Programming and simulating chemical reaction networks on a surface

Partial mean-field model for neurotransmission dynamics

This article addresses reaction networks in which spatial and stochastic effects are of crucial importance. For such systems, particle-based models allow us to describe all microscopic details with high accuracy. However, they suffer from computational inefficiency if particle numbers and density get too large. Alternative coarse-grained-resolution models reduce computational effort tremendously, e.g., by replacing the particle distribution by a continuous concentration field governed by reaction-diffusion PDEs. We demonstrate how models on the different resolution levels can be combined into hybrid models that seamlessly combine the best of both worlds, describing molecular species with large copy numbers by macroscopic equations with spatial resolution while keeping the spatial-stochastic particle-based resolution level for the species with low copy numbers. To this end, we introduce a simple particle-based model for the binding dynamics of ions and vesicles at the heart of the neurotransmission process. Within this framework, we derive a novel hybrid model and present results from numerical experiments which demonstrate that the hybrid model allows for an accurate approximation of the full particle-based model in realistic scenarios.

Leveraging Steric Moieties for Kinetic Control of DNA Strand Displacement Reactions

DNA strand displacement networks are a critical part of dynamic DNA nanotechnology and are proven primitives for implementing chemical reaction networks. Precise kinetic control of these networks is important for their use in a range of applications. Among the better understood and widely leveraged kinetic properties of these networks are toehold sequence, length, composition, and location. While steric hindrance has been recognized as an important factor in such systems, a clear understanding of its impact and role is lacking. Here, a systematic investigation of steric hindrance within a DNA toehold-mediated strand displacement network was performed through tracking kinetic reactions of reporter complexes with incremental concatenation of steric moieties near the toehold. Two subsets of steric moieties were tested with systematic variation of structures and reaction conditions to isolate sterics from electrostatics. Thermodynamic and coarse-grained computational modeling was performed to gain further insight into the impacts of steric hindrance. Steric factors yielded up to 3 orders of magnitude decrease in the reaction rate constant. This pronounced effect demonstrates that steric moieties can be a powerful tool for kinetic control in strand displacement networks while also being more broadly informative of DNA structural assembly in both DNA-based therapeutic and diagnostic applications that possess elements of steric hindrance through DNA functionalization with an assortment of chemistries.

A General Path-Integral Monte Carlo Method for Exact Simulations of Chemical Reaction Networks

Chemical Reaction Networks (CRNs) are stochastic many-body systems used to model real-world chemical systems through a differential Master Equation (ME); analytical solutions to these equations are only known for the simplest systems. In this paper, we construct a path-integral inspirited framework for studying CRNs. Under this scheme, the time-evolution of a reaction network can be encoded in a Hamiltonian-like operator. This operator yields a probability distribution which can be sampled, using Monte Carlo Methods, to generate exact numerical simulations of a reaction network. We recover the grand probability function used in the Gillespie Algorithm as an approximation to our probability distribution, which motivates the addition of a leapfrog correction step. To assess the utility of our method in forecasting real-world phenomena, and to contrast it with the Gillespie Algorithm, we simulated a COVID-19 epidemiological model using parameters from the United States for the Original Strain and the Alpha, Delta and Omicron Variants. By comparing the results of these simulations with official data, we found that our model closely agrees with the measured population dynamics, and given the generality of this framework it can also be applied to study the spread dynamics of other contagious diseases.

Modular reconfiguration of DNA origami assemblies using tile displacement

The power of natural evolution lies in the adaptability of biological organisms but is constrained by the time scale of genetics and reproduction. Engineeringartificial molecular machines should not only include adaptability as a core feature but also apply it within a larger design space and at a faster time scale. A lesson from engineering electromechanical robots is that modular robots can perform diverse functions through self-reconfiguration, a large-scale form of adaptation. Molecular machines made of modular, reconfigurable components may form the basis for dynamic self-reprogramming in future synthetic cells. To achieve modular reconfiguration in DNA origami assemblies, we previously developed a tile displacement mechanism in which an invader tile replaces another tile in an array with controlled kinetics. Here, we establish design principles for simultaneous reconfigurations in tile assemblies using complex invaders with distinct shapes. We present toehold and branch migration domain configurations that expand the design space of tile displacement reactions by two orders of magnitude. We demonstrate the construction of multitile invaders with fixed and variable sizes and controlled size distributions. We investigate the growth of three-dimensional (3D) barrel structures with variable cross sections and introduce a mechanism for reconfiguring them into 2D structures. Last, we show an example of a sword-shaped assembly transforming into a snake-shaped assembly, illustrating two independent tile displacement reactions occurring concurrently with minimum cross-talk. This work serves as a proof of concept that tile displacement could be a fundamental mechanism for modular reconfiguration robust to temperature and tile concentration.

A Theoretical Framework for Implementable Nucleic Acids Feedback Systems

Chemical reaction networks can be utilised as basic components for nucleic acid feedback control systems' design for Synthetic Biology application. DNA hybridisation and programmed strand-displacement reactions are effective primitives for implementation. However, the experimental validation and scale-up of nucleic acid control systems are still considerably falling behind their theoretical designs. To aid with the progress heading into experimental implementations, we provide here chemical reaction networks that represent two fundamental classes of linear controllers: integral and static negative state feedback. We reduced the complexity of the networks by finding designs with fewer reactions and chemical species, to take account of the limits of current experimental capabilities and mitigate issues pertaining to crosstalk and leakage, along with toehold sequence design. The supplied control circuits are quintessential candidates for the first experimental validations of nucleic acid controllers, since they have a number of parameters, species, and reactions small enough for viable experimentation with current technical capabilities, but still represent challenging feedback control systems. They are also well suited to further theoretical analysis to verify results on the stability, performance, and robustness of this important new class of control systems.

A localized DNA finite-state machine with temporal resolution

The identity and timing of environmental stimulus play a pivotal role in living organisms in programming their signaling networks and developing specific phenotypes. The ability to unveil history-dependent signals will advance our understanding of temporally regulated biological processes. Here, we have developed a two-input, five-state DNA finite-state machine (FSM) to sense and record the temporally ordered inputs. The spatial organization of the processing units on DNA origami enables facile modulation of the energy landscape of DNA strand displacement reactions, allowing precise control of the reactions along predefined paths for different input orders. The use of spatial constraints brings about a simple, modular design for the FSM with a minimum set of orthogonal components and confers minimized leaky reactions and fast kinetics. The FSM demonstrates the capability of sensing the temporal orders of two microRNAs, highlighting its potential for temporally resolved biosensing and smart therapeutics.

Solving 0-1 Integer Programming Problem Based on DNA Strand Displacement Reaction Network

Chemical reaction networks (CRNs) based on DNA strand displacement (DSD) can be used as an effective programming language for solving various mathematical problems. In this paper, we design three chemical reaction modules by using the DNA strand displacement reaction as the basic principle, with a weighted reaction module, sum reaction module, and threshold reaction module. These modules are used as basic elements to form chemical reaction networks that can be used to solve 0-1 integer programming problems. The problem can be solved through the three steps of weighting, sum, and threshold, and then the results of the operations can be expressed through a single-stranded DNA output with fluorescent molecules. Finally, we use biochemical experiments and Visual DSD simulation software to verify and evaluate the chemical reaction networks. The results have shown that the DSD-based chemical reaction networks constructed in this paper have good feasibility and stability.

Stability Based on PI Control of Three-Dimensional Chaotic Oscillatory System via DNA Chemical Reaction Networks

The classical proportional integral (PI) controller of SISO linear system is realized by DNA chemical reaction networks (CRNs) in the previous work. Up to now, few works have been done to realize PI controller of chaotic system through DNA CRNs. In this paper, a three-dimensional chaotic oscillatory system and a PI controller of three-dimensional chaotic oscillatory system are proposed by DNA CRNs. The CRNs of chaotic oscillatory system are made up of catalysis modules, degradation module and annihilation module then chemical reaction equations can be compiled into three-dimensional chaotic oscillatory system by the law of mass action to generate chaotic oscillatory signals. The CRNs of PI controller are designed by an integral module, a proportion module and an addition module, which can be compiled into PI controller for stabilizing chaotic oscillatory signals. The simulations of Matlab and Visual DSD are given to show our design achieving the PI control of a three-variable chaotic oscillatory system.

DNAr: An R Package to Simulate and Analyze CRN and DSD Networks

Chemical reaction networks (CRNs) have been proposed as an abstraction for molecular computing. DNA strand displacement (DSD) reactions are good candidates to realize this endeavor, since DNA strands can be wired to implement the desired dynamic behavior in a test tube. Specialists use simulators to help them design such chemical systems before experimental implementation. In this sense, we present the DNAr package, an alternative open-source tool, developed in R language, for users from multidisciplinary areas. The current version of our tool offers functions to simulate CRNs, convert a formal CRN into a DSD network, interpret results, export to Visual DSD, and create libraries. Here, we use the consensus CRN to show DNAr features and a neural network model to demonstrate scalability, simulating more than 600 chemical reactions in a few minutes.