61 research outputs found
How bacterial cells and colonies move on solid substrates
Many bacteria rely on active cell appendages, such as type IV pili, to move
over substrates and interact with neighboring cells. Here, we study the motion
of individual cells and bacterial colonies, mediated by the collective
interactions of multiple pili. It was shown experimentally that the substrate
motility of Neisseria gonorrhoeae cells can be described as a persistent random
walk with a persistence length that exceeds the mean pili length. Moreover, the
persistence length increases for a higher number of pili per cell. With the
help of a simple, tractable stochastic model, we test whether a tug-of-war
without directional memory can explain the persistent motion of single
Neisseria gonorrhoeae cells. While the persistent motion of single cells indeed
emerges naturally in the model, a tug-of-war alone is not capable of explaining
the motility of microcolonies, which becomes weaker with increasing colony
size. We suggest sliding friction between the microcolonies and the substrate
as the missing ingredient. While such friction almost does not affect the
general mechanism of single cell motility, it has a strong effect on colony
motility. We validate the theoretical predictions by using a three-dimensional
computational model that includes explicit details of the pili dynamics, force
generation and geometry of cells.Comment: 25 pages, 17 figure
Limit theorems for L\'evy walks in dimensions: rare and bulk fluctuations
We consider super-diffusive L\'evy walks in dimensions when
the duration of a single step, i.e., a ballistic motion performed by a walker,
is governed by a power-law tailed distribution of infinite variance and finite
mean. We demonstrate that the probability density function (PDF) of the
coordinate of the random walker has two different scaling limits at large
times. One limit describes the bulk of the PDF. It is the dimensional
generalization of the one-dimensional L\'evy distribution and is the
counterpart of central limit theorem (CLT) for random walks with finite
dispersion. In contrast with the one-dimensional L\'evy distribution and the
CLT this distribution does not have universal shape. The PDF reflects
anisotropy of the single-step statistics however large the time is. The other
scaling limit, the so-called 'infinite density', describes the tail of the PDF
which determines second (dispersion) and higher moments of the PDF. This limit
repeats the angular structure of PDF of velocity in one step. Typical
realization of the walk consists of anomalous diffusive motion (described by
anisotropic dimensional L\'evy distribution) intermitted by long ballistic
flights (described by infinite density). The long flights are rare but due to
them the coordinate increases so much that their contribution determines the
dispersion. We illustrate the concept by considering two types of L\'evy walks,
with isotropic and anisotropic distributions of velocities. Furthermore, we
show that for isotropic but otherwise arbitrary velocity distribution the
dimensional process can be reduced to one-dimensional L\'evy walk
Formation and Dissolution of Bacterial Colonies
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 Materia
Elasticity-based polymer sorting in active fluids: A Brownian dynamics study
While the dynamics of polymer chains in equilibrium media is well understood
by now, the polymer dynamics in active non-equilibrium environments can be very
different. Here we study the dynamics of polymers in a viscous medium
containing self-propelled particles in two dimensions by using Brownian
dynamics simulations. We find that the polymer center of mass exhibits a
superdiffusive motion at short to intermediate times and the motion turns
normal at long times, but with a greatly enhanced diffusivity. Interestingly,
the long time diffusivity shows a non-monotonic behavior as a function of the
chain length and stiffness. We analyze how the polymer conformation and the
accumulation of the self-propelled particles, and therefore the directed motion
of the polymer, are correlated. At the point of maximal polymer diffusivity,
the polymer has preferentially bent conformations maintained by the balance
between the chain elasticity and the propelling force generated by the active
particles. We also consider the barrier crossing dynamics of actively-driven
polymers in a double-well potential. The barrier crossing times are
demonstrated to have a peculiar non-monotonic dependence, related to that of
the diffusivity. This effect can be potentially utilized for sorting of
polymers from solutions in \textit{in vitro} experiments.Comment: 11 pages, 7 figure
How the Motility Pattern of Bacteria Affects Their Dispersal and Chemotaxis
Most bacteria at certain stages of their life cycle are able to move actively; they can swim in a liquid or crawl on various surfaces. A typical path of the moving cell often resembles the trajectory of a random walk. However, bacteria are capable of modifying their apparently random motion in response to changing environmental conditions. As a result, bacteria can migrate towards the source of nutrients or away from harmful chemicals. Surprisingly, many bacterial species that were studied have several distinct motility patterns, which can be theoretically modeled by a unifying random walk approach. We use this approach to quantify the process of cell dispersal in a homogeneous environment and show how the bacterial drift velocity towards the source of attracting chemicals is affected by the motility pattern of the bacteria. Our results open up the possibility of accessing additional information about the intrinsic response of the cells using macroscopic observations of bacteria moving in inhomogeneous environments
Periodic ethanol supply as a path toward unlimited lifespan of Caenorhabditis elegans dauer larvae
The dauer larva is a specialized stage of worm development optimized for survival under harsh conditions that have been used as a model for stress resistance, metabolic adaptations, and longevity. Recent findings suggest that the dauer larva of Caenorhabditis elegans may utilize external ethanol as an energy source to extend their lifespan. It was shown that while ethanol may serve as an effectively infinite source of energy, some toxic compounds accumulating as byproducts of its metabolism may lead to the damage of mitochondria and thus limit the lifespan of larvae. A minimal mathematical model was proposed to explain the connection between the lifespan of a dauer larva and its ethanol metabolism. To explore theoretically if it is possible to extend even further the lifespan of dauer larvae, we incorporated two natural mechanisms describing the recovery of damaged mitochondria and elimination of toxic compounds, which were previously omitted in the model. Numerical simulations of the revised model suggested that while the ethanol concentration is constant, the lifespan still stays limited. However, if ethanol is supplied periodically, with a suitable frequency and amplitude, the dauer could survive as long as we observe the system. Analytical methods further help to explain how feeding frequency and amplitude affect lifespan extension. Based on the comparison of the model with experimental data for fixed ethanol concentration, we proposed the range of feeding protocols that could lead to even longer dauer survival and it can be tested experimentally
The hierarchical packing of euchromatin domains can be described as multiplicative cascades
The genome is packed into the cell nucleus in the form of chromatin. Biochemical approaches have revealed that chromatin is packed within domains, which group into larger domains, and so forth. Such hierarchical packing is equally visible in super-resolution microscopy images of large-scale chromatin organization. While previous work has suggested that chromatin is partitioned into distinct domains via microphase separation, it is unclear how these domains organize into this hierarchical packing. A particular challenge is to find an image analysis approach that fully incorporates such hierarchical packing, so that hypothetical governing mechanisms of euchromatin packing can be compared against the results of such an analysis. Here, we obtain 3D STED super-resolution images from pluripotent zebrafish embryos labeled with improved DNA fluorescence stains, and demonstrate how the hierarchical packing of euchromatin in these images can be described as multiplicative cascades. Multiplicative cascades are an established theoretical concept to describe the placement of ever-smaller structures within bigger structures. Importantly, these cascades can generate artificial image data by applying a single rule again and again, and can be fully specified using only four parameters. Here, we show how the typical patterns of euchromatin organization are reflected in the values of these four parameters. Specifically, we can pinpoint the values required to mimic a microphase-separated state of euchromatin. We suggest that the concept of multiplicative cascades can also be applied to images of other types of chromatin. Here, cascade parameters could serve as test quantities to assess whether microphase separation or other theoretical models accurately reproduce the hierarchical packing of chromatin
The hierarchical packing of euchromatin domains can be described as multiplicative cascades
The genome is packed into the cell nucleus in the form of chromatin. Biochemical approaches have revealed that chromatin is packed within domains, which group into larger domains, and so forth. Such hierarchical packing is equally visible in super-resolution microscopy images of large-scale chromatin organization. While previous work has suggested that chromatin is partitioned into distinct domains via microphase separation, it is unclear how these domains organize into this hierarchical packing. A particular challenge is to find an image analysis approach that fully incorporates such hierarchical packing, so that hypothetical governing mechanisms of euchromatin packing can be compared against the results of such an analysis. Here, we obtain 3D STED super-resolution images from pluripotent zebrafish embryos labeled with improved DNA fluorescence stains, and demonstrate how the hierarchical packing of euchromatin in these images can be described as multiplicative cascades. Multiplicative cascades are an established theoretical concept to describe the placement of ever-smaller structures within bigger structures. Importantly, these cascades can generate artificial image data by applying a single rule again and again, and can be fully specified using only four parameters. Here, we show how the typical patterns of euchromatin organization are reflected in the values of these four parameters. Specifically, we can pinpoint the values required to mimic a microphase-separated state of euchromatin. We suggest that the concept of multiplicative cascades can also be applied to images of other types of chromatin. Here, cascade parameters could serve as test quantities to assess whether microphase separation or other theoretical models accurately reproduce the hierarchical packing of chromatin
Rectification of Bacterial Diffusion in Microfluidic Labyrinths
In nature as well as in the context of infection and medical applications, bacteria often have to move in highly complex environments such as soil or tissues. Previous studies have shown that bacteria strongly interact with their surroundings and are often guided by confinements. Here, we investigate theoretically how the dispersal of swimming bacteria can be augmented by microfluidic environments and validate our theoretical predictions experimentally. We consider a system of bacteria performing the prototypical run-and-tumble motion inside a labyrinth with square lattice geometry. Narrow channels between the square obstacles limit the possibility of bacteria to reorient during tumbling events to an area where channels cross. Thus, by varying the geometry of the lattice it might be possible to control the dispersal of cells. We present a theoretical model quantifying diffusive spreading of a run-and-tumble random walker in a square lattice. Numerical simulations validate our theoretical predictions for the dependence of the diffusion coefficient on the lattice geometry. We show that bacteria moving in square labyrinths exhibit enhanced dispersal as compared to unconfined cells. Importantly, confinement significantly extends the duration of the phase with strongly non-Gaussian diffusion, when the geometry of channels is imprinted in the density profiles of spreading cells. Finally, in good agreement with our theoretical findings, we observe the predicted behaviors in experiments with E. coli bacteria swimming in a square lattice labyrinth created in a microfluidic device. Altogether, our comprehensive understanding of bacterial dispersal in a simple two-dimensional labyrinth makes the first step toward the analysis of more complex geometries relevant for real world applications
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