Physica A 454 (2016) 117–128 Contents lists available at ScienceDirect Physica A journal homepage: www.elsevier.com/locate/physa Codon information value and codon transition-probability distributions in short-term evolution M.A. Jiménez-Montaño a , H.F. Coronel-Brizio a,b , A.R. Hernández-Montoya a,c,∗ , A. Ramos-Fernández d,e a Center for Research on Artificial Intelligence, University of Veracruz, Sebastián Camacho No. 5, Col. Centro, C.P. 91000, Xalapa, Ver., Mexico b Faculty of Physics, University of Veracruz, Circuito Gonzalo Aguirre Beltrán s/n, Zona Universitaria, CP 91000, Xalapa, Veracruz, Mexico c Ph. D. Program on Science, Technology and Society (DCTS), Centro de Investigación y de Estudios Avanzados del IPN (Cinvestav), Av. Instituto Politécnico Nacional 2508, Col. San Pedro Zacatenco, Delegación Gustavo A. Madero, Código Postal 07360 Apartado Postal: 14-740, 07000 México, D.F., Mexico d Institute of Biotechnology and Applied Ecology (INBIOTECA), University of Veracruz, Av. de las Culturas Veracruzanas No.101, Col. E. Zapata, C.P. 91090, Xalapa, Veracruz, Mexico e Red Biodiversidad y Sistemática, Instituto de Ecología, A. C. (INECOL), A.P. 63, Xalapa, Veracruz, Mexico highlights • Inverse power-laws fit two-fold degenerated codons; they have high information values. • Exponentials fit Four-fold degenerated codons; they have low information values. • Six-fold degenerated codons are considered to be doubly assigned. • We propose a codon-level model for acid substitutions in short-term protein evolution. • Ordering codons according to their value, orders them according to their degeneracy. article info Article history: Received 21 May 2015 Received in revised form 19 December 2015 Available online 27 February 2016 Keywords: Codon Value of information Fitting Power law Exponential Reduced empirical matrix abstract To understand the way the Genetic Code and the physical–chemical properties of coded amino acids affect accepted amino acid substitutions in short-term protein evolution, taking into account only overall amino acid conservation, we consider an underlying codon-level model. This model employs codon pair-substitution frequencies from an empirical matrix in the literature, modified for single-base mutations only. Ordering the degenerated codons according to their codon information value (Volkenstein, 1979), we found that three-fold and most of four-fold degenerated codons, which have low codon values, were best fitted to rank-frequency distributions with constant failure rate (exponentials). In contrast, almost all two-fold degenerated codons, which have high codon values, were best fitted to rank-frequency distributions with variable failure rate (inverse power-laws). Six-fold degenerated codons are considered to be doubly assigned. The exceptional behavior of some codons, including non-degenerate codons, is discussed. © 2016 Elsevier B.V. All rights reserved. ∗ Corresponding author at: Center for Research on Artificial Intelligence, University of Veracruz, Sebastián Camacho No. 5, Col. Centro, C.P. 91000, Xalapa, Ver., Mexico. E-mail addresses: ajimenez@uv.mx (M.A. Jiménez-Montaño), alhernandez@uv.mx (A.R. Hernández-Montoya). http://dx.doi.org/10.1016/j.physa.2016.02.043 0378-4371/© 2016 Elsevier B.V. All rights reserved.