Overall estimated standard uncertainties of thermal parameters
based on Maximum likelihood residual.
Overall ESU gives an idea about uncertainties of B-values of
averagely defined atoms (atoms with B-values equal to average
B-value)
N_a
(sigma_B)2 = 8 ----------------------------------------------
sumi {(1/Sigma - (E_o)2 (1-m2)(SUM_AS)s4}
SUM_AS = (sigma_A)2/Sigma2)
N_a = number of atoms
Sigma = (sigma_{E;exp})2 + epsilon (1-{sigma_A)2)
E_o = normalized structure factors
sigma_{E;exp} = experimental uncertainties of normalized
structure factors
sigma_A = <cos 2 pi s delta_x> SQRT(Sigma_P/Sigma_N)
estimated using maximum likelihood
Sigma_P = sum_{atoms in model} f2
Sigma_N = sum_{atoms in crystal} f2
f = is form factor of atoms
delta_x = expected error
m = is figure of merit of phases of reflection
included in summation delta_x expected error
s = reciprocal space vector
epsilon = multiplicity of diffracting plane
summation is over all reflections included in refinement
Reference for sigma_A estimation:
"Refinement of Macromolecular Structures by the
Maximum-Likelihood Method:" G.N. Murshudov, A.A.Vagin and
E.J.Dodson,(1997) Acta Crystallogr. D53, 240-255
Reference for ESU_ML estimation:
"Simplified error estimation a la Cruickshank in macromolecular
crystallography", Murshudov G.N. & Dodson E.J. in the "CCP4
Newsletter on protein crystallography" Number 33 ed. M.Winn