Mammal

Klamt et al. proposed in [1] a Boolean model of the TCR signalling pathway. The model encompasses 40 regulatory components. In this version of the model an auto-regulation has been added on each input.

Analysis

This model has been studied in [2], using novel algorithms for the analysis of feedback circuits and the determination of stable states. The stable state analysis shows seven stable states, listed bellow. Each stable state corresponds to a different input combination, except "111". Indeed, the systems shows an oscilatory behaviour under full activation.

The feedback circuit analysis shows nine circuits, besides the three auto-activation on the inputs. Only one of these circuits is functional: (ZAP70, cCbl). This negative circuit is functional in presence of LCK and TCRphos which can only be maintained in presence of the three inputs. This circuit drives the oscillatory behaviour observed under full activation.

References

On the basis of a previous modelling study by Novak and Tyson [1] , we have recently proposed a generic Boolean model of the core network controlling the restriction point of the mammalian cell cycle [2].

For proper logical parameter values, the simulation of this Boolean model leads to dynamical behaviours (sequences of activations and inactivations of key regulatory products) in qualitative agreement with current experimental data.

However, as kinetic details are still lacking, many different (in)activation pathways are compatible with existing data, including fully synchronous transition pathways. To further evaluate these different possibilities, we have analysed the asymptotical behaviour of this network under synchronous versus asynchronous updating assumptions. Furthermore, we consider intermediate updating strategies to improve the computation of asymptotical properties depending on available kinetic data. This approach has been implemented through user-defined priority classes in the logical modelling and simulation software GINsim.

Regulatory Graph

The Figure 1 presents the regulatory graph corresponding to our Boolean model of the restriction point control for the mammalian cell cycle. In this graph, each node represents the activity of a key regulatory element, whereas the edges represent functional interactions between these elements. Blunt arrows stand for inhibitory effects, whereas normal arrows stand for activations. Details and justifications can be found in [2].

Figure 1: Regulatory graph

Simulations

Depending on CycD activity at the initial state, our model can lead to two different asymptotical behaviour:

• In the absence of CycD (representing a lack of growth factors), the system is quickly trapped in a stable state with (only) Rb, p27 and Cdh1 stably activated.
• In the presence of CycD, the system reaches a unique (multi-)cycle attractor, whose complexity depends on the updating assumption selected.

To illustrate the impact of the updating assumption, we present here the cyclic attractors (terminal, maximal, strongly connected components) corresponding to three different updating assumptions:

• Synchronous updating: all updating calls are applied simultaneously; as shown in Figure 2-A, the terminal cycle contains 7 states.
• Asynchronous updating: competing updating calls lead to alternative transitions; as shown in Figure 2-B, the terminal attractor contains 112 states.
• Mixed a/synchronous updating: the regulatory components are distributed into four different priority classes; as shown in Figure 2-C, the attractor contains 18 states. We have first built two priority classes, which arguably group faster versus slower biochemical processes. In the highest ranked transition priority class, we have included the degradations of E2F, CycE, CycA, Cdc20, UbcH10, CycB, as well as all transitions (in both directions) for CycD, Rb, p27 (Kip1) and Ccdh1. The remaining transitions correspond to synthesis rates (of E2F, CycE, CycA, Cdc20, UbcH10, and CycB) and are grouped in a lower priority class. Using these two priority classes, both considered under the asynchronous assumption, we still obtain a single terminal strongly connected component (not shown) involving 34 states (to compare with 7 in the standard synchronous treatment, versus 112 in the fully asynchronous case without priority). The analysis of this component reveals that some pathways are clearly unrealistic, as they skip the activation of some specific cyclin, for example. To eliminate these spurious pathways, one can further refine the priority classes, taking into account additional information. Here, we can exploit the fact that several transitions are controlled by similar regulatory mechanisms to group them in synchronous classes.

(A) synchronous	(B) asynchronous	(C) mixed

Figure 2: attractors, depending on the updating policy (Node order in the state labelling: CycD Rb E2F CycE CycA p27Kip1 Cdc20 Cdh1 UbcH10 CycB)

Mutant simulations

References