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As far as we know that smallest polypeptide chain length is 60 amino acids - so if we found an Open Reading Frame (ORF) of about 60 codons without the interruption of stop codon we can consider it to be a possible coding region or gene.

The fifth order Markov Model uses hexameric frequency to predict coding regions, however this doesn't seem very specific.

Why wouldn't we use higher order Markov Models with higher frequencies and more specificity? Wouldn't increasing the order of Markov models prevent false positive results?

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    $\begingroup$ We do not, in fact, know that "the smallest polypeptide chain length is 60 amino acids". That is a purely artificial cutoff, not a biologically meaningful one. There are undoubtedly many, many functional polypeptides that are much smaller but that have not been correctly annotated. $\endgroup$ – iayork Dec 23 '15 at 15:39
  • $\begingroup$ You also have to remember that higher order Eukaryotic genes are interrupted. If the exons in the gene you are looking for are all less than 180 nucleotides, then you are going to miss it. you also have to factor in splice acceptor and splice donor sites, alternate splice forms, codons for methionine that do not indicate the start of the reading frame, etc. Think of it this way; by increasing the stringency, you are throwing out more information. Most of that information is bad, but not all of it, which means that you are creating the situation where you miss things you want. $\endgroup$ – AMR Dec 23 '15 at 18:09
  • $\begingroup$ 1. Why are you so sure that people stick to 5-order Marcov Chains? 2. This boils down to training the state transition matrix, i.e. increasing order leads to increasing the number of possible k-mers exponentially, hence at some point your sample becomes insufficient to estimate transition rates with enough confidence, let alone the computational complexity. $\endgroup$ – Eli Korvigo Dec 23 '15 at 22:56
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The problem with increasingly complex HMMs is that their parameter space tends to explode with the nth-order of the HMMs. Higher number of parameters is often not great because it reduces the possible number of observations that go into training each parameter and can increase overfitting of the model.

From the information that you are providing it is possible that the 5th order model reaches the sweet spot of having great performance with a reasonably contained parameter space.

It is not clear how your model also works.

Is each state a single nucleotide or a single KMER?

Is it a generalized HMM with separate states for exons and introns with the KMERs being observations?

Work by the Bier lab has shown that 5-mers are very good at telling apart enhancers from background using a SVM model for classification. In your context it seems pretty reasonable to use 6-mers to find genes given this finding.

For more details please check "Biological Sequence Analysis" by Sean Eddy and the work of Dr. Michael Brent @ Washington University in Saint Louis (his lab has done a lot of research on HMMs for gene finding).

It'd be useful to have one or few paper references behind your question.

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