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Register a new userLAMMPS Framework for Dynamic Bonding and an Application Modeling DNA
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Authors
Carsten Svaneborg
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We have extended the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) to support directional bonds and dynamic bonding. The framework supports stochastic formation of new bonds, breakage of existing bonds, and conversion between bond types. Bond formation can be controlled to limit the maximal functionality of a bead with respect to various bond types. Concomitant with the bond dynamics, angular and dihedral interactions are dynamically introduced between newly connected triplets and quartets of beads, where the interaction type is determined from the local pattern of bead and bond types. When breaking bonds, all angular and dihedral interactions involving broken bonds are removed. The framework allows chemical reactions to be modeled, and use it to simulate a simplistic, coarse-grained DNA model. The resulting DNA dynamics illustrate the power of the present framework.
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During the last decade coarse-grained nucleotide models have emerged that allow us to DNA and RNA on unprecedented time and length scales. Among them is oxDNA, a coarse-grained, sequence-specific model that captures the hybridisation transition of DNA and many structural properties of single- and double-stranded DNA. oxDNA was previously only available as standalone software, but has now been implemented into the popular LAMMPS molecular dynamics code. This article describes the new implementation and analyses its parallel performance. Practical applications are presented that focus on single-stranded DNA, an area of research which has been so far under-investigated. The LAMMPS implementation of oxDNA lowers the entry barrier for using the oxDNA model significantly, facilitates future code development and interfacing with existing LAMMPS functionality as well as other coarse-grained and atomistic DNA models.
In recent years significant attention has been attracted to proposals which utilize DNA for nanotechnological applications. Potential applications of these ideas range from the programmable self-assembly of colloidal crystals, to biosensors and nanoparticle based drug delivery platforms. In Chapter I we introduce the system, which generically consists of colloidal particles functionalized with specially designed DNA markers. The sequence of bases on the DNA markers determines the particle type. Due to the hybridization between complementary single-stranded DNA, specific, type-dependent interactions can be introduced between particles by choosing the appropriate DNA marker sequences. In Chapter II we develop a statistical mechanical description of the aggregation and melting behavior of particles with DNA-mediated interactions. In Chapter III a model is proposed to describe the dynamical departure and diffusion of particles which form reversible key-lock connections. In Chapter IV we propose a method to self-assemble nanoparticle clusters using DNA scaffolds. A natural extension is discussed in Chapter V, the programmable self-assembly of nanoparticle clusters where the desired cluster geometry is encoded using DNA-mediated interactions. In Chapter VI we consider a nanoparticle based drug delivery platform for targeted, cell specific chemotherapy. In Chapter VII we present prospects for future research: the connection between DNA-mediated colloidal crystallization and jamming, and the inverse problem in self-assembly.
We construct a theoretical model for the dynamics of a microscale colloidal particle, modeled as an interval, moving horizontally on a DNA-coated surface, modelled as a line coated with springs that can stick to the interval. Averaging over the fast DNA dynamics leads to an evolution equation for the particle in isolation, which contains both friction and diffusion. The DNA-induced friction coefficient depends on the physical properties of the DNA, and substituting parameter values typical of a 1$mu$m colloid coated densely with weakly interacting DNA gives a coefficient about 100 times larger than the corresponding coefficient of hydrodynamic friction. We use a mean-field extension of the model to higher dimensions to estimate the friction tensor for a disc rotating and translating horizontally along a line. When the DNA strands are very stiff and short, the friction coefficient for the disc rolling approaches zero while the friction for the disc sliding remains large. Together, these results could have significant implications for the dynamics of DNA-coated colloids or other ligand-receptor systems, implying that DNA-induced friction between colloids can be stronger than hydrodynamic friction and should be incorporated into simulations, and that it depends nontrivially on the type of relative motion, possibly causing the particles to assemble into out-of-equilibrium metastable states governed by the pathways with the least friction.
By combining analytical results and simulations of various coarse-grained models we investigate the minimal energy shape of DNA minicircles which are torsionally constrained by an imposed over or undertwist. We show that twist-bend coupling, a cross interaction term discussed in the recent DNA literature, induces minimal energy shapes with a periodic alternance of parts with high and low curvature resembling rounded polygons. We briefly discuss the possible experimental relevance of these findings. We finally show that the twist and bending energies of minicircles are governed by renormalized stiffness constants, not the bare ones. This has important consequences for the analysis of experiments involving circular DNA meant to determine DNA elastic constants.
We perform a spatially resolved simulation study of an AND gate based on DNA strand displacement using several lengths of the toehold and the adjacent domains. DNA strands are modelled using a coarse-grained dynamic bonding model {[}C. Svaneborg, Comp. Phys. Comm. 183, 1793 (2012){]}. We observe a complex transition path from the initial state to the final state of the AND gate. This path is strongly influenced by non-ideal effects due to transient bubbles revealing undesired toeholds and thermal melting of whole strands. We have also characterized the bound and unbound kinetics of single strands, and in particular the kinetics of the total AND operation and the three distinct distinct DNA transitions that it is based on. We observe a exponential kinetic dependence on the toehold length of the competitive displacement operation, but that the gate operation time is only weakly dependent on both the toehold and adjacent domain length. Our gate displays excellent logical fidelity in three input states, and quite poor fidelity in the fourth input state. This illustrates how non-ideality can have very selective effects on fidelity. Simulations and detailed analysis such as those presented here provide molecular insights into strand displacement computation, that can be also be expected in chemical implementations.
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