Biological Physics

Enzymes associated with a specific biochemical pathway are often co-localized into large "molecular factories". However, despite its ubiquity the functional consequences of clustering enzymes together in this way remain poorly understood. We have studied the impact of different spatial distributions of enzymes on the flux of a reaction pathway, finding that in different parameter regimes a clustered or distributed enzyme distribution may be preferable. more

The emergence of collective motion in fish schools and bird flocks constitutes a ubiquitous and fascinating phenomenon in nature. One reason might be the emergence of highly dynamic, coherently moving spatial patterns such as clusters, swirls or waves, and the fact that the patterns commonly extend over length scales much larger than the size of the individuals. more

Establishment of cell polarity—or symmetry breaking—relies on local accumulation of polarity regulators. Although simple positive feedback is sufficient to drive symmetry breaking, it is highly sensitive to stochastic fluctuations typical for living cells. Here, by integrating mathematical modelling with quantitative experimental validations, we show that in the yeast Saccharomyces cerevisiae a combination of actin- and guanine nucleotide dissociation inhibitor-dependent recycling of the central polarity regulator Cdc42 is needed to establish robust cell polarity at a single site during yeast budding. more

In cells, long DNA and RNA polymers are formed with the help of sophisticated enzymes.
However, it is unclear how these information-carrying polymers could have spontaneously
formed in the "premordial soup" without enzymes. Here, we demonstrate a mutual positive
feedback between the chemical polymerization reaction and a physical non-equilibrium
process. This feedback circle leads to a dramatic enhancement of the probability to
generate long molecules from dilute solutions of monomers. more

Understanding the stability of ecological networks is of pivotal importance in theoretical biology. An intriguing question is how coexistence and extinction of species depend on the interaction network between species. Is it the topology of the network that sets the level of biodiversity? And how important is the strength of a single interaction link? One paradigm to address these biologically relevant questions from a theoretical point of view is the conservative Lotka-Volterra system. In this work, we introduce a general classification of coexistence scenarios in conservative Lotka-Volterra networks with an arbitrary number of species. more

The genomes of all eukaryotic organisms are highly packaged into a dynamic structure termed chromatin. On the lowest level of packaging, the structure consists of a "beads-on-a-string" arrangement, where nucleosome "particles" are connected by free DNA "linkers". A large body of recent experimental and theoretical work suggests that this structure can be appropriately described, on a coarse-grained physical level, within the theory of 1D interacting gas systems. In this work, we study which properties are required of such an interacting gas model to yield a "unified" description of nucleosome patterns in different species. more

Localized wave fronts are a fundamental feature of biological systems from cell biology to ecology. The stability of these wave fronts is often paramount to the fate of these systems. As an example, in the embryogenesis of Drosophila melanogaster the stable localization of the Hunchback protein is pivotal for the embryo's development. more

The length of microtubules and their dynamics underly subtle regulation in a cell. One
important player in microtubule length control are depolymerizing proteins kinesin-8. In
our work we explain a mechanism how these motor proteins are able to efficiently regulate
filament length. more

Reaction-diffusion dynamics provide a versatile framework for intracellular self-organization phenomena. The Min system in E. coli employs such mechanisms to ensure precise cell division by its ability to dynamically adapt to cell geometry. Under which conditions patterns emerge, how patterns are regulated by cell shape, and how such systems can be investigated in cellular geometries are the major aspects considered in our work. more

Microbes providing public goods are widespread in nature despite running the risk of being exploited by free-riders. However, the precise ecological factors supporting cooperation are still puzzling. more

Advances in carbohydrate sequencing technologies have revealed the tremendous complexity of the glycome. Understanding the biological function of carbohydrates requires the identification and quantification of carbohydrate interactions with biomolecules. more

Nanopore translocation experiments are increasingly applied to probe the secondary structures of RNA and DNA molecules. We report two vital steps toward establishing nanopore translocation as a tool for the systematic an quantitative analysis of polynucleotide folding more

Even simple active systems can show a plethora of intriguing phenomena and often we find complexity were we would have expected simplicity. more

Assembly and disassembly dynamics of microtubules (MTs) is tightly controlled by MT associated proteins. Here, we investigate how plus-end-directed depolymerases of the kinesin-8 family regulate MT depolymerization dynamics. Employing an individual-based model, we reproduce experimental findings. Moreover, crowding is identified as the key regulatory mechanism of depolymerization dynamics. more

Much of the complexity observed in gene regulation originates from cooperative protein-DNA binding. While studies of the target search of proteins for their specific binding sites on the DNA have revealed design principles for the quantitative characteristics of protein-DNA interactions, no such principles are known for the cooperative interactions between DNA-binding proteins. more

A poorly understood step in the transition from a chemical to a biological world is the emergence of self-replicating molecular systems. We study how a precursor for such a replicator might arise in a hydrothermal RNA reactor, which accumulates longer sequences from unbiased monomer influx and random ligation. more

Existing theoretical models of evolution focus on the relative fitness advantages of different mutants in a population while the dynamic behavior of the population size is mostly left unconsidered. In this work we introduce an agent-based stochastic model which combines the growth dynamics of the population and its internal evolution. Our model thereby accounts for the fact that both evolutionary and growth dynamics are based on individual reproduction events and hence are highly coupled and stochastic in nature. more

The emergence of collective motion such as exhibited by systems ranging from flocks of animals, self-propelled microorganisms or the cytoskeleton is an ubiquitous and fascinating self-organization phenomenon. All these systems display similar phenomenologies, even though the particular underlying physics is genuinely different, ranging from hydrodynamic interaction to steric or inelastic repulsion, attraction, to more complex interactions mediated by linker proteins or molecular motors. Examples for similarities are the inherent polarity of the constituents, a density-dependent transition to ordered phases or the existence of huge density fluctuations. This suggests universal organizing principles underlying pattern formation; an idea followed by hydrodynamic models valid on large scales. more

Within the last five years, knowledge about nucleosome organization on the genome has grown dramatically. To a large extent this has been achieved by an increasing number of experimental studies determining nucleosome positions at high resolution over entire genomes. Particular attention has been paid to promoter regions, where a canonical pattern has been established: a nucleosome free region with pronounced adjacent oscillations in the nucleosome density. In our study, we tested to what extent this pattern may be quantitatively described by a minimal physical model, a one-dimensional gas of impenetrable particles, commonly referred to as the “Tonks gas”. more

The capacity to reprogram and control cell functions in a specified manner is needed in many areas of biotechnology, bioengineering and medicine. Biological “computers”, or “automata” have been proposed as a way to achieve this capacity. These systems are modular biological networks that in principle should be able to convert an arbitrary specified set of biological input signals into specified responses (output) according to a desired set of rules, or program. Challenging aspects hereby are modularity, programmability as well as scalability of a given system. more

Systems with a large number of interacting particles are almost always too complex to analyse on the level of individual particle variables. In equilibrium thermodynamics, entropy is a global variable - applying to the system as a whole - that very efficiently characterizes the system's behaviour. However, many biological and ecological systems operate far from thermal equilibrium, and therefore the concept of thermodynamic entropy can no longer be naively applied to them. Still, it is very desirable to find global variables that provide a characterization of the system. more

One aim of modern biotechnology is the controlled assembly and manipulation of structures. The simplest building blocks for constructing structures are rodlike polymers. The next higher level of complexity concerning building blocks is achieved with ringlike polymers. On the nano scale level the effective shape of such building blocks is governed by the interplay of entropic forces on the one hand and elastic stiffness and steric hindrance of the polymer segments on the other hand. Entropic forces lead to a coiled, cigar-like shape. This is opposed by elastic bending stiffness, which favors non-curved conformations. This poses the question how strong each of these molecular based forces contribute and how they affect the resulting shape of the building blocks. more

200 Jahre nach Darwins Geburt und 150 Jahre nach dem Erscheinen seines revolutionären Werkes „Die Entstehung der Arten“ wissen wir: Evolution ist weit mehr als eine interessante Theorie, sie ist unvermeidlicher Fakt.Doch die Implikationen der so einfachen wie fundamentalen Gesetzmäßigkeit von Mutation, Vererbung und Auslese bergen immense Komplexität und werfen noch viele offenen Fragen auf. An Einzellern lässt sich Evolution in Echtzeit studieren und, in Verbindung mit Konzepten der statistischen Physik, einige ihrer grundlegenden Mechanismen aufdecken. more

The struggle for survival between competing bacteria species in a petri dish can create beautiful spiral patterns until one type conquers all the available space, destroying the entangled structure. Kerr and colleagues made this observation when they mixed three E. coli populations exhibiting cyclic dominance: A beats B beats C beats A. As derived by Tobias Reichenbach, Mauro Mobilia, and Erwin Frey, the mobility of the bacteria, that is, their spatial relocation rate, is crucial for the stability of coexistence. An applet recently published on The Wolfram Demonstrations Project allows anyone to simulate a spatial rock-paper-scissors game and observe the role mobility plays, whereas another applet shows the evolution of such populations if spatial effects are ignored. more

Microorganisms employ a wealth of gene regulatory mechanisms to adjust their growth programs to variations in the environment. It was pointed out long ago by Savageau that the particular mode of gene regulation employed may be correlated with the “demand” on the regulated gene, i.e., how frequently the gene product is needed in its natural habitat. An evolutionary “use-it-or-lose-it” principle was proposed to govern the choice of gene regulatory strategies. more

Translocation through nanopores has emerged as a new experimental technique to probe the physical properties of biomolecules. The question of how the typical translocation time for a single unstructured polymer depends on its length has already triggered many theoretical and computational studies. We address this question for structured RNA molecules where the breaking of base-pairing patterns is the main barrier for translocation. more

Up to 50 species extinct each day on earth. While this large number is supposedly due to human influence, a certain rate of species extinction is unavoidable. It reflects competition of different
species as well as their (missing) ability to adapt to changing environments. Together with speciation (meaning the formation of new species) and selection it allows for evolutionary change. In the common understanding of Darwinian evolution, this change tends to increase fitness, as of two competing species the "stronger" one survives. more

Chip-based fluidic systems offer enormous prospects for analyzing,
sorting, and manipulating complex molecules such as DNA and proteins. To
this end, much fundamental research, both experimental and theoretical, is
still required. We contribute a theoretical study on an obstacle for these
applications: the formation of knots in long polymers, e.g. DNA, upon
threading into narrow channels or pores. more

Biodiversity in ecological systems is often maintained by
self-arrangement of the interacting individuals into spatial patterns.
In our article, we investigate the effects of such self-organizing
spatial patterns theoretically, and find that, in most cases, they
support species diversity. However, we also identify a situation where a
convective (Eckhaus) instability of patterns results in rapid species
extinction. more

Microtubules are cytoskeletal protein filaments that play an essential role in a multitude of cell functions in all eucaryotes. While specialized structures such as cilia, flagellae and axons require microtubule lengths of up to several hundred micrometers, fundamental tasks like cell division and intracellular transport involve microtubules with lengths that are comparable to or smaller than typical eucaryotic cell sizes (10-20 micrometer).The standard model for semiflexible polymers is the wormlike chain which envisions a homogeneous, isotropic, continuously flexible rod characterized by its bending stiffness. We have shown that this standard model fails for microtubules, mainly due to the highly anisotropic molecular architecture where protofilaments are arranged in parallel to form a hollow tube of 25 nanometer in diameter. more

Noise and spatial degrees of freedom characterize pattern formation in biological systems. As an example, laboratory experiments on microbial communities have shown that different bacterial strains on Petri dishes self-organize into irregular clusters if bacteria are static. However, the theoretical description of such noisy, out-of-equilibrium patterns constitutes considerable challenges. Here, we devise an analytic approach that is generally applicable when individuals are mobile. Recently, we have shown that mobility has crucial impact on the maintenance of biodiversity in ecological systems. Here, we explore the influence of mobility on pattern formation properties. more

Following the trajectory of a random walk or likewise a flexible polymer one finds that the typical overall shape is cigar-like, prolate. Intuitively one would assume a spherical appearance, but this implies rotational averaging. Flexible and moreover semiflexible polymers are the building blocks of various biological processes, since DNA and cytoskeletal filaments belong to the class of semiflexible polymers. The shape of a polymer is important for its mobility in heterogeneous media like the cytoplasm, the depletion forces between larger complexes in polymer solution or the accessibility of specific sites along the polymer to enzymes. Our recent work shows that semiflexible polymer rings such as DNA plasmids or viral DNA exhibit distinct shapes depending on their flexibility. more

Conformational transitions in macromolecular complexes often involve the reorientation of lever-like structures. Using a simple theoretical model, we show that the rate of such transitions is drastically enhanced if the lever is bendable, e.g. at a localized "hinge". Surprisingly, the transition is fastest with an intermediate flexibility of the hinge. In this intermediate regime, the transition rate is also least sensitive to the amount of "cargo" attached to the lever arm, which could be exploited by molecular motors. To explain this effect, we generalize the Kramers-Langer theory for multi-dimensional barrier crossing to configuration dependent mobility matrices. more

An astonishing biodiversity exists within the earth's ecosystems. While being of essential importance to the viability of ecological systems, conceptual explanations of such diversity pose major challenges. Indeed, in a naive understanding of Darwinian evolution, two interacting species would compete for resources until only the fitter one survives (competitive exclusion principle). Non-hierarchical competitions between species have been found to help resolving this apparent paradox, and promote biodiversity. more

To ensure adaptability of cytoskeletal organization cells exploit the dynamic interplay between semi-flexible filamentous polymers such as microtubules or F-actin using a multitude of associated binding proteins. In particluar, the local elastic properties are regulated by the activation of auxiliary proteins which e.g. cross-link and/or bundle the filamentous networks into complex scaffolds. In this Letter we show that above a critical concentration of the actin binding protein (ABP) fascin, a solution of actin filaments organizes into a homogeneous network whose building blocks are bundles only. more

The wormlike chain (WLC) has emerged as the standard model for the description of semiflexible polymers. The defining property of a WLC is a mechanical bending stiffness that is an intrinsic material constant of the polymer. Within this framework, numerous correlation and response functions have been calculated, providing a comprehensive picture of the equilibrium and dynamical properties of WLCs. Another important emerging class of semiflexible polymers consists of bundles of WLCs. Unlike standard WLCs, wormlike bundles (WLB) have a state-dependent bending stiffness that derives from a generic interplay between the high stiffness of the individual filaments and their soft relative sliding motion. We demonstrate that this state-dependence gives rise to fundamentally new behavior that cannot be reproduced trivially using existing relations for WLCs. In an article just published in PRL we explore the consequences of a state-dependent bending stiffness on the statistical mechanics of isolated WLBs, as well as on the scaling behavior of their entangled solutions and crosslinked networks. more

With help of a light microscope one can see single chromosomes, the closest packed form of DNA. Not only during cell division, but throughout the whole cell cycle, DNA in eucaryotes is packed in one way or another. On the smallest scale, DNA is wrapped around histones and forms nucleosomes. The readout of information - between cell divisions - is controlled by so called transcription factors, which can bind to DNA without ATP consumption. How can that be if DNA is packed? more

Materials as different as granular matter, colloidal suspensions or lithospheric block systems share the common property that they may exist in a highly fragile state. While in principle able to withstand static shear stresses, small changes in the loading conditions may lead to large scale structural rearrangements or even to the complete fluidization of the material. To understand the extraordinary mechanical properties of these systems new concepts have to be developed that go beyond the application of classical elasticity theory and that sufficiently reflect the presence of the microstructure. more

Bundles of filamentous actin (F-actin) form primary structural components of a broad range of cytoskeletal processes including filopodia, sensory hair cell bristles and microvilli. Actin-binding proteins (ABPs) allow the cell to tailor the dimensions and mechanical properties of the bundles to suit specific biological functions. Therefore, it is important to obtain quantitative knowledge on the effect of ABPs on the mechanical properties of F-actin bundles. Here we measure the bending stiffness of F-actin bundles crosslinked by three ABPs that are ubiquitous in eukaryotes. We observe distinct regimes of bundle bending stiffness that differ by orders of magnitude depending on ABP type, concentration and bundle size. more

Cars jamming in city centers or on highways belong to our every-day experience. In the present work, we theoretically explore such traffic phenomena occurring at a much smaller size, on the nanometer scale. At these tiny lengths, the fields of biological physics and information technology become increasingly intertwined. Still, different paradigms rule in these areas. Brownian motion governs biological systems, e.g., it drives molecular motors along parallel one-dimensional filaments in cells, serving as transport engines. On the other hand, quantum effects become visible in the field of electronic information processing. more

We find that microtubules, essential structural elements in living cells, grow stiffer as they grow longer, an unexpected property that could lead to advances in nano-materials development. more