Native contacts

Let us consider a stochastic system described by a generic variable C. This variable may stand for the position of a bead in an optical trap, the velocity field of a fluid, the current passing through a resistance, of the number of native contacts in a protein. A trajectory or path V in configurational space is described by a discrete sequence of configurations in phase space. 

The best candidate structure from the FTDOCK computations only established 13% of the native contacts, as opposed to 51% when starting... 

Figure 8 The impact of hot-spot residue pair conformations on contact formation during docking of barnase (bn) and barstar (bs). Contact formation (as measured by the percentage of native contacts) during the first 100 ps of torsion dynamics simulations is shown see text for details.

The results of simulating barnase-barstar association after 100 ps of simple multiple copy MD without ensemble enriching are shown in Figure 9. Whereas contact formation in the simple multiple copy MD simulation has leveled off after the initial 100 ps, ensemble enriching with a linear scoring function is able to shift the ensemble population toward a higher number of established native contacts. Compared to the side-chain torsion dynamics... 

Figure 9 Formation of native contacts during a multiple copy MD simulation with and without ensemble enriching after an initial 100 ps multiple copy MD simulation see text for details. Ensembles that each consist of 10 barnase and 10 barstar copies are simulated, giving rise to 100 putative complexes. The thick lines show the mean and standard deviations, along with the best/worst values for the ensemble enriching method. The superposed thin lines show the corresponding data for the plain multicopy MD simulations without ensemble enriching.

Each axis of the segmental Q-coordinates is given by the fractional native contact Qs i,j) between a pair of different segments i and j when j > i, or within segment i when i = j ... 

The number of native contacts between i and j (within i when i = j) in X... 

By fc-mcans cluster analysis with Euclidean distance in the segmental Q-coordinates, we divided the structure ensemble of the MD unfolding trajectories into nine clusters [25]. The clustering was performed using all data obtained for the authentic and recombinant proteins, and the clusters were numbered in the order of the distance from the native structure. Figure 2.10(c)-(f) shows protein structures in four representative clusters (Clusters 1, 4, 5, and 9), in which Cluster 1 is almost identical to the native structure with all of the 17 Q-coordinates close to unity, whereas Cluster 9, which lost 84% of its native contacts, represents the unfolded state. 

To further characterize the structural changes of goat a-lactalbumin during unfolding, we examined the probability distributions of the following four structural parameters in each of the nine clusters of the structural ensemble of MD trajectories (1) the fractional native contact (Q) of the entire molecule, (2) the RMSD of C atoms between a pair of structures that belong to the same cluster, (3) the solvent-accessible surface area (SASA) of hydrophobic side chains, and (4) the SASA of hydrophilic side chains [25]. 

Fig. 5. Free energy landscape of a lattice model protein (see Sect. 2.2), as a function of two order parameters, the number of contacts C and the number of native contacts Qo (see Sect. 2.3). Unlike the energy landscape funnel picture, the free energy shows two stable states separated by a barrier (the transition state). Extended unfolded conformers quickly collapse to the molten globule, and have to overcome a barrier to folding to the native state. The funnel picture is thus reconciled with the two-state concept of a free energy barrier. Reprinted from Dinner et ah. Trends Biochem. Sci. 25, 331, (2000) with permission from Elsevier...

The number of native contacts is an important and often used parameter in protein folding descriptions. A contact is made when the a-carbons of non-adjacent residues are within a 6 A distance. A native contact is a contact that also occurs in a reference configuration representing the native state. This reference configuration can be taken from, for instance, the Protein Database (PDB) or from simulations (e.g. the most likely structure, minimum free energy, etc). The number of native contacts can be evaluated for arbitrary configurations and measures the similarity between the configuration of interest... 

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