Investigation of viral DNA packaging using molecular mechanics models

Abstract

A simple molecular mechanics model has been used to investigate optimal spool-like packing conformations of double-stranded DNA molecules in viral capsids with icosahedral symmetry. The model represents an elastic segmented chain by using one pseudoatom for each ten basepairs (roughly one turn of the DNA double helix). Force constants for the various terms in the energy function were chosen to approximate known physical properties, and a radial restraint was used to confine the DNA into a sphere with a volume corresponding to that of a typical bacteriophage capsid. When the DNA fills 90% of the spherical volume, optimal packaging is obtained for coaxially spooled models, but this result does not hold when the void volume is larger. When only 60% of the spherical volume is filled with DNA, the lowest energy structure has two layers, with a coiled core packed at an angle to an outer coaxially spooled shell. This relieves bending strain associated with tight curvature near the poles in a model with 100% coaxial spooling. Interestingly, the supercoiling density of these models is very similar to typical values observed in plasmids in bacterial cells. Potential applications of the methodology are also discussed.

Introduction

Some bacteriophage have linear double-stranded DNA (ds-DNA) genomes that are tightly packaged into a roughly spherical volume inside the viral capsid [5]. The packaging of genomic DNA poses two problems for bacteriophage. First, a very high degree of condensation is required, with the final DNA concentration being on the order of 300 mg/ml [18]. This must be achieved without the benefit of higher order protein–DNA structures like those found in eukaryotic chromatin. Second, ejection of the DNA at the time of infection requires that the DNA not be knotted or entangled.

Diverse models have been proposed for the packaging of phage ds-DNA. The DNA might have local ordering but no long-range ordering, so that it is a liquid crystal [22]. Alternatively, there may be overall ordering into a fairly well-defined geometry. Among the latter possibilities are coaxial spooling [12], [31], spiral folding [6], folded coaxial spooling [38], and a folded toroid [17]. Recent cryo-electron microscopy experiments appear to be most consistent with coaxial spooling, at least for bacteriophage T7 [8].

The issue of viral packaging has received renewed importance because of the quality of data from cryo-electron microscopy, and because of other experimental developments. Single molecule measurements are now capable of measuring the forces and pressures generated during packaging [19], [40], and new 2D gel electrophoretic methods allow the quantitative determination of the relative frequencies of differently knotted conformers of closed circular DNAs like those found in bacteriophage P4 [47]. Furthermore, DNA packing in lipid complexes resembles packing in bacteriophage, with obvious implications for gene therapy [37]. Accurate modeling tools should assist in the interpretation of these and future experiments. Here we focus on the spooling model and its consequences, using P4 as a model.

Low resolution models for DNA can be used to examine issues of DNA packaging, supercoiling and knotting [26], [30]. A number of approaches have been used to model DNA molecules in the size range 1–30 kilobasepairs (kb). The molecules have been described mathematically using finite elements [2], [54], Fourier series [56], and B-splines [14], [35], [36]. DNA can also be treated as a segmented chain, using bead models (pseudoatom representations) suitable for hydrodynamic and molecular mechanics algorithms [20], [23], [27], [28], [43], [48], and that is the approach we use here.

Unlike traditional molecular mechanics models in which each atom is represented as a point mass [29], low resolution models use a reduced representation, with appropriate pseudoatoms representing pieces of the structure. Our original model [43] used three pseudoatoms to define the plane of each basepair. The potential energy function was parameterized so that the elastic moduli for stretching, bending and twisting deformations matched those for double helical DNA. The model is thus a discretized approximation to a continuum elastic model. It has been used to investigate a number of questions about the structure, topology and dynamics of small closed circular DNAs [41], [45], [46].

Here we investigate the packaging of molecules in the size range of genomic phage DNA inside viral capsids, approximating the icosahedron by a sphere. Since we are using the model to investigate questions of global organization rather than local structural details, we do not need atomic detail, or even to represent each basepair. ds-DNA in bacteriophage does not differ significantly from normal B-DNA [1] and does not interact strongly with the capsid [39], so we can use a very simple model with a single pseudoatom to represent one turn of the double helix. This reduces the computational requirements and permits rapid calculations on molecules in the size range 10–30 kb. A variety of traditional molecular mechanics algorithms (energy minimization; Monte Carlo; simulated annealing; molecular dynamics (MD); Brownian dynamics) can be used to refine static models, to sample conformational space, to estimate average properties of thermodynamic ensembles, and to investigate conformational transitions.