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Utilisateur:Holcman2/Brouillon

Active Flow Networks (AFN) is a network where the motion of particle inside is propel by an active mechanism [1][2]. This type of network is used to study the motion in biological medium such as organelles, including the Endoplasmic Reticulum (ER) [3]. In AFN, the flow between the nodes of a network are actively driven, as opposed to passive transport by diffusion[4]. Active transport requires energy consumption, found in biological systems with the form of ATP. Another example of AFN is given by the slime mold Physarum polycephalum which is growing as a network[5], where the motion is driven an active flow.

Active Flow Networks in Biology

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A biological network consists of an ensemble of nodes connected by branches, lines or wires. Materials can move inside a network by various modes such as passive diffusion or active motion. Active motion results in a deterministic motion at least in part of the network[6].

Active Flow Networks in Physics

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In electronics, diodes or resistances form network consuming electrical energy. Theories based on mathematical graph theory and physicochemical reaction rate theory are used to quantify mass-conserving active flow networks [1]. Diode networks have also been introduced in percolation problems by constructing neighbouring lattice sites that transmit connectivity or information in one direction only[7] [8].

Active Flow Network in transportation

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This AFN is generated by an active transport mechanism occurring in the network. Transport can be unidirectional, which is reminiscent of train transportation when there is only one rail. It can also represent communication (telephone), where the recevier waits that the emtter stop speaking to start. In a general frame, there is a limiting capacity due to a maximal amount of commodities that can travel inside a branch connecting two nodes [9].

Active Flow Networks in medicine

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Arteries and vein generate a network where the blood flow is pulsed by the heart contraction cycle. The flow is model using complex fluid mechanics (Navier-stokes equations) that could be coupled to the structure [10] [11]. Red blood cells are transported inside these networks [12] and high pressure resistance could be due in part to red blood cell trafficking jam but also to capillary (largest pressure drops occur in the smallest vessels), especially in the brain[13] [14]. Blood flow is an active process further modulated by neuronal activity[15]

Properties of Active Flow Network (AFN) inside the Endoplasmic Reticulum

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Active Flow Network have specfic properties: for a network represented by a graph (G,N), with N nodes connected by junctions, there are two interesting properties [16] called Trapping and backtracking in AFN.

Trapping is a propety where mouving molecules are trapped and thus are synchornized.

Backtracking is a property showing that a previously visited nodes is usually not to be immediately visited again.

Under these two effects (trapping and backtracking), the network exploration is slower when compared to a undirectional network or diffusion, where such situation does not occur. [16]

Remarks: AFN models can be used to study data extracted by fluorescence recovery after photobleaching (FRAP), single particle trajectories or photoactivation.

References

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  1. ↑ a et b Stochastic cycle selection in active flow networks Francis G. Woodhouse, Aden Forrow, Joanna B. Fawcett, Jörn Dunkel Proceedings of the National Academy of Sciences Jul 2016, 113 (29) 8200-8205; DOI: 10.1073/pnas.1603351113
  2. ↑ (en) Garavello Mauro., Traffic flow on networks., American Institute of Mathematical Sciences, (ISBN 1-60133-000-6, OCLC 255485562, lire en ligne)
  3. ↑ Gia K Voeltz, Melissa M Rolls et Tom A Rapoport, « Structural organization of the endoplasmic reticulum », EMBO Reports, vol. 3, no 10,‎ , p. 944–950 (ISSN 1469-221X, PMID 12370207, PMCID 1307613, DOI 10.1093/embo-reports/kvf202, lire en ligne)
  4. ↑ (en) P. J. Lamberson, « Diffusion in Networks », sur The Oxford Handbook of the Economics of Networks, (ISBN 978-0-19-994827-7, DOI 10.1093/oxfordhb/9780199948277.013.11, consulté le ), p. 478–503
  5. ↑ Karen Alim, Gabriel Amselem, François Peaudecerf, Michael P. Brenner et Anne Pringle, « Random network peristalsis in Physarum polycephalum organizes fluid flows across an individual », Proceedings of the National Academy of Sciences, vol. 110, no 33,‎ , p. 13306–13311 (PMID 23898203, PMCID 3746869, DOI 10.1073/pnas.1305049110, Bibcode 2013PNAS..11013306A)
  6. ↑ « Intracellular Transport - an overview | ScienceDirect Topics », sur www.sciencedirect.com (consulté le )
  7. ↑ S. Redner, Journal of Physics A: Mathematical and General 14, L349 (1981).
  8. ↑ S. R. Broadbent and J. M. Hammersley, in Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 53 (Cambridge University Press, 1957) pp. 629–641.
  9. ↑ « Active Traffic Management: Approaches: Active Transportation and Demand Management - FHWA Operations », sur ops.fhwa.dot.gov (consulté le )
  10. ↑ R. Guibert, C. Fonta, and F. Plourabouffe, A new ap- proach to model confined suspensions flows in complex networks: application to blood ow," Transport in porous media, vol. 83, no. 1, pp. 171{194, 2010.
  11. ↑ N. Bessonov, A. Sequeira, S. Simakov, Y. Vassilevskii, and V. Volpert, \Methods of blood flow modelling," Mathematical modelling of natural phenomena, vol. 11, no. 1, pp. 1{25, 2016.
  12. ↑ A. R. Pries, T. W. Secomb, P. Gaehtgens, and J. Gross, Blood flow in microvascular networks. experiments and simulation.," Circulation research, vol. 67, no. 4, pp. 826{ 834, 1990.
  13. ↑ G. Hartung, C. Vesel, R. Morley, A. Alaraj, J. Sled, D. Kleinfeld, and A. Linninger, Simulations of blood as a suspension predicts a depth dependent hematocrit in the circulation throughout the cerebral cortex," PLoS computational biology, vol. 14, no. 11, p. e1006549, 2018.
  14. ↑ I. G. Gould, P. Tsai, D. Kleinfeld, and A. Linninger, The capillary bed offers the largest hemodynamic resistance to the cortical blood supply," Journal of Cerebral Blood Flow & Metabolism, vol. 37, no. 1, pp. 52{68, 2017.
  15. ↑ P. Blinder, P. S. Tsai, J. P. Kaufhold, P. M. Knutsen, H. Suhl, and D. Kleinfeld, \The cortical angiome: an interconnected vascular network with noncolumnar patterns of blood flow," Nature neuroscience, vol. 16, no. 7, p. 889, 2013.
  16. ↑ a et b M. Dora D. Holcman, Active flow network generates molecular transport by packets: case of the Endoplasmic Reticulum, Proceeding Royal Soc B, London 2020
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