A Note on Gene Expression Data

Array data are invariably expressed in the form of ratios, so a preliminary
discussion is required to indicate how these are normally represented. When
expression ratios are shown numerically, they are most commonly expressed in
logarithmic space, typically to the base 2, i.e., ratio = log2(red intensity/green
intensity). The resulting ratios have the property of being symmetrical about
zero, and a negative sign denotes ratios with a larger denominator (making it
much easier to grasp the size of such ratios, since these ratios are no longer
compressed between 0 and 1, as occurs in real space). Although the base used
is not critical, base 2 logarithms are commonly employed because ratios thus
expressed are easily converted to “fold inductions” in real space, owing to the
familiarity of powers of two as used in the binary numbering system (i.e., a
log2-transformed ratio of 4 = 24 = a 16-fold in difference in real space). Note
that logarithms to the base 10 are seldom employed, for the simple reason that
most biologically relevant ratios tend to fall in the 1- to 10- or 1- to 100-fold
range. However, even when ratios are log transformed, it is still diffi cult to make
sense of columns of numbers, and therefore sensible alternatives are required.