# Manders’ Colocalization Coefficients

Calculate Manders’ colocalization coefficients between two channels within regions of interest. Returns coefficients M_{1} and M_{2} or their signal-weighted variants within each region of interest (ROI). Manders’ colocalization coefficients are effectively the fraction of signal on one channel that is colocalized with signal on another channel. They are strongly dependent on the selection of appropriate thresholds on each channel, used to define areas of colocalization.

## Input Parameters

#### Image

Expects arbitrary bit-depth images with at least 2 channels.

Type: Image File (`net.imagej.Dataset`)

#### Region of Interest

Set of ROIs defining the regions for which correlations will be calculated.

Type: ROI Set (file) (`imagej.data.overlay.AbstractOverlay[]`)

#### Channel 1 and 2 (1-based index)

First and second channels on which to calculate correlations. Specified using 1-based indeces (`1 ≤ x ≤ # of channels`).

Type: Integer (`int`)

#### Channel 1 and 2 Thresholds

Threshold values for each channel.

Type: Numeric (`double`)

#### Signal-weighted

If `false`, calculate standard Manders’ colocalization coefficients. If `true`, calculate signal-weighted colocalization coefficients.

Type: Logical (`boolean`)

## Results

One result row is produced for each ROI.

#### M1

Manders’ colocalization coefficient for signal on the first channel with signal on the second channel.

Standard:

∑_{{A+B}}(1) ⁄ ∑_{{A}}(1)

Signal-weighted:

∑_{{A+B}}(A_{i}) ⁄ ∑_{{A}}(A_{i})

`A`_{i}, the value on channel 1 at pixel `i`.

`B`_{i}, the value on channel 2 at pixel `i`.

`{A}`, the set of pixels where `A`_{i} is above the threshold.

`{A+B}`, the set of pixels where both `A`_{i} and `B`_{i} are above their respective thresholds.

Type: Numeric (`float`)

#### M2

Manders’ colocalization coefficient for signal on the second channel with signal on the first channel.

Standard:

∑_{{A+B}}(1) ⁄ ∑_{{B}}(1)

Signal-weighted:

∑_{{A+B}}(B_{i}) ⁄ ∑_{{B}}(B_{i})

`A`_{i}, the value on channel 1 at pixel `i`.

`B`_{i}, the value on channel 2 at pixel `i`.

`{A}`, the set of pixels where `A`_{i} is above the threshold.

`{A+B}`, the set of pixels where both `A`_{i} and `B`_{i} are above their respective thresholds.

Type: Numeric (`float`)

## Reference

Dunn KW, Kamocka MM, McDonald JH. A practical guide to evaluating colocalization in biological microscopy. Am J Physiol Cell Physiol. 2011. doi: 10.1152/ajpcell.00462.2010