Urmi Majumder

Self-assembly has been immensely successful in creating complex patterns at the molecular scale. However, the use of self-assembly techniques at the macroscopic level has so far been limited to the formation of simple patterns. For example, in a number of prior works, self-assembling units or tiles formed aggregates based on the polarity of magnetic pads on their sides. The complexity of the resulting assemblies was limited, however, due to the small variety of magnetic pads that were used: namely just positive or negative polarity. This paper addresses the key challenge of increasing the variety of magnetic pads for tiles, which would allow the tiles to self-assemble into more complex patterns. We introduce a barcode scheme which potentially allows for the generation of arbitrarily complex structures using magnetic self-assembly at the macro-scale. This paper focuses on the design and optimization of this barcode scheme. We also present a physical model based on Newtonian mechanics and Maxwellian magnetics. Additionally, we present a software simulation system that correctly models the attachment, orientation and binding of these tiles using magnetic interactions as well as external forces (e.g. wind) which provide energy to the system. We further demonstrate how we can use our simulation results to extract a higher level kinetic model which can be used to predict assembly yield on a larger scale and to provide better insight into the dynamics of our physical system.

Whiplash PCR (WPCR), due to Hagiya et al, is a novel technique for autonomous molecular computation where a state machine is implemented with a single stranded DNA molecule and state transition is driven by polymerase and thermal cycles. The significance of WPCR computation lies in the fact that while other forms of autonomous molecular computing such as tiling assembly or Benenson automata operate based on global rules, it is possible to execute multiple WPCR machines, each holding its own distinct program, in parallel. However, since each transition requires a thermal cycle, multi-step WPCR machines are laborious and time-consuming. Hence they limit program execution to only a few steps. To date, no WPCR protocol has been developed which is both autocatalytic (self-executing) and isothermal (with no change in temperature). In this paper, we describe such a protocol for computing with WPCR which uses a combination of strand displacement and DNA polymerization. Our designs include (1) a protocol where transition rules cannot be reused in subsequent computing (2) a protocol where rules can be reused using an auxiliary strand displacement event. We also compute the state transition likelihood and rate in this protocol and present a DNA sequence design of a 3-state machine along with an experimental verification plan.

Since its inception, the focus of DNA self-assembly based nanostructures has mostly been on one-time assembly. However, DNA nanostructures are very fragile and prone to damage. Knowing the extent of damage that can occur under various physical conditions can be useful in making robust designs for self-assembled nanostructures. Thus in this paper, we present simple models for estimating the extent of damage in DNA nanostructures due to various external forces. We note that these models have not been validated against experimental data and are only meant to serve as a basis for designing DNA nanostructures that are robust to external damage. We conclude with a discussion on computing the probability of repair of a damaged nanostructure.

The theoretical basis of computational self-assembly dates back to the idea of Wang tiling models in the early 1960s. More recently, it has been recognized that self-assembly is a promising route to nano-scale computation and there have been many experimental demonstrations of self-assembling DNA tiles performing computation. Winfree proposed abstract irreversible (only tile accretion is allowed) models for the self-assembly process that can perform universal computation. Realism, however, requires us to develop models and analysis for reversible tiling models, where tile dissociation is also allowed so that we can measure various thermodynamic properties. To date, however, the stochastic analysis of reversible tiling processes has only been done for one-dimensional assemblies and has not been extended to two or three dimensional assemblies. In this paper we discuss how we can extend prior work in one dimension by Adleman et al. to higher dimensions. We describe how these self-assembly processes can be modeled as rapidly mixing Markov Chains. We characterize chemical equilibrium in the context of self-assembly processes and present a formulation for the equilibrium concentration of various assemblies. Since perfect equilibrium can only be reached in infinite time, we further derive the distribution of error around equilibrium. We present the first known direct derivation of the convergence rates of two and three-dimensional assemblies to equilibrium. Finally we observe that even when errors are allowed in the self-assembly model, the distribution over assemblies converge to uniform distribution with only small number of random association/dissociation events. We conclude with some thoughts on how to relax some of our model constraints.

While algorithmic DNA self-assembly is, in theory, capable of forming complex patterns, its experimental demonstration has been limited by significant assembly errors. In this paper we describe a novel protection/deprotection strategy to strictly enforce the direction of tiling assembly growth to ensure the robustness of the assembly process. Tiles are initially inactive, meaning that each tile’s output pads are protected and cannot bind with other tiles. After other tiles bind to the tile’s input pads, the tile transitions to an active state and its output pads are exposed, allowing further growth. We prove that an activatable tile set is an instance of a compact, error-resilient and self-healing tile-set. We also describe a DNA design for activatable tiles and a deprotection mechanism using DNA polymerase enzymes and strand displacement. We conclude with a discussion on some applications of activatable tiles beyond computational tiling.

Self-repair is essential to all living systems, providing the ability to remain functional in spite of gradual damage. In the context of self-assembly of self-repairing synthetic biomolecular systems, recently a method for transforming a set of DNA tiles into its self-healing counterpart at the cost of increasing the lattice area by a factor of 25 was developed (Winfree). The overall focus of this paper, however, is to develop compact designs for self-repairing tiling assemblies with reasonable constraints on crystal growth. Specifically, we use a special class of DNA tiling designs called reversible tiling which when carefully designed can provide inherent self-repairing capabilities to patterned DNA lattices. We further prove that we can transform any irreversible computational DNA tile set to its reversible counterpart and hence improve the self-repairability of the computational lattice. But doing the transform with an optimal number of tiles, is still an open question.