Residue-Based Coarse Graining
Residue-Based Coarse Graining: Coarse-Grained Lipid-Protein Model
The CG models for molecular dynamics (MD) reduce the overall system size compared with all-atom models by mapping clusters of atoms onto CG beads. The CG models were applied successfully to study the lipid assembly on a micrometer length scale and on a microsecond time scale. Assembly of liposomes, micelles, inverted hexagonal phases, and lipid bilayers have been achieved using the CG modeling. Protein CG MD models were also developed, primarily for use in protein folding simulations. However, the construction of a reliable protein CG model proved to be a difficult task, due to the complexity of the proteins, as opposed to the lipids.
An example of coarse-grained polypeptide.
The molecular complexes that participate in biological processes are comprised of proteins, lipids, nucleic acids, and many other types of molecules. To make the CG MD models more general it is important to include various molecular types in the model, particularly proteins, since most of the cellular machinery is made of these chemicals. Therefore it is not surprising that an ongoing effort in many biophysical groups around the world is to create a reliable CG MD model that would include the descriptions of lipids, proteins and corresponding solvent (water with ions), and, ultimately, also nucleotides and other biomolecules.
Based on the Marrink's et. al CG model for lipids, we have proposed a new protein-lipid CG model. In the framework of this new model, clusters of ~10 atoms (including hydrogen) are substituted by a single GC bead: four water molecules become one ``water'' bead; an ion with its hydration shell becomes an ``ion'' bead; functional groups of the lipids are reduced to single CG beads, and each amino-acid is represented by two CG beads - one for the backbone and one for the side-chain (except for the glycine, which is represented by a single backbone CG bead).
After building the structure of the CG system, one needs to define the rules determining its dynamics. Following a common approach in molecular modeling, we assume that the CG beads are the point-like masses that obey the Newtonian mechanics interacting through the effective potentials. As it is usually done for the all-atom force-fields, in the CG model we use a limited set of potentials. The bonded beads are connected by harmonic springs, and harmonic angular potentials help to maintain the shape of the molecular chains. The long-range interaction is represented by the Lennard-Jones 6-12 potential, and also by the Coulomb potential: if the cluster of atoms mapped onto a CG bead has the total electric charge q, then the CG bead assumes the charge 0.7q. The factor of 0.7 here serves to reproduce the screening created by the water; for the same reason, the dielectric constant of the medium in which the system is immersed is set to 20 (as opposed to 80 for the bulk macroscopic water). Other parameters for the potentials are adapted from the Marrink's CG model for lipids; the bond lengths and angles for the protein CG model are extracted from the averaging of corresponding distances and angles over several all-atom protein structures.
The CG models by their very nature are limited to the description of large-scale processes (large in comparison with atomic scale). Since the fine details of interatomic interactions are not taken into account in the CG models, their use is not appropriate for such systems where the interactions between single atoms may considerably influence the observed results. However, the CG approach is appropriate for studies driven by large conformational changes or depending on the general molecular properties such as hydrophobicity. In general, any process which is not dependent on the minute mutual positions of atoms, may be studied with CG methods.
Application of the CG model: simulation of the nanodisc
CG lipid models rely on the hydrophobic and hydrophilic properties of lipids to accurately describe the dynamics of assembly. An important example of the protein-lipid complex whose properties and structure are also mainly determined by the hydrophobic and hydrophilic nature of the constituents are the high-density lipoproteins (HDL), the particles comprised of helical amphipathic proteins which wrap around a lipid bilayer core. The simple amphipathic helical structure of these proteins appear to be ideal for the application of a protein-lipid CG model. We have utilized nanodiscs, a discoidal HDL mimic, being developed by our collaborator Steve Sligar (U. Illinois at Urbana-Champaign) to test our CG protein-lipid model. Results of CG MD simulations using the MD program NAMD showed that the CG model was able to reproduce the stability of nanodiscs as well as to shed light on the assembly process of these protein-lipid particles.
Nanodisc shown in (a) all-atom and in (b) CG description.
Coarse-graining reduces the number of particles by a factor of ~10.
Computational speed-up.
The developed protein-lipid CG model proved to gain a substantial speed-up in comparison with all-atom simulations. While in the latter case the time step is limited to 1-2 fs, our CG simulations can run with 25-50 fs time step (because of the greater masses of the particles and smoother potentials for their interactions). The possible speed-up depends on the computer power at hand. For example, simulating a 300,000-particle all-atom system on 48 processors, we obtained 0.1 ns of dynamics in one day. The same system in CG representation comprised 30,000 particles and reached performance was 150 ns in a day, because of the smaller number of particles per processor and larger integration time step. Accordingly, the speed-up in this case is 1500 times.