Accurate statistics for local sequence alignment with position-dependent scoring by rare-event sampling

Abstract

BackgroundMolecular database search tools need statistical models to assess the significance for the resulting hits. In the classical approach one asks the question how probable a certain score is observed by pure chance. Asymptotic theories for such questions are available for two random i.i.d. sequences. Some effort had been made to include effects of finite sequence lengths and to account for specific compositions of the sequences. In many applications, such as a large-scale database homology search for transmembrane proteins, these models are not the most appropriate ones. Search sensitivity and specificity benefit from position-dependent scoring schemes or use of Hidden Markov Models. Additional, one may wish to go beyond the assumption that the sequences are i.i.d. Despite their practical importance, the statistical properties of these settings have not been well investigated yet.ResultsIn this paper, we discuss an efficient and general method to compute the score distribution to any desired accuracy. The general approach may be applied to different sequence models and and various similarity measures that satisfy a few weak assumptions. We have access to the low-probability region ("tail") of the distribution where scores are larger than expected by pure chance and therefore relevant for practical applications. Our method uses recent ideas from rare-event simulations, combining Markov chain Monte Carlo simulations with importance sampling and generalized ensembles. We present results for the score statistics of fixed and random queries against random sequences. In a second step, we extend the approach to a model of transmembrane proteins, which can hardly be described as i.i.d. sequences. For this case, we compare the statistical properties of a fixed query model as well as a hidden Markov sequence model in connection with a position based scoring scheme against the classical approach.ConclusionsThe results illustrate that the sensitivity and specificity strongly depend on the underlying scoring and sequence model. A specific ROC analysis for the case of transmembrane proteins supports our observation.

Pharmacophore Alignment Search Tool (PhAST): Significance Assessment of Chemical Similarity

“…Third, it has been shown that the results obtained with Rare Event Sampling with one and two random sequences are not identical but show serious differences 56. As we pointed out, the query sequence is not random and it makes sense to keep it fixed.…”

“…We identified the Gumbel distribution with Gaussian correction as best approximation for the empirical alignment score distributions obtained with Rare Event Sampling . This combination has been suggested before for local alignments of protein sequences of shorter length 55,56. The sequences generated with PhAST are not of biological origin.…”

“…The reason for this modification is that in a virtual screening, the query molecule is not ‘random’ at all. The same modification was investigated previously in combination with position specific scoring and yielded realistic results for protein sequence alignments 56. Random sequences were composed based on symbol frequencies f i as shown in Table 1.…”

“…Rare Event Sampling was used before for local sequence alignments 54–56. It is based on a Markov Chain with states C i consisting of the sequence pair ( X , Y i ) with alignment score s i and transition probabilities p Ci,Cj between them.…”

“…However, the results obtained from our curve fitting experiments and evaluations of goodness‐of‐fit can give a general idea of the character of those distributions and identify distribution types that are better approximations of the real distribution than others. We compared sampled distributions to fitted Gaussian, Gumbel, modified Gumbel and three‐parameter Gamma distributions 51,55,56,81. Goodness of fit was evaluated using the root mean squared deviation ( RMSD ), the scaled root mean squared distribution ( SRMSD , obtained by scaling the RMSD using the standard error82), a measure we developed specifically for this purpose taking into account the standard error and sampling accuracy ( Z ‐deviation), and the p ‐value slope error ( PSE ).…”