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Reconstructing the gradient source position from steady-state fluxes to small receptors.

ABSTRACT: Recovering the position of a source from the fluxes of diffusing particles through small receptors allows a biological cell to determine its relative position, spatial localization and guide it to a final target. However, how a source can be recovered from point fluxes remains unclear. Using the Narrow Escape approach for an open domain, we compute the diffusion fluxes of Brownian particles generated by a steady-state gradient from a single source through small holes distributed on a surface in two dimensions. We find that the location of a source can be recovered when there are at least 3 receptors and the source is positioned no further than 10 cell radii away, but this condition is not necessary in a narrow strip. The present approach provides a computational basis for the first step of direction sensing of a gradient at a single cell level.

SUBMITTER: Dobramysl U

PROVIDER: S-EPMC5772644 | biostudies-literature | 2018 Jan

REPOSITORIES: biostudies-literature

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Reconstructing the gradient source position from steady-state fluxes to small receptors.

Dobramysl Ulrich U Holcman David D

Scientific reports 20180117 1

Recovering the position of a source from the fluxes of diffusing particles through small receptors allows a biological cell to determine its relative position, spatial localization and guide it to a final target. However, how a source can be recovered from point fluxes remains unclear. Using the Narrow Escape approach for an open domain, we compute the diffusion fluxes of Brownian particles generated by a steady-state gradient from a single source through small holes distributed on a surface in ...[more]

PMID: 29343770

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Project description:The â??small perturbationâ?? approach is critical in studying the â??steady stateâ?? of a biological system. In our experiments, small perturbations were generated by applying a series of repeating intermittent small doses of ultraviolet radiation to a human keratinocyte cell line, HaCaT. The biological response was assessed by monitoring the gene expression profiles using a high reliability and high resolution cDNA microarray system. Following intermittent 10 J/m2 UVB small perturbations, two opposite classes of genes, down-regulated and up-regulated, exhibited an immediate response followed by relaxation between each small perturbation, but were prolonged down- or up-regulated without relaxation while larger doses (233 or 582.5 J/m2) of UVB were applied. A repeated cycle pattern of gene expression following small perturbations is an indication of the existence of steady states. This cycle pattern is suppressed when large perturbations are applied. We believe that this is a universal phenomenon. In our experiments, the functions of up-regulated genes were mainly associated with anti-proliferation, anti-mitogenesis, and apoptosis. On the other hand, down-regulated genes were mainly related to proliferation, mitogenesis, and anti-apoptosis. In conclusion, this study experimentally proves the concept of steady state at the transcription level and demonstrates the feasibility of using small perturbation approaches for investigating steady states. This study could also set a foundation of computational systems biology, which has implicitly used the concept of steady state. Keywords: time course Three UVB exposures are indicated by UV at time points of 0, 8 and 16 hours. T1, T2, T3, T4, T5, and T6 denote the sampling time points. T1, T3 and T5 are allocated 30 minutes after the corresponding UVB irradiation. T2, T4 and T6 are allocated 8 hours after each UVB irradiation. At each sampling time point, two samples (control and UV-irradiated) are collected. See supplementary file Loop_design.pdf for further explanation.

Dataset Information

Reconstructing the gradient source position from steady-state fluxes to small receptors.

Publications

Reconstructing the gradient source position from steady-state fluxes to small receptors.

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