Crystals that count! Physical principles and experimental investigations of DNA tile self-assembly

Algorithmic DNA tiles systems are fascinating. From a theoretical perspective, they can result in simple systems that assemble themselves into beautiful, complex structures through fundamental interactions and logical rules. As an experimental technique, they provide a promising method for programmably assembling complex, precise crystals that can grow to considerable size while retaining nanoscale resolution. In the journey from theoretical abstractions to experimental demonstrations, however, lie numerous challenges and complications.

In this thesis, to examine these challenges, we consider the physical principles behind DNA tile self-assembly. We survey recent progress in experimental algorithmic self-assembly, and explain the simple physical models behind this progress. Using direct observation of individual tile attachments and detachments with an atomic force microscope, we test some of the fundamental assumptions of the widely-used kinetic Tile Assembly Model, obtaining results that fit the model to within error. We then depart from the simplest form of that model, examining the effects of DNA sticky end sequence energetics on tile system behavior. We develop theoretical models, sequence assignment algorithms, and a software package, StickyDesign, for sticky end sequence design.

As a demonstration of a specific tile system, we design a binary counting ribbon that can accurately count from a programmable starting value and stop growing after overflowing, resulting in a single system that can construct ribbons of precise and programmable length. In the process of designing the system, we explain numerous considerations that provide insight into more general tile system design, particularly with regards to tile concentrations, facet nucleation, the construction of finite assemblies, and design beyond the abstract Tile Assembly Model.

Finally, we present our crystals that count: experimental results with our binary counting system that represent a significant improvement in the accuracy of experimental algorithmic self-assembly, including crystals that count perfectly with 5 bits from 0 to 31. We show some preliminary experimental results on the construction of our capping system to stop growth after counters overflow, and offer some speculation on potential future directions of the field.

Theoretical investigations of experimental gravitation

This thesis has two basic themes: the investigation of new experiments which can be used to test relativistic gravity, and the investigation of new technologies and new experimental techniques which can be applied to make gravitational wave astronomy a reality.

Advancing technology will soon make possible a new class of gravitation experiments: pure laboratory experiments with laboratory sources of non-Newtonian gravity and laboratory detectors. The key advance in techno1ogy is the development of resonant sensing systems with very low levels of dissipation. Chapter 1 considers three such systems (torque balances, dielectric monocrystals, and superconducting microwave resonators), and it proposes eight laboratory experiments which use these systems as detectors. For each experiment it describes the dominant sources of noise and the technology required.

The coupled electro-mechanical system consisting of a microwave cavity and its walls can serve as a gravitational radiation detector. A gravitational wave interacts with the walls, and the resulting motion induces transitions from a highly excited cavity mode to a nearly unexcited mode. Chapter 2 describes briefly a formalism for analyzing such a detector, and it proposes a particular design.

The monitoring of a quantum mechanical harmonic oscillator on which a classical force acts is important in a variety of high-precision experiments, such as the attempt to detect gravitational radiation. Chapter 3 reviews the standard techniques for monitoring the oscillator; and it introduces a new technique which, in principle, can determine the details of the force with arbitrary accuracy, despite the quantum properties of the oscillator.

The standard method for monitoring the oscillator is the "amplitude- and-phase" method (position or momentum transducer with output fed through a linear amplifier). The accuracy obtainable by this method is limited by the uncertainty principle. To do better requires a measurement of the type which Braginsky has called "quantum nondemolition." A well-known quantum nondemolition technique is "quantum counting," which can detect an arbitrarily weak force, but which cannot provide good accuracy in determining its precise time-dependence. Chapter 3 considers extensively a new type of quantum nondemolition measurement - a "back-action-evading" measurement of the real part X₁ (or the imaginary part X₂) of the oscillator's complex amplitude. In principle X₁ can be measured arbitrarily quickly and arbitrarily accurately, and a sequence of such measurements can lead to an arbitrarily accurate monitoring of the classical force.

Chapter 3 describes explicit gedanken experiments which demonstrate that X₁ can be measured arbitrarily quickly and arbitrarily accurately, it considers approximate back-action-evading measurements, and it develops a theory of quantum nondemolition measurement for arbitrary quantum mechanical systems.

In Rosen's "bimetric" theory of gravity the (local) speed of gravitational radiation v_g is determined by the combined effects of cosmological boundary values and nearby concentrations of matter. It is possible for v_g to be less than the speed of light. Chapter 4 shows that emission of gravitational radiation prevents particles of nonzero rest mass from exceeding the speed of gravitational radiation. Observations of relativistic particles place limits on v_g and the cosmological boundary values today, and observations of synchrotron radiation from compact radio sources place limits on the cosmological boundary values in the past.