Convergence rate estimation for the TKF91 model of biological sequence length evolution.

Area of Science:

• Evolutionary biology
• Computational biology
• Bioinformatics

Background:

• The TKF91 model describes biological sequence evolution, including length changes via a birth-death process.
• A key assumption is that ancestral sequences have an equilibrium length distribution, which lacks rigorous investigation.

Purpose of the Study:

• To rigorously investigate the validity of the equilibrium length distribution assumption in the TKF91 model.
• To determine the rate of convergence to equilibrium for the TKF91-BD process.
• To compare the convergence speed of TKF91-BD with other evolutionary models.

Main Methods:

• Derivation of explicit upper and lower bounds for the rate of convergence to equilibrium.
• Analysis of protein sequences (alpha and beta globins) and nucleotide sequences.
• Parameter inference from empirical sequence data.
• Comparison with Jukes-Cantor and Kimura models.

Main Results:

• The TKF91-BD process converges too slowly for protein sequences, failing to reach equilibrium on realistic timescales.
• For nucleotide sequences, convergence is faster but results in unrealistically small equilibrium lengths.
• The Jukes-Cantor model shows significantly faster convergence for both sequence types.
• The Kimura model's convergence speed is comparable to TKF91-BD for nucleotide sequences.

Conclusions:

• The equilibrium length assumption of the TKF91 model is questionable for protein evolution due to slow convergence.
• The TKF91 model's predictions for nucleotide sequence length evolution may be unrealistic.
• Alternative models like Jukes-Cantor offer faster convergence rates, suggesting potential improvements for evolutionary modeling.