The Pearson's correlation coefficient is not a universally superior colocalization metric. Response to ‘Quantifying colocalization: the MOC is a hybrid coefficient – an uninformative mix of co-occurrence and correlation’

In their correspondence, Adler and Parmryd reiterated their conclusion that “the Manders' overlap coefficient (MOC) is not suitable for making measurements of colocalization by correlation or co-occurrence” (Adler and Parmryd, 2010). As a result, they also challenge one of the main points of our Review (Aaron et al., 2018) in which we advocate that there is no one superior colocalization coefficient, and that complex biological situations would require the proper implementation of the optimal coefficient, either to measure signal overlap or to measure signal correlation. They claim that we have not provided any observation to alter their conclusion that the Pearson correlation coefficient (PCC) is superior.

Unfortunately, to make such an assertion is to completely miss the illustration presented in Fig. 4 of our Review (Aaron et al., 2018). In this figure, we present two situations wherein MOC and PCC offer two contrasting results, which are not merely interpretative, they are numerical and substantive. This observation shows that changes in co-occurrence can take place independently of any alterations in correlation, and vice versa. This is a main takeaway message of the article.

To further illustrate this point, we have expanded on Fig. 4A from our manuscript here. In Fig. 1 below, simulated data are presented in image 1–4, whereby an increasing amount of non-overlapping green signal is overlaid onto a static red signal. This represents a common type of experimental question wherein the primary parameter to be addressed is the extent to which two biological signals overlap. The correlation between the intensity signals would be of secondary importance. Calculation of the MOC and PCC values for each image indicates that while the overall co-occurrence decreases as expected, the change in correlation (as measured by the PCC) is negligible. This indicates that under some circumstances, the MOC will be sensitive to changes in image characteristics, while the PCC will not.

The figure above also highlights an important factor that Adler and Parmyrd unfortunately seemed to have ignored in their steadfast claim that one coefficient is superior to another: given a multicolor image, the MOC and PCC are each calculated using different sets of pixel pairs. As described in Fig. 1 of our Review (Aaron et al., 2018), the MOC is applicable over the ‘union’ of the above-threshold regions of the two channels, while PCC should be calculated across the ‘intersection’ of the above-threshold regions of the two channels. This fact was, ironically, described by Adler and Parmryd (2010), and highlighted by others (Dunn et al., 2011). This distinction by itself should be more than sufficient to completely negate the assertion that one coefficient is inherently superior, since the two coefficients do not even consider the same set of pixel pairs. However, in keeping with the intended didactic spirit of our Review, we will explore this problem further using biological examples.

Based on the observation presented in Fig. 6 of our Review, Adler and Parmryd also argue that since PCC reported more dramatic difference between two image pairs than MOC, it cements their claim that the MOC is inferior to correlation-based methods. However, this claim has been challenged with actual biological examples by Dunn et al. (Fig. 4E in Dunn et al., 2011). In fact, Dunn et al. made the same conclusion as ours by stating that “even if two probes co-occur on the same cellular structures, there may be no reason that they should co-occur in fixed proportion to one another. … for studies in which proportional codistribution is not necessarily expected, PCC can provide a poor measure of colocalization.”

To further the point, we considered a pair of two-color images, showing mouse embryonic fibroblasts (MEFs) stably expressing TOMM20–Halo, which is labeled with Janelia Fluor 646 dye, to mark mitochondria, and TFAM–mNeonGreen, to label the location of mitochondrial DNA, shown in Fig. 2. The experiments were designed to measure mtDNA release over time from macropores in mitochondria during the apoptotic cascade. The data shown here are two time points from one of many similar experiments, which has been previously published (McArthur et al., 2018), and are adapted with permission.

Similar to what is seen in Fig. 1, this example highlights a situation where an MOC measurement can detect changes between two multichannel images, while the PCC does not. In this case, the MOC allows us to better infer a relative change in association between mitochondria and mtDNA during apoptosis, leveraging signal overlap as a parameter and not signal correlation.

In addition, contrary to the assertion of Adler and Parmyrd, there is nothing wrong with reporting ‘hybrid’ coefficients. As an analogy, while the information of height and weight of a patient are important to a physician, the hybrid value of body mass index or BMI would be a better predictor of cardiovascular health than the pure metrics of ‘height’ or ‘weight’. It all depends on what information is important to the question being asked.

From these examples, we cannot accept the claim of Adler and Parmryd that PCC is simply superior under all conditions, as there is evidence presented here, in our original Review (Aaron et al., 2018) and elsewhere (Dunn, et al., 2011) to reject such an acceptance. Taken together, these observations leave no room for such a narrow interpretation of how these statistical models should be applied to a myriad of highly complex biological situations, wherein the signals, structures and hypothesis-driven questions vary widely. This is the essence of the scientific discourse presented here. The mathematics of any colocalization metric are readily available for all to implement accordingly. Subsequent wholesale advocacy for or opposition to a particular metric is erroneous, biased and misleading. Likewise, we are also fully aware that the group has published numerous papers advocating a certain approach to reporting colocalization. However, the fact that a quantitative approach has been advocated for more than a decade lends it no immunity from being reexamined and, more importantly, from being refined and improved when evidence warrants such an effort.

Ultimately, the only important metric that truly matters in practice is whether these coefficients constitute a sufficient toolbox for biologists to utilize when tackling a wide range of possible biological questions – from how strongly the signals of two channels correlate with one another, to the degree of overlap two biological structures exhibit. Evidence presented here proves that to advocate only a single coefficient is to deny biologists the full set of current tools. And with that, we return to the take-home message of our original Review. We firmly stand by our cautionary note that there is indeed no one ‘superior’ coefficient that is applicable to all biological scenarios, and that specific biological questions of researchers should guide the selection of MOC, PCC, or SRCC (or the right combination) as relevant measures of colocalization.