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Approximation of a compound-exchanging cell by a Dirac point

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Approximation of a compound-exchanging cell by a Dirac point. / Yang, Xiao; Peng, Qiyao; Hille, Sander C.
In: IFAC-PapersOnLine, Vol. 59, No. 1, 27.03.2025, p. 73-78.

Research output: Contribution to Journal/Magazine › Conference article › peer-review

Harvard

Yang, X, Peng, Q & Hille, SC 2025, 'Approximation of a compound-exchanging cell by a Dirac point', IFAC-PapersOnLine, vol. 59, no. 1, pp. 73-78. https://doi.org/10.1016/j.ifacol.2025.03.014

APA

Yang, X., Peng, Q., & Hille, S. C. (2025). Approximation of a compound-exchanging cell by a Dirac point. IFAC-PapersOnLine, 59(1), 73-78. https://doi.org/10.1016/j.ifacol.2025.03.014

Vancouver

Yang X, Peng Q, Hille SC. Approximation of a compound-exchanging cell by a Dirac point. IFAC-PapersOnLine. 2025 Mar 27;59(1):73-78. doi: 10.1016/j.ifacol.2025.03.014

Author

Yang, Xiao ; Peng, Qiyao ; Hille, Sander C. / Approximation of a compound-exchanging cell by a Dirac point. In: IFAC-PapersOnLine. 2025 ; Vol. 59, No. 1. pp. 73-78.

Bibtex

@article{41bfabb0086045a7b982264e4e5f56c1,
title = "Approximation of a compound-exchanging cell by a Dirac point",
abstract = "Communication between single cells or higher organisms by means of diffusive compounds is an important phenomenon in biological systems. Modelling therefore often occurs, most straightforwardly by a diffusion equation with suitable flux boundary conditions at the cell boundaries. Such a model will become computationally inefficient and analytically complex when there are many cells, even more so when they are moving. We propose to consider instead a point source model. Each cell is virtually reduced to a point and appears in the diffusion equation for the compound on the full spatial domain as a singular reaction term in the form of a Dirac delta {\textquoteleft}function{\textquoteright} (measure) located at the cell{\textquoteright}s centre. In this model, it has an amplitude that is a non-local function of the concentration of compound on the (now virtual) cell boundary. We prove the well-posedness of this particular parabolic problem with non-local and singular reaction term in suitable Sobolev spaces. We show for a square bounded domain and for the plane that the solution cannot be H1-smooth at the Dirac point. Further, we show a preliminary numerical comparison between the solutions to the two models that suggests that the two models are highly comparable to each other.",
author = "Xiao Yang and Qiyao Peng and Hille, {Sander C.}",
year = "2025",
month = mar,
day = "27",
doi = "10.1016/j.ifacol.2025.03.014",
language = "English",
volume = "59",
pages = "73--78",
journal = "IFAC-PapersOnLine",
issn = "2405-8963",
publisher = "IFAC Secretariat",
number = "1",

}

RIS

TY - JOUR

T1 - Approximation of a compound-exchanging cell by a Dirac point

AU - Yang, Xiao

AU - Peng, Qiyao

AU - Hille, Sander C.

PY - 2025/3/27

Y1 - 2025/3/27

N2 - Communication between single cells or higher organisms by means of diffusive compounds is an important phenomenon in biological systems. Modelling therefore often occurs, most straightforwardly by a diffusion equation with suitable flux boundary conditions at the cell boundaries. Such a model will become computationally inefficient and analytically complex when there are many cells, even more so when they are moving. We propose to consider instead a point source model. Each cell is virtually reduced to a point and appears in the diffusion equation for the compound on the full spatial domain as a singular reaction term in the form of a Dirac delta ‘function’ (measure) located at the cell’s centre. In this model, it has an amplitude that is a non-local function of the concentration of compound on the (now virtual) cell boundary. We prove the well-posedness of this particular parabolic problem with non-local and singular reaction term in suitable Sobolev spaces. We show for a square bounded domain and for the plane that the solution cannot be H1-smooth at the Dirac point. Further, we show a preliminary numerical comparison between the solutions to the two models that suggests that the two models are highly comparable to each other.

AB - Communication between single cells or higher organisms by means of diffusive compounds is an important phenomenon in biological systems. Modelling therefore often occurs, most straightforwardly by a diffusion equation with suitable flux boundary conditions at the cell boundaries. Such a model will become computationally inefficient and analytically complex when there are many cells, even more so when they are moving. We propose to consider instead a point source model. Each cell is virtually reduced to a point and appears in the diffusion equation for the compound on the full spatial domain as a singular reaction term in the form of a Dirac delta ‘function’ (measure) located at the cell’s centre. In this model, it has an amplitude that is a non-local function of the concentration of compound on the (now virtual) cell boundary. We prove the well-posedness of this particular parabolic problem with non-local and singular reaction term in suitable Sobolev spaces. We show for a square bounded domain and for the plane that the solution cannot be H1-smooth at the Dirac point. Further, we show a preliminary numerical comparison between the solutions to the two models that suggests that the two models are highly comparable to each other.

U2 - 10.1016/j.ifacol.2025.03.014

DO - 10.1016/j.ifacol.2025.03.014

M3 - Conference article

VL - 59

SP - 73

EP - 78

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

SN - 2405-8963

IS - 1

ER -