Fuß et al., (2006). Bistable switching and excitable behaviour in the activation of Src at mitosis.
September 2011, model of the month by Denis Brun Original model: BIOMD0000000069
Protein tyrosine kinase Src play a vital role in numerous cellular functions, mainly related to cell growth and embryonic development. It has the ability to act as a mediator of these processes at mitosis in all higher vertebrates cells and therefore by its very nature Src is also involved in various human cancers when deregulated.
Despite being reportedly a keystone for the cell’s development, the biochemical networks where Src is involved in, is still a black-box and biologists have yet to come up with a clear modelisation of its interactions with other proteins present in the cell.
Fuß et al., [1, BIOMD0000000069] focused their study on Src interaction with two other proteins: CSK (C-terminal kinase), and PTPalpha (Protein Tyrosine phosphatase alpha).
This model is intended to highlight an important feature in cellular signaling which is bistability. The biochemical system can switch to two different discrete steady states in response to a signal. Such bistable behaviour can act as an 'on' or 'off' switch in many cellular functions (that can be for example, in response to a signal triggered by an extracellular phenomenon.)
Figure 1: Src system model. Figure taken from .
Figure 2: Bistability with respect to CSK activity. The simulation plot (obtained using Copasi v4.7 (Build 34)) reproduces figure 3 of the paper.
It has been shown that, Src can regulate its own activity via autophosphorylation, besides PTPalpha's ability to dephosphorylate some of Src’s phosphorylation site (Tyr529) and thus acting as an external positive feedback loop. In contrast, CSK can deactivate this Tyr529 phosphorylation site and therefore tend to decrease Src’s activity.
The model implemented by Fuß et al., is a simple system of seven differential equations derivated from mass action law kinetics that describe the interaction between SRC, CSK and PTPalpha. You can see in Figure 1 that everything revolves around Src, which is the central species involved in the system.
Figure 2 is a copasi steady-state phase plot analysis of Src and PTPalpha activities with respect to CSK’s initial input. It reproduces the phase-plan diagram (Figure 3) of Fuß et al. Basically heavy lines stand for stable solutions while dotted parts are the results of unstable steady states solutions. If the system is perturbed by a small amount, equilibrium will shift towards a stable solution.
The model allows to study the influence of physiological parameters involved in bistability as well. For example, the dephosphorylation rate (k2) for Src, affect Src’s equilibrium itself as shown in Figure 3. Two new bifurcation points come out from the diagram showing the existence of a bistable region for k2 values between 0.67 and 1.3 and that the activation is not possible under a dephosphorylation rate (k2) of 0.67.
To conclude, Fuß et al have implemented a simple model that effectively reflects the bistable behaviour of Src at mitosis under the regulation of Cbp (CSK binding protein, also known as PAG) and CSK, that could explain accurately the all-or-nothing response Src can yield and therefore act as a chemical switch for cell processes.
Influence of physiological parameters involved in bistability. The plot shows the src activity at different k2 values. The simulation plot (obtained using Copasi v4.7 (Build 34)) reproduces figure 5A of the paper.
Bistable switching and excitable behaviour in the activation of Src at mitosis. Bioinformatics 22(14):e158-65, 2006. [CiteXplore]