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PubMed1992

Dynamic programming algorithms for biological sequence comparison.

Efficient dynamic programming algorithms are available for a broad class of protein and DNA sequence comparison problems. These algorithms require computer time proportional to the product of the lengths of the two sequences being compared [O(N2)] but require memory space proportional only to the sum of these lengths [O(N)]. Although the requirement for O(N2) time limits use of the algorithms to the largest computers when searching protein and DNA sequence databases, many other applications of these algorithms, such as calculation of distances for evolutionary trees and comparison of a new sequence to a library of sequence profiles, are well within the capabilities of desktop computers. In particular, the results of library searches with rapid searching programs, such as FASTA or BLAST, should be confirmed by performing a rigorous optimal alignment. Whereas rapid methods do not overlook significant sequence similarities, FASTA limits the number of gaps that can be inserted into an alignment, so that a rigorous alignment may extend the alignment substantially in some cases. BLAST does not allow gaps in the local regions that it reports; a calculation that allows gaps is very likely to extend the alignment substantially. Although a Monte Carlo evaluation of the statistical significance of a similarity score with a rigorous algorithm is much slower than the heuristic approach used by the RDF2 program, the dynamic programming approach should take less than 1 hr on a 386-based PC or desktop Unix workstation. For descriptive purposes, we have limited our discussion to methods for calculating similarity scores and distances that use gap penalties of the form g = rk. Nevertheless, programs for the more general case (g = q+rk) are readily available. Versions of these programs that run either on Unix workstations, IBM-PC class computers, or the Macintosh can be obtained from either of the authors.

Algorithms↗

PubMed1986

A dynamic programming algorithm for finding alternative RNA secondary structures.

Dynamic programming algorithms that predict RNA secondary structure by minimizing the free energy have had one important limitation. They were able to predict only one optimal structure. Given the uncertainties of the thermodynamic data and the effects of proteins and other environmental factors on structure, the optimal structure predicted by these methods may not have biological significance. We present a dynamic programming algorithm that can determine optimal and suboptimal secondary structures for an RNA. The power and utility of the method is demonstrated in the folding of the intervening sequence of the rRNA of Tetrahymena. By first identifying the major secondary structures corresponding to the lowest free energy minima, a secondary structure of possible biological significance is derived.

Animals↗

PubMed1992

Dynamic programming algorithms for restriction map comparison.

For most sequence comparison problems there is a corresponding map comparison algorithm. While map data may appear to be incompatible with dynamic programming, we show in this paper that the rigor and efficiency of dynamic programming algorithms carry over to the map comparison algorithms. We present algorithms for restriction map comparison that deal with two types of map errors: (i) closely spaced sites for different enzymes can be ordered incorrectly, and (ii) closely spaced sites for the same enzyme can be mapped as a single site. The new algorithms are a natural extension of a previous map comparison model. Dynamic programming algorithms for computing optimal global and local alignments under the new model are described. The new algorithms take about the same order of time as previous map comparison algorithms. Programs implementing some of the new algorithms are used to find similar regions within the Escherichia coli restriction map of Kohara et al.

Algorithms↗

PubMed1990

Determining minimum energy conformations of polypeptides by dynamic programming.

A combinatorial optimization approach is used for solving the multiple-minima problem when determining the low-energy conformations of short polypeptides. Each residue is represented by a finite number of discrete states corresponding to single residue local minima of the energy function. These precomputed values constitute a search table and define the conformational space for discrete minimization by a generalized dynamic programming algorithm that significantly limits the number of intermediate conformations to be generated during the search. Since dynamic programming involves stagewise decisions, it results in buildup-type procedures implemented in two different forms. The first procedure predicts a number of conformations by a completely discrete search and these are subsequently refined by local minimization. The second involves limited continuous local minimization within the combinatorial algorithm, generally restricted to two dihedral angles in a buildup step. Both procedures are tested on 17 short peptides previously studied by other global minimization methods but involving the same potential energy function. The discrete method is extremely fast, but proves to be successful only in 14 of the 17 test problems. The version with limited local minimization finds, however, conformations in all the 17 examples that are close to the ones previously presented in the literature or have lower energies. In addition, results are almost independent of the cutoff energy, the most important parameter governing the search. Although the limited local minimization increases the number of energy evaluations, the method still offers substantial advantages in speed.

Algorithms↗

PubMed1990

Alignment of protein sequences using secondary structure: a modified dynamic programming method.

A method for comparison of protein sequences based on their primary and secondary structure is described. Protein sequences are annotated with predicted secondary structures (using a modified Chou and Fasman method). Two lettered code sequences are generated (Xx, where X is the amino acid and x is its annotated secondary structure). Sequences are compared with a dynamic programming method (STRALIGN) that includes a similarity matrix for both the amino acids and secondary structures. The similarity value for each paired two-lettered code is a linear combination of similarity values for the paired amino acids and their annotated secondary structures. The method has been applied to eight globin proteins (28 pairs) for which the X-ray structure is known. For protein pairs with high primary sequence similarity (greater than 45%), STRALIGN alignment is identical to that obtained by a dynamic programming method using only primary sequence information. However, alignment of protein pairs with lower primary sequence similarity improves significantly with the addition of secondary structure annotation. Alignment of the pair with the least primary sequence similarity of 16% was improved from 0 to 37% 'correct' alignment using this method. In addition, STRALIGN was successfully applied to seven pairs of distantly related cytochrome c proteins, and three pairs of distantly related picornavirus proteins.

Amino Acid Sequence↗

PubMed1988

Smoothing noisy data using dynamic programming and generalized cross-validation.

Smoothing and differentiation of noisy data using spline functions requires the selection of an unknown smoothing parameter. The method of generalized cross-validation provides an excellent estimate of the smoothing parameter from the data itself even when the amount of noise associated with the data is unknown. In the present model only a single smoothing parameter must be obtained, but in a more general context the number may be larger. In an earlier work, smoothing of the data was accomplished by solving a minimization problem using the technique of dynamic programming. This paper shows how the computations required by generalized cross-validation can be performed as a simple extension of the dynamic programming formulas. The results of numerical experiments are also included.

Algorithms↗

PubMed1990

Definition of general topological equivalence in protein structures. A procedure involving comparison of properties and relationships through simulated annealing and dynamic programming.

A protein is defined as an indexed string of elements at each level in the hierarchy of protein structure: sequence, secondary structure, super-secondary structure, etc. The elements, for example, residues or secondary structure segments such as helices or beta-strands, are associated with a series of properties and can be involved in a number of relationships with other elements. Element-by-element dissimilarity matrices are then computed and used in the alignment procedure based on the sequence alignment algorithm of Needleman & Wunsch, expanded by the simulated annealing technique to take into account relationships as well as properties. The utility of this method for exploring the variability of various aspects of protein structure and for comparing distantly related proteins is demonstrated by multiple alignment of serine proteinases, aspartic proteinase lobes and globins.

Amino Acid Sequence↗

PubMed1969