All randomized synthetic oligonucleotides were synthesized by Purimex RNA/DNA Oligonucleotides (Grebenstein, Germany), using standard phosphoamidite chemistry with equally pre-mixed bases at random positions, and were purified via HPLC. Diversity standard oligonucleotide templates were converted to dsDNA by PCR in PTC200-cycler (Biozym Scientific, Hess. Oldendorf, Germany). Briefly, 100 µl reactions with 2 µM primers Ri5 and PO4Ri3 (obtained from Operon, Cologne, Germany with 20 pmol standard oligonucleotide template, 1.5 mM MgCl₂, (Promega, USA), 5 U GoTaq®-polymerase (Promega) using four cycles and an annealing temperature of 55°C, yielding an 80 bp PCR product. Residual single-stranded DNA and primers were removed by S1-nuclease (Roboklon, Berlin, Germany) treatment for 15 min at 55°C in S1-buffer (Roboklon). Resulting dsDNA PCR-products were purified by binding to sbeadex® magnetic particles (AGOWA, Berlin, Germany) according to manufacturers’ protocol. DNA yield was determined spectrophotometrically (Nanodrop).

The assay was performed using the SYBR Green PCR Core Kit (Applied Biosystems, USA) in 96 well plates with a Biorad Lightcycler device. Each well contained 1.5 µg of dsDNA sample diluted in 50µl buffer. Reannealing measurements were initiated by denaturation for 2 min at 95°C, and subsequent annealing for 180 min at the respective constant annealing temperature taking one measurement per minute. Remelting was performed starting at 20°C with incremental steps of 0.5°C for 7 s until the final temperature of 98°C was reached.

Chemical synthesis of oligonucleotides allows the incorporation of random nucleotides at predefined positions. One randomized nucleotide N yields four different sequences and any further randomized nucleotide adds to the diversity exponentially with D = 4^N, where N is the number of randomized nucleotides. An even distribution of randomized bases was chosen over a cluster, in order to mimic naturally occurring situations such as somatic hypermutation in the hypervariable regions of T-cell receptors. We thought that the stringency for small sequence differences is stronger in such an arrangement than in consecutively randomized areas. By this method we designed several oligonucleotide libraries with varying numbers of random nucleotides denoted 2–20 N, based on a single template sequence flanked by conserved primers (Figure 1 and Table 1). The synthetic oligonucleotides were converted to dsDNA by four cycles of PCR and treated by S1 nuclease to remove any unpaired ssDNA. We confirmed the introduction of all four nucleotides at the randomized positions by batch sequencing the oligonucleotides with the conventional Sanger method. Other randomized oligonucleotides obtained from the same supplier, synthesized by the same method, have been subjected to next generation sequencing. Those displayed less than 3.2% deviation from ideal 25% distribution for any base in more than 700 000 sequenced bases in randomized regions (data not shown).

As expected we observed that the annealing kinetics varied with the diversity of the used oligonucleotide library. However, despite prolonged annealing times of up to 6 h, the SYBR green fluorescence of 10N and higher stayed well below 50% of its initial value, which made the determination of a C₀t_1/2 value impossible for libraries with diversities higher than 10⁶ (Figure 2a). Triplicate experiments were variable at low diversities (Supplementary Figure 1) and the observed kinetics did not fit the calculations proposed by Baum and McCune (⁷), especially when diversities exceeded 4 × 10³.

We observed that the remelting curves following an annealing step were much more reproducible in terms of melting temperature (Supplementary Figure 2) and characteristic for each of the assayed diversities (Figure 2a and b). Differences are more obvious in the remelting assay when compared with the profiles obtained in the preceding reannealing assay. On an increase in diversity, a decrease in melting temperature from 86°C towards 75°C was detected, denoting the amount of imperfectly formed heteroduplex. We noticed that the threshold of this shift was partly dependent on the applied annealing temperature. An annealing temperature close to the initial melting point of 80°C leads to a shift towards the heteroduplex population for comparatively low diversities (8 N, 10⁵); higher annealing temperatures yielded curves that followed the same pattern as the unmelted, perfectly hybridized samples as described earlier (⁷,⁸). Using the lower annealing temperatures of 78°C and 76°C, the shift occurs gradually in higher diversities of 10 N (10⁶) and 12 N (10⁷), respectively (Supplementary Figure 3). The choice of the annealing temperature will determine the resolution in a given diversity range. Generally, this data demonstrates that there is no continuous linear correlation that determines the annealing kinetics, especially for higher diversities.

As most naturally occurring pools of nucleic acids consist of unevenly distributed sequences, we attempted to simulate this situation by admixtures of varying diversities. The retrieved remelting profiles indicate that by greatly increasing diversity, the pool assumes the kinetics of the lower diversity. This differs from the data provided by Baum and McCune (⁷), where one clone was mixed to a final concentration of 50% with a pool of 96 different sequences. Thus strong disparities in clonal distribution may yield misleading values by all melting and annealing kinetics methods.

We applied our new diversity standard to analyze the population dynamics of an aptamer selection against daunomycin (⁹). We compared PCR aliquots from each selection round (Figure 2c) with our diversity standard (Figure 2b) from the relative distribution of peaks and amplitudes in the remelting assay. The initial population quickly collapses from the initial 10¹⁵ (25 N) pool to 10⁷ (12 N) after just two rounds of selection. The relative plateau of gradual decrease from 10⁶ (10 N) to 4 × 10⁴ (6 N) correlates with the emergence of moderate binders in the fifth selection round (¹⁰). The final diversity of the tenth round was 1 in 16 (2 N) matching the results obtained by cloning and sequencing (⁹).