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Drift correction for single-molecule imaging by molecular constraint field, a distance minimum metric.

Han R, Wang L, Xu F, Zhang Y, Zhang M, Liu Z, Ren F, Zhang F - BMC Biophys (2015)

Bottom Line: There are two advantages of our method: First, because our method does not require space binning of positions of molecules but directly operates on the positions, it is more natural for single molecule imaging techniques.Second, our method can estimate drift with a small number of positions in each temporal bin, which may extend its potential application.The effectiveness of our method has been demonstrated by both simulated data and experiments on single molecular images.

View Article: PubMed Central - PubMed

Affiliation: Key Lab of Intelligent Information Processing and Advanced Computing Research Lab, Institute of Computing Technology, Chinese Academy of Sciences, Beijing, 100190 China ; University of Chinese Academy of Sciences, Beijing, China.

ABSTRACT

Background: The recent developments of far-field optical microscopy (single molecule imaging techniques) have overcome the diffraction barrier of light and improve image resolution by a factor of ten compared with conventional light microscopy. These techniques utilize the stochastic switching of probe molecules to overcome the diffraction limit and determine the precise localizations of molecules, which often requires a long image acquisition time. However, long acquisition times increase the risk of sample drift. In the case of high resolution microscopy, sample drift would decrease the image resolution.

Results: In this paper, we propose a novel metric based on the distance between molecules to solve the drift correction. The proposed metric directly uses the position information of molecules to estimate the frame drift. We also designed an algorithm to implement the metric for the general application of drift correction. There are two advantages of our method: First, because our method does not require space binning of positions of molecules but directly operates on the positions, it is more natural for single molecule imaging techniques. Second, our method can estimate drift with a small number of positions in each temporal bin, which may extend its potential application.

Conclusions: The effectiveness of our method has been demonstrated by both simulated data and experiments on single molecular images.

No MeSH data available.


The values of the mean Δd and the standard deviation σd of residual over the T=40 time intervals for the data set Radio, as a function of molecule number per temporal bin n and localization precision ξ.The values of the meanΔd and the standard deviationσd of residual over theT=40 time intervals for the data set Radio, as a function of molecule number per temporal binn and localization precisionξ.(a) Curve of residual Δd in different localization precisions ξ, as a function of molecule numbers n. (b) Curve of residual’s standard deviation σd in different localization precisions ξ, as a function of molecule numbers n. (c) Curve of residual Δd in different molecule numbers n, as a function of localization precisions ξ. (d) Curve of residual’s standard deviation σd in different molecule numbers n, as a function of localization precisions ξ.
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Fig8: The values of the mean Δd and the standard deviation σd of residual over the T=40 time intervals for the data set Radio, as a function of molecule number per temporal bin n and localization precision ξ.The values of the meanΔd and the standard deviationσd of residual over theT=40 time intervals for the data set Radio, as a function of molecule number per temporal binn and localization precisionξ.(a) Curve of residual Δd in different localization precisions ξ, as a function of molecule numbers n. (b) Curve of residual’s standard deviation σd in different localization precisions ξ, as a function of molecule numbers n. (c) Curve of residual Δd in different molecule numbers n, as a function of localization precisions ξ. (d) Curve of residual’s standard deviation σd in different molecule numbers n, as a function of localization precisions ξ.

Mentions: It is also known that the position localization precision and molecule numbers per temporal bin affect the performance of drift compensation [9]. Experiments in different molecule numbers per temporal bin (denoted by n) and localization precision (denoted by ξ) of data set Grid and Radio were carried out to illustrate the impact. The mean Δd and the standard deviation σd of residual over the T=40 temporal intervals were calculated for each simulation. Figures 7 and 8 illustrate the curves of Δd and σd as a function of n and ξ. For both Figures 7 and 8, sub-fig (a) (c) represent the same Δd and sub-fig (b) (d) represent the same σd, in two different views. The tendencies of the mean residual and the standard deviation of the residual under changes in n and ξ are consistent. Judging from Figure 7(a) and (b), we can find that our method behaves well in the situations in which the localization precision ξ≤40 for data set Grid. Under the condition that localization precision ξ≤80 and molecule numbers per bin n≥500, the accuracy of drift compensation by our method can reach to 2∼10 nm. Comparing Figure 8(a) (b) to Figure 7(a) (b), we find that the performance of our method in data set Radio is not as good as that in Grid when ξ=80. The reason why there is such a difference is that when the localization precision reaches ξ=80, the localization uncertainty is so large compared to the width of the line structure in Radio (80 nm) that it degenerates the sampling of the molecule distribution. Our method performs not good when ξ=120 nm (the width of line in Grid) and the molecule number per bin n is very small. The performance of our method is impacted by bias sampling or mal-sampling, because our method is based on the direct recovery of position distributions. Nevertheless, according to recent studies [1,13], localization precisions are usually controlled to 10∼35 nm in 2D, which makes the low localization precision not a problem for our method. Judging from sub-fig (c) and (d), we can find that n=500 is sufficient to support a good performance of our method. Additionally, if the localization precision ξ≤20 nm, judging from Figures 7 and 8, we can conclude that our method can compensate the sample drift to a residual of 20∼40 nm with 40 molecule positions per temporal bin and to a residual of about 15 nm with 100 molecule positions per temporal bin. Readers who are interest in the details of the performance of our method in the cases where n=40 and ξ=0 nm can refer to the Appendix.Figure 7


Drift correction for single-molecule imaging by molecular constraint field, a distance minimum metric.

Han R, Wang L, Xu F, Zhang Y, Zhang M, Liu Z, Ren F, Zhang F - BMC Biophys (2015)

The values of the mean Δd and the standard deviation σd of residual over the T=40 time intervals for the data set Radio, as a function of molecule number per temporal bin n and localization precision ξ.The values of the meanΔd and the standard deviationσd of residual over theT=40 time intervals for the data set Radio, as a function of molecule number per temporal binn and localization precisionξ.(a) Curve of residual Δd in different localization precisions ξ, as a function of molecule numbers n. (b) Curve of residual’s standard deviation σd in different localization precisions ξ, as a function of molecule numbers n. (c) Curve of residual Δd in different molecule numbers n, as a function of localization precisions ξ. (d) Curve of residual’s standard deviation σd in different molecule numbers n, as a function of localization precisions ξ.
© Copyright Policy - open-access
Related In: Results  -  Collection

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Fig8: The values of the mean Δd and the standard deviation σd of residual over the T=40 time intervals for the data set Radio, as a function of molecule number per temporal bin n and localization precision ξ.The values of the meanΔd and the standard deviationσd of residual over theT=40 time intervals for the data set Radio, as a function of molecule number per temporal binn and localization precisionξ.(a) Curve of residual Δd in different localization precisions ξ, as a function of molecule numbers n. (b) Curve of residual’s standard deviation σd in different localization precisions ξ, as a function of molecule numbers n. (c) Curve of residual Δd in different molecule numbers n, as a function of localization precisions ξ. (d) Curve of residual’s standard deviation σd in different molecule numbers n, as a function of localization precisions ξ.
Mentions: It is also known that the position localization precision and molecule numbers per temporal bin affect the performance of drift compensation [9]. Experiments in different molecule numbers per temporal bin (denoted by n) and localization precision (denoted by ξ) of data set Grid and Radio were carried out to illustrate the impact. The mean Δd and the standard deviation σd of residual over the T=40 temporal intervals were calculated for each simulation. Figures 7 and 8 illustrate the curves of Δd and σd as a function of n and ξ. For both Figures 7 and 8, sub-fig (a) (c) represent the same Δd and sub-fig (b) (d) represent the same σd, in two different views. The tendencies of the mean residual and the standard deviation of the residual under changes in n and ξ are consistent. Judging from Figure 7(a) and (b), we can find that our method behaves well in the situations in which the localization precision ξ≤40 for data set Grid. Under the condition that localization precision ξ≤80 and molecule numbers per bin n≥500, the accuracy of drift compensation by our method can reach to 2∼10 nm. Comparing Figure 8(a) (b) to Figure 7(a) (b), we find that the performance of our method in data set Radio is not as good as that in Grid when ξ=80. The reason why there is such a difference is that when the localization precision reaches ξ=80, the localization uncertainty is so large compared to the width of the line structure in Radio (80 nm) that it degenerates the sampling of the molecule distribution. Our method performs not good when ξ=120 nm (the width of line in Grid) and the molecule number per bin n is very small. The performance of our method is impacted by bias sampling or mal-sampling, because our method is based on the direct recovery of position distributions. Nevertheless, according to recent studies [1,13], localization precisions are usually controlled to 10∼35 nm in 2D, which makes the low localization precision not a problem for our method. Judging from sub-fig (c) and (d), we can find that n=500 is sufficient to support a good performance of our method. Additionally, if the localization precision ξ≤20 nm, judging from Figures 7 and 8, we can conclude that our method can compensate the sample drift to a residual of 20∼40 nm with 40 molecule positions per temporal bin and to a residual of about 15 nm with 100 molecule positions per temporal bin. Readers who are interest in the details of the performance of our method in the cases where n=40 and ξ=0 nm can refer to the Appendix.Figure 7

Bottom Line: There are two advantages of our method: First, because our method does not require space binning of positions of molecules but directly operates on the positions, it is more natural for single molecule imaging techniques.Second, our method can estimate drift with a small number of positions in each temporal bin, which may extend its potential application.The effectiveness of our method has been demonstrated by both simulated data and experiments on single molecular images.

View Article: PubMed Central - PubMed

Affiliation: Key Lab of Intelligent Information Processing and Advanced Computing Research Lab, Institute of Computing Technology, Chinese Academy of Sciences, Beijing, 100190 China ; University of Chinese Academy of Sciences, Beijing, China.

ABSTRACT

Background: The recent developments of far-field optical microscopy (single molecule imaging techniques) have overcome the diffraction barrier of light and improve image resolution by a factor of ten compared with conventional light microscopy. These techniques utilize the stochastic switching of probe molecules to overcome the diffraction limit and determine the precise localizations of molecules, which often requires a long image acquisition time. However, long acquisition times increase the risk of sample drift. In the case of high resolution microscopy, sample drift would decrease the image resolution.

Results: In this paper, we propose a novel metric based on the distance between molecules to solve the drift correction. The proposed metric directly uses the position information of molecules to estimate the frame drift. We also designed an algorithm to implement the metric for the general application of drift correction. There are two advantages of our method: First, because our method does not require space binning of positions of molecules but directly operates on the positions, it is more natural for single molecule imaging techniques. Second, our method can estimate drift with a small number of positions in each temporal bin, which may extend its potential application.

Conclusions: The effectiveness of our method has been demonstrated by both simulated data and experiments on single molecular images.

No MeSH data available.