Recent Contract Accomplishments: July, 2003
Duke, NYU, and Caltech are characterizing various novel DNA tiles, and investigating the use of these and related tiles to form DNA lattices.
Duke has characterized various 1D tilings of tiles; these form long cylinders which may be able to capture linear structures (e.g., morphologically similar to carbon nanotubes). We are investigating modifications of the TX molecules with additional Holiday junctions between the top and bottom dsDNA, so the resulting tile, a “Cylindrical TX tile” (CTX), has a cylindrical conformation and we will investigate the use of these and related families of DNA tiles to form 3D DNA lattices based on hybrids of CTX plus more conventional DX and TX tiles. We are investigating design of DNA molecular building blocks (MBBs) that can be rigidly attached to DNA lattices with a known orientation.
We have succeeded in experimentally demonstrating our novel method to construct an aperiodic patterned DNA lattice (Barcode Lattice) by a self-assembly process utilizing directed nucleation of DNA tiles around a scaffold DNA strand. Goals of this work include transfer of information from a single strand of DNA into an observable pattern on large lattice sheets (1D -> 2D information transfer). The displayed patterns are designed to be more complex than the simple periodic patterns so far demonstrated in DX and TX tile superstructures. Duke has succeeded in constructing “barcode” DNA tile lattices which display microscopically observable banding patterns. As a first step, the patterns are instantiated with a single pixel per tile and two possible states per pixel determined by the presence or absence of an extra stem-loop of DNA on the tile face projecting out of the lattice plane. Results were obtained by examining assembled structures using atomic force microscopy (AFM). The formation and observation of this barcode lattice is equivalent to the transfer of information encoded on a 1-dimensional strand of DNA on to a 2-dimensional DNA lattice. Therefore, this technique may be adapted to function as a visual readout method.
We have succeeded in producing patterned lattice assembled around scaffold strands spanning five tiles (~60 X 70 nm) and by adding sticky ends to the flanking tiles we were able to produce large (~3 X 10 micron) lattice which displays the target banding pattern with 5-tile periodicity. This work is the first directed nucleation assembly of barcode patterned DNA Lattices. We also made an implementation of a second 5-tile barcode pattern. The patterning is determined by a 327-base scaffold DNA strand constructed by ligation of shorter synthetic DNA oligos. The scaffold DNA strand provides to the DNA lattice barcode patterning information represented by the presence or absence of DNA hairpin loops protruding from the DNA lattice. Self-assembly of multiple DNA tiles (in this case 5 tiles) around the scaffold strand was demonstrated to result in a patterned lattice containing barcode information of 01101. We obtained AFM images of pieces of barcode lattice formed by directed nucleation of DX tiles; the 600x600 nm AFM image of barcode lattice designed to display an aperiodic pattern of stripes. This image was collected by LaBean and Yan during a recent visit to Winfree’s lab at CalTech. SPM imaging has been essential for evaluation of these structures. A recent paper, which experimentally demonstrated for the first time our method for programmed molecular patterning, was published in PNAS: Hao Yan, Thomas H. LaBean, Liping Feng, and John H. Reif, Directed Nucleation Assembly of Barcode Patterned DNA Lattices, Proceedings of the National Academy of Science(PNAS), 10.1073/pnas.1032954100, Jun 23, (2003). See also http://www.cs.duke.edu/~reif/publicity/DNAbarcode.publicity/DNAbarcode.publicity.html .
We are now working on further increases in the length of the repeat unit, as well as construction of general tile sets for propagating 1D information into observable 2D banding patterns.
Duke has targeted gold nanospheres into desired patterns by templating with DNA lattices. Our long-term goal has been to use self-assembling DNA templates to fabricate nanostructures with novel and technologically significant electronic transport properties. Materials displaying useful electrical characteristics are organized into desired patterns via the self-ordering properties of DNA complementarity. We made use of well-known gold-sulfur chemistry for binding of gold nanospheres to our DNA lattice. First, thiolated oligonucleotide was incorporated into the DNA lattice such that the -SH group is displayed on the free end of the stem helix protruding from the lattice at fixed sites. Gold nanoparticles have been added to the annealed lattice and should bind the immobile sulfur. Alternatively, thiolated oligonucleotide can be reacted directly with gold nanoparticles to yield single-strand DNA labeled gold that can be subsequently annealed to its complementary strand displayed on the lattice on protruding stem helices. We employ DNA lattice to impose patterns of interest on the assembling gold, thereby allowing increasingly complex constructs with only small changes in the overall scheme. The final step in the production of long continuous wires involves fusion of the immobilized spheres in the presence of dissolved gold salt and hydroxylamine. We incorporated thiol containing oligonucleotides into TAO AB lattice with surprising results (see below subsection on tubular DNA nanostructures). The thiols appear to be forming disulfide bridges under the conditions tested which distorts the flat lattice sheets into regular sized filaments. We are adapting the conditions to reestablish flat sheets and also working with metallization of the filament structures. We have begun our studies using gold-sulfur chemistry and are also developing other methods for targeting and immobilization of gold, other metals and single-wall carbon nanotubes. At the same time we are performing experiments to verify the proposed tube structure of the observed filaments. We are currently designing a 3 tile set which should assemble into 3-layer “barrels” of uniform diameter (similar to the long filaments) yet unable to grow to great lengths. By producing fixed length “barrels” we plan to directly observe the results of the redesign by AFM, but we also hope to obtain images (perhaps by TEM) of the cross-section of the tubes that will allow more accurate measurement of the tube size.
Duke has made significant advances toward nanoelectronic goals including successful metallization of TAO lattice nanotubes with specific nanogold attachment and targeted silver deposition on silicon oxide substrate. Electron beam lithography techniques are currently being used to write electrical contacts to the metallized DNA nanotube wires. We have succeeded in both halves of the process i) construction of fully metallized DNA nanotubes and ii) e-beam electrode writing. We are now combining the two. Current/voltage measurements on single wires will be completed soon. Comparison will be made between wires deposited onto preformed electrodes and wires deposited first followed by specific electrode etching. Duke is also investigating alternative DNA metallization strategies including the glutaraldehyde/silver method pioneered by the Braun group (Science 297 72-75, 2002) and the use of gold enhancement (NanoProbes, Inc.) since gold is more resistant to oxidation than silver.
Duke has succeeded in design, assembly, and characterization of a new type of DNA tile (referred to as 4x4) and lattice formed from 4x4 tiles. Improvements over previous tile structures include a square aspect ratio which will help regularize the pixel array, sticky-end connections in four directions (north, south, east, and west) within the lattice plane rather than the two direction (east and west) connections utilized in most previous DNA tile arrays (DX and TX tiles). Self-assembly of hydrogen-bonded two-dimensional array with this motif generate ‘waffle’ like lattices with repeating cavities of ~15.6x15.6 nm. We have started to target gold nanoparticles to the 4x4 DNA lattices and plan to execute conductivity measurements on the metalilzed 4x4 DNA lattices. Future work will be to target protein or other macromolecules to the cavity produced by self-assembly of this lattice. We have also designed and built a variant 4x4 lattice in which neighboring tiles are flipped bottom-to-top through the lattice plane so tiles alternate their orientation such that any deviations in the tile structure from the ideal will tend to cancel each other out instead of being accumulated. This “corrugated 4x4” structure is able to form larger lattice sheets and fewer undesired, long tubular structures.
The Duke team has made great progress toward several important project goals including increasing the complexity of 2D patterns displayed on the surface of DNA tiling assemblies and prototyping new and improved versions of the new 4x4 tiling system. Further demonstrations of DX barcode lattices were completed in order to show the ease with which the surface patterns can be reprogrammed. We have constructed and observed aperiodic tile lattices displaying two different patterns: 01101 and 10010. The information for the patterns were encoded on a scaffold strand of DNA as stem-loops sticking out of the tile plane and were observable by AFM. This result advances our efforts both to work toward displaying more and more complex surfaces patterns and also to develop a visual output method which translates 1D information encoded on a DNA strand into 2D pictures displayed on a DNA lattice surface. The Duke group has also produced further variants of the new 4x4 DNA tile. The 4x4 has sticky end and helix stacking interactions in four directions (N, S, E, W) in the lattice plane, rather than the two directions (E, W) found in the DX and TX tiling lattices. We have initial results on a TXx4 tile which is composed of 4 TX tiles joined around a central cavity similar to the 4 four-arm junctions in the 4x4 structure. So far the TXx4 has not yielded lattice pieces as large as those seen for the 4x4, but we hope to improve these constructs over the next few months. We also have initial data on the immobilization of streptavidin onto well-formed 4x4 lattice via binding to biotin molecules covalently bond to oligonucleotides integral to the 4x4 tiles.
Duke and Caltech continued development of software for DNA sequence design. Duke has improved existing software for design of DNA nanostructures and their DNA sequences and tested that software for the design of improved triple-crossover and single-strand DNA tiles.
A research objective of Caltech is development of a mathematical/algorithmic framework for design of multi-strand DNA complexes. We have begun to formulate the DNA design problem in terms of partition functions, to examine tractable models of DNA pseudo-knots and folding kinetics, and to develop software for specifying and creating 3D molecular models of DNA structures. We have been testing our algorithms on a variety of design tasks, including tiles and nucleating structures for de-multiplexing RAM lattice and other algorithmic self-assembly systems.
Caltech developed the first known algorithm for computing partition functions for possibly pseudo-knotted, single-stranded DNA structures [R.M. Dirks and N.A. Pierce, “Partition Function Calculations for Nucleic Acid Secondary Structure Including Pseudoknots”, J. Comput. Chem., in press]. This allows the calculation of the probability that a desired target structure will result for a given DNA sequence and provides an avenue for establishing both positive and negative design of DNA structures.
The pseudoknot partition function algorithm has recently been extended to compute the base pairing probabilities for all base pairs in the design (R.M. Dirks and N.A. Pierce, in preparation). We are using partition function and kinetic DNA folding algorithms to systematically evaluate a variety of DNA sequence design algorithms [R.M. Dirks, M. Lin, E. Winfree and N.A. Pierce, “Paradigms for Computational Nucleic Acid Design”, in preparation]. We have also established a framework for energy calculations on multi-stranded DNA complexes, and we are initiating work coding algorithms for minimum free-energy, partition functions, and stochastic kinetic simulations. Programming of the multistranded algorithms is now underway (J. Shaeffer, R.M. Dirks).
At Caltech, the de novo design (R.M. Dirks) of an allosteric ribozyme that specifically cleaves RNA has now been studied experimentally (I. See). Preliminary results show that reversible on/off functionality is achieved. Ongoing work is intended to demonstrate quantitative control over the yield. Other experimental work is focused on the design of a DNA walker (J.-S. Shin). The track for the walker is composed of short DNA strands that assemble to form a nicked helix with periodic single-stranded toeholds. FRET studies have been used to demonstrate that the introduction of a three nucleotide hinge at the base of each toehold allows the track to form linearly within a single segment. TEM experiments are now underway to ascertain the rigidity of the track at longer length scales. The track has also been employed as a memory device . One bit experiments have been successfully performed using FRET and a 4-bit experiment using gold nano-beads and TEM is being prepared. Experiments have also been performed to study the kinetics of DNA hybridization for a number of these structures. This work complements theoretical work on hybridization kinetics (J. Bois) that is intended to determine the nature of kinetic traps during the hybridization process.
Caltech has continued investigation of various assembly techniques for patterned 1D and 2D DNA lattices of moderate length, using techniques of unmediated algorithmic self-assembly and directed nucleation assembly. We have achieved very high resolution (~2nm) imaging of DNA structures under physiological buffers, which is giving us greater insight into the geometry of the lattices. Additionally, we have been able observe crystal formation in real time, which will allow us to study and control 2D crystal growth on the mica surface. We have identified strategies for patterning surfaces at the nanometer scale, including patterns required for nanoelectronic circuits, such as a RAM memory array and addressing circuits [M. Cook, P.W.K. Rothemund, E. Winfree, “Self-assembled Circuit Patterns”, submitted]. We will soon move this project toward experimental realization using algorithmic DNA self-assembly, beginning with an unbounded binary counter (a component of the demultiplexing RAM pattern).
Caltech has designed and synthesized strands for a preliminary two-dimensional algorithmic self-assembly system, and we have shown by atomic force microscopy that both 1-tile-thick and 2-tile-thick linear borders for the lattice form reliably. We are working to dope this assembly with a seed to grow an X-shaped border; the 2x2 nucleus forms and can be imaged; initial experiments with extended X-shaped structures have indicated that greater theoretical understanding is necessary. We plan to continue this investigation using our real-time movie technology to watch growth of the patterns from defined seeds. Sidestepping these issues, we have recently been successful demonstrating algorithmic self-assembly from long PCR-generated template strands
[P.W.K. Rothemund, N. Papadakis, E. Winfree, “Algorithmic Self-assembly of DNA Sierpinski Triangles”, submitted]. In the best samples, error rates are between 1 and 3 percent per step, and perfect assemblies with over one hundred tiles have been observed. However, many undesired side-reactions still occur, and we need to learn how to minimize them.
Similar to the Duke efforts described above, Caltech researchers have encountered tubular structures formed by DNA tiles, in this case TX and DAE double-crossover tiles with no chemical modifications. AFM microscopy indicates that the DAE tubes consist of between 4 to 8 tiles in cross-section, with the long axis of the tube equal to the long axis of the tiles. We are collaborating with Deborah Fygenson at UCSB to study the biophysical characteristics of these tubes, such as the persistence length (tensile strength) and the kinetics of assembly, and the design determinants for lattice formation [A. Nkodo, P.W.K. Rothemund, N. Papadakis, E. Winfree, D. Fygensen, “Programmable Self-assembly and Dynamics of DNA Nanotubes”, in preparation].
In the Seeman lab at NYU, the goals for the period are largely devoted to defining DNA motifs that are compatible with 3D self-assembly. We have designed at two different motifs that produce some extent of X-ray diffraction, one, a TX motif diffracting to ~7.5 Ā and a DX motif diffracting to ~8 Ā.
We have suspected that the problems with these crystals result from DNA helicities incommensurate the design. We have screened molecules with varied helicities to solve this problem. By themselves, screening helicities did not solve the problem, although we have been able to produce a variety of non-diffracting solids.
In a new direction, we are also pursuing strategies to protect ourselves from tile writhe, as well as to establish more precisely the structures of the tiles.
We have also altered crystallization protocols to include thermal as well as precipitant crystallizations. We have suspected that the lack of diffracting material from thermal protocols has been due to the presence of incompletely formed molecules in solution at the time of solidification. Melting studies of both species (tiles and crystals) have confirmed this hypothesis. In addition, the first cooling displays hysteresis, but the second does not. We are using this fact to improve cooling protocols.
In the current quarter, we have explored other 3D designs, such as a triangle-like motif that spans 3-space. We have obtained diffraction to ~11Ā, but the motif is not well-behaved. We are improving its design, as this is a very encouraging result.
Selected Recent Publications
Liping Feng, Sung Ha Park, Yan Liu, Yan Liu, John H. Reif, and Hao Yan, A Two State DNA Lattice Actuated by DNA Motors, accepted to Angewandte Chemie [International Edition], to appear 2003
Liping Feng, Sung Ha Park, Yan Liu, Yan Liu, John H. Reif, and Hao Yan, A Two State DNA Lattice Actuated by DNA Motors, accepted to Angewandte Chemie [International Edition], to appear 2003
Dage Liu, John H. Reif, Thomas H. LaBean, DNA Nanotubes, Construction and Characterization of Filaments Composed of TX-tile Lattice. DNA Based Computers (DNA8), Sapporo, Japan, June 10-13, 2002, (Edited by Masami Hagiya and Azuma Ohuchi), Lecture Notes in Computer Science, No. 2568, Springer-Verlag, New York, (2003), pages 10-21.
C. Mao, LaBean, T.H. Reif, J.H., Seeman, Logical Computation Using Algorithmic Self-Assembly of DNA Triple-Crossover Molecules, Nature, vol. 407, Sept. 28 2000, pp. 493–495; C. Erratum: Nature 408, 750-750(2000).
LaBean, T.H., Yan, H., Kopatsch, J., Liu, F., Winfree, E., Reif, J.H., and Seeman, N.C. (2000) Construction, Analysis, Ligation, and Self-Assembly of DNA Triple Crossover Complexes. J. Am. Chem. Soc. 122, 1848-1860.
J. H. Reif, DNA Lattices: A Programmable Method for Molecular Scale Patterning and Computation, special issue on Bio-Computation, Computer and Scientific Engineering Magazine, IEEE Computer Society, Vol. 4, No. 1, February 2002, pp 32-41.
J. H. Reif, The Emergence of the Discipline of Biomolecular Computation in the US, invited paper to the special issue on Biomolecular Computing, New Generation Computing, edited by Masami Hagiya, Masayuki Yamamura, and Tom Head, Vol. 20, No. 3, pp. 217-236, (2002).
J. H. Reif, Molecular Assembly and Computation: From Theory to Experimental Demonstrations, plenary paper, 29-th International Colloquium on Automata, Languages, and Programming(ICALP), Málaga, Spain (July 8, 2002). Published in volume 2380 of Lecture Notes in Computer Science, New York, pages 1-21, 2002.
J. H. Reif, The Design of Autonomous DNA Nanomechanical Devices, Walking and Rolling DNA. DNA Based Computers (DNA8), Sapporo, Japan, June 10-13, 2002, (Edited by Masami Hagiya and Azuma Ohuchi), Lecture Notes in Computer Science, No. 2568, Springer-Verlag, New York, (2003), pages 22-37.
John H. Reif, Perspectives: Successes and Challenges, Science, 296: 478-479, April 19, 2002.
J.H. Reif and T. H. LaBean, Computationally Inspired Biotechnologies: Improved DNA Synthesis and Associative Search Using Error-Correcting Codes and Vector-Quantization, Sixth International Meeting on DNA Based Computers (DNA6), ,Leiden, The Netherlands, (June, 2000) eds. A. Condon & G Rozenberg. Lecture Notes in Computer Science, Vol. 2054, Springer-Verlag 2001, pp. 145-172.
J.H. Reif, T.H. LaBean, and N.C. Seeman, Challenges and Applications for Self-Assembled DNA Nanostructures, Proc. Sixth International Workshop on DNA-Based Computers, Leiden, The Netherlands, June, 2000., Edited by A. Condon and G. Rozenberg. Lecture Notes in Computer Science, Springer-Verlag, Berlin Heidelberg, vol. 2054, 2001, pp. 173-198.
Zheng Sun and John H. Reif, On Energy-minimizing Paths on Terrains for a Mobile Robot, 2003 IEEE International Conference on Robotics and Automation(ICRA2003), Taipei, Taiwan, May 12-17, 2003.
Hao Yan, Thomas H. LaBean, Liping Feng, and John H. Reif, Directed Nucleation Assembly of Barcode Patterned DNA Lattices, Proceedings of the National Academy of Science(PNAS), (to appear June, 2003).
Hao Yan, Liping Feng, Thomas H. LaBean, and John Reif, Parallel Molecular Computation of Pair-Wise XOR Using DNA "String Tile, Ninth International Meeting on DNA Based Computers (DNA9), Madison, Wisconsin, June 2-4, 2003, (Edited by Junghuei Chen and John Reif), to appear in Lecture Notes in Computer Science, Springer-Verlag, New York, (2003).
Hao Yan, Sung Ha Park, Liping Feng, John Reif, and Thomas H. LaBean, 4x4 DNA Tile and Lattices: Characterization, Self-Assembly and Metallization of a Novel DNA Nanostructure Motif, Ninth International Meeting on DNA Based Computers (DNA9), Madison, Wisconsin, June 2-4, 2003, (Edited by Junghuei Chen and John Reif), to appear in Lecture Notes in Computer Science, Springer-Verlag, New York, (2003).
A. Carbone and N.C. Seeman, Circuits and Programmable Self-Assembling DNA Structures, Proc. Nat. Acad. Sci. (USA) 99 12577-12582 (2002).
X. Zhang, H. Yan, Z. Shen and N.C. Seeman, Paranemic Cohesion of Topologically-Closed DNA Molecules, J Am. Chem. Soc.124, 12940-12941 (2002).
S. Xiao, F. Liu, A. Rosen, J.F. Hainfeld, N.C. Seeman, K.M. Musier-Forsyth & R.A. Kiehl, Self-Assembly of Nanoparticle Arrays by DNA Scaffolding, J. Nanoparticle Research 4, 313-317 (2002).
A. Carbone and N.C. Seeman, Fractal Designs Based on DNA Parallelogram Structures, Natural Computing 1, 469-480 (2002).
L. Zhu, O. dos Santos, N.C. Seeman and J.W. Canary, Reaction of N3-Benzoyl-3’, 5’-O-(di-tert-butylsilanediyl)uridine with Hindered Electrophiles: Intermolecular N3 to 2'-O Protecting Group Transfer, Nucleosides, Nucleotides & Nucleic Acids 21, 723-735 (2002).
H. Yan, X. Zhang, Z. Shen and N.C. Seeman, A Robust DNA Mechanical Device Controlled by Hybridization Topology, Nature 415, 62-65 (2002).
N.C. Seeman, DNA in a Material World, Nature 421, 33-37 (2003).
N.C. Seeman, Structural DNA Nanotechnology: A New Organizing Principle for Advanced Nanomaterials, Materials Today 6 (7), 24-29 (2003).
P. Sa-Ardyen, N. Jonoska and N.C. Seeman, Self-Assembling DNA Graphs, DNA-Based Computers VIII, LNCS 2568, Springer-Verlag, Berlin, 1-9 (2003).
H. Yan and N.C. Seeman, Edge-Sharing Motifs in DNA Nanotechnology. Journal of Supramolecular Chemistry 1, 229-237 (2003).
N.C. Seeman, DNA Nanotechnology, Encyclopedia of Supramolecular Chemistry, in press (2003).
N. Jonoska, P. Sa-Ardyen and N.C. Seeman, Compuatation by Self-Assembly of DNA Graphs, Genetic Programming and Evolvable Machines, in press (2003)..
N.C. Seeman, DNA: Beyond the Double Helix, IUPAC Proceedings, in press (2003).
P. Sa-Ardyen, A.V. Vologodskii and N.C. Seeman, Structural Properties of DNA Double Crossover Molecules. Biophysical Journal, in press, (2003).
A. Carbone and N.C. Seeman, Coding and Geometrical Shapes in Nanostructures: a Fractal DNA-Assembly, Natural Computing, in press (2003).
Niles A. Pierce and Erik Winfree, "Protein Design is NP-Hard", Protein Engineering 15, 779-782 (2002).
Robert M. Dirks and Niles A. Pierce, “Partition Function Calculations for Nucleic Acid Secondary Structure Including Pseudoknots”, J. Comput. Chem., in press.
M. Cook, P. Rothemund, E. Winfree,
Self-Assembled Circuit Patterns, Ninth International Meeting on DNA Based Computers (DNA9), Madison, Wisconsin, June 2-4, 2003, (Edited by Junghuei Chen and John Reif), to appear in Lecture Notes in Computer Science, Springer-Verlag, New York, (2003). Also submitted for publication, 2003.
Robert M. Dirks and Niles A. Pierce, Partition Function Calculations for Nucleic Acid Secondary Structure Including Pseudoknots, J. Comput. Chem., in press (2003).
Robert M. Dirks, M. Lin, E. Winfree and Niles A. Pierce, Paradigms for Computational Nucleic Acid Design, in prepartion (2003).
Robert M. Dirks and Niles A. Pierce, Base Pairing Probabilities for Nucleic Acid Secondary Structure Including Pseudoknots”, in preparation (2003).
A. Nkodo, P.W.K. Rothemund, N. Papadakis, E. Winfree, D. Fygensen, Programmable Self-assembly and Dynamics of DNA Nanotubes, in preparation (2003).
Niles A. Pierce and Erik Winfree, Protein Design is NP-Hard, Protein Engineering 15, 779-782 (2002).
R. Schulman, E. Winfree, One-Dimensional Boundaries for DNA Tile Self-Assembly, Ninth International Meeting on DNA Based Computers (DNA9), Madison, Wisconsin, June 2-4, 2003, (Edited by Junghuei Chen and John Reif), to appear in Lecture Notes in Computer Science, Springer-Verlag, New York, (2003). Also submitted for publication, 2003.
P. Rothemund, N. Papadakis, E. Winfree, Algorithmic Self-Assembly of DNA Sierpinski Triangles, Ninth International Meeting on DNA Based Computers (DNA9), Madison, Wisconsin, June 2-4, 2003, (Edited by Junghuei Chen and John Reif), to appear in Lecture Notes in Computer Science, Springer-Verlag, New York, (2003). Also submitted for publication, 2003.
E. Winfree, R. Bekbolatov,
Proofreading Tile Sets: Error Correction for Algorithmic Self-Assembly, Ninth
International Meeting on DNA Based Computers (DNA9), Madison, Wisconsin,
June 2-4, 2003, (Edited by Junghuei Chen and John
Reif), to appear in Lecture Notes in Computer Science, Springer-Verlag, New
York, (2003). Also submitted for publication, 2003.
J. Kim, D. Zhang, E. Winfree, In Vitro Transcriptional Circuits, Ninth International Meeting on DNA Based Computers (DNA9), Madison, Wisconsin, June 2-4, 2003, (Edited by Junghuei Chen and John Reif), to appear in Lecture Notes in Computer Science, Springer-Verlag, New York, (2003). Also submitted for publication, 2003.