Paradigms for computational nucleic acid design

Abstract

The design of DNA and RNA sequences is critical for many endeavors, from DNA nanotechnology, to PCR-based applications, to DNA hybridization arrays. Results in the literature rely on a wide variety of design criteria adapted to the particular requirements of each application. Using an extensively studied thermodynamic model, we perform a detailed study of several criteria for designing sequences intended to adopt a target secondary structure. We conclude that superior design methods should explicitly implement both a positive design paradigm (optimize affinity for the target structure) and a negative design paradigm (optimize specificity for the target structure). The commonly used approaches of sequence symmetry minimization and minimum free-energy satisfaction primarily implement negative design and can be strengthened by introducing a positive design component. Surprisingly, our findings hold for a wide range of secondary structures and are robust to modest perturbation of the thermodynamic parameters used for evaluating sequence quality, suggesting the feasibility and ongoing utility of a unified approach to nucleic acid design as parameter sets are refined further. Finally, we observe that designing for thermodynamic stability does not determine folding kinetics, emphasizing the opportunity for extending design criteria to target kinetic features of the energy landscape.

Figure 1

(a) Feedback loop for evaluating nucleic acid sequence designs and methodologies. (b) Positive and negative design paradigms. Two sequences are evaluated using an empirical potential on both the desired target structure and an undesired structure. Using a positive design paradigm, sequence A would be selected since it exhibits a stronger affinity than sequence B for the target structure (i.e. lower ΔG). Using a negative design paradigm, sequence B would be selected since it exhibits specificity for the target structure while sequence A exhibits specificity for the undesired structure. To provide a common basis for comparison, ΔG = 0 for a strand with no base pairs. (c) Canonical loops of nucleic acid secondary structure: hairpin loops, stacked base pairs, a bulge loop, an interior loop and a multiloop. These loop structures are all nested (i.e. there are no crossing arcs in the corresponding polymer graph with the backbone drawn as a straight line). (d) A sample pseudoknot with base pairs a·f and c·h (with a < c) that fail to satisfy the nesting property a < c < h < f, yielding crossing arcs in the corresponding polymer graph.

Figure 2

RNA multiloop. (a) Histograms for 100 sequence designs based on probability of sampling the target graph, p(s∗). The color legend applies to all plots. (b) Histograms for the same 100 sequence designs based on average number of incorrect nucleotides, n(s∗). (c) Base-pairing probabilities P_i,j for the median sequence based on p(s∗). Square sizes correspond to P_i,j ≥ {0.5,0.05,0.005}, respectively. The target structure is identical to that obtained by optimizing probability (black) or the average number of incorrect nucleotides (not shown). (d) p(s∗) versus free energy, ΔG(s∗). Each dot corresponds to one of 100 sequences designed using each method. Each bold square corresponds to the median over the 100 sequences designed using each method. (e) p(s∗) versus median folding time, t(s∗), over 1000 kinetic trajectories starting from random coil initial conditions. Dots and squares are interpreted as in (d).

Figure 3

RNA model perturbation study. For the multiloop designs of Figure 2, the top-ranked sequence for each method based on p(s∗) is re-examined using 1000 randomized potential functions where every parameter is independently adjusted by an amount uniformly distributed on ±10%, ±20% or ±50%. The original probabilities are depicted as dashed lines.

Figure 4

RNA multiloop variations. Design performance based on (a) p(s∗) and (b) n(s∗) with stem α = (4,6,8) and single-stranded multiloop regions β = (0,2,4). Surfaces show the mean values plus and minus one standard deviation for 100 independently designed sequences. The results for optimizing average incorrect nucleotides (not shown) are nearly indistinguishable from those obtained by optimizing probability.

Figure 5

Large RNA multiloop. See caption for Figure 2a–c.

Figure 6

RNA pseudoknot. See caption for Figure 2a–c.