chengde mao- the emergence of complexity: lessons from dna

8/3/2019 Chengde Mao- The Emergence of Complexity: Lessons from DNA

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PLoS Biology | www.plosbiology.org 2036

How did life emerge from asoup of chemicals? How dopatterns such as schools of

fish form from individuals? How dovoting patterns emerge? Such a diversearray of problems seems completelyunrelated. However, they all involveemergence of complexity. Whenindividuals come together, they formpatterns, structures, and organizationsthat cannot be discerned from theindividuals alone. The study of theemergence of complexity is one of

the most active and important areasof research. It is important not only

for understanding nature, but also fortechnological applications, includingthe fabrication of large-scale integrated

nanocircuits using a bottom-upapproach, and the preparation ofmultifunctional smart nanomaterials.

DNA evolved to be the primarycarrier of genetic informationbecause of its extraordinary chemicalproperties. These same propertiesalso make DNA an excellent systemfor the study of self-assembly and self-organization. Two complementarymolecules of single-stranded DNAhave paired bases that bond with

each other and form the well-knowndouble helix structure. Two moleculesof double-stranded DNA (duplexes)can further associate together if theyhave complementary single-strandedoverhangs (sticky ends). Intermolecularinteractions can be precisely predictedby WatsonCrick basepairing (adenineto thymidine and guanine to cytosine).And, these interactions are structurallyunderstood at the atomic level. Giventhe diversity of the DNA sequences, wecan easily engineer a large number of

pairs of DNA duplexes that associatewith each other with sequence

specificity and in a well-defined fashion.This property is not common amongother molecular systems. Small organic

and inorganic molecular pairs caninteract with each other with specificityand in well-defined structures, but thenumber of such pairs is limited andtheir chemistry varies greatly. Proteinmolecules, such as antibodyantigenpairs, have great diversity and highspecificity. However, it is extremelydifficult, if not impossible, to predicthow proteins interact with each other.In contrast, DNA as a molecular systemfulfills all the aforementioned criteria.

In nature, DNA occurspredominantly as a linear molecule,and if its conformations were limitedto linearity, it would not be very usefulfor studying self-assembly. Fortunately,branched DNA structures can beengineered. Holliday junctions, forexample, are intermediates that occurduring genetic recombination. Tomodel Holliday junctions, a stable four-arm junction has been constructed inwhich, by design, no two strands arefully complementary to each other

(Kallenback et al. 1983; Seeman 2003)(Figure 1A). For example, the 5 half of

Open access, freely available online

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The Emergence of Complexity:

Lessons from DNAChengde Mao

Citation: Mao C (2004) The emergence of complexity:Lessons from DNA. PLoS Biol 2(12): e431.

Copyright: 2004 Chengde Mao. This is an open-ac-cess article distributed under the terms of the Cre-ative Commons Attribution License, which permitsunrestricted use, distribution, and reproduction inany medium, provided the original work is properlycited.

Abbreviations: 1D, one dimensional; 2D, two dimen-sional; DX, double crossover; TX, triple crossover; XOR,exclusive OR

Chengde Mao is in the Department of Chemistry, Pur-due University, West Lafayette, Indiana, United Statesof America. E-mail: [email protected]

DOI: 10.1371/journal.pbio.0020431

DOI: 10.1371/journal.pbio.0020431.g001

Figure 1. Basic DNA Structures for Self-Assembly(A) A four-arm junction and (B) its three-dimensional structure; (C) a DNA DX; and (D) a DNA TX.

December 2004 | Volume 2 | Issue 12 | e431


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strand 2 is complementary to the3 half of strand 1, but the 3 halfof strand 2 is complementary tothe 5 half of strand 3 insteadof that of strand 1. Combiningbranched structures and theexcellent molecular recognitionof DNA, we are ready to

engineer complicated DNAnanostructures and use them forstudying self-assembly.

Extensive studies have shownthat the four-arm junctionadopts an X-shape structure(Figure 1B) under physiologicalconditions, and the anglebetween its two helical domainscan vary widely (Lilley 2000).It is impossible to constructwell-defined large structuresfrom flexible components. Toovercome this problem, several

well-behaved DNA motifs have beenengineered. Double crossover (DX)(Fu and Seeman 1993) and triplecrossover (TX) (LaBean et al. 2000)molecules are two early examples(Figure 1C and 1D). In such molecules,two or three DNA duplexes lie side byside. Two neighboring duplexes arejoined by two crossovers, which preventany duplex from twisting against itsneighbor duplex. Thus, the interhelicalangles become fixed at 0. Othermotifs quickly followed, including theparanemic crossover motif (Shen et al.

2004), rhombus/parallelogram motif(Mao et al. 1999), cross motif (Yan etal. 2003), and several triangle motifs(Chelyapov et al. 2004; Ding et al. 2004;Liu et al. 2004). They all are stable,rigid, and readily designed for self-assembly.

One simple example of self-assemblyis the formation of two-dimensional(2D) periodic arrays or 2D crystals. Thisis also one of the greatest successes inthe field of DNA self-assembly (Figure2). The first 2D DNA crystals wereassembled from DX motifs (Winfree

et al. 1998). In a 2D crystal, eachDX molecule contains four stickyends (AA and BB) distributedon its two component duplexes. Thecomplementarity of the sticky endsis designed in such a way that a DXmolecule will interact with anotherfour DX molecules through its foursticky ends. Any two DX molecules caninteract with each other though onlyone pair of sticky ends. Any pair ofsticky end interactions will position the

two DX molecules in a conformationsuch that no other sticky ends fromthese two molecules are in sufficientproximity to interact. As a result of thisdesign, regularly ordered 2D arrayshave formed (Figure 2). Followingsimilar strategies, others have designedDNA motifs to assemble into 2D arrays,whose symmetries include tetragonal(Yan et al. 2003), pseudohexagonal(Mao et al. 1999; Liu et al. 2004), andhexagonal (Chelyapov el al. 2004; Dinget al. 2004).

Inspired by early theoretical

suggestions (Winfree 1998),experimental exploration of aperiodicself-assembly immediately followed.One study applied algorithmic self-assembly to TX molecules (Figure 3)(Mao et al. 2000). The assembling ruleexclusive OR (XOR) is encoded inthe TX molecules. Consider the valueof all inputs and outputsas either 1 or 0. For XORoperations, if two inputsare the same, the outputwill be 0; otherwise,the output will be 1. If

molecules X and Y arethe input and output,respectively, Y

imolecule

takes the input from theX

iand Y

i

1molecules.

In other words, thevalues of the X

iand Y

i

1molecules determine

what Y molecule will beincorporated. There arefour different types of Ymolecules, whose inputs

are (1, 1), (1, 0), (0, 1), and (0,0). These four, and only four,Y molecules are enough tosatisfy any input combination.Two C molecules connect theinput and output molecules,which is necessary for thecharacterization but not essential

for the self-assembly process.Sticky ends between the Xmolecules and the C moleculesare longer than those betweenY molecules and between Y andX or C molecules. Thus, theC and X molecules assemblefirst to form the inputs becausethe association between longersticky ends is more stable thanthose between the shorter ones.Then the output Y moleculesassemble to the assembled Cand X molecules. In that study

(Mao et al. 2000), two different inputcombinations were used, and oneof them is shown in Figure 3. Theresulting DNA structures are periodicwith respect to the backbones, butthey are aperiodic in their sequences.Though the resulting four-byte one-dimensional (1D) structures are quitesimple, this study demonstrated thataperiodic structures are achievablethrough self-assembly.

Winfree and co-workers in thisissue ofPLoS Biologyhave extendedthe algorithmic self-assembly strategy

from 1D to 2D (Rothemund et al.2004). This achievement is certainly amilestone in the field of self-assembly.It overcomes a great challenge, as thestructural complexity dramaticallyincreases from 1D to 2D structures.These researchers have appliedthe same XOR algorithms to DX


Figure 2. Self-Assembly of a 2D DX ArrayEach rod represents a DNA duplex. The geometriccomplementarity represents the sequencecomplementarity of sticky ends.


Figure 3. Self-Assembly of a 1D Aperiodic TX Array Based on XOROperationThe value of any input or output is binary, either 1 or 0.If two inputs are the same, the output is 0; otherwise, theoutput is 1.



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molecules in their study and achievedfractal structures, Sierpinski triangles(Figure 4). External inputs are in the

bottom row. Each row takes inputsfrom the row immediately below,and sends the operation outputs tothe row immediately above. Eachposition takes two inputs (identicalor non-identical) from lower leftand lower right positions, and sendsidentical output to both upper leftand upper right positions. The arrowsindicate the direction of informationflow, or assembly sequences. In theirexperiment, the rules are encodedin DX molecules. This study isconceptually straightforward, but

the experimental challenges aretremendous. One key challenge isassembly fidelity. The right moleculeshave to compete with partially matchedmolecules. The concentrations ofthe competing molecules furthercomplicate the fidelity issue, as somemolecules could be rapidly depletedfrom the solution. In that sense, thecurrent work is quite stunning eventhough the assembly is far from perfect.

In principle, a wide rangeof 2D patterns could begenerated with the same setof molecules and the samestrategy, changing only thefirst row of the assembly,which specifies the externalinputs. Realization of this

goal will critically rely onthe elimination of assemblyerrors, or the introduction oferror corrections (Winfreeand Bekbolatov 2004).

The current workrepresents a neat approachto understanding theemergence of complexity. Itintegrates both simulationand wet chemistry. It

also provides a plausible approachto nanofabrications. Over thelast decade, a variety of methods

have been developed, which usebiomacromolecules as templates tofabricate nanostructures (Braun el al.1998; Douglas and Young 1998; Mucicet al. 1998; Fu et al. 2004). Limitedby the complexity of the availablebiomacromolecular templates, simplenanostructures are the usual result:mostly nanowires, nanoparticles, andsimple aggregates of nanoparticles.The current work illustrates thepossibility of generating morecomplicated structures and promisesunprecedented structural complexity

for nanomaterials.

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Figure 4. Schematic Representation of Self-Assembly of aSierpinski Triangle Based on XOR OperationThe values in the bottom row are the inputs.


chengde mao- the emergence of complexity: lessons from dna

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