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Quantifying colocalization: thresholding, void voxels and the H(coef).

Adler J, Parmryd I - PLoS ONE (2014)

Bottom Line: Intensity thresholding is complicated by variations in the intensity of individual nuclei and their intensity relative to their surroundings.The cases are distinct and we argue that it is only relevant to measure correlation using pixels that contain both fluorophores and, when the fluorophores are in different places, to just report the lack of co-occurrence and omit these uninformative negative correlation.But biology is not homogenous and distributions also reflect physico-chemical properties, targeted delivery and retention.

View Article: PubMed Central - PubMed

Affiliation: Department of Immunology, Genetics and Pathology, Science for Life Laboratory, Uppsala University, Uppsala, Sweden.

ABSTRACT
A critical step in the analysis of images is identifying the area of interest e.g. nuclei. When the nuclei are brighter than the remainder of the image an intensity can be chosen to identify the nuclei. Intensity thresholding is complicated by variations in the intensity of individual nuclei and their intensity relative to their surroundings. To compensate thresholds can be based on local rather than global intensities. By testing local thresholding methods we found that the local mean performed poorly while the Phansalkar method and a new method based on identifying the local background were superior. A new colocalization coefficient, the H(coef), highlights a number of controversial issues. (i) Are molecular interactions measurable (ii) whether to include voxels without fluorophores in calculations, and (iii) the meaning of negative correlations. Negative correlations can arise biologically (a) because the two fluorophores are in different places or (b) when high intensities of one fluorophore coincide with low intensities of a second. The cases are distinct and we argue that it is only relevant to measure correlation using pixels that contain both fluorophores and, when the fluorophores are in different places, to just report the lack of co-occurrence and omit these uninformative negative correlation. The H(coef) could report molecular interactions in a homogenous medium. But biology is not homogenous and distributions also reflect physico-chemical properties, targeted delivery and retention. The H(coef) actually measures a mix of correlation and co-occurrence, which makes its interpretation problematic and in the absence of a convincing demonstration we advise caution, favouring separate measurements of correlation and of co-occurrence.

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Related in: MedlinePlus

The effect of void pixels on the Hcoef and r.(A) The copy fraction was used to vary the correlation, shown using scattergrams. The range shown by the false colour scale is 0–124. The two lower panels show individual pixels from a small part of the corresponding images. Note that the lowest panel does not change. For more details see the Methods section. (B), (C) and (D) illustrate the effect of changing the copy fraction and in addition setting differing fractions of the pixels in both images to zero intensity. (A), (B) and (C) have linear distributions of intensities, with mean of 128 and a width of 200 while D has a mean of 128 with a Gaussian distribution with a SD of 24. (E) The effect of applying an offset of 32 to one image. Both images originally had a mean of 128, a linear distribution of intensities with a width of 200 and no empty pixels. r is unaffected by offset and the corresponding graph is the 0% in panel B.
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pone-0111983-g005: The effect of void pixels on the Hcoef and r.(A) The copy fraction was used to vary the correlation, shown using scattergrams. The range shown by the false colour scale is 0–124. The two lower panels show individual pixels from a small part of the corresponding images. Note that the lowest panel does not change. For more details see the Methods section. (B), (C) and (D) illustrate the effect of changing the copy fraction and in addition setting differing fractions of the pixels in both images to zero intensity. (A), (B) and (C) have linear distributions of intensities, with mean of 128 and a width of 200 while D has a mean of 128 with a Gaussian distribution with a SD of 24. (E) The effect of applying an offset of 32 to one image. Both images originally had a mean of 128, a linear distribution of intensities with a width of 200 and no empty pixels. r is unaffected by offset and the corresponding graph is the 0% in panel B.

Mentions: The performance of r and the newly introduced Hcoef was compared (Figure 5) using a sequence of incrementally changing distributions (Figure 5A) produced by varying the copy fraction. When the original intensity distributions have a linear distributions (Figure 5B and C), the Pearson correlation coefficient r changes over its full range, −1 to +1, while the Hcoef has a more limited response, from 0.7 to 1.2, a smaller part of its full range which can extend from 0, no co-occurrence, towards infinity, when all the fluorescence co-occurs in a single voxel of a large image. The response detected by the Hcoef is even more limited when the distribution of intensities used in the simulated images is Gaussian, arguably more representative of biological images, rather than linear (Figure 5D). The reported change over the full correlation range is then only from 0.965 to 1.035. r with a Gaussian distribution is not shown since the difference from 5B is marginal.


Quantifying colocalization: thresholding, void voxels and the H(coef).

Adler J, Parmryd I - PLoS ONE (2014)

The effect of void pixels on the Hcoef and r.(A) The copy fraction was used to vary the correlation, shown using scattergrams. The range shown by the false colour scale is 0–124. The two lower panels show individual pixels from a small part of the corresponding images. Note that the lowest panel does not change. For more details see the Methods section. (B), (C) and (D) illustrate the effect of changing the copy fraction and in addition setting differing fractions of the pixels in both images to zero intensity. (A), (B) and (C) have linear distributions of intensities, with mean of 128 and a width of 200 while D has a mean of 128 with a Gaussian distribution with a SD of 24. (E) The effect of applying an offset of 32 to one image. Both images originally had a mean of 128, a linear distribution of intensities with a width of 200 and no empty pixels. r is unaffected by offset and the corresponding graph is the 0% in panel B.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4222960&req=5

pone-0111983-g005: The effect of void pixels on the Hcoef and r.(A) The copy fraction was used to vary the correlation, shown using scattergrams. The range shown by the false colour scale is 0–124. The two lower panels show individual pixels from a small part of the corresponding images. Note that the lowest panel does not change. For more details see the Methods section. (B), (C) and (D) illustrate the effect of changing the copy fraction and in addition setting differing fractions of the pixels in both images to zero intensity. (A), (B) and (C) have linear distributions of intensities, with mean of 128 and a width of 200 while D has a mean of 128 with a Gaussian distribution with a SD of 24. (E) The effect of applying an offset of 32 to one image. Both images originally had a mean of 128, a linear distribution of intensities with a width of 200 and no empty pixels. r is unaffected by offset and the corresponding graph is the 0% in panel B.
Mentions: The performance of r and the newly introduced Hcoef was compared (Figure 5) using a sequence of incrementally changing distributions (Figure 5A) produced by varying the copy fraction. When the original intensity distributions have a linear distributions (Figure 5B and C), the Pearson correlation coefficient r changes over its full range, −1 to +1, while the Hcoef has a more limited response, from 0.7 to 1.2, a smaller part of its full range which can extend from 0, no co-occurrence, towards infinity, when all the fluorescence co-occurs in a single voxel of a large image. The response detected by the Hcoef is even more limited when the distribution of intensities used in the simulated images is Gaussian, arguably more representative of biological images, rather than linear (Figure 5D). The reported change over the full correlation range is then only from 0.965 to 1.035. r with a Gaussian distribution is not shown since the difference from 5B is marginal.

Bottom Line: Intensity thresholding is complicated by variations in the intensity of individual nuclei and their intensity relative to their surroundings.The cases are distinct and we argue that it is only relevant to measure correlation using pixels that contain both fluorophores and, when the fluorophores are in different places, to just report the lack of co-occurrence and omit these uninformative negative correlation.But biology is not homogenous and distributions also reflect physico-chemical properties, targeted delivery and retention.

View Article: PubMed Central - PubMed

Affiliation: Department of Immunology, Genetics and Pathology, Science for Life Laboratory, Uppsala University, Uppsala, Sweden.

ABSTRACT
A critical step in the analysis of images is identifying the area of interest e.g. nuclei. When the nuclei are brighter than the remainder of the image an intensity can be chosen to identify the nuclei. Intensity thresholding is complicated by variations in the intensity of individual nuclei and their intensity relative to their surroundings. To compensate thresholds can be based on local rather than global intensities. By testing local thresholding methods we found that the local mean performed poorly while the Phansalkar method and a new method based on identifying the local background were superior. A new colocalization coefficient, the H(coef), highlights a number of controversial issues. (i) Are molecular interactions measurable (ii) whether to include voxels without fluorophores in calculations, and (iii) the meaning of negative correlations. Negative correlations can arise biologically (a) because the two fluorophores are in different places or (b) when high intensities of one fluorophore coincide with low intensities of a second. The cases are distinct and we argue that it is only relevant to measure correlation using pixels that contain both fluorophores and, when the fluorophores are in different places, to just report the lack of co-occurrence and omit these uninformative negative correlation. The H(coef) could report molecular interactions in a homogenous medium. But biology is not homogenous and distributions also reflect physico-chemical properties, targeted delivery and retention. The H(coef) actually measures a mix of correlation and co-occurrence, which makes its interpretation problematic and in the absence of a convincing demonstration we advise caution, favouring separate measurements of correlation and of co-occurrence.

Show MeSH
Related in: MedlinePlus