Biodiversity is essential to the viability of ecological systems. Species diversity in ecosystems is promoted by cyclic, non-hierarchical interactions among competing populations. Central features of such non-transitive relations are represented by the 'rock-paper-scissors' game, in which rock crushes scissors, scissors cut paper, and paper wraps rock. In combination with spatial dispersal of static populations, this type of competition results in the stable coexistence of all species and the long-term maintenance of biodiversity. However, population mobility is a central feature of real ecosystems: animals migrate, bacteria run and tumble. Here, we observe a critical influence of mobility on species diversity. When mobility exceeds a certain value, biodiversity is jeopardized and lost. In contrast, below this critical threshold all subpopulations coexist and an entanglement of travelling spiral waves forms in the course of time. We establish that this phenomenon is robust; it does not depend on the details of cyclic competition or spatial environment. These findings have important implications for maintenance and temporal development of ecological systems and are relevant for the formation and propagation of patterns in microbial populations or excitable media.

The emergence of collective motion exhibited by systems ranging from flocks of animals to self-propelled microorganisms to the cytoskeleton is a ubiquitous and fascinating self-organization phenomenon. Similarities between these systems, such as the inherent polarity of the constituents, a density-dependent transition to ordered phases or the existence of very large density fluctuations, suggest universal principles underlying pattern formation. This idea is followed by theoretical models at all levels of description: micro- or mesoscopic models directly map local forces and interactions using only a few, preferably simple, interaction rules, and more macroscopic approaches in the hydrodynamic limit rely on the systems' generic symmetries. All these models characteristically have a broad parameter space with a manifold of possible patterns, most of which have not yet been experimentally verified. The complexity of interactions and the limited parameter control of existing experimental systems are major obstacles to our understanding of the underlying ordering principles. Here we demonstrate the emergence of collective motion in a high-density motility assay that consists of highly concentrated actin filaments propelled by immobilized molecular motors in a planar geometry. Above a critical density, the filaments self-organize to form coherently moving structures with persistent density modulations, such as clusters, swirls and interconnected bands. These polar nematic structures are long lived and can span length scales orders of magnitudes larger than their constituents. Our experimental approach, which offers control of all relevant system parameters, complemented by agent-based simulations, allows backtracking of the assembly and disassembly pathways to the underlying local interactions. We identify weak and local alignment interactions to be essential for the observed formation of patterns and their dynamics. The presented minimal polar-pattern-forming system may thus provide new insight into emerging order in the broad class of active fluids and self-propelled particles.

We study a one-dimensional totally asymmetric exclusion process with random particle attachments and detachments in the bulk. The resulting dynamics leads to unexpected stationary regimes for large but finite systems. Such regimes are characterized by a phase coexistence of low and high density regions separated by domain walls. We use a mean-field approach to interpret the numerical results obtained by Monte Carlo simulations, and we predict the phase diagram of this nonconserved dynamics in the thermodynamic limit.

The successful design of nanofluidic devices for the manipulation of biopolymers requires an understanding of how the predictions of soft condensed matter physics scale with device dimensions. Here we present measurements of DNA extended in nanochannels and show that below a critical width roughly twice the persistence length there is a crossover in the polymer physics. DOI: 10.1103/PhysRevLett.94.196101 PACS numbers: 81.16.Nd, 82.35.Lr, 82.39.Pj Top-down approaches to nanotechnology have the potential to revolutionize biology by making possible the construction of chip-based devices that can not only detect and separate single DNA molecules by size [1-4] but also-it is hoped in the future-actually sequence at the single molecule level [5]. While a number of top-down approaches have been proposed, all these approaches have in common the confinement of DNA to nanometer scales, typically 5-200 nm. Confinement alters the statistical mechanical properties of DNA. A DNA molecule in a nanochannel will extend along the channel axis to a substantial fraction of its full contour length [1,6]. Moreover, confinement is expected to alter the Brownian dynamics of the confined molecule [1]. While the study of confined DNA is interesting from a physics perspective, it is also critical for device design, potentially leading to new applications of nanoconfinement (for example, the use of nanochannels to prestretch and stabilize DNA before threading through a nanopore [5]). Moreover, available models [7][8][9][10][11] and simulations [12,13] are unable to account for the effect of varying confinement over the entire range of scales used in nanodevices. The theory gives asymptotic results valid only in limits that are not necessarily compatible with device requirements [1].Consider a DNA molecule of contour length L, width w, and persistence length P confined to a nanochannel of width D with D less than the radius of gyration of the molecule. When D P, the molecule is free to coil in the nanochannel and the elongation is due entirely to excluded volume interactions between segments of the polymer greatly separated in position along the backbone (see Fig. 1). de Gennes developed a scaling argument for the average extension of a confined self-avoiding polymer [8,12] which was later generalized by Schaefer and Pincus to the case of a persistent self-avoiding polymer [14]. The de Gennes theory predicts an extension r that scales with D in the following way:If the aspect ratio of the channel is not unity, i.e., the width D D 1 does not equal the depth D 2 , then Eq. (1) is still valid provided that D is replaced by the geometric average of the dimensions. As the channel width drops below the persistence length, the physics is dominated not by excluded volume but by the interplay of confinement and intrinsic DNA elasticity. In the strong confinement limit D P, backfolding is energetically unfavorable and contour length is stored exclusively in deflections made by the polymer with the walls. These deflections occur on average over th...

We discuss a new class of driven lattice gas obtained by coupling the one-dimensional totally asymmetric simple exclusion process to Langmuir kinetics. In the limit where these dynamics are competing, the resulting non-conserved flow of particles on the lattice leads to stationary regimes for large but finite systems. We observe unexpected properties such as localized boundaries (domain walls) that separate coexisting regions of low and high density of particles (phase coexistence). A rich phase diagram, with high an low density phases, two and three phase coexistence regions and a boundary independent "Meissner" phase is found. We rationalize the average density and current profiles obtained from simulations within a mean-field approach in the continuum limit. The ensuing analytic solution is expressed in terms of Lambert W -functions. It allows to fully describe the phase diagram and extract unusual mean-field exponents that characterize critical properties of the domain wall. Based on the same approach, we provide an explanation of the localization phenomenon. Finally, we elucidate phenomena that go beyond mean-field such as the scaling properties of the domain wall.

We study the elasticity of a two-dimensional random network of rigid rods ("Mikado model"). The essential features incorporated into the model are the anisotropic elasticity of the rods and the random geometry of the network. We show that there are three distinct scaling regimes, characterized by two distinct length scales on the elastic backbone. In addition to a critical rigidiy percolation region and a homogeneously elastic regime we find a novel intermediate scaling regime, where the elasticity is dominated by bending deformations.PACS numbers: 87.16. Ka, 62.20.Dc, 82.35.Pq The elasticity of cells is governed by the cytoskeleton, a partially crosslinked network of relatively stiff filaments forming a several 100 nm thick shell called the actin cortex [1]. While the statistical properties of single cytoskeletal filaments are by now relatively well understood [2,3], theoretical concepts for the elasticity of stiff polymer networks are still evolving. One major open question is to understand how stresses and strains are transmitted in such networks. In synthetic gels that are formed by rather flexible chain molecules the response to macroscopic external forces is -on the level of single filaments -isotropic and entropic in origin. It is generally believed that macroscopic stresses are transmitted in such a way that the local deformations within the network stay affine, i.e. that the end-to-end distance of individual filaments follows the macroscopic shear deformation [4]. In contrast, the building blocks of the actin cortex are semiflexible polymers, whose hallmark is an extremly long persistence length ℓ p , which is comparable to the total contour length ℓ. As a consequence, the response of such stiff polymers to external forces shows a pronounced anisotropy [5]. Consider a semiflexible polymer with one end clamped at a fixed orientation. When forces are applied at the other end transverse to the tangent vector at the clamped end, the response may be characterized by a transverse spring coefficient k ⊥ (ℓ) = 3κ/ℓ 3 proportional to the bending modulus κ. Whereas this response is of purely mechanical origin, the linear response for longitudinal forces is due to the presence of thermal undulations, which tilt parts of the polymer contour with respect to the force direction. The corresponding effective spring coefficient k (ℓ) = 6κ 2 /(k B T ℓ 4 ) is proportional to κ 2 /T indicating the breakdown of linear response for very stiff filaments. In a typical network one expects the distance between crosslinks ℓ c to be much smaller than the persistence length and filament length. Hence we have k (ℓ c )/k ⊥ (ℓ c ) = 2ℓ p /ℓ c ≫ 1, i.e. the elastic response of the filaments is indeed highly anisotropic.These anisotropic elastic properties of individual filaments suggests that the macroscopic elasticty of networks will not only depend on the number of crosslinks and the density of filaments, but also on the geometry and architecture of the network. For very regular networks such as a triangular lattice the longitudin...

Microtubules are hollow cylindrical structures that constitute one of the three major classes of cytoskeletal filaments. On the mesoscopic length scale of a cell, their material properties are characterized by a single stiffness parameter, the persistence length ഞp. Its value, in general, depends on the microscopic interactions between the constituent tubulin dimers and the architecture of the microtubule. Here, we use single-particle tracking methods combined with a fluctuation analysis to systematically study the dependence of ഞ p on the total filament length L. Microtubules are grafted to a substrate with one end free to fluctuate in three dimensions. A fluorescent bead is attached proximally to the free tip and is used to record the thermal fluctuations of the microtubule's end. The position distribution functions obtained with this assay allow the precise measurement of ഞ p for microtubules of different contour length L. Upon varying L between 2.6 and 47.5 m, we find a systematic increase of ഞp from 110 to 5,035 m. At the same time we verify that, for a given filament length, the persistence length is constant over the filament within the experimental accuracy. We interpret this length dependence as a consequence of a nonnegligible shear deflection determined by subnanometer relative displacement of adjacent protofilaments. Our results may shine new light on the function of microtubules as sophisticated nanometer-sized molecular machines and give a unified explanation of seemingly uncorrelated spreading of microtubules' stiffness previously reported in literature.nanomechanics ͉ protofilaments ͉ single-particle tracking ͉ thermal fluctuation analysis T he mechanics of living cells is largely determined by the cytoskeleton, a self-organizing and highly dynamic network of filamentous proteins of different lengths and stiffnesses (1). Understanding the elastic response of purified cytoskeletal filaments is fundamental for the elucidation of the rheological behavior of the cytoskeleton. Microtubules (MTs) are hollow cylindrical filaments formed by, on average, 13 tubulin protofilaments (PFs) assembled in parallel. The MT outer and inner diameters are Ϸ25 and 15 nm, respectively. In cells, MTs are generally 1-10 m long, whereas in axons their length can be 50-100 m (2).The tubular structure of MTs implies a minimal crosssectional area, hence a high strength and stiffness combined with low density. In recent years, the mechanical properties of MTs have been investigated by several experimental approaches, such as thermal fluctuations (3-6), atomic force microscopy (AFM) (7-10), and optical tweezers (11-13).The standard reference model to describe the mechanical properties of a biopolymer on length scales much larger than any microscopic scale (the tube diameter for MTs) is the worm-like chain model (14,15). It is characterized in terms of a flexural rigidity (neglecting torsional rigidity). The combined effect of flexural rigidity and thermal fluctuations on the conformation of the filament is given by the ratio ...

We calculate the distribution function of the end-to-end distance of a semiflexible polymer with large bending rigidity. This quantity is directly observable in experiments on single semiflexible polymers (e.g., DNA, actin) and relevant to their interpretation. It is also an important starting point for analyzing the behavior of more complex systems such as networks and solutions of semiflexible polymers. To estimate the validity of the obtained analytical expressions, we also determine the distribution function numerically using Monte Carlo simulation and find good quantitative agreement.