Quantitative evaluation and reversion analysis of the attractor landscapes of an intracellular regulatory network for colorectal cancer
© The Author(s). 2017
Received: 21 December 2016
Accepted: 31 March 2017
Published: 5 April 2017
Cancer reversion, converting the phenotypes of a cancer cell into those of a normal cell, has been sporadically observed throughout history. However, no systematic analysis has been attempted so far.
To investigate this from a systems biological perspective, we have constructed a logical network model of colorectal tumorigenesis by integrating key regulatory molecules and their interactions from previous experimental data. We identified molecular targets that can reverse cancerous cellular states to a normal state by systematically perturbing each molecular activity in the network and evaluating the resulting changes of the attractor landscape with respect to uncontrolled proliferation, EMT, and stemness. Intriguingly, many of the identified targets were well in accord with previous studies. We further revealed that the identified targets constitute stable network motifs that contribute to enhancing the robustness of attractors in cancerous cellular states against diverse regulatory signals.
The proposed framework for systems analysis is applicable to the study of tumorigenesis and reversion of other types of cancer.
KeywordsCancer reversion Logical model Systemic approach Colorectal cancer Reversion target Attractor landscape evaluation Functional network motif Systems biology
Cancer is one of leading causes of death according to the World Health Organization since 2000 . The most common features of cancer are uncontrolled proliferation, epithelial-mesenchymal transition (EMT), and stemness . Although these features and their underlying mechanisms were extensively studied, cancer still remains as a complex disease with no single cure probably due to a lack of systematic approach. Cancer is evolved from normal cells which are transformed by a number of genetic mutations accumulated in various signaling pathways during tumorigenesis . Such alterations often make cancer cells more robust than normal cells to an external apoptotic stimulus such as targeted drugs in therapeutic approach. Apoptosis is the programmed cell death, and triggering it is the ultimate therapeutic goal for most cancer. However, tumor-selective apoptosis is not always possible, and it is more likely to cause side effects to normal cells. Therefore, there have been increasing demands for an alternative anti-cancer therapeutic strategy by which the uncontrolled state of cancer cells could be reversed back to the normal cellular state while preventing normal cells from undergoing apoptosis . Finding this strategy based on cancer reversion requires the development of a systemic analysis for quantitative evaluation of a cancerous state. Through such an analysis, we could comprehensively characterize important features of cancer and also identify promising drug targets for cancer reversion.
Since the first observation of cancer reversion phenomenon from teratoma into normal cells in 1907 , numerous reports have shown that cancer reversion can occur both in vitro and in vivo [6–8]. For instance, inhibition of overexpressed PPARγ has been shown to trigger differentiation of colorectal cancer which is the second leading cause of cancer mortality in the United States . However, previous studies were limited to present the phenomenon itself without providing a systematic or mechanistic analysis. To reveal the underlying mechanism of cancer reversion and to discover specific targets for the reversion in a systematic way, a simplified but essential molecular regulatory network model needs to be constructed [10, 11].
The behavior of a cellular system is caused by complicated interactions of molecules that form a complex molecular interaction network. The steady states of all the molecules can be represented by an attractor state of the network which corresponds to a cellular phenotype . However, indeed, the functional properties and phenotypes of a cell are mainly determined by the steady states of specific important molecules, not all the molecules . Cancer can be understood as a functional disease triggered by the disturbance of such steady states of functional molecules by the accumulation of somatic mutations . The complexity of the molecular interaction network implicates the existence of inherent functional redundancy. So, there might exist some control targets that can drive the cancerous cellular states into normal-like states although multiple molecules in the network are already disturbed by the occurrence of mutations during tumorigenesis . In this respect, cancer reversion might be realizable by converting the steady state of important molecules to that of a normal cell through a systems approach .
In this study, we have constructed a simplified but essential molecular regulatory network model of a colorectal cancer cell to investigate the underlying mechanism of cancer reversion. Most previous studies focused on specific mutations accumulated in various signaling pathways which were frequently observed with cancer reversion phenomena in colorectal cancer [17, 18]. We have manually integrated such information through an extensive survey of literatures and databases, and identified essential regulatory interactions between key molecules. We have employed a Boolean network model to describe the logical relationship of molecular interactions. Then, we have explored the cancer reversion mechanism by systematically perturbing all of the molecular components in our network model and evaluating the resulting changes of the attractor landscape with respect to uncontrolled proliferation, EMT, and stemness. From this analysis, we have identified a set of promising control targets for cancer reversion, and some of them are in accord with previous experimental observations. Moreover, we have analyzed functional network motifs that are relevant to the target nodes and their stability in order to understand the underlying mechanism of cancer reversion. As a result, we found that cancer reversion can occur by the alleviating the robustness of the intracellular gene regulatory network. Therefore, our study provides new insight into the cancer reversion mechanism through a systematic way of identifying the control targets.
Construction of an essential molecular regulatory network model of colorectal cancer
Network update logic formation based on biological action mechanisms
The connectivity matrix in which basal levels of the weighted sum logics and mutation profiles for simulation are summarized in Additional file 4. The nodes are synchronously updated at each time step. We also attempted to apply the asynchronous update rule and found that the resulting point attractors and their basins were conserved in both update rules. Since the overall basin size of point attractors has reached more than 80% of all the initial states in our result, we concluded that the phenotypic features of attractor landscapes from both update rules were similar. The biological and analytical validities of synchronous update logic are explained in Additional file 2: Figures S1. The entities of the connectivity matrix are translated from the logical equations of the Boolean operators with our custom code using Matlab® 2014b, while the entities of basal column vector are driven from experimental data. The source codes for mathematical simulations are included in Additional file 5.
General concepts of simulation analysis on the network model
For large-scale networks, it is usually difficult to obtain the whole state transition diagram by a full search because of the computational limitations. Therefore, in our network model (N = 34), we estimated the attractor landscape by investigating the state transition diagram from a number of randomly sampled initial states such as 100,000. This initial population was sufficiently large for reliable reproduction of major attractor states, and thus the phenotypic scores of attractor landscapes were varied within very small (±2%) deviation from the average score of 100 repetitions. During the perturbation analysis and validation of our network model, node perturbations and mutation profiles were implemented by pinning the state of the corresponding nodes into either 0 or 1. To qualitatively evaluate the various input-output relationships of our network, we have employed the proposed method from Helikar et al. . In this simulation, the activation ratio of eight marker nodes was measured as increasing the stochastic activity levels of three input nodes independently.
Quantitative normal-like score evaluations of attractor landscapes
Node perturbation analysis to identify reversion targets
To identify the cancer reversion targets based on the normal-like score, we have performed a node perturbation analysis by systematically perturbing the molecular activity of each node in the network. There are three types of perturbation: activation, inhibition, and restoration perturbations. An activation or inhibition perturbation fixes the state of that node to 1 or 0, respectively, while a restoration perturbation restores the basal level of that node back to the value in normal colon cell. During a single node perturbation analysis, we have obtained several potent cancer reversion targets in the case of when the normal-like score of the network landscape has been increased after perturbation . During a double nodes perturbation analysis, we have classified perturbation types into three: synergistic, additive and antagonistic. For instance, we measure how much the normal-like score increases after performing single- and double-node perturbations with node A and B. If the increase of normal-like score during the double-node perturbation is larger, similar or smaller than the sum of the normal-like scores from the individually perturbed nodes A and B, then each incident can be classified as synergistic, additive or antagonistic, respectively. The range between increased normal-like scores has been calculated as 20% in average after performing double node perturbation in various pairs. Additional explanations are in Additional file 2: Figures S2.
Functional network motif analysis to explore the reversion mechanisms
Synergistic effects usually arise from emergent properties of a complex network due to the close interactions of molecules in the network such as feedback loops or network kernels . Synergistic pairs of cancer reversion targets strongly interact with each other and constitute functional network motifs in which every node show a similar consequence in the normal-like score for the same node perturbation type. Moreover, fixing a node in the functional motif may decrease the ability of other nodes in the motif to increase the normal-like score by their perturbation. A functional network motif can be understood as a functional unit block for cancer reversion. If a node in a network motif is mutated, cancer reversion could not be achievable with any perturbations among other nodes in the motif. Rather, additional perturbation of nodes in the other network motifs could induce cancer reversion . Based on these assumptions, we have extracted the functional network motifs by the procedure below. First, we calculated the increase of normal-like score by perturbing one of the cancer reversion targets, “A”. Second, we systematically fixed any single node and calculated again the increase of normal-like score by the node “A”. Third, we selected one fixed node, “B”, which mostly decreased the normal-like score, as a member of functional network motif with the node A. Next, we repeated this process with fixing the node B in order to find another node, “C”, which mostly decrease the normal-like score. Finally, we repeated these processes until the increased normal-like score by the perturbation of A became smaller enough to neglect. After determining the entire members of the functional network motif with this algorithm, we have identified the motifs from the original colorectal cancer regulatory network. After curating the network, we have tested the stability of each motif by comparing the averaged node activities over every attractor in colorectal cancer with those of perturbed colorectal cancer (see Additional file 2: Figures S3 for additional explanations about motif stability analysis).
Robustness analysis of various sequences of mutations
To determine the robustness of the network against external perturbations, we examined the number of attractors and the average basin size of five major attractors. If the number of attractors is small or the average basin size of major attractors is large, external perturbation could hardly change the network state that stays in an attractor state, which makes the network robust to external perturbations . During the robustness analysis, the entire attractor landscapes have been simulated while accumulating the node state fixation into either 0 or 1. We have investigated the robustness of a network against the external signals as mutations were accumulated, by tracking the changes in the number of attractors and average basin size of attractions from five major attractors (Additional file 2: Figures S4).
Proposed network model recapitulating the various cancer reversion phenomena
With our logical network model of colorectal cancer, we have tested whether it can successfully recapitulate both the dynamics of colon cancer cell and various cancer reversion phenomena reported in previous studies . First, using our logical network model, we have simulated the various input-output relationships observed in normal colon cells under various conditions. Figure 3b shows that the functional relationships between three input stimuli and eight cell state markers of the network in the previous studies are reproduced by our network model, confirming that our network model successfully implemented the dynamics of normal colon cell [19–21]. Next, we have projected the 12 mutation profiles sets randomly selected from four consensus molecular subtypes (CMS) of colorectal cancer into our network model to obtain 48 CMS network models . Guinney et al. have clustered colorectal cancer into four distinctive subtypes based on the statistical differences of gene expression data. From evaluation of the CPSs for each CMS, the network models were well clustered according to the CMS in the three-dimensional space of CPSs (Fig. 3c). This result indicates that our network model was successfully transformed into that of a colon cancer cell with the mutation profiles. Thus, our three-dimensional scoring system is sufficient to capture phenotypic characteristics of colorectal cancer such as CMS profiles. Moreover, the CMS4 network models were predicted to be on the most malignant state, which is well in accord with the work of Guinney et al. . To further test the validity of our network model, we have simulated the cancer reversion for colorectal cancer network models by restoring the basal level of APC. During the simulation, the mutation profiles were obtained from the patients’ data in Sottoriva et al. . We observed that the reversion phenomenon was enhanced most significantly in cancer network with KRAS hyperactivation, APC deletion, and p53 deletion (Fig. 3d) . Together, these results indicate that our network model and its dynamics effectively demonstrated the biological characteristics of normal colon cell and the cancer reversion phenomena in colorectal cancer.
Systematic identification of cancer reversion targets by single node perturbation analysis
Four stable network motifs that critically enhance the robustness of cancer cell networks
Our single node perturbation simulation has suggested 11 cancer reversion targets. We further analyzed double nodes perturbation to find the synergistic pairs among seven targets by applying inhibition or activation perturbation, where restoration perturbation was not considered due to the complexity of simulation analysis. As a result, we identified three synergistic pairs (KRAS-Akt, Akt-PP2A, and PP2A-KRAS) which were selected when an increase in the normal-like score for two node perturbation is larger than the sum of increases for individual node perturbations (Fig. 4b). The synergistic effects observed in double node perturbation simulation imply the existence of functional motifs that act as a functional unit block for cancer reversion. Thus, we have parsed the motif which is composed of the synergistic pairs among the cancer reversion target nodes. Interestingly, every node in synergistic pairs is included in the EGF signal transduction pathway. As a result, the synergistic pairs act together as a functional motif which controls the EGF signal propagation to the remaining network nodes ranked at the lower level of hierarchy (Fig. 4c). Our result indicates that perturbing any multiple nodes in the functional motif could induce synergistic effects on cancer reversion, which might be an effective strategy to trigger the cancer reversion with minimum number of control nodes. The double nodes perturbation results are summarized in Additional file 6 and Additional file 2: Figures S7.
The cancer reversion mechanism revealed by perturbing the stable network motifs
The systemic view of cancer biology has been highlighted for a long time. The hallmarks of cancer have known to be associated with the complex dynamics of molecular interaction networks . A variety of network models of cancer cells has been previously established to investigate such dynamic features of the network from a systems biological perspective. However, previous studies have mainly focused on qualitative assessments of cancer such as changes in input-output relationships in cancer cells or comparison of major attractors between normal and cancer cells [19, 40]. For instance, a recent study employed a network modeling approach to identify control targets for anti-cancer treatment by qualitatively examining the changes of basin size between major attractors, such as proliferation and apoptosis . However, these system-based studies still have fundamental limitations in systematic control for cancer reversion because there is no quantitative evaluation of cancer status. In our study, the resulting normal-like score of a whole attractor landscape is determined by a set of several functional characteristics related to cancer malignancy and their weights that reflect the malignancy rank of experimental data. Thus, the normal-like score not only contains the phenotypic features of the whole attractor landscape but also quantitatively define the phenotypic malignancy. Moreover, the previous study based on the attractor ratio analysis has a limit in estimating whether a specific control will cause improvement or regression of malignancy due to a lack of quantitative evaluation of attractor landscape. Our scoring system is able to not only explore the most efficient drug target among multiple targets but also quantify its efficiency, which allows a systematic control for cancer reversion. Furthermore, the quantitative analysis of attractor landscapes based on the normal-like scoring system can be utilized for various types of cancer as well as colorectal cancer in order to identify effective control targets in a systemic approach. There still remains a limitation in our study in that the reconstructed essential regulatory network model is not complete although we have examined the robustness of our result (see Additional file 2). Hence, it would be a challenging future study to further expand the network model and validate it by experiments.
Dysfunctions of cancer cells arise from a series of mutations accumulated during tumorigenesis. The permanent alterations of a molecular interaction network by these accumulated mutations seem to prevent cancer reversion by locking cancer cells to the cancerous state. Although cancer reversion has been studied for decades and identified key molecules of high importance, it remains difficult to understand how cancer reversion can be achieved . Current cancer therapies are usually performed in terms of tumor regression by inducing apoptosis in cancer cells. However, tumor regression is often accompanied by unwanted regression of normal cells, one of the frequent side effects of cancer treatments . To overcome these side effects, we focused on restoring the functional phenotypes of cancer cells to those of normal cells rather than tumor regression. To achieve this, we have set the cell cycle arrest index to be of greater importance than that of apoptosis in order to approach cancer reversion without inducing apoptosis in normal cells. In addition to cell cycle arrest, the attractor landscape was assessed by EMT and stemness, representative functional phenotypes of cancerous states, to quantify the transformation to a normal-like state. Taken together, we suggest that the reverse control based on these phenotypes can return cancer cells to functionally normal cellular states, which can pave the way to new anti-cancer treatments.
To investigate the underlying mechanism of colorectal cancer reversion from a systems perspective, we have constructed a logical network model of colorectal tumorigenesis by integrating key regulatory molecules and their interactions from an extensive survey of literature and experimental data. We established a Boolean network model and validated its logical rules for every node in order to create a biologically relevant molecular regulatory network that can mimic the signaling dynamics and tumorigenesis in a colorectal cell. By systematically perturbing each of the molecules in the network, we identified cancer reversion targets that can transform cancerous cellular states to normal-like states. Moreover, we quantitatively evaluated the resulting changes of the attractor landscape through our scoring system with respect to uncontrolled proliferation, EMT, and stemness. Interestingly, many of the identified molecular targets were well in agreement with previous studies. We further revealed that the identified targets constitute functionally stable network motifs that contribute to enhancing the robustness of attractors in a cancerous state against various external regulatory signals. Our study provides a new approach to understanding colorectal tumorigenesis and offers promising targets that can drive cancer reversion.
V-Akt murine thymoma viral oncogene homolog
Adenomatous polyposis coli
Cyclin-dependent kinase inhibitor 2A
Breast cancer 1
Consensus Molecular Subtype
Copy number alteration
Cancer proximity score
E2 family transcription factor 1
Epidermal growth factor
Genome-scale Integrated Analysis of gene Networks in Tissues
Human Protein Atlas
Kyoto Encyclopedia of Genes and Genomes
Cyclin-dependent kinase inhibitor 1A
Pathway Interaction Database
Protein phosphatase 2
Peroxisome proliferator-activated receptor γ
The Cancer and Geonome Atlas
Tumor protein p53
This work was supported by the National Research Foundation of Korea (NRF) grants funded by the Korea Government, the Ministry of Science, and ICT & Future Planning (2014R1A2A1A10052404).
Availability of data and materials
The data supporting the results of this article are included within the article and its additional files.
K.-H.C. designed the project and supervised the research; Y.K. constructed the colon cancer regulatory network; Y.K. performed mathematical modeling and analysis; Y.K., S.C., D.S. and K.-H.C. wrote the manuscript. All authors read and approved the final manuscript.
The authors declared that they have no competing interests.
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