97 research outputs found
Stochastic Reaction-Diffusion Systems in Biophysics: Towards a Toolbox for Quantitative Model Evaluation
We develop a statistical toolbox for a quantitative model evaluation of
stochastic reaction-diffusion systems modeling space-time evolution of
biophysical quantities on the intracellular level. Starting from space-time
data , as, e.g., provided in fluorescence microscopy recordings, we
discuss basic modelling principles for conditional mean trend and fluctuations
in the class of stochastic reaction-diffusion systems, and subsequently develop
statistical inference methods for parameter estimation. With a view towards
application to real data, we discuss estimation errors and confidence
intervals, in particular in dependence of spatial resolution of measurements,
and investigate the impact of misspecified reaction terms and noise
coefficients. We also briefly touch implementation issues of the statistical
estimators. As a proof of concept we apply our toolbox to the statistical
inference on intracellular actin concentration in the social amoeba
Dictyostelium discoideum
Modeling random crawling, membrane deformation and intracellular polarity of motile amoeboid cells
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.Peer ReviewedPostprint (published version
Diffusivity estimation for activatorâinhibitor models: theory and application to intracellular dynamics of the actin cytoskeleton
A theory for diffusivity estimation for spatially extended activatorâinhibitor dynamics
modeling the evolution of intracellular signaling networks is developed in the math-
ematical framework of stochastic reactionâdiffusion systems. In order to account for
model uncertainties, we extend the results for parameter estimation for semilinear
stochastic partial differential equationsPostprint (published version
Adaptive microfluidic gradient generator for quantitative chemotaxis experiments
Chemotactic motion in a chemical gradient is an essential cellular function
that controls many processes in the living world. For a better understanding
and more detailed modelling of the underlying mechanisms of chemotaxis,
quantitative investigations in controlled environments are needed. We
developed a setup that allows us to separately address the dependencies of the
chemotactic motion on the average background concentration and on the gradient
steepness of the chemoattractant. In particular, both the background
concentration and the gradient steepness can be kept constant at the position
of the cell while it moves along in the gradient direction. This is achieved
by generating a well-defined chemoattractant gradient using flow photolysis.
In this approach, the chemoattractant is released by a light-induced reaction
from a caged precursor in a microfluidic flow chamber upstream of the cell.
The flow photolysis approach is combined with an automated real-time cell
tracker that determines changes in the cell position and triggers movement of
the microscope stage such that the cell motion is compensated and the cell
remains at the same position in the gradient profile. The gradient profile can
be either determined experimentally using a caged fluorescent dye or may be
alternatively determined by numerical solutions of the corresponding physical
model. To demonstrate the function of this adaptive microfluidic gradient
generator, we compare the chemotactic motion of Dictyostelium discoideum cells
in a static gradient and in a gradient that adapts to the position of the
moving cell
Cargo size limits and forces of cell-driven microtransport
The integration of motile cells into biohybrid microrobots offers unique
properties such as sensitive responses to external stimuli, resilience, and
intrinsic energy supply. Here we study biohybrid microtransporters that are
driven by amoeboid Dictyostelium discoideum cells and explore how the speed of
transport and the resulting viscous drag force scales with increasing radius of
the spherical cargo particle. Using a simplified geometrical model of the
cell-cargo interaction, we extrapolate our findings towards larger cargo sizes
that are not accessible with our experimental setup and predict a maximal cargo
size beyond which active cell-driven transport will stall. The active forces
exerted by the cells to move a cargo show mechanoresponsive adaptation and
increase dramatically when challenged by an external pulling force, a mechanism
that may become relevant when navigating cargo through complex heterogeneous
environments
From single to collective motion of social amoebae: a computational study of interacting cells
The coupling of the internal mechanisms of cell polarization to cell shape deformations and subsequent cell crawling poses many interdisciplinary scientific challenges. Several mathematical approaches have been proposed to model the coupling of both processes, where one of the most successful methods relies on a phase field that encodes the morphology of the cell, together with the integration of partial differential equations that account for the polarization mechanism inside the cell domain as defined by the phase field. This approach has been previously employed to model the motion of single cells of the social amoeba Dictyostelium discoideum, a widely used model organism to study actin-driven motility and chemotaxis of eukaryotic cells. Besides single cell motility, Dictyostelium discoideum is also well-known for its collective behavior. Here, we extend the previously introduced model for single cell motility to describe the collective motion of large populations of interacting amoebae by including repulsive interactions between the cells. We performed numerical simulations of this model, first characterizing the motion of single cells in terms of their polarity and velocity vectors. We then systematically studied the collisions between two cells that provided the basic interaction scenarios also observed in larger ensembles of interacting amoebae. Finally, the relevance of the cell density was analyzed, revealing a systematic decrease of the motility with density, associated with the formation of transient cell clusters that emerge in this system even though our model does not include any attractive interactions between cells. This model is a prototypical active matter system for the investigation of the emergent collective dynamics of deformable, self-driven cells with a highly complex, nonlinear coupling of cell shape deformations, self-propulsion and repulsive cell-cell interactions. Understanding these self-organization processes of cells like their autonomous aggregation is of high relevance as collective amoeboid motility is part of wound healing, embryonic morphogenesis or pathological processes like the spreading of metastatic cancer cells.Postprint (published version
How cortical waves drive fission of motile cells
Cytokinesisâthe division of a cell into two daughter cellsâis a key step in cell growth and proliferation. It typically occurs in synchrony with the cell cycle to ensure that a complete copy of the genetic information is passed on to the next generation of daughter cells. In animal cells, cytokinesis commonly relies on an actomyosin contractile ring that drives equatorial furrowing and separation into the two daughter cells. However, also contractile ring-independent forms of cell division are known that depend on substrate-mediated traction forces. Here, we report evidence of an as yet unknown type of contractile ring-independent cytokinesis that we termed wave-mediated cytofission. It is driven by self-organized cortical actin waves that travel across the ventral membrane of oversized, multinucleated Dictyostelium discoideum cells. Upon collision with the cell border, waves may initiate the formation of protrusions that elongate and eventually pinch off to form separate daughter cells. They are composed of a stable elongated wave segment that is enclosed by a cell membrane and moves in a highly persistent fashion. We rationalize our observations based on a noisy excitable reactionâdiffusion model in combination with a dynamic phase field to account for the cell shape and demonstrate that daughter cells emerging from wave-mediated cytofission exhibit a well-controlled size.Postprint (published version
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
Statistical parameter inference of bacterial swimming strategies
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 λ, the tumble time râ1, the swimming speed v0, the strength of speed fluctuations Ï, the relative height of speed jumps η, the thermal value for the rotational diffusion coefficient D0, and the enhanced rotational diffusivity during tumbling DT. 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.DFG, 87159868, GRK 1558: Kollektive Dynamik im Nichtgleichgewicht: in kondensierter Materie und biologischen Systeme
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