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>_<i>f</i> = 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>_<i>f</i> = 1 mm/min) at <i>t</i>₁ and turned off again at <i>t</i>₃.

<p>While the flow is off (<i>t</i> ≤ <i>t</i>₁), the cells show target patterns. After it turns on at <i>t</i>₁, there is a short disordered phase until flow-driven waves fully develop, which travel downstream at <i>v</i>_{∥,<i>on</i>} = 0.99 ± 0.03 mm/min. At time <i>t</i>₃, the flow is turned off and the waves still propagate further downstream at slower speed of <i>v</i>_{∥,<i>off</i>} = 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>_∥, b) wave speed in transversal direction <i>v</i>_⊥, c) wave period <i>T</i>, and d) wave front thickness as a function of imposed flow velocity <i>V</i>_<i>f</i>.

<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>_<i>f</i> = 15 mm/min. Top and bottom panels show cAMP waves in simulations with two different initial conditions in the state of the cells.</p