The MXAN procedure: a new method for analysing the XANES spectra of metallo- proteins to obtain structural quantitative information M. Benfatto, a * S. Della Longa b and C. R. Natoli a a Laboratori Nazionali di Frascati dell'INFN, CP13, 00044 Frascati, Italy, and b Universita' dell'Aquila, Via Vetoio, loc. Coppito II, 67100 l'Aquila, Italy. E-mail: benfatto@lnf.infn.it The ®rst quantitative analyses are reported of the Fe K-edge polarized X-ray absorption near-edge structure (XANES) of a single crystal of the iron protein carbonmonoxy-myoglobin (MbCO) and of its cryogenic photoproduct Mb*CO. The COÐFe±heme local structure has been determined using a novel ®tting procedure, named MXAN, which is able to ®t the XANES part (from the edge to about 200 eV) of experimental X-ray absorption data. This method is based on the comparison between the experimental spectrum and several theoretical spectra that are generated by changing the relevant geometrical parameters of the site around the absorbing atom. The theoretical spectra are derived in the framework of the full multiple-scattering approach. The MXAN procedure is able to recover information about the symmetry and atomic distances, and the solution is found to be independent of the starting conditions. The extracted local structure of Mb*CO includes an FeÐCO distance of 3.08 (7) A Ê , with a tilting angle between the heme normal and the FeÐ C vector of 37 (7)  and a bending angle between the FeÐC vector and the CÐO bond of 31 (5)  Keywords: X-ray absorption near-edge spectroscopy (XANES); data analysis. 1. Introduction The low-energy part of an XAS spectrum (the XANES region) is of great interest for biological studies since it is extremely sensitive to the structural details of the absorbing site (overall symmetry, distances and bond angles). Therefore, in principle, an almost complete recovery of the geometrical structure within 6±7 A Ê from the absorbing site can be achieved from the experimental data. Structural information on protein-metal sites can be obtained with atomic resolution, in any state of the protein sample (crystal, solution), and this information can then be either compared with known X-ray structures at high resolution or used to obtain information on proteins that have proven dif®cult to crystallize (Hasnain & Hodgson, 1999; Cruickshank, 1999). Moreover, electronic information about the metal site, like its charge and spin state, can be deduced from an accurate interpretation of the XAS spectrum. Furthermore, the effects of the atomic thermal disorder are limited, because the Debye±Waller-like term is almost independent of temperature at low energies. In fact, any multiple-scattering (MS) signal of order n can be written as a sine function whose arguments contain the term 2kR tot , where R tot is the total length of the n-order MS path. Consequently the associated total Debye±Waller factor contains the term exp(2k 2  2 ), which gives the strongest contribution to the Debye± Waller factor and is almost equal to unity at low k values. Therefore, in principle, different main conformational states of a protein-metal site can be investigated, and their structure can be extracted, if the site's conformational equilibrium is modulated (e.g. by pH or temperature changes) or destabilized (e.g. by light trig- gering) to obtain each of its different speci®c states (Della Longa et al., 1998). However, the quantitative analysis of the full XAS spectrum, including the edge, is a complex many-body problem that requires an adequate treatment and time-consuming algorithms in order to calculate the absorbing cross section in the framework of the full multiple-scattering approach. Because of these dif®culties, analyses of the pre-edge and low-energy parts of XAS spectra (up to 50± 100 eV) have been exploited so far only on qualitative grounds: either by comparison with model compounds or as an aid for EXAFS studies or more advanced investigations, such as those based on the analysis of contributions related to correlation functions of orders higher than two (Filipponi & Di Cicco, 1995). Few attempts have been made to quantify the theoretical sensi- tivity of the low-energy part of the spectrum to the structural para- meters. In the few examples that can be found in the literature, quantitative comparisons between experimental data and ab initio calculations are mostly related to known structural compounds (Binsted & Hasnain, 1996). This fact arose mainly because of the lack of a ®tting procedure based on the full MS approach. Such a ®tting procedure should allow the exact calculation of the photoabsorption cross section from the edge and should avoid any a priori selection of the relevant MS paths. Recently some of us have proposed (Benfatto & Della Longa, 2001) and applied to several systems (Della Longa et al., 2001) a new method for performing a quantitative analysis of the XANES energy range, i.e. from the edge up to 200 eV. The method, called MXAN, is based on a comparison between experimental data and many theo- retical spectra that are calculated by varying selected structural parameters of an initial putative structure, i.e. a well de®ned initial geometrical con®guration around the absorber. Hundreds of different geometrical con®gurations are needed to obtain the best ®t to the experimental data. However, the XANES spectra that are related to these con®gurations are calculated in a reasonable time. The optimization in the parameter space is achieved by the mini- mization of the square residual function in the parameter space. The calculations are performed in the energy space without involving any Fourier-transform algorithm; polarized spectra can be easily analysed because the calculations are performed by the full MS approach. 2. The MXAN procedure The MXAN procedure uses the set of programs developed by the Frascati theory group (Natoli & Benfatto, 1986; Tyson et al., 1992 and references therein): in particular, VGEN, a generator of muf®n-tin potentials, and the CONTINUUM code for the calculation of the full multiple-scattering cross section. The optimization in the space of the parameters is achieved using the MINUIT routines of the CERN library; a single best-®t procedure takes typically 8 h on a UNIX scalar -VAX machine for a calculation involving six ®tting para- meters in a cluster of 35 atoms. The MINUIT routines minimize the square residual function S 2  n P m i1 w i y th i  y exp i   " 1 i   2 = P m i1 w i ; 1 where n is the number of independent parameters, m is the number of data points, y th i and y exp i are the theoretical and experimental values of absorption, " i are the individual errors in the experimental data set, and w i are statistical weights. For w i = constant = 1, the square resi- dual function S 2 becomes the statistical  2 function. The application of the software package to several test cases shows that the best-®t J. Synchrotron Rad. (2003). 10, 51±57 # 2003 International Union of Crystallography  Printed in Great Britain ± all rights reserved 51 research papers