Bifurcation Analysis of Oscillation Patterns in an NF-κB Signal Pathway Model
Oscillations play key roles in many cellular processes and there is an increasing interest in understanding how such oscillations occur. Systems analysis method will help to investigate the cell oscillation behaviour that is not always apparent experimentally. Bifurcation analysis has proven to be a powerful tool to identify the presence of complex behaviour of dynamic systems by showing the relationship between a systems steady-state behavior and the parameter variations. For a system with different oscillation patterns,bifurcation analysis is capable of unravelling the parameter domain for damped and sustained oscillations. The Nuclear factor-κB (NF-κB) is involved in a variety of cellular processes including immune response,inflammation, and apoptosis. Previous experiment and modelling studies revealed the damped oscillation of NF-κB in the nucleus (NF-κBn)1,2. In this work, based on a mathematical model represented by ordinary differential equations 1,3, we use bifurcation analysis to explore the conditions under which the limit cycle oscillation of NF-κBn can be produced.Bifurcation analysis shows that when the total concentration of NF-κB and its complexes is made to reach a threshold level identified as the Hopf bifurcation (HB) point, the concentration of NF-κBn will present sustained oscillations ultimately with or without external stimuli leading to the IKKs activation.Under the assumption that the IKK decay rate is zero,it is further observed that when the total IKK level is kept constant in certain range, a lower total concentration of NF-κB also suffices sustained oscillations in this system. These results can be illustrated in Fig.1 and 2, where C1 is the total NF-κB concentration and C2 is the total IKK concentration when the IKK decay rate is taken to be zero. In Fig.1, when C1 is lower than the HB point, the concentration of NF-κBn exhibits damped oscillation (We use steady state to indicate the damped oscillation since NF-κBn will eventuaily stay at a steady state value). However, when C1 is higher than the HB point, the system shows sustained oscillation. Further bifurcation analysis with two control parameters is shown in Fig.2, in which the system has sustained oscillations when C1 and C2 fall in the area labeled as oscillation. All the states will reach stable steady states when C1 and C2 are in the steady state region. The influence of the reaction coefficients on the location of Hopf bifurcation points has also been analyzed by means of parametric sensitivity analysis. It is found that about a dozen of reaction rate parameters have significant impacts on the distance between the two Hopf bifurcation points of the diagram (Fig.3). The sensitivity analysis together with bifurcation information further proves the key role of IκBα in this signaling pathway.
Hong Yue Baoyun Lu
Department of Electronic and Electrical Engineering, University of Strathclyde, Glasgow, UK Institut Institute of Automation, Chinese Academy of Science, Beijing, China
国际会议
The 7th Asia-Pacific Bioinformatics Conference(第七届亚太生物信息学大会)
北京
英文
886
2009-01-01（万方平台首次上网日期，不代表论文的发表时间）