The isorelational library is a set of oligonucleotides that can be defined with the following formula:

wAxA + wCxC + wGxG + wTxT = C

where wA, wC, wG, wT are weights of the nucleotides A, C, G and T, respectively, xA, xC, xG, xT are numbers of appropriate nucleotides in the oligonucleotide, and C is a constant that characterize the oligonucleotides from the library.

In the standard library (called sometimes isometric) the weights are equal wA = wC = wG = wT and constant C is the length of the oligonucleotides. Thus, all the oligonucleotides have equal length, usually denoted as l, and such oligonucleotides are called l-mers.

The isothermic library is characterized by the temperature T of the oligonucleotides, which is in fact melting temperature of oligonucleotide duplexes. Weights satisfy the conditions: wA= wT, wC= wG and 2wA= wC. It is assumed that wA = wT = 2 and wC = wG = 4 degrees.

One isothermic library is not sufficient to cover all DNA sequences. However, two isothermic libraries of temperatures differing by 2 degrees can cover any DNA sequence. Moreover, shifts between starting points of two consecutive oligonucleotides are not greater than 1 (in isometric libraries shifts between starting points of two consecutive oligonucleotides are always equal 1).

Detailed description of the isothermic libraries is present in the following paper.
* J. Blazewicz, P. Formanowicz, M. Kasprzak, W.T. Markiewicz, "Sequencing by hybridization with isothermic oligonucleotide libraries", Discrete Applied Mathematics 145 (2004) 40-51.