Statistical Mechanics and Computation of DNA Self-Assembly

25 May 2011, 16:00 → 28 May 2011, 19:00 Europe/Stockholm

Hotel Arkipelag, Mariehamn, Finland

Erik Aurell (KTH), Mikko Alava (Aalto University), Pekka Orponen (TKK), Ralf Eichhorn (Nordita), Ralf Metzler (Technical University of Munich)

Summary

The meeting was held May 25-28 2011 in Mariehamn, Finland. A list of participants and the final program can be found following the links to the left of the screen.

Background to the field

This workshop intended to bring together scientists interested in the self-assembly of DNA nanostructures. DNA origami uses the specific Watson-Crick base-pairing between complementary nucleic acids on many different short strands which in solution self-assemble to large complex yet programmable shapes. They hold promise for providing a versatile "toolbox" to engineer and manufacture complex nano-machinery with manifold applications in biotechnology and nanoelectronics.

The workshop aim was to cross-fertilize experimental approaches to DNA origami and other examples of DNA self-assembly with computational methods used to design and predict specific origami structures. Potential applications of such DNA self-assembling into pre-determined shapes were also discussed. Additionally, the workshop covered some more general aspects of the physics of DNA.

The venue was Hotel Arkipelag in downtown Mariehamn, the capital of the province of Åland, Finland. The Åland archipelago, lying between Sweden and mainland Finland, is easily reachable by ferry from Stockholm (Sweden), from Turku (Finland), and from Helsinki (Finland). In addition, there are flights from Sweden and Finland.

The meeting was generously supported by NORDITA, The Swedish Science Research Council, the National Graduate School in Materials Physics (Finland) NGSMP, the National Graduate School in Computational Sciences (Finland) FICS, and the Center for Industrial and Applied Mathematics (Sweden) CIAM. <par>

Main sponsors:

Wednesday, 25 May

16:45 → 22:50 Ferry session

16:45 break

17:00 Finicky and Sloppy Molecular Beacons

Molecular beacons are hairpin-shaped oligonucleotide probes that undergo a fluorogenic conformational change upon binding to PCR amplicons. They can be labeled with differently colored fluorophores, enabling multiplex assays to be carried out in sealed reaction tubes. They can be designed to be “finicky”, so that they only bind to amplicons from a single species, or they can be designed to be “sloppy”, so that they bind to amplicons from many different species. The set of melting temperatures obtained from the probe-target hybrids that are formed with a limited set of differently colored, sloppy molecular beacon probes uniquely identifies which bacterial species is present in a clinical sample (from a list of more than a hundred species). Alternatively, the unique set of colors that appear in a screening assay containing as many as 35 combinatorially color-coded, finicky molecular beacon probes identifies the infectious agent. The use of molecular beacons in digital PCR formats will enable many different targets in a single clinical sample to be simultaneously identified and quantitated.

Speaker: Prof. Fred Kramer (Public Health Research Institute)

18:15 break

18:45 Sequence, shape, function: a primer to DNA origami

Advanced molecular self-assembly with ‘DNA origami’ offers a unique route for building custom shaped high-complexity objects that are commensurate in size to biological macromolecules. DNA origami objects can be used as platforms for placing, orienting, and even manipulating biological molecules in user defined ways. Thus, DNA origami objects can not only help improve existing experimental methods in the molecular biosciences but they also open completely new avenues of exploration. In our laboratory we have set out to develop custom 'nano’ instrumentation based on DNA origami that complements single-molecule-level methods for observing and manipulating biological macromolecules. Among other goals, we seek to enable the study of adhesive interactions between biomolecules in unprecedented detail. We also aim to develop tools for unraveling the conformational dynamics of proteins at work in novel ways. More long term, we hope to be able to create a biologically inspired nanotechnology including devices that are capable of performing complex tasks such as enzymatic catalysis or molecular transport for human purposes. In my lecture I will focus on an introduction to DNA origami, our near-term applications, and report about some of our efforts in analyzing and improving molecular self-assembly reactions with DNA origami.

Speaker: Prof. Hendrik Dietz (Technische Universität München)

20:00 Dinner

Thursday, 26 May

09:00 → 18:00 Statistical mechanics

09:15 Self-assembly of DNA into nanoscale three-dimensional shapes

I will present a general method for solving a key challenge for nanotechnology: programmable self-assembly of complex, three-dimensional nanostructures. Previously, scaffolded DNA origami had been used to build arbitrary flat shapes 100 nm in diameter and almost twice the mass of a ribosome. We have succeeded in building custom three-dimensional structures that can be conceived as stacks of nearly flat layers of DNA. Successful extension from two-dimensions to three-dimensions in this way depended critically on calibration of folding conditions. This general capability for building complex, three-dimensional nanostructures will pave the way for the manufacture of sophisticated devices bearing features on the nanometer scale.

Speaker: Prof. William Shih (Harvard Medical School)

10:00 break

10:30 Assembly of single-walled carbon nanotubes on DNA-origami templates through streptavidin-biotin interaction

I present work where we propose a novel method for the controlled positioning of carbon nanotubes on DNA self-assembled structures. The method is based on the use of streptavidin (STV)–biotin interaction. Precise assembly of both a single CNT and CNT cross-junctions on DNA-origami templates with relatively high yield is demonstrated. The results thus make an essential contribution to the toolbox of nanowire assembly on DNA origami templates.

Speaker: Prof. Päivi Törmä (Aalto University)

11:15 On the theory of cost and benefit - experiments and theory

Speaker: Prof. Erez Dekel (Weizmann Institute of Science)

12:00 Lunch

14:30 Free-form design of 3D DNA nanostructures using vHelix for Autodesk Maya

CAD software for the design of 3D DNA origami nanostructures have been reported previously. In caDNAno by Shawn Douglas, and the more recent CanDo package by Castro and co-workers the focus has been on designing structures where parallel helices are packed in a square-, or honeycomb-lattice. In our recent efforts in building a DNA nanopore, there has been a need for a design software that allows a little bit more freedom in the orientations of the double helices with respect to each other. To this end we have implemented a plug-in for the 3D modeling software Autodesk Maya. Here we present this plug-in, called vHelix, and demonstrate how it can be used to easily design previously untested DNA geometries.

Speaker: Prof. Björn Högberg (Karolinska Institute)

15:15 Microfluidic tools for DNA analysis, manipulation and separation

We present our recent studies concerning micro-and nanofluidic devices that are capable of detecting, manipulating and separating single DNAs with different lengths and conformations [1,2] and with complexed molecules such as polymerases or chemotherapeutics [3,4]. The first device consists of a straight microchannel structured with an array of non-conducting posts, which create dielectrophoretic traps when a voltage is applied. The escape process of DNA molecules migrating through the structure can be modelled using Kramers’ rate theory and quantitative values for DNA polarizability are extractable. The same principle can be exploited to separate single linear and supercoiled DNA molecules by length and conformation within less than 4 minutes. The central element of the second device is a 3D-structured microfluidic channel with a bended constriction that reduces the channel height to about 670 nm. At this barrier, dielectrophoretic forces selectively deflect DNA with a bound agent (proteins or antibiotics) and let the uncomplexed DNA fragments pass unhindered. As the device operates continuously, no actual separation time exists and the separated samples can be immediately collected or post-processed. The result of the separation can be observed in real-time allowing for an on-line optimization of the parameters of separation during operation. As a proof-of-principle, we demonstrate the separation of DNA molecules with different length and DNA/polymerase as well as DNA/Actinomycin D complexes from uncomplexed DNA. [1] J. Regtmeier, T.T. Duong, R. Eichhorn, D. Anselmetti, A. Ros, Analytical Chemistry 79, 3925-3932 (2007) [2] J. Regtmeier, R. Eichhorn, L. Bogunovic, A. Ros, D. Anselmetti, Analytical Chemistry 82, 7141-7149 (2010) [3] M. Everwand, D. Anselmetti, J. Regtmeier, Proceedings of the µTAS 2010, 19-21 (2010) [4] M. Everwand, R. Eichhorn, J. Regtmeier, D. Anselmetti, in preparation

Speaker: Dr Lukas Bogunovic (Universität Bielefeld)

16:00 Coffee break

16:30 Thermodynamics of RNA hybridization inferred from out of equilibrium unzipping experiments

We have recently developed a methodology to infer the free energy of hybridization of DNA with a single molecule technique (Huguet et al., PNAS 107, 15431 (2010)). It consists in unzipping a molecule of DNA of a few thousands of base pairs with optical tweezers. These pulling experiments provide a force vs. distance curve that is analyzed to obtain the free energy of formation of the Nearest-Neighbor motifs. However, this technique is only valid for quasistatic pulling experiments. We have extended our technique to out of equilibrium experiments, in which the force vs. distance curves are not quasistatic anymore. So we are able to analyze the data obtained from pulling experiments on RNA, which exhibits much more hysteresis than DNA. The main advantage of this technique is that it circumvents the problems of bulk experiments such as aggregation of molecules or self-catalization of biomolecules at certain salt concentrations or pH. The results pave the way to establish the single-molecule unzipping experiments as a reliable technique to extract the free energy of formation of the motifs of biomolecules.

Speaker: Dr Josep Maria Huguet (Universitat de Barcelona)

17:15 Coarse-grained modelling of DNA and DNA self-assembly

We have recently proposed a coarse-grained model of DNA [1] which captures much of the thermodynamic and physical changes associated with DNA duplex formation from isolated single strands, in particular representing double-stranded hybridization, hairpin formation and single-stranded stacking consistently for the first time. Despite this, the model is suciently simple to allow the study of processes occurring on long timescales, and as such provides access to the physics of nanostructure formation and nanomachine operation. Here we present the model, and explore applications to DNA tweezers, a two-footed DNA walker and DNA origami. [1] T. E. Ouldridge, A. A. Louis, and J. P. K. Doye, Phys. Rev. Lett. 104, 178101 (2010).

Speaker: Dr Thomas Ouldridge (Oxford University)

Friday, 27 May

09:00 → 17:00 Computation

09:15 Toward a Programmable Chemistry with Strand Displacement Cascades

What challenges must be overcome before engineers can design molecules and their interactions with ease? The ideas of abstraction and modularity allowed the creation of software and hardware systems of extreme complexity consisting of millions of lines of code and hundreds of millions of transistors. Mimicking software and hardware engineering, an approach to the molecular challenge is to find a basic set of interactions that can be composed in various ways without interference, and then create a hierarchy of modules of increasing complexity leading to the desired higher-level function. Nucleic acids are a very promising candidate for the underlying molecular substrate for such modular systems, and have been used to construct a variety of nanoscale structures, mechanical nanomachines, sensors, and information processing devices. Nucleic acids are also biologically compatible and potentially capable of interfacing with existing cellular machinery, hinting at the eventual possibility of therapeutic applications. "Strand-displacement cascades" describes the technology combining toehold-mediated branch migration, toehold blocking by hybridization, and toehold exchange, to enable coupled cascades of strand displacement reactions. The promise of this technology is that all the necessary nucleic acid interactions can be systematically programmed using a few simple rules, and composed into hierarchically assembled complex systems. My talk will review developments both in the theory and experimental practice of strand displacement cascades. Computer theoretic abstractions have had a key role in thinking about strand displacement cascades: chemical reaction networks, process algebras, digital circuits, state machines, as well as special-purpose algebras have all been harnessed as organizing principles. I will review the utility of such abstractions for the engineering of complex networks of molecular interactions, focusing particularly on chemical reaction networks as an intermediate abstraction layer (eg how digital circuits can be compiled to chemical reaction networks which in turn can be compiled to strand displacement cascades). I will also review the art of designing domain sequences, as well as the available modeling and simulation tools, and outline our first steps toward experimentally realizing certain dynamical systems such as oscillators that may become parts of future embedded control modules. In the final part of the talk I will review the substantial remaining engineering challenges.

Speaker: Prof. David Soloveichik (University of Washington)

10:00 Coffee break

10:30 The termination problem in self-assembly

We consider the algorithmic problem of determining if a given self-assembly system is terminating, that is, if an unbounded growth may happen or not. We prove that this question is undecidable even in the simple tiling model of self-assembly, by showing that no algorithm is able to determine if a given set of Wang tiles can form on the plane an infinite path where consecutive tiles match with each other. We also consider the analogous problem of determining whether given tiles can form a correctly tiled loop, and prove its undecidability.

Speaker: Prof. Jarkko Kari (University of Turku)

11:15 DNA codeword design: theory and application

Finding large sets of single DNA strands that do not crosshybridize to themselves or to their complements is an important problem in DNA computing, self-assembly, DNA memories and phylogenetic analyses, because of their error correction and prevention properties. The problem is in itself NP-complete, even in very simplified versions using any single reasonable measure that approximates the Gibbs energy, thus practically excluding the possibility of finding any efficient procedure to find maximal sets efficiently. After a quick survey of advances in this area in the last few years, we focus on a novel combinatorial/geometric framework to analyze this problem. In this framework, codeword design is reduced to finding large sets of strands maximally separated in DNA spaces and therefore the size of such sets depends on the geometry of these DNA spaces. We present a new general technique to embed DNA spaces in Euclidean spaces and thus, among others, reduce the word design problem to the well known sphere packing problem in information theory. The embedding sheds some insights into the geometry of DNA spaces by enabling a quantitative analysis via well established approximations of the Gibbs energy, namely the nearest neighbor model of duplex formation. The main tool is an efficiently computable combinatorial approximation which is also a mathematical metric. As illustration, we show two applications to produce provably nearly optimal codeword sets (modulo the goodness of the Gibbs energy approximation) and a new methodology for phylogenetic analyses in Biology. We conclude with a brief discussion of some qualitative properties of the Gibbs energy landscapes for short DNA oligo spaces.

Speaker: Prof. Max Garzon (The University of Memphis)

12:00 Lunch

14:30 On Recycling and its Limits in Strand Displacement Systems

We consider recycling, or reuse of molecules, in chemical reaction systems and their DNA strand displacement realizations. Recycling happens when a product of one reaction is a reactant in a later reaction. Recycling has the benefits of reducing consumption, or waste, of molecules and of avoiding fuel depletion. We will describe a binary counter that recycles molecules efficiently while incurring just a moderate slowdown compared to alternative counters that do not recycle strands. This counter is an n-bit binary reflecting gray code counter; it advances through 2^n states while consuming just O(n) molecules. In the strand displacement realization of this counter, the waste---total number of nucleotides of the DNA strands consumed---is O(n^3), while alternative counters have waste proportional to 2^n. We also show limits to the potential for recycling strands. In particular, our n-bit counter fails to work correctly when many copies of the species that represent the state (bits) of the counter are present initially.

Speaker: Prof. Anne Condon (University of British Columbia)

15:15 Building a DNA brain

Not long after Adleman showed that DNA can serve as a computing substrate, Baum proposed using DNA to build an associative memory larger than the brain. Attempts to bring these ideas to fruition have been hindered by requirements for enzymes or manual experimental steps. Here our interest is in DNA strand displacement circuits that can perform neural network computation autonomously. We make use of a simple DNA gate architecture that has recently allowed experimental scale-up of multilayer digital circuits. We developed a systematic procedure for transforming arbitrary linear threshold circuits (an artificial neural network model) into DNA strand displacement cascades. We demonstrated our approach by successfully implementing several small neural networks, including a Hopfield associative memory that has four fully connected artificial neurons. This tiny DNA brain can play a game called ``read your mind" (a variation of ``20 questions") with a human. As an alternative to Baum's goal, our results suggest that DNA strand displacement cascades could be used to embed ``intelligence'' within autonomous chemical systems, capable of recognizing patterns of molecular events, making decisions and responding to the environment.

Speaker: Dr Lulu Qian (Caltech)

16:00 Coffee break

16:30 A Design Framework for Carbon Nanotube Circuits Affixed on DNA Origami Tiles

Recent years have witnessed a burst of experimental activity concerning algorithmic self-assembly of nanostructures, motivated at least in part by the potential of this approach as a radically new manufacturing technology. Our specific interest is in the self-assembly of Carbon-Nanotube Field Effect Transistor (CNFET) circuits. In the present work, we propose a generic framework for the design of CNFET circuits comprising a "universal" set of 14 functionalised DNA origami tiles. With a proper selection of "glues" on the tiles, any desired CNFET circuit can be self-assembled from this basis.

Speaker: Dr Eugen Czeizler (Aalto University)

17:00 → 19:00 Poster session

Saturday, 28 May

09:00 → 13:00 Synthesis

09:15 Growth of arbitrarily shaped metal nanoparticles templated by DNA origami

The directed metallization of DNA origami nanostructures could give rise to self-assembling materials with novel optical and electronic properties. We show that three-dimensional (3D) DNA origami structures can be converted into gold nanoparticles of designed shapes by a two- step metallization process: Positively charged 1.4 nm gold nanoclusters adsorb to the negatively charged DNA objects followed by electroless deposition of gold from solution. Using this strategy, nanoparticles with a narrow size distribution and controllable shapes and dimensions are created. This site-directed metallization constitutes a general and easy route for shape-defined growth of continuously metallized objects, such as nanorods, nanodonuts, cuboids and kites of controlled sizes and lengths.

Speaker: Prof. Tim Liedl (LMU München)

10:00 Coffee break

10:30 Algorithmic Self-Assembly of DNA: Theory and Experiment

Self-assembly is a fundamental process in the self-organization of biological as well as non-biological structures. Passive self-assembly of molecular units, being driven just by thermodynamic binding energies and the geometrical structure of the molecules, would seem to be the simplest case to study -- but it can be remarkably complicated. In fact, in a model of generalized crystal growth abstracted as the self-assembly of Wang tiles, passive self-assembly can be shown to be Turing universal. This leads to a number of theoretical observations: complex shapes that have concise algorithmic descriptions can be self-assembled from a small number of parts; these self-assembled structures can perform error correction during growth and can self-heal after damage; and as a simple form of self-replication, algorithmic crystals could provide an abiological example of Darwinian evolution. In our lab, we have been working to demonstrate these principles experimentally, using molecular Wang tiles constructed from DNA.

Speaker: Prof. Erik Winfree (Caltech)

11:15 Dynamical nanosystems made from DNA, RNA, and occasionally a few other components

The highly predictable interactions between DNA or RNA molecules have been utilized for the construction of a large variety of molecular structures and devices. For instance, the recently developed DNA origami technique facilitates the molecular assembly of two- and even three-dimensional nano-objects with almost arbitrary shape - and with nanometric precision. These structures can be used as molecular scaffolds for the arrangement of nanoscale objects such as nanoparticles or proteins into specific geometries. Such assemblies may help to exploit distance or geometry dependent - chemical or physical - interactions between these components. In addition to the realization of static molecular nanostructures one of the major promises of molecular nanotechnology is the creation of dynamic molecular assemblies such as molecular switches, actuators, and biochemical circuits. A few examples of such assemblies will be described, and also our recent attempts to characterize these structures with fluorescence microscopic techniques.

Speaker: Prof. Friedrich Simmel (TU Munchen)

12:00 Lunch