Lattice models and Monte Carlo methods for simulating DNA origami self-assembly

Prediction and Control in DNA Nanotechnology

DNA nanotechnology is a rapidly developing field that uses DNA as a building material for nanoscale structures. Key to the field's development has been the ability to accurately describe the behavior of DNA nanostructures using simulations and other modeling techniques. In this Review, we present various aspects of prediction and control in DNA nanotechnology, including the various scales of molecular simulation, statistical mechanics, kinetic modeling, continuum mechanics, and other prediction methods. We also address the current uses of artificial intelligence and machine learning in DNA nanotechnology. We discuss how experiments and modeling are synergistically combined to provide control over device behavior, allowing scientists to design molecular structures and dynamic devices with confidence that they will function as intended. Finally, we identify processes and scenarios where DNA nanotechnology lacks sufficient prediction ability and suggest possible solutions to these weak areas.

Simulations of DNA-Origami Self-Assembly Reveal Design-Dependent Nucleation Barriers

Nucleation is the rate-determining step in the kinetics of many self-assembly processes. However, the importance of nucleation in the kinetics of DNA-origami self-assembly, which involves both the binding of staple strands and the folding of the scaffold strand, is unclear. Here, using Monte Carlo simulations of a lattice model of DNA origami, we find that some, but not all, designs can have a nucleation barrier and that this barrier disappears at lower temperatures, rationalizing the success of isothermal assembly. We show that the height of the nucleation barrier depends primarily on the coaxial stacking of staples that are adjacent on the same helix, a parameter that can be modified with staple design. Creating a nucleation barrier to DNA-origami assembly could be useful in optimizing assembly times and yields, while eliminating the barrier may allow for fast molecular sensors that can assemble/disassemble without hysteresis in response to changes in the environment.

Lattice model on the rate of DNA hybridization

We develop a lattice model on the rate of hybridization of the complementary single-stranded DNAs (c-ssDNAs). Upon translational diffusion mediated collisions, c-ssDNAs interpenetrate each other to form correct (cc), incorrect (icc), and trap correct contacts (tcc) inside the reaction volume. Correct contacts are those with exact registry matches, which leads to nucleation and zipping. Incorrect contacts are the mismatch contacts which are less stable compared to tcc, which can occur in the repetitive c-ssDNAs. Although tcc possess registry match within the repeating sequences, they are incorrect contacts in the view of the whole c-ssDNAs. The nucleation rate (k_{N}) is directly proportional to the collision rate and the average number of correct contacts (〈n_{cc}〉) formed when both c-ssDNAs interpenetrate each other. Detailed lattice model simulations suggest that 〈n_{cc}〉∝L/V where L is the length of c-ssDNAs and V is the reaction volume. Further numerical analysis revealed the scaling for the average radius of gyration of c-ssDNAs (R_{g}) with their length as R_{g}∝sqrt[L]. Since the reaction space will be approximately a sphere with radius equals to 2R_{g} and V∝L^{3/2}, one obtains k_{N}∝1/sqrt[L]. When c-ssDNAs are nonrepetitive, the overall renaturation rate becomes as k_{R}∝k_{N}L, and one finally obtains k_{R}∝sqrt[L] in line with the experimental observations. When c-ssDNAs are repetitive with a complexity of c, earlier models suggested the scaling k_{R}∝sqrt[L]/c, which breaks down at c=L. This clearly suggests the existence of at least two different pathways of renaturation in the case of repetitive c-ssDNAs, viz., via incorrect contacts and trap correct contacts. The trap correct contacts can lead to the formation of partial duplexes which can keep the complementary strands in the close proximity for a prolonged timescale. This is essential for the extended 1D slithering, inchworm movements, and internal displacement mechanisms which can accelerate the searching for the correct contacts. Clearly, the extent of slithering dynamics will be inversely proportional to the complexity. When the complexity is close to the length of c-ssDNAs, the pathway via incorrect contacts will dominate. When the complexity is much less than the length of c-ssDNA, pathway via trap correct contacts would be the dominating one.

Nonequilibrium self-assembly of multiple stored targets in a dimer-based system

Nonequilibrium self-assembly can be found in various biological processes where chemical potential gradients are exploited to steer the system to a desired organized structure with a particular function. Microtubules, for example, are composed of two globular protein subunits, α-tubulin and β-tubulin, which bind together to form polar dimers that self-assemble a hollow cylinder structure in a process driven by GTPase activity. Inspired by this process, we define a generic self-assembly lattice model containing particles of two subunits, which is driven out-of-equilibrium by a dimer-favoring local driving force. Using Monte Carlo simulations, we characterize the ability of this system to restore pre-encoded target structures as a function of the initial seed size, interaction energy, chemical potential, number of target structures, and strength of the nonequilibrium drive. We demonstrate some intriguing consequences of the drive, such as a smaller critical seed and an improved target assembly stability, compared to the equilibrium scenario. Our results can expand the theoretical basis of nonequilibrium self-assembly and provide deeper understanding of how nonequilibrium driving can overcome equilibrium constraints.

Design Approaches and Computational Tools for DNA Nanostructures

Designing a structure in nanoscale with desired shape and properties has been enabled by structural DNA nanotechnology. Design strategies in this research field have evolved to interpret various aspects of increasingly more complex nanoscale assembly and to realize molecular-level functionality by exploring static to dynamic characteristics of the target structure. Computational tools have naturally been of significant interest as they are essential to achieve a fine control over both shape and physicochemical properties of the structure. Here, we review the basic design principles of structural DNA nanotechnology together with its computational analysis and design tools.

IDDRRA: A novel platform, based on Geant4-DNA to quantify DNA damage by ionizing radiation

PURPOSE

This study proposes a novel computational platform that we refer to as IDDRRA (DNA Damage Response to Ionizing RAdiation), which uses Monte Carlo (MC) simulations to score radiation induced DNA damage. MC simulations provide results of high accuracy on the interaction of radiation with matter while scoring the energy deposition based on state-of-the-art physics and chemistry models and probabilistic methods.

METHODS

The IDDRRA software is based on the Geant4-DNA toolkit together with new tools that were developed for the purpose of this study, including a new algorithm that was developed in Python for the design of the DNA molecules. New classes were developed in C++ to integrate the GUI and produce the simulation's output in text format. An algorithm was also developed to analyze the simulation's output in terms of energy deposition, Single Strand Breaks (SSB), Double Strand Breaks (DSB) and Cluster Damage Sites (CDS). Finally, a new tool was developed to implement probabilistic SSB and DSB repair models using MC techniques.

RESULTS

This article provides the first benchmarks that the user of the IDDRRA tool can use to validate the functionality of the software as well as to provide a starting point to produce different types of DNA simulations. These benchmarks incorporate different kind of particles (e-, e+, protons, electron spectrum) and DNA molecules.

CONCLUSION

We have developed the IDDRRA tool and demonstrated its use to study various aspects of the modeling and simulation of a DNA irradiation experiment. The tool is expandable and can be expanded by other users with new benchmarks and applications based on the user's needs and experience. New functionality will be added over time, including the quantification of the indirect damage.

Investigation into the mechanism and dynamics of DNA association and dissociation utilizing kinetic Monte Carlo simulations

In this work, we present a kinetic Markov state Monte Carlo model designed to complement temperature-jump (T-jump) infrared spectroscopy experiments probing the kinetics and dynamics of short DNA oligonucleotides. The model is designed to be accessible to experimental researchers in terms of both computational simplicity and expense while providing detailed insights beyond those provided by experimental methods. The model is an extension of a thermodynamic lattice model for DNA hybridization utilizing the formalism of the nucleation-zipper mechanism. Association and dissociation trajectories were generated utilizing the Gillespie algorithm and parameters determined via fitting the association and dissociation timescales to previously published experimental data. Terminal end fraying, experimentally observed following a rapid T-jump, in the sequence 5'-ATATGCATAT-3' was replicated by the model that also demonstrated that experimentally observed fast dynamics in the sequences 5'-C(AT)_nG-3', where n = 2-6, were also due to terminal end fraying. The dominant association pathways, isolated by transition pathway theory, showed two primary motifs: initiating at or next to a G:C base pair, which is enthalpically favorable and related to the increased strength of G:C base pairs, and initiating in the center of the sequence, which is entropically favorable and related to minimizing the penalty associated with the decrease in configurational entropy due to hybridization.

Reconfigurable T-junction DNA Origami

DNA self-assembly allows the construction of nanometre-scale structures and devices. Structures with thousands of unique components are routinely assembled in good yield. Experimental progress has been rapid, based largely on empirical design rules. Herein, we demonstrate a DNA origami technique designed as a model system with which to explore the mechanism of assembly. The origami fold is controlled through single-stranded loops embedded in a double-stranded DNA template and is programmed by a set of double-stranded linkers that specify pairwise interactions between loop sequences. Assembly is via T-junctions formed by hybridization of single-stranded overhangs on the linkers with the loops. The sequence of loops on the template and the set of interaction rules embodied in the linkers can be reconfigured with ease. We show that a set of just two interaction rules can be used to assemble simple T-junction origami motifs and that assembly can be performed at room temperature.

Numerical calculation of free-energy barriers for entangled polymer nucleation

The crystallization of entangled polymers from their melt is investigated using computer simulation with a coarse-grained model. Using hybrid Monte Carlo simulations enables us to probe the behavior of long polymer chains. We identify solid-like beads with a centrosymmetry local order parameter and compute the nucleation free-energy barrier at relatively high supercooling with adaptive-bias windowed umbrella sampling. Our results demonstrate that the critical nucleus sizes and the heights of free-energy barriers do not significantly depend on the molecular weight of the polymer; however, the nucleation rate decreases with the increase in molecular weight. Moreover, an analysis of the composition of the critical nucleus suggests that intra-molecular growth of the nucleated cluster does not contribute significantly to crystallization for this system.

Ionizing Radiation and Complex DNA Damage: Quantifying the Radiobiological Damage Using Monte Carlo Simulations

Ionizing radiation is a common tool in medical procedures. Monte Carlo (MC) techniques are widely used when dosimetry is the matter of investigation. The scientific community has invested, over the last 20 years, a lot of effort into improving the knowledge of radiation biology. The present article aims to summarize the understanding of the field of DNA damage response (DDR) to ionizing radiation by providing an overview on MC simulation studies that try to explain several aspects of radiation biology. The need for accurate techniques for the quantification of DNA damage is crucial, as it becomes a clinical need to evaluate the outcome of various applications including both low- and high-energy radiation medical procedures. Understanding DNA repair processes would improve radiation therapy procedures. Monte Carlo simulations are a promising tool in radiobiology studies, as there are clear prospects for more advanced tools that could be used in multidisciplinary studies, in the fields of physics, medicine, biology and chemistry. Still, lot of effort is needed to evolve MC simulation tools and apply them in multiscale studies starting from small DNA segments and reaching a population of cells.