Nature of amino acid substitutions in homologous proteins during evolution
Abstract Replacement substitutions of mitochondrial cytochrome c and α- and β-chains of haemoglobin have been studied by considering the structural similarity among amino acid residues at the secondary and tertiary structural levels. Secondary structural similarity explains ∼70% while tertiary structural similarity explains ∼50% of observed replacements for most of the cases. These structural similarities could not account for all the replacement substitutions. The study was extended to consider the composition of codons, and the chemical nature and polarity of the replacing and replaced residues. These also could not individually account for all the affected replacements. In general, no property of amino acid residues is conserved for substitutions occurring at any single position during evolution of proteins.
This paper addresses the application of convergence rules of gradient-type discrete algorithms to discrete adaptive control algorithms for linear timeinvariant systems, which are based on Lyapunov's like functions , in order to improve the transient performances based on fast adaptation . In particular, the adaptation covergence is increased as a generalized or filtered error increases through the application of Armijo rule for regulating the decrease of each Lyapunov's-like function on which the particular adaptation algorithm is based. The proposed scheme can be implemented with minor modifications in systems subject to unmodelled dynamics if some weak knowledge on such a dynamics is available consisting of upper-bounds of the dimension and norm of the unmodelled parameter vector.