Abstract
In a phageλgenetic 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 phageλOR 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.
Highlights
Bistability is a salient feature of phage λ genetic switch
In the case when the model parameters are not precisely known, it is useful to study the influence of parameter uncertainty on system dynamics
Our result has shown that, compared with selfprohibition, the mutual prohibition is more influential on system dynamics
Summary
Bistability is a salient feature of phage λ genetic switch. Mathematical models with a number of parameters have been established to describe its bistable behavior. Reference [17] developed a model that has 13 binding energy related parameters with uncertainty ranges around 0.5 kcal/mol. Reference [19] reported that single point mutation of DNA leads to ±2 kcal/mol change for binding free energy. Due to these parameter uncertainties, it is often desired to analyze the effect of these parameters on system dynamics. We are interested in analyzing bistable ranges for binding energy related parameters Some other parameters such as protein degradation rate and protein synthesis rate with respect to gene transcription have already been proved that their variations may lead to the loss of bistability [3, 24]. We need to precisely determine the values of those sensitive parameters in the model because otherwise we may not get an effective bistable switch
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