Mathematical modelling of cytokines, MMPs and fibronectin fragments in osteoarthritic cartilage

J Math Biol. 2017 Oct;75(4):985-1024. doi: 10.1007/s00285-017-1104-y. Epub 2017 Feb 17.


Osteoarthritis (OA) is a degenerative disease which causes pain and stiffness in joints. OA progresses through excessive degradation of joint cartilage, eventually leading to significant joint degeneration and loss of function. Cytokines, a group of cell signalling proteins, present in raised concentrations in OA joints, can be classified into pro-inflammatory and anti-inflammatory groups. They mediate cartilage degradation through several mechanisms, primarily the up-regulation of matrix metalloproteinases (MMPs), a group of collagen-degrading enzymes. In this paper we show that the interactions of cytokines within cartilage have a crucial role to play in OA progression and treatment. We develop a four-variable ordinary differential equation model for the interactions between pro- and anti-inflammatory cytokines, MMPs and fibronectin fragments (Fn-fs), a by-product of cartilage degradation and up-regulator of cytokines. We show that the model has four classes of dynamic behaviour: homoeostasis, bistable inflammation, tristable inflammation and persistent inflammation. We show that positive and negative feedbacks controlling cytokine production rates can determine either a pre-disposition to OA or initiation of OA. Further, we show that manipulation of cytokine, MMP and Fn-fs levels can be used to treat OA, but we suggest that multiple treatment targets may be essential to halt or slow disease progression.

Keywords: Cytokine; Modelling; Non-linear dynamics; Osteoarthritis; Simulation.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Cartilage, Articular / metabolism
  • Cytokines / metabolism*
  • Feedback, Physiological
  • Fibronectins / metabolism*
  • Humans
  • Inflammation / etiology
  • Inflammation / metabolism
  • Inflammation / therapy
  • Mathematical Concepts
  • Matrix Metalloproteinases / metabolism*
  • Models, Biological*
  • Osteoarthritis / etiology
  • Osteoarthritis / metabolism*
  • Osteoarthritis / therapy
  • Peptide Fragments / metabolism


  • Cytokines
  • Fibronectins
  • Peptide Fragments
  • Matrix Metalloproteinases