Healing assessment of tile sets for error tolerance in DNA self-assembly

An assessment of the effectiveness of healing for error tolerance in DNA self-assembly tile sets for algorithmic/nano-manufacturing applications is presented. Initially, the conditions for correct binding of a tile to an existing aggregate are analysed using a Markovian approach; based on this analysis, it is proved that correct aggregation (as identified with a so-called ideal tile set) is not always met for the existing tile sets for nano-manufacturing. A metric for assessing tile sets for healing by utilising punctures is proposed. Tile sets are investigated and assessed with respect to features such as error (mismatched tile) movement, punctured area and bond types. Subsequently, it is shown that the proposed metric can comprehensively assess the healing effectiveness of a puncture type for a tile set and its capability to attain error tolerance for the desired pattern. Extensive simulation results are provided.     

Error tolerant DNA self-assembly using (2k - 1)x(2k - 1) snake tile sets.

DNA self-assembly has been advocated as a possible technique for bottom-up manufacturing of scaffolds for computing systems in the nanoscale region. However, self-assembly is affected by different types of errors (such as growth and facet roughening) that severely limit its applicability. Different methods for reducing the error rate of self-assembly using tiles as basic elements have been proposed. A particularly effective method relies on snake tile sets that utilize a square block of even size (i.e., 2k x 2k tiles, k = 2, 3, . . .). In this paper, an odd-sized square block [i.e., (2k - 1) x (2k - 1)] is proposed as basis for the snake tile set. Compared with other tile sets, the proposed snake tile sets achieve a considerable reduction in error rate at a very modest reduction in growth rate. Growth and facet roughening errors are considered and analytical results are presented to prove the reduction in error rate compared with an even-sized snake tile set. Simulation results are provided.     

Error Tolerant DNA Self-Assembly Using ( $hbox{2}k-hbox{1}$)$times$( $hbox{2}k-hbox{1}$) Snake Tile Sets

DNA self-assembly has been advocated as a possible technique for bottom-up manufacturing of scaffolds for computing systems in the nanoscale region. However, self-assembly is affected by different types of errors (such as growth and facet roughening) that severely limit its applicability. Different methods for reducing the error rate of self-assembly using tiles as basic elements have been proposed. A particularly effective method relies on snake tile sets that utilize a square block of even size (i.e., 2k times 2k tiles, k = 2, 3,.. .). In this paper, an odd-sized square block [i.e., (2k -1) times (2k - 1)] is proposed as basis for the snake tile set. Compared with other tile sets, the proposed snake tile sets achieve a considerable reduction in error rate at a very modest reduction in growth rate. Growth and facet roughening errors are considered and analytical results are presented to prove the reduction in error rate compared with an even-sized snake tile set. Simulation results are provided.     

Reducing facet nucleation during algorithmic self-assembly

Algorithmic self-assembly, a generalization of crystal growth, has been proposed as a mechanism for bottom-up fabrication of complex nanostructures and autonomous DNA computation. In principle, growth can be programmed by designing a set of molecular tiles with binding interactions that enforce assembly rules. In practice, however, errors during assembly cause undesired products, drastically reducing yields. Here we provide experimental evidence that assembly can be made more robust to errors by adding redundant tiles that "proofread" assembly. We construct DNA tile sets for two methods, uniform and snaked proofreading. While both tile sets are predicted to reduce errors during growth, the snaked proofreading tile set is also designed to reduce nucleation errors on crystal facets. Using atomic force microscopy to image growth of proofreading tiles on ribbon-like crystals presenting long facets, we show that under the physical conditions we studied the rate of facet nucleation is 4-fold smaller for snaked proofreading tile sets than for uniform proofreading tile sets.     

Optimum coding framework for error detection in the self-assembly of the Sierpinski triangle

This study presents a coding framework by which DNA self-assembly can be analysed for error detection. The proposed framework relies on coding and mapping functions that allow establishing the correctness of bonding each tile based on the codes of the tiles along a so-called traversal path. This method is different from the one that relies on comparing the pattern to be assembled (as defined by the tile set) and the current aggregate (as resulting from previously assembled tiles). As a widely used pattern and instantiation of this process, the Sierpinski triangle self-assembly is analysed in detail. The Sierpinski triangle is therefore utilised as an example to show the application of the proposed method. Different properties are proposed and its optimum coding is achieved for error detection. Simulation results are presented.     

Precise Simulation Model for DNA Tile Self-Assembly

Self-assembling DNA complexes have been intensively studied in recent years aiming to achieve bottom-up construction of nanoscale objects. Among them a DNA complex called the DNA tile is known for its high programmability. DNA tiles can form 2-D crystals with programmable patterns via self-assembly. In order to create a wide range of complex objects by algorithmic self-assembly, we need a methodology to predict its behavior. To estimate the behavior, we can use thermodynamic simulations based on the Monte Carlo method. However, the previous simulation model assumed some simplified conditions and was not able to adequately explain the results of crystal growth experiments. Here, we propose the realistic tile assembly model, in which we are able to simulate the detailed conditions of the experimental protocols. By this model, the results of experiments (e.g., error rates, growth rate, and the formation and melting temperatures) are reproduced with high reliability. We think this model is useful to predict the behavior of DNA self-assembly and to design various types of DNA complexes.      

Toward reliable algorithmic self-assembly of DNA tiles: a fixed-width cellular automaton pattern

Bottom-up fabrication of nanoscale structures relies on chemical processes to direct self-assembly. The complexity, precision, and yield achievable by a one-pot reaction are limited by our ability to encode assembly instructions into the molecules themselves. Nucleic acids provide a platform for investigating these issues, as molecular structure and intramolecular interactions can encode growth rules. Here, we use DNA tiles and DNA origami to grow crystals containing a cellular automaton pattern. In a one-pot annealing reaction, 250 DNA strands first assemble into a set of 10 free tile types and a seed structure, then the free tiles grow algorithmically from the seed according to the automaton rules. In our experiments, crystals grew to approximately 300 nm long, containing approximately 300 tiles with an initial assembly error rate of approximately 1.4% per tile. This work provides evidence that programmable molecular self-assembly may be sufficient to create a wide range of complex objects in one-pot reactions.     

Two computational primitives for algorithmic self-assembly: copying and counting

Copying and counting are useful primitive operations for computation and construction. We have made DNA crystals that copy and crystals that count as they grow. For counting, 16 oligonucleotides assemble into four DNA Wang tiles that subsequently crystallize on a polymeric nucleating scaffold strand, arranging themselves in a binary counting pattern that could serve as a template for a molecular electronic demultiplexing circuit. Although the yield of counting crystals is low, and per-tile error rates in such crystals is roughly 10%, this work demonstrates the potential of algorithmic self-assembly to create complex nanoscale patterns of technological interest. A subset of the tiles for counting form information-bearing DNA tubes that copy bit strings from layer to layer along their length.     

DNA nanotube formation based on normal mode analysis

Ever since its inception, a popular DNA motif called the cross tile has been recognized to self-assemble into addressable 2D templates consisting of periodic square cavities. Although this may be conceptually correct, in reality certain types of cross tiles can only form planar lattices if adjacent tiles are designed to bind in a corrugated manner, in the absence of which they roll up to form 3D nanotube structures. Here we present a theoretical study on why uncorrugated cross tiles self-assemble into counterintuitive 3D nanotube structures and not planar 2D lattices. Coarse-grained normal mode analysis of single and multiple cross tiles within the elastic network model was carried out to expound the vibration modes of the systems. While both single and multiple cross tile simulations produce results conducive to tube formations, the dominant modes of a unit of four cross tiles (one square cavity), termed a quadruplet, fully reflect the symmetries of the actual nanotubes found in experiments and firmly endorse circularization of an array of cross tiles.     

Finite element analysis of tile-reinforced composite structural armor subjected to bending loads

Composite structural armor (CSA) is a multi-functional structure that provides ballistic protection, stiffness and strength at minimum weight. It consists of a multi-layered architecture of polymer composites, rubber and ceramic tiles, stacked in a precise manner to obtain optimal ballistic performance. In the present work, the finite element method is used to conduct a detailed analysis of the mechanisms of load transfer and deformation of CSA subjected to bending loads. The results from two modeling approaches (three-dimensional and two-dimensional simulations) are compared to assess the accuracy of the computationally efficient two-dimensional model. The calculated deflections and surfaces strains from both models are found to agree very well with experimental results. The stress transfer between the layers is further analyzed using the two-dimensional model and the resulting through-thickness strain and stress distributions are discussed. It is found that the deformation of this multi-layered construction is complex and dependent upon the mechanism of stress transfer between the outer surface layer and the ceramic tiles. The effect on non-linear behavior of the constituent materials is investigated. The gap filled with polymer that separates adjacent ceramic tiles is shown to significantly influence the stiffness and strength of CSA. It is found that the plastic deformation of the resin corresponds to the onset of non-linear structural response.     

Polarizability of G4-DNA observed by electrostatic force microscopy measurements

G4-DNA, a quadruple helical motif of stacked guanine tetrads, is stiffer and more resistant to surface forces than double-stranded DNA (dsDNA), yet it enables self-assembly. Therefore, it is more likely to enable charge transport upon deposition on hard supports. We report clear evidence of polarizability of long G4-DNA molecules measured by electrostatic force microscopy, while coadsorbed dsDNA molecules on mica are electrically silent. This is another sign that G4-DNA is potentially better than dsDNA as a conducting molecular wire.     

Robustness analysis of radial base function and multi-layered feed-forward neural network models

In this paper, two popular types of neural network models (radial base function (RBF) and multi-layered feed-forward (MLF) networks) trained by the generalized delta rule, are tested on their robustness to random errors in input space. A method is proposed to estimate the sensitivity of network outputs to the amplitude of random errors in the input space, sampled from known normal distributions. An additional parameter can be extracted to give a general indication about the bias on the network predictions. The modelling performances of MLF and RBF neural networks have been tested on a variety of simulated function approximation problems. Since the results of the proposed validation method strongly depend on the configuration of the networks and the data used, little can be said about robustness as an intrinsic quality of the neural network model. However, given a data set where ‘pure’ errors from input and output space are specified, the method can be applied to select a neural network model which optimally approximates the nonlinear relations between objects in input and output space. The proposed method has been applied to a nonlinear modelling problem from industrial chemical practice. Since MLF and RBF networks are based on different concepts from biological neural processes, a brief theoretical introduction is given.     

NMR studies of artificial double-crossover DNA tiles

This report documents the design and characterization of DNA molecular nanoarchitectures consisting of artificial double crossover DNA tiles with different geometry and chemistry. The Structural characterization of the unit tiles, including normal, biotinylated and hairpin loop structures, are morphologically studied by atomic force microscopy. The specific proton resonance of the individual tiles and their intra/inter nucleotide relationships are verified by proton nuclear magnetic resonance spectroscopy and 2-dimensional correlation spectral studies, respectively. Significant up-field and down-field shifts in the resonance signals of the individual residues at various temperatures are discussed. The results suggest that with artificially designed DNA tiles it is feasible to obtain structural information of the relative base sequences. These tiles were later fabricated into 2D DNA lattice structures for specific applications such as protein arrangement by biotinylated bulged loops or pattern generation using a hairpin structure.     

Intrinsic DNA curvature of double-crossover tiles

A theoretical model which takes into account the structural distortion of double-crossover DNA tiles has been studied to investigate its effect on lattice formation sizes. It has been found that a single vector appropriately describes the curvature of the tiles, of which a higher magnitude hinders lattice growth. In conjunction with these calculations, normal mode analysis reveals that tiles with relative higher frequencies have an analogous effect. All the theoretical results are shown to be in good agreement with experimental data.     

Nanolattices of Switchable DNA‐Based Motors

Miniaturization is an important aspect of device fabrication. Despite the advancements of modern top‐down approaches, scaling‐down to the sub‐nanometer size is still a challenge. As an alternative, bottom‐up approaches, such as the use of DNA as an engineering material, are therefore emerging, allowing control of matter at the single‐molecule level. A DNA‐based self‐assembly method for the construction of switchable DNA devices is descrbied here based on G‐quadruplex moieties, which are patterned on quasi‐planar DNA arrays with nanoscale precision. The reversible switching of the devices is triggered by addition of DNA sequences (‘fuels’) and translated into linear extension/contractile movements. The conformational change of the devices was visualized by atomic force microscopy and FRET spectroscopy. Steady state fluorescence spectroscopy indicated that scaffolding of the G4 motors to either individual tiles or extended superlattices had no significant impact on the switching and optical performance of the system. However, time‐resolved spectroscopy revealed that ordering in the microstructural environment enhances the fraction of molecules subject to FRET. Altogether, our study confirms that DNA superstructures are well‐suited scaffolds for accommodation of mechanically switchable units and thus opens the door to the development of more sophisticated nanomechanical devices.     

A Virtual Puncture Surgery System Based on Multi-Layer Soft Tissue and Force Mesh

Puncture is a common operation in surgery, which involves all kinds of tissue materials with different geometry and mechanical properties. As a new cross-disciplinary research area, Virtual Surgery (VS) makes simulation of soft tissue in puncture operation possible in virtual environment. In this paper, we introduce a VS-based puncture system composed by three-layer soft tissue, simulated with spherical harmonic function (SHF), which is covered with a force mesh, constructed by mass spring model (MSM). The two models are combined together with a parameter of SHF named surface radius, which provides MSM with real-time deformation data needed in force calculation. Meanwhile, force calculation, divided into the surface spring force and the puncture damping force, makes the force presentation better accord to the corresponding tissue characteristics. Moreover, a deformation resumption algorithm is leveraged to simulate the resumption phenomenon of the broken tissue surface. In evaluation experiment, several residents are invited to grades our model along with other four mainstream soft tissue models in terms of 7 different indicators. After the evaluation, the scores are analyzed by a comprehensive weighted grading method. Experiment results show that the proposed model has better performance during puncture operation than other models, and can well simulate surface resumption phenomenon when tissue surface is broken.     

A Cell Method Stress Analysis in Thin Floor Tiles Subjected to Temperature Variation

The Cell Method is applied in order to model the debonding mechanism in ceramic floor tiles subjected to positive thermal variation. The causes of thermal debonding, very usual in radiant heat floors, have not been fully clarified at the moment. There exist only a few simplified analytical approaches that assimilate this problem to an eccentric tile compression, but these approaches introduce axial forces that, in reality, do not exist. In our work we have abandoned the simplified closed form solution in favor of a numerical solution, which models the interaction between tiles and sub-base more realistically, when the positive thermal variation increases the volume of the sub-base. The thermal problem has been approached as a contact problem in a composite structure. In particular, the kinematic and equilibrium conditions have been imposed at the interface between lower part, which is the sub-base, and the upper part, which is composed by the adhesive, the tiles, and the grouting between the tiles. The failure condition has been studied in the Mohr-Coulomb plane by using the Leon criterion, a unifying criterion that combines the shear stress with traction and compression. Therefore, we employed a unique failure criterion both for the nodes at the interface between sub-base and adhesive (which undergo a shear/tensile failure or a shear failure) and the nodes at the interface between tiles and grouting (which undergo a tensile failure). This allowed us to model the tile debonding both in the horizontal and in the vertical interfaces, while previous FEM codes treated the tile debonding only on the horizontal interfaces. The numerical analyses were performed in parametric modality, by varying the geometric and mechanical characteristics of the model. Particular attention was devoted to the modeling of thin tiles, a new type of ceramic tiles, for which there are no yet consensus standards.     

Likelihood-based inference for a frailty-copula model based on competing risks failure time data

A competing risks phenomenon arises in industrial life tests, where multiple types of failure determine the working duration of a unit. To model dependence among marginal failure times, copula models and frailty models have been developed for competing risks failure time data. In this paper, we propose a frailty-copula model, which is a hybrid model including both a frailty term (for heterogeneity among units) and a copula function (for dependence between failure times). We focus on models that are useful to investigate the reliability of marginal failure times that are Weibull distributed. Furthermore, we develop likelihood-based inference methods based on competing risks data, including accelerated failure time models. We also develop a model-diagnostic procedure to assess the adequacy of the proposed model to a given dataset. Simulations are conducted to demonstrate the operational performance of the proposed methods, and a real dataset is analyzed for illustration. We make an R package “gammaGumbel” such that users can apply the suggested statistical methods to their data.     

Implicit constitutive modelling for viscoplasticity using neural networks

Up to now, a number of models have been proposed and discussed to describe a wide range of inelastic behaviours of materials. The fatal problem of using such models is however the existence of model errors, and the problem remains inevitably as far as a material model is written explicitly. In this paper, the authors define the implicit constitutive model and propose an implicit viscoplastic constitutive model using neural networks. In their modelling, inelastic material behaviours are generalized in a state-space representation and the state-space form is constructed by a neural network using input–output data sets. A technique to extract the input–output data from experimental data is also described. The proposed model was first generated from pseudo-experimental data created by one of the widely used constitutive models and was found to replace the model well. Then, having been tested with the actual experimental data, the proposed model resulted in a negligible amount of model errors indicating its superiority to all the existing explicit models in accuracy. © 1998 John Wiley & Sons, Ltd.     

A comprehensive Bayesian approach for model updating and quantification of modeling errors

This paper presents a comprehensive Bayesian approach for structural model updating which accounts for errors of different kinds, including measurement noise, nonlinear distortions stemming from the linearization of the model, and modeling errors due to the limited predictability of the latter. In particular, this allows the computation of any type of statistics on the updated parameters, such as joint or marginal probability density functions, or confidence intervals. The present work includes four main contributions that make the Bayesian updating approach feasible with general numerical models: (1) the proposal of a specific experimental protocol based on multisine excitations to accurately assess measurement errors in the frequency domain; (2) two possible strategies to represent the modeling error as additional random variables to be inferred jointly with the model parameters; (3) the introduction of a polynomial chaos expansion that provides a surrogate mapping between the probability spaces of the prior random variables and the model modal parameters; (4) the use of an evolutionary Monte Carlo Markov Chain which, in conjunction with the polynomial chaos expansion, can sample the posterior probability density function of the updated parameters at a very reasonable cost. The proposed approach is validated by numerical and experimental examples.