Synthetic molecular machines for active self-assembly : prototype algorithms, designs, and experimental study

Computer science and electrical engineering have been the great success story of the twentieth century. The neat modularity and mapping of a language onto circuits has led to robots on Mars, desktop computers and smartphones. But these devices are not yet able to do some of the things that life takes for granted: repair a scratch, reproduce, regenerate, or grow exponentially fast–all while remaining functional.

This thesis explores and develops algorithms, molecular implementations, and theoretical proofs in the context of “active self-assembly” of molecular systems. The long-term vision of active self-assembly is the theoretical and physical implementation of materials that are composed of reconfigurable units with the programmability and adaptability of biology’s numerous molecular machines. En route to this goal, we must first find a way to overcome the memory limitations of molecular systems, and to discover the limits of complexity that can be achieved with individual molecules.

One of the main thrusts in molecular programming is to use computer science as a tool for figuring out what can be achieved. While molecular systems that are Turing-complete have been demonstrated [Winfree, 1996], these systems still cannot achieve some of the feats biology has achieved.

One might think that because a system is Turing-complete, capable of computing “anything,” that it can do any arbitrary task. But while it can simulate any digital computational problem, there are many behaviors that are not “computations” in a classical sense, and cannot be directly implemented. Examples include exponential growth and molecular motion relative to a surface.

Passive self-assembly systems cannot implement these behaviors because (a) molecular motion relative to a surface requires a source of fuel that is external to the system, and (b) passive systems are too slow to assemble exponentially-fast-growing structures. We call these behaviors “energetically incomplete” programmable behaviors. This class of behaviors includes any behavior where a passive physical system simply does not have enough physical energy to perform the specified tasks in the requisite amount of time.

As we will demonstrate and prove, a sufficiently expressive implementation of an “active” molecular self-assembly approach can achieve these behaviors. Using an external source of fuel solves part of the the problem, so the system is not “energetically incomplete.” But the programmable system also needs to have sufficient expressive power to achieve the specified behaviors. Perhaps surprisingly, some of these systems do not even require Turing completeness to be sufficiently expressive.

Building on a large variety of work by other scientists in the fields of DNA nanotechnology, chemistry and reconfigurable robotics, this thesis introduces several research contributions in the context of active self-assembly.

We show that simple primitives such as insertion and deletion are able to generate complex and interesting results such as the growth of a linear polymer in logarithmic time and the ability of a linear polymer to treadmill. To this end we developed a formal model for active-self assembly that is directly implementable with DNA molecules. We show that this model is computationally equivalent to a machine capable of producing strings that are stronger than regular languages and, at most, as strong as context-free grammars. This is a great advance in the theory of active self- assembly as prior models were either entirely theoretical or only implementable in the context of macro-scale robotics.

We developed a chain reaction method for the autonomous exponential growth of a linear DNA polymer. Our method is based on the insertion of molecules into the assembly, which generates two new insertion sites for every initial one employed. The building of a line in logarithmic time is a first step toward building a shape in logarithmic time. We demonstrate the first construction of a synthetic linear polymer that grows exponentially fast via insertion. We show that monomer molecules are converted into the polymer in logarithmic time via spectrofluorimetry and gel electrophoresis experiments. We also demonstrate the division of these polymers via the addition of a single DNA complex that competes with the insertion mechanism. This shows the growth of a population of polymers in logarithmic time. We characterize the DNA insertion mechanism that we utilize in Chapter 4. We experimentally demonstrate that we can control the kinetics of this re- action over at least seven orders of magnitude, by programming the sequences of DNA that initiate the reaction.

In addition, we review co-authored work on programming molecular robots using prescriptive landscapes of DNA origami; this was the first microscopic demonstration of programming a molec- ular robot to walk on a 2-dimensional surface. We developed a snapshot method for imaging these random walking molecular robots and a CAPTCHA-like analysis method for difficult-to-interpret imaging data.

Beyond Watson and Crick : programming the self-assembly and reconfiguration of DNA nanostructures based on stacking interactions

Life is the result of the execution of molecular programs: like how an embryo is fated to become a human or a whale, or how a person’s appearance is inherited from their parents, many biological phenomena are governed by genetic programs written in DNA molecules. At the core of such programs is the highly reliable base pairing interaction between nucleic acids. DNA nanotechnology exploits the programming power of DNA to build artificial nanostructures, molecular computers, and nanomachines. In particular, DNA origami—which is a simple yet versatile technique that allows one to create various nanoscale shapes and patterns—is at the heart of the technology. In this thesis, I describe the development of programmable self-assembly and reconfiguration of DNA origami nanostructures based on a unique strategy: rather than relying on Watson-Crick base pairing, we developed programmable bonds via the geometric arrangement of stacking interactions, which we termed stacking bonds. We further demonstrated that such bonds can be dynamically reconfigurable.

The first part of this thesis describes the design and implementation of stacking bonds. Our work addresses the fundamental question of whether one can create diverse bond types out of a single kind of attractive interaction—a question first posed implicitly by Francis Crick while seeking a deeper understanding of the origin of life and primitive genetic code. For the creation of multiple specific bonds, we used two different approaches: binary coding and shape coding of geometric arrangement of stacking interaction units, which are called blunt ends. To construct a bond space for each approach, we performed a systematic search using a computer algorithm. We used orthogonal bonds to experimentally implement the connection of five distinct DNA origami nanostructures. We also programmed the bonds to control cis/trans configuration between asymmetric nanostructures.

The second part of this thesis describes the large-scale self-assembly of DNA origami into two-dimensional checkerboard-pattern crystals via surface diffusion. We developed a protocol where the diffusion of DNA origami occurs on a substrate and is dynamically controlled by changing the cationic condition of the system. We used stacking interactions to mediate connections between the origami, because of their potential for reconfiguring during the assembly process. Assembling DNA nanostructures directly on substrate surfaces can benefit nano/microfabrication processes by eliminating a pattern transfer step. At the same time, the use of DNA origami allows high complexity and unique addressability with six-nanometer resolution within each structural unit.

The third part of this thesis describes the use of stacking bonds as dynamically breakable bonds. To break the bonds, we used biological machinery called the ParMRC system extracted from bacteria. The system ensures that, when a cell divides, each daughter cell gets one copy of the cell’s DNA by actively pushing each copy to the opposite poles of the cell. We demonstrate dynamically expandable nanostructures, which makes stacking bonds a promising candidate for reconfigurable connectors for nanoscale machine parts.

Intramolecular conflict : conformation and self-assembly of architecturally complex macromolecules in solution

The solution behavior of linear polymer chains is well understood, having been the subject of intense study throughout the previous century. As plastics have become ubiquitous in everyday life, polymer science has grown into a major field of study. The conformation of a polymer in solution depends on the molecular architecture and its interactions with the surroundings. Developments in synthetic techniques have led to the creation of precision-tailored polymeric materials with varied topologies and functionalities. In order to design materials with the desired properties, it is imperative to understand the relationships between polymer architecture and their conformation and behavior. To meet that need, this thesis investigates the conformation and self-assembly of three architecturally complex macromolecular systems with rich and varied behaviors driven by the resolution of intramolecular conflicts. First we describe the development of a robust and facile synthetic approach to reproducible bottlebrush polymers (Chapter 2). The method was used to produce homologous series of bottlebrush polymers with polynorbornene backbones, which revealed the effect of side-chain and backbone length on the overall conformation in both good and theta solvent conditions (Chapter 3). The side-chain conformation was obtained from a series of SANS experiments and determined to be indistinguishable from the behavior of free linear polymer chains. Using deuterium-labeled bottlebrushes, we were able for the first time to directly observe the backbone conformation of a bottlebrush polymer which showed self-avoiding walk behavior. Secondly, a series of SANS experiments was conducted on a homologous series of Side Group Liquid Crystalline Polymers (SGLCPs) in a perdeuterated small molecule liquid crystal (5CB). Monodomain, aligned, dilute samples of SGLCP-b-PS block copolymers were seen to self-assemble into complex micellar structures with mutually orthogonally oriented anisotropies at different length scales (Chapter 4). Finally, we present the results from the first scattering experiments on a set of fuel-soluble, associating telechelic polymers. We observed the formation of supramolecular aggregates in dilute (≤0.5wt%) solutions of telechelic polymers and determined that the choice of solvent has a significant effect on the strength of association and the size of the supramolecules (Chapter 5). A method was developed for the direct estimation of supramolecular aggregation number from SANS data. The insight into structure-property relationships obtained from this work will enable the more targeted development of these molecular architectures for their respective applications.

Self-assembly of brush polymers

The unique structure and properties of brush polymers have led to increased interest in them within the scientific community. This thesis describes studies on the self-assembly of these brush polymers.

Chapter 2 describes a study on the rapid self-assembly of brush block copolymers into nanostructures with photonic bandgaps spanning the entire visible spectrum, from ultraviolet to near infrared. Linear relationships are observed between the peak wavelengths of reflection and polymer molecular weights. This work enables "bottom-up" fabrication of photonic crystals with application-tailored bandgaps, through synthetic control of the polymer molecular weight and the method of self-assembly.

Chapter 3 details the analysis of the self-assembly of symmetrical brush block copolymers in bulk and thin films. Highly ordered lamellae with domain spacing ranging from 20 to 240 nm are obtained by varying molecular weight of the backbone. The relationship between degree of polymerization and the domain spacing is reported, and evidence is provided for how rapidly the brush block copolymers self-assemble and achieve thermodynamic equilibrium.

Chapter 4 describes investigations into where morphology transitions take place as the volume fraction of each block is varied in asymmetrical brush block copolymers. Imaging techniques are used to observe a transition from lamellar to a cylindrical morphology as the volume fraction of one of the blocks exceeds 70%. It is also shown that the asymmetric brush block copolymers can be kinetically trapped into undulating lamellar structures by drop casting the samples.

Chapter 5 explores the capability of macromolecules to interdigitate into densely grafted molecular brush copolymers using stereocomplex formation as a driving force. The stereocomplex formation between complementary linear polymers and brush copolymers is demonstrated, while the stereocomplex formation between complementary brush copolymers is shown to be restricted.

A molecular dynamics study of the microscopic properties of simple dense fluids

The microscopic properties of a two-dimensional model dense fluid of Lennard-Jones disks have been studied using the so-called "molecular dynamics" method. Analyses of the computer-generated simulation data in terms of "conventional" thermodynamic and distribution functions verify the physical validity of the model and the simulation technique.

The radial distribution functions g(r) computed from the simulation data exhibit several subsidiary features rather similar to those appearing in some of the g(r) functions obtained by X-ray and thermal neutron diffraction measurements on real simple liquids. In the case of the model fluid, these "anomalous" features are thought to reflect the existence of two or more alternative configurations for local ordering.

Graphical display techniques have been used extensively to provide some intuitive insight into the various microscopic phenomena occurring in the model. For example, "snapshots" of the instantaneous system configurations for different times show that the "excess" area allotted to the fluid is collected into relatively large, irregular, and surprisingly persistent "holes". Plots of the particle trajectories over intervals of 2.0 to 6.0 x 10^-12 sec indicate that the mechanism for diffusion in the dense model fluid is "cooperative" in nature, and that extensive diffusive migration is generally restricted to groups of particles in the vicinity of a hole.

A quantitative analysis of diffusion in the model fluid shows that the cooperative mechanism is not inconsistent with the statistical predictions of existing theories of singlet, or self-diffusion in liquids. The relative diffusion of proximate particles is, however, found to be retarded by short-range dynamic correlations associated with the cooperative mechanism--a result of some importance from the standpoint of bimolecular reaction kinetics in solution.

A new, semi-empirical treatment for relative diffusion in liquids is developed, and is shown to reproduce the relative diffusion phenomena observed in the model fluid quite accurately. When incorporated into the standard Smoluchowski theory of diffusion-controlled reaction kinetics, the more exact treatment of relative diffusion is found to lower the predicted rate of reaction appreciably.

Finally, an entirely new approach to an understanding of the liquid state is suggested. Our experience in dealing with the simulation data--and especially, graphical displays of the simulation data--has led us to conclude that many of the more frustrating scientific problems involving the liquid state would be simplified considerably, were it possible to describe the microscopic structures characteristic of liquids in a concise and precise manner. To this end, we propose that the development of a formal language of partially-ordered structures be investigated.