ABSTRACTWe recently reported the design for a DNA nano-device that canrecord and store molecular signals. Here we present an evolu-tionary algorithm tailored to optimising nucleic acid sequencesthat predictively fold into our desired target structures. In our ap-proach, a DNA device is �rst speci�ed abstractly: the topology ofthe individual strands and their desired foldings into multi-strandcomplexes are described at the domain-level. Initially, this designis decomposed into a set of pairwise strand interactions. �en, weoptimize candidate domains, such that the resulting sequences foldwith high accuracy into desired target structures both (a) individ-ually and (b) jointly, but also (c) to show high a�nity for bindingdesired partners and simultaneously low a�nity to bind with anyundesired partner. As optimization heuristic we use a genetic al-gorithm that employs a linear combination of the above scores.Our algorithm was able to generate DNA sequences that satisfy allgiven criteria. Even though we cannot establish the theoreticallyachievable optima (as this would require exhaustive search), oursolutions score 90% of an upper bound that ignores con�icting ob-jectives. We envision that this approach can be generalized towardsa broad class of toehold-mediated strand displacement systems.
ACM Reference format:Jerzy Kozyra, Harold Fellermann, Ben Shirt-Ediss, Annunziata Lopiccolo,and Natalio Krasnogor. 2017. Optimizing nucleic acid sequences for amolecular data recorder. In Proceedings of the Genetic and EvolutionaryComputation Conference 2017, Berlin, Germany, July 15–19, 2017 (GECCO’17), 8 pages.DOI: h�p://dx.doi.org/10.1145/3071178.3071345
1 INTRODUCTIONDeoxyribonucleic acid (DNA) and ribonucleic acid (RNA) nanotech-nology has developed into a vibrant research area with numerouspotential applications in molecular computing, bio-manufacturing,and smart therapeutics [19]. At its core, this research exploits thenatural Watson-Crick complementarity of DNA and RNA, whichcauses nucleic acid strands in solution to hybridize spontaneouslywith complementary regions of the same strand or other strands.
�is programmability of nucleic acids has brought about numer-ous structural nano-devices based on DNA assembly [1, 3, 8], DNAorigami [7, 12, 16, 21], and hybrid assemblies where DNA is linkedwith other functional molecules [9, 11].
DNA nanotechnology can be dynamically functionalized viatoehold-mediated strand displacement (see grey box on Figure 1).�ese systems feature short stretches of unpaired, single-strandednucleotides (referred to as toeholds) and DNA strands with par-tially identical sequences whose competition for common bindingpartners can induce dynamical shape changes in the DNA/RNAassemblies. Strand displacement causes potentially irreversiblestructural changes of the nano-device that has been used for pro-gramming dynamical behavior such as mechanical actuation [24]and molecular computation [4, 15, 18].
We have recently reported the design for a dynamic DNA nano-structure that implements a molecular signal recorder [10]. �issignal recorder is implemented as a linear chain of partially comple-mentary DNA strands which represent data as well as operations.�roughout its operations, the structure exposes a unique bindingsite, at which it can be commanded—by addition of appropriatestrands to the test tube—to either record a signal or to release the
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GECCO ’17, July 15–19, 2017, Berlin, Germany J. Kozyra et al.
l* A
(S) Start
(P) Push
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Figure 1: A DNA nano-device that implements a signalrecorder via DNA hybridization and strand displacement.
last signal that had been recorded (similar to a stack data structure).In addition to recording and reading, the recorder provides an ad-ditional operation to release the entire recorded signal chain froma potential solid support. �is operation, as well as two additionalreporter strands, have been included for experimental characteri-zation and should not interfere with the principal operation. Fig-ure 1 shows the domain level speci�cation of all ten involved DNAstrands of the signal recorder and its three modes of operation.All data and operations are implemented via single stranded DNAstrands that interact through DNA hybridization (marked with Hin the diagram) and toehold-mediated strand displacement (SD).All processes are designed to be energetically downhill—driven bythe binding energy of the closing toehold domains—in order tomaximize robustness of the device.
As typical for the discipline, the design in Figure 1 employs anabstract domain level speci�cation, where individual nucleic acidstrands are resolved down to sequences of not further speci�ednucleotide stretches (denoted by a, b, c , etc.), rather than at theprimary sequence level. In this domain level speci�cation, domainscan be speci�ed to be fully complementary (denoted by a∗, b∗, c∗,etc.) and are otherwise assumed to be non-interfering. While theparticular nucleotide sequences of the domains are not determined,their lengths are dictated by geometry and energy considerationsand are thus part of the domain level speci�cation. Also part of thedesign are intra-molecular and inter-molecular foldings that thestrands should obey once assembled.
Determining nucleic acid sequences that reliably implement agiven design is thus an important problem in DNA nanotechnology.
Whereas its more prominent inverse problem—to determine thestructure a given sequence of nucleobases would fold into—can besolved e�ciently and exactly [20], the nucleic acid design problemhas been proven to be NP-complete [17] and is typically approachedusing heuristics [5, 26, 27]. Not only is this problem characterizedby a vast, discrete, and ragged search space (in our case 4208 ≈1.69 × 10125 potential designs), but it is also notoriously di�cult tospecify what constitutes a “good design”.
Most commonly, heuristics employ a set of trial solutions whichare scored by some metric that involves secondary structure foldingpredictions, i.e. solutions to the inverse problem. (�e aim of theheuristic is then to iteratively reduce the distance between thegiven design and the best trial solution). It has been demonstratedthat the most successful metrics optimize both a�nity (a strongtendency of the candidate solution to fold into the target structure)as well as speci�city (a negligible tendency of the candidate solutionto fold into another structure) of the foldings [5, 6].
One noteworthy example of a so�ware suite for the design ofnucleic acid structures and devices is NUPACK [22, 23]. At its core,it performs an optimization of the complex ensemble defect corre-sponding to the average number of incorrectly paired nucleotides atequilibrium (evaluated over the ensemble of the test tube). As such,NUPACK ensures the correct folding of the desired complex whileminimizing the concentration of undesired “o�-target” complexes.
Optimization criteria that are purely based on folding pro�lesperform very successfully when optimizing nucleotice sequencesfor individual DNA or RNA foldings, and have even been gener-alized to operate over pairwise and multistrand foldings [13, 25].However, by solely considering secondary structure, they fail toaddress important aspects that emerge when optimizing systems ofinteracting nucleic acid molecules.
In our example signal recorder design, for instance, it is notonly important that strands fold into given constructs, but also thathybridization and strand displacement reactions occur with highyield. For if reactions do not proceed to completion, inaccuraciescan accumulate over several cycles of signal recording, which mighteventually result in the data structure not being able to record anysignals, to record too many signals, or to record the wrong signals.
In this article, we propose a novel scoring function for the nu-cleic acid design problem that applies the criteria of a�nity andspeci�city to the hybridization and branch migration reactionsof a DNA nano-device design. A�er introducing this favourableequilibrium concentrations score and demonstrating how it can beincorporated into existing scoring schemes, we perform ensemblesof optimization runs with and without this score contribution andpresent our results, before concluding with a general discussion.
2 SCORING FUNCTIONS FOR NUCLEIC ACIDOPTIMIZATION
�e signal recorder designs are evaluated based on two factors:desired secondary structure and binding probabilities. We imple-mented the following partial scoring functions: (i) single-strandedfolding Ssf, (ii) pairwise folding Spf and (iii) favourable equilibriumconcentrations Sfec. �e �rst two scores employ secondary struc-ture prediction and a metric that selects for high structure a�nityand speci�city as discussed in Reference [6]. �e third score applies
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Optimizing nucleic acid sequences for a molecular data recorder GECCO ’17, July 15–19, 2017, Berlin, Germany
the same criteria of a�nity and speci�city to the readiness withwhich desired or undesired reactions take place.
Single stranded folding. Firstly, we evaluate the ability of a singleDNA strand to fold into its speci�ed target structure (as shown inFigure 1 top). Using the secondary structure predictor of the Vien-naRNA 2.0 so�ware suite [13], we calculate the partition functionof all secondary structures that x might fold into.1
For any strand x , let |x | denote its length and dx ∈ {0, 1} |x |a vector whose component dxi = 1 if base i is speci�ed in thedesign of x to be bound and 0 otherwise. Further, let px ∈ [0, 1] |x |denote a vector whose i-th component pxi denotes the Boltzmannprobability (obtained from the partition function) that base i ofstrand x is paired with another base. �e single-stranded foldingscore Ssf is then de�ned as the normalized Euclidean distance || · ||between dx and px as
Ssf (x ) = 1 − 1|x |||dx − px ||. (1)
Note that 0 ≤ Ssf ≤ 1 and Ssf (x ) = 1 if x folds unambiguously intoits target structure.
Pairwise folding. Secondly, we score the ability of two DNAstrands to bind with each other as speci�ed by the design (shownin Figure 1 center and bo�om). To obtain this score, we decomposethe multi-strand structure of an assembled signal recorder into theset of all its pairwise strand interactions (e.g. SP, PQ, RX).
For each pair x andy of strands, we denote by dxy ∈ {0, 1} |x |+ |y |the desired co-folding pro�le, and calculate—using ViennaRNA’scofold algorithm—the partition function for the pairwise folding ofstrand x with y, from which we derive the Boltzmann probabilityvector pxy ∈ [0, 1] |x |+ |y | . �e pairwise folding score Spf is thende�ned as
Spf (x ,y) = 1 − 1|x | + |y |
||dxy − pxy ||. (2)
Care has been taken for the push-signal interactions which occurin two variants PX (PY), binding via domains B and C , and XP(YP), binding via domain A. To characterize both variants, thefolding predictor has been invoked with constraints that preventthe strands to interact in the respective other domain (e.g. domainA is forbidden to participate in the PX interaction).
Favourable Equilibrium Concentrations. Another requirement forreactions in our signal recorder chemistry is that desired reactionsshould be thermodynamically spontaneous and therefore likely tohappen (in the absence of kinetic traps), whereas undesired cross-reactions should be thermodynamically non-spontaneous and thusminimized. Maximization of desired reactions thus improves thea�nity of the design, whereas minimization of undesired reactionsimproves its speci�city.
A �rst, simple approach to this scoring function might be:
S = −∑
i ∈Rdesired
wi∆G◦i +
∑j ∈Rundesired
w j∆G◦j , (3)
which is maximized when (i) the desired reactions each have amaximally negative standard Gibb’s free energy change ∆G◦ and1 Single and pairwise partition functions have been calculated with ViennaRNA’sRNAfold and RNAcofold programs, using DNA interaction parameters from Refer-ence [14] at 21◦C.
(ii) the undesired reactions each have a close to zero or positive∆G◦. �e ∆G◦ for bimolecular reactions can be calculated by ther-modynamic structure prediction algorithms such as ViennaRNA orNUPACK [25].
�e expression for S above is not easy to normalize, however.Moreover, this scoring function also neglects the concentrationsof the reaction species involved. At equilibrium in a �nite-sizedsystem, the amount that a reaction A + B AB is shi�ed towardthe “le�” (to reactants) or toward the “right” (to products) dependson the total concentration of the strands A and B in the system,in addition to the standard Gibb’s free energy change ∆G◦ of thereaction. Taking into account these concerns, developed below isan improved expression for this score.
For a single bimolecular reaction A + B AB in a �xed volume,it can be shown that the equilibrium concentration of product AB,denoted [AB]eq, is the minimum positive solution to the quadraticequation
[AB]2eq −(CA +CB +
1Keq
)[AB]eq +CACB = 0, (4)
where Keq = e−∆G◦RT is the Van’t Ho� expression of the reaction
equilibrium constant, CA = [A]0 + [AB]0 is the conserved totalconcentration of A strands in the system and CB = [B]0 + [AB]0is the conserved total concentration of B strands. Initial speciesconcentrations are denoted with zero subscripts. Equilibrium con-centrations of the A and B strands are respectively:
[A]eq = CA − [AB]eq (5)[B]eq = CB − [AB]eq (6)
Equations (4)-(6) permit to calculate, for a single bimolecularreaction, the equilibrium concentrations of reactant and productspecies taking into account both ∆G◦ for the reaction and thetotal concentration of strands initially present. For this reaction, a’reaction completion percent’ function ε can be de�ned:
ε (∆G◦,CA,CB ) =2[AB]eqCA +CB
, (7)
such that ε = 1 when allA,B strands in the system are in the productcomplex AB at equilibrium, and ε = 0 when all A,B strands in thesystem are reactants and no product complex is formed. A reactioncompletion curve may be drawn (Figure 2) denoting reaction ∆G◦
(x-axis) versus reaction completion percent ε (y-axis), for di�erentvalues of total strand concentration CA + CB . Observe that thereaction completion curves of Figure 2 shi� to the le� as CA +CBdecreases, and to the right as CA +CB increases.
Our signal recorder chemistry, however, does not consist of a sin-gle reaction: rather, it consists of a set of interconnected reactions.An analytical expression for the equilibrium point of the whole sys-tem is not possible to derive, and so it would appear that function εcannot be calculated for our signal recorder chemistry. A solutionto this dilemma is found by realising that any (well-stirred) systemof interconnected bimolecular reactions can be logically viewed asa series of separate but communicating single bimolecular reactionsub-systems. As the reaction proceeds, these single bimolecularreaction sub-systems exchange strands, causing the total strandnumber CA +CB in each sub-system to �uctuate. At equilibrium,these �uctuations die out and the global system stabilizes.
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GECCO ’17, July 15–19, 2017, Berlin, Germany J. Kozyra et al.
CA
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Equilibrium is concentration dependent
99% 70%products reactants
70% 99%
Figure 2: How total strand concentration CA + CB a�ectsamount of product at equilibrium for reaction A + B ABat 21◦C, when the reaction has di�erent values of Gibb’sfree energy of binding. Inside the white region, the reactionequilibrium point is concentration dependent. �is regionis avoided.
�erefore, at equilibrium, we can treat the system as a series ofindependent reactions, and still apply the insights that were devel-oped above (shown in Figure 2) for single bimolecular reactions.�e exact equilibrium point of the system need not be calculated.All that needs to be ensured are two weaker conditioins: bimolecu-lar reactions which are ’desirable’ should have a ∆G◦ such that evenwith a handful of strands (low CA +CB ) the reaction will converttoward 100% products at equilibrium. �en, according to Figure 2,even asCA +CB increases, such reaction subsystems will remain at100% product conversion at equilibrium. Conversely, ’undesirable’bimolecular reactions in our signal recorder chemistry should have∆G◦ such that even if all strands in the reaction system were par-ticipating in this reaction (high CA +CB ), the reaction will remainas 100% reactants at equilibrium. �en, according to Figure 2, evenas CA +CB decreases, such reaction subsystems will remain closeto 0% product conversion at equilibrium.
�erefore, we de�ne the favourable equilibrium score Sfec of asingle reaction r ∈ Rdesired ∪ Rundesired as
Sfec (r ) =
ε (∆G◦r ,ClowA ,C
lowB ) if r ∈ Rdesired
1 − ε (∆G◦r ,ChighA ,C
highB ) otherwise.
(8)
For our signal recorder chemistry, we set C lowA = C low
B = 10−18Mand C
highA = C
highB = 10−5M. Note that 0 ≤ Sfec ≤ 1, and that
the score approaches 1 when leaving the concentration-dependentzone in Figure 2.
Overall Score Function. To summarize, the three scoring func-tions were developed to evaluate various aspects of the signalrecorder design. Each individual function is normalized to givea score in range 0 ≤ s ≤ 1. However, the function Ssf is used toevaluate 13 individual strand structures within the signal recorder
design. �ese strands engage in 25 desired pairwise interactionswhich are evaluated by function Spf. Finally, function Sfec evaluates86 combinations of pairwise interactions (where 25 are desired and61 are undesired). �is imbalance raises an issue, namely, how doesone combine these objective functions? Using a linear combina-tion improves the readability of the results and allows for easy anddescriptive comparison between di�erent design aspects.
We established, through several trial runs of the genetic algo-rithm (described in next section) and upon visual inspection of theobtained results, that the most promising overall score functionis given by a linear combination of the scoring functions whereeach score is weighted by the inverse of the number of factors in itsclass, i.e., each scoring class is given equal weight. �us, we de�nethe overall score function as
Stotal =1|S|
∑x ∈S
Ssf (x )
+1|P |
∑(x,y )∈P
Spf (x ,y) +1|R |
∑r ∈R
Sfec (r ), (9)
where S is the set of all speci�ed DNA strands, P the set of allpairwise speci�cations, R = Rdesired ∪ Rundesired the set of allspeci�ed reactions, and vertical bars denote set cardinality. Weremark that 0 ≤ Stotal ≤ 3.
�e �ne-tuning of the parameters for the overall score functionas well as the addition of evaluators for reaction kinetics are le�for future research.
3 GENETIC ALGORITHM FOR SEQUENCEOPTIMIZATION
Genetic algorithms (GAs) are a class of heuristics for solving op-timization and search problems by mimicking the processes ofnatural selection. �ey rely on genetic operators (such as selection,crossover and mutation) to quickly evolve a near-optimal solutionfor a given objective function. �e key advantage of using GAs isthat they are e�ective in navigating a large and complex searchspace for which li�le is known.
We based our custom-built GA on the free and open-sourceinspyred2 framework. �e novel elements that we introduced areobjective functions (previous section) as well as genetic operatorsand the design encoding (described below). �e source code ofour algorithm together with the design speci�cation is availableonline3 and the reader is encouraged to examine it.
In our representation, an individual gene encodes the nucleotidesequences of a domain, and the concatenation of all genes forms thegenotype of a candidate solution (see Figure 3a). Our code allowsto constrain parts of domains to prede�ned nucleobases (e.g. basesequences recognized by a restriction enzyme), but this feature hasnot been explored in this study.
�e phenotype of a candidate solution is expressed as a completedesign of nucleic acid strands assembled from the domains of itsgenotype (Figure 1). �e phenotype is then evaluated using theoverall score function Stotal de�ned in Equation (9).
�e variator combines existing solutions (from the parents pop-ulation) into other, possibly unexplored solutions that form the2Available at: h�ps://pypi.python.org/pypi/inspyred3Available at: h�ps://bitbucket.org/J3ny/ga-mdr
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Optimizing nucleic acid sequences for a molecular data recorder GECCO ’17, July 15–19, 2017, Berlin, Germany
TCGATC ATCAGAT GCCTGT TGCATCACCGTAAGA B C X Yd..wa)
b)
c)
d)
NNNNNNN
N
P1 P2
F1 F2
Figure 3: Genotype representation (a) and three geneticoperators: (b) domain mutation (c) point mutation (d)crossover.
o�spring population. We utilize three genetic operators which areapplied to individuals with a certain probability and independentlyof one another. �ese are:
• single-gene mutation: a gene is picked at random4 andassigned a random nucleotide sequence – i.e. equivalentto reinitializing the entire domain (with probability 0.02).
• single-nucleotidemutation: similar to above, but ratherthan mutating the entire gene a nucleotide at random po-sition is mutated into another type of nucleotide (withprobability 0.25).
• crossover: is a standard one-point crossover in which acrossover point is set to a random nucleotide position atthe random domain. All nucleotides beyond that point areswapped between the two parents (with probability 0.8).
�rough initial experiments with the algorithm parameters (i.e.population size, number of generations) we established 100 indi-viduals over 500 generations to work well. �e selector is a defaulttournament selector; using random sampling it pulls two di�erentindividuals from the population and selects one with the higherscore. �is procedure is repeated until 100 parents are selected forrecombination and mutation. In the last step, the replacer discardsthe worst 2% of the o�spring population and retains the top 2% ofparents population as survivors (i.e. elite individuals). �e evolu-tion is run for 500 generations, and thus the terminator stops thegenetic algorithm when a total of 5 × 104 individuals have beenevaluated. An individual solution with the highest score is thenreported.
�eGAwas run in two variants: the �rst variant uses all availablepartial scoring functions (i.e. Ssf, Spf and Sfec) for optimization,while the second variant ignores the Sfec (the two variants aredenoted by (+FEC) and (-FEC) respectively). For comparison, weperformed similar optimization of the signal recorder design usingNUPACK. Each of the three heuristics was run 20 times; yielding20 di�erent “winning” designs. For additional comparison, we4In our case “picked at random” implies sampling from a discrete uniform distribution(i.e. each outcome is equally likely to happen).
1.6 1.8 2.0 2.2 2.4 2.6 2.8
GA (+FEC)
GA (-FEC)
NUPACK
Random
Stotal
0.4 0.5 0.6 0.7 0.8 0.9 1.0
GA (+FEC)
GA (-FEC)
NUPACK
Random
Ssf
0.4 0.5 0.6 0.7 0.8 0.9 1.0
GA (+FEC)
GA (-FEC)
NUPACK
Random
Spf
0.4 0.5 0.6 0.7 0.8 0.9 1.0
GA (+FEC)
GA (-FEC)
NUPACK
Random
Sfec
Figure 4: Comparison of the design scores for di�erentheuristics. Each data point is marked with a dot whilethe boxes show the quartiles of each distribution (whiskersmark the rest of the distribution as a fraction of interquar-tile range).
generated 20 solutions where a random sequence is assigned toeach domain in the design (referred to as Random heuristic).
4 RESULTS�e results of the 20 highest scoring solutions for each heuristicare shown in Figure 4 (top), together with a decomposition of thetotal scores into the individual score contributions (below).
At �rst glance, the three heuristics seem to produce designsof similar quality: the overall score function Stotal ranges fromapproximately 2.4 to 2.7 (where the maximum is 3.0) for two GAvariants, while NUPACK designs are scored slightly lower. For theRandom heuristic the bulk of the distribution lies above 2.0 whichis an interesting result; it implies that a signi�cant part of the scoreStotal may be a�ributed to the way the design is speci�ed (i.e. withsome domains being complementary by construction).
A closer inspection reveals that the heuristics optimize for dif-ferent objectives. For instance, NUPACK excels in Ssf and sys-tematically yields high-quality single-stranded foldings, which are
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GECCO ’17, July 15–19, 2017, Berlin, Germany J. Kozyra et al.
occasionally outmatched only by GA (-FEC). On the other hand, GA(+FEC) does not perform so well in this criterion and has relativelybroad Ssf distribution, while Random is far from optimum. Althoughthe la�er is expected, as the random assignment may result in ahigh ratio of undesired base pairing among random domains, theGA (+FEC) performance is somehow intriguing when comparedwith GA (-FEC). It indicates that including the function Sfec as partof the optimization has a dramatic e�ect on the individual foldingsof strands.
For the scoring function Spf both variants of GA outperformNUPACK and Random; however, none of the candidate designsconsidered here has a near-perfect Spf score (unlike for the otherscoring functions). Moreover, the Random heuristic scores evenhigher for pairwise folding than for single-stranded folding, whichis yet another sign of correct folding “by construction”.
Lastly, the scoring function Sfec, which evaluates spontaneity ofthe desired and undesired reactions, is being optimized only whenit is explicitly included as part of the optimization heuristic. Incomparison, both GA (-FEC) and NUPACK have a slightly lowerSfec score than the Random approach. �e relatively high score Sfecfor Random could be explained by the poor folding of individualstrands (recall Ssf scoring) which potentially leaves fewer basesavailable for undesired interactions.
We point out that obtaining high scores in Ssf and Spf does notautomatically translate to a high Sfec score (see Figure 5). Ourresults suggest that the opposite could be true and, in the case ofour design, the quality of single-stranded folding may need to besacri�ced for an optimal Sfec score.
In order to show that these di�erences are statistically signi�cantwe performed Mann–Whitney U test on pairs of partial scores. Inonly two cases, the di�erence in scores is not statistically signi�cant;i.e. the di�erence between GA (-FEC) and NUPACK for Sfec score(p = 0.617) and Ssf score (p = 0.172). For all other cases, oneheuristic always yields signi�cantly di�erent results (p ≤ 5 × 10−5).
�e heatmap in Figure 6 decipts the binding energies of all pair-wise interactions among all DNA strands of our signal recorderobtained from GA (+FEC) optimization. Desired interactions aremarked with a check mark in the table. All other interactionsare undesired. Green colors indicate high negative binding ener-gies (strong binding) whereas red coloring indicates weak binding.White coloring indicates regions where Sfec is concentration de-pendent.
It is apparent that our algorithm is able to maximize all desiredbinding energies and minimize most of the undesired interactions.Note that few interactions failed to be optimized: Start-Read, for ex-ample, has a high binding a�nity even though a low a�nity wouldbe desired. �is is because the two strands share a complementarydomain (A), which prevents the algorithm from optimizing againstthis binding, especially since the same domain is responsible for de-sired binding in other strand pairings. Several interactions (mainlyregarding the report strands) remain in the suboptimal concentra-tion dependent region, which is likely due to the short length ofthese domains. Some pairwise minimum energy folding structuresare shown for illustration, of which A1 and A2 are desired, B isundesired and avoidable, whereas C is undesired and unavoidable.
�2 0 2SF-zscore
�2
�1
0
1
2
FEC-z
scor
e
Heuristic
GA (+FEC)
GA (-FEC)
NUPACK
Random
�2 0 2PF-zscore
�2
�1
0
1
2
FEC-z
scor
e
Heuristic
GA (+FEC)
GA (-FEC)
NUPACK
Random
Figure 5: Correlations diagrams with normalised partialscoring functions for di�erent heuristics.
Another aspect, that was not implicitly investigated here, are themanufacturing constraints which are restricting the DNA oligonu-cleotide synthesis. Even if the in silico solution exists, the actualsequence might be extremely di�cult to manufacture and purify. Inpractice, it entails that the �nal construct has to satisfy the synthesisconstraints of a DNA synthesis service. For that instance, guanine-rich sequences are known to form problematic G-quadruplexes [2].Other considerations typically include identi�cation of homopoly-mers, interspersed and tandem repeats, and GC-content.
For this reason, we further examined the solutions generated bydi�erent heuristics. We discovered that all 20 design produced byGA (-FEC) could not be manufactured - the individual sequencestend to contain pa�erns of one repeated nucleotide and those repe-titions are adjacent to each other (in the worst case 17 consecutiveguanine bases). Also, the same problem was encountered duringNUPACK optimization which we mitigated by constraining thealgorithm to avoid regions of four consecutive nucleotides of thesame type.
Interestingly, designs produced by GA (+FEC) did not su�er fromthe same issue which we assume to be an indirect consequence ofSfec optimiztion. In the future, such synthesis constraints should be
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Optimizing nucleic acid sequences for a molecular data recorder GECCO ’17, July 15–19, 2017, Berlin, Germany
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GAAAUAAGAGGAGA CA
UC
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nucleotide binding probability
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Figure 6: Free energies of binding (top) and example pair-wise foldings (bottom) for the sequence-optimized DNAstrands, calculated using ViennaRNA at 21◦C.
incorporated directly into the algorithm as an additional evaluationcriterium.
5 DISCUSSIONIn this paper, we have used a genetic algorithm to generate nucleicacid sequences that optimize the functioning of a DNA nano-device,
namely a molecular signal recorder. Because of the di�culty todetermine what constitutes a good design, we have evaluated can-didate solutions with multiple score functions, based on individualand pairwise folding, as well as the promiscuity of both desiredand undesired reactions. While the approaches based on foldingproperties of strands are generally acknowledged, methods whichguarantee high or low reaction turnover are currently lacking. Yet,this criterion is essential for dynamic nano-devices which requirethe operation cycle to be strictly and carefully controlled. To thebest of our knowledge, our favourable equilibrium concentrationscore is a novel contribution.
We found that the three partial scoring functions are optimizingcompeting objectives. Ultimately, from the end user point of view,what ma�ers mostly is the best individual, which can then be syn-thesized and tested in the laboratory. �emost promising candidatesolution that was produced by the algorithm is evaluated at ap-proximately 90% of the ideal Stotal score. Although, for this design,the single-stranded folding of individual strands is not optimal, wehighlight that for dynamic systems of this kind the self-assemblingproperties and e�ciency of operations of the device are most vital.
We envision that our scoring functions can be used for opti-mization of nucleic acid sequences for DNA nano-technologies ingeneral, provided that the designs do not involve massive structuralrearrangements, in which case the decomposition of the designinto pairwise interacting components would not capture importantenergetic contributions associated with the structural changes.
Future e�orts should focus on the inclusion of score functionsthat evaluate the kinetics of DNA folding and strand displacementto further improve DNA nano-technology designs. Also, one mightconsider using a multi-objective pareto-based optimization algo-rithm (or another alternative to the conventional GA) in order toimprove the search.
6 ACKNOWLEDGMENTS�is work was supported by grants EP/J004111/2, EP/L001489/2and EP/N031962/1.
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