Natasha Jonoska

A Signal-Passing DNA-Strand-Exchange Mechanism for Active Self-Assembly of DNA Nanostructures†

DNA nanostructured tiles play an active role in their own self-assembly in the system described herein whereby they initiate a binding event that produces a cascading assembly process. We present DNA tiles that have a simple but powerful property: they respond to a binding event at one end of the tile by passing a signal across the tile to activate a binding site at the other end. This action allows sequential, virtually irreversible self-assembly of tiles and enables local communication during the self-assembly process. This localized signal-passing mechanism provides a new element of control for autonomous self-assembly of DNA nanostructures.

Reciprocal DNA nanomechanical devices controlled by the same set strands.

Reciprocating devices are key features in macroscopic machines. We have adapted the DNA PX-JX(2) device to a reciprocal format. The PX-JX(2) device is a robust sequence-dependent nanomachine, whose state is established by a pair of control strands that set it to be either in the PX state or in the JX(2) state. The two states differ by a half-turn rotation between their ends. Here we report the construction of a pair of reciprocal PX-JX(2) devices, wherein the control strands leading to the PX state in one device lead to the JX(2) state in the other device and vice versa. The formation, transformation, and reciprocal motions of these two device systems are confirmed using gel electrophoresis and atomic force microscopy. This system is likely to be of use for molecular robotic applications where reciprocal motions are of value in addition its inherent contribution to molecular choreography and molecular aesthetics.

A Programmable Transducer Self-Assembled from DNA

A transducer consists of an input/output alphabet, a finite set of states, and a transition function. From an input symbol applied to a given state, the transition function determines the next state, and an output symbol. Using DNA, we have constructed a transducer that divides a number by 3. The input consists of a series of individually addressable 2-state DNA nanomechanical devices that control the orientations of a group of flat 6-helix DNA motifs; these motifs have edge domains tailed in sticky ends corresponding to the numbers 0 and 1. Three-domain DNA molecules (TX tiles) act as computational tiles that correspond to the transitions that the transducer can undergo. The output domain of these TX tiles contains sticky ends that also correspond to 0 or 1. Two different DNA tiles can chelate these output domains: A 5 nm gold nanoparticle is attached to the chelating tile that binds to 0-domains and a 10 nm gold nanoparticle is attached to the chelating tile that binds to 1-domains. The answer to the division is represented by the series of gold nanoparticles, which can be interpreted as a binary number. The answers of the computation are read out by examination of the transducer complexes under a transmission electron microscope. The start or end points of the output sequence can be indicated by the presence of a 15 nm gold nanoparticle. This work demonstrates two previously unreported features integrated in a single framework: [1] a system that combines DNA algorithmic self-assembly with DNA nanomechanical devices that control that input, and [2] the arrangement of non-DNA species, here metallic nanoparticles, through DNA algorithmic self-assembly. The nanomechanical devices are controlled by single-stranded DNA strands, allowing multiple input sequences to be applied to the rest of the system, thus guiding the algorithmic self-assembly to a variety of outputs.

Regular splicing languages must have a constant

In spite of wide investigations of finite splicing systems in formal language theory, basic questions, such as their characterization, remain unsolved. In search for understanding the class of finite splicing systems, it has been conjectured that a necessary condition for a regular language L to be a splicing language is that L must have a constant in the Schutzenbergers sense. We prove this longstanding conjecture to be true. The result is based on properties of strongly connected components of the minimal deterministic finite state automaton for a regular splicing language.

On stoichiometry for the assembly of flexible tile DNA complexes

Given a set of flexible branched junction DNA molecules with sticky-ends (building blocks), called here “tiles”, we consider the problem of determining the proper stoichiometry such that all sticky-ends could end up connected. In general, the stoichiometry is not uniform, and the goal is to determine the proper proportion (spectrum) of each type of molecule within a test tube to allow for complete assembly. According to possible components that assemble in complete complexes we partition multisets of tiles, called here “pots”, into classes: unsatisfiable, weakly satisfiable, satisfiable and strongly satisfiable. This classification is characterized through the spectrum of the pot, and it can be computed in PTIME using the standard Gauss-Jordan elimination method. We also give a geometric description of the spectrum as a convex hull within the unit cube.

DNA splicing: computing by observing

Motivated by several techniques for observing molecular processes in real-time we introduce a computing device that stresses the role of the observer in biological computations and that is based on the observed behavior of a splicing system. The basic idea is to introduce a marked DNA strand into a test tube with other DNA strands and restriction enzymes. Under the action of these enzymes the DNA starts to splice. An external observer monitors and registers the evolution of the marked DNA strand. The input marked DNA strand is then accepted if its observed evolution follows a certain expected pattern. We prove that using simple observers (finite automata), applied on finite splicing systems (finite set of rules and finite set of axioms), the class of recursively enumerable languages can be recognized.

Structural DNA nanotechnology: molecular construction and computation

Structural DNA nanotechnology entails the construction of objects, lattices and devices from branched DNA molecules. Branched DNA molecules open the way for the construction of a variety of N-connected motifs. These motifs can be joined by cohesive interactions to produce larger constructs in a bottom-up approach to nanoconstruction. The first objects produced by this approach were stick polyhedra and topological targets, such as knots and Borromean rings. These were followed by periodic arrays with programmable patterns. It is possible to exploit DNA structural transitions and sequence-specific binding to produce a variety of DNA nanomechanical devices, which include a bipedal walker and a machine that emulates the translational capabilities of the ribosome. Much of the promise of this methodology involves the use of DNA to scaffold other materials, such as biological macromolecules, nanoelectronic components, and polymers. These systems are designed to lead to improvements in crystallography, computation and the production of diverse and exotic materials. Branched DNA can be used to emulate Wang tiles, and it can be used to construct arbitrary irregular graphs and to address their colorability.

Describing self-assembly of nanostructures

We outline an algebraic model for describing complex structures obtained through self-assembly of molecular building blocks and show that, with this model, the assembled structure can be associated to a language and it can be determined up to congruence.

DNA Cages with Icosahedral Symmetry in Bionanotechnology

Blueprints for polyhedral cages with icosahedral symmetry made of circular DNA molecules are provided. The basic rule is that every edge of the cage is met twice in opposite directions by the DNA strand(s), and vertex junctions are realized by a set of admissible junction types. As nanocontainers for cargo storage and delivery, the icosidodecahedral cages are of special interest because they have the largest volume per surface ratio of all cages discussed here.

Russian Doll Genes and Complex Chromosome Rearrangements in Oxytricha trifallax

Ciliates have two different types of nuclei per cell, with one acting as a somatic, transcriptionally active nucleus (macronucleus; abbr. MAC) and another serving as a germline nucleus (micronucleus; abbr. MIC). Furthermore, Oxytricha trifallax undergoes extensive genome rearrangements during sexual conjugation and post-zygotic development of daughter cells. These rearrangements are necessary because the precursor MIC loci are often both fragmented and scrambled, with respect to the corresponding MAC loci. Such genome architectures are remarkably tolerant of encrypted MIC loci, because RNA-guided processes during MAC development reorganize the gene fragments in the correct order to resemble the parental MAC sequence. Here, we describe the germline organization of several nested and highly scrambled genes in Oxytricha trifallax. These include cases with multiple layers of nesting, plus highly interleaved or tangled precursor loci that appear to deviate from previously described patterns. We present mathematical methods to measure the degree of nesting between precursor MIC loci, and revisit a method for a mathematical description of scrambling. After applying these methods to the chromosome rearrangement maps of O. trifallax we describe cases of nested arrangements with up to five layers of embedded genes, as well as the most scrambled loci in O. trifallax.