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Matricial direct methods were used to phase 28 strong low-resolution (100-19 Å) structure factors of crystalline yeast tRNAfMet (P6422, z = 12) which had not been phased by multiple isomorphous replacement (MIR). The starting phase set was composed of 107 terms in the resolution range 32-14 Å which had been phased by MIR. Extending the phase set to the strong low-resolution terms significantly improved the electron-density map. The goal of establishing a well defined molecular boundary was clearly achieved and provided the basis of a successful structure determination to 4.0 Å resolution. The phases determined by direct methods deviated from the phases subsequently calculated from the refined atomic coordinates by an unweighted average value of 73°; 36% of these were determined with a figure of merit greater than 0.75 and showed a discrepancy of only 44°. The accuracy of the phases determined by matricial methods compared favorably with those of the starting MIR phase set. An analysis of the resolution dependence of the intensities suggests plausible substructures as the basis of the normalization leading to the successful extension of phases to very low resolution.
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