Programming Molecular Devices using Nucleic Acid Hairpins

Nucleic Acid hairpins have been a subject of study for the last four decades. They are composed of single strand that is

hybridized to itself, and the central section forming an unhybridized loop. In nature, they stabilize single stranded RNA, serve as nucleation

sites for RNA folding, protein recognition signals, mRNA localization and regulation of mRNA degradation. On the other hand,

DNA hairpins in biological contexts have been studied with respect to forming cruciform structures that can regulate gene expression.

The use of DNA hairpins as fuel for synthetic molecular devices, including locomotion, was proposed and experimental demonstrated in 2003. They

were interesting because they bring to the table an on-demand energy/information supply mechanism.

The energy/information is hidden (from hybridization) in the hairpin’s loop, until required.

The energy/information is harnessed by opening the stem region, and exposing the single stranded loop section.

The loop region is now free for possible hybridization and help move the system into a thermodynamically favourable state.

The hidden energy and information coupled with

programmability provides another functionality, of selectively choosing what reactions to hide and

what reactions to allow to proceed, that helps develop a topological sequence of events.

Hairpins have been utilized as a source of fuel for many different DNA devices. In this thesis, we program four different

molecular devices using DNA hairpins, and experimentally validate them in the

laboratory. 1) The first device: A

novel enzyme-free autocatalytic self-replicating system composed entirely of DNA that operates isothermally. 2) The second

device: Time-Responsive Circuits using DNA have two properties: a) asynchronous: the final output is always correct

regardless of differences in the arrival time of different inputs.

b) renewable circuits which can be used multiple times without major degradation of the gate motifs

(so if the inputs change over time, the DNA-based circuit can re-compute the output correctly based on the new inputs).

3) The third device: Activatable tiles are a theoretical extension to the Tile assembly model that enhances

its robustness by protecting the sticky sides of tiles until a tile is partially incorporated into a growing assembly.

4) The fourth device: Controlled Amplification of DNA catalytic system: a device such that the amplification

of the system does not run uncontrollably until the system runs out of fuel, but instead achieves a finite

amount of gain.

Nucleic acid circuits with the ability

to perform complex logic operations have many potential practical applications, for example the ability to achieve point of care diagnostics.

We discuss the designs of our DNA Hairpin molecular devices, the results we have obtained, and the challenges we have overcome

to make these truly functional.

On Provable Algorithms for Determination of Continuous Protein Interdomain Motions from Residual Dipolar Couplings

Dynamics of biomolecules over various spatial and time scales are essential for biological functions such as molecular recognition, catalysis and signaling. However, reconstruction of biomolecular dynamics from experimental observables requires the determination of a conformational probability distribution. Unfortunately, these distributions cannot be fully constrained by the limited information from experiments, making the problem an ill-posed one in the terminology of Hadamard. The ill-posed nature of the problem comes from the fact that it has no unique solution. Multiple or even an infinite number of solutions may exist. To avoid the ill-posed nature, the problem needs to be regularized by making assumptions, which inevitably introduce biases into the result.

Here, I present two continuous probability density function approaches to solve an important inverse problem called the RDC trigonometric moment problem. By focusing on interdomain orientations we reduced the problem to determination of a distribution on the 3D rotational space from residual dipolar couplings (RDCs). We derived an analytical equation that relates alignment tensors of adjacent domains, which serves as the foundation of the two methods. In the first approach, the ill-posed nature of the problem was avoided by introducing a continuous distribution model, which enjoys a smoothness assumption. To find the optimal solution for the distribution, we also designed an efficient branch-and-bound algorithm that exploits the mathematical structure of the analytical solutions. The algorithm is guaranteed to find the distribution that best satisfies the analytical relationship. We observed good performance of the method when tested under various levels of experimental noise and when applied to two protein systems. The second approach avoids the use of any model by employing maximum entropy principles. This 'model-free' approach delivers the least biased result which presents our state of knowledge. In this approach, the solution is an exponential function of Lagrange multipliers. To determine the multipliers, a convex objective function is constructed. Consequently, the maximum entropy solution can be found easily by gradient descent methods. Both algorithms can be applied to biomolecular RDC data in general, including data from RNA and DNA molecules.