UNIQUIMER 3D, A software system for struc
Contents
1. as shown in Fig 4 Insert DHA Strand DNA Strand Number of DNA Bases 21 Initial Direction 1 00 0 00 o oo Initial Position 270 00 9 97 o o0 Figure 4 DNA Double Helical Domain Insertion The top textbox allows the user to input the number of base pairs of the DNA double helix The middle textbox is for inputting the initial direction of the DNA double helix The bottom textbox is for inputting the initial position of the DNA double helix A grouping operation is embedded in our system so that multiple DNA double helices with DNA customized nodes can be regrouped for further manipulation or management The grouped components are maintained in a tree structure parent children structure that is consistent with the system hierarchy Two more operations are defined for DNA constructions 1 the opening operation that breaks the con secutive DNA nodes 2 the closing operation that connects two open nodes The two operations redefine connectivity between DNA nodes Invalid polarities are automatically detected by the system and will not be allowed as illustrated in Fig 5 l nvalid Figure 5 Valid and invalid closing operations Part IV Geometrical Optimization offers ways to change the geometrical appearance of a designed structure Given the user defined structure hierarchy and connectivity a state is defined2. On Lis Dos ees Dp diy dyeing Dias E is a function mapping from 0 IT to nonnegative real numbers Euistance 18 defined as the sum of squared differences of the distance between each pair of connected nodes and a constant d d is chosen to be the distance between any two consecutive DNA nodes on the same helix which is 63 05 Therefore with a user defined connectivity map C lt 01 p1 gt lt 02 P2 gt lt Ok Pk gt Figure 6 Illustration of the smoothness term where o and ps s 1 2 k denote user connected nodes and lt gt denotes connectivity k Edistance NS P o P ps d 2 s 1 where is the Euclidean norm and P is a function that denotes the position of a node It should be noted that os ps is either a node on a helix or a DNA customized node If the node is on a helix it will have position R O h t T where O t T and h h h7 depend on the working structure If the node is a DNA customized node 7 its position is simply Lj depending on the structure The second term Esmoothness in our energy function refines the smoothness of the user connection of DNA double helical domains In an ideal case of DNA strand connection the B form DNA s helical structures are preserved As shown in Fig 6 two DNA double helices are joined together by connecting nodes cs and ps An optimal angle between the two vectors formed by any three neighboring DNA nod
3. 30 Version 1 0 Be View Options Grouping Optimization Sequence Help mil DAX HE Welcome to UNIQUIMER 3D Version 1 01 X x a ol UNIQUIMER 3D Welcome to UNIQUIMER 3D Overview UNIQUIMER 30 is a DMA construction and sequence computing tool that allows users to realize their DNA structure and review it in a real time 3D wrtual world Optimization algonthm is used to minimize the energy of the predefined structure Features With UNIQUIMIER 30 user can define a complex DMA structure with e Predefined frameworks Perspective saving and loading a Naime toolbars incorporating real time sonneloaded dragging Customized ONA construction a Structural optirnization Completely customizable look and feel What s new in 1 07 UNIQUIMER 30 adds the following features a New GUI outlook e New DNA transformation user interface Lots of bug fixes See HELP for more information Sea A EspaeSer Arol Fae ibam information bo appear here ie Ce coe lt anajaza OT B EOE BABS EDES Figure 1 System User Interface Figure 2 System Hierarchy Figure 3 DNA Double Helical Domain helix is defined to be a ray casting from the parent node to the center position of the topmost base pair along the center pole A double helical domain can be added to the 3D canvas by clicking on the DNA Strand button in the Control Panel
4. Comp is defined as L a b 0 otherwise Comp a b Q D1 D2 Dn is the set of DNA double helical domains D 2 is a particular double helical domain with D base pairs lt Mt MI gt lt M MZ gt a lt NM P yt il gt given the digit d that represents for the length of potential mismatching segment a score function is defined as 12 Di d d J 5 5 Compl Pairi HE dl 11 The score function J is a numerical representation of the expected formation of the structure consisting of a set of DNA double helical domains Y In real self assembly process potential mismatching cases will result in secondary structure formation S 51 59 5 is the set of DNA strands S Z is a particular strand with S bases 441 ea We then define another score function J taking into account all potential mismatching cases as a comparison with the value we get from J Since J is the most optimal score J is always greater than or equal to J The difference between these J and J indicates how likely the strands Z with generated sequences will self assemble into the expected structure The less difference between the values we get from J and J the more likely Y will self assemble into the expected structure formation IF Sil d F Sj d y Comp Y Pain NPt ae d i 0 p 0 j 0 q 0 J is designed to find all potential mismatching cases which is equivalent to string matching in t
5. can insert translate rotate items by making use of the Control Panel docked on the right bottom side of the window The center window is the 3D display canvas Part III Building a Motif In UNIQUIMER 8D DNA strands can be manipulated on a 3D canvas addition deletion translation rotation etc Basic DNA components can be joined together at crossover points to build certain motifs This part contains an explanation of all the steps that are necessary to create a DNA motif The basic building block is the DNA double helical domain The most basic element and the lowest level of our system hierarchy is the DNA base pair Each DNA base pair consists of a pair of nucleotide residues DNA nodes hereinafter connected by hydrogen bonds and DNA nodes are rendered as spheres Phosphodiester linkages and hydrogen bonds are rendered as lines of different colors in the 3D space Individual nucleotide residues DNA customized nodes hereinafter are also modeled and rendered as spheres in our system The double helical domain contains a parent node rendered as box a green strand and a blue strand as shown in Fig 3 The polarity of the double helical domain is defined Starting from the parent node the green strand is pointing upwards all the way to the topmost base and the blue strand then pointing downwards till reaching the parent node The parent node determines the position of the double helix The direction of double UAIQUIMER
6. in designing SDN Following the tutorial you will find a possible workflow for creating a DNA motif Following this workflow may help you avoid problems later on After that we will describe how to make use of the energy minimization functionality to optimize the geometrical shape of a designed structure Then we will demonstrate how to apply sequence generation algorithm to your design At the end of the documentation you will find a summary of our work Part II Getting Started This part helps you getting started It starts with an explanation of how to install UNIQUIMER 3D UNIQUIMER 3D can be accessed from http ihome ust hk for free The first step is to grab a copy of the UNIQUIMER 3D zip archive then uncompress the file to your local hard drive The folder Structures contains a collection of some default existed motifs such as holiday junction 4x4 tile cube tetrahedron etc The folder Report holds a collection of all the HTML reports you generate for a designed structure You will also find the ex ecutable file namely UNIMQUIMER3D exe in the unzipped parent directory The major user interface of UNIQUIMER 8D is shown in Fig 1 There is a Item List tree control on the left docking window All the SDN information are maintained in this control as a tree structure A Information Window is docked on the left bottom side that displays the detailed information of the user selections Users
7. UNIQUIMER 3D A software system for struc tural DNA nanotechnology design analysis and evaluation Manual for version 1 0 User s Guide to the UNIQUIMER 3D Version 1 0 http ihome ust hk Jinhao Zhu Yongli Mi Email csnickle gmail com keymix ust hk December 30 2008 Contents I Introduction II Getting Started III Building a Motif IV Geometrical Optimization V Sequence Generation VI Summary 10 12 Part I Introduction A user friendly software system UNIQUIMER 8D was developed for structural DNA nanotechnology that consists of 3D visualization internal energy minimization sequence generation and construction of motif array simulations 2D tiles amp 3D lattices functionalities The system can be used to check the structural deformation and design errors under scaled up conditions UNIQUIMER 8D aims to facilitate the design of novel DNA motifs for the DNA nanotechnology and has been tested for the design of both existing motifs holiday junction 4x4 tile DX DNA tetrahedron DNA cube etc and not existing motif soccer ball A de novel sequence generation algorithm is integrated into the system UNIQUIMER 8D was developed for the Windows environment and is provided free of charge to the non profit research institutions In this user manual documentation we start with an explanation of how to install UNIQUIMER 3D Next a short tutorial is given that explains most of the features that you ll need
8. address this issue We will consider the simulated annealing method that can sample a wider range of conformations compared with other gradient based local minimization methods We will also work on the modeling down to the molecular level with precise atomic positional control since rotations of each bond in the backbone structure will result in different conformations of the entire design and the construction using different forms of DNA or even RNA This will be updated into our next release and will enable controls of the base and sugar It will be much more accurate compared with the current version that models only simplified DNA PDB format of exportation will also be supported by then 13
9. e taken into consideration for UNIQUIMER 8D The first one to follow is the pairing up rule of A T G C i e certain segments should be complementary respectively as shown in Fig 9 In order to avoid segment mismatching cases as much as possible there is the second rule to limit the length of repetitive segments It is illustrated in Fig 10 If the requirement is set to have no repetitive segments of 4 base pairs the sequence does not meet the requirement However if the requirement is set to have no repetitive segments of 5 base pairs the sequence will pass As the main restriction used for sequence generation the maximum length of repetitive segment should be set as short as possible to prevent mismatching cases If the value is set to be 3 there will be no repetitive segment with a length of 4 or more bases Suppose we want to do sequence generation for a structure of a DNA double helical domain with 100 base pairs The total number of combinations for segments with a length of 3 bases is only 4 64 so if the maximum length of repetitive segment is set to be 3 there would be not enough candidates to fill in the 98 100 3 1 blanks of segments with a length of 3 bases Therefore no solution could be found in this case However if the value is set to be A instead the possible combinations increase to 44 256 There are enough candidates available in this case and the generator will find a solution In general the maximum length of repeti
10. erms of conjugating one of the segment to search for all matchings of this conjugation from a given set of segments The conjugate operation is based on DNA complementarity A T G C T A C G Consider segment N NP meg a as the template it is equivalent to essentially searching on strand j for the total number of conjugate segments As a result Boyer Moore string search algorithm is adopted for J Our score functions take a structure with sequence and the length of potential mismatching segment d as input A set of sequence generated for n times of a structure is denoted as 2 n The corresponding numbers of potential mismatching cases are denoted as Q Jy Wig ay nega Jn A tuple Af Q 9 is associated Q min Q AY Q is selected for a specific d The sequence generation dialog is shown is Fie 11 The user has options to specify the maximum length of repetitive segment and a exclusion set The result of the sequence generation is saved to a text file in the parent directory namely strandSequence_All txt It contains all the sequences of each individual strand of the structure sequence ee General Sticky End Max Number of Repeatitive 4 Exclude Set Cancel Figure 11 Sequence Generation Dialog Part VI Summary With all these built in features users can easily design analyze and evaluate different structures Especially the energy minimization functi
11. es on the same helix 0 0 07 is defined to be OsO o_o R O optimal aLCcos e ee optimal is a constant that equals to 24 53 It is desirable to have a connection Os0 O0 0 0 ah 7 ps0 that forms the same angle Ooptimal With both oso and p ps Therefore the smoothness term is defined S as O sO O Esmoothness DD arccos i BCR Onima T loso loses O arccos Pols alia Oomima N 3 lesol Noses The summation is over all connections between nodes o and ps on the helices a4 denotes the node next to os Which is not ps o denotes the node next to of which is not os p4 denotes the node next to ps which is not os This smoothness term penalizes angular discrepancies from optimal Of the connected structure Our energy function takes O T as variables Given an initial user defined state 0 T we want to improve it using an energy minimizing technique Currently the properties are controlled using simple geometry as defined in Egistance and Esmoothness Which is a convex function As a result gradient based local minimization algorithm is considered in this version Powell s method which is an iterative optimization method that finds a local optimizer is implemented in our system for this purpose Since the result from running Powell s method greatly depends on its initial state it is very important to supply a relatively stable state with low energy as the input to Po
12. et in the 3D space and five selection boxes which allows the user to disable enable translation global local rotation or collision detection The dialog is shown in Fig 8 UNIQUIMER 8D will generate a detailed report in HTML format of the refined structure including infor mation about its hierarchy and several showcase images of the structure from different viewing angles Besides the process of energy minimization is illustrated in this report with a chart showing each iteration in this process Optimization Number of Iterations 100 Translation offset 5 Rotation offset 5 Es Translation Collision detection by Node Self Rotation Figure 8 Geometrical Optimization Dialog and the corresponding energy value Part V Sequence Generation A sequence generation algorithm is designed and integrated it to UNIQUIMER 8D The algorithm of generating sequence sacrifices storage to gains speed The idea is to compute all the possible combinations of the specific maximum length of repetitive segment starting with A T G C The combination term is an unordered collection of distinct elements usually of a prescribed size and taken from a given set This approach guarantees each of the segment is distinct in terms of sequence so that the length of repetitive segment is controlled The combinations can be pre computed and stored to a local file that can be loaded for recycling usage The same basic rules for SDN sequence generation ar
13. on can help users to obtain a relatively stable state of the working structure and the result can be very helpful for SDN prediction DNA structures without satisfactory optimized state can be screened out for wet lab experiments The main contributions of this work can be summarized as follows e Users can visualize DNA motifs and motif assemblies in a 3D environment 12 e Users can design DNA structures in a convenient and efficient way e An energy function is designed for measuring the stability of structures Our system can relax this en ergy function to predict a relatively stable structure which can validate and or predict SDN wet lab experiments e Each DNA node in a structure can be automatically assigned a tag from A T G C using a built in sequence generating algorithm and the generated sequence can be analyzed by our scoring system e A detailed HTML report is generated after the energy minimization which contains hierarchical informa tion on the refined structure showcases images of it from different viewing angles and gives information on the energy minimization As for future development a systematic analysis of our current energy minimization will be carried out down to the molecular level of DNA backbone structures The current single level algorithm makes the efficiency of the minimization process low Multi level of optimization which minimize all factors simultaneously at each iteration will be utilized to
14. tive segment is relatively bigger 10 ra E ated cil ad salary ALT WL A fim el Ge AIT TD 7 Foon SGGACCGGA FECACT TCGGTACCTG ALTACGS AATGCCCCTGGCCTA f T _ d a H D D G E os FN 4 U4 EA FN Ud Ae amp J D lr an JD KI T W a RJ T VW Wl Figure 9 Base pair matching Sequences shown in the box are subjected to complementary region for complicated structures compared with simpler structures like DX or TX The value ranges from 4 to 6 for most of the SDN structures However it could be as big as 7 or more for extremely complicated structures The maximum length of the repetitive segment in the sticky ends is set to be 3 base pairs no repetitive segment of 4 base pairs no matter what the global rule of repetitive segment length minimization is arpa ia ahs GGGACQCGGAT GGAOTTCGGTACCTGATTACG TA TH oe a ae a ae ae WT te IN ace a A 7 7 alg C A ji A AAT WLELULL 5 WLULA Figure 10 Mismatching prevention Sequnces shown in the box are two repetitive segments of 4 base pairs UNIQUIMER 3D is able calculate the number of potential mismatching cases that are hindrances of forma tion of the desired structure Given the length of potential mismatching segment a scoring system of a generated sequence for a structure is formulated as following Pair is defined as 1 a b A T T A G C C G 0 otherwise Pair a b
15. to be the entire geometric information of all of its components An energy function is designed to assign a nonnegative real number representing its stability to each state Energy function is introduced to eliminate the structural defects and design errors which might result in constructional failure thus to get a better evaluation whether or not a specific DNA structure is able to form in a stable way For random configurations of DNA strands the energy function may be very complicated However the regular and predictable double helical DNA structure makes the energy minimization relatively simple Accordingly the distance between two nucleotide residues and the smoothness of the double helix are taken into consideration So the energy function is defined as E 1 AE zerou aie AE smoothness 1 where Egistance and Esmoothness are two terms that are consistent with our motivation and A is a weight Since motif arrays are assembled by motifs and motifs are further composed of DNA double helices sticky ends and DNA customized nodes on the basic level only geometric information for DNA double helices sticky ends DNA customized nodes and the corresponding connectivity is necessary to model our energy function Given a set of n DNA double helical domains and their corresponding rotation and translation parameters O s and T s and m DNA customized nodes with translation vectors L s a state can be defined as O T where 91 02
16. well s method We first coarsely scan through states that uniformly cover the solution space T to find a state with the lowest energy Since E is a smooth function it is reasonable to assume that a global minimum exists somewhere near this state Therefore this selected state is the starting point of the Powell s method One should note that there is no guarantee that the final state which is a local minimum is a global one However if the initial state is close enough to the global minimum it can be found using Powell s method As shown in Fig 7 a and Fig 7 c certain DNA double helical domains are set to be distorted After applying energy minimization to the structures the geometrical shapes of these double helical domains are refined as shown in Fig 7 b and Fig 7 d Figure 7 Geometrical Optimization a Two distorted DNA double helical domains before energy minimization b Two refined DNA double helical domains after energy minimization c Two distorted DNA double helical domains with crossover before energy minimization d Two refined DNA double helical domains with crossover after energy minimization After the user has selected the portion needed to be optimized a energy minimization dialog is shown by selecting the Optimization in the menubar The dialog contains three textbox inputs allowing the user to specify the number of iterations the optimization algorithm will do the translation and rotation offs
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