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Molecular counting by photobleaching in protein complexes with many subunits: best practices and application to the cellulose synthesis complex.

Chen Y, Deffenbaugh NC, Anderson CT, Hancock WO - Mol. Biol. Cell (2014)

Bottom Line: The step detection algorithms account for changes in signal variance due to changing numbers of fluorophores, and the subsequent analysis avoids common problems associated with fitting multiple Gaussian functions to binned histogram data.The analysis indicates that at least 10 GFP-AtCESA3 molecules can exist in each particle.These procedures can be applied to photobleaching data for any protein complex with large numbers of fluorescently tagged subunits, providing a new analytical tool with which to probe complex composition and stoichiometry.

View Article: PubMed Central - PubMed

Affiliation: Department of Biomedical Engineering, Huck Institutes of the Life Sciences, University Park, PA 16802 Interdisciplinary Graduate Degree Program in Cell and Developmental Biology, Huck Institutes of the Life Sciences, University Park, PA 16802.

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Step size and copy number determination for simulated photobleaching data. (A) BIC values using different numbers of Gaussians in the GMM density estimation for the same distribution used in Figure 5. The best fit (smallest BIC value) was achieved with five Gaussians. (B) Corresponding fit of five Gaussians to the step size data (histogram is for display only and is not used by the GMM procedure). Red, green, yellow, pink, and purple traces represent the five Gaussians in the GMM fit, with corresponding means of 560, 921, 1376, 1811, and 2343 a.u., and relative weights of 0.461, 0.341, 0.162, 0.028, and 0.008. The SD, which is assumed to be identical for all modes, is 135.9 a.u. Blue line is the overall density. The unitary step size is calculated as , where Pi and μi are the relative weight and the mean, respectively, of the ith peak, resulting in a value of 528.3 a.u. (C) Predicted unitary step size as a function of SNR and copy number, demonstrating good performance for copy number <12 at SNR ≥ 1 and copy number of 20 at SNR ≥ 2. Actual step size in simulated data was 500 a.u. (D) Predicted copy number from simulated photobleaching data with SNR of 2 and copy number 12. Peak position from KDE (black line) corresponds to mean copy number of 12.3. (E) Predicted copy number across different SNR ratios. Similar to the step size estimate, a break point at SNR < 2 was seen for prediction on copy number 20.
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Figure 6: Step size and copy number determination for simulated photobleaching data. (A) BIC values using different numbers of Gaussians in the GMM density estimation for the same distribution used in Figure 5. The best fit (smallest BIC value) was achieved with five Gaussians. (B) Corresponding fit of five Gaussians to the step size data (histogram is for display only and is not used by the GMM procedure). Red, green, yellow, pink, and purple traces represent the five Gaussians in the GMM fit, with corresponding means of 560, 921, 1376, 1811, and 2343 a.u., and relative weights of 0.461, 0.341, 0.162, 0.028, and 0.008. The SD, which is assumed to be identical for all modes, is 135.9 a.u. Blue line is the overall density. The unitary step size is calculated as , where Pi and μi are the relative weight and the mean, respectively, of the ith peak, resulting in a value of 528.3 a.u. (C) Predicted unitary step size as a function of SNR and copy number, demonstrating good performance for copy number <12 at SNR ≥ 1 and copy number of 20 at SNR ≥ 2. Actual step size in simulated data was 500 a.u. (D) Predicted copy number from simulated photobleaching data with SNR of 2 and copy number 12. Peak position from KDE (black line) corresponds to mean copy number of 12.3. (E) Predicted copy number across different SNR ratios. Similar to the step size estimate, a break point at SNR < 2 was seen for prediction on copy number 20.

Mentions: Density estimation by a Gaussian mixture model (GMM) can provide predictions of peak position for each mode in a way that avoids the drawbacks of KDE. In this method, the distribution of steps is estimated by a mixture of Gaussians, and the means and variances of these Gaussians are obtained by maximizing the expected posterior probability, computationally achieved by expectation–maximization algorithms (Dempster et al., 1977). However, one uncertainty of this method is in choosing the number of Gaussians, k, to be fitted to the data, which can alter the fitting results. To provide an objective method for choosing the number of Gaussians, we fitted the step amplitude data using the Gaussian mixture model by an increasing number of Gaussians and determined the BIC value associated with each fit. The optimal number of Gaussians was defined as the number that gave the lowest BIC value, which for the simulated photobleaching data was 5 (Figure 6, A and B). The different peaks were assumed to be multiples of the unitary photobleaching amplitude, and the mean unitary step size was calculated as a weighted average of each peak, giving a value of 528.3 a.u. This estimate is within 6% of the step size value of 500 a.u. that was chosen for these simulated photobleaching data.


Molecular counting by photobleaching in protein complexes with many subunits: best practices and application to the cellulose synthesis complex.

Chen Y, Deffenbaugh NC, Anderson CT, Hancock WO - Mol. Biol. Cell (2014)

Step size and copy number determination for simulated photobleaching data. (A) BIC values using different numbers of Gaussians in the GMM density estimation for the same distribution used in Figure 5. The best fit (smallest BIC value) was achieved with five Gaussians. (B) Corresponding fit of five Gaussians to the step size data (histogram is for display only and is not used by the GMM procedure). Red, green, yellow, pink, and purple traces represent the five Gaussians in the GMM fit, with corresponding means of 560, 921, 1376, 1811, and 2343 a.u., and relative weights of 0.461, 0.341, 0.162, 0.028, and 0.008. The SD, which is assumed to be identical for all modes, is 135.9 a.u. Blue line is the overall density. The unitary step size is calculated as , where Pi and μi are the relative weight and the mean, respectively, of the ith peak, resulting in a value of 528.3 a.u. (C) Predicted unitary step size as a function of SNR and copy number, demonstrating good performance for copy number <12 at SNR ≥ 1 and copy number of 20 at SNR ≥ 2. Actual step size in simulated data was 500 a.u. (D) Predicted copy number from simulated photobleaching data with SNR of 2 and copy number 12. Peak position from KDE (black line) corresponds to mean copy number of 12.3. (E) Predicted copy number across different SNR ratios. Similar to the step size estimate, a break point at SNR < 2 was seen for prediction on copy number 20.
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Related In: Results  -  Collection

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Figure 6: Step size and copy number determination for simulated photobleaching data. (A) BIC values using different numbers of Gaussians in the GMM density estimation for the same distribution used in Figure 5. The best fit (smallest BIC value) was achieved with five Gaussians. (B) Corresponding fit of five Gaussians to the step size data (histogram is for display only and is not used by the GMM procedure). Red, green, yellow, pink, and purple traces represent the five Gaussians in the GMM fit, with corresponding means of 560, 921, 1376, 1811, and 2343 a.u., and relative weights of 0.461, 0.341, 0.162, 0.028, and 0.008. The SD, which is assumed to be identical for all modes, is 135.9 a.u. Blue line is the overall density. The unitary step size is calculated as , where Pi and μi are the relative weight and the mean, respectively, of the ith peak, resulting in a value of 528.3 a.u. (C) Predicted unitary step size as a function of SNR and copy number, demonstrating good performance for copy number <12 at SNR ≥ 1 and copy number of 20 at SNR ≥ 2. Actual step size in simulated data was 500 a.u. (D) Predicted copy number from simulated photobleaching data with SNR of 2 and copy number 12. Peak position from KDE (black line) corresponds to mean copy number of 12.3. (E) Predicted copy number across different SNR ratios. Similar to the step size estimate, a break point at SNR < 2 was seen for prediction on copy number 20.
Mentions: Density estimation by a Gaussian mixture model (GMM) can provide predictions of peak position for each mode in a way that avoids the drawbacks of KDE. In this method, the distribution of steps is estimated by a mixture of Gaussians, and the means and variances of these Gaussians are obtained by maximizing the expected posterior probability, computationally achieved by expectation–maximization algorithms (Dempster et al., 1977). However, one uncertainty of this method is in choosing the number of Gaussians, k, to be fitted to the data, which can alter the fitting results. To provide an objective method for choosing the number of Gaussians, we fitted the step amplitude data using the Gaussian mixture model by an increasing number of Gaussians and determined the BIC value associated with each fit. The optimal number of Gaussians was defined as the number that gave the lowest BIC value, which for the simulated photobleaching data was 5 (Figure 6, A and B). The different peaks were assumed to be multiples of the unitary photobleaching amplitude, and the mean unitary step size was calculated as a weighted average of each peak, giving a value of 528.3 a.u. This estimate is within 6% of the step size value of 500 a.u. that was chosen for these simulated photobleaching data.

Bottom Line: The step detection algorithms account for changes in signal variance due to changing numbers of fluorophores, and the subsequent analysis avoids common problems associated with fitting multiple Gaussian functions to binned histogram data.The analysis indicates that at least 10 GFP-AtCESA3 molecules can exist in each particle.These procedures can be applied to photobleaching data for any protein complex with large numbers of fluorescently tagged subunits, providing a new analytical tool with which to probe complex composition and stoichiometry.

View Article: PubMed Central - PubMed

Affiliation: Department of Biomedical Engineering, Huck Institutes of the Life Sciences, University Park, PA 16802 Interdisciplinary Graduate Degree Program in Cell and Developmental Biology, Huck Institutes of the Life Sciences, University Park, PA 16802.

Show MeSH