Sudheer Sahu

Programming DNA Tube Circumferences

Synthesizing molecular tubes with monodisperse, programmable circumferences is an important goal shared by nanotechnology, materials science, and supermolecular chemistry. We program molecular tube circumferences by specifying the complementarity relationships between modular domains in a 42-base single-stranded DNA motif. Single-step annealing results in the self-assembly of long tubes displaying monodisperse circumferences of 4, 5, 6, 7, 8, 10, or 20 DNA helices.

Autonomous programmable DNA nanorobotic devices using DNAzymes

A major challenge in nanoscience is the design of synthetic molecular devices that run autonomously (that is, without externally mediated changes per work-cycle) and are programmable (that is, their behavior can be modified without complete redesign of the device). DNA-based synthetic molecular devices have the advantage of being relatively simple to design and engineer, due to the predictable secondary structure of DNA nanostructures and the well-established biochemistry used to manipulate DNA nanostructures. However, ideally we would like to minimize the use of protein enzymes in the design of a DNA-based synthetic molecular device. We present the design of a class of DNA-based molecular devices using DNAzyme. These DNAzyme-based devices are autonomous, programmable, and further require no protein enzymes. The basic principle involved is inspired by a simple but ingenious molecular device due to Tian et al. [Y. Tian, Y. He, Y. Chen, P. Yin, C. Mao, A DNAzyme that walks processively and autonomously along a one-dimensional track, Angew. Chem. Intl. Ed. 44 (2005) 4355-4358] that used DNAzyme to traverse on a DNA nanostructure, but was not programmable in the sense defined above (it did not execute computations). Our DNAzyme-based designs include (1) a finite state automaton, DNAzyme FSA that executes finite state transitions using DNAzymes, (2) extensions to it including probabilistic automaton and non-deterministic automaton, and (3) its application as a DNAzyme router for programmable routing of nanostructures on a 2D DNA addressable lattice. Furthermore, we give a medical-related application, DNAzyme doctor that provides transduction of nucleic acid expression: it can be programmed to respond to the underexpression or overexpression of various strands of RNA, with a response by the release of an RNA. (The behavior of our nucleic acid transduction devices is similar to those of the prior paper of Benenson [Y. Benenson, B. Gil, U. Ben-Dor, R. Adar, E. Shapiro, An autonomous molecular computer for logical control of gene expression, Nature 429 (2004) 423-429], but ours have the advantage that they operate without the use of any protein enzymes.)

A DNA Nanotransport Device Powered by Polymerase ϕ29

Polymerases are a family of enzymes responsible for copying or replication of nucleic acids (DNA or RNA) templates and hence sustenance of life processes. In this paper, we present a method to exploit a strand-displacing polymerase phi29 as a driving force for nanoscale transportation devices. The principal idea behind the device is strong strand displacement ability of phi29, which can displace any DNA strand from its template while extending a primer hybridized to the template. This capability of phi29 is used to power the movement of a target nanostructure on a DNA track. The major advantage of using a polymerase driven nanotransportation device as compared to other existing nanorobotical devices is its speed. phi29 polymerase can travel at the rate of 2000 nucleotides per minute at room temperature, which translates to approximately 680 nm min(-1) on a nanostructure. We also demonstrate transportation of a DNA cargo on a DNA track with the help of fluorescence resonance electron transfer data.

A self-assembly model of time-dependent glue strength

We propose a self-assembly model in which the glue strength between two juxtaposed tiles is a function of the time they have been in neighboring positions. We then present an implementation of our model using strand displacement reactions on DNA tiles. Under our model, we can demonstrate and study catalysis and self-replication in the tile assembly. We then study the tile complexity for assembling shapes in our model and show that a thin rectangle of size k x N can be assembled using O(logN/loglogN) types of tiles.

Design of autonomous DNA cellular automata

Recent experimental progress in DNA lattice construction, DNA robotics, and DNA computing provides the basis for designing DNA cellular computing devices, i.e. autonomous nano-mechanical DNA computing devices embedded in DNA lattices. Once assembled, DNA cellular computing devices can serve as reusable, compact computing devices that perform (universal) computation, and programmable robotics devices that demonstrate complex motion. As a prototype of such devices, we recently reported the design of an Autonomous DNA Turing Machine, which is capable of universal sequential computation, and universal translational motion, i.e. the motion of the head of a single tape universal mechanical Turing machine. In this paper, we describe the design of an Autonomous DNA Cellular Automaton (ADCA), which can perform parallel universal computation by mimicking a one-dimensional (1D) universal cellular automaton. In the computation process, this device, embedded in a 1D DNA lattice, also demonstrates well coordinated parallel motion. The key technical innovation here is a molecular mechanism that synchronizes pipelined “molecular reaction waves” along a 1D track, and in doing so, realizes parallel computation. We first describe the design of ADCA on an abstract level, and then present detailed DNA sequence level implementation using commercially available protein enzymes. We also discuss how to extend the 1D design to 2D.

Complexity of graph self-assembly in accretive systems and self-destructible systems

Self-assembly is a process in which small objects autonomously associate with each other to form larger complexes. It is ubiquitous in biological constructions at the cellular and molecular scale and has also been identified by nanoscientists as a fundamental method for building nano-scale structures. Recent years have seen convergent interest and efforts in studying self-assembly from mathematicians, computer scientists, physicists, chemists, and biologists. However most complexity theoretical studies of self-assembly utilize mathematical models with two limitations: (1) only attraction, while no repulsion, is studied; (2) only assembled structures of two dimensional square grids are studied. In this paper, we study the complexity of the assemblies resulting from the cooperative effect of repulsion and attraction in a more general setting of graphs. This allows for the study of a more general class of self-assembled structures than the previous tiling model. We define two novel assembly models, namely the accretive graph assembly model and the self-destructible graph assembly model, and identify a fundamental problem in them: the sequential construction of a given graph. We refer to it as the Accretive Graph Assembly Problem (AGAP) and the Self-Destructible Graph Assembly Problem (DGAP), in the respective models. Our main results are: (i) AGAP is NP-complete even if the maximum degree of the graph is restricted to 4 or the graph is restricted to be planar with maximum degree 5; (ii) counting the number of sequential assembly orderings that result in a target graph (#AGAP) is #P-complete; and (iii) DGAP is PSPACE-complete even if the maximum degree of the graph is restricted to 6 (this is the first PSPACE-complete result in self-assembly). We also extend the accretive graph assembly model to a stochastic model, and prove that determining the probability of a given assembly in this model is #P-complete.

Capabilities and limits of compact error resilience methods for algorithmic self-assembly in two and three dimensions

Winfree’s pioneering work led the foundations in the area of error-reduction in algorithmic self-assembly[26], but the construction resulted in increase of the size of assembly. Reif et. al. contributed further in this area with compact error-resilient schemes [15] that maintained the original size of the assemblies, but required certain restrictions on the Boolean functions to be used in the algorithmic self-assembly. It is a critical challenge to improve these compact error resilient schemes to incorporate arbitrary Boolean functions, and to determine how far these prior results can be extended under different degrees of restrictions on the Boolean functions. In this work we present a considerably more complete theory of compact error-resilient schemes for algorithmic self-assembly in two and three dimensions. First we consider two-dimensional algorithmic self-assembly. We present an error correction scheme for reduction of errors from e to e2 for arbitrary Boolean functions in two dimensional algorithmic self-assembly. Then we characterize the class of Boolean functions for which the error reduction can be done from e to e3, and present an error correction scheme that achieves this reduction. Then we prove ultimate limits on certain classes of compact error resilient schemes: in particular we show that they can not provide reduction of errors from e to e4 is for any Boolean functions. Further, we develop the first provable compact error resilience schemes for three dimensional tiling self-assemblies. We also extend the work of Winfree on self-healing in two-dimensional self-assembly[25] to obtain a self-healing tile-set for three-dimensional self-assembly.

Design and simulation of self-repairing DNA lattices

Self-repair is essential to all living systems, providing the ability to remain functional in spite of gradual damage. In the context of self-assembly of self-repairing synthetic biomolecular systems, recently Winfree developed a method for transforming a set of DNA tiles into its self-healing counterpart at the cost of increasing the lattice area by a factor of 25. The overall focus of this paper, however, is to develop compact designs for self-repairing tiling assemblies with reasonable constraints on crystal growth. Specifically, we use a special class of DNA tiling designs called reversible tiling which when carefully designed can provide inherent self-repairing capabilities to patterned DNA lattices. We further note that we can transform any irreversible computational DNA tile set to its reversible counterpart and hence improve the self-repairability of the computational lattice. But doing the transform with an optimal number of tiles, is still an open question.

Autonomous programmable nanorobotic devices using DNAzymes

A major challenge in nanoscience is the design of synthetic molecular devices that run autonomously and are programmable. DNA-based synthetic molecular devices have the advantage of being relatively simple to design and engineer, due to the predictable secondary structure of DNA nanostructures and the well-established biochemistry used to manipulate DNA nanostructures. We present the design of a class of DNAzyme based molecular devices that are autonomous, programmable, and further require no protein enzymes. The basic principle involved is inspired by a simple but ingenious molecular device due to Mao et al [25]. Our DNAzyme based designs include (1) a finite state automata device, DNAzyme FSA that executes finite state transitions using DNAzymes, (2) extensions to it including probabilistic automata and non-deterministic automata, (3) its application as a DNAzyme router for programmable routing of nanostructures on a 2D DNA addressable lattice, and (4) a medical-related application, DNAzyme doctor that provide transduction of nucleic acid expression: it can be programmed to respond to the underexpression or overexpression of various strands of RNA, with a response by release of an RNA.

Compact Error-Resilient Computational DNA Tilings

The self-assembly process for bottom-up construction of nanostructures is of key importance to the emerging scientific discipline Nanoscience. However, algorithmic self-assembly at the molecular scale is prone to a quite high rate of error. Such high error rate is a major barrier to large-scale experimental implementation of algorithmic DNA tilings. The goals of this paper are to develop theoretical methods for compact error-resilient algorithmic DNA tilings and to analyze these methods by thermodynamic analysis and computer simulation. Prior work by Winfree provided an innovative approach to decrease tiling self-assembly mismatch errors without decreasing the intrinsic error rate of assembling a single tile. However, his technique resulted in a final structure larger than the original one (four times larger for decreasing the error to , nine times for to ). In this paper, we describe various compact error-resilient tiling methods that do not increase the size of the tiling assembly. These methods apply to the assembly of Boolean arrays which perform input sensitive computations (among other computations). Our 2-way (3-way) overlay redundancy construction decreases the error rate from to approximately ( ), without increasing the size of the assembly. As in Winfree’s constructions, the number of distinct tile types required is also increased in our error-resilient tiling constructions. These results were further validated using computer simulation.