Describing the movement of molecules in reduced-dimension models

Savage, Natasha S (2021) Describing the movement of molecules in reduced-dimension models. [Preprint]

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Official URL: http://dx.doi.org/10.1038/s42003-021-02200-3

Abstract

When addressing spatial biological questions using mathematical models, symmetries within the system are often exploited to simplify the problem by reducing its physical dimension. In a reduced-dimension model molecular movement is restricted to the reduced dimension, changing the nature of molecular movement. This change in molecular movement can lead to quantitatively and even qualitatively different results in the full and reduced systems. Within this manuscript we discuss the condition under which restricted molecular movement in reduced-dimension models accurately approximates molecular movement in the full system. For those systems which do not satisfy the condition, we present a general method for approximating unrestricted molecular movement in reduced-dimension models. We will derive a mathematically robust, finite difference method for solving the 2D diffusion equation within a 1D reduced-dimension model. The methods described here can be used to improve the accuracy of many reduced-dimension models while retaining benefits of system simplification.

Item Type:	Preprint
Additional Information:	Main Text. Methods. Supplementary Text. References
Uncontrolled Keywords:	Cell Membrane, Cytoplasm, Solutions, Diffusion, Algorithms, Models, Biological, Models, Chemical, Biophysical Phenomena
Depositing User:	Symplectic Admin
Date Deposited:	03 Nov 2020 09:21
Last Modified:	18 Jan 2023 23:23
DOI:	10.1038/s42003-021-02200-3
Open Access URL:	https://arxiv.org/abs/2011.01069
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3105978