# Is a heat-map of gene expression more informative if Z-scores are used instead of actual expression measurement values?

I have a heat-map of gene expression measurements (log2-transformed microarray signals, after inter-microarray data normalization, etc.) that I am using to illustrate the expression of 72 genes ('rows' of the heat-map) which I had identified as differentially expressed among different sub-groups of the 60 samples ('columns' of the heat-map, ordered by sub-groups) of my study. The ranges of gene measurements are within the 1-12 range (e.g., 4-8 for gene X, 2-10 for gene Y, and so on). It is a two-color heat-map, with the brightest green, black, and brightest red colors of the color scale used for values 1, 4 and 12, respectively.

A reviewer has commented that the heat-map will be more informative if Z-scores of the gene expression measurements are used instead. I don't get this because to me it seems that the heat-map will be less informative; Z-scoring will reduce the dimensionality of the data as one can no longer compare one gene to another for a given sample.

Can anyone comment on this? Thanks.

An image showing the current and reviewer-proposed heat-maps can be seen here: http://i.imgur.com/a2hmT.png

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Sorry that this isn't my field so probably others would know from the context; but what are the three dimensions (horizontal position, vertical position, and color) of your heatmap? Is the reviewer suggesing just changing whatever is currently mapped to colour to be a standardised version the same variable (standardisation of some sort - again apologies I don't know what this means in your case), in which case I don't see how it reduces the dimensionality you are showing. Doesn't make it a good idea, of course, that depends on what you are trying to see. – Peter Ellis Sep 11 '12 at 9:24
Thanks for the comment. I have clarified some details in the question, and have added a link to an image of the heat-map. – user4045 Sep 11 '12 at 10:44
Thanks, that helps me understand (as does @fosgen's answer). It's nothing to do with your question, but in passing, I strongly recommend avoiding relying on red-green contrasts, because of the color blindness problem. – Peter Ellis Sep 11 '12 at 10:58

The answer depends on what kind of comparison have to be shown on the figure. If we want to show differences between genes, it is good to make Z-score by samples (force each sample to have zero mean and standard deviation=1). If we want to show differences between samples, it is good to make Z-score by genes (force each gene to have zero mean and standard deviation=1). Original heat-map contains both information. So the phrase that it is "less informative" does not suit here. But redundant information makes useful information hard to see. Z-scoring does not reduce dimensionality, but throw away information about means and standard deviations in rows or columns (genes or samples). Think what information and what comparison you are discussing in paper and make proper Z-scoring if some information is redundant, else if all is useful - leave the original heat-map and explain this point to your reviewer.

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 Looking at your figure, I can suggest that standartization by genes may be helpful. Try it and see whether the resulted heat-map supports your inferences more clearly. Note that mir-1826 expression is constant, and thus may be deleted from figure, but mentioned in text. Also, you may add mean expression value near each gene in order to save the possibility of gene comparison after Z-scoring – O_Devinyak Sep 11 '12 at 11:25

What the reviewer may be referring to is the bottom legend of your figure. It goes from 1 to 12, with 4 right in the middle, which is discomforting. This makes your absolute log expression values difficult to interpret, because when a gene goes from bright green to black, its expression level is multiplied by 16, but when it goes from black to bright red, it is multiplied by 256. In short, I don't think your figure could be "more informative", but the information could be more intuitive.

As explained by @fosgen, Z-scores are centered and normalized, so the user can interpret a color as $x$ standard deviations from the mean and have an intuitive idea of the relative variation of that value.

Like @fosgen, I think you should go for standardization by gene (standardization by cell type does not make sense to me in that context). Black will be the average expression across different cell types (set to 0) and the color distribution will be symmetrical on both sides.

Showing the (relative) gene-wise variation of expression is standard in the field, but you might have specific reasons to show the (absolute) log2-microarray measurements, in which case you can expose them to the reviewers. But I would still straigthen the color gradient to ease interpretation.

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 Thanks! I have provided a link in the question to an image that shows both types of heat-maps next to each other. – user4045 Sep 11 '12 at 20:56 Good job!! This is less of a color explosion :D It also draws the emphasis on the diagonal square which show the groups of genes up-regulated or down-regulated in the groups of cells. The information is the same, but I personally find it more intuitive. – gui11aume Sep 11 '12 at 21:03