Generalized logical model based on network topology to capture the dynamical trends of cellular signaling pathways

Abstract

Background: Cellular responses to extracellular perturbations require signaling pathways to capture and transmit the signals. However, the underlying molecular mechanisms of signal transduction are not yet fully understood, thus detailed and comprehensive models may not be available for all the signaling pathways. In particular, insufficient knowledge of parameters, which is a long-standing hindrance for quantitative kinetic modeling necessitates the use of parameter-free methods for modeling and simulation to capture dynamic properties of signaling pathways.

Results: We present a computational model that is able to simulate the graded responses to degradations, the sigmoidal biological relationships between signaling molecules and the effects of scheduled perturbations to the cells. The simulation results are validated using experimental data of protein phosphorylation, demonstrating that the proposed model is capable of capturing the main trend of protein activities during the process of signal transduction. Compared with existing simulators, our model has better performance on predicting the state transitions of signaling networks.

Conclusion: The proposed simulation tool provides a valuable resource for modeling cellular signaling pathways using a knowledge-based method.

Fig. 1

The workflow of simulation using the proposed model. The activity level of X is calculated based on its own previous activity with a degradation rate, and the activation and inhibition effects produced by the signals transmitted from its parent nodes

Fig. 2

Signaling pathways constructed based on the dataset in [18]. Round rectangles and ellipses represent signaling proteins (or stimuli) and cell fates, respectively. The signals that have measurements in the dataset [18] are represented by dark blue nodes. Each activation interaction is denoted as a green edge with an arrow head and each inhibition interaction is represented by a red edge with a flat-head

Fig. 3

Comparison of simulation-based predictions made by using SimBoolNet, GINsim and the proposed simulator. Two different inputs are used: (1) EGFR and TNFR are perturbed at the beginning of the simulation with input levels 0.5 and 0.8, respectively, and (2) EGFR is inhibited at the 10th iteration with input level -1 and TNFR is activated at the 20th iteration with input level 0.8. The edge weights of activation and blockage are set to 0.7 and 0.8, respectively, for both inputs. The simulation is executed for 100 iterations. a–c The plots of simulation results using the proposed model for EGFR, TNFR and ERK, under two different inputs. d–f The plots of SimBoolNet results under input 1 and 2, respectively. Please note that the two curves are totally overlap for TNFR in (e). g–i GINsim simulation results for EGFR, TNFR and ERK. Each run of GINsim simulation executes 8 iterations before reaching the stable state

Fig. 4

a The influence of different initial values on simulations. The initial value does not change the main trend of the state transition and the level of the stable state. b The influence of different edge weights to simulations. Each of the 32 signals shows a small range of the correlations between the simulated and the background trends, indicating that the proposed model is robust to different edge weights

Fig. 5

The plots of the simulated and real data in the control group. The blue and green curves are the simulated data using the proposed model and SimBoolNet, respectively. The red dots are the real data. The four panels (a), (b), (c) and (d) correspond to the plots of four proteins EGFR, Casp8, p53 and JNK, respectively