The authors have declared that no competing interests exist.
Conceived and designed the experiments: RRS. Performed the experiments: SC RNP. Analyzed the data: SC RRS. Wrote the paper: SC RNP RRS.
Hedgehog is an evolutionarily conserved developmental pathway, widely implicated in controlling various cellular responses such as cellular proliferation and stem cell renewal in human and other organisms, through external stimuli. Aberrant activation of this pathway in human adult stem cell line may cause different types of cancers. Hence, targeting this pathway in cancer therapy has become indispensable, but the non availability of detailed molecular interactions, complex regulations by extra- and intra-cellular proteins and cross talks with other pathways pose a serious challenge to get a coherent understanding of this signaling pathway for making therapeutic strategy. This motivated us to perform a computational study of the pathway and to identify probable drug targets. In this work, from available databases and literature, we reconstructed a complete hedgehog pathway which reports the largest number of molecules and interactions to date. Using recently developed computational techniques, we further performed structural and logical analysis of this pathway. In structural analysis, the connectivity and centrality parameters were calculated to identify the important proteins from the network. To capture the regulations of the molecules, we developed a master Boolean model of all the interactions between the proteins and created different cancer scenarios, such as Glioma, Colon and Pancreatic. We performed perturbation analysis on these cancer conditions to identify the important and minimal combinations of proteins that can be used as drug targets. From our study we observed the under expressions of various oncoproteins in Hedgehog pathway while perturbing at a time the combinations of the proteins GLI1, GLI2 and SMO in Glioma; SMO, HFU, ULK3 and RAS in Colon cancer; SMO, HFU, ULK3, RAS and ERK12 in Pancreatic cancer. This reconstructed Hedgehog signaling pathway and the computational analysis for identifying new combinatory drug targets will be useful for future
Signal transduction system represents an elegant circuitry of the cell that translates external and internal cues into appropriate cellular responses. These signaling pathways are generally organized into three main parts: Input, Intermediate and Output
Several concerted efforts are being made to dissect different signaling pathways, such as MAPK, Apoptosis, mTOR etc. and the related molecular mechanisms that control the cancer development of a cell or tissue in an organism
The flow of molecular excitation in any signal transduction pathway follows a complex branching pattern of cascade, therefore it is worth mentioning that targeting an individual protein in signaling pathways, such as Hedgehog, would not be fruitful to prevent its malfunction in a cancer situation. A current review by Li et al.
Identification of drug targets by experimental approach sometimes becomes difficult as it requires more time and resources. Moreover, the complex regulatory networks of gene expression, entire networks of the metabolic reactions and large-scale proteomics data are now available to study response of pathways (modules) to different perturbations. Given the vast amounts of data at each level, it is a challenge to interpret the information emanating from individual assays and integrate results from multiple levels. Recent developments in integrative approaches, bioinformatics tools, mathematical and computational methods have become indispensable in understanding and analyzing such data from experimental studies. Diverse approaches for qualitative and quantitative methods and modeling of signaling pathways have been used to answer several biological questions in signaling systems
Moreover, identification of a combination of proteins as a drug target in Hedgehog pathway for cancer therapy requires the complete understanding of the entire mechanisms of this pathway in human cell. In order to achieve this, one needs comprehensive and most up to date information or a map of Hedgehog pathway that may help to analyze the pathway more deeply and accurately. Unfortunately, as far as the literature and biological signaling database are concerned, there is no comprehensive pathway map available for studying the Hedgehog pathway. Even, search of different popular database (See Table S1 of
In this paper, collating the data from different database and literature, we present a master model of the Hedgehog pathway. Our extensive data mining and text extraction procedures from literature sources helped us to identify many proteins and their interactions that were not included in the existing database. To the best of our knowledge in this article we have presented a Hedgehog pathway map that is the largest Hedgehog pathway map of human till date. In comparison to existing popular database, the newly reconstructed Hedgehog map consists 57 proteins, 6 cellular or phenotypic expression and 96 hyper-interactions, which is highest. In
In this work, one of our main objectives was to provide an extensive and up to date Hedgehog signaling map that can serve both experimental as well as theoretical biology communities. In
Total 57 proteins included in this pathway figure. The green and red arrows are indicating Activation/Production and Inhibition process respectively. The black arrows indicate the nuclear translocation process. All the proteins of this network are allocated into four main regions with different color codes: Extracellular and Membrane (Blue); Cytoplasm (Red); Nucleus (Green); and Output (Yellow). The output proteins are linked with various cellular responses (cross talk with other pathways or phenotypic expressions) with black dotted arrow.
In
In this region, we included three hedgehog ligands: Sonic Hedgehog (SHH), Indian Hedgehog (IHH) and Desert Hedgehog (DHH). These are the ligands that bind to the receptor proteins Patched1 (PTCH1) and Patched2 (PTCH2) of a hedgehog target or responsive cell
In this region, we included total 16 protein molecules. All the three isoforms of GLI transcription factors GLI1, GLI2 and GLI3 were included. GLI was found in Cytoplasm as well as in Nucleus and was the main target component protein for Hedgehog pathway activation
In the nuclear region of the Hedgehog pathway map, we included 13 molecules those were mainly transcription factor, co-activator or co-repressor. The activated transcription factors GLI1, GLI2 and GLI3 translocate into the nucleus as Nuclear GLI1 (NUC_GLI1), Nuclear GLI2 (NUC_GLI2) and GLI3 active (GLI3_A)
This region does not specify any cellular location. We included this section separately to identify the proteins produced at the end of Hedgehog pathway. We considered a signaling network as an input-output system where the ligands and extracellular proteins were the inputs, the proteins produced as a response to these inputs at the end of this pathway could be thought as Output proteins. There were total 15 proteins including GLI1, PTCH1 and HHIP included in this section. The total numbers of proteins shown in this region are highest compare to any other published human specific Hedgehog pathway map to the best of our knowledge. Besides, all the proteins in this region were colored as yellow, except PTCH1, HHIP and GLI1. The reason was, after the production or translation, these three proteins translocate to their corresponding cellular locations and perform their activity in the pathway. In order to show this feedback mechanism, we kept their color similar to the color coded in their actual cellular location. Production of PTCH1 and HHIP proteins in this pathway switch “ON” a “negative feedback” mechanism and thus control further hedgehog pathway activation through ligand dependent way. It was experimentally proved that the Hedgehog Interacting Protein 1(HHIP) represses the Hedgehog ligands by directly binding with them and the higher concentration of PTCH1 in membrane would help to repress further SMO activation
In order to show the cross connections of the output proteins with the other pathway or cellular functions, we kept this section at the end of our pathway figure. There were 6 cellular responses included which were Cell Proliferation, Cell cycle progression, Anti-Apoptosis, Epithelial–Mesenchymal Transition (EMT), Wnt signal and Notch signal. We showed the connections of produced proteins with these cellular responses by black dotted arrow in the pathway figure.
To understand the detail activity of these molecules in the Hedgehog pathway and to perform the structural analysis, we modeled the reconstructed pathway map by two approaches: Graph theoretic and Logical (see the Methods section).
The reconstructed Hedgehog pathway (
The colored circles represent the nodes or proteins of the pathway and the black arrows indicate an edge or connection between two nodes of the network. The nodes are colored according to their sub cellular locations in the cell (
In
We further analyzed this network from three perspectives: i) Connectivity ii) Centrality and iii) All pairs shortest path.
We performed this analysis to know the number of connections of each protein with all other proteins in the network. Three types of parameters (IN DEGREE, OUT DEGREE and TOTAL DEGREE) were used in this section (see the Methods section). We calculated and presented these three parameters for each protein of the Hedgehog signaling network in
Heat map of the values of the parameters used in Connectivity and Centrality analysis. The names of the proteins or nodes are arranged row wise (Y-axis) according to the position of their corresponding region (
The heat map (
Parameters | Extracellular and Ligands | Cytoplasm | Nucleus | Output proteins |
DHH(3), IHH(4), SHH(6), PTCH1(9), PTCH2(3), HHIP(6) | GLI1(24), GLI2(8) | NOT FOUND | ||
DISPATCHED(3), HHAT(3), HHIP (3) | GLI1(6) | NOT FOUND | ||
DHH(5), IHH(6), SHH(8), PTCH1(11), HHIP(9) | GLI1(30), GLI2(10) |
From
We also extracted the proteins which had the TOTAL-DEGREE higher than the average total-degree 4.91.
We measured the ‘Centrality score’ of each node or protein in the network after identifying the important “Hub proteins” from the network. In the connectivity analysis, we found some important nodes or proteins which were forming important ‘Hub’ in the whole network structure. In that case we gave the highest importance to a node on the basis of its total number of connections or degree value. Albeit in biological as well as any real world network the importance of a node or a protein does not depend only on its number of connections or neighbors
In this analysis, at first, we calculated ‘
Also, we calculated
This parameter was used to calculate the shortest paths between every pair of nodes or proteins in the hedgehog pathway
The Graph theoretic analysis of the hedgehog signaling network helped us to find out some important proteins in the network on the basis of some important topological parameters. The parameters which we used in our network were able to identify the proteins that played crucial role to operate the hedgehog pathway normally. Several experimental studies proved that over or under expression of these identified proteins would cause abnormal activation or inhibition of hedgehog pathway and lead to uncontrolled cell proliferation or cancer stage in various types of cell lines
We simulated the logical models of the Hedgehog pathway for normal scenario as well as for three different types of cancer i.e. Glioma, Colon and Pancreatic cancer in CellNetAnalyzer
In
TS: Treated Scenario; NS: Normal Scenario; GS: Glioma Scenario. The green arrow heads are indicating the minimal combination of proteins which was inhibited in the drug treated perturbation analysis. (A) Represents number of Upstream activator proteins (Y-axis) activating the proteins (X-axis) representing significant variations. Compared to the normal scenario, proteins, SHH, SMO, GLI1, GLI2, and output proteins BMI, SNAI1, BCL2 and Cyclins, are activated by maximum number of upstream activator proteins. On drug treated perturbation of SMO, GLI1 and GLI2, the number of activators of the output proteins become zero. (B) Represents number of Upstream inhibitory proteins (Y-axis) inhibiting the proteins (X-axis) representing significant variations. The numbers of upstream inhibitor proteins in normal versus Glioma scenario remain same. Similar perturbation results are observed as in (A). (C) Represents number of Downstream proteins (Y-axis) activated by the proteins (X-axis) representing significant variations. The number of downstream proteins activated in normal versus Glioma remains same. On perturbation of SMO, GLI1 and GLI2, the number of downstream proteins activated by these proteins is reduced to zero. (D) Represents number of Downstream proteins (Y-axis) inhibited by the proteins (X-axis) representing significant variations. The number of downstream proteins inhibited in normal versus Glioma remains the same.
TS: Treated Scenario; NS: Normal Scenario; CC: Colon Cancer Scenario. The green arrow heads are indicating the minimal combination of proteins which was inhibited in the drug treated perturbation analysis. (A) Represents number of Upstream activator proteins (Y-axis) activating the proteins (X-axis) representing significant variations. Compared to the normal scenario, proteins, SHH, IHH, SMO, GLI1, GLI2 and output proteins BMI, SNAI1, BCL2 and Cyclins are activated by maximum number of upstream activator proteins. On drug treated perturbation of SMO, HFU, ULK3 and RAS, the number of activators of the output proteins become zero. (B) Represents number of upstream inhibitory proteins (Y-axis) inhibiting the proteins (X-axis) representing significant variations. The numbers of upstream inhibitor proteins in normal versus Colon cancer scenario remain same. Similar perturbation results are observed as in (A). (C) Represents number of downstream proteins (Y-axis) activated by the proteins (X-axis) representing significant variations. The number of downstream proteins activated in normal versus Colon cancer scenario remains same. On perturbation of SMO, HFU, ULK3 and RAS, the number of downstream proteins activated by these proteins is reduced to zero. (D) Represents number of downstream proteins (Y-axis) inhibited by the proteins (X-axis) representing significant variations. The numbers of downstream proteins inhibited in normal versus Colon cancer scenario remain same.
TS: Treated Scenario; NS: Normal Scenario; PC: Pancreatic Cancer Scenario. The green arrow heads are indicating the minimal combination of proteins which was inhibited in the drug treated perturbation analysis. (A) Represents number of Upstream activator proteins (Y-axis) activating the proteins (X-axis) representing significant variations. Compared to the normal scenario, proteins, SHH, IHH, SMO, GLI1, GLI2 and output proteins BMI, SNAI1, BCL2 and Cyclins are activated by maximum number of upstream activator proteins. On drug treated perturbation of SMO, HFU, ULK3, RAS and ERK12, the number of activators of the output proteins become zero. (B) Represents number of upstream inhibitory proteins (Y-axis) inhibiting the proteins (X-axis) representing significant variations. The numbers of upstream inhibitor proteins in normal versus Pancreatic cancer scenario remain same. Similar perturbation results are observed as in (A). (C) Represents number of downstream proteins (Y-axis) activated by the proteins (X-axis) representing significant variations. The numbers of downstream proteins activated in normal versus Pancreatic Cancer remain same. On perturbation of SMO, HFU, ULK3, RAS and ERK12, the number of downstream proteins activated by these proteins is reduced to zero. (D) Represents number of downstream proteins (Y-axis) inhibited by the proteins (X-axis) representing significant variations. The numbers of downstream proteins inhibited in normal versus Pancreatic cancer scenario remain same.
In case of ‘Canonical hedgehog pathway’ (i.e. NS or Normal Scenario), we found that at time scale 2 Sonic hedgehog (SHH) was activating overall 26 different proteins (from
In case of Glioma, we considered the over expression of hedgehog ligand SHH
In
The above results helped us to identify the key proteins that could be used as target proteins for our perturbation analysis or combinatorial drug treatment scenario (TS). At the time of the perturbation study, we also looked into the biological relevance of that target key proteins. We identified that SHH, SMO, STK36, RAS, TWIST, ERK12, HFU, ULK3 were activating the GLI transcription factors in the cytoplasm of Glioma cell and due to this activation, the output proteins were over-expressed at the end of this pathway. It was experimentally proved that SMO plays a very crucial role to activate STK36 as well as GLI1 in cytoplasm
In order to determine the other factors, we revisited our graph theoretical analysis and identified the IN-DEGREE neighbors of GLI proteins from cytoplasm. We found that the upstream activators (IN-DEGREE neighbors) of GLI1 and GLI2 proteins in cytoplasm were HFU, ULK3, ERK12, RAS and TWIST. We then selectively perturbed the logical states of these activators in Glioma scenario (GS), but unfortunately, none of the activators were able to inhibit the activation of GLI proteins alone in the cytoplasm. Only the perturbation of all these activators at a time was useful, but this combination of perturbation was not biologically feasible as several proteins had to be blocked in this perturbation study. Therefore, in order to suppress the GLI activation in cytoplasm, we directly blocked the activity of GLI1 and GLI2 in cytoplasm and also SMO in membrane of the Glioma scenario (GS) by putting ‘0’ or “OFF” as their logical states. As a result of this perturbation simulation, we observed that the expressions of the output proteins were blocked in Glioma scenario (GS).The dependency matrix obtained were used to extract the total number of proteins that were directly activated or inhibited by each protein in the pathway in this drug treated scenario (TS). The result was presented in
We found that in case of Colon cancer, along with IHH and SHH ligands, activated RAS/RAK pathway also up-regulated the activity of the GLI proteins in colorectal cancer cell
These findings helped us to identify the combination of potential drug targetable proteins in Hedgehog pathway for Colon cancer cell lines. We perturbed the activation signal from SHH and IHH via PATCHED (PTCH1/2) and SMO proteins to GLI transcription factors and the interactions between HFU, ULK3 and RAS with GLI proteins. In order to do that we put the logical state of SMO, HFU, ULK3 and RAS as ‘0’ (Zero) and performed the combinatorial drug perturbation or Treatment simulation (TS). We found that the total number of the activated proteins by GLI1, GLI2 and GLI3 were decreased and the expression of the HFU, ULK3 and RAS proteins were blocked (comparing Colon cancer and Treated scenario of
In case of pancreatic cancer, we found the expression of IHH, PTCH1 and SMO in pancreatic cancer cell line, which signified their role of hedgehog pathway activation in this type of cancer formation
The experimentally observed expression data of each protein for all three types of cancer was presented in
EXP: Experimental data observed from published literatures; SIM1: Simulation 1 performed using the expressions data from Table S4 of
In case of Glioma Grade IV cell line, we found the expression level (UP as Red and DOWN as Blue) of 33 proteins out of 57 proteins (See the first column of
In case of Colon cancer scenario, we considered the protein expression of colon cancer cell line data and the up regulation of SHH, PTCH1, HHIP, GLI1, GLI3_Active and PDGFRA were identified from this experiment (See the first column of
These results clearly signify that the expression values that we considered from in Table S4 of
Earlier we mentioned (Introduction section) that the currently available SMO protein inhibitor Cyclopamine or its closed derivative drug Vismodegib were only effective in the suppression of hedgehog pathway activation in cancer cell, where the pathway was abnormally activated by mutation in SMO or by the over expressions of hedgehog ligands SHH, DHH and/or IHH. The main mechanism of these molecules was to inhibit the function of SMO, so that it could not activate GLI proteins in cytoplasm via STK36. Therefore, the effectiveness of these SMO inhibitor molecules were always questionable if the pathway got activated by some intracellular activators molecules through cross talk with other pathways or by the loss of some tumor suppressor proteins inside the cell. In this article, our main objective was to find out the effects of those cross talking molecules, such as RAS, TWIST, ERK12, NOTCH1 or the loss of functions of few tumor suppressor proteins such as SUFU, GAS1, SUFU, NUMB, SNO in the three types of cancer scenarios discussed earlier. In order to check the effectiveness of SMO inhibition in the treatment of three types of cancers we performed the model simulation by only inhibiting the SMO expression levels (
First columns of (A), (B) and (C) represent the expressions of the proteins found after inhibiting SMO in Glioma, Colon and Pancreatic cancer models, respectively. Second columns of (A) represents the expressions of the proteins observed in the treatment scenario by perturbing SMO, GLI1 and GLI2 in combination in the same Glioma model; (B) represents the expressions of the proteins in the treatment scenario by perturbing SMO, HFU, ULK3, and RAS in combination in the same Colon cancer model; (C) represents the expressions of the proteins in the treatment scenario by perturbing SMO, HFU, ULK3, ERK12, and RAS in combination in the same Pancreatic cancer model. (D), (E) and (F) represent the identified alternative pathways (shown by solid green arrows) that remain active even after the inhibition of SMO in membrane (pathway shown by broken red arrows) by its inhibitor molecule (i.e. Cyclopamine, Vismodegib etc. ) in Glioma, Colon and Pancreatic cancer scenarios, respectively.
In order to identify the alternative pathways or connections present in the hedgehog pathway, which was activating the GLI transcription factors after inhibiting SMO, we calculated the dependency matrices (
Identification of these alternative pathways clearly showed that in order to suppress the hedgehog pathway activity completely in these three types of cancer cell lines, only the SMO inhibition would not be effective, as there were other molecules/proteins which were still activating the pathway. Our
Several attempts have been made so far to study the Hedgehog signaling pathway from experimental as well as theoretical and computational perspective. Dillon et al.
In our study, at first we reconstructed the Hedgehog signaling network using the information available from various sources and tried to include as many as possible target output proteins of this pathway. We included the connections of the output proteins JAGGED2, WNT, SFRP, CYCLIN_B, CYCLIN_D, CYCLIN_D2, CYCLIN_E, OPN, SNAI1, CMYC, BMI, BCL2, FOXM1 and PDGFRΑ with the phenotypic outcomes or cellular responses (like Cell proliferation, Cell cycle progression and Endothelial to Mesenchymal Transition etc.) and also with three other important pathways, WNT, NOTCH and Anti-Apoptosis
In this work, we performed two types of computational analysis, Graph theoretical and Boolean or Logical analysis. In order to identify the important proteins from the network, the parameters (like Degree; all pair Shortest paths; Eigenvector, Betweenness and Closeness centrality) were used in the graph theoretical analysis. We observed that GLI1 was the most important protein within the entire network and formed a “hub”, as it was showing high values in all kinds of network parameters measured in this analysis. Therefore from our analysis it can be easily assumed that perturbation (i.e. mutation, malfunction, high or low expression etc.) of this protein or node in Hedgehog signaling network will affect the normal network function and may cause several types of cancers, which is also found in experimental observation, as in Glioma, Colon and Pancreatic cancer cell lines GLI1 shows over expression
In the case of Eigenvector centrality score, GLI1, SMO, PTCH1, GLI3_A had shown significant scores. It is implied that these proteins did not have only high number of connections but also connected with other highly prestigious node that had higher number of connections in the network. It was also interesting to observe that although GLI1 and GLI2 had higher number of connections in the network, the eigenvector centrality of GLI2 was low compare to GLI1. The reason behind this kind of behavior was the connection of GLI1 with another higher central node NUC_GLI1 in the network. On the other hand while comparing the number of down-stream activated proteins of these two proteins, we found that GLI2 had higher number of down-stream activated proteins compared to GLI1. This result was also reflected in our Logical analysis, where we observed that in case of Glioma, Colon and Pancreatic cancer scenarios the number of upstream activator/inhibitor species and downstream activated species of NUC_GLI1 was high compared to the NUC_GLI2 (
In order to analyze the importance of this signaling pathway as well as the individual proteins involved in Glioma, Colon and Pancreatic cancer cell lines, we developed Boolean or Logical models or scenarios. We found that, if we perturbed the logical states of SMO, GLI1 and GLI2 proteins from 1 to 0 in Glioma model, it will be possible to suppress the expression of various output proteins (e.g. JAGGED2, WNT, SFRP, CYCLIN_B, CYCLIN_D, CYCLIN_D2, CYCLIN_E, OPN, SNAI1, CMYC, BMI, BCL2, FOXM1, PDGFRΑ etc.) as well as the phenotypic expressions of the Glioma affected cell (
In case of Colon cancer scenario, we found that inhibition of SMO, HFU, ULK3 and RAS was useful to suppress the expressions of various responsive proteins of Hedgehog pathway (
From our analysis, we also suggested a minimal combination of proteins, SMO, HFU, ULK3, RAS and ERK12, the expressions of which needed to be inhibited so as to control the effect of mutated hedgehog signaling pathway in pancreatic cancer by suppressing the activity of different proteins responsible for uncontrolled cellular proliferation (
The model was validated with existing microarray data for these three types of cancer (
Like all other
Hedgehog signaling pathway is widely implicated in controlling various cellular responses and plays a cardinal role in different cellular processes including carcinogenesis. Malfunctioning of this pathway can mostly lead to cancer in various cell line of human. The role of few important proteins such as PTCH1, SMO, GLI etc., in this pathway has already been identified to be responsible for various types of cancers, such as Glioma, Colon and Pancreatic. Targeting this pathway in these types of cancers would be helpful, but prior to that, extensive knowledge regarding this pathway, its interactions and roles with the proteins of other important signaling pathways is necessary. Hence, there is a need for an accurate, comprehensive pathway map of Hedgehog, detailing all the species and interactions involved in the functioning of the pathway. Moreover, to control the pathway activity, most of the studies till now have mainly focused to develop a drug which only inhibit single proteins, such as GLI (ligand dependent way) or PTCH1 or SMO in the membrane and may not be able to cure the cancers caused by some other intracellular proteins apart from sole mutation in GLI or PTCH1 or SMO. Hence identification of alternative targets (single or combinatory) for administration of drugs is itself a challenging problem in this direction.
Through Reconstruction, Graph theoretical and Boolean analysis of the pathway, our study was aimed in this direction to get an insight about the signaling proteins in the Hedgehog pathway along with identification of alternate drug targets for Glioma, Colon and Pancreatic cancer, where the pathway is known to become mutated. We reconstructed a new Hedgehog signaling map by collating the data from various database and literature sources. The Hedgehog signaling map shown in this article is a large, extensive and informative network to the best of our knowledge. This map was also used for structural and logical analysis in our study. In structural analysis, we analyzed the network topology, identified few important proteins, and showed the robustness of the entire Hedgehog signaling network. The computational results are supported by available experimental observations from literature. On the other hand, in logical analysis, we constructed a single master model of the whole interactions using simple Boolean operators and created the models for normal and three types of cancer: Glioma, Colon and Pancreatic cancer. The simulations of this model also lead to identification of important proteins that can be used as probable drug targets for these cancers and the result is supported by experimental findings from literature.
Comparing the cancer scenarios with normal scenario, we found some important minimal combinations of proteins which may be used as a probable drug targets for further
Initially we tried to construct a comprehensive map of Hedgehog pathway map from biological database. We searched 21 different signal transduction and Protein-Protein interaction database for that purpose (See Table S1 of
This reconstructed pathway map (
In order to convert the whole hedgehog signaling pathway into a graph or network model
The parameters “In-Degree”, “Out-Degree”, “Total Degree”, “Betweenness Centrality”, “Closeness Centrality”, and “Eigenvector Centrality” were calculated on the basis of the adjacency matrix A. Then we made a network file in ‘.net’ format (default input format of the network manipulation and visualization software ‘Pajek’
A brief description of the parameters used in our study is given below:
It refers the total number of nodes (activations or inhibitions) that are directly acting on a particular node in the network
The total number of interactions (activations or inhibitions) that are acting by a particular node on the other nodes in the network
It refers the total number of in-degree and out-degree of a particular node
It refers that a node in a network will be more central if it is connected to many central nodes in the network
Now, if we consider the above
It is the ratio of the number of shortest paths that pass through the node to the total number of shortest paths of all the nodes to all the other nodes. It signifies that how a node is important in the shortest paths of all the other nodes of the network
The Closeness centrality of a node is defined as the inverse of sum of the total length of the distances or shortest paths of that node to the other nodes
It refers the minimum number of intermediate links or connections that have to traverse from one node ‘
The entire Hedgehog signaling network was organized into a three layered system of input, intermediate and output, with input signals orchestrating cellular responses to output via intermediate molecules. To visualize and analyze the Hedgehog signal transduction network, we constructed the Logical or Boolean Interaction Hyper-graph with large number of nodes and interactions or hyper-arc
In order to construct a logical model for hedgehog signaling network, at first we considered the input and output nodes. Mainly the proteins, which did not have upstream connection in the reconstructed pathway map (
We know that the molecular species of a biological signaling network is highly interconnected and interdependent with each other. Using this phenomena one can easily construct Boolean or Logical equations that could show their inter relationship with each other within the network. We manually formed the Boolean equations among all the nodes of the hedgehog signaling network using our biological understanding of the interactions from various literature sources. The entire list of the Boolean equations is available in Table S5 of
Using the master model of Boolean equations, we performed our simulation analysis in CellNetAnalyzer
After performing the “time scale 2” simulation for each scenario, the entire simulation results provided in “Results” section and the logical steady states of the output proteins in Table S4 of
In order to identify the important proteins which were responsible for a particular cancer, we compared the total number of upstream effectors and downstream effected proteins of each protein of that cancer scenario with each protein of normal scenario. From these comparisons we identified the proteins that were showing significant variation in cancer scenarios with respect to the normal scenario. We then extracted those identified proteins from each cancer scenarios and this helped us to identify the sole or combination of target proteins for the perturbation analysis. Among these identified proteins we selected few minimal combinations of target proteins in perturbations analysis, based on the results from Graph theoretical analysis and also biological feasibility of targeting these proteins in cancer cell. Finally we choose these minimal combinations of such proteins for each cancer scenarios that could be perturbed in the
A brief description of a few logical formalisms used in our study is given below:
An interaction hyper-arc is a set of the arcs which connects more than one node to a particular single node. Therefore, a hyper-arc may contain more than one node at its source end (input) but one node at its sink end (output). A hyper-graph (
In several network it has been found that the product of a reaction is actually producing the reactant or interacting back with one of the reactants of the reaction. This type of connections or arcs or edge is basically form a “loop” in the network and as the output comes back again to its input or source nodes, hence this type of connection is called feedback loop. Feedback loop may be positive or negative depending on the nature of its connection. In our hedgehog signaling model, we have found that GLI1 helps to activate GLI3_A and as a result GLI3_A produces GLI1. This is an example of positive feedback loop whereas production of PTCH1 or HHIP from GLI1 or NUC_GLI1 is an example of Negative feedback loop. It is also worth mentioning that to perform these kinds feedback analysis one should assign time scale to the reactions where feedback loop reactions would be in higher time scale compare to the reactions executed by the inputs.
When the logical states of the nodes reach to a certain constant or steady state value with the state of the associated logical functions or equations, such that the switching of logical values of the nodes stop during infinite time scale, then such state is called logical steady state.
The updates of the logical states of the nodes in a Boolean network can be updated synchronously or asynchronously. In the Synchronous model, the logical state
We simulated our model using both the synchronous and asynchronous updating approaches in Odefy (software package used in CellNetAnalyzer
It is a matrix (
The simulation results shown for all three types of cancer was done through in-silico logical analysis, but in order to validate our model with cancer cell line specific experimental data, we considered the microarray expression data (UP or DOWN regulated) of the proteins for Glioma Grade IV (accession numbers GSE4290) and Pancreatic cancer cell line (accession numbers GSE16515) from EBI ArrayExpress Atlas
The expression levels of few proteins from both the microarray data were not found significant as their corresponding
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We thank Ms. Sonia Chothani and Ms. Noopur Sinha for their help in collating some data for pathway reconstruction. We also thank Mr. Ravindra S Patake and Mr. Abhishek Subramanian for their careful reading of the manuscript. We are grateful to The Director, CSIR-National Chemical Laboratory, Pune for providing the required infrastructures related to this work.