X-ray methods based on synchrotron technology have the promise of providing time-resolved structural data based on the high flux and brightness of the X-ray beams. One of the most closely examined problems in this area of time-resolved structure determination has been the examination of intermediates in ligand binding to myoglobin. Recent crystallographic experiments using synchrotron radiation have identified the protein tertiary and heme structural changes that occur upon photolysis of the myoglobin--carbon monoxide complex at cryogenic temperatures [Schlichting, I., Berendzen, J., Phillips, G., & Sweet, R. (1994) Nature 371, 808--812]. However, the precision of protein crystallographic data (approximately 0.2 A) is insufficient to provide precise metrical details of the iron--ligand bond lengths. Since bond length changes on this scale can trigger reactivity changes of several orders of magnitude, such detail is critical to a full understanding of metalloprotein structure--function relationships. Extended X-ray absorption fine structure (EXAFS) spectroscopy has the potential for analyzing bond distances to a precision of 0.02 A but is hampered by its relative insensitivity to the geometry of the backscattering atoms. Thus, it is often unable to provide a unique solution to the structure without ancillary structural information. We have developed a suite of computer programs that incorporate this ancillary structural information and compute the expected experimental spectra for a wide ranging series of Cartesian coordinate sets (global mapping). The programs systematically increment the distance of the metal to various coordinating ligands (along with their associated higher shells). Then, utilizing the ab initio EXAFS code FEFF 6.01, simulated spectra are generated and compared to the actual experimental spectra, and the differences are computed. Finally, the results for hundreds of simulations can be displayed (and compared) in a single plot. The power of this approach is demonstrated in the examination of high signal to noise EXAFS data from a photolyzed solution sample of the myoglobin--carbon monoxide complex at 10 K. Evaluation of these data using our global mapping procedures placed the iron to pyrrole nitrogen average distances close to the value for deoxymyoglobin (2.05 +/- 0.01 A), while the distance from iron to the proximal histidine nitrogen is seen to be 2.20 +/- 0.04 A. It is also shown that one cannot uniquely position the CO ligand on the basis of the EXAFS data alone, as a number of reasonable minima (from the perspective of the EXAFS) are observed. This provides a reasonable explanation for the multiplicity of solutions that have been previously reported. The results presented here are seen to be in complete agreement with the crystallographic results of Schlichting et al. (1994) within the respective errors of the two techniques; however, the extended X-ray absorption fine structure data allow the iron--ligand bond lengths to be precisely defined. An examination of the available spectroscopic data, including EXAFS, shows that the crystallographic results of Schlichting et al. (1994) are highly relevant to the physiological solution state and must be taken into account in any attempt to understand the incomplete relaxation process of the heme iron for the Mb*CO photoproduct at low temperature.