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V N Maiorov

Publications and source records attributed to V N Maiorov.

17 recordsLinked to original sources
PubMed1996

(Probably) all possible protein folds at low resolution.

For decades, a large number of investigators have been sifting the database of experimentally determined three-dimensional protein structures to discover recurring patterns of all types. Now that there are over a thousand such structures available, the natural question is whether we have seen all substantially different protein folds, and if not, how many have yet to be discovered? Answering the question can be broken down into three steps: (1) choose the range and domain for a similarity function, then (2) choose a particular similarity function, and (3) construct a corresponding protein model space that can be searched for dissimilar structures. In our analysis of the problem, we first chose to examine different conformations of the same protein, taking into account only C alpha atomic coordinates. In particular, we do not compare proteins of different chain lengths on the basis of some kind of gapped alignment. Secondly, we use a measure of conformational similarity based on rigid body superposition that emphasizes overall geometric resemblance, rather than agreement in secondary structure, for example. Third, we employed the discrete cosine transform to construct exhaustive sets of globular self-avoiding C alpha traces that were all different from each other by a given level. These sets of artificial structures were not too large to explicitly enumerate as long as the level of dissimilarity was high, and the chain flexibility was low. For chains flexible enough to match all experimental structures of 170 residue or less that are not beta-barrels, we find 128 artificial structures, of which 28 resemble nothing in the Protein Data Bank.

Amino Acid Sequence↗
PubMed1995

How many protein folding motifs are there?

As the three-dimensional structures of more and more proteins are determined by experiment, discovering substantially novel folding motifs becomes ever rarer. The natural question is how many motifs are there and how many have already been found? In order to answer this in at least one plausible and well-defined sense, we have chosen a quantitative measure of conformational similarity, rho (based on optimal rigid body superposition), and a means of generating all possible three-dimensional chain conformations using the discrete cosine transform. How many different folding motifs there are then depends on the specified cutoff in rho and on the flexibility allowed for the model polypeptide chain. For single chain proteins having no more than about 170 residues and which are not beta-barrels, there are only about 128 motifs that differ by rho > 1.0 (an extremely vague level of similarity), of which so far only 100 have been seen experimentally. The remaining 28 can be viewed as very low-resolution models of either undiscovered novel folds or violations of unknown principles of protein folding.

Models, Theoretical↗
PubMed1995

Size-independent comparison of protein three-dimensional structures.

Protein structures are routinely compared by their root-mean-square deviation (RMSD) in atomic coordinates after optimal rigid body superposition. What is not so clear is the significance of different RMSD values, particularly above the customary arbitrary cutoff for obvious similarity of 2-3 A. Our earlier work argued for an intrinsic cutoff for protein similarity that varied with the number of residues in the polypeptide chains being compared. Here we introduce a new measure, rho, of structural similarity based on RMSD that is independent of the sizes of the molecules involved, or of any other special properties of molecules. When rho is less than 0.4-0.5, protein structures are visually recognized to be obviously similar, but the mathematically pleasing intrinsic cutoff of rho < 1.0 corresponds to overall similarity in folding motif at a level not usually recognized until smoothing of the polypeptide chain path makes it striking. When the structures are scaled to unit radius of gyration and equal principle moments of inertia, the comparisons are even more universal, since they are no longer obscured by differences in overall size and ellipticity. With increasing chain length, the distribution of rho for pairs of random structures is skewed to higher values, but the value for the best 1% of the comparisons rises only slowly with the number of residues. This level is close to an intrinsic cutoff between similar and dissimilar comparisons, namely the maximal scaled rho possible for the two structures to be more similar to each other than one is to the other's mirror image. The intrinsic cutoff is independent of the number of residues or points being compared. For proteins having fewer than 100 residues, the 1% rho falls below the intrinsic cutoff, so that for very small proteins, geometrically significant similarity can often occur by chance. We believe these ideas will be helpful in judging success in NMR structure determination and protein folding modeling.

Computer Graphics↗
PubMed1994

Significance of root-mean-square deviation in comparing three-dimensional structures of globular proteins.

In the study of globular protein conformations, one customarily measures the similarity in three-dimensional structure by the root-mean-square deviation (RMSD) of the C alpha atomic coordinates after optimal rigid body superposition. Even when the two protein structures each consist of a single chain having the same number of residues so that the matching of C alpha atoms is obvious, it is not clear how to interpret the RMSD. A very large value means they are dissimilar, and zero means they are identical in conformation, but at what intermediate values are they particularly similar or clearly dissimilar? While many workers in the field have chosen arbitrary cutoffs, and others have judged values of RMSD according to the observed distribution of RMSD for random structures, we propose a self-referential, non-statistical standard. We take two conformers to be intrinsically similar if their RMSD is smaller than that when one of them is mirror inverted. Because the structures considered here are not arbitrary configurations of point atoms, but are compact, globular, polypeptide chains, our definition is closely related to similarity in radius of gyration and overall chain folding patterns. Being strongly similar in our sense implies that the radii of gyration must be nearly identical, the root-mean-square deviation in interatomic distances is linearly related to RMSD, and the two chains must have the same general fold. Only when the RMSD exceeds this level can parts of the polypeptide chain undergo nontrivial rearrangements while remaining globular. This enables us to judge when a prediction of a protein's conformation is "correct except for minor perturbations", or when the ensemble of protein structures deduced from NMR experiments are "basically in mutual agreement".

Protein Conformation↗
PubMed1994

Learning about protein folding via potential functions.

Over the last few years we have developed an empirical potential function that solves the protein structure recognition problem: given the sequence for an n-residue globular protein and a collection of plausible protein conformations, including the native conformation for that sequence, identify the correct, native conformation. Having determined this potential on the basis of only some 6500 native/nonnative pairs of structures for 58 proteins, we find it recognizes the native conformation for essentially all compact, soluble, globular proteins having known native conformations in comparisons with 10(4) to 10(6) reasonable alternative conformations apiece. In this sense, the potential encodes nearly all the essential features of globular protein conformational preference. In addition it "knows" about many additional factors in protein folding, such as the stabilization of multimeric proteins, quaternary structure, the role of disulfide bridges and ligands, proproteins vs. processed proteins, and minimal strand lengths in globular proteins. Comparisons are made with other sorts of protein folding problems, and applications in protein conformational determination and prediction are discussed.

Models, Molecular↗
PubMed1992

Contact potential that recognizes the correct folding of globular proteins.

We have devised a continuous function of interresidue contacts in globular proteins such that the X-ray crystal structure has a lower function value than that of thousands of protein-like alternative conformations. Although we fit the adjustable parameters of the potential using only 10,000 alternative structures for a selected training set of 37 proteins, a grand total of 530,000 constraints was satisfied, derived from 73 proteins and their numerous alternative conformations. In every case where the native conformation is adequately globular and compact, according to objective criteria we have developed, the potential function always favors the native over all alternatives by a substantial margin. This is true even for an additional three proteins never used in any way in the fitting procedure. Conformations differing only slightly from the native, such as those coming from crystal structures of the same protein complexed with different ligands or from crystal structures of point mutants, have function values very similar to the native's and always less than those of alternatives derived from substantially different crystal structures. This holds for all 95 structures that are homologous to one or another of various proteins we used. Realizing that this potential should be useful for modeling the conformation of new protein sequences from the body of protein crystal structures, we suggest a test for deciding whether a nearly correct approximation to the native conformation has been found.

Animals↗
PubMed1989

An automatic search for similar spatial arrangements of alpha-helices and beta-strands in globular proteins.

A fast search algorithm to reveal similar polypeptide backbone structural motifs in proteins is proposed. It is based on the vector representation of a polypeptide chain fold in which the elements of regular secondary structures are approximated by linear segments (Abagyan and Maiorov, J. Biomol. Struct. Dyn. 5, 1267-1279 (1988)). The algorithm permits insertions and deletions in the polypeptide chain fragments to be compared. The fast search algorithm implemented in FASEAR program is used for collecting beta alpha beta supersecondary structure units in a number of alpha/beta proteins of Brookhaven Data Bank. Variation of geometrical parameters specifying backbone chain fold is estimated. It appears that the conformation of the majority of the fragments, although almost all of them are right-handed, is quite different from that of standard beta alpha beta units. Apart from searching for specific type of secondary structure motif, the algorithm allows automatically to identify new recurrent folding patterns in proteins. It may be of particular interest for the development of tertiary template approach for prediction of protein three-dimensional structure as well for constructing artificial polypeptides with goal-oriented conformation.

Algorithms↗
PubMed1988

Solution spatial structure of 'long' neurotoxin M9 from the scorpion Buthus eupeus by 1H-NMR spectroscopy.

1H-NMR spectra of Buthus eupeus neurotoxin M9 (66 amino acid residues, four disulfide bonds) reveal two slowly exchangeable conformations at acidic pH. The spatial structure of the conformer prevailing under physiologically relevant conditions has been determined from two-dimensional 1H-NMR data treated by means of a distance geometry algorithm and refined by molecular modelling. Interrelation between the structure and function of mammalian neurotoxin M9 is discussed by comparing its conformation with those of the scorpion insectotoxins which exhibit different biological specificity (insectotoxins v-2, v-3 and I5A).

Amino Acid Sequence↗
PubMed1988

A simple qualitative representation of polypeptide chain folds: comparison of protein tertiary structures.

A new simple quantitative representation of three-dimensional structure of globular proteins is proposed which is useful for comparison of distantly related problems, computer sorting of large sets of conformations, and search of structurally similar domains in protein data base. The folding course of the polypeptide backbone is approximated by a set of successive vectors corresponding to the elements of regular secondary structure (e.g. alpha-helices, strands of beta-sheets) and non-regular segments. The parameters specifying the spatial organization of segments in this vector model are internal coordinates, namely, lengths of the vectors, planar and dihedral angles. Quantitative representation proposed allows to circumvent the problem of insertions/deletions and to avoid the stage of best superposition during protein comparison. An application was made to the comparison of three-dimensional structures of scorpion toxins Centruroides sculpturatus Ewing v-3, Buthus eupeus M9 and I5A, which have different chain lengths and low sequence similarity.

Models, Molecular↗
PubMed1978

[Morphometric features of changes in the neurons of the jejunum in the aging body].

It is common observation that in aged people, the number of processes in long-axonal and equal-axonal neurons decreases. Quantitative ratio of these neurons changes, as well. While at mature age long-axonal/equal-axonal ratio is 3 : 1, at old age it makes 1 : 2. In dogs, unlike in human beings, the old age influences neither the number of processes, nor the quantitative ratio of the neurons mentioned.

Adult↗