Natural Move Monte Carlo: Sampling Collective Motions in Proteins

Protein and RNA structures are built up in a hierarchical fashion: from linear chains and random coils (primary) to local substructures (secondary) that make up a subunit’s 3D geometry (tertiary) which in turn can interact with additional subunits to form homomeric or heteromeric multimers (quaternary). The metastable nature of the folded polymer enables it to carry out its function repeatedly while avoiding aggregation and degradation. These functions often rely on structural motions that involve multiple scales of conformational changes by moving residues, secondary structure elements, protein domains or even whole subunits collectively around a small set of degrees of freedom.

The modular architecture of antibodies, makes them amenable to act as an example for this phenomenon. Using MD simulations and fluorescence anisotropy experiments Kortkhonjia et al. observed that Ig domain motions in their antibody of interest were shown to correlate on two levels: 1) with laterally neighbouring Ig domains (i.e. VH with VL and CH1 with CL) and 2) with their respective Fab and Fc regions.

Correlated Motion

Correlated motion between all residue pairs of an antibody during an MD simulation. The axes identify the residues whereas the colours light up as the correlation in motion increases. The individual Ig domains as well as the two Fabs and the Fc can be easily identified. ref: Kortkhonjia, et al., MAbs. Vol. 5. No. 2. Landes Bioscience, 2013.

This begs the question: Can we exploit these molecular properties to reduce dimensionality and overcome energy barriers when sampling the functional motions of metastable proteins?

In 2012 Sim et al. have published an approach that allows for the incorporation of these collective motions (they call them “Natural Moves”) into simulation. Using simple RNA model structures they have shown that explicitly sampling large structural moves can significantly accelerate the sampling process in their Monte Carlo simulation. By gradually introducing DOFs that propagate increasingly large substructures of the molecule they managed to reduce the convergence time by several orders of magnitude. This can be ascribed to the resulting reduction of the search space that narrows down the sampling window. Instead of sampling all possible conformations that a given polynucleotide chain may take, structural states that differ from the native state predominantly in tertiary structure are explored.

Reduced Dimensionality

Reducing the conformational search space by introducing Natural Moves. A) Ω1 (residue-level flexibility) represents the cube, Ω2 (collective motions of helices) spans the plane and Ω3 (collective motions of Ω2 bodies) is shown as a line. B) By integrating multiple layers of Natural Moves the dimensionality is reduced. ref: Sim et al. (2012). PNAS 109(8), 2890–5. doi:10.1073/pnas.1119918109

It is important to stress, however, that in addition to these rigid body moves local flexibility is maintained by preserving residue level flexibility. Consequently, the authors argue, high energy barriers resulting from large structural rearrangements are reduced and the resulting energy landscape is smoothened. Therefore, entrapment in local energy minima becomes less likely and the acceptance rate of the Monte Carlo simulation is improved.

Although benchmarking of this method has mostly relied on case studies involving model RNA structures with near perfect symmetry, this method has a natural link to near-native protein structure sampling. Similarly to RNA, proteins can be decomposed into local substructures that may be responsible for the main functional motions in a given protein. However, due to the complexity of protein motion and limited experimental data we have a limited understanding of protein dynamics. This makes it a challenging task to identify suitable decompositions. As more dynamic data emerges from biophysical methods such as NMR spectroscopy and databases such as www.dynameomics.org are extended we will be able to better approximate protein motions with Natural Moves.

In conclusion, when applied to suitable systems and when used with care, there is an opportunity to breathe life into the static macromolecules of the pdb, which may help to improve our understanding of the heterogeneous structural landscape and the functional motions of metastable proteins and nanomachines.

Leave a Reply