Sudheer Sahu Department of Computer Science, Duke University Advisor: Prof. John Reif Committee: Prof. John Board, Prof. Alex Hartemink, Prof. Thom LaBean, Prof. Kamesh Munagala, Prof. Xiaobai Sun DNA Based Self-assembly and Nanorobotics: Theory and Experiments

Self-assembly Fundamental process in nature Recent uses in nanoscale constructions Tile [Yan03] Algorithmic Self-assembly: Universal Computation [Winfree96] [Seeman91] [Rothemund05] 4x4 tile [Park06]

Tile Assembly Models Glue Σ Strength function : g: Σ x Σ → R g(σ,σ’) > 0 if σ = σ’ = 0 otherwise Temperature  Tile-system (T,S,g,  ) Adleman’s Reversible Model Winfree’s Kinetic Model Generalized Models Winfree’s Tile Assembly Model

Capabilities and Limitations of Redundancy Based Compact Error Resilient Methods Sudheer Sahu, John H. Reif DNA12, LNCS 4287, , 2006 Submitted to Algorithmica

Input 1 Input 2 Output 1 Output 2 Output 1 = Input 1 XOR Input 2 Output 2 = Input 1 XOR Input 2 Pad [Rothemund04] Algorithmic Self-Assembly

Winfree’s seminal work Goel’s snake tiling Reif’s compact error resiliency Nucleation Errors[Schulman05] ( Excerpted from Winfree 03 ) Error rate    2 Assembly size increased by 4 Original tiles: Error resilient tiles: Work in Error correction Original tiles: Error resilient tiles: XYZ XYYZ Error checking pads

Error Model The assembly takes place in a kinetic manner, but the error analysis is done at equilibrium When the system is in equilibrium, the probability that a mismatch occurs is ε Independent errors Emphasis on the correctness of complete assembly Redundancy based compact error resilience scheme

Two Dimensional Assembly Input: U(i,j), V(i,j) Output: U(i+1,j)=U(i,j)OP 1 V(i,j) V(i,j+1)=U(i,j)OP 2 V(i,j) U(I,j) U(i+1,j) V(I,j) V(I,j+1) T(i,j) Theorem: There exists a redundancy based compact error resilient scheme to reduce error from ε to ε 2 for arbitrary boolean functions OP 1 and OP 2. T(i,j) U(i,j) V(i,j) U(i,j+1) U(i+1,j) V(i+1,j) U(i+1,j+1) U(i,j) V(i+1,j) V(i,j+1)U(i,j+1)V(i+1,j+1)

Capabilities and Limits Input functions2D3D ε 2 ArbitraryYes ε3 ε3 ArbitraryNoconjecture, No ε 3 RestrictedYes ε 3 Outside restrictedNoconjecture, No ε 4 ArbitraryNo ε4 ε4 AnyNoconjecture, No

A Self-assembly Model with Time Dependent Glue Strength Sudheer Sahu, Peng Yin, John Reif DNA11, LNCS 3892, , 2006 Submitted to Algorithmica

Time Dependent Glue Model Glue strength increases monotonically before becoming constant Glue strength function Time for maximum strength Minimum interaction time

Implementation using Strand Displacement A Bs1s1 s2s2 s3s3

Catalysis

Self-Replication A-B acts as a catalyst for formation of C-D which in turn acts as a catalyst for the formation of A-B Two states: Dormant state Replicating state Low probability of going from dormant to replicating state

Tile Complexity Minimum number of distinct tile types required to construct a shape uniquely nxn square [Standard model,Adleman01] k x m k rectangle O(k+m) [Standard model, Aggarwal04] Thin rectangle (kxn for k < ) [Standard Model, Aggarwal04] [Time dependent Glue Model]

Construction of thin rectangles Construct a j x n rectangle using O(j+n 1/j ) type of tiles, where j > k. The glue of bottom k rows become strong after mit, and the glue of top j-k rows (volatile rows) do not.

Shapes with holes nxn square with a hole of k x k in center Upper Bound in our model: Grow four rectangles

DNA based Nanorobotical devices B-Z transition device [Mao, Seeman 99] DNA-fuelled Molecular machine [Yurke et al 00] DNA Biped walker [Sherman et al 04] Advantages of DNA-based synthetic molecular devices: simple to design and engineer well-established biochemistry used to manipulate DNA nanostructures [Yan et al 02] [Shin et al 04]

DNA based Nanorobotical devices Unidirectional DNA Walker [Yin et al 04] Major challenges: Autonomous (without externally mediated changes per work-cycle) Programmable (their behavior can be modified without complete redesign of the device) DNA motor powered by Nicking enzyme [Bath et al 05] [Tian et al 05]

A Framework for Modeling DNA Based Molecular Systems Sudheer Sahu, Bei Wang, John Reif DNA12, LNCS 4287, , 2006 Submitted to Journal of Computational and Theoretical Nanoscience

Simulation Gillespi method mostly used in simulating chemical systems [Gillespi77, Gillespi01, Kierzek02] Work done in nanorobotic simulators: –Virtual Test Tubes [Garzon00] –VNA simulator[Hagiya] –Hybrisim [Ichinose] –Thermodynamics of unpseudo-knotted multiple interacting DNA strands in a dilute solution [Dirks06] Two components/layers –Physical Simulation [of molecular conformations] –Kinetic Simulation [of hybridization, dehybridization and strand displacements based on kinetics, dynamics and topology]

Modeling DNA Strands Single strand –Gaussian chain model [Fixman73,Kovac82] –Freely Jointed Chain [Flory69] –Worm-Like Chain [Marko94,Marko95, Bustamante00,Klenin98,Tinoco02] Double strands –Similar but parameters differ Complex structures

MCSimulation Generated by random walk in three dimensions Change in x i in time Δt, Δx i = R i R i : Gaussian random variable W(R i ) = (4Aπ) -3/2 exp(-R i /4A) where A = DΔt Stretching Energy = (0.5Y)Σ i (u i -l 0 ) 2 [Zhang01] Bending Energy = (K B TP/l 0 )Σ i cos(θ i ) [Doyle05, Vologdskii04] Twisting Energy [Klenin98] Electrostatic Energy [Langowski06,Zhang01] Repeat m* = RandomConformation(m) ΔE = E(m*) – E(m) x ε [0,1] until ((ΔE 0 & x<exp(-ΔE/K B T)) m = m* Bad!!! Good!!!

Hybridization Nearest neighbor model –Thermodynamics of DNA structures that involves mismatches and neighboring base pairs beyond the WC pairing. ΔG° = ΔH° – TΔS° ΔH° = ΔH° ends +ΔH° init +Σ k€{stacks} ΔH k ° ΔS° = ΔS° ends +ΔS° init +Σ k€{stacks} ΔS k ° On detecting a collision between two strands –Probabilities for all feasible alignments is calculated. –An alignment is chosen probabilistically

Dehybridization Reverse rate constant k r =k f exp(ΔG°/RT) Concentration of A = [A] Reverse rate R r =k r [A] Change in concentration of A in time Δt Δ[A] = R r Δt Probability of dehybridization of a molecule of A in an interval of Δt = Δ[A] /[A] = k r Δt

Strand Displacement Random walk –direction of movement of branching point chosen probabilistically –independent of previous movements Biased random walk (in case of mismatches) –Migration probability towards the direction with mismatches is substantially decreased G° ABC, G° rABC, G° lABC ΔG° r = G° rABC - G° ABC ΔG° l = G° lABC - G° ABC P r = exp(-ΔG° r /RT) P l = exp(-ΔG° l /RT)

Algorithm Initialize While t ≤ T do Physical Simulation Collision Detection Event Simulation Hybridization Dehybridization Strand Displacement t=t+Δt m i MList do MCSimulation(m i ) m i,m j MList if collide(m i,m j ) e=ColEvent(m i,m j ) enqueue e in CQ While CQ is nonempty e= dequeue(CQ) Hybridize(e) Update MList if potential_strand_displacement event enqueue SDQ For no. of element in SDQ e = dequeue(SDQ) e* = StrandDisplacement(e) if e* is incomplete strand displacement enqueue e* in SDQ Update MList m i MList b bonds of m i if potential_dehybridization(b) breakbond(b) if any bond was broken Perform a DFS on graph on m i Every connected component is one new molecule formed Update MList

Algorithm Analysis In each simulation step: –A system of m molecules each consisting of n segments. –MCsimulation loop runs f(n) times before finding a good configuration. –In every run of the loop the time taken is O(n). –Time for each step of physical simulation is O(mnf(n)). –Collision detection takes O(m 2 n 2 ) –For each collision, all the alignments between two reacting strands are tested. O(cn), if number of collisions detected are c. –Each bond is tested for dehybridization. O(bm), if no. of bonds per molecule is b. For every broken bond, DFS is required and connected components are evaluated. O(b 2 m) Time taken in each step is O(m 2 n 2 +mn f(n) )

Extensions…. Physical Simulation of Hybridization –What happens in the time-interval between collision and bond formation? –What is the conformation and location of the hybridized molecule? Enzymes –Ligase, Endonuclease Hairpins, pseudoknots More accurate modeling –Electrostatic forces –Loop energies –Twisting energies

Autonomous Programmable Nanorobotic Devices Using DNAzymes John Reif, Sudheer Sahu DNA13, LNCS 4848, 66-78, 2008 Submitted to Theoretical Computer Science

DNAzyme based nanomechanical devices DNAzyme crawler [Tian et al 05] DNAzyme tweezer [Chen et al 04] Autonomous Programmable Require no protein enzymes Polycatalytic Assemblies [Pei et al 06]

Our DNAzyme based designs 1.DNAzyme FSA: a finite state automata device, that executes finite state transitions using DNAzymes extensions to probabilistic automata and non- deterministic automata, 2.DNAzyme Router: for programmable routing of nanostructures on a 2D DNA addressable lattice 3.DNAzyme Doctor : a medical-related application to provide transduction of nucleic acid expression. can be programmed to respond to the under- expression or over-expression of various strands of RNA, with a response by release of an RNA operates without use of any protein enzymes.

FSA

DNAzyme FSA (inputs) x1a1x2a2 b2x1b1 x2x1a1 x2 a x1a1 x2 a2 0 b2x1b1 x2 1 Active Input: Input that is being read by FSA currently 010 x1a1x2a2 b2x1b1 x2x1a1 x2 a2 t1t2 t1 t2t1t2 t1

DNAzyme FSA(State Transitions) x1a1 x2 a2 0 b2x1b1 x2 1

Step by step execution of a 0-transition

Choosing next transition

Complete Finite State Machine Non-deterministic finite automata Probabilistic automata Reusable system No. of DNAzymes proportional to the no. of transitions

DNAzyme Router…. Input: Go right 1 Go down Input: [Park et al 06 ] [Rothemund 05] Input string acts as program for the robot Non-destructive Multiple robots walking together

DNAzyme Doctor (state diagram) Shapiro Device [uses protein enzymes]

Design Principle We need AND operation We need a way to test for the under- expression and over-expression conditions

Detecting RNA Expression y 1,y 2,y 3,y 4 characteristic sequence of RNAs R 1, R 2, R 3, R 4 A threshold concentration of y 1, y 2, y 3, y 4 is thrown in the solution, therefore lack of y 3, y 4 causes excess of y 3 and y 4, respectively.

DNAzyme Doctor : In Action

A DNA Nanotransportation Device Powered by Polymerase Φ29 Sudheer Sahu, Thom LaBean, John Reif To be submitted

Polymerase Driven Nanomotor Replication of DNA RNA template –Sustain life processes Protector Strand Q Stopper Sequence Phi29 –Exceptional strand displacement abilities Wheel slips on the track and not rolls T P P T PQ T W

Experimental Method

Results Track Circularization Circular Track and Wheel Intertwined

Results Brakes Nick Crossing Nanomotor

Basic Design For FRET Experiments FRET Internal Cy5: Absorbance peak=648nm Emission peak=668nm Iowa Black RQ: Range nm Absorbance peak=667nm

Cargo not dislodged…..

Moved from Point A….

Reached point B…..

Summary and Future Conjectures Self-Healing Implementation Kinetic Analysis Error Correction Tile-complexity Implementation Ligase,Endonuclease Hairpins,Pseudoknots, Electrostatic forces Loop energies, Twisting energies Mechanisms wrt conformations Non-planar FSA Implementation Drive motor on 2D patterns Nanoparticle transportation

Publication List 1.J. H. Reif, S. Sahu, P. Yin, ``Compact Error-Resilient Computational DNA Tiling Assemblies'', DNA10, LNCS, 3384, , P. Yin, A. J. Turberfield, S. Sahu, J. H. Reif, ``Design of an Autonomous DNA Nanomechanical Device Capable of Universal Computation and Universal Translational Motion'', DNA10, LNCS, 3884, , J. H. Reif, T. H. LaBean, S. Sahu, H. Yan, P. Yin, ``Design, Simulation, and Experimental Demonstration of Self-Assembled DNA Nanostructures and DNA Motors'', LNCS, 3566, Unconventional Programming Paradigms, , J. H. Reif, S. Sahu, P. Yin, ``The Complexity of Graph Self-Assembly in Accretive Systems and Self-Destructible Systems'', DNA11, LNCS, 3892, , P. Yin, S. Sahu, J. H. Reif, ``Autonomous DNA Cellular Automata'', DNA11, LNCS, 3892, , S. Sahu, P. Yin, J. H. Reif, ``A Self-Assembly Model of DNA Tiles with Time Dependent Glue Strength'', DNA11, LNCS, 3892, , Submitted to Algorithmica. 7.U. Majumder, S. Sahu, T. H. LaBean, J. H. Reif, ``Design and Simulation of Self-Repairing DNA Lattices'', DNA12, LNCS, 4287, , S. Sahu, B. Wang, J. H. Reif, ``A Framework for Modeling DNA based Molecular Systems'', DNA12, LNCS, 4287, , Submitted to J. theor. and comp. nanoscience. 9.S. Sahu, J. H. Reif, ``Capabilities and Limits of Compact Error Resilience Methods for Algorithmic Self-Assembly in Two and Three Dimensions'', DNA12, LNCS, 4287, , submitted to algorithmica. 10.P. Yin, S. Sahu, R. Hariadi, H. M. T. Choi, S. H. Park, B. Walters, T. H. LaBean, J. H. Reif, ``On Constructing Tile-less DNA Ribbons and Tubes'', DNA12, Submitted to Journal. 11.U. Majumder, S. Sahu, and J. H. Reif, ``Reversible self-assembly of squares as a rapidly mixing markov chain'', FNANO07, Submitted to J. theor. and comp. nanoscience. 12. J. H. Reif, S. Sahu, ``Autonomous Programmable DNA Nanorobotical Devices using DNAzymes'', DNA13, Submitted to TCS. 13.S. Sahu, T.H. LaBean, J.H.Reif, “A DNA Nanotransport Device Powered by Polymerase Φ29”, In preparation.