In sillico experiments
"Now experiments of this kind have one admirable property and condition: they never miss or fail. For since they are applied, not for the purpose of producing any particular effect, but only for discovering the natural cause of some effect, they answer the end equally well which ever way they turn out; for they settle the question."
–F. Bacon.
Simulational approaches to protein folding
During the last 15 years significant progress has been achieved towards the understanding of the kinetics and mechanisms of protein folding. The synergistic link between computer simulations and in vitro experiments has proven particularly fruitful in this endeavor. There are essentially three ways to study protein folding with computers:
Lattice models & Monte Carlo simulations
In a lattice model a minimal protein representation is considered; amino acids (aa) are represented by beads of uniform size that occupy the vertices of a three-dimensional lattice (see bottom pannel in the figure). The peptide bond, which covalently connects aa along the polypeptide chain, is represented by sticks with uniform lenght representing the lattice spacing. Protein energetics is typically modelled via a contact Hamiltonian and the interaction energy parameters between bead pairs are either taken from the Go (ultra-specific) or with the Miyazawa-Jernigan (sequence specific) potentials. In order to explore protein's relaxation towards the native state the Metropolis Monte Carlo algorithm together with the kink-jump move set is commonlly employed.
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C-alpha models & Langevin Molecular Dynamics
The C-alpha model is the simplest (but not simpler!) off-lattice protein representation; in this case the aa residues are replaced by beads (typically, but not necessarilly, of uniform size) whose positions (obtainable from the PDB), correspond to the locations of the C-alpha atoms of the protein backbone. In this case the energy of the protein system includes the so-called bonded terms, which ensure the regidity of the backbone (e.g. peptide bond lenght and Ramachandran angle bias), and non-bonded terms that account for contact interactions between pairs of amino acid residues. Typically, a van der Waals-like potential, which rewards native interactions and disfavours non-native ones (i.e. a Go-type potential), is used to ensure that the native state corresponds to the global energy minimum. The relaxation of the protein towards the native state is modelled by Langevin equations of motion. Accordingly, the effects of the solvent upon the protein residues are considered through a friction term, which lead to the slow motion of the macromolecular segments, and a random force, which mimics the bombardment forces that the solvent molecules exert on the macromolecule, and balances the energy dissipation introduced by friction. The equations of motion are integrated by means of a suitable predictor-corrector scheme.
Full Atomistic models & Molecular Dynamics
Simulations of protein folding, in the context of coarse-grained models (on and off-lattice), allow researchers to tackle fundamental questions that are prohibitive to the prediction-oriented models. On the other hand, full atomistic molecular dynamics (FAMD) simulations are carried out at the highest level of detail of both protein and solvent, and therefore have the potential to be an excelent complement to studies carried out in vitro. The effects of considering different forces (covalent bonds, electrostatic, van der Waals etc.) in the system's force field ( the GROMACS, CHARMM and AMBER are examples of available force fields that are commonly used to perform simulations of protein folding) can be analyzed by tracking the system's conformational evolution. Because of the large complexity of representation, the large number of atoms often exceeding 10 000, and the need to take very small time steps due to the fast oscillations of the covalent bond, the time scales accessible by FAMD, using current computer hardware and algorithms, fall short of the experimentally observed protein folding time scales. Nevertheless, FAMD can be particularly usefull to carry out unfolding simulations since the temperature and pressure conditions applied in this situation greatly speed up the dynamics.
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