Table of Contents
Computational Biology Journal
Volume 2014, Article ID 465216, 11 pages
Research Article

Bifurcation Analysis for Phage Lambda with Binding Energy Uncertainty

Ning Xu,1,2 Xue Lei,3 Ping Ao,3 and Jun Zhang1,2

1Joint Institute of UMich-SJTU, Shanghai Jiao Tong University, Shanghai 200240, China
2Key Laboratory of System Control and Information Processing, Ministry of Education, Shanghai 200240, China
3Shanghai Center for Systems Biomedicine, Shanghai Jiao Tong University, Shanghai 200240, China

Received 30 October 2013; Accepted 25 December 2013; Published 3 February 2014

Academic Editor: Jose Nacher

Copyright © 2014 Ning Xu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In a phage genetic switch model, bistable dynamical behavior can be destroyed due to the bifurcation caused by inappropriately chosen model parameters. Since the values of many parameters with biological significance often cannot be accurately acquired, it is thus of fundamental importance to analyze how and to which extent the system dynamics is influenced by model parameters, especially those parameters pertaining to binding energies. In this paper, we apply a Jacobian method to investigate the relation between bifurcation and parameter uncertainties on a phage OR model. By introducing bistable range as a measure of system robustness, we find that RNA polymerase binding energies have the minimum bistable ranges among all the binding energies, which implies that the uncertainties on these parameters tend to demolish the bistability more easily. Moreover, parameters describing mutual prohibition between proteins Cro and CI have finite bistable ranges, whereas those describing self-prohibition have infinity bistable ranges. Hence, the former are more sensitive to parameter uncertainties than the latter. These results help to understand the influence of parameter uncertainties on the bifurcation and thus bistability.