Sequence-dependent thermodynamics of a coarse-grained DNA model

Biophysically inspired rational design of structured chimeric substrates for DNAzyme cascade engineering

The development of large-scale molecular computational networks is a promising approach to implementing logical decision making at the nanoscale, analogous to cellular signaling and regulatory cascades. DNA strands with catalytic activity (DNAzymes) are one means of systematically constructing molecular computation networks with inherent signal amplification. Linking multiple DNAzymes into a computational circuit requires the design of substrate molecules that allow a signal to be passed from one DNAzyme to another through programmed biochemical interactions. In this paper, we chronicle an iterative design process guided by biophysical and kinetic constraints on the desired reaction pathways and use the resulting substrate design to implement heterogeneous DNAzyme signaling cascades. A key aspect of our design process is the use of secondary structure in the substrate molecule to sequester a downstream effector sequence prior to cleavage by an upstream DNAzyme. Our goal was to develop a concrete substrate molecule design to achieve efficient signal propagation with maximal activation and minimal leakage. We have previously employed the resulting design to develop high-performance DNAzyme-based signaling systems with applications in pathogen detection and autonomous theranostics.

Close encounters with DNA

Over the past ten years, the all-atom molecular dynamics method has grown in the scale of both systems and processes amenable to it and in its ability to make quantitative predictions about the behavior of experimental systems. The field of computational DNA research is no exception, witnessing a dramatic increase in the size of systems simulated with atomic resolution, the duration of individual simulations and the realism of the simulation outcomes. In this topical review, we describe the hallmark physical properties of DNA from the perspective of all-atom simulations. We demonstrate the amazing ability of such simulations to reveal the microscopic physical origins of experimentally observed phenomena. We also discuss the frustrating limitations associated with imperfections of present atomic force fields and inadequate sampling. The review is focused on the following four physical properties of DNA: effective electric charge, response to an external mechanical force, interaction with other DNA molecules and behavior in an external electric field.

COFFDROP: A Coarse-Grained Nonbonded Force Field for Proteins Derived from All-Atom Explicit-Solvent Molecular Dynamics Simulations of Amino Acids

We describe the derivation of a set of bonded and nonbonded coarse-grained (CG) potential functions for use in implicit-solvent Brownian dynamics (BD) simulations of proteins derived from all-atom explicit-solvent molecular dynamics (MD) simulations of amino acids. Bonded potential functions were derived from 1 μs MD simulations of each of the 20 canonical amino acids, with histidine modeled in both its protonated and neutral forms; nonbonded potential functions were derived from 1 μs MD simulations of every possible pairing of the amino acids (231 different systems). The angle and dihedral probability distributions and radial distribution functions sampled during MD were used to optimize a set of CG potential functions through use of the iterative Boltzmann inversion (IBI) method. The optimized set of potential functions—which we term COFFDROP (COarse-grained Force Field for Dynamic Representation Of Proteins)—quantitatively reproduced all of the “target” MD distributions. In a first test of the force field, it was used to predict the clustering behavior of concentrated amino acid solutions; the predictions were directly compared with the results of corresponding all-atom explicit-solvent MD simulations and found to be in excellent agreement. In a second test, BD simulations of the small protein villin headpiece were carried out at concentrations that have recently been studied in all-atom explicit-solvent MD simulations by Petrov and Zagrovic (PLoS Comput. Biol.2014, 5, e1003638). The anomalously strong intermolecular interactions seen in the MD study were reproduced in the COFFDROP simulations; a simple scaling of COFFDROP’s nonbonded parameters, however, produced results in better accordance with experiment. Overall, our results suggest that potential functions derived from simulations of pairwise amino acid interactions might be of quite broad applicability, with COFFDROP likely to be especially useful for modeling unfolded or intrinsically disordered proteins.

A Coarse-Grained Model of Unstructured Single-Stranded DNA Derived from Atomistic Simulation and Single-Molecule Experiment

A simple coarse-grained model of single-stranded DNA (ssDNA) was developed, featuring only two sites per nucleotide that represent the centers of mass of the backbone and sugar/base groups. In the model, the interactions between sites are described using tabulated bonded potentials optimized to reproduce the solution structure of DNA observed in atomistic molecular dynamics simulations. Isotropic potentials describe nonbonded interactions, implicitly taking into account the solvent conditions to match the experimentally determined radius of gyration of ssDNA. The model reproduces experimentally measured force-extension dependence of an unstructured DNA strand across 2 orders of magnitude of the applied force. The accuracy of the model was confirmed by measuring the end-to-end distance of a dT14 fragment via FRET while stretching the molecules using optical tweezers. The model offers straightforward generalization to systems containing double-stranded DNA and DNA binding proteins.

Coupling between hydrogen atoms transfer and stacking interaction in adenine-thymine/guanine-cytosine complexes: a theoretical study

Four different complexes of two base pairs, an adenine-thymine and a guanine-cytosine one, have been studied in order to understand the modifications induced by the staking interaction between the two base pairs on the hydrogen atoms transfers between the bases in either base pair. The inclusion of these two kinds of interactions allows us to clarify if some properties, as the mechanism of hydrogen transfer, is exclusively a local effect of a base pair or can be modified by a more long-range interaction between the base pairs. The results on these four complexes are compared with those of the monomeric systems, the A-T and G-C base pair, and with those of the A-T and G-C dimers. The specificity of each complex and of each hydrogen bond has been analyzed.

An experimentally-informed coarse-grained 3-Site-Per-Nucleotide model of DNA: structure, thermodynamics, and dynamics of hybridization

A new 3-Site-Per-Nucleotide coarse-grained model for DNA is presented. The model includes anisotropic potentials between bases involved in base stacking and base pair interactions that enable the description of relevant structural properties, including the major and minor grooves. In an improvement over available coarse-grained models, the correct persistence length is recovered for both ssDNA and dsDNA, allowing for simulation of non-canonical structures such as hairpins. DNA melting temperatures, measured for duplexes and hairpins by integrating over free energy surfaces generated using metadynamics simulations, are shown to be in quantitative agreement with experiment for a variety of sequences and conditions. Hybridization rate constants, calculated using forward-flux sampling, are also shown to be in good agreement with experiment. The coarse-grained model presented here is suitable for use in biological and engineering applications, including nucleosome positioning and DNA-templated engineering.

The power of coarse graining in biomolecular simulations

Computational modeling of biological systems is challenging because of the multitude of spatial and temporal scales involved. Replacing atomistic detail with lower resolution, coarse grained (CG), beads has opened the way to simulate large-scale biomolecular processes on time scales inaccessible to all-atom models. We provide an overview of some of the more popular CG models used in biomolecular applications to date, focusing on models that retain chemical specificity. A few state-of-the-art examples of protein folding, membrane protein gating and self-assembly, DNA hybridization, and modeling of carbohydrate fibers are used to illustrate the power and diversity of current CG modeling.

Gels of DNA nanostars never crystallize

Using state-of-the-art numerical techniques, we show that, upon lowering the temperature, tetravalent DNA nanostars form a thermodynamically stable, fully bonded equilibrium gel. In contrast to atomic and molecular network formers, in which the disordered liquid is always metastable with respect to some crystalline phase, we find that the DNA nanostar gel has a lower free energy than the diamond crystal structure in a wide range of concentrations. This unconventional behavior, here verified for the first time in a realistic model, arises from the large arm flexibility of the DNA nanostars, a property that can be tuned by design. Our results confirm the thermodynamic stability of the recently experimentally realized DNA hydrogels.

Perspective: Coarse-grained models for biomolecular systems

By focusing on essential features, while averaging over less important details, coarse-grained (CG) models provide significant computational and conceptual advantages with respect to more detailed models. Consequently, despite dramatic advances in computational methodologies and resources, CG models enjoy surging popularity and are becoming increasingly equal partners to atomically detailed models. This perspective surveys the rapidly developing landscape of CG models for biomolecular systems. In particular, this review seeks to provide a balanced, coherent, and unified presentation of several distinct approaches for developing CG models, including top-down, network-based, native-centric, knowledge-based, and bottom-up modeling strategies. The review summarizes their basic philosophies, theoretical foundations, typical applications, and recent developments. Additionally, the review identifies fundamental inter-relationships among the diverse approaches and discusses outstanding challenges in the field. When carefully applied and assessed, current CG models provide highly efficient means for investigating the biological consequences of basic physicochemical principles. Moreover, rigorous bottom-up approaches hold great promise for further improving the accuracy and scope of CG models for biomolecular systems.

Collective translational and rotational Monte Carlo moves for attractive particles

Virtual move Monte Carlo is a Monte Carlo (MC) cluster algorithm forming clusters via local energy gradients and approximating the collective kinetic or dynamic motion of attractive colloidal particles. We carefully describe, analyze, and test the algorithm. To formally validate the algorithm through highlighting its symmetries, we present alternative and compact ways of selecting and accepting clusters which illustrate the formal use of abstract concepts in the design of biased MC techniques: the superdetailed balance and the early rejection scheme. A brief and comprehensive summary of the algorithms is presented, which makes them accessible without needing to understand the details of the derivation.

Coarse-graining DNA for simulations of DNA nanotechnology

To simulate long time and length scale processes involving DNA it is necessary to use a coarse-grained description. Here we provide an overview of different approaches to such coarse-graining, focussing on those at the nucleotide level that allow the self-assembly processes associated with DNA nanotechnology to be studied. OxDNA, our recently-developed coarse-grained DNA model, is particularly suited to this task, and has opened up this field to systematic study by simulations. We illustrate some of the range of DNA nanotechnology systems to which the model is being applied, as well as the insights it can provide into fundamental biophysical properties of DNA.

Coarse-grained simulations of DNA overstretching

We use a recently developed coarse-grained model to simulate the overstretching of duplex DNA. Overstretching at 23 °C occurs at 74 pN in the model, about 6-7 pN higher than the experimental value at equivalent salt conditions. Furthermore, the model reproduces the temperature dependence of the overstretching force well. The mechanism of overstretching is always force-induced melting by unpeeling from the free ends. That we never see S-DNA (overstretched duplex DNA), even though there is clear experimental evidence for this mode of overstretching under certain conditions, suggests that S-DNA is not simply an unstacked but hydrogen-bonded duplex, but instead probably has a more exotic structure.

DNA hybridization kinetics: zippering, internal displacement and sequence dependence

Although the thermodynamics of DNA hybridization is generally well established, the kinetics of this classic transition is less well understood. Providing such understanding has new urgency because DNA nanotechnology often depends critically on binding rates. Here, we explore DNA oligomer hybridization kinetics using a coarse-grained model. Strand association proceeds through a complex set of intermediate states, with successful binding events initiated by a few metastable base-pairing interactions, followed by zippering of the remaining bonds. But despite reasonably strong interstrand interactions, initial contacts frequently dissociate because typical configurations in which they form differ from typical states of similar enthalpy in the double-stranded equilibrium ensemble. Initial contacts must be stabilized by two or three base pairs before full zippering is likely, resulting in negative effective activation enthalpies. Non-Arrhenius behavior arises because the number of base pairs required for nucleation increases with temperature. In addition, we observe two alternative pathways—pseudoknot and inchworm internal displacement—through which misaligned duplexes can rearrange to form duplexes. These pathways accelerate hybridization. Our results explain why experimentally observed association rates of GC-rich oligomers are higher than rates of AT- rich equivalents, and more generally demonstrate how association rates can be modulated by sequence choice.

Inferring bulk self-assembly properties from simulations of small systems with multiple constituent species and small systems in the grand canonical ensemble

In this paper, we generalize a methodology [T. E. Ouldridge, A. A. Louis, and J. P. K. Doye, J. Phys.: Condens. Matter 22, 104102 (2010)] for dealing with the inference of bulk properties from small simulations of self-assembling systems of characteristic finite size. In particular, schemes for extrapolating the results of simulations of a single self-assembling object to the bulk limit are established in three cases: for assembly involving multiple particle species, for systems with one species localized in space and for simulations in the grand canonical ensemble. Furthermore, methodologies are introduced for evaluating the accuracy of these extrapolations. Example systems demonstrate that differences in cluster concentrations between simulations of a single self-assembling structure and bulk studies of the same model under identical conditions can be large, and that convergence on bulk results as system size is increased can be slow and non-trivial.

DNA cruciform arms nucleate through a correlated but asynchronous cooperative mechanism

Inverted repeat (IR) sequences in DNA can form noncanonical cruciform structures to relieve torsional stress. We use Monte Carlo simulations of a recently developed coarse-grained model of DNA to demonstrate that the nucleation of a cruciform can proceed through a cooperative mechanism. First, a twist-induced denaturation bubble must diffuse so that its midpoint is near the center of symmetry of the IR sequence. Second, bubble fluctuations must be large enough to allow one of the arms to form a small number of hairpin bonds. Once the first arm is partially formed, the second arm can rapidly grow to a similar size. Because bubbles can twist back on themselves, they need considerably fewer bases to resolve torsional stress than the final cruciform state does. The initially stabilized cruciform therefore continues to grow, which typically proceeds synchronously, reminiscent of the S-type mechanism of cruciform formation. By using umbrella sampling techniques, we calculate, for different temperatures and superhelical densities, the free energy as a function of the number of bonds in each cruciform arm along the correlated but asynchronous nucleation pathways we observed in direct simulations.