title: Control and inhibition analysis of complex formation processes.
abstract: BACKGROUND
  Proteolytic degradation of the extracellular matrix (ECM) is a key event in tumour metastasis and invasion. Matrix metalloproteinases (MMPs) are a family of endopeptidases that degrade most of the components of the ECM. Several broad-spectrum MMP inhibitors (MMPIs) have been developed, but have had little success due to side effects. Thus, it is important to develop mathematical methods to provide new drug treatment strategies. Matrix metalloproteinase 2 (MMP2) activation occurs via a mechanism involving complex formation that consists of membrane type 1 MMP (MT1-MMP), tissue inhibitor of matrix metalloproteinase 2 (TIMP2) and MMP2. Here, we focus on developing a method for analysing the complex formation process.
  
  
  RESULTS
  We used control analysis to investigate inhibitor responses in complex formation processes. The essence of the analysis is to define the response coefficient which measures the inhibitory efficiency, a small fractional change of concentration of a targeting molecule in response to a small fractional change of concentration of an inhibitor. First, by using the response coefficient, we investigated models for general classes of complex formation processes: chain reaction systems composed of ordered steps, and chain reaction systems and site-binding reaction systems composed of unordered multi-branched steps. By analysing the ordered step models, we showed that parameter-independent inequalities between the response coefficients held. For the unordered multi-branched step models, we showed that independence of the response coefficients with respect to equilibrium constants held. As an application of our analysis, we discuss a mathematical model for the MMP2 activation process. By putting the experimentally derived parameter values into the model, we were able to conclude that the TIMP2 and MMP2 interaction is the most efficient interaction to consider in selecting inhibitors.
  
  
  CONCLUSIONS
  Our result identifies a new drug target in the process of the MMP2 activation. Thus, our analysis will provide new insight into the design of more efficient drug strategies for cancer treatment.
authors.affiliation: Division of Mathematical Science, Department of Systems Innovation, Graduate School of Engineering Science, Osaka University, Toyonaka, Japan. t-saito@sigmath.es.osaka-u.ac.jp
authors.forename: Takashi
authors.initials: T
authors.lastname: Saitou
authors.forename: Keiko
authors.initials: K
authors.lastname: Itano
authors.forename: Daisuke
authors.initials: D
authors.lastname: Hoshino
authors.forename: Naohiko
authors.initials: N
authors.lastname: Koshikawa
authors.forename: Motoharu
authors.initials: M
authors.lastname: Seiki
authors.forename: Kazuhisa
authors.initials: K
authors.lastname: Ichikawa
authors.forename: Takashi
authors.initials: T
authors.lastname: Suzuki
mesh_terms: D010450:Endopeptidases / Q000378:metabolism*; D005109:Extracellular Matrix / Q000378:metabolism*; D006801:Humans; D007700:Kinetics; D053511:Matrix Metalloproteinase 14 / Q000378:metabolism; D020778:Matrix Metalloproteinase 2 / Q000378:metabolism; D008962:Models, Theoretical; D009361:Neoplasm Invasiveness; D011480:Protease Inhibitors / Q000494:pharmacology; D013598:Systems Theory; D019716:Tissue Inhibitor of Metalloproteinase-2 / Q000378:metabolism
chemical_list: D011480:Protease Inhibitors; C560823:TIMP2 protein, human; D019716:Tissue Inhibitor of Metalloproteinase-2; D010450:Endopeptidases; D020778:Matrix Metalloproteinase 2; D053511:Matrix Metalloproteinase 14