Temperature factors atoms

LSBF refines the values of the scale factor, overall temperature factor, atomic parameters (site occupancy, positional, and temperature factors) in order to minimize the difference in Fo h) and Fdh). The algorithm is based on ORFLS (1962), and the refinement is based on F(h). We made the following improvements (i) solve the normal equation by a block-diagonal matrix approximation or full matrix (ii) handle the anomalous dispersion (iii) treat several dumping factors by the user s option (iv) calculate intra/interbond distance and angle (v) unify the input/output format and the weight for DS SYSTEM. 

Equation (Bl.8.6) assumes that all unit cells really are identical and that the atoms are fixed hi their equilibrium positions. In real crystals at finite temperatures, however, atoms oscillate about their mean positions and also may be displaced from their average positions because of, for example, chemical inlioniogeneity. The effect of this is, to a first approximation, to modify the atomic scattering factor by a convolution of p(r) with a trivariate Gaussian density function, resulting in the multiplication ofy ([Pg.1366]

The temperature factor (together with the Cartesian coordinates) is the result of the rcfincincnt procedure as specified by the REMARK 3 record. High values of the temperature factor suggest cither disorder (the corresponding atom occupied different positions in different molecules in the crystal) or thermal motion (vibration). Many visualisation programs (e.g., RasMol [134] and Chime [155]) have a special color scheme designated to show this property. 

They compared the PME method with equivalent simulations based on a 9 A residue-based cutoflF and found that for PME the averaged RMS deviations of the nonhydrogen atoms from the X-ray structure were considerably smaller than in the non-PME case. Also, the atomic fluctuations calculated from the PME dynamics simulation were in close agreement with those derived from the crystallographic temperature factors. In the case of DNA, which is highly charged, the application of PME electrostatics leads to more stable dynamics trajectories with geometries closer to experimental data [30]. A theoretical and numerical comparison of various particle mesh routines has been published by Desemo and Holm [31]. 

The relative molecular dynamics fluctuations shown in Figure 7-17 can be compared with the crystallographic B-factors, which are also called temperature factors. The latter name, especially, indicates the information content of these factors they show how well defined within the X-ray structure the position of an atom is. Atoms with high temperature have an increased mobility. In principle, this is the same information as is provided by the molecular dynamics fluctuations. Using Eq. (48), the RMS fluctuation of an atom j can be converted into a B-factor... 

The Bragg peak intensity reduction due to atomic displacements is described by the well-known temperature factors. Assuming that the position can be decomposed into an average position, ,) and an infinitesimal displacement, M = 8R = Ri — (R,) then the X-ray structure factors can be expressed as follows ... 

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. 

The atomic amplitude functions take account of the atomic F- factor, the temperature factor, the Lorentz factor, and the polarization factor. 

The atomic reflecting power Fn as a function of sin B/l or of dhjcl depends on the structure of the atom and also on the forces exerted on the atom by surrounding atoms, inasmuch as the temperature factor (also a function of dh]c ) is included in the J -curve. Values of F for various atoms have been tabulated by Bragg and West. Nov it is convenient to introduce the concept of the atomic amplitude function An, defined by the equation... 

The atomic temperature factors obtained after crystallographic refinement are significantly higher for cys530 than for the other site cysteine residues. This is also true when the Ni ion is compared to the Fe center. This may reflect conformational disorder due to the fact that the crystals are made of a mixture of different Ni states (40% Ni-A, 10% Ni-B, and 50% of an EPR-silent species) (52). 

The four values correspond to the difference in temperature factors for atoms connected by a bond length, for atoms connected by a bond angle, for P-0 bond lengths, and for phosphate atoms connected by a bond angle or for atoms involved in hydrogen bonding. 

The atomic temperature factor, or B factor, measures the dynamic disorder caused by the temperature-dependent vibration of the atom, as well as the static disorder resulting from subtle structural differences in different unit cells throughout the crystal. For a B factor of 15 A2, displacement of an atom from its equilibrium position is approximately 0.44 A, and it is as much as 0.87 A for a B factor of 60 A2. It is very important to inspect the B factors during any structural analysis a B factor of less than 30 A2 for a particular atom usually indicates confidence in its atomic position, but a B factor of higher than 60 A2 likely indicates that the atom is disordered. 

One simple case of disordered structure involves many of the long charged side chains exposed to solvent, particularly lysines. For example, 16 of the 19 lysines in myoglobin are listed as uncertain past C8 and 5 of them for all atoms past C/J (Watson, 1969) for ribonuclease S Wyckoff et al. (1970) report 6 of the 10 lysine side chains in zero electron density in trypsin the ends of 9 of the 13 lysines refined to the maximum allowed temperature factor of 40 (R. Stroud and J. Chambers, personal communication) and in rubredoxin refined at 1.2 A resolution the average temperature factor for the last 4 atoms in the side chain is 9.2 for one of the four lysines versus 43.6, 74.4, and 79.3 for the others. Figure 57 shows the refined electron density for the well-ordered lysine and for the best of the disordered ones in ru-... 

Fig. 57. Model and electron density in rubredoxin after refinement at 1.2 A resolution, for (a) the well-ordered lysine, Lys-46 (temperature factor average of 9.2 for the outer four atoms of the side chain) (b) the best of the disordered lysines, Lys-3 (temperature factor average of 43.6 for the outer four side chain atoms). From Watenpaugh et al. (1980), Fig. 12, with permission.

A small problem arises when the crystal thickness and temperature factors are refined simultaneously, because these parameters are highly correlated. Raising both the thickness and the temperature factors results in almost the same least-squares sum. This is not an artifact of the calculation method but lies in the behavior of nature. Increasing the Debye-Waller factor of an atom means a less peaked scattering potential, which in turn results in a less sharply peaked interaction with the ncident electron wave. It can be shown that a thickness of 5 nm anc B=2 will give about the same results as a thickness of 10 nm and B=6 A. ... 

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