Influence of fast advective flows on pattern formation of <i>Dictyostelium discoideum</i> - Fig 11

<p>a) The wave pattern at the time point that the flow of magnitude <i>V</i>_<i>f</i> = 1 mm/min is turned on (<i>t</i>₁ in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0194859#pone.0194859.g010" target="_blank">Fig 10</a>), and b) at time <i>t</i>₂, 8 min later. c) The fully developed waves shortly before turning off the flow at time <i>t</i>₃ and d) the waves at time <i>t</i>₄, shortly after switching off the flow.</p

Influence of fast advective flows on pattern formation of <i>Dictyostelium discoideum</i> - Fig 1

<p>a) Schematic representation of the reaction-diffusion model used, reproduced from [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0194859#pone.0194859.ref016" target="_blank">16</a>]. b) Phase diagram showing the different regimes depending on the production <i>σ</i> and degradation <i>k</i>_<i>e</i>. Stable regime in white, where one stable steady state exists, excitable regime in orange, 3 steady states, one of which is excitable and the other two unstable. Oscillatory regime in purple, one unstable steady state surrounded by a limit cycle. Convectively unstable regime in light blue, one steady state which is convectively unstable. Bistable regime in green, two stable steady states. The red line marks the trajectory that the developmental path follows. Simulations with fixed parameters used the ones marked by the black asterisk. c) Cell state over time for a cell starting with <i>t</i>_<i>s</i> = 0. The color coding is the same as b).</p

Space-time plot of numerical simulations using the developmental path scheme.

<p>The advecting flow is initially <i>V</i>_<i>f</i> = 1 mm/min and stops at <i>t</i> = 250 min.</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

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

Influence of fast advective flows on pattern formation of <i>Dictyostelium discoideum</i> - Fig 5

<p>a) A half-parabolic shaped wave front observed at <i>V</i>_<i>f</i> = 10 mm/min. b) Two stripe-like waves initiating at top and bottom boundaries for flow speed of <i>V</i>_<i>f</i> = 15 mm/min.</p

Influence of fast advective flows on pattern formation of <i>Dictyostelium discoideum</i> - Fig 7

<p>a) Wave profile comparison between the two- and three-component models at imposed flow velocity of <i>V</i>_<i>f</i> = 5 mm/min. b) Wave thickness vs imposed flow for the different models; calculated as 2.355 times the square root of the second moment. Two-component model in black, three-component model in blue.</p

Aggregation process observed in a bright field microscope at <i>V</i>_<i>f</i> = 10 mm/min.

<p>Cone-shaped aggregation domains with long stream lines are visible in panel e).</p

Space-time plot of numerical simulations using the developmental path scheme and a stepwise incremental flow.

<p>Initial flow velocity <i>V</i>_<i>f</i> = 1.0 mm/min, incremented at <i>t</i> = 220 min to <i>V</i>_<i>f</i> = 2.0 mm/min, and again increased to <i>V</i>_<i>f</i> = 3.0 mm/min at <i>t</i> = 250 min.</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