Predicting the functionally relevant conformational motions of macromolecular complexes is among the grand challenges of computational structural biology. If met, it would significantly enrich our understanding of molecular level events underpinning the molecular machinery of life by complementing experimental advances (X-ray crystallography, cryo-electron microscopy, NMR) on macromolecular structure determination. Unfortunately, success is not yet entirely at hand and universally applicable solutions have been constantly sought.
Overcoming computational limitations in being able to explore the entire (functionally relevant) conformational space for a given macromolecular assembly is a necessary condition for success. Unfortunately, the most physically intuitive Cartesian or generalized (e.g. dihedral) coordinate based exploration of the conformational space by molecular dynamics or Monte Carlo will rarely lead to the discovery of all functionally indispensable structural poses of a macromolecular system even if the interaction between constituent atoms are well understood.
MOSAICS offers a rich variety of user defined coordinates (degrees of freedom or DoF) in combination with a variety of conformational sampling algorithms (e.g. Multicanonical Markov Chain Monte Carlo) guiding the exploration of the conformational space. The most unique feature of MOSAICS is Hierarchical Nature Move Monte Carlo (see below) with primary application areas on the atomistic modelling of nucleic acids (DNA and RNA). It is compatible with most of the widely used empirical all-atom energy functions and statistical (knowledge based) potentials. For proteins the recommended use is one of the available coarse-grained models.
Hierarchical Natural Move Monte Carlo (HNM-MC)[1] enables sampling of the entire conformational space of atomistic nucleic acid systems of composed of hundreds of nucleotides. The unique (often experimentally inferred) set of DoFs, Li , i = 1, …, n span conformational subspaces of increasing sizes, which characterize from the most collective (Ωs) to the most refined (Ωf) degrees of freedom such that Ωs = Ωn ⊂ Ωn-1 ... ⊂ Ω1 = Ωf, with each subspace representing a desired level of the hierarchy. In this way the energy surface, E: Ωf → ℜ along highest order collective DoFs, Ln are smoothed by introducing a hierarchical set of finer lower order DoFs, Ln-1,…,L1. Figure 1 presents such set of hierarchical DoFs spanning related subspaces (n=3) for a large fractal-like RNA composed of four 4-way junctions.
Figure 1: (A) Example of three embedded subspaces, (Ω1, Ω2, Ω3) spanned by hierarchical degrees of freedom L1, L2, L3 of a large fractal-like RNA modeled by Hierarchical Natural Move Monte Carlo (HNMMC). Ω1, Ω2 and Ω3 spaces represent the arrangement of individual and groups of nucleotides in helices and four helix arms, respectively. The relative size of each subspace is illustrated by a geometric analogy: Ω1 spans the volume of cube (red), Ω2 spans the plane abcd (green) and Ω3, spans the line cb (blue). Source
Figure 2 illustrates the practical implementation of the method by using hierarchical embedding of DoFs so that the conventional base pair and base step moves of nucleotides can be combined with the movement of entire helices or groups of helices as rigid bodies. In this way collective motions preserving the structural hierarchy are supported by the relaxation of the system at the base step, base pair levels and even internally (not shown) within the nucleotides by the relaxation of internal torsional and bend angles. The potenal break of covalent bonds and deviation from ideal stereochemistry are repaired ‘on the fly’ by using efficient chain closure algorithms.
Figure 2: Illustration of the hierarchical embedding process for degrees of freedom (DoFs) ranging from the base pair, base step parameters to the orientational and translational DoFs of entire helices and higher level structural regions (dotted boxes) composed of helix pairs. The figure has been constructed using figure 2 from Ref. [2] Source
The potential impact of these new methods has been demonstrated by notable works such as a comprehensive investigation of the protein fold universe, aiding the design of RNA nanostructures and fitting molecular structures against their Cryo-electron microscopy images. As such, our objectives include both the mechanistic study of structural phenomena using purely computational investigations and the better interpretation of experimental results.
Representative publications on completed application projects and related algorithmic developments can be found here. Source
[1] Sim, A.Y., Levitt, M., and Minary, P. (2012). Modeling and design by hierarchical natural moves. Proc. Natl. Acad. Sci. U. S. A. 109: 2890-2895.
[2] Sim, A.Y., Minary, P., and Levitt, M. (2012). Modeling nucleic acids. Curr. Opin. Struct. Biol. 22(3): 273-278.