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

Influence of a New Form of Bolted Connection on the Mechanical Behaviors of a PC Shear Wall

A variety of forms of connection in precast reinforced concrete (PC) have been proposed, but the impact of the connection forms on the shear wall remains to be studied. In this paper, through quasi-static experiments and numerical simulations, the influences of a new form of bolted connection on the mechanical behaviors of the PC shear wall are investigated. The results show that the strain of the connector is less than the yield strain and the failure does not occur in the connector; the mechanical behaviors of this connection form of the PC shear wall are equivalent to those of the cast-in-place reinforced concrete (RC) shear wall. Meanwhile, reasonable suggestions are put forward for the design of the connector from the pretightening force, bolt number, and axial compression ratio. This implies that this form of bolted connection has little influence on the mechanical behaviors of the PC shear wall and design suggestions can be used in practical projects

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

<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

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

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

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

<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