Configurational entropy in protein-peptide binding: computational study of Tsg101 ubiquitin E2 variant domain with an HIV-derived PTAP nonapeptide

Abstract

Configurational entropy is thought to influence biomolecular processes, but there are still many open questions about this quantity, including its magnitude, its relationship to molecular structure, and the importance of correlation. The mutual information expansion (MIE) provides a novel and systematic approach to extracting configurational entropy changes due to correlated motions from molecular simulations. We present the first application of the MIE method to protein-ligand binding using multiple molecular dynamics simulations to study the association of the ubiquitin E2 variant domain of the protein Tsg101 and an HIV-derived nonapeptide. This investigation utilizes the second-order MIE approximation, which accounts for correlations between all pairs of degrees of freedom. The computed change in configurational entropy is large and has a major contribution from changes in pairwise correlation. The results also reveal intricate structure-entropy relationships. Thus, the present analysis suggests that in order for a model of binding to be accurate, it must include a careful accounting of configurational entropy changes.

Figure 1

Schematic representation of the 6 translational/rotational (trans/rot) degrees of freedom used to define the relative position and orientation of the receptor and ligand within the Tsg101•PTAP molecular complex. Defining the pseudo bond B (dashed line) creates two pseudoangles and three pseudodihedrals.

Figure 2

Convergence plots of −T ΔS ⁽¹⁾ (in kcal mol⁻¹) as a function of the number of MD snapshots. The data shown indicate the entropy contributions from (a) sets of coordinates and (b) molecular components. These correspond, respectively, to the bottom row and right-hand column of Table 1.

Figure 3

Convergence plots of ΣT ΔI₂ (kcal mol⁻¹) as a function of the number of MD snapshots, or the peptide-peptide (Frames a – f), peptide-trans/rot (Frames g – i), and trans/rot-trans/rot (Frame j) correlations.

Figure 4

Convergence plots of ΣT ΔI₂(kcal mol⁻¹) as a function of the number of MD snapshots, for the peptide-Tsg101 (Frames a – i) and trans/rot-Tsg101 (Frames j – l) correlations. The dashed lines correspond to contributions from all Tsg101 residues and the solid lines correspond to the top 15 contributing residues of Tsg101 (see text).

Figure 5

The main figure shows the top and side views of a contour plot of the peptide-Tsg101 pairwise mutual information contributions, summed by residue and reported as T I₂ (kcal mol ⁻¹). The inset provides the cumulative distribution of the fraction of Tsg101 residues contributing a mutual information, summed over peptide residues, greater than a given value of T ΔI₂.

Figure 6

Convergence plots of ΣT ΔI₂ (kcal mol⁻¹) as a function of the number of MD snapshots, the Tsg101-Tsg101 correlations. The dashed lines correspond to contributions from all Tsg101 residues, and the solid lines correspond to the top 15 contributing residues (see text).

Figure 7

Changes in PDFs of the torsion angles of PTAP (a–d) and Tsg101 (e–h) that lose the most uncorrelated entropy on binding. Dashed lines: free state. Solid lines: bound state. The heavy bonds indicate the central bond of the dihedral. The entropic free energy changes, −T ΔS, (kcal mol⁻¹) are given in the upper-right corner of each frame.

Figure 8

Changes in the joint (contours) and marginal(line graphs) PDFs of torsional pairs with largest increases in mutual information on binding for Tsg101-PTAP pairs (a, b), PTAP-PTAP pairs (c, d) and Tsg101-Tsg101 pairs (e, f). Red: before binding; blue: after binding. The central bonds of the dihedrals are identified with heavy lines and the mutual information changes are reported as free energy contributions (kcal mol⁻¹) in the upper-right corner of each frame.

Figure 9

Comparison of the actual histogrammed PDFs (red, blue) with PDFs estimated by the QHA (orange, green), for three sample torsional pairs. Red and orange: before binding. Blue and green: after binding.

Figure 10

Structure-entropy relationships of Tsg101. The top row of figures diagrams (a) the backbones considered to contact the PTAP ligand [56], (b) the 15 residues with the largest uncorrelated (first-order) entropy changes, and (c) the 15 residues with the largest pairwise mutual informations with the PTAP ligand as a whole. The mutual information value assigned to a given TSG101 residue is the sum of the mutual information values of all of its atoms with all ligand atoms. The bottom shows the secondary structure and sequence of Tsg101. The red residues in the top and bottom sequences correspond, respectively, to those highlighted in (b) and (c) The underlined residues correspond to the contact points shown in (a).

Figure 11

Surface plot of Tsg101 colored by −T ΔS ⁽¹⁾ per residue. Red indicates a increase in entropy (increased motion) and blue indicates a decrease in entropy (decreased motion) on binding. The views are (a) “front”, (b) “back”, and (c) “top”. The ligand is colored green. The inset shows the convergence of the entropy associated with the red stripe along the “back” of the receptor.

Figure 12

Heat plots of (a) C_α-C_α distances in the Tsg101•PTAP complex; (b) pairwise mutual information contributions summed by residue; and (c) change in pairwise mutual information summed by residue, with the change in first-order entropy per residue shown above. The secondary structure of Tsg101, with the contact residues [56] highlighted in red, is shown below each frame. All values are reported as T I₂ in kcal mol⁻¹.