Principles and Overview of Sampling Methods for Modeling Macromolecular Structure and Dynamics

Abstract

Investigation of macromolecular structure and dynamics is fundamental to understanding how macromolecules carry out their functions in the cell. Significant advances have been made toward this end in silico, with a growing number of computational methods proposed yearly to study and simulate various aspects of macromolecular structure and dynamics. This review aims to provide an overview of recent advances, focusing primarily on methods proposed for exploring the structure space of macromolecules in isolation and in assemblies for the purpose of characterizing equilibrium structure and dynamics. In addition to surveying recent applications that showcase current capabilities of computational methods, this review highlights state-of-the-art algorithmic techniques proposed to overcome challenges posed in silico by the disparate spatial and time scales accessed by dynamic macromolecules. This review is not meant to be exhaustive, as such an endeavor is impossible, but rather aims to balance breadth and depth of strategies for modeling macromolecular structure and dynamics for a broad audience of novices and experts.

Fig 1. Free-energy landscape of GB3 obtained with work in [302] using chemical shifts as collective variables.

Panel A shows a two-dimensional projection of sampled conformations. The x-axis shows values of the CamShift collective variables for each conformation, which measures the difference between the wet-laboratory and calculated chemical shifts for the backbone. The y-axis shows the backbone RMSD between each conformation and the reference structure (PDB ID 2oed). Some selected conformations, from extended to compact, are highlighted, drawn with the Visual Molecular Dynamics (VMD) software [303]. Panel B shows a conformation with the lowest backbone RMSD (0.5 Å) from the reference structure. Such native-like conformations are visited multiple times by the method. Panel C draws hydrophobic side chains to illustrate that the internal packing of these side chains is practically identical to that observed in the reference structure. This figure is reproduced with permission of the executive editor of PNAS from article Granata et al., 2013 [302].

Fig 2. Probing of coupled motions in the Eg5 kinesin motor domains in [91] through accelerated MD simulations.

The top panel shows the structure and catalytic cycle of the kinesin motor domain. The ATPase catalytic site sits at the top of the β-sheet, flanked by three highly-conserved loops (P-loop, SI, and SII) connected to helices (also annotated) on either side of the sheet. The secondary structure topology is drawn, with β -strands drawn as triangles and α-helices as circles. The kinesin catalytic cycle is shown: Kinesin (K) has a weak affinity for the microtubule in the ADP-state. ADP release is followed by strong microtubule-binding. ATP binding may occur followed by hydrolysis and product release to regenerate the weakly-bound ADP state. The bottom panel projects conformations sampled by 200 nanosecond-long accelerated MD every 20 picoseconds on the two principal modes of motion. The latter are obtained through principal component analysis of collected X-ray structures for wildtype and variant Eg5. Three simulations are highlighted, the nucleotide-free (APO) one in (A), ADP-bound one in (B), and ATP-bound one in (C). The nucleotide-free simulation covers more of the conformation space, whereas restricted sampling is observed when Eg5 is bound to ATP or ADP. One of the conclusions in [91] is that structural changes from the ADP- to ATP-bound states which are evident in the collection of X-ray structures, are encoded in the intrinsic dynamics of the nucleotide-free motor domain; the nucleotides effectively rigidify the motor domain by narrowing the conformation space accessible by it, as evident in the restricted sampling observed through accelerated MD. This figure is reused from Scarabelli et al., 2013. CC-BY PLOS ONE [91].

Fig 3. Sampling of the ensemble of closed-to-open and open-to-closed transition trajectories in AdK through the DIMS method [334].

An ensemble of 330 DIMS trajectories is compared to 45 Escherichia coli AdK X-ray structures. The conformations in each trajectory are projected onto a progress variable δRMSD measured as the RMSD of the conformation from the closed AdK structure (PDB ID 1ake:A) minus the RMSD of the conformation from the open AdK structure (PDB ID 4ake:A). For each of the 45 collected X-ray structures and each trajectory, the conformation in the trajectory closest in backbone RMSD to an X-ray structure is recorded, and the δRMSD value of the conformation along a trajectory is recorded. A probability distribution is then constructed for each X-ray structure over all DIMS trajectories to indicate where an X-ray structure is located along the simulated trajectories. The color bar indicates the probability density. The median of each distribution is marked by a white circle. The X-ray structures whose PDB IDs are listed on the y-axis are rank ordered based on the median. The second white line traces the location of the median when the simulations are repeated to sample open-to-closed transition trajectories. Out of 45 structures sorted by δRMSD, about 24 are closed-state structures, four are open, and 17 are intermediates. This work is an example of the capability of computational methods to elucidate transitions in detail and accurately map the location of experimentally determined structures in the transitions. This figure is adapted from Beckstein et al., 2009 [334]. The image was created by O. Beckstein.

Fig 4. Predicting a pathogen’s resistance mutations [452].

(A) Pictured is an illustration of a game between scientists and bacteria. For every drug that scientists develop against bacteria (a “move”), bacteria respond with mutations that confer resistance to the drug. This paper shows that these “moves” by bacteria can be predicted in silico ahead of time by the Osprey protein design algorithm. Donald, Anderson, and coworkers used Osprey to prospectively predict in silico mutations in Staphylococcus aureus against a novel preclinical antibiotic, and validated their predictions in vitro and in resistance selection experiments. Image (A) was created for this paper by Lei Chen and Yan Liang (L2Molecule.com). (B–C) Computationally predicting drug resistance mutations early in the discovery phase would be an important breakthrough in drug development. The most meaningful predictions of target mutations will show reduced affinity for the drug (C) while maintaining viability in the complex context of a cell (B). The protein design algorithm, K* in Osprey, was used to predict a single nucleotide polymorphism in the target DHFR that confers resistance to an experimental antifolate (Compound 1) in the preclinical discovery phase. Excitingly, the mutation was also selected in bacteria under antifolate pressure, confirming the prediction of a viable molecular response to external stress. Images (B–C) were created by Adegoke Ojewole in the Bruce Donald Lab, Duke University.