A sequence-dependent rigid-base model of DNA

Abstract

A novel hierarchy of coarse-grain, sequence-dependent, rigid-base models of B-form DNA in solution is introduced. The hierarchy depends on both the assumed range of energetic couplings, and the extent of sequence dependence of the model parameters. A significant feature of the models is that they exhibit the phenomenon of frustration: each base cannot simultaneously minimize the energy of all of its interactions. As a consequence, an arbitrary DNA oligomer has an intrinsic or pre-existing stress, with the level of this frustration dependent on the particular sequence of the oligomer. Attention is focussed on the particular model in the hierarchy that has nearest-neighbor interactions and dimer sequence dependence of the model parameters. For a Gaussian version of this model, a complete coarse-grain parameter set is estimated. The parameterized model allows, for an oligomer of arbitrary length and sequence, a simple and explicit construction of an approximation to the configuration-space equilibrium probability density function for the oligomer in solution. The training set leading to the coarse-grain parameter set is itself extracted from a recent and extensive database of a large number of independent, atomic-resolution molecular dynamics (MD) simulations of short DNA oligomers immersed in explicit solvent. The Kullback-Leibler divergence between probability density functions is used to make several quantitative assessments of our nearest-neighbor, dimer-dependent model, which is compared against others in the hierarchy to assess various assumptions pertaining both to the locality of the energetic couplings and to the level of sequence dependence of its parameters. It is also compared directly against all-atom MD simulation to assess its predictive capabilities. The results show that the nearest-neighbor, dimer-dependent model can successfully resolve sequence effects both within and between oligomers. For example, due to the presence of frustration, the model can successfully predict the nonlocal changes in the minimum energy configuration of an oligomer that are consequent upon a local change of sequence at the level of a single point mutation.

Coarse-graining DNA for simulations of DNA nanotechnology

“…30 Similarly, the need to describe hybridization rules out those coarse-grained models which are intended just to describe dsDNA and do not dissociate. [31][32][33][34][35][36][37] Therefore, the minimal unit must at most be at the level of a single nucleotide. It is interesting to note that Lankaš et al found that the level of the base also provides a more appropriate level to capture the local dynamics of DNA than that of the base pair.…”

“…The first, which we term the "bottom-up" approach, is to fit the model to results (typically correlation functions) from a finer-grained model, which is usually an empirical all-atom model (e.g. AMBER, CHARMM), [35][36][37]63,64,[67][68][69] although fitting to energies obtained from electronic structure calculations (albeit in the absence of water) 65 has also been performed. The second "topdown" approach is to directly fit the parameters of a physically motivated potential to reproduce measured experimental properties, e.g.…”

Contributions of Sequence to the Higher-Order Structures of DNA

“…The interactions of nucleosomes in these chains mirror the patterns of internucleosomal association captured in mesoscale simulations, and the polymeric behavior reflects these local properties (17). Specifically, the rest states correspond to the mean values of the rigid-body parameters over the set of mesoscale structures, and the range of deformations reflects the covariance of parameters along lines analogous to those used in basepair-level treatments of DNA (6,64).…”

“…The elements within the blocks are the elastic moduli governing the fluctuations of parameters for the designated nucleosome pairs. The values are extracted from the covariance of rigid-body parameters along the lines of those used in basepair-level treatments of DNA (6,64). (B) The differences in local nucleosome structure and deformability resurface in snapshots of longer chains captured in nucleosome-level simulations (17), here 300-nucleosome (~50,000 bp) chromatin constructs guided by the rigid-body parameters of oligonucleosomes with (left) 168-bp and (right) 171-bp nucleosome repeating lengths.…”

“…The interactions of nucleosomes in these chains mirror the patterns of internucleosomal association captured in mesoscale simulations, and the polymeric behavior reflects these local properties (17). Specifically, the rest states correspond to the mean values of the rigid-body parameters over the set of mesoscale structures, and the range of deformations reflects the covariance of parameters along lines analogous to those used in basepair-level treatments of DNA (6,64).Simulated polymeric constructs with half-integral repeats tend to flex more than those with nucleosomes at the nexthighest integral spacing but less than those with nucleosomes at the next-lowest integral spacing, and the changes in stiffness show an overall exponential decay with an increase in spacing (17). The long fibers thus carry structural and energetic information that is potentially relevant to the global folding and organization of chromosomes.…”