The interpretation of protein structures: total volume, group volume distributions and packing density

Following the general procedure of Bernal &; Finney (1967) using Voronoi polyhedra, volumes occupied by all the atoms, or groups of atoms, in lysozyme and ribonuclease S have been estimated from the atomic co-ordinates provided by crystal structure studies. The average packing density for the interior of both proteins is close to 0.75, which is in the middle of the range found for crystals of most small organic molecules. For all atom types the mean packing densities fall between 0.7 and 0.8 with standard deviations between ± 0.1 and ± 0.2. It is suggested that simple geometrical packing considerations may provide useful criteria in guiding and evaluating trial structures in theoretical studies of protein folding, especially the association of distant parts of a peptide chain.Packing densities averaged over a relatively small number of atoms (5 to 15) appear to vary substantially in different parts of the same protein. Low densities representing packing defects may permit relatively easy motions, for example in an active site. Surrounding areas of high density may serve as relatively incompressible regions which transmit or correlate motions over considerable distances.The total volume of each of these two proteins as derived from the co-ordinate list appears to be larger than that estimated from the partial specific volume by 7 to 10%. If this volume difference is attributed to a change in the packing of water in a monolayer surrounding the protein, it would correspond to an average decrease, relative to bulk water, of 1 to 2 ų per water molecule in this monolayer. Such a change is about half of the decrease that occurs on the melting of ice.     

Automated interpretation of electron density maps as applied to Bence-Jones protein Rhe

Previous results obtained from the computerized interpretation (Greer, 1976) of a 3.0 Å electron density map of Bence—Jones protein Rhe have been compared with results (Wang et al., 1979) obtained by classical Richards' box techniques (Richards, 1968). Although the overall agreement between the two models is generally good, the computerized results contain several significant errors in the assignment of α-carbon atoms, which in our opinion are unlikely to be corrected without using human intervention together with other methods. However this test does show that the computerized method has potential.     

Application of the automated interpretation of electron density maps to Bence-Jones protein Rhe

The automated system for interpreting electron density maps of proteins has been applied to a newly calculated map of Bence-Jones protein Rhe. In order to test the methods and criteria incorporated in the program system, interpretation of Rhe was performed independently of the interpretation by Wang et al. (1974, 1975a,b²), who have used classical Richards box techniques. The automated system produced a single polypeptide chain which accounts for the whole molecule. Much of the secondary structure is detected and atomic co-ordinates are built for most of the main-chain atoms. The results indicate that the program system is able to interpret and build provisional main-chain co-ordinates for an electron density map of reasonable quality.     

Three-dimensional pattern recognition: an approach to automated interpretation of electron density maps of proteins

A procedure is outlined for reducing the high resolution electron density map of a protein to a set of connected thin lines which follow the density. The side chain representations are removed from this skeleton leaving primarily main chain, disulfide bridges and very strong hydrogen bonds. Crystallographic and local operators are used to separate one protein molecule from the neighboring chains in the crystal. Provisional α-carbon positions along the skeletal main chain are derived by application of the “4 Å rule”.The application of these methods to the 2.0 Å electron density map of ribonuclease S (Wyckoff et al., 1970) is described. The skeleton of the isolated molecule that is produced in this fashion provides a good over-all view of the three-dimensional folding of the protein. The results suggest that the skeleton representation can be a valuable supplement to the present methods of map interpretation and a significant step towards complete automation of the interpretation process.The three-dimensional pattern recognition procedures described may have much broader applications than the protein structure problem for which they have been developed.     

Spin and electron distributions in heme-cyanide models and hemeproteins

Proton NMR spectra of low-spin Fe(III) cyanoprotoheme as prosthetic group in a number of proteins are presented. The diagonally positioned 1-, 5- and 3-, 8-methyl groups obey shifts proportional to the Fe(III)/(II) reduction potential Em7, which indicates a pseudo-contact interaction. The correlation with Em7 is understandable if one postulates an enhanced rhombic distortion, dominating the Fe-methyl dipolar interactions. Hartree-Fock-Slater quantum chemical calculations show no significant changes of spin density as a function of the Fe-L5 distance, except at the iron atom and predominantly in the 3dxz and 3dyz orbitals. 4p orbitals, on the other hand, uphold most of the changes of electron density. We also observe a principal difference in the amino acid sequences in the heme-accommodating pocket of oxygen carriers and two-electron transmitters.     

The interpretation of scanning electron micrographs

The problem of the interpretation of images of biological objects in the scanning electron microscope is discussed. The influence of preparative techniques, drying and coating methods on the final image is illustrated by reference to higher plant protoplasts. Methods for confirming the presence of new structural detail are suggested. An attempt is made to illustrate and introduce the need for a higher standard of interpretative and critical skill in the presentation of results obtained by means of scanning electron microscopy.     

Molecular interactions in protein crystals: solvent accessible surface and stability

The accessible surface areas of 58 monomeric and dimeric proteins, when measured in the crystalline environment, are found to be simply related to molecular weight. The loss of accessible surface when the proteins go from a free to their crystalline environment is well defined, implying that the hydrophobic interaction, which has been found to contribute to protein folding and stability in living systems, also contributes to protein crystal stability.     

Change in electron and spin density upon electron transfer to haem

Haems are the cofactors of cytochromes and important catalysts of biological electron transfer. They are composed of a planar porphyrin structure with iron coordinated at the centre. It is known from spectroscopy that ferric low-spin haem has one unpaired electron at the iron, and that this spin is paired as the haem receives an electron upon reduction (I. Bertini, C. Luchinat, NMR of Paramagnetic Molecules in Biological Systems, Benjamin/Cummins Publ. Co., Menlo Park, CA, 1986, pp. 165-170; H.M. Goff, in: A.B.P. Lever, H.B. Gray (Eds.), Iron Porphyrins, Part I, Addison-Wesley Publ. Co., Reading, MA, 1983, pp. 237-281; G. Palmer, in: A.B.P. Lever, H.B. Gray (Eds.), Iron Porphyrins, Part II, Addison-Wesley Publ. Co., Reading, MA, 1983, pp. 43-88). Here we show by quantum chemical calculations on a haem a model that upon reduction the spin pairing at the iron is accompanied by effective delocalisation of electrons from the iron towards the periphery of the porphyrin ring, including its substituents. The change of charge of the iron atom is only approx. 0.1 electrons, despite the unit difference in formal oxidation state. Extensive charge delocalisation on reduction is important in order for the haem to be accommodated in the low dielectric of a protein, and may have impact on the distance dependence of the rates of electron transfer. The lost individuality of the electron added to the haem on reduction is another example of the importance of quantum mechanical effects in biological systems.     

Radial distributions of water—water distances in protein crystals

An accurate protein crystallographic structure determination requires a knowledge of the solvent contribution to the diffraction pattern. As resolutions improve, research groups are reporting coordinates of large numbers of water molecules. We examine the accuracy of these coordinates by presenting radial distributions of water—water distances from refinements at different stages and interpreting them in terms of preferred hydrogen-bonding distances and problems in solvent electron density map interpretation. Marked differences between the distributions suggest that wide variations exist in the water molecule selection and refinement criteria employed by different research groups which mask possible real differences in solvent structure.     

Change in electron and spin density upon electron transfer to haem

Haems are the cofactors of cytochromes and important catalysts of biological electron transfer. They are composed of a planar porphyrin structure with iron coordinated at the centre. It is known from spectroscopy that ferric low-spin haem has one unpaired electron at the iron, and that this spin is paired as the haem receives an electron upon reduction (I. Bertini, C. Luchinat, NMR of Paramagnetic Molecules in Biological Systems, Benjamin/Cummins Publ. Co., Menlo Park, CA, 1986, pp. 165-170; H.M. Goff, in: A.B.P. Lever, H.B. Gray (Eds.), Iron Porphyrins, Part I, Addison-Wesley Publ. Co., Reading, MA, 1983, pp. 237-281; G. Palmer, in: A.B.P. Lever, H.B. Gray (Eds.), Iron Porphyrins, Part II, Addison-Wesley Publ. Co., Reading, MA, 1983, pp. 43-88). Here we show by quantum chemical calculations on a haem a model that upon reduction the spin pairing at the iron is accompanied by effective delocalisation of electrons from the iron towards the periphery of the porphyrin ring, including its substituents. The change of charge of the iron atom is only approx. 0.1 electrons, despite the unit difference in formal oxidation state. Extensive charge delocalisation on reduction is important in order for the haem to be accommodated in the low dielectric of a protein, and may have impact on the distance dependence of the rates of electron transfer. The lost individuality of the electron added to the haem on reduction is another example of the importance of quantum mechanical effects in biological systems.