title: Evolutionary models for insertions and deletions in a probabilistic modeling framework.
abstract: BACKGROUND
  Probabilistic models for sequence comparison (such as hidden Markov models and pair hidden Markov models for proteins and mRNAs, or their context-free grammar counterparts for structural RNAs) often assume a fixed degree of divergence. Ideally we would like these models to be conditional on evolutionary divergence time. Probabilistic models of substitution events are well established, but there has not been a completely satisfactory theoretical framework for modeling insertion and deletion events.
  
  
  RESULTS
  I have developed a method for extending standard Markov substitution models to include gap characters, and another method for the evolution of state transition probabilities in a probabilistic model. These methods use instantaneous rate matrices in a way that is more general than those used for substitution processes, and are sufficient to provide time-dependent models for standard linear and affine gap penalties, respectively. Given a probabilistic model, we can make all of its emission probabilities (including gap characters) and all its transition probabilities conditional on a chosen divergence time. To do this, we only need to know the parameters of the model at one particular divergence time instance, as well as the parameters of the model at the two extremes of zero and infinite divergence. I have implemented these methods in a new generation of the RNA genefinder QRNA (eQRNA).
  
  
  CONCLUSIONS
  These methods can be applied to incorporate evolutionary models of insertions and deletions into any hidden Markov model or stochastic context-free grammar, in a pair or profile form, for sequence modeling.
authors.affiliation: Department of Genetics, Washington University School of Medicine, 4444 Forest Park Blvd., Saint Louis, Missouri 63108, USA. elena@genetics.wustl.edu
authors.forename: Elena
authors.initials: E
authors.lastname: Rivas
mesh_terms: D000465:Algorithms; D005075:Biological Evolution; D019295:Computational Biology / Q000379:methods*; D003198:Computer Simulation; D019143:Evolution, Molecular; D017353:Gene Deletion; D016013:Likelihood Functions; D008390:Markov Chains; D008954:Models, Biological; D008957:Models, Genetic; D015233:Models, Statistical; D008962:Models, Theoretical; D008969:Molecular Sequence Data; D009154:Mutation; D011336:Probability; D011487:Protein Conformation; D017434:Protein Structure, Tertiary; D012313:RNA / Q000737:chemistry; D012333:RNA, Messenger / Q000378:metabolism; D017422:Sequence Analysis, DNA; D020539:Sequence Analysis, Protein; D017423:Sequence Analysis, RNA; D012984:Software; D013997:Time Factors
chemical_list: D012333:RNA, Messenger; D012313:RNA