Conceived and designed the experiments: RA AS RSW XL TPL. Performed the experiments: AS RSW AL. Analyzed the data: AS RSW XL TPL RA. Contributed reagents/materials/analysis tools: AS RSW IA. Wrote the paper: AS RA.
The authors have declared that no competing interests exist.
The blood cancer T cell large granular lymphocyte (TLGL) leukemia is a chronic disease characterized by a clonal proliferation of cytotoxic T cells. As no curative therapy is yet known for this disease, identification of potential therapeutic targets is of immense importance. In this paper, we perform a comprehensive dynamical and structural analysis of a network model of this disease. By employing a network reduction technique, we identify the stationary states (fixed points) of the system, representing normal and diseased (TLGL) behavior, and analyze their precursor states (basins of attraction) using an asynchronous Boolean dynamic framework. This analysis identifies the TLGL states of 54 components of the network, out of which 36 (67%) are corroborated by previous experimental evidence and the rest are novel predictions. We further test and validate one of these newly identified states experimentally. Specifically, we verify the prediction that the node SMAD is overactive in leukemic TLGL by demonstrating the predominant phosphorylation of the SMAD family members Smad2 and Smad3. Our systematic perturbation analysis using dynamical and structural methods leads to the identification of 19 potential therapeutic targets, 68% of which are corroborated by experimental evidence. The novel therapeutic targets provide valuable guidance for wetbench experiments. In addition, we successfully identify two new candidates for engineering longlived T cells necessary for the delivery of virus and cancer vaccines. Overall, this study provides a bird'seyeview of the avenues available for identification of therapeutic targets for similar diseases through perturbation of the underlying signal transduction network.
TLGL leukemia is a blood cancer characterized by an abnormal increase in the abundance of a type of white blood cell called T cell. Since there is no known curative therapy for this disease, identification of potential therapeutic targets is of utmost importance. Experimental identification of manipulations capable of reversing the disease condition is usually a long, arduous process. Mathematical modeling can aid this process by identifying potential therapeutic interventions. In this work, we carry out a systematic analysis of a network model of T cell survival in TLGL leukemia to get a deeper insight into the unknown facets of the disease. We identify the TLGL status of 54 components of the system, out of which 36 (67%) are corroborated by previous experimental evidence and the rest are novel predictions, one of which we validate by followup experiments. By deciphering the structure and dynamics of the underlying network, we identify component perturbations that lead to programmed cell death, thereby suggesting several novel candidate therapeutic targets for future experiments.
Living cells perceive and respond to environmental perturbations in order to maintain their functional capabilities, such as growth, survival, and apoptosis. This process is carried out through a cascade of interactions forming complex signaling networks. Dysregulation (abnormal expression or activity) of some components in these signaling networks affects the efficacy of signal transduction and may eventually trigger a transition from the normal physiological state to a dysfunctional system
Network representation, wherein the system's components are denoted as nodes and their interactions as edges, provides a powerful tool for analyzing many complex systems
A Boolean network model of T cell survival signaling in the context of TLGL leukemia was previously constructed by Zhang
The shape of the nodes indicates the cellular location: rectangular indicates intracellular components, ellipse indicates extracellular components, and diamond indicates receptors. Node colors reflect the current knowledge on the state of these nodes in leukemic cells: highly active components in TLGL are shown in red, inhibited nodes are shown in green, nodes that have been suggested to be deregulated are in blue, and the state of white nodes is unknown. Conceptual nodes (Stimuli, Stimuli2, P2, Cytoskeleton signaling, Proliferation, and Apoptosis) are represented by yellow hexagons. An arrowhead or a short perpendicular bar at the end of an edge indicates activation or inhibition, respectively. The inhibitory edges from Apoptosis to other nodes are not shown. The full names of the node labels are given in
StuckatON/OFF fault is a very common dysregulation of biomolecules in various cancer diseases
In this paper, we carry out a detailed analysis of the TLGL signaling network by considering all possible initial states to probe the longterm behavior of the underlying disease. We employ an asynchronous Boolean dynamic framework and a network reduction method, which we previously proposed
Any biological regulatory network can be represented by a directed graph
Boolean models belong to the class of discrete dynamic models in which each node of the network is characterized by an ON (1) or OFF (0) state and usually the time variable
In order to evaluate the state of each node at a given time instant, synchronous as well as asynchronous updating strategies have been proposed
A Boolean network with
It should be noted that the fixed points of a Boolean network are the same for both synchronous and asynchronous methods. In order to obtain the fixed points of a system one can solve the set of Boolean equations independent of time. To this end, we first fix the state of the source nodes. We then determine the nodes whose rules depend on the source nodes and will either stabilize in an attracting state after a time delay or otherwise their rules can be simplified significantly by plugging in the state of the source nodes. Iteratively inserting the states of stabilized nodes in the rules (i.e. employing logical steady state analysis) will result in either the fixed point(s) of the system, or the partial fixed point(s) and a remaining set of equations to be solved. In the latter case, if the remaining set of equations is too large to obtain its fixed point(s) analytically, we take advantage of the second step of our reduction method
The topology (structure) and the function of biological networks are closely related. Therefore, structural analysis of biological networks provides an alternative way to understand their function
All patients met the clinical criteria of TLGL leukemia with increased numbers (>80%) of CD3^{+}CD8^{+} T cells in the peripheral blood. Patients received no treatment at the time of sample acquisition. Peripheral blood specimens from LGL leukemia patients were obtained and informed consents signed for sample collection according to a protocol approved by the Institutional Review Board of Penn State Hershey Cancer Institute. PBMC were isolated by FicollHypaque gradient separation, as described previously
Western blot was performed to detect PhosphoSmad2 (PSmad2) and PhosphoSmad3 (PSmad3) in activated normal CD3^{+}CD8^{+} cells (CD3^{+}CD8^{+} cells >90%) compared with PBMC (CD3^{+}CD8^{+} cells >80%) from TLGL leukemia patients. Normal CD3^{+}CD8^{+} T cells were isolated by a human CD8^{+} T cell enrichment cocktail RosetteSep kit (Stemcell Technology) from four normal donors, then cultured in RPMI1640 supplemented with 10% fetal bovine serum in presence of PHA (1 µg/mL) for 1 day followed by IL2 (500 IU/mL) for 3 days (lanes 1–4). The equal loading of protein was confirmed by probing with total Smad2 or Smad3. PhosphoSmad2 (Ser465/467), Smad2, PhosphoSmad3 (Ser423/425) and Smad3 antibodies were purchased from Cell Signaling Technology Inc. (Beverly, MA).
The TLGL signaling network reconstructed by Zhang
To reduce the computational burden associated with the large state space (more than 10^{18} states for 60 nodes), we simplified the TLGL network using the reduction method proposed in
The full names of the nodes can be found in
Next, we identified the attractors (longterm behavior) of the subnetwork represented in
In this graph the left binary digit of the node identifier indicates the state of CTLA4 and the right digit represents the state of TCR. The directed edges represent state transitions allowed by updating a single node's state; selfloops appear when a node is updated but its state does not change.
The bottom subgraph exhibits the normal fixed point, as well as two TLGL (disease) fixed points in which Apoptosis is OFF. The only difference between the two TLGL fixed points is that the node P2 is ON in one fixed point and OFF in the other, which was expected due to the presence of a selfloop on P2 in
Since the state transition graph of the bottom subgraph given in
Node  Boolean rule 
S1P  S1P* = NOT (Ceramide OR Apoptosis) 
FLIP  FLIP* = NOT (DISC OR Apoptosis) 
Fas  Fas* = NOT (S1P OR Apoptosis) 
Ceramide  Ceramide* = Fas AND NOT (S1P OR Apoptosis) 
DISC  DISC* = (Ceramide OR (Fas AND NOT FLIP)) AND NOT Apoptosis 
Apoptosis  Apoptosis* = DISC OR Apoptosis 
Our attractor analysis revealed that this subnetwork has two fixed points, namely 000001 and 110000 (the digits from left to right represent the state of the nodes in the order as listed from top to bottom in
We found by simulations that for the simplified network of
It contains 64 states of which the state shown with a dark blue symbol is the normal fixed point and the state shown in red is the TLGL fixed point. States denoted by light blue symbols are uniquely in the basin of attraction of the normal fixed point whereas the states in pink can only reach the TLGL fixed point. Gray states, on the other hand, can lead to either fixed point.
These probabilities are computed starting from the states that are shared by both basins of attraction (see graycolored states illustrated in
Based on the subnetwork analysis and considering the states of the nodes that stabilized at the beginning based on the logical steady state analysis, we conclude that the whole TLGL network has three attractors, namely the normal fixed point wherein Apoptosis is ON and all other nodes are OFF, representing the normal physiological state, and two TLGL attractors in which all nodes except two, i.e. TCR and CTLA4, are in a steady state, representing the disease state. These TLGL attractors are given in the second column of
Node  TLGL state  Ref.  Fixed point the disruption leads to  Size of exclusive basin of normal fixed point  Ref. 
DISC  OFF 

Normal  100% 

Ceramide  OFF 

Normal  100% 

Caspase  OFF 

Normal  100%  
SPHK1  ON 

Normal  100% 

S1P  ON 

Normal  100% 

PDGFR  ON 

Normal  100% 

GAP  OFF*  Normal  100%  
RAS  ON*  Normal  100% 


MEK  ON 

Normal  100% 

ERK  ON  Normal  100% 


IL2RBT  ON 

Normal  100%  
IL2RB  ON 

Normal  100%  
STAT3  ON 

Normal  100% 

BID  OFF 

Normal  100%  
MCL1  ON 

Normal  100% 

SOCS  OFF*  Both  81%  
JAK  ON 

Both  81% 

PI3K  ON 

Both  75% 

NFκB  ON 

Both  75% 

Fas  OFF 

Both  72%  
sFas  ON 

Both  72%  
TBET  ON 

Both  63%  
RANTES  ON 

Both  63%  
PLCG1  ON*  Both  63%  
FLIP  ON 

Both  56%  
IL2  OFF 

Both  56%  
IAP  ON*  Both  56%  
TNF  ON*  Both  56%  
BclxL  OFF 

Both  56%  
GZMB  ON 

Both  56%  
IL2RA  OFF 

Both  56%  
NFAT  ON*  Both  56%  
GRB2  ON*  Both  56%  
IFNGT  ON  Both  56%  
TRADD  OFF*  Both  56%  
ZAP70  OFF*  Both  56%  
LCK  ON 

Both  56%  
FYN  ON*  Both  56%  
IFNG  OFF 

Both  56%  
SMAD  ON*  This study  Both  56%  
GPCR  ON  Both  56%  
TPL2  ON 

Both  56%  
A20  ON 

Both  56%  
IL2RAT  OFF 

Both  56%  
CREB  OFF*  Both  56%  
P27  ON*  Both  56%  
P2  ON/OFF  Both  56%  
FasT  ON 

TLGL  0%  
FasL  ON 

TLGL  0%  
Cytoskeleton signaling  ON*  —  —  
Proliferation  OFF 

—  —  
Apoptosis  OFF 

—  —  
TCR  Oscillate*  —  —  
CTLA4  Oscillate*  —  — 
Evidence in NKLGL leukemia.
Experimental evidence exists for the deregulated states of 36 (67%) components out of the 54 predicted TLGL states as summarized in the third column of
The predicted TLGL states of these 17 components can guide targeted experimental followup studies. As an example of this approach, we tested the predicted overactivity of the node SMAD (see
Western blot detection of phosphorylated Smad2 or Smad3, and total Smad2 (i.e. the sum of phosphorylated and nonphosphorylated Smad2) or Smad3 in activated normal T cells compared with peripheral blood mononuclear cells from TLGL leukemia patients confirms that Smad2 or Smad3 is unphosphorylated (inactive) in normal T cells and predominantly phosphorylated (active) in TLGL cells.
A question of immense biological importance is which manipulations of the TLGL network can result in consistent activationinduced cell death and the elimination of the dysregulated (diseased) behavior. We can rephrase and specify this question as which node perturbations (knockouts or constitutive activations) lead to a system that has only the normal fixed point. These perturbations can serve as candidates for potential therapeutic interventions. To this end, we performed node perturbation analysis using both structural and dynamic methods.
For the structural analysis, using the TLGL network (
Our goal of identifying node state manipulations that lead to the apoptosis of the abnormally surviving TLGL cells can be translated into the graphtheoretical problem of finding key nodes that mediate paths to the node ∼Apoptosis. Elimination of these nodes has the potential to make ∼Apoptosis unreachable, or in other words to make Apoptosis the only reachable outcome. The TLGL fixed point determined in dynamic analysis serves as a list of candidate deletions. Accordingly, we separately deleted each node that stabilizes at ON in the TLGL fixed point, and each complementary node whose corresponding original node stabilizes at OFF in the TLGL fixed point (see
These values are based on the relative reduction of the number of paths from PDGF to ∼Apoptosis after considering the cascading effects of node disruptions. The complementary nodes are denoted by the corresponding original nodes with a symbol ‘∼’ as prefix representing ‘negation’.
To identify manipulations of the TLGL network leading to the existence of only the normal fixed point, we first considered the following scenario. We assumed that the TLGL network is the simplified network given in
Reverse the state of one node at a time in the TLGL fixed point for only the first time step, and keep updating the system. This intervention may be accomplished by a pharmacological intervention on a TLGL cell.
Reverse the state of one node in the TLGL fixed point permanently and continue updating other nodes. This intervention may be accomplished by genetic engineering of a TLGL cell.
Considering all possible initial states, fix the state of one node in the opposite of its TLGL state and keep updating other nodes. This intervention may be accomplished by genetic engineering of a population of CTLs.
For the first perturbation approach, we found that only the trivial case of flipping the state of Apoptosis to ON leads exclusively to the normal fixed point. Using the second perturbation approach, we observed that fixing S1P at OFF or Apoptosis at ON eliminates the TLGL fixed point. In addition, fixing either Ceramide or DISC at ON results in a new fixed point which is similar to the normal fixed point of the unperturbed system, with the only difference that the disrupted node's state is fixed at ON as long as the cell is alive. Using the last perturbation approach, we found a result identical to that of the second approach, indicating that the nodes S1P, Ceramide, and DISC are candidate therapeutic targets for the simplified subnetwork. Experiments also confirm that Ceramide and DISC can serve as therapeutic targets
Next we focused our attention to the effects of node disruptions on the whole network to make biologically testable predictions about the occurrence of the disease state under different conditions. To this end, we followed the third approach delineated above. More precisely, for each node disruption we fixed the state of that node in the opposite of its stabilized state in the TLGL fixed point given in
In general, two types of fixed points were observed, the normal fixed point with Apoptosis being ON and all other nodes being OFF, and similartoTLGL fixed points with Apoptosis being OFF and the state of some nodes being different from the wildtype TLGL fixed point due to the disruption imposed on the network. We still consider these latter fixed points as the TLGL fixed point. A summary of the node disruption results, including the fixed point(s) obtained after the disruption as well as the size of the exclusive basin of attraction of the normal fixed point in the respective reduced model, is given in the fourth and fifth columns of
There is corroborating literature evidence for several of the therapeutic targets predicted by our analysis. For example, it was found experimentally that STAT3 knockdown by using siRNA or downregulation of MCL1 through inhibiting STAT3 induces apoptosis in leukemic TLGL
For the cases where both fixed points are still reachable, our analysis of the relative size of the basins of attraction (i.e. percentage of the whole relevant state space) of the fixed points and the probabilities of reaching the fixed points (see
We performed the perturbation analysis using a dynamic method as well as a structural method. How do the results compare? From the dynamic analysis, a node is classified as an important mediator of the TLGL fixed point if reversing its state from the value it achieves in the TLGL fixed point will lead the system to have only the normal fixed point. From the structural analysis, a node can be classified as an important mediator of the TLGL behavior if its importance value (see
SP+CE represents the simple path measure considering cascading effects of node deletions, and SPCE represents the simple path measure without considering cascading effects of node deletions.
Interestingly, for all the components whose manipulation lead the system to have only the normal fixed point according to the dynamic analysis (the first 15 components in
We note that there are four cases, namely, TBET, FLIP, IAP, and TNF, which were identified as important based on the structural method while their disruption maintains the existence of both fixed points based on dynamic analysis and the size of the exclusive basin of attraction of the normal fixed point is either close to or the same as that of the wildtype system. This may be partly due to the fact that in the state space analysis we consider all possible initial conditions for the system, whereas the topological analysis implicitly refers to only one initial condition, wherein three source nodes are ON and all other nodes are OFF. Another potential reason regarding the discrepancies between the structural and dynamic perturbation results might be related to the structural method's use of the simple path measure rather than the elementary signaling modes (ESMs, see
In this paper we presented a comprehensive analysis of the TLGL survival signaling network to unravel the unknown facets of this disease. By using a reduction technique, we first identified the fixed points of the system, namely the normal and TLGL fixed points, which represent the healthy and disease states, respectively. This analysis identified the TLGL states of 54 components of the network, out of which 36 (67%) are corroborated by previous experimental evidence and the rest are novel predictions. These new predictions include RAS, PLCG1, IAP, TNF, NFAT, GRB2, FYN, SMAD, P27, and Cytoskeleton signaling, which are predicted to stabilize at ON in TLGL leukemia and GAP, SOCS, TRADD, ZAP70, and CREB which are predicted to stabilize at OFF. In addition, we found that the node P2 can stabilize in either the ON or OFF state, whereas two nodes, TCR and CTLA4, oscillate. We have experimentally validated the prediction that the node SMAD is overactive in leukemic TLGL by demonstrating the predominant phosphorylation of the SMAD family members Smad2 and Smad3. The predicted TLGL states of other nodes provide valuable guidance for targeted experimental followup studies of TLGL leukemia.
Among the predicted states, the ON state of Cytoskeleton signaling may not be biologically relevant as this node represents the ability of T cells to attach and move which is expected to be reduced in leukemic TLGL compared to normal T cells. This discrepancy may be due to the fact that the network contains insufficient detail regarding the regulation of the cytoskeleton, as there is only one node, FYN, upstream of Cytoskeleton signaling in the network. While the network is able to successfully capture survival signaling without necessarily capturing the cytoskeleton signaling, this discrepancy suggests that followup experimental studies should be conducted to determine the relationship between cytoskeleton signaling and survival signaling in the TLGL network. We note that in the case of perturbation of TBET, PI3K, NFκB, JAK, or SOCS, the node Cytoskeleton signaling exhibits oscillatory behavior induced by oscillations in TCR. At present it is not known whether this predicted behavior is relevant.
Using the general asynchronous (GA) Boolean dynamic approach, we analyzed the basins of attraction of the fixed points. We found that the basin of attraction of the normal fixed point is larger than that of the TLGL fixed point. The trajectories starting from each initial state toward the TLGL fixed point (
We took one step further by performing a perturbation analysis using dynamical and structural methods to identify the interventions leading to the disappearance of the disease fixed point. We note that our study has a dramatically larger scope than the previous key mediator analysis of Zhang
Multistability (having multiple steady states) is an intrinsic dynamic property of many disease networks
Negative feedback loops can be a source of oscillations
Our study revealed that both structural and dynamic analysis methods can be employed to identify therapeutic targets of a disease, however, they differ in implementation efficiency as well as the scope and applicability of the results. The structural analysis does not require mapping of the state space and thus is less computationally intensive and is more feasible for large network analysis, but it may not capture all the initial states and thus may miss or inaccurately identify some important features. The dynamic analysis method, while computationally intensive, yields a comprehensive picture of the state transition graph, including all possible fixed points of the system, their corresponding basins of attraction, as well as the relative frequency of trajectories leading to each fixed point. We demonstrated that the limitations related to the vast state space of large networks can be overcome by judicious use of the network reduction technique that we developed in our previous study
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The authors would like to thank Dr. Ranran Zhang for fruitful discussions.