Multiscale simulations of protein landscapes: using coarse-grained models as reference potentials to full explicit models

Abstract

Evaluating the free-energy landscape of proteins and the corresponding functional aspects presents a major challenge for computer simulation approaches. This challenge is due to the complexity of the landscape and the enormous computer time needed for converging simulations. The use of simplified coarse-grained (CG) folding models offers an effective way of sampling the landscape but such a treatment, however, may not give the correct description of the effect of the actual protein residues. A general way around this problem that has been put forward in our early work (Fan et al., Theor Chem Acc 1999;103:77-80) uses the CG model as a reference potential for free-energy calculations of different properties of the explicit model. This method is refined and extended here, focusing on improving the electrostatic treatment and on demonstrating key applications. These applications include: evaluation of changes of folding energy upon mutations, calculations of transition-states binding free energies (which are crucial for rational enzyme design), evaluations of catalytic landscape, and evaluations of the time-dependent responses to pH changes. Furthermore, the general potential of our approach in overcoming major challenges in studies of structure function correlation in proteins is discussed.

Keywords: Coarse Grained model; dielectric constants; free energy calculations; proton transfer.

Figure 1

A schematic illustration of the conversion of an explicit side chain to its simplified equivalent. The position of the explicit C_β is preserved, using a dummy atom, named D, and the geometrical center of the side chain heavy atoms is represented in the simplified model by the effective atom, named X.

Figure 2

The thermodynamic cycle used to calculate the change in free energy Δg_ep for a generic process. Having calculated the free energy change of the simple model, Δg_sp, umbrella sampling can be used to calculate the free energy change ΔΔg_sp→ep for the initial and final states to obtain Δg_ep.

Figure 3

The Ramachandran diagram for alanine dipeptide, obtained by the explicit model (A) and the simplified model (B).

Figure 4

The system used as a benchmark for the behavior of the self energy term in non polar environment. The backbone conformation of protein 1SSO residues 21-56 was taken, and the fully hydrophobic sequence after the mutations is reported in the Figure. The figure describes the hydrophobic environment generated around Glu29, buried by residues 22-33 and 43-56.

Figure 5

The thermodynamic cycles used to calculate the change in free energy of unfolding upon mutation (see text for details)

Figure 6

A three dimensional representation of pseudo wild type ubiquitin. Asp21, which is involved in the mutational study, is represented explicitly.

Figure 7

The fluctuations of the energy difference between the explicit and simplified potentials, obtained during (A) FEP/MD, (B) Monte Carlo, simulations

Figure 8

The cycle used to evaluate mutational effects on transition states binding free energies.

Figure 9

A schematic description of the mMjCM active sites, depicting key residues that are involved in the binding of the transition-state analogue (bold).

Figure 10

Simulation of the proton transport process in protein 1SSO, upon change of the bulk pH from 0 to 7. The graph describes the relaxation of the overall free energy, while the insert figures describe the migration of the “active” protons. Residue sites are depicted in this figure as squares, which are sometimes occupied by a proton (black circle), and sometimes they are empty. Protons can move between residue sites, or between residue sites and the surrounding bulk.