Modeling Structural Dynamics of Biomolecular Complexes by Coarse-Grained Molecular Simulations

Abstract

Due to hierarchic nature of biomolecular systems, their computational modeling calls for multiscale approaches, in which coarse-grained (CG) simulations are used to address long-time dynamics of large systems. Here, we review recent developments and applications of CG modeling methods, focusing on our methods primarily for proteins, DNA, and their complexes. These methods have been implemented in the CG biomolecular simulator, CafeMol. Our CG model has resolution such that ∼10 non-hydrogen atoms are grouped into one CG particle on average. For proteins, each amino acid is represented by one CG particle. For DNA, one nucleotide is simplified by three CG particles, representing sugar, phosphate, and base. The protein modeling is based on the idea that proteins have a globally funnel-like energy landscape, which is encoded in the structure-based potential energy function. We first describe two representative minimal models of proteins, called the elastic network model and the classic Go̅ model. We then present a more elaborate protein model, which extends the minimal model to incorporate sequence and context dependent local flexibility and nonlocal contacts. For DNA, we describe a model developed by de Pablo's group that was tuned to well reproduce sequence-dependent structural and thermodynamic experimental data for single- and double-stranded DNAs. Protein-DNA interactions are modeled either by the structure-based term for specific cases or by electrostatic and excluded volume terms for nonspecific cases. We also discuss the time scale mapping in CG molecular dynamics simulations. While the apparent single time step of our CGMD is about 10 times larger than that in the fully atomistic molecular dynamics for small-scale dynamics, large-scale motions can be further accelerated by two-orders of magnitude with the use of CG model and a low friction constant in Langevin dynamics. Next, we present four examples of applications. First, the classic Go̅ model was used to emulate one ATP cycle of a molecular motor, kinesin. Second, nonspecific protein-DNA binding was studied by a combination of elaborate protein and DNA models. Third, a transcription factor, p53, that contains highly fluctuating regions was simulated on two perpendicularly arranged DNA segments, addressing intersegmental transfer of p53. Fourth, we simulated structural dynamics of dinucleosomes connected by a linker DNA finding distinct types of internucleosome docking and salt-concentration-dependent compaction. Finally, we discuss many of limitations in the current approaches and future directions. Especially, more accurate electrostatic treatment and a phospholipid model that matches our CG resolutions are of immediate importance.

Coarse-Grained Protein Models and Their Applications

“…The choice of representation determines to a large extent the possible options of force field and sampling, i.e., the compromise between accuracy and computational efficiency. 87,407 The smaller the number of explicitly treated united atoms (or pseudoatoms) representing fragments of protein chains, the faster simulation, and the lower accuracy. Very efficient models based on three/four united atoms per amino acid residue accelerate simulations by 3−4 orders of magnitude in comparison with classical all-atom MD simulations.…”

Exploring the Free Energy Landscape of Nucleosomes

“…Due to the coarse graining, we note the simulation timescale cannot be converted precisely into real time units. 50 In any event, we checked the convergence of the simulations by performing rigorous error analysis of the calculated free energy profiles (See the SI Section: Convergence of the simulation for details). Since the simulations were performed without periodic boundary conditions, we introduced a constraint on the radius of gyration of the histone core complex when the protein assembly is studied without the presence of the DNA in order to prevent molecules from diffusing too far away from each other unproductively.…”

The Oligomerization Landscape of Histones

“…Trajectories were combined for later data analysis after removing the first 10 ns in every run to account for thermal equilibration. Note that the coarse-graining timescale cannot be directly converted into real time since it could be at least 10 times larger than that in the atomistic MD simulations (58). The convergences of all simulations were verified by the root-mean-squared inner-product (RMSIP) analysis, which are provided in Supplemental Section 4.…”