Draft:Triangulation sensing
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Comment: Requires complete rewrite and more references to prove notability. The Herald (Benison) (talk) 07:01, 4 February 2024 (UTC)
Triangulation sensing is a theory describing the computational steps of a cell containing on its surface small windows, to recover the location of a source emitting random particles in a medium. This is particularly relevant for neuron navigation in the Brain..[1][2]. Reconstructing the source location allows the cell to triangulate its position. The reconstruction steps of the gradient source from the fluxes of diffusing particles arriving to small absorbing receptors are
- Arrival of the Brownian particles to the small windows
- Counting of the particles
- Inversion of the Laplace's equation to estimate the position from the fluxes
- Possible noise reduction by applying the same procedure to several triplets [3]
The mathematical formulation consists in considering diffusing molecules that have to bind to N narrow windows located on the surface of a three dimensional shaped object, typically a ball (in dimension 3) or a disk in dimension 2. The number N can range between 10 and 50, but can be much higher for other receptor types. Individual Brownian particles are released from a source at position outside the ball. The triangulation sensing method consists in reconstructing the source position from estimated steady-state fluxes at each narrow window for fast binding (i.e. the probability density has an absorbing boundary condition at the windows).[4]
To reconstruct the location of a source from the measured fluxes, at least three windows are needed. Reconstructing the source location [5] requires to invert a system equation. With $N>3$ windows, numerical procedures are used to find the position of the source .
References:
- ^ Kolodkin, A. L.; Tessier-Lavigne, M. (2010-12-01). "Mechanisms and Molecules of Neuronal Wiring: A Primer". Cold Spring Harbor Perspectives in Biology. 3 (6): a001727. doi:10.1101/cshperspect.a001727. ISSN 1943-0264. PMC 3098670. PMID 21123392.
- ^ Blockus, Heike; Chédotal, Alain (August 2014). "The multifaceted roles of Slits and Robos in cortical circuits: from proliferation to axon guidance and neurological diseases". Current Opinion in Neurobiology. 27: 82–88. doi:10.1016/j.conb.2014.03.003. ISSN 0959-4388. PMID 24698714. S2CID 8858588.
- ^ Dobramysl, U., & Holcman, D. (2018). Reconstructing the gradient source position from steady-state fluxes to small receptors. Scientific reports, 8(1), 1-8.
- ^ Shukron, O., Dobramysl, U., & Holcman, D. (2019). Chemical Reactions for Molecular and Cellular Biology. Chemical Kinetics: Beyond The Textbook, 353.
- ^ Schuss, Zeev (2009). Theory and applications of stochastic processes : an analytical approach. Springer. ISBN 978-1-4614-2542-7. OCLC 1052813540.