Here, we examine algorithm performance for the special case in which test tube design reduces to complex design: a target test tube containing one on-target complex and no off-target complexes.
Figures B.3 and B.4 demonstrate that the performance of the current algorithm and the previously published single-complex design algorithm [83] is similar for the (dimer) on-target structures in the engineered and random test sets, respectively. Typical designs surpass the desired design quality (normalized ensemble defect ≤ 0.01; panel a), with the current algorithm overshooting the stop condition by a smaller margin. Typical design costs range from a fraction of a second for 50-nt on-target dimers in the engineered test set (B.3b) to 70 seconds for 400-ht on-target dimers in the random test set (B.4b). Starting from random initial sequences, the desired design quality can be
0 1 2 3 4 5 6 7 8 Fraction of parent nodes 0.0
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Figure B.2: Extent of multiple split point usage. a) Cumulative of the number of children per parent, b) cumulative histogram of the maximum number of children for any parent node in each complex, c) histogram of the maximum number of children for any parent node in each design. All data is for final decompositions for the engineered test set. RNA design at 37◦C.
achieved with a broad range of GC contents, with typical GC content less than 60% starting for both test sets. As the depth of the decomposition tree increases with increasing on-target size, the relative design cost, costdes/costeval, decreases asymptotically towards the 4/3 optimality bound for typical design trials (panel B.3d).
B.3.1 Sequence initialization
Figure B.5 compares algorithm performance using different GC contents for random seeding and reseeding. Sequences were initialized with either random sequences (default), random sequences using only A and U, or random sequences using only G and C. The desired design quality is achieved independent of the initial conditions (panel a), with the typical design cost increasingly marginally if the initial sequence contains only G and C (panel b). Designs initiated with random AU or with random GC sequences illustrate that the desired design quality can be typically achieved over a broad range of GC contents (0.4 to 0.75). The typical cost of test tube design relative to a single evaluation of the test tube ensemble defect is within a factor of 4 (panel d).
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Figure B.3: Algorithm performance for complex design using the on-target structures from the engi- neered test set. Comparison of the current test tube design algorithm (solid lines) to the previously published single-complex design algorithm [83] (dashed lines). a) Design quality. The stop condition is depicted as a dashed line. b) Design cost. c) Sequence composition. The initial GC content is depicted as a dashed line. d) Cost of sequence design relative to a single evaluation of the objective function. The optimality bound is depicted as a dashed line. RNA design at 37 ◦C. Each tube contains a single on-target dimer and no off-targets. There are 100 target tubes for each on-target size.
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Figure B.4: Algorithm performance for complex design using the on-target structures from the random test set. Comparison of the current test tube design algorithm (solid lines) to the previously published single-complex design algorithm [83] (dashed lines). a) Design quality. The stop condition is depicted as a dashed line. b) Design cost. c) Sequence composition. The initial GC content is depicted as a dashed line. d) Cost of sequence design relative to a single evaluation of the objective function. The optimality bound is depicted as a dashed line. RNA design at 37 ◦C. Each tube contains a single on-target dimer and no off-targets. There are 100 target tubes for each on-target size.
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Figure B.5: Effect of sequence initialization on algorithm performance. a) Design quality. The stop condition is depicted as a dashed line. b) Design cost. c) Sequence composition. The GC contents used for seeding/reseeding are depicted as dashed lines. d) Cost of sequence design relative to a single evaluation of the objective function. RNA design at 37 ◦C for the subset of the engineered test set with 100-nt on-targets.
B.3.2 RNA vs DNA design
Figure B.6 compares RNA and DNA design. DNA designs are performed in 1 M Na+ at 25◦C to reflect that DNA systems are typically engineered for room temperature studies. In comparison to RNA design, DNA design leads to similar design quality (panel a), marginally higher design cost (panels b and d), and comparable GC content (panel c).