Flexibility and packing in proteins - PubMed (original) (raw)

Flexibility and packing in proteins

Bertil Halle. Proc Natl Acad Sci U S A. 2002.

Abstract

Structural flexibility is an essential attribute, without which few proteins could carry out their biological functions. Much information about protein flexibility has come from x-ray crystallography, in the form of atomic mean-square displacements (AMSDs) or B factors. Profiles showing the AMSD variation along the polypeptide chain are usually interpreted in dynamical terms but are ultimately governed by the local features of a highly complex energy landscape. Here, we bypass this complexity by showing that the AMSD profile is essentially determined by spatial variations in local packing density. On the basis of elementary statistical mechanics and generic features of atomic distributions in proteins, we predict a direct inverse proportionality between the AMSD and the contact density, i.e., the number of noncovalent neighbor atoms within a local region of approximately 1.5 nm(3) volume. Testing this local density model against a set of high-quality crystal structures of 38 nonhomologous proteins, we find that it accurately and consistently reproduces the prominent peaks in the AMSD profile and even captures minor features, such as the periodic AMSD variation within alpha helices. The predicted rigidifying effect of crystal contacts also agrees with experimental data. With regard to accuracy and computational efficiency, the model is clearly superior to its predecessors. The quantitative link between flexibility and packing density found here implies that AMSDs provide little independent information beyond that contained in the mean atomic coordinates.

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Figures

Figure 1

Figure 1

Radial distribution of nonhydrogen atoms around each α carbon in parvalbumin (2

pvb

), computed from Eq. 6. The thick black curve is the average of the 107 gray curves.

Figure 2

Figure 2

Normalized contact density distribution (binned to integral n values) for all 6,231 α carbons in the set of 38 proteins (black) and for the uniform-sphere model described in the text (gray). For the latter case, the n = 100 bar has been truncated at about 25% of its real height, P(100) = 0.196.

Figure 3

Figure 3

Experimental (dots) and calculated (curve) AMSD profiles for the α carbons in S. marcescens endonuclease (1

ql

0). Predicted AMSDs are based on contact densities including all nonhydrogen protein atoms in the crystal. Experimental points are color coded according to secondary structure: α helix (blue), β strand (red), and turn (orange).

Figure 4

Figure 4

Experimental (dots) and calculated (curves) AMSD profiles for the α carbons in B. caldolyticus cold-shock protein (1

c

9

o

). Predicted AMSDs are based on contact densities including all nonhydrogen protein atoms in the crystal (thick black curve) or only atoms in the same protein molecule as the reference α carbons (thin blue curve). Experimental points are color coded according to secondary structure: α helix (blue), β strand (red), and turn (orange).

Figure 5

Figure 5

AMSD profile for all nonhydrogen atoms in the Kunitz-type domain (C5) from the α-3 chain of human type VI collagen (2

knt

). Circles represent experimental backbone (filled) and side-chain (open) AMSDs, and curves represent predicted AMSDs on the basis of contact densities including all nonhydrogen protein atoms in the crystal (thick black curve, Δ = 0.63, ρ = 0.72) or only atoms in the same protein molecule as the reference atoms (thin blue curve, Δ = 0.64, ρ = 0.76). Experimental points for atoms in disulfide Cys residues are colored orange.

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