Probing protein mechanics: residue-level properties and their use in defining domains

Abstract

It is becoming clear that, in addition to structural properties, the mechanical properties of proteins can play an important role in their biological activity. It nevertheless remains difficult to probe these properties experimentally. Whereas single-molecule experiments give access to overall mechanical behavior, notably the impact of end-to-end stretching, it is currently impossible to directly obtain data on more local properties. We propose a theoretical method for probing the mechanical properties of protein structures at the single-amino acid level. This approach can be applied to both all-atom and simplified protein representations. The probing leads to force constants for local deformations and to deformation vectors indicating the paths of least mechanical resistance. It also reveals the mechanical coupling that exists between residues. Results obtained for a variety of proteins show that the calculated force constants vary over a wide range. An analysis of the induced deformations provides information that is distinct from that obtained with measures of atomic fluctuations and is more easily linked to residue-level properties than normal mode analyses or dynamic trajectories. It is also shown that the mechanical information obtained by residue-level probing opens a new route for defining so-called dynamical domains within protein structures.

FIGURE 1

Force constant histogram for the residues of an (Ala)₁₃ α-helix. The inserted schematic graphics show movements of the Cα backbone after an imposed restraint D_i = 0.2 Å on the central residue and on a residue close to the C-terminal. For visibility, the length of the displacement vectors has been increased by an order of magnitude.

FIGURE 2

Force constant histogram for the residues of SNase calculated using an all-atom representation. Secondary structures are indicated along the abscissa as gray bars for β-sheets and black bars for α-helices. The bold line shows the force constants calculated using the coarse-grained model. The fine line shows the inverse square fluctuations calculated with the coarse-grained model (fitted using a proportionality constant and then shifted up the ordinate by 4 nN Å⁻¹ for clarity).

FIGURE 3

Response of SNase to imposed restraints: (a) a colored backbone representation of the calculated force constants. The blue→green→red scale corresponds to increasing values. (b) Movement of the restrained Cα atoms for D_i = 0.2 Å. For visibility, the length of the movement vectors has been increased by an order of magnitude. The images in figures 3, 5, 6, and 7 were prepared using VMD (Humphrey et al., 1996).

FIGURE 4

Number of domains detected as a function of the threshold value T (Å). The curves shown from bottom to top correspond respectively to catenin, cadherin, the D-ribose binding protein (open), the cadherin dimer, and pepsin. The arrow on the abscissa shows the chosen threshold of 0.35 Å.

FIGURE 5

(a) Mechanical domain structure derived for SNase. The secondary-structure cartoon representation shows four domains colored respectively in blue, red, yellow, and purple. (b) An exploded CPK view of the protein domains (colored as in a) showing the residues with the highest force constants in green.

FIGURE 6

Mechanical domain structures of a variety of proteins: (a) calmodulin, (b) γB-crystallin, (c) guanylate kinase, (d) cadherin, (e) LAO, (f) α-catenin, (g) D-ribose binding protein (open), (h) D-ribose binding protein (closed), (i) pepsin, and (j) cadherin dimer. Only the protein backbones are shown.

FIGURE 7

Exploded CPK views showing that the residues associated with the highest force constants (in green) are principally found at the interface regions between mechanical domains: (a) calmodulin, (b) γB-crystallin, (c) guanylate kinase, (d) cadherin, (e) LAO, (f) α-catenin, (g) D-ribose binding protein (open), (h) D-ribose binding protein (closed), (i) pepsin, and (j) cadherin dimer. The domain colors are the same as in Fig. 6.