Temperature factors, protein

Yuan, Z., Zhao, J. and Wang, Z. X. (2003). Flexibility analysis of enzyme active sites by crystallographic temperature factors. Protein Eng. 16(2), 109-114. 

The atoms of a protein s structure are usually defined by four parameters, three coordinates that give their position in space and one quantity, B, which is called the temperature factor. For well refined, correct structures these B-values are of the order of 20 or less. High B-values, 40 or above, in a local region can be due to flexibility or slight disorder, but also serve as a warning that the model of this region may be incorrect. 

For proteins the X-ray structures usually are not determined at high enough resolution to use anisotropic temperature factors. Average values for B in protein structures range from as low as a few A2 for well-ordered structures to 30 A2 for structures involving flexible surface loops. Using equation 3.6, one can calculate the root mean square displacement fu2 for a well-ordered protein structure at approximately 0.25 A (for B = 5 A2) and for a not-so-well-ordered structure at... 

Refinement takes place by adjusting the model to find closer agreement between the calculated and observed structure factors. For proteins the refinements can yield R-factors in the range of 10-20%. An example taken from reference 10 is instructive. In a refinement of a papain crystal at 1.65-A resolution, 25,000 independent X-ray reflections were measured. Parameters to be refined were the positional parameters (x, y, and z) and one isotropic temperature factor parameter... 

In summary, there are three important generalizations about error estimation in protein crystallography. The first is that the level of information varies enormously as a function primarily of resolution, but also of sequence knowledge and extent of refinement. The second generalization is that no single item of information is completely immune from possible error. If the electron density map is available or indicators such as temperature factors are known from refinement, then it is possible to tell which parameters are most at risk. The third important generalization is that errors occur at a very low absolute rate 95% of the reported information is completely accurate, and it represents a detailed and objective storehouse of knowledge with which all other studies of proteins must be reconciled. 

Particularly interesting seems to be the conclusion of Schreck and Ludwig [27], who hypothesized that the barometric resistance of micro-organisms is caused by a mechanical factor, but is also dependent upon the protein-structure of microbes, as there is a deep relationship between the effect of pressure and temperature on proteins and micro-organisms. In other words, pressure acts on proteins located in specific sites where they are particularly sensitive to mechanical stress. 

With small molecules, it is usually possible to obtain anisotropic temperature factors during refinement, giving a picture of the preferred directions of vibration for each atom. But a description of anisotropic vibration requires six parameters per atom, vastly increasing the computational task. In many cases, the total number of parameters sought, including three atomic coordinates, one occupancy, and six thermal parameters per atom, approaches or exceeds the number of measured reflections. As mentioned earlier, for refinement to succeed, observations (measured reflections and constraints such as bond lengths) must outnumber the desired parameters, so that least-squares solutions are adequately overdetermined. For this reason, anisotropic temperature factors for proteins have not usually been obtained. The increased resolution possible with synchrotron sources and cryocrystallography will make their determination more common. With this development, it will become possible to obtain better estimates of uncertainties in atom positions than those provided by the Luzzati method. 

The final R-factor and structural parameters exceed the standards described in Section I and attest to the high quality of this model. Atom locations are precise to an average of 0.34 A. about one-fifth of a carbon-carbon covalent bond length. The plot of temperature factors shows greater variability and range for side-chain atoms, as expected, and shows no outlying values. The model defines the positions of all amino-acid residues in the protein. 

In the X-ray analysis of a protein crystal structure, solvent molecules appear as spheres of electron density in difference Fourier maps calculated at the end of a refinement. In a strict sense, the electron density map exhibits preferred.s/tes of hydration which are occupied by freely interchanging solvent molecules. This electron density is well defined for the tightly bound solvent molecules and can be as spurious as just above background for ill-defined molecules which exhibit large temperature factors and/or only partly occupied atomic positions. Since these two parameters are correlated in least-squares refinement, this gives rise to methodological problems. 

The first serious attempt at interpreting the protein hydration by crystallographic methods was nude 1978 on rubvedoxin, a molecule consisting of only 54 amino adds [835]. The refinement by conventional (unconstrained) least squares methods included a total of 127 water sites and converged at an R-factor of 12.7% with 1.2 A resolution data. The water oxygen atoms were added to the model only if their temperature factors were <50 A2 and their electron density was >0.3 e/A3, i.e., corresponding to the electron density expected for liquid water, 0.34 e/A3. 

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