# Problem 85

## Primary tabs

codon frequencies via equilibrium states for some potential''?

## Tags

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### BHM

by "codon" maybe he is referring to genetics; there was work done on codon frequencies in genetics starting in the 1970's; see [1].

### References

1. [goel1972method] Goel NS, Rao GSubba, Yčas M, Bremermann HJ, King L.  1972.  Journal of theoretical biology. 35:399–457.

### David Koslicki and I wrote a

David Koslicki and I wrote a paper in this spirit; see [1]. The question of finding “some potential” is exactly the right one. We obtained a locally constant potential (depending on 3 symbols, thus giving a weight to each nucleotide triplet) by training computationally against the data set provided by the human genome. Of course, when Bowen wrote this note, neither this data set nor the computational power required to train against it were available.  We also experimented with using the GC-content of each nucleotide triplet to determine a potential function. We discuss different approaches to selecting a potential in sections 3.7 and 3.8 of our paper.

Speaking personally, I find it fascinating that Bowen considered the possibility of using the theory of equilibrium states in genomic analysis. I am well aware of the great debt that the majority of my work owes to Bowen - I was unaware that this idea was anticipated by him too!

### References

1. [MR3294965] Koslicki D, Thompson DJ.  2015.  J. Math. Biol.. 70:45–69.

### In Krick,Teresa, David A.

In Krick,Teresa, David A. Shub, Nina Verstraete, Diego U. Ferreiro, Leonardo G. Alonso, Michael Shub and Ignacio E.Sanchez,Amino acid metabolism conﬂicts with protein diversity,Molecular Biology and Evolution, Advance Access, August 18,2014 we show that maximizing the entropy minus the energetic cost of using amino acids  with a given frequency gives a good fit to actual amino acid  frequency. I was also unaware of Rufus' suggestion in this direction.