This article examines the presence of the empirical tendency known as the Menzerath-Altmann Law (MAL) on protein secondary structures. MAL is related to optimization principles observed in natural languages and in genetic information on chromosomes or protein domains. The presence of MAL is examined on a non-redundant dataset of 4728 proteins by verifying significant, negative correlations and testing classical and newly proposed formulas by fitting the observed trend. We conclude that the lengths of secondary structures are specifically dependent on their number inside the protein sequence, while possibly reflecting the formula proposed in this paper. This behavior is observed on average but is individually avoidable and possibly driven by a latent cost function. The data suggest that MAL could provide a useful guiding principle in protein design.
Keywords: Menzerath–Altmann law; empirical law; formula fitting; proteins; quantitative linguistics; secondary structures.