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A dual controllability analysis of influenza virus-host protein-protein interaction networks for antiviral drug target discovery

Background Host factors of influenza virus replication are often found in key topological positions within protein-protein interaction networks. This work explores how protein states can be manipulated through controllability analysis: the determination of the minimum manipulation needed to drive the cell system to any desired state. Here, we complete a two-part controllability analysis of two protein networks: a host network representing the healthy cell state and an influenza A virus-host network representing the infected cell state. In this context, controllability analyses aim to identify key regulating host factors of the infected cell’s progression. This knowledge can be utilized in further biological analysis to understand disease dynamics and isolate proteins for study as drug target candidates. Results Both topological and controllability analyses provide evidence of wide-reaching network effects stemming from the addition of viral-host protein interactions. Virus interacting and driver host proteins are significant both topologically and in controllability, therefore playing important roles in cell behavior during infection. Functional analysis finds overlap of results with previous siRNA studies of host factors involved in influenza replication, NF-kB pathway and infection relevance, and roles as interferon regulating genes. 24 proteins are identified as holding regulatory roles specific to the infected cell by measures of topology, controllability, and functional role. These proteins are recommended for further study as potential antiviral drug targets. Conclusions Seasonal outbreaks of influenza A virus are a major cause of illness and death around the world each year with a constant threat of pandemic infection. This research aims to increase the efficiency of antiviral drug target discovery using existing protein-protein interaction data and network analysis methods. These results are beneficial to future studies of influenza virus, both experimental and computational, and provide evidence that the combination of topology and controllability analyses may be valuable for future efforts in drug target discovery. Electronic supplementary material The online version of this article (10.1186/s12859-019-2917-z) contains supplementary material, which is available to authorized users.


Introduction
The development of computational methods to identify key host factors that allow viruses to interrupt and control healthy cell functions will greatly aid in the prediction of novel anti-viral drug targets 1 . Traditional systems biology approaches to understanding cell dynamics during infection include the creation of detailed kinetic models for intercellular signaling pathways. While these models are advantageous in understanding the disease state in a quantitative way, they require experimentallyderived or estimated parameters and training data [2][3][4] , without which complications can arise and an accurate model can quickly become unattainable. Further, modeling studies are often limited to specific pathways which fails to consider the total cellular environment as an interdependent system.
Alternatively, network analysis methods applied to protein-protein interaction (PPI) data have been used to model cell-wide systemic changes associated with disease, changes in cell function, or cell fate 5 . This strategy provides a holistic understanding of system behavior by viewing proteins as interdependent states, regardless of specific interaction mechanisms, and allows for the exploration of cell level relationships. The field of network theory is well established; basic network metrics like degree and betweenness 6 have repeatedly revealed the importance of specific proteins within biological processes that cannot be found from traditional modeling approaches [7][8][9][10][11] . Disease networks have identified genes involved with cancer [12][13][14][15] , demonstrated that the genes responsible for similar diseases are likely to interact with each other 16,17 , and predicted novel drug targets 18,19 .
There is precedent for network studies of many common viruses including hepatitis C 20,21 , SARS 16,22 , HIV [22][23][24][25][26] , and influenza virus 16,[27][28][29][30] . Past work studying the effects of influenza virus in PPI networks has focused on identifying host factors involved in virus replication and improving the prediction of drug targets, but ends with an analysis of basic topological measurements. While this provides a general overview of the state of the network, it is a static snapshot of the cell and, therefore, fails to capture the dynamic nature of the cell. Therefore, the next logical step in analyzing biological networks lies in understanding how these dynamic systems can be manipulated and exploited to manage biological properties.
In classic control theory, controllability is the idea that a deterministic system can be driven to any final state in finite time given an external input 31 . This is commonly applied to linear, time invariant dynamic systems, where is an matrix of state coefficients that describes how molecule states, , interact within the system and is a matrix of input weights describing how external influences, ( ), impact the system. In general, a system is controllable if the controllability matrix, is full rank, . This means that the system can be manipulated to reach any desired combination of states within all of state space following the defined input, . In total, a controllability analysis identifies the key components of a system that must be manipulated to drive desired system outcomes 32 .
An example PPI network in Fig. 1a, is transformed into its state space matrix representation in Fig. 1b. With the inclusion of two independent inputs ( 4 and 0 ), the controllability matrix in Fig. 1c  importance in the ability of an external set of inputs to fully control the network. Controllability classification is founded in "driver node" Full rank ∴ System is fully controlled Figure 1: (a) An example protein-protein interaction network with three proteins and two protein translation process inputs. The state space representation (b) of the same network demonstrates that the change in state of a protein's concentration is a function of its current state and an input process. A classic controllability analysis (c) demonstrates that this system is fully controllable and could, therefore, be driven to any possible state change in every protein.
calculations: identifying the network components which must be manipulated for the system to be fully controlled (analogous to determining the non-zero elements of the matrix in classic controllability). Without manipulation, driver nodes will remain unaffected by changes to the rest of the system, rendering the total system uncontrollable. A set of driver nodes (size 6 ) that is capable of controlling the total network is called a minimum input set (MIS). The MIS is not unique and the number of possible MISs scales exponentially with the size of the network 33 . After a primary MIS is calculated, two methods of controllability node classification can be used.
In the first method by Liu et al. 34 , the MIS is re-calculated (size 6 ′) after removing each node from the network. The node is then classified by its effect on the manipulation required to control the network, where an increase in the size of the MIS makes it more difficult to control the network and a decrease in the size of the MIS makes it easier to control the network. The absence of: an indispensable node increases the number of driver nodes ( 6 ′ > 6 ), a dispensable node decreases the number of driver nodes ( 6 ′ < 6 ), and a neutral node has no effect on the number of driver nodes ( 6 ′ = 6 ). This method has previously been applied to many network types such as gene regulatory networks, food webs, citation networks, and PPI networks to better understand what drives the dynamics of each system 26,34 . While it is useful to observe the structural changes to the network in the absence of singular nodes, this method only considers one possible MIS.
In a second classification method by Jia et al. 35 , a node is classified by its role across all possible MISs. A critical node is included in all possible MISs, an intermittent node is included in some possible MISs, and a redundant node is not included in any possible MISs. This method places each node in the broader context of all possible control configurations.
In total, this study aims to determine key host factors with regulatory roles specific to the influenza virus-infected cell state for the prediction of novel antiviral targets. We have completed a two-part controllability analysis of a host PPI network (HIN) and a hybrid network of human host PPI data combined with influenza A virus-host protein interaction data (VIN). The controllability characteristics of influenza virus interacting host proteins and driver proteins are compared to the characteristics of the total network. A set of 24 host factors that hold value topologically, in controllability, and functionally are identified as candidates for further study in drug development based on their specialized behavior during influenza infection.

Topology of the Host Interaction Network and Virus Integrated Network
The directed PPI network from Vinayagam et al 36  interactions. This network is referred to as the "Virus Integrated Network" (VIN).
Degree and betweenness calculations were completed for the HIN and VIN. As expected, the only proteins with altered degree after the addition of virus interactions to the network are the 752 IAV interacting proteins (Marked in blue in Fig. 2a). This shift is significant for the group of IAV interacting proteins as compared to all proteins in both the VIN (log scaled median of IAV interacting proteins: 1.04; log scaled median of all proteins: 0.70; student t-test of log scaled data p < 2.20x10 -16 ) and the HIN (log scaled median of IAV interacting proteins: 0.85; log scaled median of all proteins: 0.70; Student t-test of log scaled data p: 5.97x10 -12 ). The degree distributions of both networks are scale free (Fig. S1).
Because betweenness is sensitive to the information flow through all proteins instead of only neighboring proteins, 2,735 proteins exhibit an increase in betweenness after the addition of IAV interactions. Of these proteins, 207 proteins' log betweenness exhibits an increase of 2 or more in the VIN compared to the HIN (Fig. 2b). This suggests that the addition of IAV interactions has an effect on network topology that reaches over 3.5 times the number of host proteins that are directly interacting with IAV proteins. The betweenness shift in the group of IAV interacting host proteins is significant as compared to all proteins in both the VIN (Log scaled median of IAV interacting proteins:  ). This is a result of being the limited protein set responsible for information flow from the viral proteins to the rest of the network.

Driver proteins
Driver proteins (nodes) are the foundation of both types of controllability calculations, representing the protein set which must be manipulated for the system to be fully controlled. The proteins are identified through maximum matching algorithms 38 . The HIN and VIN both require 6 = 2,463 driver proteins to achieve controllability, suggesting that the magnitude of network control is unchanged by the influence of the IAV interactions. However, the identity of driver proteins shifts slightly as the 11 viral proteins replace 11 host proteins within the primary MIS as drivers in the VIN. Table 1 lists their identities along with the shortest distance to an IAV protein in the network, degree, and betweenness. Of these 11 proteins, only five are directly interacting with IAV proteins. One of the remaining proteins is two steps (two interactions and one connecting protein) from any IAV protein, and the remaining five proteins are three steps from any IAV protein. Lastly, analysis finds that 8.9% of all driver proteins are also IAV interacting proteins, meaning the intersection of the two protein groups of interest comprise only 3.5% of the total network. There is a significant increase in the betweenness of driver proteins depending on their status as IAV interacting or IAV non-interacting proteins (Fisher test p < 2.2x10 -16 ) where there is no significant difference in degree of the same groups (Fisher test p: 0.7161). This is further evidence that the addition of virus interactions to the network magnifies information flow through the proteins most involved in controlling network behavior. Liu controllability was calculated (see Methods) for all proteins of the HIN and VIN (as shown in Table 2 with and without parentheses, respectively). The addition of IAV interactions to the network has no effect on the distribution of Liu classifications of host proteins, and consequently, the IAV Interacting proteins. Upon entry to the VIN, the 11 IAV proteins are classified as neutral, meaning their removal does not alter the number of driver proteins required to control the VIN (N D = N D '). This reveals that the absence of singular proteins from the system is not enough to disturb the existing control structure under Liu controllability. We developed an analysis to test if IAV is selectively targeting host proteins based on controllability characteristics. 10,000 random sets of 752 proteins (the number of IAV interacting proteins) were pulled from the host proteins of the VIN. Their Liu type distributions were plotted against the classification results of IAV interacting proteins, driver proteins, and all proteins in the VIN (Fig. 3a-c). The randomly sampled sets closely resemble all proteins of the network, not the true interacting protein set, suggesting that Liu controllability behavior of interacting proteins is not a coincidence of network construction (one-sided p = 0.51, 0.49, and 0.50 for indispensable, neutral, and dispensable, respectively). IAV interacting proteins tend to be indispensable compared to the percentage of all proteins that are indispensable (Fig. 3a). This suggests that viruses prefer to interact with proteins that are vital to cellular control. Driver proteins are very likely to be dispensable proteins compared to the percent of all proteins that are dispensable (Fig. 3c). Further, the mean and median log degree and betweenness of the randomly sampled protein sets is significantly lower than the same measurements of the true IAV interacting set (p < 2.2x10 -16 , 2.2x10 -16 , Fig. 4

Jia Controllability
Jia controllability was calculated (see Methods) for all proteins of the HIN and VIN (as shown in Table 3 with and without parentheses, respectively). Unlike in Liu controllability, there is a small disturbance to Jia type distributions of host proteins after the addition of virus interactions. 24 host proteins shift from being classified as critical (a member of all MISs) to intermittent (a member of some MISs) proteins. Identities of these proteins (deemed "Jia proteins") can be found in Table 4 along with the shortest distance to an IAV protein in the network and protein degree and betweenness. The two most notable changes in degree and betweenness between the HIN and VIN are EPH receptor A2 (EPHA2) with an increase of 1 and 93, respectively, and transferrin receptor (TFRC), with an increase of 3 and 164, respectively. All 24 Jia proteins are driver and IAV interacting proteins which, as mentioned, only comprises 3.5% of the total network.
There are only two proteins (EPHA2 and HNRNPA0) that are also members of the Liu protein set. 45% of IAV interacting proteins are never drivers, suggesting that they are always manipulated by neighboring host proteins within any possible control configuration. IAV interacting proteins are not enriched for driver proteins (Fisher test p: 0.14). Again, a randomized protein set was created to test if IAV may be selectively interacting with host proteins based on their controllability characteristics. 10,000 random sets of 752 proteins (the number of IAV interacting proteins) were sampled from the host proteins of the VIN. Their Jia type distributions were plotted against the classification results of IAV interacting proteins, driver proteins, and all proteins in the VIN (Fig. 3d-f).
As with the Liu classification, the random sets closely resemble the total network (onesided p = 0.50, 0.51, and 0.50 for critical, intermittent, and redundant, respectively).
While there are no redundant driver proteins by definition, driver proteins are more likely to be intermittent proteins than critical proteins (Fig. 3d-e), where more than 75% of all driver proteins are missing from at least one possible MIS. This means the majority of possible driver proteins are able to be controlled by a neighboring protein in at least one MIS. IAV interacting proteins tend to be redundant compared to the total number of proteins that are redundant (Fig. 3f). This suggests that viruses prefer to interact with proteins that are part of existing control structures to receive input from neighboring proteins.

DISCUSSION
In total, this two-part network controllability analysis for a host protein-protein interaction network (HIN) and an integrated influenza virus-host protein-protein interaction network (VIN) aims to enhance the prediction of antiviral drug targets for influenza A virus. While Liu controllability methods have previously been applied to study PPI networks 26   shift between the two networks, particularly in IAV interacting proteins, supplies evidence that the topological effect of viral infection is wide reaching (Tables 1 and 4).
Further, a comparison of driver protein betweenness for those that are also IAV interacting proteins in comparison to those that are not shows a significant difference.
By definition, driver proteins that are IAV interacting are not receiving control influence from viral proteins and require additional external influence to achieve network control.
However, the increased betweenness of proteins that are both driver and IAV interacting proteins suggests that this group is still of great importance to information flow through the network. This is one example where differences in network topology measures can emphasize the importance of select proteins that are overlooked by controllability principles. where control is initiated. The increased population of redundant IAV interacting proteins (Jia controllability: never a driver protein, Fig. 3f) when compared to the random expectation indicates that more IAV interacting proteins are always being manipulated internally than would be expected by chance. This means that they are fully incorporated into the control structure of the VIN. From these two results, one can conclude that IAV interacting proteins contribute to both the "gate" (the ease of entering the system) and the "heart" (the proteins responsible for propagating control through the system) of the network control structure during infection. These findings support the idea that viruses are likely to interact with proteins which offer an advantage to total network control.
Similarly, both sets of controllability results demonstrate that driver proteins play interesting roles in the network control structure. The large population of dispensable driver proteins (Liu controllability: 6 ′ < 6 , Table 2) signifies that the majority of driver proteins are making it more difficult to control the network by requiring more external inputs to control system behavior. In their absence, the number of driver proteins would decrease and it would theoretically be easier for a viral attack to compromise the network control structure. As such, a possible strategy for drug development could be to protect these proteins from drastic changes to abundance. Over 75% of driver proteins are classified as intermittent (Jia controllability: sometimes a driver protein, Table 3), meaning there is at least one MIS where these driver proteins are not drivers, and receive control influence through internal propagation. This lends itself to the idea of viral escape routes: under pressure, virus proteins could utilize alternative pathways to maintain system control and reach the goal of hijacking cellular function.
The method of controllability implementation used identifies protein sets of interest through changes to classification between the HIN and VIN. Unfortunately, Liu classification methods do not detect a change between the two networks in this study.
As it is a measure of the robustness of the network to structural changes in the absence of each protein, this suggests that the HIN upholds its typical control structure during IAV infection. This could be a consequence of the interaction data used or it may be that the strategy applied here cannot distinguish between the behavior of healthy and diseased states. Knowing the extent of changes to cell behavior within immune response pathways [47][48][49] , apoptosis signaling 50,51 , and transcriptional processes [52][53][54] during infection, the IAV infected cell can be interpreted as  where approximately 20% of proteins in the Vinayagam network are classified as the same, though there is 89% overlap in directed edges between the two networks. This suggests that methods for predicting protein interactions may over represent these key proteins within the analysis, even in combination with experimental results. However, larger networks will move towards a more complete analysis of infected cell behavior and possibly reveal further proteins of interest. Therefore, the future of this field depends on continued establishment of large, confident, directed PPI networks.

Protein-protein interaction network
The host protein-protein interaction network used was downloaded from Vinayagam et al 36 . A confidence level cutoff of 0.7 was used, creating the HIN. Influenza A virus-host interactions from Watanabe et al 37 were narrowed to interactions which contained host proteins already found in host network interactions to avoid skewing degree and betweenness network metrics. These interactions were directly integrated into the host network, creating the VIN. All analysis was completed in R 3.4.3 using the igraph package.

Liu classification
Calculations for Liu classification were adopted from Liu et al 34 . For a network of n nodes, a set of driver nodes for the bipartite representation of the network, 6 , is found using a maximum matching algorithm such as Hopcroft-Karp 38 . Each node of the network is iteratively removed ( 8 = − 1) and maximum matching, N D ', is reevaluated.

Jia classification
Calculations for Jia classification were adopted from Jia et al 35 . For a network of n nodes, a set of driver nodes for the bipartite representation of the network, 6 , is found using a maximum matching algorithm such as Hopcroft-Karp 38 . For all 6 , control adjacent nodes were identified iteratively and an input graph was created as dictated in Zhang et al 68 . The input graph was used to classify nodes as critical (in all minimum input sets), neutral (in some minimum input sets), or redundant (in no minimum input sets).