title: The organization of domains in proteins obeys Menzerath-Altmann's law of language.
abstract: BACKGROUND
  The combination of domains in multidomain proteins enhances their function and structure but lengthens the molecules and increases their cost at cellular level.
  
  
  METHODS
  The dependence of domain length on the number of domains a protein holds was surveyed for a set of 60 proteomes representing free-living organisms from all kingdoms of life. Distributions were fitted using non-linear functions and fitted parameters interpreted with a formulation of decreasing returns.
  
  
  RESULTS
  We find that domain length decreases with increasing number of domains in proteins, following the Menzerath-Altmann (MA) law of language. Highly significant negative correlations exist for the set of proteomes examined. Mathematically, the MA law expresses as a power law relationship that unfolds when molecular persistence P is a function of domain accretion. P holds two terms, one reflecting the matter-energy cost of adding domains and extending their length, the other reflecting how domain length and number impinges on information and biophysics. The pattern of diminishing returns can therefore be explained as a frustrated interplay between the strategies of economy, flexibility and robustness, matching previously observed trade-offs in the domain makeup of proteomes. Proteomes of Archaea, Fungi and to a lesser degree Plants show the largest push towards molecular economy, each at their own economic stratum. Fungi increase domain size in single domain proteins while reinforcing the pattern of diminishing returns. In contrast, Metazoa, and to lesser degrees Protista and Bacteria, relax economy. Metazoa achieves maximum flexibility and robustness by harboring compact molecules and complex domain organization, offering a new functional vocabulary for molecular biology.
  
  
  CONCLUSIONS
  The tendency of parts to decrease their size when systems enlarge is universal for language and music, and now for parts of macromolecules, extending the MA law to natural systems.
authors.affiliation: Illinois Informatics Institute, Urbana, IL, 61801, USA. shahzad2@illinois.edu.
authors.forename: Khuram
authors.initials: K
authors.lastname: Shahzad
authors.affiliation: Department of Cell and Developmental Biology, Urbana, IL, 61801, USA. mitten@life.illinois.edu.
authors.forename: Jay E
authors.initials: JE
authors.lastname: Mittenthal
authors.affiliation: Illinois Informatics Institute, Urbana, IL, 61801, USA. gca@illinois.edu.|Department of Crop Sciences, Evolutionary Bioinformatics Laboratory, University of Illinois, 332 NSRC, Urbana, IL, 61801, USA. gca@illinois.edu.
authors.forename: Gustavo
authors.initials: G
authors.lastname: Caetano-Anollés
mesh_terms: D000818:Animals; D019143:Evolution, Molecular; D006801:Humans; D007802:Language; D017434:Protein Structure, Tertiary; D020543:Proteome / Q000737:chemistry* / Q000378:metabolism*; D040901:Proteomics
chemical_list: D020543:Proteome