Jacobi Iteration for Solving Linear Equations Based on DNA Strand Displacement

DNA strand displacement (DSD) has recently become a common technology for constructing molecular devices, with a number of useful systems experimentally demonstrated. To help with DSD system design, various researchers are developing formal definitions to model DNA strand displacement systems. With these models a DSD system can be defined, described by a Chemical Reaction Network, simulated, and otherwise analyzed. Meanwhile, the research community is trying to use DSD to do increasingly complex tasks, while also trying to make DSD systems simpler and more robust. I suggest that formal modeling of DSD systems can be used not only to analyze DSD systems, but to guide their design. For instance, one might prove that a DSD system that implements a certain function must use a certain mechanism. As an example, I show that a physically reversible DSD system with no pseudoknots, no effectively trimolecular reactions, and using 4-way but not 3-way branch migration, cannot be a systematic implementation of reactions of the form \(A \rightleftharpoons B\) that uses a constant number of toehold domains and does not crosstalk when multiple reactions of that type are combined. This result is a tight lower bound in the sense that, for most of those conditions, removing just that one condition makes the desired DSD system possible. I conjecture that a system with the same restrictions using both 3-way and 4-way branch migration still cannot systematically implement the reaction \(A + B \rightleftharpoons C\).

We present an implementation of an in vitro signal recorder based on DNA assembly and strand displacement. The signal recorder implements a stack data structure in which both data as well as operators are represented by single stranded DNA The stack grows by adding push and write bricks and shrinks in last-in-first-out manner by adding pop and read bricks. We report the design of the signal recorder and its mode of operations and give experimental results from capillary electrophoresis as well as transmission electron microscopy that demonstrate the capability of the device to store and later release several successive signals. We conclude by discussing potential future improvements of our current results.

DNA strand displacement technique is widely used in DNA programming, DNA biosensors, and gene analysis. In DNA strand displacement, leaky reactions can cause DNA signals decay and detecting DNA signals fails. The mostly used method to avoid leakage is cleaning up after upstream leaky reactions, and it remains a challenge to develop reliable DNA strand displacement technique with low leakage. In this work, we address the challenge by experimentally evaluating the basic factors, including reaction time, ratio of reactants, and ion concentration to the leakage in DNA strand displacement. Specifically, fluorescent probes and a hairpin structure reporting DNA strand are designed to detect the output of DNA strand displacement, and thus can evaluate the leakage of DNA strand displacement reactions with different reaction time, ratios of reactants, and ion concentrations. From the obtained data, mathematical models for evaluating leakage are achieved by curve derivation. As a result, it is obtained that long time incubation, high concentration of fuel strand, and inappropriate amount of ion concentration can weaken leaky reactions. This contributes to a method to set proper reaction conditions to reduce leakage in DNA strand displacement.

In recent years, DNA strand displacement technology has been become an integral part of DNA computing, which is proved that the complement circuit is played an important role in computer circuits. In this paper, a four-bit complement logic circuit based on DNA strand displacement is designed and simulated. Through the analysis about the simulation results, which is proved that the designed circuit is reliable, and the four-bit complement logic circuit based on DNA strand displacement design is also shown that the DNA strand displacement has a bright future in the construction of large-scale logic circuits.

DNA strand displacement technology performs well in sensing and programming DNA segments. In this work, we construct DNA molecular systems based on DNA strand displacement performing computation of logic gates. Specifically, a class of so-called “DNA neurons” are achieved, in which a “smart” way inspired by biological neurons encoding information is developed to encode and deliver information using DNA molecules. The “DNA neuron” is bistable, that is, it can sense DNA molecules as input signals, and release “negative” or “positive” signals DNA molecules. We design intelligent DNA molecular systems that are constructed by cascading some particularly organized “DNA neurons”, which could perform logic computation, including AND, OR, XOR logic gates, automatically. Both simulation results using visual DSD (DNA strand displacement) software and experimental results are obtained, which shows that the proposed systems can detect DNA signals with high sensitivity and accretion; moreover, the systems can process input signals automatically with complex nonlinear logic. The method proposed in this work may provide a new way to construct a sensitive molecular signal detection system with neurons spiking behavior in vitro, and can be used to develop intelligent molecular processing systems in vivo.

In recent years, DNA strand displacement technology has played a significant role in DNA computing. In this paper, a five-bit square-root digital logic circuit based on DNA strand displacement is designed by using a simple DNA reaction mechanism. The whole reaction process of logic circuit operations can be programmed and simulated through using the Visual DSD simulation software. According to the simulation results, the square-root logic circuit is feasible to achieve the desired logical computations. Through analyzing the simulation results, the feasibility of the designed circuit is demonstrated. And it is proves that DNA strand displacement may have a great potential and bright prospect in the construction of large-scale logic circuits.

In recent years, DNA strand displacement technology has developed rapidly with the advantages of high-performance parallel computing and large information capacity. DNA strand displacement technology is a dynamic DNA nanotechnology developed on the basis of DNA self-assembly technology. DNA strand displacement technology can realize dynamic connection between input signal and output signal, and it is a method for constructing logic gates and logic circuits. According to the basic principle of DNA strand displacement, this paper studies the specific function of the molecular logic circuit model, and constructs a logic circuit with three input and nine output. Then a biochemical logic circuit is built based on the dual-rail thought and the construction of seesaw gate. Finally, DNA strand displacement simulation platform Visual DSD is used to verify the rationality of the model. It lays the foundation for constructing complex logic circuits.

In molecular programming, the Chemical Reaction Network model is often used to describe systems of interacting molecules. This model can describe either real systems, allowing us to analyze and determine their computational function; or describe hypothetical systems, with known computational function but perhaps no known physical example. One significant breakthrough in the field is that any Chemical Reaction Network can be approximated by a system using DNA Strand Displacement mechanisms. This allows the Chemical Reaction Network model to be treated like a programming language, where programs can be written in the abstract and then compiled into physical molecules. Given a programming language and a proof-of-concept compiler, one would want to take the compiler from the proof-of-concept stage into a more reliable, more systematic, and better understood process. This thesis is made up of my contributions to that effort. First, given a programming language and a compiler, it would be useful to formally verify that the compiler is correct. My collaborators, Qing Dong and Erik Winfree, and I defined a Chemical Reaction Network-specific form of bisimulation equivalence, which can compare two such networks and verify that one is (or is not) a correct implementation of the other. For example, the compiler-produced DNA circuit can be verified as an implementation of its abstract program, although this is not the only possible use. After defining this concept of equivalence, we show that it can be checked by algorithm; although various parts of the problem are NP-complete or PSPACE-complete, we give algorithms that meet these lower bounds. We also prove a number of interesting properties of Chemical Reaction Network bisimulation equivalence, including transitivity and modularity properties which are particularly useful for stepwise checking of large systems. We further extend this bisimulation method to linear Polymer Reaction Networks, a strictly more powerful abstraction which has been occasionally used in molecular programming. Again we prove complexity hardness results, which in this case are as expected uncomputable in the general case; however, many practical systems can still be verified, and we give one such example. Finally, we use bisimulation to identify a class of single-locus networks that are practical to implement. Thus we show a method of verification which can simplify use of the above-mentioned compiler by proving general statements of correctness about its results. Second, given a programming language and a concept of compiling it, it would be useful to optimize the result of the compilation. One particular area of optimization is the number of DNA strands per prepared complex; some experiments suggest that systems with no more than 2 strands per complex are more robust. Lulu Qian and I developed some proposed DNA Strand Displacement schemes for general Chemical Reaction Network implementations with no more than 2 strands per complex, and a number of other desirable properties. Meanwhile, having been shown to be useful for many reasons, the mechanisms of DNA Strand Displacement have recently been formalized, abstracted, and analyzed. I show that this formalization, combined with the bisimulation methods above, can prove various statements about the limits of DNA Strand Displacement systems. For example, a set of desirable conditions including the 2-strand limit cannot be achieved by any general Chemical Reaction Network implementation scheme. I also observe that two of the new schemes we discovered, each meeting all but one condition of the impossible set, were found in the process of coming up with this proof. I thus argue that through formalization of DNA Strand Displacement we can have a more systematic method of finding and designing molecular programs, and of knowing when the programs we want do not exist.

A strand graph semantics for DNA-based computation

Summary: The Visual DSD (DNA Strand Displacement) tool allows rapid prototyping and analysis of computational devices implemented using DNA strand displacement, in a convenient web-based graphical interface. It is an implementation of the DSD programming language and compiler described by Lakin et al. (2011) with additional features such as support for polymers of unbounded length. It also supports stochastic and deterministic simulation, construction of continuous-time Markov chains and various export formats which allow models to be analysed using third-party tools.Availability: Visual DSD is available as a web-based Silverlight application for most major browsers on Windows and Mac OS X at http://research.microsoft.com/dna. It can be installed locally for offline use. Command-line versions for Windows, Mac OS X and Linux are also available from the web page.Contact: aphillip@microsoft.comSupplementary Information:Supplementary data are available at Bioinformatics online.

The development of engineered biochemical circuits that exhibit adaptive behavior is a key goal of synthetic biology and molecular computing. Such circuits could be used for long-term monitoring and control of biochemical systems, for instance, to prevent disease or to enable the development of artificial life. In this article, we present a framework for developing adaptive molecular circuits using buffered DNA strand displacement networks, which extend existing DNA strand displacement circuit architectures to enable straightforward storage and modification of behavioral parameters. As a proof of concept, we use this framework to design and simulate a DNA circuit for supervised learning of a class of linear functions by stochastic gradient descent. This work highlights the potential of buffered DNA strand displacement as a powerful circuit architecture for implementing adaptive molecular systems.

DNA computing has the advantages of high parallelism and large storage. In this paper, DNA strand displacement techniques are applied to binary to decimal system. In the field of DNA calculation, binary numerical calculation is relatively mature, but it is difficult to implement decimal calculation. So it is very necessary to study the conversion of binary system to decimal system. In this paper, DNA strand displacement are used to construct a logic model that converts binary system into decimal system. The output strand is obtained through DNA strand displacement reaction in the logical device, and the decimal result is judged by the number of hairpin structures formed. The model has good operability, flexibility.

Operant conditioning reflects the ability of organisms to adapt and learn. By implementing operant conditioning neural networks, complex brain-like behaviors can be simulated and learned at the molecular level. In this paper, an operant conditioning circuit with blocking effect and overshadowing effect is proposed by DNA strand displacement technique. The network can achieve blocking and overshadowing effects in the presence of multiple inputs. First, we construct DNA memristors using DNA strand displacement technology. The constructed DNA memristors are plastic and nonvolatile, which is very similar to biological synapses. The synaptic circuits constructed by DNA memristors have short-term plasticity, long-term plasticity, potentiation plasticity and depression plasticity. Second, the learning module, forgetting module, synaptic module, decision module and feedback module are constructed, and the operant conditioning circuit is realized. In addition, the operant conditioning circuit has relearning effect. Blocking and masking effects can also be achieved in the presence of multiple inputs. Finally, the reliability of the circuit is verified by the simulation of Visual DSD software. Our work demonstrates the potential of DNA molecules to build complex intelligent systems and provides an idea for using DNA molecules to achieve artificial intelligence.

DNA has emerged as a powerful substrate for programming information processing machines at the nanoscale. Among the DNA computing primitives used today, DNA strand displacement (DSD) is arguably the most popular, with DSD-based circuit applications ranging from disease diagnostics to molecular artificial neural networks. The outputs of DSD circuits are generally read using fluorescence spectroscopy. However, due to the spectral overlap of typical small-molecule fluorescent reporters, the number of unique outputs that can be detected in parallel is limited, requiring complex optical setups or spatial isolation of reactions to make output bandwidths scalable. Here, we present a multiplexable sequencing-free readout method that enables real-time, kinetic measurement of DSD circuit activity through highly parallel, direct detection of barcoded output strands using nanopore sensor array technology (Oxford Nanopore Technologies’ MinION device). These results increase DSD output bandwidth by an order of magnitude over what is currently feasible with fluorescence spectroscopy.

A new enzyme-free system for colorimetric Cu2+ detection, which relies on target-triggered DNAzymes and toehold-mediated DNA strand-displacement circuits, is described. The system employs a DNAzyme designed to undergo self-cleavage in the presence of Cu2+ and release a catalyst strand that triggers a sequential toehold-mediated strand displacement reaction. This event leads to the release of a split G-quadruplex DNAzyme strand that is initially caged and inactivated by a blocker strand. A fuel strand is further incorporated for the recycling of the catalyst strand to promote another toehold-mediated strand displacement event, which consequently produces a large number of active split G-quadruplex DNAzymes. By employing this design principle, target Cu2+ was very successfully identified with a detection limit of 1.31 nm based on the distinct colorimetric signal developed by the oxidation of 2,2'-azino-bis(3-ethylbenzothiazoline)-6-sulfonic acid promoted by the peroxidase mimicking activity of the released G-quadruplex DNAzymes. Finally, the practical capability of this sensing system was very successfully demonstrated by its use to reliably determine Cu2+ in tap water.