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Draft:Triangulation sensing

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  • Comment: Tried to improve the article a bit, but there's simply large swathes of it that are entirely unsourced. MWFwiki (talk) 20:57, 22 May 2025 (UTC)
  • Comment: Please clean up formatting and prose to be more encyclopedic. Refer to WP:MOS Bluethricecreamman (talk) 16:27, 23 December 2024 (UTC)
  • Comment: Issues have not been fixed since the last decline. LR.127 (talk) 01:18, 18 September 2024 (UTC)
  • Comment: Requires complete rewrite and more references to prove notability. The Herald (Benison) (talk) 07:01, 4 February 2024 (UTC)


Triangulation sensing refers to the use of multiple signals or sources of information to accurately determine the location, orientation, or movement of a biological object or entity in space. Borrowing its name from the geometric principle of triangulation—where the position of an unknown point is established by measuring angles or distances from multiple known points—this concept underpins a variety of biological processes, ranging from cellular navigation to the spatial orientation of entire organisms.[1]

Navigation

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Many organisms employ a suite of navigational strategies that integrate diverse environmental cues. Migratory birds, for instance, combine information from the Earth's magnetic field, the position of the sun and stars, and even olfactory landmarks to chart long-distance routes.[2][3] Similarly, marine turtles and fish use a geomagnetic “map sense” in concert with celestial cues and olfactory gradients to home in on distant feeding and breeding grounds.[4]

Chemical gradients

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Cells such as bacteria and immune cells harness triangulation sensing to decode chemical gradients within their environments. During chemotaxis, a cell detects small differences in the concentration of signaling molecules across its surface. For example, the bacterium Escherichia coli moves toward higher concentrations of attractants by comparing the binding events at receptors distributed around its cell body.[5][6]

Mechanical sensing

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In addition to chemical cues, many organisms rely on mechanical signals to gauge spatial orientation. Plants, for example, adjust their growth in response to directional light (phototropism) and gravity (gravitropism) by integrating tension and compression signals across their tissues.[7][8]

Neuronal triangulation

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Triangulation sensing also plays a critical role in the nervous system. Neurons in the hippocampus and entorhinal cortex—place cells, grid cells, and head‐direction cells—work in concert to create an internal map of the external world.[9][10][11] Moreover, during neuronal development the growth cone at the tip of an extending axon navigates by interpreting extracellular chemical gradients, transforming these molecular fluxes into directional cues essential for accurate circuit wiring.[12][13]

Physical model

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At the core of triangulation sensing lies a physical model describing how diffusing molecules—such as morphogens or transcription factors—interact with cellular receptors. In this model, molecules released from a source undergo Brownian motion until they encounter small, absorbing receptor windows on a cell’s surface. The rate at which these particles arrive, or molecular flux, provides quantitative information that can be used to estimate the source’s location.[14]

Reconstruction of gradient source location

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The reconstruction of a gradient source from diffusing particles involves the following steps:

  1. Arrival of Diffusing Particles – Particles are released from the source and diffuse until hitting receptors.
  2. Counting Particle Arrivals – Receptors count bound particles over time, estimating the flux at each site.
  3. Source Position Estimation – Combining these fluxes solves the inverse problem of Laplace's equation to pinpoint the source.[15]
  4. Reduction of Fluctuations – Accuracy improves as more receptors are added, averaging out stochastic arrival noise.

Mathematical formulation

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The mathematical framework[14] builds on diffusion theory. For N narrow absorbing windows on the surface of a sphere or disk, one imposes rapid‐binding boundary conditions at each window. The steady‐state flux at each receptor then yields a system of equations whose unknowns are the source coordinates.[16]

Numerical and computational elements

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In large‐N systems (e.g. N > 10), hybrid stochastic simulations—merging deterministic PDE solvers with random‐walk particle tracking—can dramatically cut run‐times while retaining localization precision.[17]

References

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  1. ^ Dobramysl U, Holcman D. Computational methods and diffusion theory in triangulation sensing to model neuronal navigation. *Rep Prog Phys.* 2022;85(10):104601. doi:10.1088/1361-6633/ac906b
  2. ^ Wiltschko R, Wiltschko W. Magnetic orientation and magnetoreception in birds and other animals. *J Comp Physiol A.* 2006;192(8):675–689. doi:10.1007/s00359-006-0123-7
  3. ^ Alerstam T. *Bird Migration*. Cambridge University Press; 1990.
  4. ^ Lohmann KJ, Lohmann CMF, Putman NF. Magnetic maps in animals: nature’s GPS. *J Exp Biol.* 2008;211(24):3697–3705. doi:10.1242/jeb.017650
  5. ^ Berg HC, Brown DA. Chemotaxis in *Escherichia coli* analysed by three‐dimensional tracking. *Nature.* 1972;239(5374):500–504. doi:10.1038/239500a0
  6. ^ Sourjik V, Wingreen NS. Responding to chemical gradients: bacterial chemotaxis. *Curr Opin Cell Biol.* 2012;24(2):262–268. doi:10.1016/j.ceb.2012.02.005
  7. ^ Briggs WR, Christie JM. Phototropins 1 and 2: versatile plant blue‐light receptors. *Trends Plant Sci.* 2002;7(5):204–210. doi:10.1016/S1360-1385(02)02287-8
  8. ^ Moulia B, Frangne N. Mechanosensing and mechanoresponse in plants: travelling along the cell wall. *J Exp Bot.* 2022;73(17):5892–5912. doi:10.1093/jxb/erac295
  9. ^ O’Keefe J, Dostrovsky J. The hippocampus as a spatial map: preliminary evidence from unit activity in the freely-moving rat. *Brain Res.* 1971;34(1):171–175. doi:10.1016/0006-8993(71)90358-1
  10. ^ Hafting T, Fyhn M, Molden S, Moser MB, Moser EI. Microstructure of a spatial map in the entorhinal cortex. *Nature.* 2005;436(7052):801–806. doi:10.1038/nature03721
  11. ^ Taube JS, Muller RU, Ranck JB Jr. Head-direction cells recorded from the postsubiculum in freely moving rats. I. Description and quantitative analysis. *J Neurosci.* 1990;10(2):420–435. doi:10.1523/JNEUROSCI.10-02-00420.1990
  12. ^ Kolodkin AL, Tessier-Lavigne M. Mechanisms and molecules of neuronal wiring: a primer. *Cold Spring Harb Perspect Biol.* 2010;3(6):a001727. doi:10.1101/cshperspect.a001727
  13. ^ Blockus H, Chédotal A. The multifaceted roles of Slits and Robos in cortical circuits: from proliferation to axon guidance and neurological diseases. *Curr Opin Neurobiol.* 2014;27:82–88. doi:10.1016/j.conb.2014.03.003
  14. ^ a b Dobramysl U, Holcman D. Computational methods and diffusion theory in triangulation sensing to model neuronal navigation. *Rep Prog Phys.* 2022;85(10):104601. doi:10.1088/1361-6633/ac906b
  15. ^ Dobramysl U, Holcman D. Reconstructing the gradient source position from steady-state fluxes to small receptors. *Sci Rep.* 2018;8(1):10458. doi:10.1038/s41598-018-28514-x
  16. ^ Shukron O, Dobramysl U, Holcman D. Chemical reactions for molecular and cellular biology. *Chem Kinet: Beyond Textbook.* 2019:353–371.
  17. ^ Erban R, Chapman SJ. Stochastic modelling of reaction–diffusion processes: algorithms for bimolecular reactions. *Phys Biol.* 2009;6(4):046001. doi:10.1088/1478-3975/6/4/046001
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