Viral Evolved Inhibition Mechanism of the RNA Dependent Protein Kinase PKR's Kinase Domain, a Structural Perspective

The protein kinase PKR activated by viral dsRNA, phosphorylates the eIF2α, which inhibit the mechanism of translation initiation. Viral evolved proteins mimicking the eIF2α block its phosphorylation and help in the viral replication. To decipher the molecular basis for the PKR’s substrate and inhibitor interaction mechanisms, we carried the molecular dynamics studies on the catalytic domain of PKR in complex with substrate eIF2α, and inhibitors TAT and K3L. The studies conducted show the altered domain movements of N lobe, which confers open and close state to the substrate-binding cavity. In addition, PKR exhibits variations in the secondary structural transition of the activation loop residues, and inter molecular contacts with the substrate and the inhibitors. Phosphorylation of the P+1 loop at the Thr-451 increases the affinity of the binding proteins exhibiting its role in the phosphorylation events. The implications of structural mechanisms uncovered will help to understand the basis of the evolution of the host-viral and the viral replication mechanisms.


Introduction
Protein Kinase R (PKR) or Eukaryotic translation initiation factor 2-alpha kinase 2 (EIF2AK2) is an interferon-induced protein, activated by the presence of double stranded RNA (dsRNA) plays a critical role in anti-viral and anti-proliferative defense mechanisms at the cellular levels [1]. PKR belongs to a group of kinases that block the protein synthesis in response to stress signals by the phosphorylation of the α-subunit of translation initiation factor eIF2 [2]. Presence of dsRNA amid viral invasion, cytokine and growth factor deprivation are the principal stress signals induced for the PKR activation [3,4]. The α-subunit of the translation initiation factor eIF2, a GTP bound protein initiates the first step of the translation mechanism of transferring the methionyl-tRNA to the small ribosomal subunit [5]. PKR blocks protein synthesis by specific phosphorylation of eIF2α at Ser51 modulating the substrate to an inhibitor of its GDP-GTP exchange factor eIF2B [6].
PKR, a 551 amino acid protein consists of a N-terminal dsRNA binding regulatory domain (amino acids 1-170), a C-terminal kinase (amino acids 261-551) catalytic domain and a central region of incognito function. Like all eukaryotic protein kinases, PKR has a smaller, more dynamic amino-terminal lobe (N lobe) and a larger, stable, mostly helical carboxyl-terminal lobe (C lobe) [7]. The N lobe consists of a twisted five-strand antiparallel β sheet (denoted β1 to β5); two helices, α1 and α2 flank the grooves of the β sheet. The C lobe comprises of two paired antiparallel β strands (β7-β8 and β6-β9) and eight α helices (αD to αJ). The activation segment (residues 432-458) positioned between αE and αEF in the lower catalytic lobe serves the Phospho regulatory function. Three very stable helices (αE, αF, and αH) form the core of the C-lobe, whereas the αG-helix, in contrast, is more solvent exposed [8].
Virus, precisely pathogenic forms have evolved novel molecular mechanisms to impair the potent antiviral role of the PKR. Direct interaction with PKR, dsRNA sequestration, PKR pseudo activator and PKR pseudo substrate are the prominent molecular mechanisms of virus involved in countering the PKR role [9]. Proteins K3L of vaccinia virus [10,11] and TAT of HIV [12,13] competitively block eIF2α phosphorylation by mimicking the three-dimensional structure of eIF2α and its mode of interaction with PKR.
PKR employs a bipartite mechanism of substrate recognition in recognizing its substrate eIF2α. Phosphorylation sites at Thr-446 and Thr-451 [14] which lie within the activation loop between kinase sub domains VII and VIII play a vital role in the phosphorylation events. T451A mutation inactivates the kinase activity of PKR, while T446A substitution of PKR was partially functional which remains unexplained at the protein structure level [15]. The mechanism by which the viral inhibitors induce the conformational changes and inhibit the PKR interactions remains unclear.
The infections caused by Human Immunodeficiency Virus (HIV) and Hepatitis C Virus (HCV) rank as two of the most important public health problems worldwide [16,17]. Hundreds of millions of people are infected with either HIV or HCV [18][19][20], and co-infection with both viruses represents a growing concern that dramatically complicates patient treatment and infection outcome. Understanding the nature and mechanisms of these host pathogen interactions has the potential to unveil novel targets for therapeutic intervention, as well as inform rational vaccine and adjuvant development aimed at protecting against infection by these viruses [21]. We employed Molecular Dynamics Studies (MDS) to understand the molecular interactions and mechanisms involved between PKR and substrate eIF2α including viral inhibitors TAT and K3L.

Protein Preparation and Docking Studies
The crystal structure of the PKR kinase domain of X-ray structure of the complex of PKR kinase domain-eIF2alpha (PDB entry 2A1A) [22] and the solution structure of the alpha subunit of human eIF2α (PDB entry 1Q8K) [23] were obtained from the PDB database. To model viral PKR inhibitory protein complexes, NMR structures HIV-1 TAT (PDB entry 1TBC) [24] and crystal structure of the K3L protein from Vaccinia virus (PDB entry 1LUZ) [25] were also retrieved from the PDB database. The missing residues of the proteins were filled using the Modeler Version 9.14 software [26,27] and the resulting structures were minimized for their energy levels.
To investigate the interaction patterns of PKR with substrate eIF2α, inhibitors K3L and TAT we performed, data driven docking with the HADDOCK server [28,29] which is ranked as best server in both prediction and scoring capabilities at the CAPRI meetings [30]. The interacting residues of the crystal structure 2A1A were used as the active site residues for PKR and the interacting residues of eIF2α Saccharomyces cerevisiae were mapped to Homo sapiens eIF structure using sequence homology. Similarly, the interacting sites of K3L [25] and TAT [31] were retrieved from literature study and docked with the above-mentioned active site of PKR as they inhibit by a competitive inhibition mechanism. The complete lists of the active residues of the proteins involved in the docking were shown in the S1 Table. Passive residues were selected automatically as the exposed surface neighbors of the active residues.
Guru Interface of HADDOCK 2.2 software was used to generate the 1000 models at the first iteration using docking rigid body EM. The best 200 structures (based on energy) were then allowed to perform a second iteration of three simulated annealing refinements. In first iteration, the proteins are considered as rigid bodies and their respective orientation is optimized. In the second simulated annealing, the side chains at the interface are allowed to move. In the third simulated annealing, both side chains and backbone at the interface are allowed to move for some conformational rearrangements. The HADDOCK server in the explicit solvent energy minimization refined the resultant 200 structures. The final stage consists of a gentle refinement by heating the system to 300 K and cooling the system to 100K. The final structures were clustered using the pairwise backbone RMSD at the interface. Upon cluster-structural analysis, 10 lowest energy models were selected, and among these, the best one was characterized based on the lowest HADDOCK score, electrostatic energy and Z-score.
Phosphorylation events of the protein complexes were exercised using the Vienna-PTM 2.0 web server (http://vienna-ptm.univie.ac.at) [32] which has automated the post-translational modifications of the pdb's. Mono-phosphorylation forms (PKR p ) of PKR complexes were generated by phosphorylating Thr on the 446 th residue to phosphothreonine. Double phosphorylation forms (PKR pp ) were generated by phophorylating Thr on 446 th and 451 th residues to phosphothreonine similar to the PKR p . Six resultant PKR complexes of eIF2α and viral proteins were minimized for the structural variations due to the phosphorylation of the residues were used as the starting point for the MD simulations.

MD Simulations
MD simulations were performed using the 4.5.5 version of the GROMACS software (www. gromacs.org) [33] using the modified force field gromos54a7 [34] available at Vienna-PTM 2.0 web server (http://vienna-ptm.univie.ac.at). Protein complexes were solvated by SPC (Single Point Charge) [35] water molecules. Adding 4, 11, 2, 6 and 13 Clions respectively neutralized the non-neutral systems of PKR pp -K3L, PKR pp -TAT, PKR p -EIF, PKR p -K3L and PKR p -TAT. Periodic boundary conditions were implemented in all directions, using a simulation cell with a distance minimum of 1.5 nm from the protein. The non-pair list was updated for every five steps of the md run. The grid neighbor searching method was applied in the simulation with a 1 nm cutoff distance for the short-range neighbor list. Electrostatic interactions were computed using the particle mesh Ewald (PME) [36] summation method with a 1nm short-range electrostatic cutoff. The short-range cutoff used for van der Waals interactions during the simulation was also 1 nm. For the temperature coupling, the solvated structures were divided into two groups (protein and non-protein) using velocity rescaling with a stochastic term. The isotropic pressure coupling was employed in the MD simulation by using the Parrinello-Rahman method [37] with a compressibility of 4.5 × 10 −5 bar -1 . During the simulation, constraints were deployed in all bands using the LINC algorithm [38], with parameters LINC-order of 4. First, each system was energyminimized for 5,000 steps each using steepest-decent and conjugate gradient algorithms; subsequently, the solvent, and ions were equilibrated for 100 ps in constant volume (NVT) and constant pressure (NPT) ensembles, respectively, while the heavy atoms of the protein were restrained harmonically using a force constant of 1000 kJ mol −1 nm −2 . Finally, six systems were performed for 50 ns MD simulations after removing all the restraints and all the trajectories were stored every 0.002 ps for further analysis.

Principal Component Analysis
Principal component analysis (PCA) reveals the functionally important high-amplitude concerted motion of bio-molecules by applying the dimensional reduction method [39]. In MD simulations, the cross-correlation fluctuations between atoms can be described by the covariance matrix. The element C ij in the matrix is defined as: where ΔR i , ΔR j is the displacement vector corresponding to i th , j th atom of the systems and h i indicates an ensemble average. PCA diagonalizes the covariance matrix to obtain orthogonal eigenvectors and the corresponding eigenvalues. The eigenvectors, are the principal components (PCs) which represent the directions of the concerted motions. The eigenvalues indicate the magnitude of the motions along the direction. In MD simulations, the first few PCs usually describe the slow and functional motions of a bio-molecular system. In this work, g_covar and the g_anaeig utilities of GROMACS were used to perform PCA to explore and compare the motion of the different complex systems.

Free-Energy Landscape
The free-energy landscape of a protein obtained using MD simulation technique allows exploring the conformations of proteins in different states. In the FEL, the local basins usually represent the conformational ensemble in the stable states, and barriers indicate the transient states [40][41][42]. Based on the cosine content, the PCs are chosen as the reaction coordinates to construct the FEL. The relative free energy between two states is calculated by where k is the Boltzmann constant, T is the absolute temperature, the reaction coordinate X is the PCs, and P(X) is the probability distribution of the system along the PCs. Considering two different PCs X 1 and X 2 the two-dimensional free-energy landscapes are obtained from the joint probability distributions P(X 1, X 2 ) of the system.

Binding Free Energies of Protein-Protein Complexes
Molecular mechanics Poisson-Boltzmann surface area (MM-PBSA) computational approach was used to estimate binding free energies of protein-protein complexes, which quantifies the strength of a bio-molecular interaction, involved in recognition or catalysis. g_mmpbsa tool inheriting functions from GROMACS as well as Adaptive Poisson-Boltzmann Solver (APBS) was used to calculate energy components [43]. The binding free energy of the protein with protein in solvent can be expressed as where G complex is the total free energy of the protein−ligand complex and G protein1 and G prtoein2 are total free energies of the isolated proteins in solvent. The free energy for each individual entity can be given where x is the protein complex. <E MM > is the average molecular mechanics potential energy in a vacuum. TS refer to the entropy contribution to the free energy in a vacuum where T and S denote the temperature and entropy, respectively. The last term <G solvation > is the free energy of solvation.

Protein-Protein Docking and Stability of MD trajectories
The missing residues S351-S354 and S542-A551 of the kinase domain of eIF2α were modeled using Modeler program. The resultant structures of PKR were docked with the eIF2α, K3L and TAT using the HADDOCK software with the mentioned docking procedures. The best structure representing the docked complex was retained based on the lowest HADDOCK score, electrostatic energy, and Z-score. Table 1 shows the HADDOCK scores and energy values of the selected complexes. The docked PKR-eIF2α shows an RMSD of 1.31 Å from the reference pdb structure 2A1A making the dockings of the Haddock server reliable. The selected structures were then subjected to post-translation modification of phosphorylation of T446 and T451 generating the six PKR p and PKR pp complexes. Further analysis was carried on the trajectory files generated from the simulation of the above complexes. The resultant trajectories of the MDS studies were further analyzed using root mean square deviation (RMSD), root mean square fluctuation (RMSF), and radius of gyration (Rg) using g_rmsd, g_sas, and g_gyrate GROMACS utilities respectively, were shown in Fig 1. RMSD and Radius of Gyration (Rg) values of the trajectory files produced a stable plot after 10 ns of simulation with a fluctuation range lesser than 2Å, thus providing the suitability to carry out the  further analysis. eIF2α bound PKR p and PKR pp molecules show rmsd plots with lesser fluctuations at 4 Å and 6 Å respectively. The rmsd plots of inhibitor bound complexes show a range of fluctuations ranging from 3 Å to 7 Å except the PKR p -TAT form which shows a lesser fluctuation at the 5 Å range due to its smaller surface area. The rmsd plots provide insight how the substrate binding equilibrated the system than the inhibitor molecules. The RMSF fluctuations calculated on the trajectory of the PKR molecules provide insight to the fluctuations induced by the bound proteins in the PKR molecules. All the complexes show a similar fluctuation pattern independent of the bound protein. The Rg plots of all the protein complexes show a lesser fluctuations ranging from 2.2 Å to 2.3 Å, which shows that the protein complexes are stable. PKR pp -eIF2α complex tends to have an Rg value greater than 0.7 nm compared to other complexes showing that the eIF2α binding to PKR pp induces less compactness in the protein complex. Thus, PKR pp maintains short term contacts with the eIF2α substrate in the complex and it can dissociate easily compared to the other mentioned proteins.

Molecular Interactions of PKR with Substrates and Inhibitors
Hydrogen bonding numbers in protein-protein interactions confers rigidity to the protein structure and specificity of intermolecular interactions.  the PKR. The double phosphorylated PKR pp -eIF2α, PKR pp -K3L, PKR pp -TAT forms show Hbond formations of phosphorylated Thr with the Arg 54, Arg 56, and Ser57 of eif2α, Lys 45 of K3L; and Lys 28 and Tyr32 of TAT. The phosphorylated Thr 446 and non-phosphorylated Thr 451 PKR p do not show any interactions with the bound substrates or inhibitors at the residual level. Stable hydrogen bonds with greater than ten percent of existence were shown in the S2 Table. Salt bridges contribute to the protein structure and also to the specificity of protein-protein interactions, were retrieved using the VMD [44] salt bridge plug-in. The plug-in considers the oxygen atoms of acidic residues and the nitrogen atoms of basic residues within the cutoff distance of 3.2 Å in at least one frame for salt bridge formations. The PKR pp forms an increased number of salt bridges with substrate eIF2α than the PKR p involving the N lobe residues Glu-342 and Asp-345,347 residues of the N lobe of PKR. The five stranded β barrel sheet of K3L protein retains the interactions with the C lobe of PKR but fails to interact with the N lobe due to its structural similarity of eIF2α, which reduces the salt bridge numbers in PKR pp and PKR p form. The TAT forms an equal number of salt bridges with the PKR p and PKR pp forms as the substrate eIF2α. The terminal residues of αG helix (residues 497, 499, 500) coordinating with the five-strand β barrel of the interacting proteins shows decreased interactions with the inhibitors K3L and TAT. Glu-28 of eIF2α and Glu-37 of K3L form salt bridges with the activation loop residue Arg-453 of the PKR, in addition Asp-23 of K3L forms salt bridges with the Arg-447 of the PKR's activation loop. TAT inhibitor lacking the β barrel structure, does not form any charged interactions with the active site residues. Table 2 provides the insight to the salt bridges exhibited by PKR with the interacting protein partners and their percentage of stability.
Aromatic interactions are important in the structural stabilization of proteins, in proteinprotein recognition, and in ligand binding and protein folding. Pdb structure captured at every 5 ns of the simulation was used to predict the aromatic interactions using the PIC web server [45]. The six PKR complexes exhibit the following aromatic-aromatic and cation-pi interactions shown in Table 3. The residue Phe 489 of PKR plays a key role in making aromatic-aromatic interaction with the substrate eIF2α and the inhibitors K3L and TAT. The cation-pi interactions of the PKR-eIF2α complexes were dominated by the interactions with helix αG of the C lobe whereas the inhibitors exhibit a direct interaction with the activation loop residues. The double phosphorylation of PKR reduces the number of aromatic interactions with both the inhibitors but the substrate eIF2α exhibits increased number of contacts due to the conformational changes induced by the phosphorylation at T451.

Binding Energy
In order to illustrate the competitive inhibition mechanism at the molecular level the trajectory files were analyzed for the binding free energies using g_mmpbsa for a time step of 250 ps, thus selecting 200 frames from the trajectory files. The resultant binding energies of six complexes were summarized in the chart. To further analyze the contribution of the PKR molecules to the binding affinity the residual contribution of each PKR residue was summarized in the plots. Both the substrates and inhibitors exhibit higher binding energy with PKR pp forms than the PKR p in their complexes. The TAT form shows an increased binding energy than eIF2α and K3L in both the PKR p and PKR pp forms proving its high inhibition activity. K3L due to its similar structural interaction mechanism of eIF2α shows similar binding energy to PKR p -EIF2Α complex.
To further analyze the role of phosphorylation events of PKR molecules we summarized the contribution to the binding affinity of activation loop residues of PKR to the free energy of binding in the Fig 3. Activation loop residues 432, 442, 446, 451 and 458 show a major contribution to the free energy of binding for the PKR and interacting proteins. TAT shows an increase in the binding energies for the major residues 432, 442, 446 and 458 in both the PKR p and PKR pp forms. Thr 451 phosphorylation shows an increased binding free energy contribution than the non-phosphorylation residues with the same protein complexes. Phosphorylation Table 3. Aromatic interactions and Cation-pi interactions of PKR with the interacting proteins. Aromatic interactions between the PKR and the interacting proteins formed during the course of simulation within 7 A°. The cation-pi interactions of PKR with the proteins formed during the course of simulation within 6 A°. The minimum distance between the residues is indicated in the brackets. --  of Thr 451 residue increases the binding energy of both the substrates and the inhibitors with PKR pp contributing to increased binding energy than the PKR p proteins.

Secondary Structural Variations in Active Loop
The capacity of the activation loop to undergo large conformational changes aids the kinase protein to switch between inactive and active states. The activation loop of the PKR protein is highly unorganized with most of the residue residing in the coiled regions. The activation loop harbors the DFG motif, which interacts with the ATP and Mg ions, and P, P+1 phosphorylation sites which play a crucial role in the substrate phosphorylation mechanisms. The major secondary structural transitions visualized using DSSP [46,47] accounted for the bend to turn transitions and coil to bend transitions to a lesser extent were shown in Fig 4. The DFG motif region of PKR pp bounded to eIF2α and TAT proteins shows a transition from turns to the 3 10 helices. Other complexes show structural transitions from turns to bends in the DFG motif region, which becomes less compact than the 3 10 helices. The S3 Table shows

PCA of the Protein Complexes
PCA performed on the simulated ensembles of the six systems as described in methods determines the concerted conformational motions relevant to protein function. The first few eigenvectors from the PCA of the trajectories captured the bulk of the protein dynamics. Fig 5(A) shows the cumulative percentages of the proportional variance contributed by the eigenvectors of the PKR complexes. The first three eigenvectors PKR pp -eIF2α complex capture ninety percent of variance in the protein motions. The other protein complexes require greater number of eigenvectors to capture the similar variance in the PKR motions. This shows that the binding of the substrate eIF2α binding with the PKR pp is more stable than the PKR p form. The inhibitors binding with the PKR forms show a relatively lesser variation than the substrate binding, suggesting that the inhibitors form a stable complex with the PKR proteins.
The 2D PC graphs of eigenvector 1 and eigenvector 2 characterizes the essential subspace of the protein complexes, a characteristic of the different folded conformation of the protein [51,52] were shown in Fig 5(B). The PKR p in complex with the substrate and inhibitor exhibited lower values than the PKR pp complex suggesting that the phosphorylation of the Thr 451 residue has a destabilizing effect on the protein complexes. TAT inhibitor bound to PKR p shows minimal conformation variations due to the few conformational changes it induces in the PKR molecule. The TAT and K3L inhibitors bound PKR occupy a fewer essential subspace in the 2D PC plots than the substrate eIF2α with both the PKR p and PKR pp proteins demonstrating that the inhibitors form a stable complex with the protein PKR irrespective of the number of the phosphorylated sites. The eIF2α bound to PKR pp occupies a larger conformational space than the PKR p protein, which exemplified the structural variations induced by the phosphorylation of Thr 451 in the complexes.

Free Energy Landscape
The first two principal component vectors were considered for the construction of the free energy landscapes (FELs). Free energy landscapes of the PKR protein complexes generated were shown in Fig 6. The higher peak in the energy profile reflects the higher stable protein complexes in the simulation trajectory. The FELs were quite different among the six systems; in particular, their energy bins were located in different regions. The PKR pp -eIF2α complex shows a two prominent energy bins on the left side and an energy bin with lesser depth energy bins on the right side. The PKR p -eIF2α has a widespread energy bin on the left side and a discontinuous energy bin spanning on the right side. The PKR pp -K3L has a smaller energy bin on the left side and two-energy bins one spanning lesser area and the other having a wider area with deeper energy bin was on the right side. The PKR p -K3L energy bins on the right side have a smaller spanning area and on to the right side was a major spanning bin with discontinuous energy distributions. The TAT complexes with the PKR pp and PKR p have energy bins spanning from the left side to the left with discontinuous energy distributions. The two least energy conformations depicting the major conformational states of the complexes were retrieved from the trajectory file and used for further analysis.

Electrostatic Interactions of the Binding Surface
The electrostatic potential maps of the binding surface area along with the aloop of PKR protein for the above selected structures from free energy landscape plot were generated using the Delphi [53] plugin of UCSF Chimera [54] program. The maps show an altered potentials for the same protein derived from the varied energy bins. The electrostatic potential maps shown in the Fig 7 provide insight to the distribution of the charge potentials on the binding surface. The PKR pp forms show an increased electropositive potential in the PKR interaction surface along with its activation loop than that of the PKR p forms. The eIF2α substrate shows a highdensity electronegative region in both the PKR forms, which aids in the retention of the binding interaction with the PKR forms. The inhibitors proteins show a minor electronegativity patch with a lesser variations on the electron density scales. In addition the inhibitors are dominated by a predominant electropositive surface area similar to the PKR forms which inhibits the transfer of a charge moiety. On the other hand, the substrate eIF2α maintains good electro potential balance in both the PKR complexes. The PKR pp form comparable to PKR p form shows an increased electropositive nature due to the presence of additional phosphate group which helps in the phosphorylation of the eIF2α.

Domain Motion Analysis
The substrates and the inhibitors bound to the protein in the complex induce the conformational transitions hinge bending which involves the movement of relatively rigid parts of a protein about flexible joints. Hingefind [55] an algorithm partitions a protein into domains of preserved geometry and subsequently characterizes the relative movements of the found domains by effective rotation axes (hinges). The residues involved in the domain organization are the axis of rotation of the Domain II and I pass through the N lobe of the PKR molecule, which exemplifies that the conformational change of domain opening in the PKR protein was The four protein complexes PKR pp -eIF2α, PKR p -eIF2α, PKR p -K3L and PKR p -TAT organized into Domain 1 and Domain 2, whereas the PKR pp inhibitor complexes with K3L and TAT have a single Domain. The N lobe residues induce a major conformational variation of the PKR in the protein complexes and contribute to a major portion Domain I and Domain II, whereas in PKR p -K3L and PKR p -TAT the C lobe contributes to the domain organization. The domain motion of PKR in PKR pp -eIF2α and PKR p -eIF2α complexes were directed away from C lobe with an angular twist of 12.0°and 17.0°respectively inducing an open conformation to the PKR molecule irrespective of the phosphorylation sites. The Domain I of the four-inhibitor complexes of PKR shows an inward movement leading to the closure of PKR binding cavity and inducing a conformational change [56,57]. The coil regions bridging the β sheets in the N lobe organize to form Domain 2 showing a higher effective angular rotation, which induces the conformational changes in N lobe region. The residues involved in the domain organization and the angular rotation of the domain were mentioned in the S4 Table. Activation loop of the PKR plays a key role in the molecular phosphorylation events by interacting with the Ser51 of eIF2α. The inhibitors bound to the PKR forms induce an inward To further analyze the altered domain motion of the PKR protein's N and C-lobe upon interacting with the substrate or inhibitor, a cross-correlation heat map was generated based on the PCA vectors using ProDy python package [58]. Comparing the cross-correlation matrices of different simulation trajectories reveal the similar features shown by the relative motions. Fig 9 shows the cross-correlation matrices of the six protein complexes generated using the PCA eigenvectors. Many regions of the protein, especially the regions of secondary structure, move in a correlated manner [59,60]. A higher degree of cross correlation among the residues was observed in the PKR p -eIF2α complex followed by the PKR p -K3L complex.
The N-lobe of all the protein complexes shows a similar inter-residual correlation whereas the C-lobe shows higher variations in inter-residual correlations due to its interactions with the substrate or the inhibitor protein. The inhibitors' binding induces a higher degree of negative Viral Inhibition Mechanism of PKR correlation in the internal domain motions of the PKR's C-terminal residues; in comparison, the substrate binding shows a higher degree of positive correlation in comparison to the inhibitor bound complexes. A similar induced negative correlation motion was observed in the activation segment residues in the inhibitor complexes with the C-lobe region and a lesser extent with the N-lobe region. The αG which interacts with the protein partners shows a positive correlation with the activation loop residues only in the PKR pp -eIF2α complex and all the other protein complexes show the negative correlation.
The correlated domain motions of the PKR protein provide insight to alter domain motions of PKR in relation to the secondary structural features. The substrate binding and the phosphorylation events of the Thr-451 decreases the negative correlation between the secondary structure elements, whereas the inhibitors binding and non-phosphorylation of Thr-451 relatively induces the negatively correlated movements in the secondary structure elements of the PKR. These positively correlated movements of the PKR elements induced by the eIF2α binding play a key role in directing the N-lobe and C-lobe an outward motion aiding in the projection of the activation segment.

Conclusion
Auto phosphorylation of the PKR is a post-translational modification, which activates the protein through multiple phosphorylations of Ser and Thr residues by autocatalysis. Multiple auto phosphorylation events appear to be an integral part of eIF-2AK family protein kinase function. Contemplating the potential role of the phosphorylation sites in the functional mechanism of the kinases will help in understanding the activation and inhibition mechanisms of eIF2-AK family kinase proteins. Thr 551 residue in addition to Thr 446 residue phosphorylation increase the interactions of PKR with eIF2α in numbers of the H bond, salt bridge and aromatic interaction formed by C-lobe and activation loop of PKR with the five stranded β barrel.
The inhibitor interacted with the PKR molecules by forming stable salt bridges, H-bonds and aromatic interactions comparable to the substrate eIF2α. Five stranded β barrel structure of K3L forms stable interactions with the αG loop of the PKR molecule. TAT protein inhibits in a distinct mechanism of interactions with the PKR spanning from N-lobe to C-lobe. Distortions induced by phosphorylation of Thr-451 in the αG helix of PKR pp forms alters its interaction pattern with the viral inhibitors by decreasing its interactions with the distorted αG helix and the activation loop residues.
The inhibitor interaction with the varied phosphorylation PKR forms shows much stability with a fewer conformational alteration whereas the substrate eIF2α shows a much varied conformational changes in the PCA plots. Though the inhibitors show lesser interactions than the substrate, the inhibitor protein complexes were stabilized with higher binding energies from the PKR protein, which involves large amounts of interaction energy contributed by the nonbonded interactions of the activation segment residues significantly by the phosphorylation of Thr 451 residue.
PC analysis of the PKR complexes gives insight to the higher conformational flexibility induced in the substrate bound complexes than the inhibitors, which prefer a stable configuration with limited conformational changes. The substrates and the inhibitors induce an altered opening and closing domain motion by inducing changes in the C-lobe of PKR protein. The inhibitor characteristic properties of inducing the conformational stability and closing domain motion offer an insight to the competitive inhibition of PKR by viral proteins and its structural alteration. The PKR pp complexes with eIF2α and TAT molecules show a functional transition from turns to 3 10 helices in the DFG motif region, whereas a similar transition was seen in the P+1 loop which interacts directly with the substrate was viewed in PKR pp -eIF2α but absent in other substrates.
The present works emphasizes on the loss or gain of contacts due to the altered phosphorylation of Thr 446 and Thr 451 residues of PKR and predicts domain motions based on the resultant structural variations. To understand the exhaustive phosphorylation and inhibition events by the substrates or the inhibitors an extensive simulation at a millisecond scale and quantum chemical calculations have to be applied on the protein complexes. The events involved in phosphorylation of eIF2α by PKR and its inhibition of cellular translation mechanism remain vague. An insight into the inhibition mechanisms evolved by the virus to control the above process will help to regulate the viral replication mechanisms in host tissues. The molecular dynamics studies provide insight into the role of auto phosphorylation of Thr 451 in substrate and inhibitor recognition mechanisms. Varied interaction patterns of viral inhibitors with PKR p and PKR pp forms discussed will help us to understand the host-viral interaction mechanisms. The newly formaed contacts between the PKR and eIF2α due to the indcution of 3 10 helix in the DFG loop (TIF) S1 Table. Active residues of proteins involved in docking. The residues of the proteins tabled below are defined as the active site residues for protein-protein docking in the HADDOCK server. (DOCX) S2 Table. Hydrogen bonds formed by PKR protein in the six complexes. Hydrogen bonds formed between the PKR protein and interacting proteins having more than ten percentage of existence during the course of the simulation. The values indicate the percentage of existence of the Hydrogen bonds.  Table. Domain motion contributing residues. Residues involved in the domain formation, which helps the PKR protein to rotate, and their effective rotational angles are indicated. (DOCX)