Diamondoids-DNANanoarchitecture: FromNanomodules Designto

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Journal ofComputational and Theoretical Nanoscience Volume 4 , Issue 1, Pages 96–106, 2007

DOI: 10.1166/jctn.2007.008

1. INTRODUCTION

Diamondoids are cage-like saturated hydrocarbons con-sisting of fused cyclohexane rings. The carbon-carbonframework of diamondoids constitutes the fundamentalrepeating unit in the diamond lattice structure. This familyof organic compounds follows the general chemical for-mula of C4n+6H4n+12. Adamantane is the first compoundof the diamondoids family with n = 1. The other mem-bers are diamantane for n = 2, triamantane for n = 3,tetramantane (n = 4) and so on (Fig. 1). Diamondoidsare divided into two major groups accounting their size:lower diamondoids which include the first three membersof diamondoids and higher diamondoids containing tetra-mantane and other larger family members.1 Adamantanewas first isolated from the natural petroleum reservoirs in1933 and synthesized subsequently. High-yield synthesisof higher diamondoids still remains a challenging task insynthesis chemistry.2�3 Recently, detection and isolation ofhigher diamondoids (up to n= 11) from certain petroleumfluids were reported and the chemical structures and iso-meric forms of higher diamondoids were studied in detail.4

Originally, Drexler5 suggested that the stiff and highlysymmetric diamondoid molecules with three dimensional(cage-like) carbon-based structures were great buildingblock materials for nanoscale machines with sub-angstromprecision at room temperature. Diamondoids have foundnumerous applications in crystal engineering and pharma-ceutical science and they are promising to find applicationsin nanotechnology as well. They also have been envisionedto act as the key components in the future mechanosyn-thesis design of nanorobots6 and an artificial red bloodcell.7–9

Adamantane is considered to be an MBB possessingsix linking groups, which is an ideal number for molec-ular building blocks. Bulky and symmetric structure ofadamantane allows several linking groups to be incorpo-rated into it without undesired intramolecular interactionsand spatial congestion. As a result, it is possible to con-struct molecular probes. An example is a molecular probewith three fluorophore groups showing an amplified signalwith no intramolecular self-quenching due to the remotedistances of fluorophores substituted on the adamantanenucleus.10 It is obvious that higher diamondoids are capa-ble of possessing more than six linking groups. The diversecapabilities of diamondoids as MBBs lie beyond their

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Diamondoids-DNA Nanoarchitecture:From Nanomodules Design to Self-Assembly

Hamid Ramezani1, G. Ali Mansoori2, and Mohammad-Reza Saberi3

1School of Pharmacy, Mashhad University of Medical Sciences, Mashhad, Iran, [email protected] 2Departments of Bio & Chemical Engineering, University of Illinois at Chicago, (M/C 063) Chicago, IL 60607-7052, USA, [email protected]

3Chemistry, School of Pharmacy & Avicenna Pharmaceutical Research Center, Mashhad Univdrsity of Medical Sciences, Mashhad, Iran, [email protected]

Diamondoids are one of the promising molecular building blocks (MBBs) proposed for the fabri-cation of a diverse range of nanostructures in molecular nanotechnology and manufacturing. The challenge is to find a route for self-assembly of these cage hydrocarbons and their application in the bottom-up synthesis. In this context, we propose a DNA-based self-assembly technique called “DNA Bridge-based Self-assembly” (DBS) to self-assemble the diamondoid molecules based upon a bottom-up strategy. The idea supporting the hypothesis is based on the well-established proofs of DNA-based self-assembly. Furthermore, the previous findings in the field of DNA nanotechnology would be inspiring to develop DBS for the construction of Diamondoid-DNA-made nanoarchitecture. The results of our computations and simulations with different molecular mechanical force fields (MM+, AMBER, BIO+, and OPLS) and different optimization algorithms (Polak-Ribiere, Fletcher-Reeves, and block-diagonal Newton-Raphson) furthermore confirm the feasibility of the formation of such hybrid nanoarchitecture.

Keywords: Diamondoids, DNA Bridge-Based Self-Assembly (DBS), Self-Assembly, Bottom-Up Nanotechnology

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a question might arise: what does fill the evolutionarygap between ongoing nanotechnological affairs and thoseadvances we are expecting in the not-too-distant future?“Self-assembly” seems to be one of the pragmatic answerspromising many splendid near-term results.14

Setting aside the positional assembly of diamondoidsas a practical plan at the moment, one could also seek aconsequential self-assembly procedure. Although a num-ber of self-assembly processes have been identified, feware suitable to meet the qualifications required for thebottom-up nano-assembly of structures. Invention of anapproach which is a perfect image of an abstract and pro-grammable self-organization to construct large nanostruc-tures still remains a demanding task.21 Generally for aself-assembly, joining together and self-organization of theMBBs are the prerequisites to the stepwise control over theself-assembly process. There are many functional groups(like carboxyl and amine groups to form amide linkage)to be substituted on a diamondoid to form chemical bondsand join each to its neighbors. Nonetheless, the challengeis how to manage the self-assembly steps by designat-ing the positions and sequences of bond formations. Eachlinking group is expected to be long and flexible enoughnot to preclude the other liking groups from attachments.Besides, to achieve a large three-dimensional (3-D) geom-etry for a nanostructure it is necessary to consider thestepwise orientational expansion of the nanostructure byputting into action proper linking groups at each step. Forexample, numbering the six linking groups of adamantanefrom 1 to 6, we must be able to select the linking groupnumber of the first MBB which must attach to a specifiedlinking group number of the second MBB and so on. Thistype of control over self-assembly process is necessaryto achieve a predetermined pattern which is the goal ofbottom-up construction of nanostructures. Thus, by design-ing appropriate MBBs reacting in a specific and selec-tive way, the early-generation of productive nanosystemswould be attained.14 Under such conditions, the Brow-nian motion-based self-assembly would play the leadingrole in the fabrication of many intricate nanosystems.14

Considering the above requirements, we proceed with theDNA-directed assembly (DDA) as a method of choicewith a view to assemble diamondoid-made nanostructuresthrough a bottom-up strategy.

In the early 1980s, Seeman started to publish a seriesof reports on the construction of immobile nucleic acidjunctions in an effort to develop structural DNA nano-technology.22 Later several branched DNA motifs wereintroduced, such as double crossover (DX),17�23 triplecrossover (TX),24 paranemic crossover (PX),25�26 DNAparallelogram,27 and DX triangle.28–30 The inspiration tobuild these DNA motifs stemmed from the Hollidayjunctions, a mobile junction between four strands ofDNA.22�31–33 On the other hand, application of sticky endedDNA double strands (Scheme 1) to the nanoassembly

Fig. 1. Chemical structures of Diamondoids: (a) Adamantane, (b) Dia-mantane, (c) Triamantane, (d) Anti-isomer of Tetramantane.

role as symmetric and cage-like central structures. Suc h capabilities are reflected in some of their unique physic-ochemical properties such as high rigidity, stability, high density, high melting point and low surface energy.1 The diverse structural and steric isomeric forms of this class of organic MBBs give us the opportunity to select the closest stereoisomer when seeking for a particular nanostructure design. There are tens of isomers for each high molec-ular weight diamondoid. On the other hand, the flexible chemistry of diamondoids is amenable to a vast number of derivatization to produce a wide range of reactants and MBBs. Over 20,000 variants of diamondoids have been identified and even more is possible, providing a rich and well-studied set of MBBs.11–13

Of considerable interest is the rigidity of diamondoids which becomes much more conspicuous when one is to employ the positional assembly approach or to produce shape-targeted nanostructures.The main idea in positional (robotic) assembly is to utilize a robotic arm (such as an AFM tip) to place the MBBs in a designed pattern to build a nanostructure.13 One of the principle problems with the mentioned approach is thermal noises causing posi-tional uncertainty, which would decline to some extent using rigid MBBs.14 Provision of rigidity is a key require-ment influencing the shapes and accordingly the func-tions of nanostructures.Lack of enough rigidity results in difficulties in construction and analysis of shape-targeted nanostructures.15� 16 Hence, rigid MBBs are the key in the formation of nanodevices and periodic arrays.11� 17

Construction of a nanostructure according to the bottom-up nanotechnology strategy not only entails appropri-ate MBBs but also an efficient assembly method.18 The mechanosynthesis is suggested for selecting reaction sites on the MBBs and controlling bond formations using a mechanical system with atomic-scale precision (such as an AFM) to accomplish molecular manufacturing.19� 20

The given atomically-directed pick-and-place operations would be achieved by a number of positioning tools called assemblers.19 In spite of numerous potential advantages of diamondoids as MBBs there is a challenging barrier against development of diamondoid-made nanostructures, namely their nanoassembly into the larger nanostructures. It is obvious that the mechanosynthesis20 is not currently applicable to the assembly of diamondoids. This is due to the present day lack of necessary nanotechnological tools to accomplish mechanosynthesis. In fact, the molec-ular manufacturing and factories might be considered as futuristic trends in nanotechnology.21 Consequently,

H. Ramezani, G.A. Mansoori, M.-R. SaberiDiamondoids-DNA Nanoarchitecture: From Nanomodules Design to Self-Assembly

J. Comput’l and Theor’ll Nanoscience 4(1): 96–106, 2007

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when following a predetermined design that would resultin a desired three dimensional (3-D) molecular geometry.This is especially the case when one is working with stickyends which make the double helices accommodate thefamiliar B-form DNA folding.15�16�48�49 The DNA’s per-sistence length is about 500 Å along which the moleculebehaves as an almost rigid rod.15�16�49 Besides structurepredictability, the rich nucleic acid chemistry is a moti-vating factor to propose DNA-incorporated diamondoid-based nanostructures. The given chemistry dates back tothe early 1950s, almost at the same time as the magiczip-like and ribbon-shaped model recognized to be inharmony with the prerequisites of cells’ genetic contentsby Watson and Crick.50 The automated phosphoramiditechemistry gives us the ability to readily synthesize awide variety of DNA sequences.50 Advances in the syn-thesis of nucleotide analogues51�52 open the new avenuestoward new derivatives with interesting therapeutic, diag-nostic and polymeric properties.53–56 The use of predictablenon-Watson-Crick base pairing patterns seems to be aless explored, and still interesting, possibility in build-ing DNA-based nanostructures.57 In addition, the DNA-modifying enzymes are also helpful to accompany thechemical modification approaches in the structural DNAnanotechnology.49

In what follows, the idea of the application of DBS inconstructing the Diamondoid-DNA-based nanoarchitecturewill be discussed. The efficiencies of different molecu-lar mechanical techniques in computational chemistry arecompared to investigate the formation of a cube-shapednanostructure. The results of computations indicate thatthe large number of hydrogen bonding between the com-plementary DNA sequences is very likely to stabilize the3-D geometry of the nanostructure.

2. COMPUTATIONAL PROCEDURES

2.1. Modeling the Nanomodules

The chemical structures of MBBs shown in Figures 2–6were built in the Hyperchem software release 7.0. Thegeometries of diamondoids and their derivatives were ini-tially optimized using the MM+ force field of molecu-lar mechanics in Hyperchem. The deoxyribonucleic acidresidues (nucleotides) were taken from the nucleic aciddatabase of Hyperchem. The sequences were chosen to bein the B-form secondary conformation (right-hand helices)as that is the most prevalent form of DNA under physio-logical conditions.58 The pucker of the furanose ring wasselected to be 2′ endo consistent with the B-form con-formation. Importing nucleotides from the Hyperchem’sdatabase takes advantages of working with the well-defined and parameterized nucleotide templates. They pos-sess structural properties and information in accordancewith their real molecular structures in nature. After build-ing the initial models, they were all optimized with the

Scheme 1. DNA sticky ends: Two double helical DNA molecules capa-ble of forming sticky ends are shown in red and blue. Hydrogen bonds between bases are highlighted by the green broken lines.The phosphate-sugar backbones are depicted as arrows oriented from the 5′ to the 3′

terminus.

process made it possible to construct purely DNA-made nanostructures.Those include the cube-shaped34–36 and also octahedron-like35� 37 nanostructures, six helix bundles,38

and DNA-made nanomechanical devices.39� 40

Of critical importance is the role of DNA in com-positional DNA nanotechnology to assemble different nanomodules.41–43 The hybridization specificity of two complementary strands and the fidelity of base pair-ing would assure a full control over assembly process in the DNA-directed assembly (DDA) approach. DNA oligomers can be used for site-selective immobilization of macromolecules to direct self-assembly process on a solid surface via DNA directed immobilization (DDI).44

To achieve DDI, at first, the desired site of the molecule is tagged by a DNA strand. Then the complementary DNA strand is fixed on a solid surface. Thus, completely specific DNA hybridization is exploited to immobilize macromolecules with controlled steric orientation. Th is method has been successfully performed to immobilize gold nanoparticles.44� 45 The multimeric nucleic acids and nucleic acid-protein conjugates are two instances proving the applicability of DNA to the assembling of nanostruc-tures.They are promising tools to fabricate nanostructured devices, DNA biochips, polymeric aggregates, microcir-cuts and many other diagnostic kits.42� 46� 47

Utilization of DNA i n t he Diamondoid-DNA-made nanoarchitecture t akes advantage of t he DNA properties based upon which DNA nanotechnology has been under-pinned.The bottom-up synthesis of nanostructures entails utilization of t hose approaches t hat would make t he final three dimensional s tructures of products predictable. Th e specificity and fidelity of Watson-Crick base pairing are powerful t ools t o devise unique DNA sequences.The pre-dictable i nteractions of t hese DNA sequences are r equired

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H.. Ramezani, G.A. Mansoori, M.-R. SaberiDiamondoids-DNA Nanoarchitecture: From Nanomodules Design to Self-Assembly

J.. Comput’l and Theor’ll Nanoscience 4(1): 96–106, 20

RESEARCHARTICLE Fig. 2. The chemical structure of MBB “i:” It consists of an adamantane

nucleus and three hexanucleotide linkers. Hydrogen atoms are removedfor clarity.

different force fields of molecular mechanics furnishedin Hyperchem. Those force fields are MM+,59 AMBER(Assisted Model Building and Energy Refinement),60–62

OPLS (Optimized Potentials for Liquid Simulations),63�64

and BIO+ which is an implementation of the CHARMM(Chemistry at HARvard Macromolecular Mechanics) forcefield65�66 in Hyperchem. For MM+, the electrostatics wasset to be based on bond dipoles while for AMBER theeffective dielectric constant was defined to be distance-dependent with the scale factor of 1. For the OPLS andBIO+ the effective dielectric constants were set to be con-stant. No cutoff distance for denying the non-bonded inter-actions was specified.

Fig. 4. The chemical structure of MBB “iii:” It consists of an undeca-mantane nucleus and four hexanucleotide linkers. Hydrogen atoms areremoved for clarity.

The Polak-Ribiere optimization algorithm was usedamong the conjugate gradient methods. The conjugategradient methods employ the first derivative of energywith respect to the Cartesian coordinates to find a localminimum along a search direction.67�68 The optimization

Fig. 5. The chemical structure of MBB “iv:” It consists of anadamantane-derived nucleus and four hexanucleotide linkers. Hydrogenatoms are removed for clarity.

Fig. 3. The chemical structure of MBB “ii:” It consists of a tetra-mantane nucleus and three hexanucleotide linkers. Hydrogen atoms are removed for clarity.



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Fig. 6. The chemical structure of MBB “v:” It consists of a cross-likeadamantane-derived nucleus and four hexanucleotide linkers. Hydrogenatoms are removed for clarity.

was continued until the root mean square (RMS) gradientreached the specified value of 0.1 kCal ·mol−1 ·Å−1. TheRMS gradient is calculated according to formula (1):69

RMSG = �3N�−1

(∑A

(�E�XA

)2

+(

�E�YA

)2

+(

�E�ZA

)2)1/2

(1)

one of the cube’s edges. The twelve edges of the cubewere thus simulated separately and then attached togetherin the Hyperchem software according to the blueprint(in Scheme 4). The nanostructure assembled manually inHyperchem was finally optimized using the MM+ forcefield of Hyperchem until the RMS gradient of 0.5 kCal ·mol−1 · Å−1 was achieved. Three different optimizationalgorithms were used to minimize the nanostructure ener-gies. The Polak-Ribiere and the Fletcher-Reeves optimiz-ers are among the conjugate gradient methods used forthis minimization.68 They use the minimization history toobtain new directions with optimized coordinates.67 Theoptimized coordinates are expected to satisfy the followingconstrain:

�V

�ri= 0 (2)

Where “V ” is the potential energy and “ri” stands forthe related Cartesian coordinates. The third optimizer usedwas the block-diagonal Newton-Raphson algorithm. Theresults of energy minimization by the aforementioned opti-mizers were recorded for further comparison and studiedfor monitoring hydrogen bonds. The electrostatic potentialsurface in Figure 8 was added in the Accelrys ViewerLite4.2 software. The visual graphics of figures representingMBBs and nanostructures were produced using the samesoftware.

3. RESULTS AND DISCUSSION

In this report The rudimentary and well-known principlesof DNA biomolecular chemistry and DNA nanotechnol-ogy (both structural and compositional)16 were exploitedto design a self-assembly procedure named DNA bridge-based self-assembly (DBS).

3.1. The DNA Bridge-Based Self-Assembly (DBS)

The main idea in DBS is to incorporate DNA strands intoa diamondoid molecule to act as linkers. DNA hybridiza-tion is a valuable tool to accomplish nanostructure self-assembly. It would enable us to control the orientation of ananostructure’s spatial extension through specific molecu-lar recognition sites existing between two complementaryDNA sequences.

Application of sticky-ended DNA segments to theassembly of diamondoids seems to be impractical. DNAis a macromolecule about 20 Å in width15�49 whilediamondoids are single and small organic molecules.Diamondoids are much smaller than a core bearing seve-ral sticky-ended DNA double strands as linking groups.Consequently, introduction of DNA double strands to thediamondoid cores sounds implausible due to the sterichindrance and size limitations. Nonetheless, DNA singlestrands might be capable of inclusion in the diamon-doid nucleuses. DNA-directed immobilization and assem-bly of nanostructures is a well-established practice proved

Where “N ” is the number of atoms, “X,” “Y ,” and “Z” are the Cartesian coordinates of atom “A,” and “E” is the energy. The whole computations were run In Vacuo without adding solvent molecules to the system explicitly. However, the solvent effects are accounted to some extent by setting the effective dielectric constants.Different ener-gies including bond, angel, dihedral, bending, and electro-static were recorded for comparison and data analysis.

2.2. Simulation of the Nanostructure

The hybridization of DNA single stranded linkers of each set of two MBBs with their complementary single stranded bridge was investigated using the Autodock Tools 3.0 soft-ware working under the Linux operating system.The two hexanucleotide linkers were defined for the software as if they had been a single strand consisting of 12 nucleotides. However, the phosphate-sugar backbone of the strand was cut between residues 6 and 7 to simulate the presence of two separate linkers but they were not displaced with respect to each other.

The above mentioned sequences were introduced to Autodock Tools as a macromolecule and the bridge sequence was designated to be the ligand.The software calculated the docking parameters and yielded the docked double helix structures. Each double helix corresponds to

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many times to be effective in different circumstances (suchas assembly of gold nanoparticles and peptides). How-ever, those self-assemblies essentially demand solid sur-face immobilization techniques to control the assemblingprocess.18�43–46

Here, we propose DBS as a bottom-up approach toself-aggregate a predetermined supramolecular structurealready devised as a blueprint. Hence, it may become pos-sible to control the nano self-assembly procedure in theliquid medium. There is no robotic arm needed, like whatis proposed for positional assembly or mechanosynthesis,to dictate the position of each MBB. Instead, the stere-oselective nature of MBBs, their sequential addition, andutilization of DNA bridges assure the placement of MBBsnear one another in a proper and specified fashion.

An MBB required for DBS consists of a diamondoids-derived nucleus and three or four DNA sequences as link-ers. As an example, assume that one is going to constructa cube-shaped nanostructure using DBS. The first stepwould be to draw a blueprint assigning the exact posi-tions of MBBs with respect to each other. Here, the term“blueprint” refers to a molecular design depicting thestructural details of a nanostructure at the theoretical level.

The following hexanucleotide linkers (L) are given inthe example (Scheme 2):L1: ATGAGCL2: CTAGCAL3: GTCATAL4: TCGTGC

The letters “A,” “T,” “G,” and “C” are representa-tive of Adenosine, Thymidine, Guanosine, and Cytidinenucleotides, respectively. Eight MBBs, each endowed withthree DNA single strands as linkers (Scheme 2), are nec-essary to form a nanostructure with the connectivity of acube. The diamondoid-derived nucleus of each MBB isplaced in one of the cube’s corners and the DNA strandscorrespond to the edges connecting the corners.

A bridging DNA sequence should be designed in such away that its first half is complementary to one of the link-ers of the MBB “a” and its second half is complementaryto one of the linkers of the neighbor MBB, let us say theMBB “b,” as represented in Scheme 3. The DNA bridgeis comprised of 10 nucleotides to bridge the two linkers

Scheme 3. The DNA Bridge-based Self-assembly (DBS): Two succes-sive MBBs, “a” and “b,” are attached together via their related DNAbridge.

and attach them together by formation of DNA doublestrands. Each linker consists of six nucleotides and thusthe two successive linkers ranged in row create a gap of12 nucleotides between two neighboring nucleuses. Onlyfive out of six nucleotides of each linker would partici-pate in DNA hybridization/double strand formation withthe DNA bridge. The first nucleotide of each linker, imme-diately attached to the diamondoid-made nucleus, wouldnot interact with the DNA bridge. It is supposed to play therole of a spacer separating the double helix structure andnucleus in order to avoid steric congestions (Scheme 3).Each bridging sequence would attach two linkers togetherand hence there exist (4)2 = 16 bridging sequences in thecase of this example.

To complete the blueprint the next assignment wouldbe to select the appropriate linkers for each MBB. Someconsiderations are to be made regarding the selectionrules. Firstly, the linkers should not be complementary ontheir own. If there are two complementary sequences onneighboring MBBs, they would interact and might formimproper local structures. The resulted false pattern ofinteraction would prevent the linkers from the formationof double helix with the bridging DNA single strand. Sec-ondly, the linkers are supposed to be adopted in such away that only one interacting sequence exists for attach-ment to the nearby MBB. In other words, the bridgingsequences used to attach an MBB to its neighbors shouldnot be identical. Otherwise, it is not possible to managethe three dimensional extension of the nanostructure.

There is a larger diversity with the combinations pos-sible for choosing three linkers out of the four givensequences provided that the orders of linkers are consid-ered. There are thus (4)3 = 64 possible states. If the orderof selection is not important there would be less possible

Scheme 2. Schematic representation of a diamondoid-DNA-made MBB: (a) Four exemplary linker (L) sequences.(b) An MBB containing a diamondoid-made nucleus ( ) and three linkers.



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states, because of many repetitive combinations regardedto be the same. For instance, the L1-L2-L3, L1-L3-L2, L2-L1-L3, L2-L3-L1, L3-L2-L1, and L3-L1-L2 are all con-sidered to be identical as a single combination. As a result,there are only 20 possible states.

Each state should be referred to as a unique MBB.These 64 possible MBBs are obtained for a given situa-tion in which each MBB possesses three linkers and thereare only four linking sequences available (i.e., sequencediversity = 4). Practically, there is no limitation for theconstruction of unique and discrepant MBBs by increas-ing the sequence diversity. On the other hand, becauseDBS is a stepwise procedure, most of the possible randominteractions among MBBs would be avoided. For exam-ple, the MBB “f” is added to the solution exclusively afterMBB “e” and therefore, its interactions with MBBs otherthan “e” are prohibited to a large amount. The specificityof base pairing between two complementary DNA singlestrands would further diminish the possibility of untowardinteractions. The characteristics already enumerated causeDBS to bring about a full control over directing the MBBstoward their predetermined positions and make their inter-actions in hand. With such a degree of capacity to directthe MBBs, utilization of unique and exclusive MBBs isno longer a prerequisite. A limited set of different MBBscould be used to self-assemble to a large nanostructure.It might be also feasible to introduce an MBB to severaldifferent distant positions of a nanostructure.

As it was already mentioned each state describes aunique combination of the three linkers substituted on adiamondoid nucleus. Eight states were selected out of the20 combinations for the linkers (Ls) as depicted below:(a) L1, L1, L1(b) L2, L2, L2(c) L3, L3, L3(d) L4, L4, L4(e) L1, L2, L4

Table I. Computed energies (kCal ·mol−1) for the MBB “i:” A comparison among different force fields ofmolecular mechanics.

MBB “i”

Bond Angel Dihedral van der Waals Electrostatic Stretch-bend PES

OPLS 5�04 76�27 175.05 −213�75 −49�88 — −7�26AMBER 8�70 81�55 232.40 −186�62 −31�99 — 104�04BIO+ 65�52 247�72 488.61 109�51 −46�82 — 864�55MM+ 42�83 505�86 278.76 27�44 −158�55 −76.35 619�99

Table II. Computed energies (kCal ·mol−1) for the MBB “ii”: A comparison among different force fields ofmolecular mechanics.

MBB “ii”


OPLS 6�36 135�09 178�058 −202�68 −49�63 — 67�20AMBER 10�48 84�99 229�37 −185�63 −31�66 — 107�56BIO+ 79�25 282�41 523�07 151�52 −44�13 — 992�13MM+ 52�85 548�99 307�79 46�86 −159�20 −84.12 713�18

Scheme 4. An example of a molecular blueprint used for designing ananostructure based on a bottom-up strategy. The apexes of arrowheadsshow the 3′ termini of the DNA sequences. The solid spheres at thecorners correspond to the positions of the Diamondoid-made nucleuses.The white arrowheads are representatives of the linkers. The bridgingsequences (drawn in red) are specified by two letters and two num-bers (for instance ba21): the letters stand for the MBBs that a bridgingsequence attaches together when they are read from the 5′ to the 3′ ter-minus and the left number is the name of linker attached to the nucleusfrom its 5′ terminus and the right number is suggestive of the secondlinker attached to its nucleus through its 3′ terminus.

(f) L1, L4, L4(g) L3, L3, L4(h) L1, L1, L3

The blueprint showing the detailed description of our cube-like nanostructure is reflected in Scheme 4. In order to

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Table III. Computed energies (kCal ·mol−1) for the MBB “iii:” A comparison among different force fieldsof molecular mechanics.

MBB “iii”


OPLS 37�05 293.28 244.35 −243�50 0 — 331�19AMBER 75�57 364.39 324.49 −162�12 0 — 602�32BIO+ 178�12 380.43 623.05 324�49 0 — 1506�10MM+ 119�69 879.06 364.18 182�01 −257�21 −98.30 1189�43

Table IV. Computed energies (kCal ·mol−1) for the MBB “iv:” A comparison among different force fields ofmolecular mechanics.

MBB “iv”


OPLS 8�13 137.76 281.75 −270�91 −172�91 — −16�17AMBER 15�97 137.67 357.37 −217�29 −81�96 — 211�76BIO+ 111�16 416.47 769.29 245�19 −116�00 — 1426�11MM+ 66�76 729.66 418.52 67�11 −251�23 −110.82 920�00

Table V. Computed energies (kCal ·mol−1) for the MBB “v:” A comparison among different force fields ofmolecular mechanics.

MBB “v”


OPLS 8�10 111.58 236.15 −269�70 −202�41 — −116�28AMBER 14�43 118.41 307.94 −227�65 −104�43 — 108�70BIO+ 119�67 449.14 821.16 277�19 −151�55 — 1515�61MM+ 69�89 749.28 437.48 72�98 −250�94 −112.94 965�75

materialize a devised blueprint a two-step cycle is to befollowed repeatedly:(1) Addition of the neighboring MBBs to the solution (Forexample, addition of “b” to “a”).(2) Addition of the related DNA bridge to the mix-ture of two MBBs (for instance, addition of ba21 bridg-ing sequence to the solution containing the MBBs “a”and “b”).

energy surfaces calculated for each MBB by differentforce fields were then compared at the RMS gradientof 0.1 kCal · mol−1 · Å−1. Tables 1–5 present differentenergies (bond, angel, dihedral, bending, and electrostatic

Table VI. Docking energies: Different energies (kCal ·mol−1) calcu-lated for docking two DNA linkers and their related DNA bridge by theAutodock Tools software. Two numbers in each cell of the first columnspecify the names of two linkers (for instance, 1+ 4 means attachmentof linker 1 to the linker 4 via their corresponding DNA bridge).

(1) Final Estimated freeNames of the intermolecular (2) Torsional energy oftwo linkers energy free energy binding = �1�+ �2�

1+1 −9�97 16.81 6.841+2 −12�72 16.81 4.091+3 −11�77 16.50 4.721+4 −11�42 16.50 5.082+1 −8�85 16.81 7.962+2 −12�58 16.50 3.922+3 −11�09 16.19 5.092+4 −10�61 16.50 5.893+1 −8�67 16.50 7.833+2 −12�26 16.19 3.933+3 −10�92 15.88 4.953+4 −10�55 16.19 5.634+1 −11�15 16.50 5.354+2 −14�08 16.50 2.424+3 −13�02 16.19 3.174+4 −12�88 16.19 3.31

The aforementioned cycle should be repeated for the intro-duction of a new MBB to the nanostructure. Therefore , by repeating the cycle MBBs would be positioned at their place one by one based upon a sequence of stepwise self-assembly procedures.

3.2. Simulation of Diamondoid-DNA-MadeNanomodules

The geometries and energies of several types of Diamondoid-DNA-made nanomodules (MBBs) were optimized using different molecular mechanical force fields. The MBBs suggested here are composed of a number of typical molecules from diamondoids family such as adamantane, tetramantane, and undecamantane as well as their derivatives (Figs.2–6).However, the number of derivatives possible for being used as nucleuses is not definitely restricted to the suggested MBBs.The potential



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Table VII. Comparison of different energy optimization algorithms: Results of energy (kCal · mol−1) min-imization obtained from different optimizers for the cube-like nanostructure using the MM+ force field ofHyperchem.

Results using the MM+ force field


Polak-Ribiere 753.68 8428.52 4422.77 41�42 −2937�28 −1244�27 9464.82Fletcher-Reeves 758.14 8412.93 4376.58 15�81 −2981�75 −1256�66 9325.06Block-Diagonal 964.17 8573.64 4487.43 266�76 −2936�66 −1491�05 9864.28

Newton-Raphson

energies) calculated by the four force fields, namelyMM+, AMBER, OPLS, and BIO+. As it is demonstratedin these tables, the OPLS force field gives the minimalenergy when comparing with the other force fields andfor the same molecule. The MBBs are comprised of arigid diamondoid nucleus and several DNA single strandswith well-defined structures. We believe that the resultsobtained from molecular mechanics and reported here arereliable. This is because the inflexibility of structures to besimulated renders them to give more reliable results.6�21

3.3. The Diamondoid-DNA-Made Nanostructure

The cross-like adamantane derivative (MBB “v” shownin Fig. 6) was selected as the nucleus because it isbulky enough to avoid steric congestion of the linkers.Its size is somehow similar to the undecamantane but itseems to be functionalized much more readily than unde-camantane. Furthermore, its sigma bonds are susceptibleof relaxation of torsional hindrance and counteraction ofmismatching disorders which might be resulted from a ring

closure by several MBBs. The docking energies calculatedconfirms the anticipation that those complementarysequences match together according to the proper patternof Watson-Crick base pairing (Table 6). From the mini-mization point of view, the conjugate gradient optimizers(Polak-Ribiere and Fletcher-Reeves) calculated improvedenergies for the nanostructure in comparison with theblock-diagonal Newton-Raphson algorithm (Table 7). Theconjugate gradient algorithms are first-order optimizersand they do not compute the second derivative matrix(Hessian matrix) directly. Instead, they employ some mea-sures to implicitly gather some second derivative infor-mation using the history of first derivatives. On the otherhand, the block-diagonal Newton-Raphson is not a fullHessian algorithm. It neglects off-diagonal blocks of theHessian. Thus, it only engages with one atom at a time.68

Overall, these differences contribute to the variable effi-ciencies of different algorithms in minimizing the energyof a molecular system. The hydrogen bonding patterns andfidelity of base pairing are still persistent after geometryoptimization by MM+ (Fig. 7). The electrostatic potential

Fig. 7. The cube-shaped nanostructure made of eight MBBs: The green dotted lines show hydrogen bonding between complementary sequences.

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Fig. 8. The cube-shaped nanostructure: (Left) The electrostatic poten-tial surface of the cube-like nanostructure.The red regions bear negative partial charges whereas the positive sites are colored in blue.(Right) The CPK (Corey-Pauling-Koltun) model of the same nanostructure reflects the square shape of each face.

surface of the nanostructure was added in Figure 8. Each face of the cube has approximate dimensions of 40×50 Å.

4. CONCLUSIONS

Application of DBS to the organization of custom-made MBBs would pave the way to establish a new type of hybrid nanoarchitecture. The bases for the fabrication of the discussed nanoarchitecture would be laid using the state-of-the-art combination of diamondoid-derived nucle-uses with the DNA nanotechnology.The ease with which the MBBs could be self-assembled through programmable and algorithmic DBS has many advantages.The results of our computations demonstrate that the predictability, peri-odicity, and bottom-up synthesis are unique merits of the aforementioned emerging nanoarchitecture.

In view of the fact that diamondoids are rigid molecules and the DNA’s persistence length is about 500 Å, utiliza-tion of DNA double strands about 40 to 70 Å in length (less than two turns) is very likely to lead to the rigid nanostructures with well-founded and predictable geome-tries.The proposed hybrid diamondoid-DNA nanoarchitec-ture could have a wide variety of applications.They range from self-assembly of nanoelectronic components to acting as the 3-D scaffolds for crystallography of biomolecules, as molecular cages for drug delivery purposes, and also as elements in molecular manufacturing of nanorobotic machinery parts, just to name a few.

Acknowledgments: HR wishes to express his appreci-ation to Leila Jahangiri for the useful discussions. This research is supported in part by a grant from MUMS.

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