General continuous-time Markov model of sequence evolution via insertions/deletions: are alignment probabilities...

Area of Science:

• Computational Biology
• Evolutionary Biology
• Bioinformatics

Background:

• Insertions and deletions (indels) are major drivers of DNA sequence divergence.
• Existing probabilistic models for indels often lack biological realism and clear links to genuine evolutionary processes.
• Current models struggle with features like overlapping indels and variable indel rates.

Purpose of the Study:

• To theoretically dissect the ab initio calculation of alignment probabilities under a genuine stochastic evolutionary model for indels.
• To extend the general substitution/insertion/deletion (SID) model to better accommodate indel processes.
• To establish conditions for factorizable alignment probabilities in indel models.

Main Methods:

• Developed a general continuous-time Markov model for sequence evolution via indels.
• Employed operator representation of indels and time-dependent perturbation theory.
• Expressed ab initio probability as a summation over alignment-consistent indel histories.

Main Results:

• Derived conditions for factorizing alignment probabilities, creating a generalized hidden Markov model (HMM).
• Distinguished evolutionary models with factorable versus non-factorable alignment probabilities.
• Identified models like the 'long indel' model and Dawg as having factorable probabilities.

Conclusions:

• The theoretical formulation provides intuitive clarity and mathematical rigor for indel evolution models.
• Advances the ab initio calculation of alignment probabilities for biologically realistic scenarios.
• Facilitates the development of more accurate sequence evolution simulators.