温度因子B-factor.docx

温度因子B-factor的概念起源于晶体研究，主要是用来体现晶体中原子构象状态的一种模糊度，实际上反映了蛋白质分子在晶体中的构象状态，B-factor越高，模糊度越大，相应部位的构象就越不稳定或柔性越强。在晶体学数据中B-factor一般是以原子为单位给出的，通常我们将其换算成相应氨基酸残基的B-factor值，从而可以分析氨基酸残基的构象稳定性或其柔性。 研究发现将蛋白质结构中B-factor值较高的氨基酸突变后部分突变体的热稳定性可以得到明显的提高。What is a B-factor?The following is heavily based onTrueblood et al., 1996and references therein.Displacement of atoms from their mean position in a crystal structure diminishes the scattered X-ray intensity. The displacement may be the result of temperature-dependent atomic vibrations or static disorder in a crystal lattice. If the atomic displacements are assumed to be harmonic and anisotropic, the attenuation of atomic scattering factors can be represented by the atomic anisotropic Gaussian Debye-Waller factorT(h)=exp82u2hsin22T(h)=exp82uh2sin22. (1)(equation 1.4.12 fromTrueblood et al., 1996). Hereuhuhis the projection of the atomic displacementuuon the direction of diffraction vectorhh,is the scattering angle andis the X-ray wavelength. The average in the exponent denotes an average over space and time. The mean-square displacements are termed anisotropic displacement parameters (ADPs) as the average depends on the direction ofhh. Referred to a Cartesian basis, an equivalent representation of eq. (1) isT(h)=exp22hTUhT(h)=exp22hTUh. (2)The ADPs define the symmetric atomic mean-square displacement tensorU=U11U12U13U12U22U23U13U23U33U=(U11U12U13U12U22U23U13U23U33). (3)An elementUijUijofUUhas dimension (length)2. If the displacements are (assumed to be) isotropic, the average in eq. (1) is constant and the Debye-Waller factor only depends on the magnitude ofhh:T(|h|)=exp82u2sin22T(|h|)=exp82u2sin22. (4)(equation 1.4.13 fromTrueblood et al., 1996). The B-factor is directly related to the mean square isotropic displacement of the atom:B=82u2B=82u2. (5)A macromolecular crystal structure is typically represented by three coordinates (X,Y,Z), anoccupancyparameter, and a temperature factor in thecoordinate sectionof PDB files (Figure 1). These parameters are estimated during a computational process crystallographers refer to asrefinement. The goal of refinement is to improve the agreement between the modeled structure and the reflections measured in the diffraction experiment. The (an)isotropic displacement parameters are variables during a typical refinement and may therefore also contain contributions of apparent displacements resulting from the use of an inadequate model or from overlooked errors in the X-ray data. The temperature factor field in theATOM recordsof PDB files normally contains the isotropic B-factor (Figure 1) orBeqBeq, the value that represents isotropic displacement of atoms that were described by anisotropic ADPs during refinement.ATOM 1 N THR A 1 17.047 14.099 3.625 1.00 13.79 N ATOM 2 CA THR A 1 16.967 12.784 4.338 1.00 10.80 C ATOM 3 C THR A 1 15.685 12.755 5.133 1.00 9.19 C ATOM 4 O THR A 1 15.268 13.825 5.594 1.00 9.85 O ATOM 5 CB THR A 1 18.170 12.703 5.337 1.00 13.02 C ATOM 6 OG1 THR A 1 19.334 12.829 4.463 1.00 15.06 O ATOM 7 CG2 THR A 1 18.150 11.546 6.304 1.00 14.23 C Figure 1Thr 1 from1crn. After the atoms identifiers the XYZ coordinates, occupancy, and B-factor are listed in theseATOM records.The term displacement parameter is preferred over temperature factor because the atomic displacements are not only a consequence of thermal vibration but also of different atomic positions in different unit cells. The equivalent B-factor can be derived from the equivalent isotropic displacement parameterUeqUeq:Beq=82Ueq=832(U11+U22+U33)Beq=82Ueq=832(U11+U22+U33). (6)UeqUeqis equivalent to the sum of the eigenvalues ofUUand represents the mean-square displacement averaged over all directions. TheANISOU records of PDB entriesnormally contain the six independent elements of thesymmetric tensorscaled by a factor 104(Figure 2).ATOM 3293 N GLY B 635 15.522 -6.753 35.480 1.00 67.46 N ANISOU 3293 N GLY B 635 7637 10155 7840 125 844 10 N ATOM 3294 CA GLY B 635 16.002 -5.527 34.860 1.00 66.06 C ANISOU 3294 CA GLY B 635 7519 9866 7715 35 723 -268 C ATOM 3295 C GLY B 635 14.981 -4.446 34.608 1.00 69.48 C ANISOU 3295 C GLY B 635 7997 10158 8244 -4 724 -496 C ATOM 3296 O GLY B 635 15.107 -3.358 35.185 1.00 71.22 O ANISOU 3296 O GLY B 635 8207 10502 8350 -17 684 -734 O Figure 2Gly 635 from3zzw. U11, U12, U13, U12, U13, and U23are stored in theANISOU recordsafter the identifier columns. The last numeric column of theATOM recordsis the equivalent B-factor, Beq, calculated from the six Uijelements (eq. 3) in the ANISOU records (eq. 6).OccupancyB-factors in PDB files commonly are seen as a measure of (local) mobility in the (macro)molecule. As mentioned above, this is only partly true.When 3D structures are solved by crystallography, then, as the name suggests, crystals are needed. And in crystals by necessity crystal artefacts are observed. The three most important artefacts are 1) crystal packing artefacts at those locations where the (macro)molecules interact with other (macro)molecules in the crystal; 2) parts of the crystal have a different conformation of the molecule (static disorder); 3) alternate locations when parts of the macromolecule are happy in multiple conformations (dynamic disorder). Crystal packing artefacts are a whole story in themselves and are not of relevance for the BDB. You find information about these artefacts in other PDB-facilities. Alternate locations are most often seen for amino acid side chains when these can have multiple rotamers that are energetically similarly favourable. If this is observed in the crystal, then you will find multiple side chain atoms with alternate location indicators A, B, etc. The occupancies normally add up to unity (Figure 3). If no alternates have been observed, the occupancy simply equals 1.00 (e.g.Figure 1,Figure 2)ATOM 435 N SER A 69 78.391 18.901 31.786 1.00 8.05 N ATOM 436 CA ASER A 69 77.622 17.702 31.446 0.70 8.36 C ATOM 437 CA BSER A 69 77.646 17.698 31.413 0.30 8.16 C ATOM 438 C SER A 69 76.425 1