Spatial Patterns in Chemically and Biologically Reacting Flows

We present here a number of processes, inspired by concepts in Nonlinear Dynamics such as chaotic advection and excitability, that can be useful to understand generic behaviors in chemical or biological systems in fluid flows. Emphasis is put on the description of observed plankton patchiness in the sea. The linearly decaying tracer, and excitable kinetics in a chaotic flow are mainly the models described. Finally, some warnings are given about the difficulties in modeling discrete individuals (such as planktonic organisms) in terms of continuous concentration fields.Comment: 41 pages, 10 figures; To appear in the Proceedings of the 2001 ISSAOS School on 'Chaos in Geophysical Flows

The effect of forcing on the spatial structure and spectra of chaotically advected passive scalars

The stationary distribution of passive tracers chaotically advected by a two-dimensional large-scale flow is investigated. The tracer field is force by resetting the value of the tracer in certain localised regions. This problem is mathematically equivalent to advection in open flows and results in a fractal tracer structure. The spectral exponent of the tracer field is different from that for a passive tracer with the usual additive forcing (the so called Batchelor spectrum) and is related to the fractal dimension of the set of points that have never visited the forcing regions. We illustrate this behaviour by considering a time-periodic flow whose effect is equivalent to a simple two-dimensional area-preserving map. We also show that similar structure in the tracer field is found when the flow is aperiodic in time.Comment: 7 pages, 9 figure

Transport and aggregation of self-propelled particles in fluid flows

An analysis of the dynamics of prolate swimming particles in laminar flow is presented. It is shown that the particles concentrate around flow regions with chaotic trajectories. When the swimming velocity is larger than a threshold, dependent on the aspect ratio of the particles, all particles escape from regular elliptic regions. For thin rodlike particles the threshold velocity vanishes; thus, the arbitrarily small swimming velocity destroys all transport boundaries. We derive an expression for the minimum swimming velocity required for escape based on a circularly symmetric flow approximation of the regular elliptic regions

Dynamics of "leaking" Hamiltonian systems

In order to understand the dynamics in more detail, in particular for visualizing the space-filling unstable foliation of closed chaotic Hamiltonian systems, we propose to leak them up. The cutting out of a finite region of their phase space, the leak, through which escape is possible, leads to transient chaotic behavior of nearly all the trajectories. The never-escaping points belong to a chaotic saddle whose fractal unstable manifold can easily be determined numerically. It is an approximant of the full Hamiltonian foliation, the better the smaller the leak is. The escape rate depends sensitively on the orientation of the leak even if its area is fixed. The applications for chaotic advection, for chemical reactions superimposed on hydrodynamical flows, and in other branches of physics are discussed

Smooth-filamental transition of active tracer fields stirred by chaotic advection

The stationary-state spatial structure of interacting chemical fields is investigated in the nondiffusive limit. The evolution of fluid parcels is described by independent dynamical systems driven by chaotic advection. The distribution can be filamental or smooth depending on the relative strength of the dispersion due to chaotic advection and the stability of the chemical dynamics. We give the condition for the smooth-filamental transition and relate the Hölder exponent of the filamental structure to the Lyapunov exponents. Theoretical findings are illustrated by numerical experiments. © 1999 The American Physical Society.Funded by a Royal Society-NATO Postdoctoral Fellowship and C. L. was funded by CICYT projects (No. MAR95-1861 and No. MAR98-0840).Peer Reviewe

Context-dependent interaction leads to emergent search behavior in social aggregates

Locating the source of an advected chemical signal is a common challenge facing many living organisms. When the advecting medium is characterized by either high Reynolds number or high Peclet number the task becomes highly non-trivial due to the generation of heterogenous, dynamically changing filamental concentrations which do not decrease monotonically with distance to the source. Defining search strategies which are effective in these environments has important implications for the understanding of animal behavior and for the design of biologically inspired technology. Here we present a strategy which is able to solve this task without the higher intelligence required to assess spatial gradient direction, measure the diffusive properties of the flow field or perform complex calculations. Instead our method is based on the collective behavior of autonomous individuals following simple social interaction rules which are modified according to the local conditions they are experiencing. Through these context-dependent interactions the group is able to locate the source of a chemical signal and in doing so displays an awareness of the environment not present at the individual level. Our model demonstrates the ability of decentralized information processing systems to solve real world problems and also illustrates an alternative pathway to the evolution of higher cognitive capacity via the emergent, group level intelligence which can result from local interactions.Comment: 3 figure

Contact inhibition of locomotion and mechanical cross-talk between cell-cell and cell-substrate adhesion determines the pattern of junctional tension in epithelial cell aggregates

We generated a computational approach to analyze the biomechanics of epithelial cell aggregates, either island or stripes or entire monolayers, that combines both vertex and contact-inhibition-of-locomotion models to include both cell-cell and cell-substrate adhesion. Examination of the distribution of cell protrusions (adhesion to the substrate) in the model predicted high order profiles of cell organization that agree with those previously seen experimentally. Cells acquired an asymmetric distribution of basal protrusions, traction forces and apical aspect ratios that decreased when moving from the edge to the island center. Our in silico analysis also showed that tension on cell-cell junctions and apical stress is not homogeneous across the island. Instead, these parameters are higher at the island center and scales up with island size, which we confirmed experimentally using laser ablation assays and immunofluorescence. Without formally being a 3-dimensional model, our approach has the minimal elements necessary to reproduce the distribution of cellular forces and mechanical crosstalk as well as distribution of principal stress in cells within epithelial cell aggregates. By making experimental testable predictions, our approach would benefit the mechanical analysis of epithelial tissues, especially when local changes in cell-cell and/or cell-substrate adhesion drive collective cell behavior.Comment: 39 pages, 8 Figures. Supplementary Information is include

Functional definition of progenitors versus mature endothelial cells reveals key SoxF-dependent differentiation process

Background: During adult life, blood vessel formation is thought to occur via angiogenic processes involving branching from existing vessels. An alternate proposal suggests that neovessels form from endothelial progenitors able to assemble the intimal layers. We here aimed to define vessel-resident endothelial progenitors in vivo in a variety of tissues in physiological and pathological situations such as normal aorta, lungs, and wound healing, tumors, and placenta, as well. Methods: Based on protein expression levels of common endothelial markers using flow cytometry, 3 subpopulations of endothelial cells could be identified among VE-Cadherin+ and CD45- cells. Results: Lineage tracing by using Cdh5cre /Rosa-YFP reporter strategy demonstrated that the CD31-/loVEGFR2lo/intracellular endothelial population was indeed an endovascular progenitor (EVP) of an intermediate CD31intVEGFR2lo/intracellular transit amplifying (TA) and a definitive differentiated (D) CD31hiVEGFR2hi/extracellular population. EVP cells arose from vascular-resident beds that could not be transferred by bone marrow transplantation. Furthermore, EVP displayed progenitor-like status with a high proportion of cells in a quiescent cell cycle phase as assessed in wounds, tumors, and aorta. Only EVP cells and not TA and D cells had self-renewal capacity as demonstrated by colony-forming capacity in limiting dilution and by transplantation in Matrigel plugs in recipient mice. RNA sequencing revealed prominent gene expression differences between EVP and D cells. In particular, EVP cells highly expressed genes related to progenitor function including Sox9, Il33, Egfr, and Pdfgrα. Conversely, D cells highly expressed genes related to differentiated endothelium including Ets1&2, Gata2, Cd31, Vwf, and Notch. The RNA sequencing also pointed to an essential role of the Sox18 transcription factor. The role of SOX18 in the differentiation process was validated by using lineage-tracing experiments based on Sox18Cre/Rosa-YFP mice. Besides, in the absence of functional SOX18/SOXF, EVP progenitors were still present, but TA and D populations were significantly reduced. Conclusions: Our findings support an entirely novel endothelial hierarchy, from EVP to TA to D, as defined by self-renewal, differentiation, and molecular profiling of an endothelial progenitor. This paradigm shift in our understanding of vascular-resident endothelial progenitors in tissue regeneration opens new avenues for better understanding of cardiovascular biology