A domain-level DNA strand displacement reaction enumerator allowing arbitrary non-pseudoknotted secondary structures

A geometric framework for reaction enumeration in computational nucleic acid devices

Cascades of DNA strand displacement reactions enable the design of potentially large circuits with complex behaviour. Computational modelling of such systems is desirable to enable rapid design and analysis. In previous work, the expressive power of graph theory was used to enumerate reactions implementing strand displacement across a wide range of complex structures. However, coping with the rich variety of possible graph-based structures required enumeration rules with complicated side-conditions. This paper presents an alternative approach to tackle the problem of enumerating reactions at domain level involving complex structures by integrating with a geometric constraint solving algorithm. The rule sets from previous work are simplified by replacing side-conditions with a general check on the geometric plausibility of structures generated by the enumeration algorithm. This produces a highly general geometric framework for reaction enumeration. Here, we instantiate this framework to solve geometric constraints by a structure sampling approach in which we randomly generate sets of coordinates and check whether they satisfy all the constraints. We demonstrate this system by applying it to examples from the literature where molecular geometry plays an important role, including DNA hairpin and remote toehold reactions. This work therefore enables integration of reaction enumeration and structural modelling.

Design and Simulation of a Multilayer Chemical Neural Network That Learns via Backpropagation

The design and implementation of adaptive chemical reaction networks, capable of adjusting their behavior over time in response to experience, is a key goal for the fields of molecular computing and DNA nanotechnology. Mainstream machine learning research offers powerful tools for implementing learning behavior that could one day be realized in a wet chemistry system. Here we develop an abstract chemical reaction network model that implements the backpropagation learning algorithm for a feedforward neural network whose nodes employ the nonlinear "leaky rectified linear unit" transfer function. Our network directly implements the mathematics behind this well-studied learning algorithm, and we demonstrate its capabilities by training the system to learn a linearly inseparable decision surface, specifically, the XOR logic function. We show that this simulation quantitatively follows the definition of the underlying algorithm. To implement this system, we also report ProBioSim, a simulator that enables arbitrary training protocols for simulated chemical reaction networks to be straightforwardly defined using constructs from the host programming language. This work thus provides new insight into the capabilities of learning chemical reaction networks and also develops new computational tools to simulate their behavior, which could be applied in the design and implementations of adaptive artificial life.

DNA strand displacement based computational systems and their applications

DNA computing has become the focus of computing research due to its excellent parallel processing capability, data storage capacity, and low energy consumption characteristics. DNA computational units can be precisely programmed through the sequence specificity and base pair principle. Then, computational units can be cascaded and integrated to form large DNA computing systems. Among them, DNA strand displacement (DSD) is the simplest but most efficient method for constructing DNA computing systems. The inputs and outputs of DSD are signal strands that can be transferred to the next unit. DSD has been used to construct logic gates, integrated circuits, artificial neural networks, etc. This review introduced the recent development of DSD-based computational systems and their applications. Some DSD-related tools and issues are also discussed.

Catalyst-Based Biomolecular Logic Gates

Regulatory processes in biology can be re-conceptualized in terms of logic gates, analogous to those in computer science. Frequently, biological systems need to respond to multiple, sometimes conflicting, inputs to provide the correct output. The language of logic gates can then be used to model complex signal transduction and metabolic processes. Advances in synthetic biology in turn can be used to construct new logic gates, which find a variety of biotechnology applications including in the production of high value chemicals, biosensing, and drug delivery. In this review, we focus on advances in the construction of logic gates that take advantage of biological catalysts, including both protein-based and nucleic acid-based enzymes. These catalyst-based biomolecular logic gates can read a variety of molecular inputs and provide chemical, optical, and electrical outputs, allowing them to interface with other types of biomolecular logic gates or even extend to inorganic systems. Continued advances in molecular modeling and engineering will facilitate the construction of new logic gates, further expanding the utility of biomolecular computing.

Programming Molecular Systems To Emulate a Learning Spiking Neuron

Hebbian theory seeks to explain how the neurons in the brain adapt to stimuli to enable learning. An interesting feature of Hebbian learning is that it is an unsupervised method and, as such, does not require feedback, making it suitable in contexts where systems have to learn autonomously. This paper explores how molecular systems can be designed to show such protointelligent behaviors and proposes the first chemical reaction network (CRN) that can exhibit autonomous Hebbian learning across arbitrarily many input channels. The system emulates a spiking neuron, and we demonstrate that it can learn statistical biases of incoming inputs. The basic CRN is a minimal, thermodynamically plausible set of microreversible chemical equations that can be analyzed with respect to their energy requirements. However, to explore how such chemical systems might be engineered de novo, we also propose an extended version based on enzyme-driven compartmentalized reactions. Finally, we show how a purely DNA system, built upon the paradigm of DNA strand displacement, can realize neuronal dynamics. Our analysis provides a compelling blueprint for exploring autonomous learning in biological settings, bringing us closer to realizing real synthetic biological intelligence.

Automated Leak Analysis of Nucleic Acid Circuits

Nucleic acids are a powerful engineering material that can be used to implement a broad range of computational circuits at the nanoscale, with potential applications in high-precision biosensing, diagnostics, and therapeutics. However, nucleic acid circuits are prone to leaks, which result from unintended displacement interactions between nucleic acid strands. Such leaks can grow combinatorially with circuit size, are challenging to mitigate, and can significantly compromise circuit behavior. While several techniques have been proposed to partially mitigate leaks, computational methods for designing new leak mitigation strategies and comparing their effectiveness on circuit behavior are limited. Here we present a general method for the automated leak analysis of nucleic acid circuits, referred to as DSD Leaks. Our method extends the logic programming functionality of the Visual DSD language, developed for the design and analysis of nucleic acid circuits, with predicates for leak generation, a leak reaction enumeration algorithm, and predicates to exclude low probability leak reactions. We use our method to identify the critical leak reactions affecting the performance of control circuits, and to analyze leak mitigation strategies by automatically generating leak reactions. Finally, we design new control circuits with substantially reduced leakage including a sophisticated proportional-integral controller circuit, which can in turn serve as building blocks for future circuits. By integrating our method within an open-source nucleic acid circuit design tool, we enable the leak analysis of a broad range of circuits, as an important step toward facilitating robust and scalable nucleic acid circuit design.

Chemical Reaction Networks’ Programming for Solving Equations

The computational ability of the chemical reaction networks (CRNs) using DNA as the substrate has been verified previously. To solve more complex computational problems and perform the computational steps as expected, the practical design of the basic modules of calculation and the steps in the reactions have become the basic requirements for biomolecular computing. This paper presents a method for solving nonlinear equations in the CRNs with DNA as the substrate. We used the basic calculation module of the CRNs with a gateless structure to design discrete and analog algorithms and realized the nonlinear equations that could not be solved in the previous work, such as exponential, logarithmic, and simple triangle equations. The solution of the equation uses the transformation method, Taylor expansion, and Newton iteration method, and the simulation verified this through examples. We used and improved the basic calculation module of the CRN++ programming language, optimized the error in the basic module, and analyzed the error’s variation over time.

BioCRNpyler: Compiling chemical reaction networks from biomolecular parts in diverse contexts

Biochemical interactions in systems and synthetic biology are often modeled with chemical reaction networks (CRNs). CRNs provide a principled modeling environment capable of expressing a huge range of biochemical processes. In this paper, we present a software toolbox, written in Python, that compiles high-level design specifications represented using a modular library of biochemical parts, mechanisms, and contexts to CRN implementations. This compilation process offers four advantages. First, the building of the actual CRN representation is automatic and outputs Systems Biology Markup Language (SBML) models compatible with numerous simulators. Second, a library of modular biochemical components allows for different architectures and implementations of biochemical circuits to be represented succinctly with design choices propagated throughout the underlying CRN automatically. This prevents the often occurring mismatch between high-level designs and model dynamics. Third, high-level design specification can be embedded into diverse biomolecular environments, such as cell-free extracts and in vivo milieus. Finally, our software toolbox has a parameter database, which allows users to rapidly prototype large models using very few parameters which can be customized later. By using BioCRNpyler, users ranging from expert modelers to novice script-writers can easily build, manage, and explore sophisticated biochemical models using diverse biochemical implementations, environments, and modeling assumptions.

This paper describes a new software package BioCRNpyler (pronounced “Biocompiler”) designed to support rapid development and exploration of mathematical models of biochemical networks and circuits by computational biologists, systems biologists, and synthetic biologists. BioCRNpyler allows its users to generate large complex models using very few lines of code in a way that is modular. To do this, BioCRNpyler uses a powerful new representation of biochemical circuits which defines their parts, underlying biochemical mechanisms, and chemical context independently. BioCRNpyler was developed as a Python scripting language designed to be accessible to beginning users as well as easily extendable and customizable for advanced users. Ultimately, we see Biocrnpyler being used to accelerate computer automated design of biochemical circuits and model driven hypothesis generation in biology.

Pairing nanoarchitectonics of oligodeoxyribonucleotides with complex diversity: concatemers and self-limited complexes

The development of approaches to the design of two- and three-dimensional self-assembled DNA-based nanostructures with a controlled shape and size is an essential task for applied nanotechnology, therapy, biosensing, and bioimaging. We conducted a comprehensive study on the formation of various complexes from a pair of oligonucleotides with two transposed complementary blocks that can be linked through a nucleotide or non-nucleotide linker. A methodology is proposed to prove the formation of a self-limited complex and to determine its molecularity. It is based on the "opening" of a self-limited complex with an oligonucleotide that effectively binds to a duplex-forming block. The complexes assembled from a pair of oligonucleotides with different block length and different linker sizes and types were investigated by theoretical analysis, several experimental methods (a gel shift assay, atomic force microscopy, and ultraviolet melting analysis), and molecular dynamics simulations. The results showed a variety of complexes formed by only a pair of oligonucleotides. Self-limited associates, concatemer complexes, or mixtures thereof can arise if we change the length of a duplex and loop-forming blocks in oligonucleotides or via introduction of overhangs and chemical modifications. We postulated basic principles of rational design of native self-limited DNA complexes of desired structure, shape, and molecularity. Our foundation makes self-limited complexes useful tools for nanotechnology, biological studies, and therapeutics.

Automated exploration of DNA-based structure self-assembly networks

Finding DNA sequences capable of folding into specific nanostructures is a hard problem, as it involves very large search spaces and complex nonlinear dynamics. Typical methods to solve it aim to reduce the search space by minimizing unwanted interactions through restrictions on the design (e.g. staples in DNA origami or voxel-based designs in DNA Bricks). Here, we present a novel methodology that aims to reduce this search space by identifying the relevant properties of a given assembly system to the emergence of various families of structures (e.g. simple structures, polymers, branched structures). For a given set of DNA strands, our approach automatically finds chemical reaction networks (CRNs) that generate sets of structures exhibiting ranges of specific user-specified properties, such as length and type of structures or their frequency of occurrence. For each set, we enumerate the possible DNA structures that can be generated through domain-level interactions, identify the most prevalent structures, find the best-performing sequence sets to the emergence of target structures, and assess CRNs' robustness to the removal of reaction pathways. Our results suggest a connection between the characteristics of DNA strands and the distribution of generated structure families.

Encryption Algorithm Based on DNA Strand Displacement and DNA Sequence Operation

DNA strand displacement is introduced in this study and used to construct an analog DNA strand displacement chaotic system based on six reaction modules in nanoscale size. The DNA strand displacement circuit is employed in encryption as a chaotic generator to produce chaotic sequences. In the encryption algorithm, we convert chaotic sequences to binary ones by comparing the concentration of signal DNA strand. Simulation results show that the encryption scheme is sensitive to the keys, and key space is large enough to resist the brute-force attacks, furthermore algorithm has a high capacity to resist statistic attack. Based on robustness analysis, our proposed encryption scheme is robust to the DNA strand displacement reaction rate control, noise and concentration detection to a certain extent.

Domain-Specific Programming Languages for Computational Nucleic Acid Systems

The construction of models of system behavior is of great importance throughout science and engineering. In bioengineering and bionanotechnology, these often take the form of dynamic models that specify the evolution of different species over time. To ensure that scientific observations and conclusions are consistent and that systems can be reliably engineered on the basis of model predictions, it is important that models of biomolecular systems can be constructed in a reliable, principled, and efficient manner. This review focuses on efforts to address this need by using domain-specific programming languages as the basis for custom design tools for researchers working on computational nucleic acid devices, where a domain-specific language is simply a programming language tailored to a particular application domain. The underlying thesis of our review is that there is a continuum of practical implementation strategies for computational nucleic acid systems, which can all benefit from appropriate domain-specific languages and software design tools. We emphasize the need for specialized yet flexible tools that can be realized using domain-specific languages that compile to more general-purpose representations.