introduction
In the world of biology, the analysis of DNA sequences is a core field. But, did you know how the intersection between computer science and biology can help us understand DNA more deeply? That’s exactly what we’re going to talk about today – using Kolmogorov complexity (also known as algorithmic entropy) to analyze DNA sequences.
What is Kolmogorov complexity?
Kolmogorov complexity, also known as algorithmic complexity or algorithmic entropy, is a way of measuring the complexity of an object or information. Simply put, the Kolmogorov complexity of an object is the length of the shortest algorithm that can describe and reproduce the object.
For example, consider the following two strings:
A: AAAAAAAAAAAAAAAAAAAA B: AGTCACTGAGCTAGTCACTG
Although both are 20 characters long, string A can be described by a short algorithm, such as: "Output 'A' 20 times." String B requires a more complex method to describe. Therefore, from Kolmogorov's perspective, A is less complex than B.
DNA sequences and Kolmogorov complexity
This measure of complexity becomes especially important when we consider DNA sequences. Because patterns, repeats, and structural properties in DNA sequences are directly related to biological function. By measuring its Kolmogorov complexity, we can get clues about its possible biological significance.
Calculate Kolmogorov complexity using Shell
Although calculating a true Kolmogorov complexity is impossible (because it is a non-computable problem), we can use some approximation methods. Here is a simple shell command that utilizes gzip compression to estimate Kolmogorov complexity: