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Colocalization coefficients evaluating the distribution of molecular targets in microscopy methods based on pointed patterns

View Article: PubMed Central - PubMed

ABSTRACT

In biomedical studies, the colocalization is commonly understood as the overlap between distinctive labelings in images. This term is usually associated especially with quantitative evaluation of the immunostaining in fluorescence microscopy. On the other hand, the evaluation of the immunolabeling colocalization in the electron microscopy images is still under-investigated and biased by the subjective and non-quantitative interpretation of the image data. We introduce a novel computational technique for quantifying the level of colocalization in pointed patterns. Our approach follows the idea included in the widely used Manders’ colocalization coefficients in fluorescence microscopy and represents its counterpart for electron microscopy. In presented methodology, colocalization is understood as the product of the spatial interactions at the single-particle (single-molecule) level. Our approach extends the current significance testing in the immunoelectron microscopy images and establishes the descriptive colocalization coefficients. To demonstrate the performance of the proposed coefficients, we investigated the level of spatial interactions of phosphatidylinositol 4,5-bisphosphate with fibrillarin in nucleoli. We compared the electron microscopy colocalization coefficients with Manders’ colocalization coefficients for confocal microscopy and super-resolution structured illumination microscopy. The similar tendency of the values obtained using different colocalization approaches suggests the biological validity of the scientific conclusions. The presented methodology represents a good basis for further development of the quantitative analysis of immunoelectron microscopy data and can be used for studying molecular interactions at the ultrastructural level. Moreover, this methodology can be applied also to the other super-resolution microscopy techniques focused on characterization of discrete pointed structures.

No MeSH data available.


Related in: MedlinePlus

Example of the calculations of the proposed EM coefficients on the model image. The particles of the labels A and B are represented by their coordinates  and  as purple crosses and yellow dots. We consider only the first image as example, so the parameter . The parameter  is the identifier of the particle ( is the th particle of type A on the th image, e.g.,  is the second particle of type A on the first image). The number of the particles of the label A is four (), and there are three particles of the label B (). An image includes four colocalizing pairs of the labels A and B, where three colocalizing particles are of type A () and two colocalizing particles are of type B (). If we assume the toy example that the first image is also the only image of the stack , we can calculate all coefficients for this single image. Because of our toy example, the last averaging operation illustrated in the figure is omitted (denominator would be equal to number one). Coefficient  (absolute number of particles, Eq. 1); ;  (average proportion of the particles, Eq. 2, 3); ;  (relative colocalization fractions, Eq. 4); ;  (summary coefficients describing the colocalizing fractions in their relation to the total number of particles on image, Eq. 6, 8) ;  (non-colocalizing fractions as part of total number of particles on image, Eqs. 7, 9); ;  (relative densities of colocalization, Eqs. 15, 16)
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Fig2: Example of the calculations of the proposed EM coefficients on the model image. The particles of the labels A and B are represented by their coordinates and as purple crosses and yellow dots. We consider only the first image as example, so the parameter . The parameter is the identifier of the particle ( is the th particle of type A on the th image, e.g., is the second particle of type A on the first image). The number of the particles of the label A is four (), and there are three particles of the label B (). An image includes four colocalizing pairs of the labels A and B, where three colocalizing particles are of type A () and two colocalizing particles are of type B (). If we assume the toy example that the first image is also the only image of the stack , we can calculate all coefficients for this single image. Because of our toy example, the last averaging operation illustrated in the figure is omitted (denominator would be equal to number one). Coefficient (absolute number of particles, Eq. 1); ; (average proportion of the particles, Eq. 2, 3); ; (relative colocalization fractions, Eq. 4); ; (summary coefficients describing the colocalizing fractions in their relation to the total number of particles on image, Eq. 6, 8) ; (non-colocalizing fractions as part of total number of particles on image, Eqs. 7, 9); ; (relative densities of colocalization, Eqs. 15, 16)

Mentions: The formula can be described also by the structured algorithmic steps of the operating computational principle. The visualization of the described pseudocode for the readers with purely biological/biomedical background is illustrated in Fig. 2. The formula consists of the following steps:


Colocalization coefficients evaluating the distribution of molecular targets in microscopy methods based on pointed patterns
Example of the calculations of the proposed EM coefficients on the model image. The particles of the labels A and B are represented by their coordinates  and  as purple crosses and yellow dots. We consider only the first image as example, so the parameter . The parameter  is the identifier of the particle ( is the th particle of type A on the th image, e.g.,  is the second particle of type A on the first image). The number of the particles of the label A is four (), and there are three particles of the label B (). An image includes four colocalizing pairs of the labels A and B, where three colocalizing particles are of type A () and two colocalizing particles are of type B (). If we assume the toy example that the first image is also the only image of the stack , we can calculate all coefficients for this single image. Because of our toy example, the last averaging operation illustrated in the figure is omitted (denominator would be equal to number one). Coefficient  (absolute number of particles, Eq. 1); ;  (average proportion of the particles, Eq. 2, 3); ;  (relative colocalization fractions, Eq. 4); ;  (summary coefficients describing the colocalizing fractions in their relation to the total number of particles on image, Eq. 6, 8) ;  (non-colocalizing fractions as part of total number of particles on image, Eqs. 7, 9); ;  (relative densities of colocalization, Eqs. 15, 16)
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5037163&req=5

Fig2: Example of the calculations of the proposed EM coefficients on the model image. The particles of the labels A and B are represented by their coordinates and as purple crosses and yellow dots. We consider only the first image as example, so the parameter . The parameter is the identifier of the particle ( is the th particle of type A on the th image, e.g., is the second particle of type A on the first image). The number of the particles of the label A is four (), and there are three particles of the label B (). An image includes four colocalizing pairs of the labels A and B, where three colocalizing particles are of type A () and two colocalizing particles are of type B (). If we assume the toy example that the first image is also the only image of the stack , we can calculate all coefficients for this single image. Because of our toy example, the last averaging operation illustrated in the figure is omitted (denominator would be equal to number one). Coefficient (absolute number of particles, Eq. 1); ; (average proportion of the particles, Eq. 2, 3); ; (relative colocalization fractions, Eq. 4); ; (summary coefficients describing the colocalizing fractions in their relation to the total number of particles on image, Eq. 6, 8) ; (non-colocalizing fractions as part of total number of particles on image, Eqs. 7, 9); ; (relative densities of colocalization, Eqs. 15, 16)
Mentions: The formula can be described also by the structured algorithmic steps of the operating computational principle. The visualization of the described pseudocode for the readers with purely biological/biomedical background is illustrated in Fig. 2. The formula consists of the following steps:

View Article: PubMed Central - PubMed

ABSTRACT

In biomedical studies, the colocalization is commonly understood as the overlap between distinctive labelings in images. This term is usually associated especially with quantitative evaluation of the immunostaining in fluorescence microscopy. On the other hand, the evaluation of the immunolabeling colocalization in the electron microscopy images is still under-investigated and biased by the subjective and non-quantitative interpretation of the image data. We introduce a novel computational technique for quantifying the level of colocalization in pointed patterns. Our approach follows the idea included in the widely used Manders’ colocalization coefficients in fluorescence microscopy and represents its counterpart for electron microscopy. In presented methodology, colocalization is understood as the product of the spatial interactions at the single-particle (single-molecule) level. Our approach extends the current significance testing in the immunoelectron microscopy images and establishes the descriptive colocalization coefficients. To demonstrate the performance of the proposed coefficients, we investigated the level of spatial interactions of phosphatidylinositol 4,5-bisphosphate with fibrillarin in nucleoli. We compared the electron microscopy colocalization coefficients with Manders’ colocalization coefficients for confocal microscopy and super-resolution structured illumination microscopy. The similar tendency of the values obtained using different colocalization approaches suggests the biological validity of the scientific conclusions. The presented methodology represents a good basis for further development of the quantitative analysis of immunoelectron microscopy data and can be used for studying molecular interactions at the ultrastructural level. Moreover, this methodology can be applied also to the other super-resolution microscopy techniques focused on characterization of discrete pointed structures.

No MeSH data available.


Related in: MedlinePlus