Lattice protein

Lattice proteins are highly simplified computer models of proteins which are used to investigate protein folding.^[1]

Because proteins are such large molecules, there are severe computational limits on the simulated timescales of their behaviour when modeled in all-atom detail. The millisecond regime for all-atom simulations was not reached until 2010,^[2] and it is still not possible to fold all real proteins on a computer. Simplification in lattice proteins is twofold: each whole residue (amino acid) is modelled as a single "bead" or "point" of a finite set of types (usually only two), and each residue is restricted to be placed on vertices of a (usually cubic) lattice. To guarantee the connectivity of the protein chain, adjacent residues on the backbone must be placed on adjacent vertices of the lattice. Sterical constraints are simply expressed by imposing that no more than one residue could be placed on the same lattice vertex. Simplifications of this kind significantly reduce the computational effort in handling the model, although even in this simplified scenario the protein folding problem is NP-complete.^[3]

Different versions of lattice proteins may adopt different types of lattice (typically square and triangular ones), in two or three dimensions, but it has been shown that generic lattices can be used and handled via a uniform approach.^[4]

Lattice proteins are made to resemble real proteins by introducing an energy function, a set of conditions which specify the interaction energy between neighbouring beads, usually those occupying adjacent lattice sites. The energy function mimics the interactions between amino acids in real proteins, which include steric, hydrophobic and hydrogen bonding effects. The beads are divided into types, and the energy function specifies the interactions depending on the bead type, just as different types of amino acids interact differently. One of the most popular lattice models, the HP model,^[5] features just two bead types—hydrophobic (H) and polar (P)—and mimics the hydrophobic effect by specifying a negative (i.e. favourable) interaction between H beads.

For any sequence in any particular structure, an energy can be rapidly calculated from the energy function. For the simple HP model, this is simply an enumeration of all the contacts between H residues that are adjacent in the structure but not in the chain. Most researchers consider a lattice protein sequence protein-like only if it possesses a single structure with an energetic state lower than in any other structure. This is the energetic ground state, or native state. The relative positions of the beads in the native state constitute the lattice protein's tertiary structure. Lattice proteins do not have genuine secondary structure; however, some researchers have claimed that they can be extrapolated onto real protein structures which do include secondary structure, by appealing to the same law by which the phase diagrams of different substances can be scaled onto one another (the theorem of corresponding states).^[6]

By varying the energy function and the bead sequence of the chain (the primary structure), effects on the native state structure and the kinetics of folding can be explored, and this may provide insights into the folding of real proteins. In particular, lattice models have been used to investigate the energy landscapes of proteins, i.e. the variation of their internal free energy as a function of conformation.

References

1. Lau, K. F. & Dill, K. A. (1989). "A lattice statistical mechanics model of the conformational and sequence spaces of proteins". Macromolecules 22 (10): 3986–97. doi:10.1021/ma00200a030.
2. "Folding@home: Paper #72: Major new result for Folding@home: Simulation of the millisecond timescale". 2010.
3. B. Berger and T. Leighton (1998). "Protein folding in the hydrophobic-hydrophilic (HP) model is NP-complete". Journal of Computational Biology 5 (1): 27–40. doi:10.1089/cmb.1998.5.27. PMID 9541869.
4. Bechini, A. (2013). "On the characterization and software implementation of general protein lattice models". PLoS ONE 8 (3): e59504. doi:10.1371/journal.pone.0059504.
5. Dill, K. A. (1985). "Theory for the folding and stability of globular proteins". Biochemistry 24 (6): 1501–9. doi:10.1021/bi00327a032. PMID 3986190.
6. Onuchic, J. N.; Wolynes, P. G.; Luthey-Schulten, Z.; Socci, N.D. (1995). "Toward an outline of the topography of a realistic protein folding funnel" (PDF). Proc. Natl. Acad. Sci. USA 92 (8): 3626–30. doi:10.1073/pnas.92.8.3626. PMC 42220. PMID 7724609.