Please visit the new BioModels platform to access the latest content. This website is no longer updated and will be retired on 31 May 2019.
BioModels Database logo

BioModels Database


Nguyen et al., (2011). Switches, excitable responses and oscillations in the Ring1B/Bmi1 ubiquitination system.

January 2017, model of the month by Thawfeek Mohamed Varusai
Original model: BIOMD0000000622


Protein ubiquitination, a fundamental process in biology, is commonly known for its role in proteasomal degradation. However, recent findings uncover other functions of protein ubiquitination, especially in the area of cell signalling. In this paper, the authors study the dynamics of ubiquitination in the Ring1B/Bmi1/H2A system [1]. Ring1B and Bmi1 are RING finger proteins that interact to form the core human Polycomb transcriptional Repressive Complex 1 (PRC1), which ubiquitinates histone H2A. Histone H2A, in its unmodified form, is known to facilitate gene transcription. However, upon monoubiquitination, H2A represses gene transcription. The (de)ubiquitinated states of H2A have been reported to have implications in various physiological and pathophysiological conditions.

Figure 2

Figure 2. Complex dynamics of the Ring1B/Bmi1/H2A ubiquitination model.
(a) Bistability and hysteresis in the Ring1B/Bmi1 system: The dotted lines show the unstable steady states of Zub (catalytically active form) and R1Bdub (targeted for degradation form). The dashed line shows the region of bistability in the system. (b) Oscillatory temporal dynamics of Zub, R1Bdub, and R1Baub (catalytically active form). (c) Excitable behaviour of the Ring1B/Bmi1 system in response to perturbations to the initial concentrations of Zub. Figure taken from [1].

Figure 1

Figure 1. Kinetic scheme of the core Ring1B/Bmi1 ubiquitination system.
This scheme was used to build the mathematical models; the reactions are described in the text. Protein-protein interactions and (de)ubiquitination reactions are shown by solid green lines. Reactions of proteasomal degradation and de novo synthesis of Bmi1 and Ring1B (shown by dashed lines) are neglected on short-timescales (<1 hr). Catalytic intermolecular interactions are shown by purple lines (the arrow thickness indicates levels of catalytic activity). R1B is Ring1B; Bmi1dub and R1Bdub are ubiquitinated forms of Bmi1 and Ring1B targeted for degradation; Z is the complex of Bmi1 and Ring1B; R1Bub, R1Baub and Zub are self-ubiquitinated forms of Ring1B (free or associated with Bmi1, see text for details).. Figure taken from [1].


Recent work has revealed surprising observations of the Ring1B/Bmi1/H2A ubiquitination system and their novel non-proteolytic functions. H2A is involved in gene silencing of PRC1-targetted genes depending upon its ubiquitination state. Temporal dynamics of H2A ubiquitination is critical for various (patho)physiological scenarios. To understand this, it is important to quantitatively investigate Ring1B/Bmi1/H2A dynamics. Furthermore, there are reasons to believe that the Ring1B/Bmi1/H2A system may harbour intricate signalling dynamics. From literature, it is known that multisite phosphorylation/dephosphorylation signalling cascades can exhibit complex system behaviours such as multistable dynamics, oscillations and excitable overshoots. Ubiquitination process is equally, if not more, complicated than protein phosphorylation mechanisms and show promise for diverse system dynamics.

Mathematical Modelling

The kinetic reaction scheme of the Ring1B/Bmi1/H2A ubiquitination network used for the model is shown in Figure 1. The authors deterministically model the Ring1B/Bmi1/H2A system using ordinary differential equations. Mass-action (MA) kinetics were used to represent protein-protein interactions and Michaelis-Menten (MM) equations were used to denote ubiquitination/deubiquitination reactions. The Ring1B/Bmi1/H2A system was modelled at two different timescales – a short duration (<1 hour) where protein degradation was ignored owing to protein abundancy and a long term (>1 hour) scenario where protein synthesis and degradation were considered in the model. This is a computational study with no experiments involved. Parameter values used for the model are mainly hypothetical and few values taken from empirical data in other literature. To address a case when MM approximations may not apply, the authors model the Ring1B/Bmi1/H2A system entirely with MA kinetics and validate their predictions. Model predictions have not been empirically validated in this study.


The Ring1B/Bmi1/H2A model predicts a range of intricate dynamics such as ON/OFF switches, mutlistable states, oscillations and excitability (Figure 2). Such complex response of the Ring1B/Bmi1 network can quantitatively and qualitatively modulate the activity of H2A ubiquitination, thereby resulting in regulating gene silencing downstream. Positive feedback mechanisms arising from the different ubiquitination steps are found to be responsible for the multistable dynamics in the system. Similar results are obtained for the short-term (without protein degradation) and the long-term (with protein synthesis and degradation) models. Model predictions were the same irrespective of the approach (MM or MA) used to formulate the equations.

Predictive Power of the Model

The authors formulate a computational Ring1B/Bmi1/H2A model in this paper. Although few of the model parameter values are taken from experiments in other literature, the overall model is not calibrated with empirical data. This reflects on the model predictions as being of low predictive power. However, this also means that the model does not pertain to any particular cell/tissue type and is generic in nature. This has the advantage of model parameter values being tailored to represent different in vivo scenarios. Furthermore, possible variations (with/without protein degradation) and alternate approaches (MA/MM kinetics) have been used in model formulation to test the robustness of the predictions. Taken together, these suggest that the Ring1B/Bmi1/H2A model in this paper can be useful as a generic and robust platform to simulate various (patho)physiological conditions.

Significance of the Model

The significance of a biological model may be determined by the contribution of the model to the obtained knowledge. This study predicts that the Ring1B/Bmi1/H2A system is capable of exhibiting complex behaviours such as switches, oscillations and overshoots arising from the diverse ubiquitination reactions. Computational modelling is critical for the results in this paper for a few reasons. Firstly, the intricate system behaviours predicted here are dynamic in nature and require extensive quantitative investigation. Experiments, if possible, will be laborious, expensive and time-consuming to identify such outcomes in the system. In silico modelling is a feasible alternate approach to obtain the same knowledge. Secondly, ubiquitination is generally considered as a simple process and not suspected to generate such complicated behaviours. Had it not been for computational approaches, it may not be possible to identify these dynamics in the Ring1B/Bmi1/H2A ubiquitination system. Thus, this work demonstrates a strong case for the application of computational modelling to understand cell signalling dynamics.

Scientific Value Added

This work illustrates the pivotal role of the PRC1 ubiquitination in governing the transcriptional activity of H2A. Model simulations show that Ring1B/Bmi1 ubiquitination network serves to convert stimulus into diverse responses namely switch-like, multistability, oscillations and excitability. These qualitatively different outputs are reflected in the ubiquitination of H2A that in turn may get translated to the corresponding gene silencing patterns. Furthermore, the authors simulate several (patho)physiological scenarios such as high Bmi1 levels that are known to occur in tumorigenesis and stem cell proliferation in this paper. Results show how the Ring1B/Bmi1/H2A system can exhibit a range of unintuitive dynamics under these conditions suggesting the complex nature of these conditions.


  1. Nguyen et al. Switches, excitable responses and oscillations in the Ring1B/Bmi1 ubiquitination system. PLoS Comput Biol. 2011; 7(12): e1002317.