between growth rates and either a reduced initial ratio of the toxin-producing strain, or a sufficiently short toxin range.

q-bio.PE↗

arXiv2014

Defect-Mediated Phase Transitions in Active Soft Matter

How do topological defects affect the degree of order in active matter? To answer this question we investigate an agent-based model of self-propelled particles, which accounts for polar alignment and short-ranged repulsive interactions. For strong alignment forces we find collectively moving polycrystalline states with fluctuating networks of grain boundaries. In the regime where repulsive forces dominate, the fluctuations generated by the active system give rise to quasi-long-range transitional order, but---unlike thermal system---without creating topological defects.

cond-mat.soft↗

arXiv2014

Effective two-dimensional model does not account for geometry sensing by self-organized proteins patterns - Supplementary document

Here we provide a thorough discussion of the model for Min protein dynamics proposed by Schweizer et al. [11]. The manuscript serves as supplementary document for our letter to the editor to appear in PNAS. Our analysis is based on the original COMSOL simulation files that were used for the publication. We show that all computational data in Schweizer et al. rely on exploitation of simulation artifacts and various unmentioned modifications of model parameters that strikingly contradict the experimental setup and experimental data. We find that the model neither accounts for MinE membrane interactions nor for any observed MinDE protein patterns. All conclusions drawn from the computational model are void. There is no evidence at all that persistent MinE membrane binding has any role in geometry sensing.

q-bio.SC↗

arXiv2014

Dynamics of a Semiflexible Polymer or Polymer Ring in Shear Flow

Polymers exposed to shear flow exhibit a rich tumbling dynamics. While rigid rods rotate on Jeffery orbits, flexible polymers stretch and coil up during tumbling. Theoretical results show that in both of these asymptotic regimes the tumbling frequency f_c in a linear shear flow of strength γscales as a power law Wi^(2/3) in the Weissenberg number Wi=γτ, where τis a characteristic time of the polymer's relaxational dynamics. For flexible polymers these theoretical results are well confirmed by experimental single molecule studies. However, for the intermediate semiflexible regime the situation is less clear. Here we perform extensive Brownian dynamics simulations to explore the tumbling dynamics of semiflexible polymers over a broad range of shear strength and the polymer's persistence length l_p. We find that the Weissenberg number alone does not suffice to fully characterize the tumbling dynamics, and the classical scaling law breaks down. Instead, both the polymer's stiffness and the shear rate are relevant control parameters. Based on our Brownian dynamics simulations we postulate that in the parameter range most relevant for cytoskeletal filaments there is a distinct scaling behavior with f_c τ*=Wi^(3/4) f_c (x) with Wi=γτ* and the scaling variable x=(l_p/L)(Wi)^(-1/3); here τ* is the time the polymer's center of mass requires to diffuse its own contour length L. Comparing these results with experimental data on F-actin we find that the Wi^(3/4) scaling law agrees quantitatively significantly better with the data than the classical Wi^(2/3) law. Finally, we extend our results to single ring polymers in shear flow, and find similar results as for linear polymers with slightly different power laws.

cond-mat.soft↗