title: Mass action models versus the Hill model: an analysis of tetrameric human thymidine kinase 1 positive cooperativity.
abstract: BACKGROUND
  The Hill coefficient characterizes the extent to which an enzyme exhibits positive or negative cooperativity, but it provides no information regarding the mechanism of cooperativity. In contrast, models based on the equilibrium concept of mass action can suggest mechanisms of cooperativity, but there are often many such models and often many with too many parameters.
  
  
  RESULTS
  Mass action models of tetrameric human thymidine kinase 1 (TK1) activity data were formed as pairs of plausible hypotheses that per site activities and binary dissociation constants are equal within contiguous stretches of the number of substrates bound. Of these, six 3-parameter models were fitted to 5 different datasets. Akaike's Information Criterion was then used to form model probability weighted averages. The literature average of the 5 model averages was K = (0.85, 0.69, 0.65, 0.51) microM and k = (3.3, 3.9, 4.1, 4.1) sec-1 where K and k are per-site binary dissociation constants and activities indexed by the number of substrates bound to the tetrameric enzyme.
  
  
  CONCLUSIONS
  The TK1 model presented supports both K and k positive cooperativity. Three-parameter mass action models can and should replace the 3-parameter Hill model.
authors.affiliation: Department of Epidemiology and Biostatistics, Case Western Reserve University, Cleveland, Ohio 44106, USA. txr24@case.edu
authors.forename: Tomas
authors.initials: T
authors.lastname: Radivoyevitch
mesh_terms: D020134:Catalytic Domain; D006801:Humans; D007700:Kinetics; D016018:Least-Squares Analysis; D008954:Models, Biological; D017711:Nonlinear Dynamics; D055503:Protein Multimerization; D020836:Protein Structure, Quaternary; D013379:Substrate Specificity; D013936:Thymidine / Q000378:metabolism; D013937:Thymidine Kinase / Q000737:chemistry* / Q000378:metabolism*
chemical_list: D013937:Thymidine Kinase; C092717:thymidine kinase 1; D013936:Thymidine