Search

We recorded large data sets of swimming trajectories of the soil bacterium Pseudomonas putida. Like other prokaryotic swimmers, P. putida exhibits a motion pattern dominated by persistent runs that are interrupted by turning events. An in-depth analysis of their swimming trajectories revealed that the majority of the turning events is characterized by an angle of phi(1) = 180 degrees (reversals). To a lesser extent, turning angles of phi(2 Sigma Sigma Sigma Sigma) = 00 are also found. Remarkably, we observed that, upon a reversal, the swimming speed changes by a factor of two on average a prominent feature of the motion pattern that, to our knowledge, has not been reported before. A theoretical model, based on the experimental values for the average run time and the rotational diffusion, recovers the mean-square displacement of P. putida if the two distinct swimming speeds are taken into account. Compared to a swimmer that moves with a constant intermediate speed, the mean-square displacement is strongly enhanced. We furthermore observed a negative dip in the directional autocorrelation at intermediate times, a feature that is only recovered in an extended model, where the nonexponential shape of the run-time distribution is taken into account.

In eukaryotes, gene expression depends on chromatin organization. However, how chromatin affects the transcription dynamics of individual RNA polymerases has remained elusive. Here, we use dual trap optical tweezers to study single yeast RNA polymerase II (Pol II) molecules transcribing along a DNA template with two nucleosomes. The slowdown and the changes in pausing behavior within the nucleosomal region allow us to determine a drift coefficient,., which characterizes the ability of the enzyme to recover from a nucleosomal backtrack. Notably, chi can be used to predict the probability to pass the first nucleosome. Importantly, the presence of a second nucleosome changes chi in a manner that depends on the spacing between the two nucleosomes, as well as on their rotational arrangement on the helical DNA molecule. Our results indicate that the ability of Pol II to pass the first nucleosome is increased when the next nucleosome is turned away from the first one to face the opposite side of the DNA template. These findings help to rationalize how chromatin arrangement affects Pol II transcription dynamics.

It is recognized now that a variety of real-life phenomena ranging from diffusion of cold atoms to the motion of humans exhibit dispersal faster than normal diffusion. L\'evy walks is a model that excelled in describing such superdiffusive behaviors albeit in one dimension. Here we show that, in contrast to standard random walks, the microscopic geometry of planar superdiffusive L\'evy walks is imprinted in the asymptotic distribution of the walkers. The geometry of the underlying walk can be inferred from trajectories of the walkers by calculating the analogue of the Pearson coefficient.

Cells can enter into a dormant state when faced with unfavorable conditions. However, how cells enter into and recover from this state is still poorly understood. Here, we study dormancy in different eukaryotic organisms and find it to be associated with a significant decrease in the mobility of organelles and foreign tracer particles. We show that this reduced mobility is caused by an influx of protons and a marked acidification of the cytoplasm, which leads to widespread macromolecular assembly of proteins and triggers a transition of the cytoplasm to a solid-like state with increased mechanical stability. We further demonstrate that this transition is required for cellular survival under conditions of starvation. Our findings have broad implications for understanding alternative physiological states, such as quiescence and dormancy, and create a new view of the cytoplasm as an adaptable fluid that can reversibly transition into a protective solid-like state. DOI: http://dx.doi.org/10.7554/eLife.09347.001, eLife digest Most organisms live in unpredictable environments, which can often lead to nutrient shortages and other conditions that limit their ability to grow. To survive in these harsh conditions, many organisms adopt a dormant state in which their metabolism slows down to conserve vital energy. When the environmental conditions improve, the organisms can return to their normal state and continue to grow. The interior of cells is known as the cytoplasm. It is very crowded and contains many molecules and compartments called organelles that carry out a variety of vital processes. The cytoplasm has long been considered to be fluid-like in nature, but recent evidence suggests that in bacterial cells it can solidify to resemble a soft glass-type material under certain conditions. When cells become dormant they stop dividing and reorganise their cytoplasm in several ways; for example, the water content drops and many essential proteins form storage compartments. However, it was not clear how cells regulate the structure of the cytoplasm to enter into or exit from dormancy. Now, Munder et al. analyse the changes that occur in the cytoplasm when baker’s yeast cells enter a dormant state. The experiments show that when yeast cells are deprived of energy – as happens during dormancy – the cytoplasm becomes more acidic than normal. This limits the ability of molecules and organelles to move around the cytoplasm. Similar results were also seen in other types of fungi and an amoeba. Munder et al. found that this increase in acidity during dormancy causes many proteins to interact with each other and form large clumps or filament structures that result in the cytoplasm becoming stiffer. A separate study by Joyner et al. found that when yeast cells are starved of sugar, two large molecules are less able to move around the cell interior. Together, the findings of the studies suggest that the interior of cells can undergo a transition from a fluid-like to a more solid-like state to protect the cells from damage when energy is in short supply. The next challenge is to understand the molecular mechanisms that cause the physical properties of the cytoplasm to change under different conditions. DOI: http://dx.doi.org/10.7554/eLife.09347.002

Many bacteria on earth exist in surface-attached communities known as biofilms. These films are responsible for manifold problems, including hospital-acquired infections and biofouling, but they can also be beneficial. Biofilm growth depends on the transport of nutrients and waste, for which diffusion is thought to be the main source of transport. However, diffusion is ineffective for transport over large distances and thus should limit growth. Nevertheless, biofilms can grow to be very large. Here we report the presence of a remarkable network of well-defined channels that form in wild-type Bacillus subtilis biofilms and provide a system for enhanced transport. We observe that these channels have high permeability to liquid flow and facilitate the transport of liquid through the biofilm. In addition, we find that spatial variations in evaporative flux from the surface of these biofilms provide a driving force for the flow of liquid in the channels. These channels offer a remarkably simple system for liquid transport, and their discovery provides insight into the physiology and growth of biofilms.

Here, we show that a problem of forced polymer loops can be mapped to an asymmetric simple exclusion process with reflecting boundary conditions. The dynamics of the particle system can be solved exactly using the Bethe ansatz. We thus can fully describe the relaxation dynamics of forced polymer loops. In the steady state, the conformation of the loop can be approximated by a combination of Fermi–Dirac and Brownian bridge statistics, while the exact solution is found by using the fermion integer partition theory. With the theoretical framework presented here we establish a link between the physics of polymers and statistics of many-particle systems opening new paths of exploration in both research fields. Our result can be applied to the dynamics of the biopolymers which form closed loops. One such example is the active pulling of chromosomal loops during meiosis in yeast cells which helps to align chromosomes for recombination in the viscous environment of the cell nucleus.

In the present paper the microscopic approach to random walk models is introduced. For any particular model it provides a rigorous way to derive the transport equations for the macroscopic density of walking particles. Although it is not more complicated than the standard random walk framework it has virtually no limitations with respect to the initial distribution of particles. As a consequence, the transport equations derived with this method almost automatically give answers to such important problems as aging and two point probability distribution.

During recombination, the DNA of parents exchange their genetic information to give rise to a genetically unique offspring. For recombination to occur, homologous chromosomes need to find each other and align with high precision. Fission yeast solves this problem by folding chromosomes in loops and pulling them through the viscous nucleoplasm. We propose a theory of pulled polymer loops to quantify the effect of drag forces on the alignment of chromosomes. We introduce an external force field to the concept of a Brownian bridge and thus solve for the statistics of loop configurations in space.

We propose an analytical method to determine the shape of density profiles in the asymptotic long time limit for a broad class of coupled continuous time random walks which operate in the ballistic regime. In particular, we show that different scenarios of performing a random walk step, via making an instantaneous jump penalized by a proper waiting time or via moving with a constant speed, dramatically effect the corresponding propagators, despite the fact that the end points of the steps are identical. Furthermore, if the speed during each step of the random walk is itself a random variable, its distribution gets clearly reflected in the asymptotic density of random walkers. These features are in contrast with more standard non-ballistic random walks.

Many organisms form colonies for a transient period of time to withstand environmental pressure. Bacterial biofilms are a prototypical example of such behavior. Despite significant interest across disciplines, physical mechanisms governing the formation and dissolution of bacterial colonies are still poorly understood. Starting from a kinetic description of motile and interacting cells we derive a hydrodynamic equation for their density on a surface. We use it to describe formation of multiple colonies with sizes consistent with experimental data and to discuss their dissolution., Comment: 3 figures, 1 Supplementary Material

We used microfluidic tools and high-speed time-lapse microscopy to record trajectories of the soil bacterium Pseudomonas putida in a confined environment with cells swimming in close proximity to a glass-liquid interface. While the general swimming pattern is preserved, when compared to swimming in the bulk fluid, our results show that cells in the presence of two solid boundaries display more frequent reversals in swimming direction and swim faster. Additionally, we observe that run segments are no longer straight and that cells swim on circular trajectories, which can be attributed to the hydrodynamic wall effect. Using the experimentally observed parameters together with a recently presented analytic model for a run-reverse random walker, we obtained additional insight on how the spreading behavior of a cell population is affected under confinement. While on short time scales, the mean square displacement of confined swimmers grows faster as compared to the bulk fluid case, our model predicts that for large times the situation reverses due to the strong increase in effective rotational diffusion.

In the present paper, the generalized continuous time random walk model with a coupled transition kernel is considered. The coupling occurs through the dependence of the waiting time probability distribution on the preceding jump length. For the description of this model, a method is suggested that includes the details of the microscopic distribution over the waiting times and arrival distances at a given point. A close analogy to the problem of a random walk with finite velocity is demonstrated for the particular case of coupling, when a waiting time is a simple function of a preceding jump length. With its help an analytical solution for the generalized random walk model is found, including both effects (finite velocity and jump dependent waiting times) simultaneously.

The relevance of spatial organization of chromatin to regulation of transcription is increasingly recognized [1]. Conversely, it was recently suggested that the level of general transcription activity affects subnuclear chromatin distribution [2]. Here, we ask how a general increase in transcription by polymerase II changes subnuclear chromatin distribution. Specifically, we used the transition of early zebrafish embryos from transcription quiescence to fully established transcription (Zygotic Genome Activation - ZGA) as a naturally occurring example of transcription level increase. General transcription activity occurs only following ZGA, i.e. 10 synchronous cell divisions after initial fertilization (three hours post fertilization). To make subnuclear distribution changes during ZGA accessible to super-resolution microscopy, we developed a dissociated cell culture protocol. Zebrafish embryos were dissociated at the 128-cell stage (three cell divisions before ZGA). Cultured cells developed transcription activity and morphological hallmarks of ZGA, confirming occurrence of native ZGA. We obtained preliminary results by wide-field fluorescence microscopy. Using fluorescently labeled histone proteins, which spontaneously bind DNA, we visualized a fine-grained chromatin structure in post-ZGA interphase nuclei in vivo. Utilizing antibody fragments (Fabs), we detected agglomerations of transcribing polymerase II in vivo. These agglomerations appeared as micron-sized, approximately spherical “transcription hot spots”. Few large transcription hot spots occurred at the 256-cell stage; in consecutive cell cycles more and smaller spots appeared. Any distinct signal of transcribing polymerase II disappeared during cell divisions, when no transcription occurs, thus confirming specificity of Fab-based detection of actively transcribing polymerase II. In the future, we will employ super-resolution microscopy to resolve the fine structure of chromatin and transcription hot spots in vivo throughout native zebrafish ZGA. [1] Gavrilov and Razin, Molecular Biology, 2015. [2] Popken et al., Nucleus, 2015.

Space-time correlation functions constitute a useful instrument from the research toolkit of continuous-media and many-body physics. We adopt here this concept for single-particle random walks and demonstrate that the corresponding space-time velocity auto-correlation functions reveal correlations which extend in time much longer than estimated with the commonly employed temporal correlation functions. A generic feature of considered random-walk processes is an effect of velocity echo identified by the existence of time-dependent regions where most of the walkers are moving in the direction opposite to their initial motion. We discuss the relevance of the space-time velocity correlation functions for the experimental studies of cold atom dynamics in an optical potential and charge transport on micro- and nano-scales., Phys. Rev. Lett., in press

Various microorganisms use chemotaxis for signaling among individuals---a common strategy for communication that is responsible for the formation of microcolonies. We model the microorganisms as autochemotactic active random walkers and describe them by an appropriate Langevin dynamics. It consists of rotational diffusion of the walker's velocity direction and a deterministic torque that aligns the velocity direction along the gradient of a self-generated chemical field. To account for finite size, each microorganism is treated as a soft disk. Its velocity is modified when it overlaps with other walkers according to a linear force-velocity relation and a harmonic repulsion force. We analyze two-walker collisions by presenting typical trajectories and by determining a state diagram that distinguishes between free walker, metastable, and bounded cluster states. We mention an analogy to Kramer's escape problem. Finally, we investigate relevant properties of many-walker systems and describe characteristics of cluster formation in unbounded geometry and in confinement.

The standard Levy walk is performed by a particle that moves ballistically between randomly occurring collisions when the intercollision time is a random variable governed by a power-law distribution. During instantaneous collision events, the particle randomly changes the direction of motion but maintains the same constant speed. We generalize the standard model to incorporate velocity fluctuations into the process. Two types of models are considered, namely (i) with a walker changing the direction and absolute value of its velocity during collisions only, and (ii) with a walker whose velocity continuously fluctuates. We present a full analytic evaluation of both models and emphasize the importance of initial conditions. We show that, in the limit of weak velocity fluctuations, the integral diffusion characteristics and the bulk of diffusion profiles are identical to those for the standard Levy walk. However, the type of underlying velocity fluctuations can be identified by looking at the ballistic regions of the diffusion profiles. Our analytical results are corroborated by numerical simulations.

The propagation of an initially localized perturbation via an interacting many-particle Hamiltonian dynamics is investigated. We argue that the propagation of the perturbation can be captured by the use of a continuous-time random walk where a single particle is traveling through an active, fluctuating medium. Employing two archetype ergodic many-particle systems, namely (i) a hard-point gas composed of two unequal masses and (ii) a Fermi-Pasta-Ulam chain we demonstrate that the corresponding perturbation profiles coincide with the diffusion profiles of the single-particle L\'{e}vy walk approach. The parameters of the random walk can be related through elementary algebraic expressions to the physical parameters of the corresponding test many-body systems.

The parasite African trypanosome swims in the bloodstream of mammals and causes the highly dangerous human sleeping sickness. Cell motility is essential for the parasite’s survival within the mammalian host. We present an analysis of the random-walk pattern of a swimming trypanosome. From experimental time-autocorrelation functions for the direction of motion we identify two relaxation times that differ by an order of magnitude. They originate from the rapid deformations of the cell body and a slower rotational diffusion of the average swimming direction. Velocity fluctuations are athermal and increase for faster cells whose trajectories are also straighter. We demonstrate that such a complex dynamics is captured by two decoupled Langevin equations that decipher the complex trajectory pattern by referring it to the microscopic details of cell behavior.

We consider a random walk model that takes into account the velocity distribution of random walkers. Random motion with alternating velocities is inherent to various physical and biological systems. Moreover, the velocity distribution is often the first characteristic that is experimentally accessible. Here, we derive transport equations describing the dispersal process in the model and solve them analytically. The asymptotic properties of solutions are presented in the form of a phase diagram that shows all possible scaling regimes, including superdiffusive, ballistic, and superballistic motion. The theoretical results of this work are in excellent agreement with accompanying numerical simulations.

We present an analytical expression for the Kolmogorov-Sinai entropy of a wet granular gas. The influence of the liquid is modeled by a hysteretic interaction force. For the dilute limit (two-particle collisions only), we find a simple expression accounting for the contribution of both the scattering states and the bound states in arbitrary dimensions. It is shown that the system is significantly more chaotic than a gas of (dry) hard spheres, as reflected by a pronounced increase of the Kolmogorov-Sinai entropy.

In this work, we study the diffusion of admixture particles in a one-dimensional velocity field given by a gradient of a random potential. This refers us to the case of random compressible flows, where previously only scaling estimates were available. We develop a general approach which allows to solve this problem analytically. With its help we derive the macroscopic transport equation and rigorously show in which cases transport can be subdiffusive. We find the Fourier-Laplace transform of the Green's function of this equation and prove that for some potential distributions it satisfies the subdiffusive equation with fractional derivative with respect to time.

The connection of problems considered in the paper by Sokolov and Metzler with stochastic transport in usual space and uniform medium is discussed.

More and more stochastic transport phenomena in various real-world systems prove to belong to the class of anomalous diffusion. This paper is devoted to the scaling of diffusion?a very fundamental feature of this transport process. Our aim is to provide a comprehensive theoretical overview of scaling properties, but also to connect it to the analysis of experimental data. Anomalous diffusion is commonly characterized by an exponent in the power law of the mean square displacement as a function of time . On the other hand, it is known that the probability distribution function of diffusing particles can be approximated by (1/t?)?(r/t?). While for classical normal diffusion this scaling relation is exact, it may not be valid globally for anomalous diffusion. In general, the exponent ? obtained from the scaling of the central part of the probability distribution function differs from the exponent ? given by the mean square displacement. In this paper we systematically study how the scaling of different moments and parts of the probability distribution function can be determined and characterized even when no global scaling exists. We consider three rigorous methods for finding, respectively, the mean square displacement exponent ?, the scaling exponent ? and the profile of the scaling function ?. We also show that alternatively the scaling exponent ? can be determined by analyzing fractional moments |r|q with . All analytical results are obtained in the framework of continuous-time random walks. For a wide class of coupled random walks, including the famous L?vy walk model, we introduce a new unifying description which allows straightforward generalizations to other systems. Finally, we show how fractional moments help to analyze experimental or simulation data consistently.

Seeing physiological processes at the nanoscale in living organisms without labeling is an ultimate goal in life sciences. Using X-ray ptychography, we explored in situ the dynamics of unstained, living fission yeast Schizosaccharomyces pombe cells in natural, aqueous environment at the nanoscale. In contrast to previous X-ray imaging studies on biological matter, in this work the eukaryotic cells were alive even after several ptychographic X-ray scans, which allowed us to visualize the chromatin motion as well as the autophagic cell death induced by the ionizing radiation. The accumulated radiation of the sequential scans allowed for the determination of a characteristic dose of autophagic vacuole formation and the lethal dose for fission yeast. The presented results demonstrate a practical method that opens another way of looking at living biological specimens and processes in a time-resolved label-free setting.

Interphase nuclei are segregated into chromatin domains, which are rich in DNA, and the interchromatin compartment1. Transcribing RNA polymerase II is found at chromatin domain margins1. It can be assumed that polymerase II is not just passively recruited to chromatin domain margins, but actively organizes chromatin and its interface with the interchromatin compartment. Here, we investigated how polymerase II activity impacts the bulk organization of chromatin in interphase nuclei. We used blastula stage zebrafish embryos as a model system. Blastula stage cell cycles last 1 hour or less, so we could readily follow the onset of transcription and chromatin organization after cell division. First, we imaged transcription and chromatin organization in vivo. To this end, we injected embryos with fluorescently labeled antibody fragments against transcribing polymerase II and the SiR-DNA live stain. We found that after cell division, no transcription occurred and chromatin was uniformly distributed throughout the nucleus. Within 2-3 minutes, individual foci of polymerase II activity occurred, which locally displaced chromatin from a surrounding pocket of 100-500 nm diameter. The number of polymerase II foci and chromatin-depleted pockets increased continuously and formed a nucleus-spanning network of transcription activity, which was embedded in a mirror image network of chromatin-dense domains. STED super-resolution microscopy of fixed embryonic cells showed the same intercalation of transcription and chromatin down to ∼50 nm length scales. To test the apparent requirement of transcription for this chromatin organization, we disrupted transcription with flavopiridol. This indeed abolished the intercalated nanostructure and led to precipitation of chromatin into compacted domains. Our findings suggest that foci of polymerase II activity locally manipulate bulk chromatin organization and integrate into a nucleus-spanning network required to maintain global nuclear architecture. 1Albiez et al. Chromosome Research 2006.