Exact distribution for the local score of one i.i.d. random sequence

Area of Science:

• Probability Theory
• Bioinformatics
• Computational Biology

Background:

• Sequence analysis in molecular biology often involves scoring subsequences.
• Existing methods for calculating local scores can be computationally intensive or provide approximations.
• Understanding the exact distribution of local scores is crucial for accurate biological sequence analysis.

Purpose of the Study:

• To derive the exact distribution of the local score H(n) for sequences of independent and identically distributed (i.i.d.) random variables.
• To develop a computationally efficient method for calculating this distribution.
• To apply the derived method to the scoring of DNA and protein sequences.

Main Methods:

• Utilized a simple Markov chain to model the sequence and derive the distribution of the maximum local score.
• Defined the local score H(n) as the maximum sum of consecutive elements in a sequence of random variables.
• Employed exact combinatorial and probabilistic techniques.

Main Results:

• The exact distribution of H(n) was successfully obtained using the proposed Markov chain approach.
• The method provides a precise mathematical framework for local score distribution.
• Demonstrated the applicability of the method to biological sequence scoring.

Conclusions:

• The Markov chain method offers an exact and efficient way to determine local score distributions.
• This technique enhances the analytical power for DNA and protein sequence scoring in bioinformatics.
• Provides a foundational tool for statistical analysis in molecular sequence data.