Journal of Computational Biology (under revision) 1996-7

Significantly Lower Entropy Estimates for Natural DNA Sequences

David Loewenstern and Peter N. Yianilos

Abstract: If DNA were a random string over its alphabet {A,C,G,T}, an optimal code would assign 2 bits to each nucleotide. We imagine DNA to be a highly ordered, purposeful molecule, and might therefore reasonably expect statistical models of its string representation to produce much lower entropy estimates. Surprisingly this has not been the case for many natural DNA sequences, including portions of the human genome. We introduce a new statistical model (compression algorithm), the strongest reported to date, for naturally occurring DNA sequences. Conventional techniques code a nucleotide using only slightly fewer bits (1.90) than one obtains by relying only on the frequency statistics of individual nucleotides (1.95). Our method in some cases increases this gap by more than five-fold (1.66) and may lead to better performance in microbiological pattern recognition applications.

One of our main contributions, and the principle source of these improvements, is the formal inclusion of inexact match information in the model. The existence of matches at various distances forms a panel of experts which are then combined into a single prediction. The structure of this combination is novel and its parameters are learned using Expectation Maximization (EM).

Experiments are reported using a wide variety of DNA sequences and compared whenever possible with earlier work. Four reasonable notions for the string distance function used to identify near matches, are implemented and experimentally compared.

We also report lower entropy estimates for coding regions extracted from a large collection of non-redundant human genes. The conventional estimate is 1.92 bits. Our model produces only slightly better results (1.91 bits) when considering nucleotides, but achieves 1.84-1.87 bits when the prediction problem is divided into two stages: i) predict the next amino acid based on inexact polypeptide matches, and ii) predict the particular codon. Our results suggest that matches at the amino acid level play some role, but a small one, in determining the statistical structure of non-redundant coding sequences.

Keywords: DNA, Information Theoretic Entropy, Expectation Maximization (EM), Data Compression, Context Modeling, Time Series Prediction.


This manuscript first appeared as an NEC Research Institute Technical Report, and was then presented at the University of Pennsylvania DIMACS Conference on Computational Biology to honor the 50th anniversary of the ENIAC, Princeton NJ, May 1996. It later was released as a DIMACS technical report. It is now submitted to and under revision for the Journal of Computational Biology, and will form part of David Lowenstern's Ph.D. thesis.