24 research outputs found
Spontaneous center formation in Dictyostelium discoideum
Dictyostelium discoideum (D.d.) is a widely studied amoeba due to its
capabilities of development, survival, and self-organization. During
aggregation it produces and relays a chemical signal (cAMP) which shows spirals
and target centers. Nevertheless, the natural emergence of these structures is
still not well understood. We present a mechanism for creation of centers and
target waves of cAMP in D.d. by adding cell inhomogeneity to a well known
reaction-diffusion model of cAMP waves and we characterize its properties. We
show how stable activity centers appear spontaneously in areas of higher cell
density with the oscillation frequency of these centers depending on their
density. The cAMP waves have the characteristic dispersion relation of trigger
waves and a velocity which increases with cell density. Chemotactically
competent cells react to these waves and create aggregation streams even with
very simple movement rules. Finally we argue in favor of the existence of
bounded phosphodiesterase to maintain the wave properties once small cell
clusters appear.Comment: Currently under review. 12 pages, 8 figures, 1 tabl
Convective Instability and Boundary Driven Oscillations in a Reaction-Diffusion-Advection Model
In a reaction-diffusion-advection system, with a convectively unstable
regime, a perturbation creates a wave train that is advected downstream and
eventually leaves the system. We show that the convective instability coexists
with a local absolute instability when a fixed boundary condition upstream is
imposed. This boundary induced instability acts as a continuous wave source,
creating a local periodic excitation near the boundary, which initiates waves
traveling both up and downstream. To confirm this, we performed analytical
analysis and numerical simulations of a modified Martiel-Goldbeter
reaction-diffusion model with the addition of an advection term. We provide a
quantitative description of the wave packet appearing in the convectively
unstable regime, which we found to be in excellent agreement with the numerical
simulations. We characterize this new instability and show that in the limit of
high advection speed, it is suppressed. This type of instability can be
expected for reaction-diffusion systems that present both a convective
instability and an excitable regime. In particular, it can be relevant to
understand the signaling mechanism of the social amoeba Dictyostelium
discoideum that may experience fluid flows in its natural habitat.Comment: 10 pages, 13 figures, published in Chaos: An Interdisciplinary
Journal of Nonlinear Scienc
Theory of light-matter interaction in nematic liquid crystals and the second Painlevé equation
We study global minimizers of an energy functional arising as a thin sample limit in the theory of light-matter interaction in nematic liquid crystals. We show that depending on the parameters various defects are predicted by the model. In particular we show existence of a new type of topological defect which we call the shadow kink. Its local profile is described by the generalized Hastings and McLeod solutions of the second Painlevé equation (Claeys et al. in Ann Math 168(2):601–641, 2008; Hastings and McLeod in Arch Ration Mech Anal 73(1):31–51, 1980). As part of our analysis we give a new proof of existence of these solutions
Cavitation controls droplet sizes in elastic media
Biological cells use droplets to separate components and spatially control
their interior. Experiments demonstrate that the complex, crowded cellular
environment affects the droplet arrangement and their sizes. To understand this
behavior, we here construct a theoretical description of droplets growing in an
elastic matrix, which is motivated by experiments in synthetic systems where
monodisperse emulsions form during a temperature decrease. We show that large
droplets only form when they break the surrounding matrix in a cavitation
event. The energy barrier associated with cavitation stabilizes small droplets
on the order of the mesh size and diminishes the stochastic effects of
nucleation. Consequently, the cavitated droplets have similar sizes and highly
correlated positions. In particular, we predict the density of cavitated
droplets, which increases with faster cooling, as in the experiments. Our model
also suggests how adjusting the cooling protocol and the density of nucleation
sites affects the droplet size distribution. In summary, our theory explains
how elastic matrices affect droplets in the synthetic system and it provides a
framework for understanding the biological case
Effective simulations of interacting active droplets
Abstract Droplets form a cornerstone of the spatiotemporal organization of biomolecules in cells. These droplets are controlled using physical processes like chemical reactions and imposed gradients, which are costly to simulate using traditional approaches, like solving the Cahn–Hilliard equation. To overcome this challenge, we here present an alternative, efficient method. The main idea is to focus on the relevant degrees of freedom, like droplet positions and sizes. We derive dynamical equations for these quantities using approximate analytical solutions obtained from a sharp interface limit and linearized equations in the bulk phases. We verify our method against fully-resolved simulations and show that it can describe interacting droplets under the influence of chemical reactions and external gradients using only a fraction of the computational costs of traditional methods. Our method can be extended to include other processes in the future and will thus serve as a relevant platform for understanding the dynamics of droplets in cells
Elastic stresses reverse Ostwald ripening
When liquid droplets nucleate and grow in a polymer network, compressive stresses can significantly increase their internal pressure, reaching values that far exceed the Laplace pressure. When droplets have grown in a polymer network with a stiffness gradient, droplets in relatively stiff regions of the network tend to dissolve, favoring growth of droplets in softer regions. Here, we show that this elastic ripening can be strong enough to reverse the direction of Ostwald ripening: large droplets can shrink to feed the growth of smaller ones. To numerically model these experiments, we generalize the theory of elastic ripening to account for gradients in solubility alongside gradients in mechanical stiffness.ISSN:1744-683XISSN:1744-684
Influence of fast advective flows on pattern formation of <i>Dictyostelium discoideum</i> - Fig 15
<p>a) Uniform cell distribution at the beginning of experiment in a flow-through microfluidic channel (<i>V</i><sub><i>f</i></sub> = 10 mm/min). b) During the propagation of the waves, the variations in cell density due to chemotactic cell movement are still negligible. c) Aggregation patterns after 8 hours starvation show cone-shaped structures with long streams downstream of the centers. d) Lateral streams, extended almost 0.5 mm in <i>y</i>-direction, start to line up in the direction of flow.</p
Space-time plot of an experiment in which the flow was initially absent, then turned on (<i>V</i><sub><i>f</i></sub> = 1 mm/min) at <i>t</i><sub>1</sub> and turned off again at <i>t</i><sub>3</sub>.
<p>While the flow is off (<i>t</i> ≤ <i>t</i><sub>1</sub>), the cells show target patterns. After it turns on at <i>t</i><sub>1</sub>, there is a short disordered phase until flow-driven waves fully develop, which travel downstream at <i>v</i><sub>∥,<i>on</i></sub> = 0.99 ± 0.03 mm/min. At time <i>t</i><sub>3</sub>, the flow is turned off and the waves still propagate further downstream at slower speed of <i>v</i><sub>∥,<i>off</i></sub> = 0.37 ± 0.03 mm/min for 30 min. They ultimately vanish on collision with waves emitted from new centers.</p
Experimental data on dependency of a) wave speed along the channel <i>v</i><sub>∥</sub>, b) wave speed in transversal direction <i>v</i><sub>⊥</sub>, c) wave period <i>T</i>, and d) wave front thickness as a function of imposed flow velocity <i>V</i><sub><i>f</i></sub>.
<p>Continuous lines represent in a), d) least square fit assuming linear scaling and in b), c) average transversal propagation velocity and wave period.</p
Elongated waves observed in simulations using a developmental path.
<p>Advecting flow <i>V</i><sub><i>f</i></sub> = 15 mm/min. Top and bottom panels show cAMP waves in simulations with two different initial conditions in the state of the cells.</p