Computational protocol: Single-WalledCarbon Nanotubes Modulate the B- toA-DNA Transition

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Protocol publication

[…] Four systems, namely, A- and B-form poly-GC and poly-AT DNA molecules, were generated using the Nucleic Acid Builder (NAB) software package, and the SWNT was generated using TubeGen 3.3., The systems were solvated via visual molecular dynamics (VMD), with 22 Na+ ions and TIP3P water to neutralize charge and represent solvent explicitly with cubic water boxes 80 Å on each side generated within the MMTSB modeling package using the CHARMM29 force field., Short-range electrostatics were truncated at 12 Å with a switching function beginning at 10 Å, while long-range electrostatics were calculated with the particle mesh Ewald method with a grid spacing of 1.0 Å and a sixth-order B-spline used for interpolation. A 2 fs time step was employed with the SHAKE algorithm as implemented in CHARMM to constrain bonds to hydrogens. The SWNT was placed initially in the same configuration relative to the DNA as that calculated in the study by Lu et al. (shown in Figure ), who used a self-consistent charge density-functional-based tight-binding method (SCC-DFTB) to determine energetics, relative stability, and electronic properties of the complexed system.Each system was minimized and then heated using Langevin dynamics and equilibrated for 2 ns, with harmonic constraints placed on heavy atoms for initial heating and released when the systems completed the equilibration phase. Harmonic constraints were then placed on all carbon atoms of the SWNT to hold them in their equilibrated positions, while another harmonic constraint held the distance between the DNA center of mass and the SWNT center of mass stable. We adopted the ΔRMSD metric as our order parameter similar to work done previously by Banavali and Roux, wherein the metric was used to study the energetics of B- to A-form DNA transitions. ΔRMSD is defined as the difference between the RMSDs of an instantaneous structure relative to two reference structures (the B and the A forms) (see below). This metric is advantageous as a reaction coordinate for smooth transitions because it neither forces the system along one particular reaction pathway nor biases it toward one reference in particular, but still retains the convenience of a single-order parameter around which one can constrain with simple harmonic potentials. In other words, the reaction coordinate structures are allowed to move around in sample space away from the two end structures, as long as the difference between RMSD (relative to the end points) is harmonically restrained in successive i-labeled umbrella potentials according to the restraint potential energy1where ki is the harmonic force constant of the ith restraint and2with r⃗ being the 3N-dimensional configurational vector of the N atoms in the system, and RMSDB = ∥r⃗ – r⃗B∥ and RMSDA = ∥r⃗ – r⃗A∥ where ∥···∥ denotes the 2-norm of the difference of the Cartesian coordinates of an instantaneous configuration r⃗ with respect to idealized A- or B-form Cartesian coordinates. In this way we apply a restraining force involving both A and B forms as reference structures, using ki as the force constant and Δρmini as the minimum around which we constrain the reaction coordinate in the i-th simulation window. The reaction coordinate Δρ is chosen such that it is a (positive) maximum if the system is in an A-like conformation, whereas Δρ is a minimum (negative) when the system is in a B-like conformation (although degenerate extrema in Δρ exist for non-A or -B forms, according to the geometry of the underlying multidimensional hyperboloids involved in the definition of the order parameter). Employing our constraint, Δρ was restrained from −5 to 5 Å with windows of 0.4 Å spacing. Each umbrella sampling window was equilibrated for 1 ns, and each window was initiated from the final coordinates of the previous window to minimize the value of the energy penalty due to our constraint from window to window. ΔRMSD for each window was binned as a histogram, and sufficient overlap between neighboring windows was accumulated as needed to achieve convergence of the PMF, which was calculated using the WHAM method., The autocorrelation function (ACF) of our reaction coordinate Δρ across simulation time t, C(t) = ⟨Δρ(0)·Δρ(t)⟩ was fitted to a single exponential e–t/τ. The decay time τ was found to be within a tenth of our simulation time, ensuring convergence of the metric and allowing for bootstrap error analysis within the WHAM implementation., Although necessary but not sufficient conditions for accuracy, error margins were found to be small enough to be considered negligible (data not shown). Furthermore, once the PMF was calculated, additional windows were run at regular intervals and intercalated between each previously run window (bringing total window separation to 2 Å), with little change observed in overall PMF curves, suggesting convergence of the calculation. […]

Pipeline specifications

Software tools VMD, DFTB
Application Protein structure analysis
Chemicals Carbon