Please use this identifier to cite or link to this item: https://hdl.handle.net/2440/100796
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Type: Journal article
Title: Spectral analysis of pair-correlation bandwidth: application to cell biology images
Author: Binder, B.
Simpson, M.
Citation: Royal Society Open Science, 2015; 2(2):140494-1-140494-15
Publisher: The Royal Society
Issue Date: 2015
ISSN: 2054-5703
2054-5703
Statement of
Responsibility: 
Benjamin J. Binder and Matthew J. Simpson
Abstract: Images from cell biology experiments often indicate the presence of cell clustering, which can provide insight into the mechanisms driving the collective cell behaviour. Pair-correlation functions provide quantitative information about the presence, or absence, of clustering in a spatial distribution of cells. This is because the pair-correlation function describes the ratio of the abundance of pairs of cells, separated by a particular distance, relative to a randomly distributed reference population. Pair-correlation functions are often presented as a kernel density estimate where the frequency of pairs of objects are grouped using a particular bandwidth (or bin width), Δ>0. The choice of bandwidth has a dramatic impact: choosing Δ too large produces a pair-correlation function that contains insufficient information, whereas choosing Δ too small produces a pair-correlation signal dominated by fluctuations. Presently, there is little guidance available regarding how to make an objective choice of Δ. We present a new technique to choose Δ by analysing the power spectrum of the discrete Fourier transform of the pair-correlation function. Using synthetic simulation data, we confirm that our approach allows us to objectively choose Δ such that the appropriately binned pair-correlation function captures known features in uniform and clustered synthetic images. We also apply our technique to images from two different cell biology assays. The first assay corresponds to an approximately uniform distribution of cells, while the second assay involves a time series of images of a cell population which forms aggregates over time. The appropriately binned pair-correlation function allows us to make quantitative inferences about the average aggregate size, as well as quantifying how the average aggregate size changes with time.
Keywords: pair-correlation; spectral analysis; spatial patterns; cell clustering; in vitro assay
Description: Published 11 February 2015
Rights: © 2015 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.
DOI: 10.1098/rsos.140494
Grant ID: http://purl.org/au-research/grants/nhmrc/1069757
http://purl.org/au-research/grants/arc/FT130100148
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Mathematical Sciences publications

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