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.

Optimal Capital Requirements in Financial Networks with Fire Sales

I explore and analyze a problem of finding the socially optimal capital requirements for financial institutions considering two distinct channels of contagion: direct exposures among the institutions, as represented by a network and fire sales externalities, which reflect the negative price impact of massive liquidation of assets.These two channels amplify shocks from individual financial institutions to the financial system as a whole and thus increase the risk of joint defaults amongst the interconnected financial institutions; this is often referred to as systemic risk. In the model, there is a trade-off between reducing systemic risk and raising the capital requirements of the financial institutions. The policymaker considers this trade-off and determines the optimal capital requirements for individual financial institutions. I provide a method for finding and analyzing the optimal capital requirements that can be applied to arbitrary network structures and arbitrary distributions of investment returns.

In particular, I first consider a network model consisting only of direct exposures and show that the optimal capital requirements can be found by solving a stochastic linear programming problem. I then extend the analysis to financial networks with default costs and show the optimal capital requirements can be found by solving a stochastic mixed integer programming problem. The computational complexity of this problem poses a challenge, and I develop an iterative algorithm that can be efficiently executed. I show that the iterative algorithm leads to solutions that are nearly optimal by comparing it with lower bounds based on a dual approach. I also show that the iterative algorithm converges to the optimal solution.

Finally, I incorporate fire sales externalities into the model. In particular, I am able to extend the analysis of systemic risk and the optimal capital requirements with a single illiquid asset to a model with multiple illiquid assets. The model with multiple illiquid assets incorporates liquidation rules used by the banks. I provide an optimization formulation whose solution provides the equilibrium payments for a given liquidation rule.

I further show that the socially optimal capital problem using the ``socially optimal liquidation" and prioritized liquidation rules can be formulated as a convex and convex mixed integer problem, respectively. Finally, I illustrate the results of the methodology on numerical examples and

discuss some implications for capital regulation policy and stress testing.