Flow-driven two-dimensional waves in colonies of <i>Dictyostelium discoideum</i>

Gholami, Azam; Zykov, V. S.; Steinbock, Oliver; Bodenschatz, Eberhard

doi:10.1088/1367-2630/17/9/093040

Cited by 6 publications

(7 citation statements)

References 22 publications

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“…We attribute this difference to the smaller advection speeds at the boundary layer which are enough to destabilize the whole system. This phenomenon was also observed in some preliminary simulations using a parabolic advection flow, 21 where the advection flow velocity is much smaller in a wider region, thus making the instability range of existence much larger.…”

Section: -Dimensional Resultssupporting

confidence: 66%

Convective instability and boundary driven oscillations in a reaction-diffusion-advection model

Vidal-Henriquez

Zykov

Bodenschatz

et al. 2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

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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 travelling 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.

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Section: -Dimensional Resultssupporting

confidence: 66%

Convective instability and boundary driven oscillations in a reaction-diffusion-advection model

Vidal-Henriquez

Zykov

Bodenschatz

et al. 2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…This differential transport of extracellular cAMP induced macroscopic wave trains that had a unique period and propagated with a velocity proportional to the imposed flow velocity downstream. This behavior was studied theoretically [ 16 , 17 ] using the two-component reaction-diffusion model proposed by Martiel-Goldbeter [ 18 ] for the production and relay of cAMP. While the theoretical results could explain much of the experimental observations, there were still open questions regarding the generation of a self supporting wave train at the inlet of the microfluidic channel and only small flow rates of up to 5 mm/min were studied.…”

Section: Introductionmentioning

confidence: 99%

Influence of fast advective flows on pattern formation of Dictyostelium discoideum

et al. 2018

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We report experimental and numerical results on pattern formation of self-organizing Dictyostelium discoideum cells in a microfluidic setup under a constant buffer flow. The external flow advects the signaling molecule cyclic adenosine monophosphate (cAMP) downstream, while the chemotactic cells attached to the solid substrate are not transported with the flow. At high flow velocities, elongated cAMP waves are formed that cover the whole length of the channel and propagate both parallel and perpendicular to the flow direction. While the wave period and transverse propagation velocity are constant, parallel wave velocity and the wave width increase linearly with the imposed flow. We also observe that the acquired wave shape is highly dependent on the wave generation site and the strength of the imposed flow. We compared the wave shape and velocity with numerical simulations performed using a reaction-diffusion model and found excellent agreement. These results are expected to play an important role in understanding the process of pattern formation and aggregation of D. discoideum that may experience fluid flows in its natural habitat.

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“…In aqueous media, swimming patterns of cells that consist of pulling, pushing, gliding, scrawling, imply that cells interactions with fluids constituents may lead to a variety of spatio-temporal patterns. Experimental and theoretical evidence showed that bacteria are collectively transported through wavy structures like solitary pulses [18][19][20][24][25][26][27][28][29][30]. Furthermore, other experimental findings suggest that hydrodynamic interactions coupled to the chemoattractant concentration gradient may guide traveling bands of bacteria at a constant speed [18][19][20].…”

Section: Introductionmentioning

confidence: 98%

“…Besides the importance of chemotaxis in the cellular realm where it plays a major role in fertilization [2][3][4], intercellular communication [5,6], wound repair [2,3], and pattern formation [3,7], it has also been reported in animal and insect ecology [4], large scale collective behavior [1,[8][9][10][11][12][13][14] and synchronization processes [5,8]. Though the literature is well furnished when it comes to chemotaxis, the various issues associated with a combination of chemical and mechanical constraints cells might feature in their natural habitats has just recently started receiving attention [10,[12][13][14][15][16][17][18][19][20][21][22]. It is known that the latter interactions may lead to interesting holistic dynamical behaviors that to the best of our knowledge remain to be fully understood.…”

Section: Introductionmentioning

confidence: 99%

“…Experimental and theoretical evidence showed that bacteria are collectively transported through wavy structures like solitary pulses [18][19][20][24][25][26][27][28][29][30]. Furthermore, other experimental findings suggest that hydrodynamic interactions coupled to the chemoattractant concentration gradient may guide traveling bands of bacteria at a constant speed [18][19][20]. Therefore the inclusion of advection rate while modeling chemotactic behaviors is expected to substantially improve our knowledge of the system.…”

Section: Introductionmentioning

confidence: 99%

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Step, dip, and bell-shape traveling waves in a (2 + 1)-chemotaxis model with traction and long-range diffusion

Kuipou

Didier

Mohamadou

et al. 2021

Preprint

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In this paper, a new (2 + 1)-dimensional chemotaxis model is introduced, the focus being the understanding of influences of cooperative mechanisms from traction forces, long-range diffusion to chemotaxis on the dynamical characteristics of waves and their transport. Applying the F-expansion method, three families of new traveling wave solutions of bacterial density and chemoattractant concentration are constructed, including step, dip, and bell-shape wave profiles. The dependence of the conditions of existence of our solutions with respect to the model parameters is fully clarified. We found that traction and long-range diffusion slow down the waves and entail the transport of a small number of particles. Surprisingly, the long-range diffusion increases the thickness of the wave but does not alter its magnitude. Amongst families of solutions constructed, dip waves travel faster may be used to explain fast coordination amongst particles. As they support the transport of large amounts of cells, step waves could explain the transport of particles in high dense media. Intensive numerical simulations corroborate with a pretty much accuracy our theoretical analysis, confirming the robustness of our predictions. Traction, long-range diffusion and chemotaxis deeply affect the wave dynamics, they must be taken into account for a better understanding of chemotaxis systems.

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Flow-driven two-dimensional waves in colonies of Dictyostelium discoideum

Cited by 6 publications

References 22 publications

Convective instability and boundary driven oscillations in a reaction-diffusion-advection model

Convective instability and boundary driven oscillations in a reaction-diffusion-advection model

Influence of fast advective flows on pattern formation of Dictyostelium discoideum

Step, dip, and bell-shape traveling waves in a (2 + 1)-chemotaxis model with traction and long-range diffusion

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