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Active flow network

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An active flow network is a graph with edges and nodes, where particles inside this graph are propelled by an active mechanism.[1][2] This type of network is used to study the motion of molecules in biological medium. Examples are organelles, including the Endoplasmic Reticulum (ER).[3] The mechanism of the flow between nodes is actively driven, as opposed to passive transport by diffusion.[4] Active transport requires energy consumption, found in the form of ATP in biological systems. The slime mold Physarum polycephalum is also growing as a network[5], where motion inside is driven an active flow.

Active flow network in transportation

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Unidirectional transportation is reminiscent of trains, cars or communication (internet, telephone), where there is a limiting capacity due to maximal amount of commodities that can travel inside a branch connecting two nodes.[6]

Active flow networks in the body

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Arteries and vein generate a network where the blood flow is pulsed by the heart contraction cycle. The flow is often model using complex fluid mechanics (Navier-stokes equations) that could be coupled to the structure.[7][8] Red blood cells are also transported inside these networks [9] 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.[10][11] Blood flow is an active process further modulated by neuronal activity.[12]

Active flow networks in electronics

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In electronics, diodes or resistances form network consuming electrical energy. Theory 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[13][14]

Properties of active flow networks inside the endoplasmic reticulum

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Active flow networks inside the endoplasmic reticulum are represented by a graph (G,N), with N nodes connected by junctions. Two time scales leads to two opposite properties, as edge can switch at random time from one direction only to the opposite one: 1- time for an edge to switch from direction to the opposite and 2-the time to move from one edge to the next one. This leads to two phenomena:

Trapping
a particle was already in the node and one edge switches an even number of times between the instant of transitions, or the particle was previously in the node and had switched to a neighbouring node before returning to the considered node.
Backtracking
a particle can jump back to the node it came from, thus wasting time by visiting again the previous node. However, in the network, this probability is affected by the direction of the edge.

Under these two effects (trapping and backtracking), the network exploration is slower when compared to a unidirectional network, where such situation does not occur.[15] AFN models can be used to intert[clarification needed] data extracted by fluorescence recovery after photobleaching, single particle trajectories or photoactivation.

References

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  1. ^ a 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. ^ Mauro., Garavello (2006). Traffic flow on networks. American Institute of Mathematical Sciences. ISBN 1-60133-000-6. OCLC 255485562.
  3. ^ Voeltz, Gia K; Rolls, Melissa M; Rapoport, Tom A (2002-10-01). "Structural organization of the endoplasmic reticulum". EMBO Reports. 3 (10): 944–950. doi:10.1093/embo-reports/kvf202. ISSN 1469-221X. PMC 1307613. PMID 12370207.
  4. ^ Lamberson, P. J. (2016-04-14). Bramoullé, Yann; Galeotti, Andrea; Rogers, Brian W (eds.). "Diffusion in Networks". The Oxford Handbook of the Economics of Networks. pp. 478–503. doi:10.1093/oxfordhb/9780199948277.013.11. ISBN 978-0-19-994827-7. Retrieved 2021-08-13.
  5. ^ Alim, Karen; Amselem, Gabriel; Peaudecerf, François; Brenner, Michael P.; Pringle, Anne (2013-08-13). "Random network peristalsis in Physarum polycephalum organizes fluid flows across an individual". Proceedings of the National Academy of Sciences. 110 (33): 13306–13311. Bibcode:2013PNAS..11013306A. doi:10.1073/pnas.1305049110. PMC 3746869. PMID 23898203.
  6. ^ "Active Traffic Management: Approaches: Active Transportation and Demand Management - FHWA Operations". Federal Highway Administration (FHWA). Retrieved 2021-08-13.
  7. ^ 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.
  8. ^ 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.
  9. ^ 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.
  10. ^ 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.
  11. ^ 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.
  12. ^ 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.
  13. ^ S. Redner, Journal of Physics A: Mathematical and General 14, L349 (1981).
  14. ^ S. R. Broadbent and J. M. Hammersley, in Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 53 (Cambridge University Press, 1957) pp. 629–641.
  15. ^ 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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