Accelerating the Finite-Element Method for Reaction-Diffusion Simulations on GPUs with CUDA.

DNA nanotechnology offers a fine control over biochemistry by programming chemical reactions in DNA templates. Coupled to microfluidics, it has enabled DNA-based reaction-diffusion microsystems with advanced spatio-temporal dynamics such as traveling waves. The Finite Element Method (FEM) is a standard tool to simulate the physics of such systems where boundary conditions play a crucial role. However, a fine discretization in time and space is required for complex geometries (like sharp corners) and highly nonlinear chemistry. Graphical Processing Units (GPUs) are increasingly used to speed up scientific computing, but their application to accelerate simulations of reaction-diffusion in DNA nanotechnology has been little investigated. Here we study reaction-diffusion equations (a DNA-based predator-prey system) in a tortuous geometry (a maze), which was shown experimentally to generate subtle geometric effects. We solve the partial differential equations on a GPU, demonstrating a speedup of ∼100 over the same resolution on a 20 cores CPU.

Molecular robots with sensors and intelligence.

CONSPECTUS: What we can call a molecular robot is a set of molecular devices such as sensors, logic gates, and actuators integrated into a consistent system. The molecular robot is supposed to react autonomously to its environment by receiving molecular signals and making decisions by molecular computation. Building such a system has long been a dream of scientists; however, despite extensive efforts, systems having all three functions (sensing, computation, and actuation) have not been realized yet. This Account introduces an ongoing research project that focuses on the development of molecular robotics funded by MEXT (Ministry of Education, Culture, Sports, Science and Technology, Japan). This 5 year project started in July 2012 and is titled "Development of Molecular Robots Equipped with Sensors and Intelligence". The major issues in the field of molecular robotics all correspond to a feedback (i.e., plan-do-see) cycle of a robotic system. More specifically, these issues are (1) developing molecular sensors capable of handling a wide array of signals, (2) developing amplification methods of signals to drive molecular computing devices, (3) accelerating molecular computing, (4) developing actuators that are controllable by molecular computers, and (5) providing bodies of molecular robots encapsulating the above molecular devices, which implement the conformational changes and locomotion of the robots. In this Account, the latest contributions to the project are reported. There are four research teams in the project that specialize on sensing, intelligence, amoeba-like actuation, and slime-like actuation, respectively. The molecular sensor team is focusing on the development of molecular sensors that can handle a variety of signals. This team is also investigating methods to amplify signals from the molecular sensors. The molecular intelligence team is developing molecular computers and is currently focusing on a new photochemical technology for accelerating DNA-based computations. They also introduce novel computational models behind various kinds of molecular computers necessary for designing such computers. The amoeba robot team aims at constructing amoeba-like robots. The team is trying to incorporate motor proteins, including kinesin and microtubules (MTs), for use as actuators implemented in a liposomal compartment as a robot body. They are also developing a methodology to link DNA-based computation and molecular motor control. The slime robot team focuses on the development of slime-like robots. The team is evaluating various gels, including DNA gel and BZ gel, for use as actuators, as well as the body material to disperse various molecular devices in it. They also try to control the gel actuators by DNA signals coming from molecular computers.

Computer-assisted design for scaling up systems based on DNA reaction networks.

In the past few years, there have been many exciting advances in the field of molecular programming, reaching a point where implementation of non-trivial systems, such as neural networks or switchable bistable networks, is a reality. Such systems require nonlinearity, be it through signal amplification, digitalization or the generation of autonomous dynamics such as oscillations. The biochemistry of DNA systems provides such mechanisms, but assembling them in a constructive manner is still a difficult and sometimes counterintuitive process. Moreover, realistic prediction of the actual evolution of concentrations over time requires a number of side reactions, such as leaks, cross-talks or competitive interactions, to be taken into account. In this case, the design of a system targeting a given function takes much trial and error before the correct architecture can be found. To speed up this process, we have created DNA Artificial Circuits Computer-Assisted Design (DACCAD), a computer-assisted design software that supports the construction of systems for the DNA toolbox. DACCAD is ultimately aimed to design actual in vitro implementations, which is made possible by building on the experimental knowledge available on the DNA toolbox. We illustrate its effectiveness by designing various systems, from Montagne et al.'s Oligator or Padirac et al.'s bistable system to new and complex networks, including a two-bit counter or a frequency divider as well as an example of very large system encoding the game Mastermind. In the process, we highlight a variety of behaviours, such as enzymatic saturation and load effect, which would be hard to handle or even predict with a simpler model. We also show that those mechanisms, while generally seen as detrimental, can be used in a positive way, as functional part of a design. Additionally, the number of parameters included in these simulations can be large, especially in the case of complex systems. For this reason, we included the possibility to use CMA-ES, a state-of-the-art optimization algorithm that will automatically evolve parameters chosen by the user to try to match a specified behaviour. Finally, because all possible functionality cannot be captured by a single software, DACCAD includes the possibility to export a system in the synthetic biology markup language, a widely used language for describing biological reaction systems. DACCAD can be downloaded online at http://www.yannick-rondelez.com/downloads/.

Tunability of the ratio of cell states after the synthetic diversification by the diversity generator.

The autonomous generation of phenotypic diversity in embryonic cell populations can be explained by Waddington's landscape. The landscape proposes that intra- and inter-cellular interactions mediate the generation of cellular diversity. Recently, we implemented, in a population of Escherichia coli, a synthetic diversification, which is governed by inter-cellular signaling mediated by acyl-homoserine lactone (AHL). The cells with the diversity generator diversified into two distinct cell states, "high" and "low," if all of the cells started from the low state. The ratio of the states after the diversification was affected by the velocity of autonomous signal accumulation, which depends on the cell density and the AHL production rate of individual cells. The dependency of the ratio on the initial cell density is reminiscent of the community effect, which is observed in animal development and is important for ES-cell differentiation. Therefore, it is worthwhile reviewing the roles of natural animal gene networks with similar topologies to the diversity generator design. The diversity generator design will also be the basis for a tool to direct cell fates on the population level in tissue engineering. Here, we discuss the tunability of the ratio of cell states by our synthetic circuit design.

Tunable synthetic phenotypic diversification on Waddington's landscape through autonomous signaling.

Phenotypic diversification of cells is crucial for developmental and regenerative processes in multicellular organisms. The diversification concept is described as the motion of marbles rolling down Waddington's landscape, in which the number of stable states changes as development proceeds. In contrast to this simple concept, the complexity of natural biomolecular processes prevents comprehension of their design principles. We have constructed, in Escherichia coli, a synthetic circuit with just four genes, which programs cells to autonomously diversify as the motion on the landscape through cell-cell communication. The circuit design was based on the combination of a bistable toggle switch with an intercellular signaling system. The cells with the circuit diversified into two distinct cell states, "high" and "low," in vivo and in silico, when all of the cells started from the low state. The synthetic diversification was affected by not only the shape of the landscape determined by the circuit design, which includes the synthesis rate of the signaling molecule, but also the number of cells in the experiments. This cell-number dependency is reminiscent of the "community effect": The fates of developing cells are determined by their number. Our synthetic circuit could be a model system for studying diversification and differentiation in higher organisms. Prospectively, further integrations of our circuit with different cellular functions will provide unique tools for directing cell fates on the population level in tissue engineering.

Construction of a genetic AND gate under a new standard for assembly of genetic parts.

BACKGROUND: Appropriate regulation of respective gene expressions is a bottleneck for the realization of artificial biological systems inside living cells. The modification of several promoter sequences is required to achieve appropriate regulation of the systems. However, a time-consuming process is required for the insertion of an operator, a binding site of a protein for gene expression, to the gene regulatory region of a plasmid. Thus, a standardized method for integrating operator sequences to the regulatory region of a plasmid is required. RESULTS: We developed a standardized method for integrating operator sequences to the regulatory region of a plasmid and constructed a synthetic promoter that functions as a genetic AND gate. By standardizing the regulatory region of a plasmid and the operator parts, we established a platform for modular assembly of the operator parts. Moreover, by assembling two different operator parts on the regulatory region, we constructed a regulatory device with an AND gate function. CONCLUSIONS: We implemented a new standard to assemble operator parts for construction of functional genetic logic gates. The logic gates at the molecular scale have important implications for reprogramming cellular behavior.

Robust and photocontrollable DNA capsules using azobenzenes.

Various three-dimensional structures have been created on a nanometer scale using the self-assembly of DNA molecules. However, ordinary DNA structures breakdown readily because of their flexibility. In addition, it is difficult to control them by inputs from environments. Here, we construct robust and photocontrollable DNA capsules using azobenzenes. This provides a method to construct DNA structures that can survive higher temperatures and can be controlled with ultraviolet irradiation.

Coupled equilibrium model of hybridization error for the DNA microarray and tag-antitag systems.

In this work, a detailed coupled equilibrium model is presented for predicting the ensemble average probability of hybridization error per chip-hybridized input strand, providing the first ensemble average method for estimating postannealing microarray/TAT system error rates. Following a detailed presentation of the model and implementation via the software package NucleicPark, under a mismatched statistical zipper model of duplex formation, error response is simulated for both mean-energy and randomly encoded TAT systems versus temperature and input concentration. Limiting expressions and simulated model behavior indicate the occurrence of a transition in hybridization error response, from a logarithmically convex function of temperature for excess inputs (high-error behavior), to a monotonic, log-linear function of temperature for dilute inputs (low-error behavior), a novel result unpredicted by uncoupled equilibrium models. Model scaling behavior for random encodings is investigated versus system size and strand-length. Application of the model to TAT system design is also undertaken, via the in silico evolution of a high-fidelity 100-strand TAT system, with an error response improved by nine standard deviations over the performance of the mean random encoding.

DNA polymerase programmed with a hairpin DNA incorporates a multiple-instruction architecture into molecular computing.

Parallelism is one of the major advantages of molecular computation. A large number of data encoded in DNA molecules can be processed simultaneously by molecular biology techniques, although only a single set of instructions has been implemented in a solution. We have developed a computing machine, called the "whiplash" machine, which is made of DNA polymerase and a hairpin DNA. This machine simulates a finite state machine, executing its own instructions encoded in the DNA moiety, and would thus be applicable to multiple-instruction operation in a solution. In the present study, we explored the feasibility of this novel type of parallelism by applying the whiplash machine in a computation of the directed Hamiltonian path problem. The possible paths in a given graph were represented with different instruction sets, which were then implemented separately by whiplash machines in a test tube. After an autonomous operation of the machines, only the machine that implemented the instruction set corresponding to the Hamiltonian path was recovered from the tube. On the basis of the efficiency of machine operation, which was experimentally determined, 10(10) different instruction sets could be implemented simultaneously in a 1-ml solution.

Equilibrium analysis of the efficiency of an autonomous molecular computer.

In the whiplash polymerase chain reaction (WPCR), autonomous molecular computation is implemented in vitro by the recursive, self-directed polymerase extension of a mixture of DNA hairpins. Although computational efficiency is known to be reduced by a tendency for DNAs to self-inhibit by backhybridization, both the magnitude of this effect and its dependence on the reaction conditions have remained open questions. In this paper, the impact of backhybridization on WPCR efficiency is addressed by modeling the recursive extension of each strand as a Markov chain. The extension efficiency per effective polymerase-DNA encounter is then estimated within the framework of a statistical thermodynamic model. Model predictions are shown to provide close agreement with the premature halting of computation reported in a recent in vitro WPCR implementation, a particularly significant result, given that backhybridization had been discounted as the dominant error process. The scaling behavior further indicates completion times to be sufficiently long to render WPCR-based massive parallelism infeasible. A modified architecture, PNA-mediated WPCR (PWPCR) is then proposed in which the occupancy of backhybridized hairpins is reduced by targeted PNA(2)/DNA triplex formation. The efficiency of PWPCR is discussed using a modified form of the model developed for WPCR. Predictions indicate the PWPCR efficiency is sufficient to allow the implementation of autonomous molecular computation on a massive scale.