Matthews coefficient probabilities: Improved estimates for unit cell contents of proteins, DNA, and protein–nucleic acid complex crystals

Abstract

Estimating the number of molecules in the crystallographic asymmetric unit is one of the first steps in a macromolecular structure determination. Based on a survey of 15,641 crystallographic Protein Data Bank (PDB) entries the distribution of V M , the crystal volume per unit of protein molecular weight, known as Matthews coefficient, has been reanalyzed. The range of values and frequencies has changed in the 30 years since Matthews first analysis of protein crystal solvent content. In the statistical analysis, complexes of proteins and nucleic acids have been treated as a separate group. In addition, the V M distribution for nucleic acid crystals has been examined for the first time. Observing that resolution is a significant discriminator of V M , an improved estimator for the probabilities of the number of molecules in the crystallographic asymmetric unit has been implemented, using resolution as additional information. , that the fraction of the crystal volume occupied by solvent ranged from 27% to 78%, with the most common value being about 43% (Matthews 1968(Matthews , 1976. Matthews defined V M , known as the Matthews coefficient, as the crystal volume per unit of protein molecular weight, and showed that V M bears a straightforward relationship to the fractional volume of solvent in the crystal. The range of V M values was found to be essentially independent of the volume of the asymmetric unit. The frequency distribution of V M for proteins is not symmetric, but has a rather sharp cutoff at the lower end, at approximately the value for close packed spheres (∼26% solvent content). Matthews recognized that the distribution of V M would be useful in preliminary studies of protein crystals to estimate the number of molecules per asymmetric unit, particularly in the molecular weight region below 70 kD, although he suggested that examples would likely be found with V M lying outside the range. Although it was also noted that higher molecular weight proteins had a tendency to form crystals with a higher fractional volume of solvent (Matthews 1976), there were not enough data to statistically determine the range of V M for such proteins.More than 30 years have passed since Matthews first analysis of protein crystal solvent content, yet the original distribution of V M is still widely used as a guide in determining the contents of the crystallographic asymmetric unit. Given the plethora of crystal forms now available in the Protein Data Bank (PDB; Berman et al. 2000), we decided

Caught in the act: the crystal structure of cleaved cathepsin L bound to the active site of Cathepsin L

“…a part of the physiological substrate histone H3 and human cathepsin L by crystallizing the complex with a catalytic mutant of the enzyme and elucidating its structure [16]. Refinement confirmed the positioning of only three amino acids from the histone H3 [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33] peptide. Our crystal packing analysis suggested that there is not enough space to accommodate all 14 peptide residues in the available space in the active site cleft.…”

“…The data set was processed with the XDSAPP [20] and scaled in the P212121 space group. The Matthews coefficient analysis [21] unambiguously defined one molecule in the asymmetric unit. The structure of cathepsin L-C25S was determined using PHASER [22] with the cathepsin L structure (PDB ID 2YJ2) [23] as the search model.…”

Improving the diffraction of apoA-IV crystals through extreme dehydration

“…During the dehydration process the unit-cell volume of the crystals decreased by 13.6%, which corresponded to a significant reduction of solvent content from 64.5 to 58.9% (Kantardjieff & Rupp, 2003;Fig. 3c).…”

Crystallization and preliminary structural analysis of theListeria monocytogenesCa2+-ATPase LMCA1

“…R meas = P h ½n h =ðn h À 1Þ 1=2 P n h i jhI h i À I h;i j= P h P n h i I h;i , where n h is the multiplicity, I h,i is the ith intensity of reflection h and hI h i is the weighted average intensity for all observations i of reflection h. R merge-F = ð P jA I h;P À A I h;Q jÞ=ð 1 2 P A I h;P À A I h;Q Þ, where I h,P and I h,Q represent the partially averaged intensities (Diederichs & Karplus, 1997). ‡ The most probable solution according to statistical sampling (Kantardjieff & Rupp, 2003). However, it also has the lowest sequence identity of the domains compared with the SERCA1a search model (28% compared with 38% overall), with truncations and deletions of secondary-structure elements and loop regions, which may in part explain this observation.…”