We study the following fundamental questions in DNA-based self-assembly and nanorobotics: How to control errors in self-assembly? How to construct complex nanoscale objects in simpler ways? How to transport nanoscale objects in programmable manner?

Fault tolerance in self-assembly: Fault tolerant self-assembly is important for nanofabrication and nanocomputing applications. It is desirable to design compact error-resilient schemes that do not result in the increase in the original size of the assemblies. We present a comprehensive theory of compact error-resilient schemes for algorithmic self-assembly in two and three dimensions, and discuss the limitations and capabilities of redundancy based compact error correction schemes.

New and powerful self-assembly model: We develop a reversible self-assembly model in which the glue strength between two juxtaposed tiles is a function of the time they have been in neighboring positions. Under our time-dependent glue model, we can rigorously study and demonstrate catalysis and self-replication in the tile assembly. We can assemble thin rectangles of size k × N using O([special characters omitted]) types of tiles in our model.

Modeling DNA-based Nanorobotical Devices: We present a framework for a discrete event simulator for DNA-based nanorobotical systems. It has two major components: a physical model and a kinetic model. The physical model captures the conformational changes in molecules, molecular motions and molecular collisions. The kinetic model governs the modeling of various reactions in a DNA nanorobotical system such as hybridization, dehybridization and strand displacement.

DNA-based molecular devices using DNAzyme: We design a class of nanodevices that are autonomous, programmable, and require no protein enzymes. Our DNAzyme based designs include (1) DNAzyme FSA, a finite state automata device, (2) DNAzyme router for programmable routing of nanostructures on two-dimensional DNA addressable lattice, and (3) DNAzyme doctor, a medical-related application that respond to the under-expression or over-expression of various RNAs, by releasing an RNA.

Nanomotor Powered by Polymerase: We, for the first time, attempt to harness the mechanical energy of a polymerase &phis;29 to construct a polymerase based nanomotor that pushes a cargo on a DNA track. Polymerase based nanomotor has advantage of high speeds of polymerase.