Generalized logical model based on network topology to capture the dynamical trends of cellular signaling pathways
© Zhang et al. 2015
Published: 11 January 2016
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.
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.
The proposed simulation tool provides a valuable resource for modeling cellular signaling pathways using a knowledge-based method.
KeywordsGeneralized logical model Signaling pathways Dynamical system Cancer
Signal transduction plays an essential role in the cellular processes in which cell responds to extracellular perturbations (e.g., the exposure to drugs or ligands). According to the signals, the cell adjust its metabolism, shape, gene expression, etc., to adapt to the environment. It is widely believed that the dysregulation of signal transduction is one of the most important pathogeneses of many human diseases including cancer. Although high-throughput experimental data show a great potential for uncovering unprecedented details of biological systems, it is still challenging to understand signaling networks at systems level. Therefore, computational simulation, which is a systems biology approach, is highly desirable for the analysis of the underlying mechanisms of how the signals are transmitted through signaling pathways.
Many existing models are able to simulate the process of signal transduction, such as Boolean network models, fuzzy logic models and kinetic models based on ordinary differential equations (ODEs). Boolean network is a simple and promising framework for the modeling of protein-protein interactions and signaling pathways. It has been used with some success in identifying stable states of a system , , simulating the influence of deletion/knockout of important nodes in a network , predicting carcinogenesis and targeted therapy outcomes , reproducing the dynamics of the yeast MAPK pathways , modeling the mammalian cell cycle  and analyzing the behaviors of the apoptosis pathways , . However, its inability of encoding graded responses and the typically sigmoidal biological relationships becomes a significant limitation since it is able to handle only binary values, i.e., a simple on/off state which is over–simplified compared with a real signaling network. To overcome this limitation, fuzzy logic models, which generalize the on/off characteristic to a continuous range from 0 to 1, have been successfully applied to analyzing the crosstalk among the TNF/EGF/Insulin-induced signaling pathways  and the liver cell responses to inflammatory stimuli . However, a large amount of prior knowledge is needed for the assembly of the membership functions and logical rules for the fuzzy logic models. On the other hand, ODEs have also been applied to modeling various biological processes, such as the simulation of physiological responses of mammalian cells to the control of cell cycle , mathematical modeling of the mechanisms for regulating the differentiation of hematopoietic stem cells , discovery of signaling pathway rewiring  and exploring the dynamics of the pathways controlling cell apoptosis , . However, ODEs-based models require a relatively detailed knowledge of kinetic parameters which is hardly available for all the pathways. Previously, we proposed a simulation tool called SimBoolNet  which is based on an extended Boolean network model. Although the performance of SimBoolNet in predicting protein activities was promising , it has limited capability of dealing with blocking effects, degradations and sequenced perturbations.
Here, we present a generalized logical model, which is capable of revealing the process of degradation, the sigmoidal biological relationships between molecules and the effects of scheduled perturbations to signaling networks. Compared with SimBoolNet  and GINsim  (a Boolean network based simulation tool), the proposed simulator can not only predict the stable states of the signal transduction system but also dynamically simulate the effects induced by various timing and ordering of perturbations. The simulations are validated using experimental phosphoproteomics data of breast cancer cells perturbed by different combinations of drug additions . The simulated time-series data of protein activity levels show significant correlations with the real time-course data, thereby demonstrating that the proposed model is able to capture the key features of the signaling pathways.
Computational model for dynamical simulation
It is suggested that cells respond to external perturbations through a time–dependent (e.g., the schedule and duration of drug addition) process . Wet–lab experiments have shown that different ordering and timing of drug additions have significantly different drug effects, such as inducing specific alterations of signaling pathways , ,  and showing different efficiencies in killing cancer cells . However, most existing simulation tools are not able to accommodate the time-staggered design of drug treatments in biological experiments. Therefore, our model introduces time-staggered perturbations to explore the effects of not only dosage, but also the schedule and duration of the perturbations to cellular systems with a knowledge-based model. The timing and the order of drug additions can be specified by users as parameters. For example, the drug can start to affect its target at the kth simulation iteration with a user-defined k. The target, input level, type of interaction (stimulation or inhibition) and schedule of the perturbations can all be specified according to user’s design of experiment.
Performance comparison on simulating signaling responses to perturbations
For comparison, we run simulations using our program based on SimBoolNet , GINsim  and the proposed model on the same network in Fig. 2. Two different inputs are introduced: (1) the input levels of EGFR and TNFR are set to 0.5 and 0.8, respectively, (2) EGFR inhibitor is added at the 10th iteration of simulation and TNFR is activated with input level 0.8 at the 20th iteration. The number of simulation iterations is set to 100. For the proposed model, the full inhibition is denoted as -1 and the perturbations can be executed at any iteration during the simulation. The degradation rate d is set to 0.2. For SimBoolNet and GINsim, the blocking effect is represented by setting the activity level of EGFR to 0 from the very first step of simulation which, to our understand, is unlikely to be a precise representation. There should be a process for the inhibitor to reduce the activity level of its target, especially when the inhibitor is not added at the beginning. The edge weights of activation and blockage are set to 0.7 and 0.8, respectively. GINsim simulation, on the other hand, does not accept parameters for edge weights and the number of iterations, and executes synchronously until the system reaches the stable state. GINsim also supports the asynchronous mode, but it is a time-consuming task due to a much larger search space than with the synchronous mode. We did not get any result from running GINsim in asynchronous mode on our network (Fig. 2) within endurable time using a desktop PC (Dell Precision T3600 workstation with Intel Xeon CPU E5–1620, 8 GB RAM and Windows 7 Professional 64–bit operating system). We have also tried other different settings of input level, edge weight and degradation rate, and the results are shown in section “Model comparison and validation with real data”.
Comparison of the computational time required for SimBoolNet, GINsim and the proposed model
Number of nodes/edges
We went on to explore the robustness of the proposed model to the variations of edge weights. In principle, we randomly generated the edge weights to run the simulations, and then checked if the activity trend of each protein remained unchanged. For a specific input (i.e., the input levels of EGFR and TNFR are both 0.5), we first randomized the weights of all the 57 edges and ran the simulation for 100 times as the background group. For each protein, the mean activity at each time point was regarded as the background trend over time. Next, we further generated 50 groups of simulations, each group consisting of 100 simulations of randomly generated edge weights. For each group, the mean activity trend of each protein was used to calculate the correlation with the background trend. Figure 4b gives the distribution of the 50 correlations between the simulated and the background trends for the 32 non-receptor nodes (ignoring the receptors EGFR, TNFR and DNA Damage because they have no incoming edges), and the proteins are ranked based on the median of the correlations. It can be seen that 21 out of 32 proteins (i.e., from PI3K to AKT) have the medians of the correlations larger than 0.8; 10 out of 32 have the medians falling into the interval 0.5 to 0.8; and only one (i.e., Proliferation) has the median which is lower than 0.5. Moreover, all the 32 signaling proteins show small ranges of the correlations between the simulated and the background trends, indicating that the proposed model is robust for capturing the dynamical trends of the signal transduction process under different settings of edge weights.
Model comparison and validation with real data
To estimate the performance of the proposed model, the simulated results using the network in Fig. 2 are compared with a real signaling dataset  containing the time-series phosphoproteomics data. In the dataset, perturbations (i.e., inhibitor of EGFR or stimuli of DNA damage or both) were applied to cells of the breast cancer cell line BT20. For each perturbation, activity levels of 32 signaling proteins (21 out of 35 are included in the network in Fig. 2) were measured at 8 time points. To simulate the perturbations, we use (i) half activation input signals (0.5) to represent the control situation where no stimuli or inhibitor is added; (ii) activation input signals (+1) to represent the addition of stimuli, i.e., the targets are fully activated; and (iii) inhibition input signals (–1) to represent the effect of inhibitors, i.e., the activity of the targets are suppressed.
Spearman correlations between simulated and real data
Inputs of the simulation in section “Model comparison and validation with real data”
DNA damage stimuli
Goodness of fit of the simulations to the real experimental measurements under drug treatments
Discussion and conclusion
In this paper, we present a model to dynamically simulate the process of intracellular signal transduction. According to a phosphoproteomics dataset , we constructed a network, which comprises 35 nodes (21 nodes have experimental measurements) and 57 edges, to do the simulation. The state of each node is calculated based on its own previous state with a degradation rate, and the activation and inhibition effects produced by the signals transmitted from its parent nodes. Different combinations of perturbations were applied to the network. The simulation results have been evaluated with the real data, demonstrating that our simulator has the ability to grasp the main dynamical trends of signal transduction. Compared with SimBoolNet  and GINsim , the proposed model shows promising performance in revealing the graded responses, the sigmoidal biological relationships and the effects of scheduled perturbations to a signaling network. Moreover, by testing the proposed model with different values of parameters (e.g., the initial activities of the proteins and the edge weights), we have shown that our method performs robustly in revealing the dynamics of the signaling pathways when the prior knowledge of the network topology is reliable.
Studying the cell responses to extracellular perturbations is a major endeavor for biomedical research and pharmaceutical industry. With the development of high-throughput experiments, large-scale data are available to help uncover important biological mechanisms at systems level. However, most existing data-driven methods  have limitations in revealing underlying molecular mechanisms. Therefore, computational simulation based on the integration of prior knowledge with data shows a great potential for revealing insights into the dynamical system of signal transduction, and thus would be a valuable complement to the data-driven methods. Although the proposed model is still limited in mapping the simulation steps to the experimental time points, we believe that the integration of both knowledge and data, such as learning the edge weights from experimental data, would be a powerful approach to understanding the signal transduction networks. In addition, generalization of the present model, which uses the synchronous updating scheme, such that it is able to deal with asynchronous dynamics, e.g., updating a randomly selected node at each time point, would also be a valuable future direction.
This article has been published as part of BMC Systems Biology Volume 10 Supplement 1, 2016: Selected articles from the Fourteenth Asia Pacific Bioinformatics Conference (APBC 2016): Systems Biology. The full contents of the supplement are available online at http://www.biomedcentral.com/bmcsystbiol/supplements/10/S1.
This research has been supported by MOE AcRF Tier 2 grant (ARC39/13, MOE2013-T2-1-079), Ministry of Education, Singapore. It is also supported in part by the Intramural Research Program of the National Library of Medicine, National Institutes of Health, U.S.A. The content of this publication does not necessarily reflect the views or policies of the Department of Health and Human Services, nor does mention of trade names, commercial products, or organizations imply endorsement by the U.S. Government. The publication cost for this article was funded by MOE AcRF Tier 2 grant (ARC39/13, MOE2013-T2-1-079), Ministry of Education, Singapore.
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