1. BioShell package
  2. SURPASS model

SURPASS model

Single United Residue per Pre-Averaged Secondary Structure fragment is a coarse-grained low resolution model for protein simulations

SURPASS representation

Deep reduction of the number of atoms in the representation results in a powerful computational speed-up and in this context ranks the model as a low resolution.

Figure 1. Schematic illustration of the projection from all-atom to coarse-grained SURPASS representation for two protein fragments: helical (left side) and β-strand (right side). Panel A illustrates an idealized “ribbon diagram”, while panel B represents the all-atom structure of example fragments. Panel C shows the corresponding α-carbon chains. Panel D illustrates the idea of the four-residue averaging of alpha carbon positions, leading to the SURPASS pseudoresidue representation. The resulting SURPASS chains (green for helical fragments and blue for the beta strand) superimposed onto the original alpha-carbon traces are shown in the last row (panel E). Note the different radii of the pseudoresidues representing helical and beta fragments reflecting different thicknesses of such fragments in real (atomistic) structures.

The number of pseudoresidues present in the modeled system corresponds to polipeptide chain size and is equal to N-3, where N is the number of amino acids in the sequence. The positions of pseudo residues are defined by averaging the coordinates of short secondary structure fragments. These fragments are replaced by a single center of interactions. The choice of four residue averaging is crucial for the local geometry of the model because leads to an almost linear shape of the SURPASS fragments representing helices or beta strands.
The SURPASS representation assumes three types of pseudo atoms depending on secondary structure assignment of the averaged fragments of protein structure:

  • pseudo atom H (helix-like) for helical (HHHH) or almost helical (HHHC, CHHH) fragments
  • pseudo atom S (like β-strand) representing centers of mass of EEEE, EEEC or CEEE, fragments
  • pseudo atom C (coil-like) for all remaining secondary structure combinations (H, E and C)

Figure 2. Visualization of protein structure (PDB code: 2gb1, chain A). Upper panel: all-atom representation by “ribbon diagram”; lower panel: SURPASS “ball-and-stick” model. Green – α-helix; cyan – loops; blue – β-sheet. definition of secondary structure assignment in the SURPASS model lead to a slight shortening (~ 2.0Å) of both helices and β-strands, and the proportional elongation of the loop fragments. A helical fragments of SURPASS pseudo atoms have a form of straight, rigid and tightly packed stick. United atoms for β-strands represent centers of more separated a-carbons. Therefore the distance between two consecutive pseudo residues type S or C is almost two times longer than such distance in helical fragments.

SURPASS force field

The generic force field for SURPASS model describes the most fundamental properties of globular proteins. The only sequence-depend ent parameters comes from secondary structure. The background for force-field derivation define regularities observed in real protein structures. The statistics is based on a redundant set of 4600 protein chains, representing all known protein families, with resolution not lower than 1.6Å and a sequence identity not greater than 60%. Described below analysis of these statistical data defines the SURPASS force field consisting of knowledge-based statistical potentials.

[Figure 1. Schematic illustration of the terms included in the SURPASS force field.]

A. Terms to create regular secondary structure - short range interactions

The deficiencies of atomic details in strongly simplified and pre-averaged SURPASS chain may cause an incorrect local geometry of the structure. To avoid this, it is necessary to transfer the structural regularities of the atomistic models onto the corresponding sets of united atoms. All generic terms: R12, R13, R14 and R15 are prepared in six variants (HH, EE, CC, HE, HC, EC) depending on the secondary structure assignments for pairs of residues located at key positions. All short-range interactions have been implemented in the force field as potential of mean field (PMF), using a one-dimensional kernel density estimator (KDE) as a method of estimating the density of the empirical distribution.

[Table 1. Secondary structure dependent short range interactions.
| term | statistic plots (6 variants) | energy plot (all-in-one) - table 4 rows x 8 columns]

[equasion and description]

Helix stiffness
Model of hydrogen bonds

In the SURPASS model only the hydrogen bonds between residues that are distant in the sequence, especially in extended structure fragments, are modeled more directly. Therefore, the formation of model hydrogen bonds depends on the fulfillment of a few simple geometrical conditions:

  • the length of the model hydrogen bond is in a range of 3.8Å to 6.0Å, and the most probable length is 4.65Å;
  • the maximum number of connections for each pseudo residue in the β-strand is 2; if there are more potential candidates for hydrogen bond formation, the best two are chosen according to the following angular criterion:
    • a hydrogen bond should be perpendicular to the main chain of both interacting β-strands and the permitted angle range is from 70˚ to 115˚;
    • the maximum allowable twist of the beta sheet, measured as the planar angle between the main chains of two adjacent β-strands, is not greater than 55˚;
    • for a pseudo residue that forms two hydrogen bonds (with two different β-strands), the planar angle between these bonds must be greater than 125˚, and 180˚ is the best orientation.

[Figure 2. Statistical analysis of the geometry of the model hydrogen bond: A – length of hydrogen pseudobonds extracted from the RDF of distance between i-th and j-th pseudoresidues in two beta strands. B – angle between two β-strands connected by a hydrogen bond. C – twist of the β-sheet measured as a planar angle between the main chains of two adjacent β-strands; D – angle between two hydrogen bonds of three connecting β-strands.]

B. Terms to control local packing (close in space)

4. Local repulsive interactions
5. Local attractive interactions: excluded volume & contacts
  • pseudo atom H (helix-like) for helical (HHHH) or almost helical (HHHC, CHHH) fragments
  • pseudo atom S (like β-strand) representing centers of mass of EEEE, EEEC or CEEE, fragments
  • pseudo atom C (coil-like) for all remaining secondary structure combinations (H, E and C)