Developing Algorithms for Quantifying the Super Resolution Microscopic Data: Applications to the Quantification of Protein-Reorganization in Bacteria Responding to Treatment by Silver Ions

Histone-like nucleoid structuring proteins (HNS) play significant roles in shaping the chromosomal DNA, regulation of transcriptional networks in microbes, as well as bacterial responses to environmental changes such as temperature fluctuations. In this work, the intracellular organization of HNS proteins in E. coli bacteria was investigated utilizing super-resolution fluorescence microscopy, which surpasses conventional microscopy by 10–20 fold in spatial resolution. More importantly, the changes of the spatial distribution of HNS proteins in E. coli, by addition of silver ions into the growth medium were explored. To quantify the spatial distribution of HNS in bacteria and its changes, an automatic method based on Voronoi diagram was implemented. The HNS proteins localized in super-resolution fluorescence microscopy were segmented and clustered based on several quantitative parameters, such as molecular areas, molecular densities, and mean inter-molecular distances of the k-th rank, all of which were computed from the Voronoi diagrams. These parameters, as well as the associated clustering analysis, allowed us to quantify how the spatial organization of HNS proteins responds to silver, and provided insight into understanding how microbes adapt to new environments

Robust nonparametric quantification of clustering density of molecules in single-molecule localization microscopy

We report a robust nonparametric descriptor,&nbsp;J&prime;(r), for quantifying the density of clustering molecules in single-molecule localization microscopy.&nbsp;J&prime;(r), based on nearest neighbor distribution functions, does not require any parameter as an input for analyzing point patterns. We show that&nbsp;J&prime;(r) displays a valley shape in the presence of clusters of molecules, and the characteristics of the valley reliably report the clustering features in the data. Most importantly, the position of the&nbsp;J&prime;(r) valley () depends exclusively on the density of clustering molecules (&rho;c). Therefore, it is ideal for direct estimation of the clustering density of molecules in single-molecule localization microscopy. As an example, this descriptor was applied to estimate the clustering density of&nbsp;ptsG&nbsp;mRNA in&nbsp;E. coli&nbsp;bacteria.</p

Robust nonparametric quantification of clustering density of molecules in single-molecule localization microscopy

<div><p>We report a robust nonparametric descriptor, <i>J</i>′(<i>r</i>), for quantifying the density of clustering molecules in single-molecule localization microscopy. <i>J</i>′(<i>r</i>), based on nearest neighbor distribution functions, does not require any parameter as an input for analyzing point patterns. We show that <i>J</i>′(<i>r</i>) displays a valley shape in the presence of clusters of molecules, and the characteristics of the valley reliably report the clustering features in the data. Most importantly, the position of the <i>J</i>′(<i>r</i>) valley () depends exclusively on the density of clustering molecules (<i>ρ</i>_<i>c</i>). Therefore, it is ideal for direct estimation of the clustering density of molecules in single-molecule localization microscopy. As an example, this descriptor was applied to estimate the clustering density of <i>ptsG</i> mRNA in <i>E. coli</i> bacteria.</p></div

Dependence of on the clustering features.

<p>(A) <i>ρ</i>_<i>c</i>, (B) <i>ρ</i>_<i>r</i>, (C) <i>R</i>_<i>c</i>, (D) <i>N</i>_<i>c</i>, (E) <i>W</i>, and (F) <i>H</i>.</p

Application of <i>J</i>′(<i>r</i>) to <i>ptsG</i> mRNA in <i>E. coli</i> bacteria.

<p>(A, B) Super-resolved images of <i>ptsG</i> mRNA labeled through FISH by (A) 7 or (B) 14 fluorescent oligonucleotide probes. Scale bar = 1 <i>μ</i>m. (C) Computed <i>J</i>′(<i>r</i>) functions from (A) and (B). (D) Estimated clustering densities from (C).</p

Changes in <i>G</i>′(<i>r</i>) and <i>J</i>′(<i>r</i>) by varying a cluster feature at a time.

<p>(A) <i>ρ</i>_<i>c</i>, (B) <i>ρ</i>_<i>r</i>, (C) <i>R</i>_<i>c</i>, (D) <i>N</i>_<i>c</i>, (E) <i>W</i>, and (F) <i>H</i>.</p

The relation is independent on all the other cluster features, <i>R</i>_<i>c</i>, <i>ρ</i>_<i>r</i>, <i>N</i>_<i>c</i>, <i>W</i>, and <i>H</i>.

<p>All data points collapse onto a single power-law curve, . Least-square fitting gives <i>α</i> = 0.76 ± 0.03.</p

<i>G</i>′(<i>r</i>) and <i>J</i>′(<i>r</i>) for data with heterogeneous clusters with two different clustering densities.

<p><i>G</i>′(<i>r</i>) and <i>J</i>′(<i>r</i>) for data with heterogeneous clusters with two different clustering densities.</p

The dependence of the relative error <i>δ</i>_{<i>ρ</i>_<i>c</i>} on the ratio of the density of clustering points (<i>ρ</i>_<i>c</i>) to the density of random points (<i>ρ</i>_<i>r</i>), <i>ρ</i>_<i>c</i>/<i>ρ</i>_<i>r</i>, at various clustering densities.

<p>The dependence of the relative error <i>δ</i>_{<i>ρ</i>_<i>c</i>} on the ratio of the density of clustering points (<i>ρ</i>_<i>c</i>) to the density of random points (<i>ρ</i>_<i>r</i>), <i>ρ</i>_<i>c</i>/<i>ρ</i>_<i>r</i>, at various clustering densities.</p

<i>G</i>(<i>r</i>), <i>F</i>(<i>r</i>) and <i>J</i>(<i>r</i>) functions, and their derivatives.

<p>(A) Simulated noise points. (B) Simulated points forming clusters with a radius of <i>R</i> = 30 nm, in the presence of noise points. (C, D) <i>G</i>(<i>r</i>), <i>F</i>(<i>r</i>) and <i>J</i>(<i>r</i>) functions calculated from the points in (A) and (B), respectively. (E, F) Derivatives, <i>G</i>′(<i>r</i>), <i>F</i>′(<i>r</i>) and <i>J</i>′(<i>r</i>), calculated from the points in (A) and (B), respectively.</p