Pattern recognition of sequence similarities in globular proteins by Fourier analysis: a novel approach to molecular evolution

The efficient computation of position-specific match scores with the fast fourier transform

Historically, in computational biology the fast Fourier transform (FFT) has been used almost exclusively to count the number of exact letter matches between two biosequences. This paper presents an FFT algorithm that can compute the match score of a sequence against a position-specific scoring matrix (PSSM). Our algorithm finds the PSSM score simultaneously over all offsets of the PSSM with the sequence, although like all previous FFT algorithms, it still disallows gaps. Although our algorithm is presented in the context of global matching, it can be adapted to local matching without gaps. As a benchmark, our PSSM-modified FFT algorithm computed pairwise match scores. In timing experiments, our most efficient FFT implementation for pairwise scoring appeared to be 10 to 26 times faster than a traditional FFT implementation, with only a factor of 2 in the acceleration attributable to a previously known compression scheme. Many important algorithms for detecting biosequence similarities, e.g., gapped BLAST or PSIBLAST, have a heuristic screening phase that disallows gaps. This paper demonstrates that FFT algorithms merit reconsideration in these screening applications.

Information content of protein sequences

The complexity of large sets of non-redundant protein sequences is measured. This is done by estimating the Shannon entropy as well as applying compression algorithms to estimate the algorithmic complexity. The estimators are also applied to randomly generated surrogates of the protein data. Our results show that proteins are fairly close to random sequences. The entropy reduction due to correlations is only about 1%. However, precise estimations of the entropy of the source are not possible due to finite sample effects. Compression algorithms also indicate that the redundancy is in the order of 1%. These results confirm the idea that protein sequences can be regarded as slightly edited random strings. We discuss secondary structure and low-complexity regions as causes of the redundancy observed. The findings are related to numerical and biochemical experiments with random polypeptides.

Evolutionary implication of genetic code deviations

We formulate the following hypothesis: Life's origin may have occurred during the lower Archaean at a time when the environmental temperature was higher than it is at present. Preliminary consequences of this hypothesis are studied from the point of view of molecular evolution. We restrict our attention to implications regarding the genetic code. We conclude that alternative assignment of termination codons may be understood in terms of: (a) the elevated temperatures to which the progenote may initially have been exposed; and (b) the subsequent response of its genome to the opportunity provided by the eventual loss of hyperthermal genetic expression during a thermal transition (TT) period, which was triggered off by the evolution of the dynamic Earth.

Quasi-periodic primary structures of core proteins of human T-lymphotropic leukemia retroviruses

Fourier analysis, previously introduced by Liquori et al. (1983, 1986), has been applied to the primary structures of two core proteins of human T-lymphotropic leukemia retroviruses HTLV-I and HTLV-II. The resulting autocorrelation functions display striking patterns that can be interpreted in terms of an approximately fourfold quasi-periodicity of the primary structures. Self-alignments of the amino acid sequences containing a few gaps are consistent with the above finding and suggest that the tertiary structure of these two homologous core proteins contains alpha-helical and delta-helical segments, the latter being characteristic of the threefold helix present in collagen structure.