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- chemotaxis (5)
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How cells establish and maintain a well-defined size is a fundamental question of cell biology. Here we investigated to what extent the microtubule cytoskeleton can set a predefined cell size, independent of an enclosing cell membrane. We used electropulse-induced cell fusion to form giant multinuclear cells of the social amoeba Dictyostelium discoideum. Based on dual-color confocal imaging of cells that expressed fluorescent markers for the cell nucleus and the microtubules, we determined the subcellular distributions of nuclei and centrosomes in the giant cells. Our two- and three-dimensional imaging results showed that the positions of nuclei in giant cells do not fall onto a regular lattice. However, a comparison with model predictions for random positioning showed that the subcellular arrangement of nuclei maintains a low but still detectable degree of ordering. This can be explained by the steric requirements of the microtubule cytoskeleton, as confirmed by the effect of a microtubule degrading drug.
Modeling random crawling, membrane deformation and intracellular polarity of motile amoeboid cells
(2018)
Amoeboid movement is one of the most widespread forms of cell motility that plays a key role in numerous biological contexts. While many aspects of this process are well investigated, the large cell-to-cell variability in the motile characteristics of an otherwise uniform population remains an open question that was largely ignored by previous models. In this article, we present a mathematical model of amoeboid motility that combines noisy bistable kinetics with a dynamic phase field for the cell shape. To capture cell-to-cell variability, we introduce a single parameter for tuning the balance between polarity formation and intracellular noise. We compare numerical simulations of our model to experiments with the social amoeba Dictyostelium discoideum. Despite the simple structure of our model, we found close agreement with the experimental results for the center-of-mass motion as well as for the evolution of the cell shape and the overall intracellular patterns. We thus conjecture that the building blocks of our model capture essential features of amoeboid motility and may serve as a starting point for more detailed descriptions of cell motion in chemical gradients and confined environments.
The actin cytoskeleton and its response to external chemical stimuli is fundamental to the mechano-biology of eukaryotic cells and their functions. One of the key players that governs the dynamics of the actin network is the motor protein myosin II. Based on a phase space embedding we have identified from experiments three phases in the cytoskeletal dynamics of starved Dictyostelium discoideum in response to a precisely controlled chemotactic stimulation. In the first two phases the dynamics of actin and myosin II in the cortex is uncoupled, while in the third phase the time scale for the recovery of cortical actin is determined by the myosin II dynamics. We report a theoretical model that captures the experimental observations quantitatively. The model predicts an increase in the optimal response time of actin with decreasing myosin II-actin coupling strength highlighting the role of myosin II in the robust control of cell contraction.
During the last decade, intracellular actin waves have attracted much attention due to their essential role in various cellular functions, ranging from motility to cytokinesis. Experimental methods have advanced significantly and can capture the dynamics of actin waves over a large range of spatio-temporal scales. However, the corresponding coarse-grained theory mostly avoids the full complexity of this multi-scale phenomenon. In this perspective, we focus on a minimal continuum model of activator–inhibitor type and highlight the qualitative role of mass conservation, which is typically overlooked. Specifically, our interest is to connect between the mathematical mechanisms of pattern formation in the presence of a large-scale mode, due to mass conservation, and distinct behaviors of actin waves.
During the last decade, intracellular actin waves have attracted much attention due to their essential role in various cellular functions, ranging from motility to cytokinesis. Experimental methods have advanced significantly and can capture the dynamics of actin waves over a large range of spatio-temporal scales. However, the corresponding coarse-grained theory mostly avoids the full complexity of this multi-scale phenomenon. In this perspective, we focus on a minimal continuum model of activator–inhibitor type and highlight the qualitative role of mass conservation, which is typically overlooked. Specifically, our interest is to connect between the mathematical mechanisms of pattern formation in the presence of a large-scale mode, due to mass conservation, and distinct behaviors of actin waves.
We provide a detailed stochastic description of the swimming motion of an E. coli bacterium in two dimension, where we resolve tumble events in time. For this purpose, we set up two Langevin equations for the orientation angle and speed dynamics. Calculating moments, distribution and autocorrelation functions from both Langevin equations and matching them to the same quantities determined from data recorded in experiments, we infer the swimming parameters of E. coli. They are the tumble rate lambda, the tumble time r(-1), the swimming speed v(0), the strength of speed fluctuations sigma, the relative height of speed jumps eta, the thermal value for the rotational diffusion coefficient D-0, and the enhanced rotational diffusivity during tumbling D-T. Conditioning the observables on the swimming direction relative to the gradient of a chemoattractant, we infer the chemotaxis strategies of E. coli. We confirm the classical strategy of a lower tumble rate for swimming up the gradient but also a smaller mean tumble angle (angle bias). The latter is realized by shorter tumbles as well as a slower diffusive reorientation. We also find that speed fluctuations are increased by about 30% when swimming up the gradient compared to the reversed direction.
We show systematic electrical impedance measurements of single motile cells on microelectrodes. Wild-type cells and mutant strains were studied that differ in their cell-substrate adhesion strength. We recorded the projected cell area by time-lapse microscopy and observed irregular oscillations of the cell shape. These oscillations were correlated with long-term variations in the impedance signal. Superposed to these long-term trends, we observed fluctuations in the impedance signal. Their magnitude clearly correlated with the adhesion strength, suggesting that strongly adherent cells display more dynamic cell-substrate interactions.
To turn or not to turn?
(2016)
Bacteria typically swim in straight runs, interruped by sudden turning events. In particular, some species are limited to a reversal in the swimming direction as the only turning maneuver at their disposal. In a recent article, Grossmann et al (2016 New J. Phys. 18 043009) introduce a theoretical framework to analyze the diffusive properties of active particles following this type of run-and-reverse pattern. Based on a stochastic clock model to mimic the regulatory pathway that triggers reversal events, they show that a run-and-reverse swimmer can optimize its diffusive spreading by tuning the reversal rate according to the level of rotational noise. With their approach, they open up promising new perspectives of how to incorporate the dynamics of intracellular signaling into coarse-grained active particle descriptions.
Biological systems with their complex biochemical networks are known to be intrinsically noisy. Here we investigate the dynamics of actin polymerization of amoeboid cells, which are close to the onset of oscillations. We show that the large phenotypic variability in the polymerization dynamics can be accurately captured by a generic nonlinear oscillator model in the presence of noise. We determine the relative role of the noise with a single dimensionless, experimentally accessible parameter, thus providing a quantitative description of the variability in a population of cells. Our approach, which rests on a generic description of a system close to a Hopf bifurcation and includes the effect of noise, can characterize the dynamics of a large class of noisy systems close to an oscillatory instability.
In this Comment, we review the results of pattern formation in a reaction-diffusion-advection system following the kinetics of the Gray-Scott model. A recent paper by Das [Phys. Rev. E 92, 052914 (2015)] shows that spatiotemporal chaos of the intermittency type can disappear as the advective flow is increased. This study, however, refers to a single point in the space of kinetic parameters of the original Gray-Scott model. Here we show that the wealth of patterns increases substantially as some of these parameters are changed. In addition to spatiotemporal intermittency, defect-mediated turbulence can also be found. In all cases, however, the chaotic behavior is seen to disappear as the advective flow is increased, following a scenario similar to what was reported in our earlier work [I. Berenstein and C. Beta, Phys. Rev. E 86, 056205 (2012)] as well as by Das. We also point out that a similar phenomenon can be found in other reaction-diffusion-advection models, such as the Oregonator model for the Belousov-Zhabotinsky reaction under flow conditions.
Live cell flattening
(2010)
Eukaryotic cell flattening is valuable for improving microscopic observations, ranging from bright field (BF) to total internal reflection fluorescence (TIRF) microscopy. Fundamental processes, such as mitosis and in vivo actin polymerization, have been investigated using these techniques. Here, we review the well known agar overlayer protocol and the oil overlay method. In addition, we present more elaborate microfluidics-based techniques that provide us with a greater level of control. We demonstrate these techniques on the social amoebae Dictyostelium discoideum, comparing the advantages and disadvantages of each method.
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 amicrofluidic 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.
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 amicrofluidic 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.
Multi-color fluorescence imaging experiments of wave forming Dictyostelium cells have revealed that actin waves separate two domains of the cell cortex that differ in their actin structure and phosphoinositide composition. We propose a bistable model of actin dynamics to account for these experimental observation. The model is based on the simplifying assumption that the actin cytoskeleton is composed of two distinct network types, a dendritic and a bundled network. The two structurally different states that were observed in experiments correspond to the stable fixed points in the bistable regime of this model. Each fixed point is dominated by one of the two network types. The experimentally observed actin waves can be considered as trigger waves that propagate transitions between the two stable fixed points.
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.
Paper-based microfluidics provide an inexpensive, easy to use technology for point-of-care diagnostics in developing countries. Here, we combine paper-based microfluidic devices with responsive hydrogels to add an entire new class of functions to these versatile low-cost fluidic systems. The hydrogels serve as fluid reservoirs. In response to an external stimulus, e.g. an increase in temperature, the hydrogels collapse and release fluid into the structured paper substrate. In this way, chemicals that are either stored on the paper substrate or inside the hydrogel pads can be dissolved, premixed, and brought to reaction to fulfill specific analytic tasks. We demonstrate that multi-step sequences of chemical reactions can be implemented in a paper-based system and operated without the need for external precision pumps. We exemplify this technology by integrating an antibody-based E. coli test on a small and easy to use paper device.
Swimming patterns of a polarly flagellated bacterium in environments of increasing complexity
(2015)
The natural habitat of many bacterial swimmers is dominated by interfaces and narrow interstitial spacings where they frequently interact with the fluid boundaries in their vicinity. To quantify these interactions, we investigated the swimming behavior of the soil bacterium Pseudomonas putida in a variety of confined environments. Using microfluidic techniques, we fabricated structured microchannels with different configurations of cylindrical obstacles. In these environments, we analyzed the swimming trajectories for different obstacle densities and arrangements. Although the overall swimming pattern remained similar to movement in the bulk fluid, we observed a change in the turning angle distribution that could be attributed to collisions with the cylindrical obstacles. Furthermore, a comparison of the mean run length of the bacteria to the mean free path of a billiard particle in the same geometry indicated that, inside a densely packed environment, the trajectories of the bacterial swimmers are efficiently guided along the open spacings.
Amoebae explore their environment in a random way, unless external cues like, e. g., nutrients, bias their motion. Even in the absence of cues, however, experimental cell tracks show some degree of persistence. In this paper, we analyzed individual cell tracks in the framework of a linear mixed effects model, where each track is modeled by a fractional Brownian motion, i.e., a Gaussian process exhibiting a long-term correlation structure superposed on a linear trend. The degree of persistence was quantified by the Hurst exponent of fractional Brownian motion. Our analysis of experimental cell tracks of the amoeba Dictyostelium discoideum showed a persistent movement for the majority of tracks. Employing a sliding window approach, we estimated the variations of the Hurst exponent over time, which allowed us to identify points in time, where the correlation structure was distorted ("outliers"). Coarse graining of track data via down-sampling allowed us to identify the dependence of persistence on the spatial scale. While one would expect the (mode of the) Hurst exponent to be constant on different temporal scales due to the self-similarity property of fractional Brownian motion, we observed a trend towards stronger persistence for the down-sampled cell tracks indicating stronger persistence on larger time scales.