Information-theoretical entropy as a measure of sequence variability

Area of Science:

• Bioinformatics
• Computational Biology
• Sequence Analysis

Background:

• Assessing variability in biological sequences is crucial for understanding protein and nucleotide function.
• Traditional measures like Vk have limitations in mathematical properties and intuitive interpretation.
• Existing methods may not fully capture the nuances of sequence diversity.

Purpose of the Study:

• To propose and evaluate information-theoretical entropy (S) as a robust measure of sequence variability.
• To compare the performance and properties of S against the traditional Vk measure.
• To analyze the mathematical underpinnings of variability in immunoglobulin sequences.

Main Methods:

• Defined information-theoretical entropy (S = -sum(pi log2 pi)) for sequence variability.
• Calculated S for protein, nucleotide, and codon sequences.
• Compared S and a related measure (Vs) with the traditional Vk measure using immunoglobulin data.

Main Results:

• Information-theoretical entropy (S) demonstrates desirable mathematical properties lacking in Vk.
• S possesses intuitive and statistical meanings that align well with the concept of variability.
• S-based measures and Vk show a high correlation in immunoglobulin sequences, explained by log-linear amino acid frequency distributions.

Conclusions:

• Information-theoretical entropy (S) is a statistically sound and intuitive measure for sequence variability.
• The high correlation between S and Vk in immunoglobulins is attributed to underlying log-linear frequency distributions.
• Further research is needed to determine if this log-linear distribution is typical across protein families.