A comparative study of structural and conformational properties of casein kinase-1 isoforms: insights from molecular dynamics and principal component analysis.

Journal of Theoretical Biology ∎ (∎∎∎∎) ∎∎∎–∎∎∎

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Journal of Theoretical Biology journal homepage: www.elsevier.com/locate/yjtbi

A comparative study of structural and conformational properties of casein kinase-1 isoforms: Insights from molecular dynamics and principal component analysis Surya Pratap Singh a,n, Dwijendra K. Gupta b a b

Center of Bioinformatics, University of Allahabad, Allahabad 211002, India Department of Biochemistry, University of Allahabad, Allahabad 211002, India

H I G H L I G H T S

In silico modeling of CK1 isoforms and their MD simulation. The conformational substates are explored to explain dynamical nature of proteins. PCA and potential energy surfaces of conformational subspaces are presented.

art ic l e i nf o

a b s t r a c t

Article history: Received 1 October 2014 Received in revised form 2 January 2015 Accepted 28 January 2015

Wnt signaling pathway regulates several developmental processes in human; however recently this pathway has been associated with development of different types of cancers. Casein kinase-1 (CK1) constitutes a family of serine–threonine protein kinase; various members of this family participate in Wnt signal transduction pathway and serve as molecular switch to this pathway. Among the known six isoforms of CK1, in human, at least three isoforms (viz. alpha, delta and epsilon) have been reported as oncogenic. The development of common therapeutics against these kinases is an arduous task; unless we have the detailed information of their tertiary structures and conformational properties. In the present work, the dynamical and conformational properties for each of three isoforms of CK1 are explored through molecular dynamics (MD) simulations. The conformational space distribution of backbone atoms is evaluated using principal component analysis of MD data, which are further validated on the basis of potential energy surface. Based on these analytics, it is suggested that conformational subspace shifts upon binding to ligands and guides the kinase action of CK1 isoforms. Further, this paper as a first effort to concurrent study of all the three isoforms of CK1 provides structural basis for development of common anticancer therapeutics against three isoforms of CK1. & 2015 Published by Elsevier Ltd.

Keywords: Wnt signaling pathway Molecular dynamics simulation Principal component analysis Conformational subspaces

1. Introduction Wnt signaling pathway is well studied signaling for its role in early embryonic development of fruit fly, Caenorhabditis elegans, mouse and human. Moreover, this pathway has also been documented to play a major role in development of cancers of various origin (colon, ovarian, prostate, etc.), with temporally deregulated (or mutant) expression of components of Wnt pathway (Klaus and Birchmeier, 2008). One of the important players in Wnt signaling

n

Corresponding author. E-mail addresses: [email protected] (S. Pratap Singh), [email protected] (D.K. Gupta).

pathway is β-catenin which is under strict regulation of glycogen synthase kinase-3β (GSK-3β). The phosphorylated β-catenin is targeted for proteasomal degradation via ubiquitination. The presence of a Wnt factors (or a deregulatory signal) β-catenin degradation is inhibited and results in elevated level of cytosolic β-catenin. Once stable in the cytosol, β-catenin, translocates to the nucleus where it engages the transcription factors such as TCF and LEF. In human, transcriptions induced by TCF4 and LEF1 ultimately results in malignancy (Polakis, 2000; Jiang et al., 2013; Chen et al., 2010; Huang et al., 2011). Casein kinase 1 (CK1) is an important family of highly conserved serine/threonine protein kinases among all the eukaryotes. Recently, CK1 has been studied as an attractive drug target for the development of anticancer therapeutics (Long et al., 2012a, 2012b).

http://dx.doi.org/10.1016/j.jtbi.2015.01.032 0022-5193/& 2015 Published by Elsevier Ltd.

Please cite this article as: Pratap Singh, S., Gupta, D.K., A comparative study of structural and conformational properties of casein kinase-1 isoforms: Insights from molecular dynamics.... J. Theor. Biol. (2015), http://dx.doi.org/10.1016/j.jtbi.2015.01.032i

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S. Pratap Singh, D.K. Gupta / Journal of Theoretical Biology ∎ (∎∎∎∎) ∎∎∎–∎∎∎

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At least six isoforms of CK1 have been reported in human (i.e. α, γ1, γ2, γ3, δ and ε), which regulate several biological processes, including signaling pathways, circadian rhythms, RNA and DNA metabolisms, etc. (Amit et al., 2002; Etchegaray et al., 2009). At least three (i.e. α, δ, and ε) out of six have been reported for their key role in cell survival and carcinogenesis via direct or indirect stabilization of β-catenin in the Wnt signaling pathway (Knippschild et al., 2005). The biological function of CK1 isoforms depends on their special catalytic site which recognizes -Ser(p) XXSer/Thr- motif to phosphorylate target protein (Xu et al., 1995). The coordinated action of CK1α and ε, over lipoprotein receptor-related protein 5 and 6 (LRP5/6), nucleates a binding site for GSK-3β at C-terminal domain of LRP5/6; thus the receptor bound GSK-3β is unable for inhibitory phosphorylation of β-catenin which causes increased half-life of β-catenin (del Valle-Perez et al., 2011). Recently, Brockschmidt et al. (2008) and Rosenberg et al. (2013) have also shown highly increased level of CK1 δ/ε in pancreatic and breast cancer cell respectively. In all these studies a remarkably high level of nuclear β-catenin has been reported pointing towards an active role of different CK1 isoforms in carcinogenesis, through Wnt-signaling pathway. The biological function of proteins directly depends upon their flexibility (McCammon, 1984; Henzler-Wildman and Kern, 2007). A crystal structure of protein represents its static average under a set of conditions, the proteins with dynamic personalities, thus the conformational changes observed during dynamics provide detailed structural as well as functional information. MD simulation is a standard computational method and is routinely used to access the molecular flexibility based upon the knowledge of the interaction potential for the particles (Karplus and Petsko, 1990; Karplus and McCammon, 2002). Here, we present a comparative study of three isoforms (α, δ and ε) of human CK1 with a particular emphasis on their dynamic etiquette under physiological condition in aqueous medium. Moreover, principal component analysis (PCA) of MD data was performed to reveal the conformational substates sampled during the dynamics of these kinases (Hayward and Go, 1995; Stein et al., 2006; Hayward and de Groot, 2008; Du et al., 2006; Li et al., 2009). Potential energy surfaces (PES), a contour map of potential energy as a function of conformational coordinates, were employed to confirm the conformational substates (Frauenfelder et al., 1991).

Further, the quality of all the structures was estimated on the basis of Ramachandran plot and Z-score analytics. In order to avoid any ambiguity, these newly built structures were named as aCK1-M, dCK1-M and eCK1-M for CK1- α, -δ and -ε respectively. 2.2. Molecular systems The pdb2gmx tool of Gromacs 4.5.5 package (van der Spoel et al., 2005; Hess et al., 2008) was used to prepare the systems with GROMOS 53a6 force field (Oostenbrink et al., 2004). Finally, each molecule was placed in the center of a cubic box with a minimum distance of 10 Å between its wall and any atom of the protein; then boxes were filled with extended simple point charge (SPC/E) water molecules (Berendsen et al., 1987; Mark and Nilsson, 2001). In order to maintain the physiological condition, i.e. to neutralize the total charge, appropriate numbers of sodium (Na þ ) and chloride (Cl ) ions were added to each system. Further, to pacify each of the three systems, energy minimization was performed with non-bonded cutoff of 9.0 Å. A total of five thousand cycles of steepest descent were carried out without any restraints to the system. The details of each system, used in molecular dynamics simulations, are tabulated in Table 1.

2.1. Protein structures

2.2.1. MD simulation Systems were equilibrated in two steps, ahead of the production dynamics, of one nanosecond (ns) simulation time with time step of 2 fs (femtoseconds). The first phase of equilibration is a heating step of 100 ps (picoseconds), under canonical ensemble (NVT), using Berendsen thermostat (Berendsen et al., 1984) with temperature coupling time of 0.1 ps. This raised system's temperature to 300 K. Moreover, during NVT ensemble the initial velocities were assigned from the Maxwell's distribution of temperature. The second equilibration step is for remaining 900 ps of equilibration period, under isothermal–isobaric (NPT) ensemble. The Parrinello–Rahman barostat (Parrinello and Rahman, 1981), with pressure coupling time of 0.1 ps, was applied to maintain homogeneous pressure throughout systems. Linear Constraint Solver (LINCS) (Hess et al., 1997) algorithm was applied to preserve the length of all bonds and the long-range electrostatic interactions were treated by the particle mesh Ewald (PME) (Darden et al., 1993) method with the non-bonded cut-off distance of 9 Å, under periodic boundary conditions. The well equilibrated systems were then passed, to production run under NPT ensembl, for computing trajectories of 20 ns (nanoseconds). Snapshots at every 2 ps intervals were collected. All simulations were run on a Linux machine with an Intel Core-i5 processor.

The native tertiary structure of human CK1-α was not found in Protein Data Bank (PDB), however, apoenzyme structures for δ and ε isoforms are available but incomplete (PDB code: 3UYS at 2.3 Å and 4HOK at 2.77 Å, CK1-δ and CK1-ε respectively). Starting from the sequence of CK1 α, (UniProt id- P48729), homology modeling was performed using a template of CK1-ε (PDB code: 4HOK at 2.77 Å) and the incomplete crystal structures of δ and ε isoforms were repaired using model refinement/loop modeling tool of Chimera 1.8.1. Modeler-9.10 (Sali and Blundell, 1993; Eswar et al., 2006) was used for all protein model construction experiments.

2.2.2. Trajectory analysis Gromacs 4.5.5 analysis tools were used for the analysis of trajectories, beginning with their stability evaluation. In order to ensure that all the three systems obeyed NPT ensemble throughout simulation period, variations in energies (potential, kinetic and total energy), temperature, pressure and density of systems were calculated. To explore the molecular plasticity, in three isoforms of CK1, root mean square deviation (RMSD) and root mean square fluctuation (RMSF) were estimated. The significant changes in elements of protein secondary structure, during evolution each

2. Materials and methodology

Tablele 1 Details of the systems used in molecular dynamics simulations. Name

Source

No. of residues

Total charge on protein

Volume (m3)

Density (kg/m3)

Number of Na þ and Cl

aCK1-M dCK1-M eCK1-M

SwissProt id P48729 PDB id 3UYS PDB id 4HOK

290 296 296

þ15 þ13 þ14

5.35172 10 25 6.39499 10 25 6.65850 10 25

984.374 1002.300 1028.140

32 and 47 38 and 51 40 and 54


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trajectory, were examined by DSSP program (Kabsch and Sander, 1983). The g_sas and g_gyrate tools were used to estimate the temporal changes in the solvent accessible surface area (SASA) and radius of gyration (Rg), respectively. 2.3. Principal component analysis In order to study the collective motions in the three isoforms of CK1, PCA was executed for three independent trajectories (Amadei et al., 1993, 1996). The covariance matrices were constructed from the backbone atoms of proteins according to 1X Cij ¼ xiðtÞ xi xjðt Þ xj n t where n is the total number of structures, t¼ 1, 2…S, xi (t) is the position coordinates with i¼1, 2, 3 … 3N. Here ‘N’ represents total number of atoms in Cartesian space, any atom at time‘t’ in three directions, to construct the covariance matrix; h:::i represents the average coordinates over all configurations and S is total simulation time. Gromacs tool g_covar was utilized to execute all the covariance analyses, which produced a covariance matrix of 3N 3N size with over 2600 eigenvectors. The first twenty eigenvectors of each system were selected, constituting over 85 percent of total variance, for the study. The snapshots at every 2 ps were collected for visual inspection of concerted motion along each eigenvector. Projections of eigenvectors to their respective trajectory, also known as Principal Components (PCs), were obtained by using g_anaeig tool. Further, 1st and 3rd PCs were selected for essential dynamics sampling since these PCs constitute high proportion of concerted motions throughout the molecules whereas the second eigenvector shows only jiggling of the C-terminus while the rest of the protein remains almost stable. 3. Result and discussions 3.1. Molecular structures The knowledge of tertiary structures of proteins is vitally important for rational drug design. The experimental techniques such as X-ray crystallography and NMR are very powerful in determining protein 3D structures (Schnell and Chou, 2008; Berardi et al., 2011; OuYang et al., 2013). Unfortunately both of these techniques are time-consuming, expensive and with their own other shortcomings. To acquire the structural information in a timely manner, protein 3D structures were developed by means of homology modeling in a series of studies (Chou et al., 2000; Wang et al., 2009, 2007; Wei et al., 2006; Chou, 2004), and were found very useful for drug development. In view of this, the homology modeling technique was adopted in the current study to predict the 3D structure of aCK1-M. Based on Ramachandran plot analysis it was confirmed that all the three structures show good distribution of amino acids over the allowed regions of the map (Suppl. Fig. 1(a)). The Ramachandran plot for aCK1-M and eCK1M revealed 100% amino acids distributed over allowed and partially allowed regions whereas that for dCK1-M showed 99.02% amino acids in allowed and partially allowed regions and 0.8% amino acids in disallowed region, shows the appreciable reliability of modeled structures; further, the Z-scores for aCK1-M ( 6.06), dCK1-M ( 6.19) and eCK1-M ( 7.13) also shows ‘near nativeness’ of these structures (Suppl. Fig. 1(b)). 3.2. Molecular dynamics simulations Many marvelous biological functions in proteins and DNA and their profound dynamic mechanisms, such as switch between

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active and inactive states (Wang and Chou, 2009), cooperative effects (Chou, 1989), allosteric transition (Wang et al., 2009), intercalation of drugs into DNA (Chou and Mao, 1988), the inhibition mechanism of PTP1B (Wang et al., 2009), the gating and inhibition mechanism of the M2 proton channel from influenza A viruses (Du et al., 2009), and the enzyme–ligand binding interaction (Wang et al., 2007), can be revealed by studying their internal motions as elaborated in a comprehensive review (Chou, 1988) and summarized in a recent paper with the title of ‘Theoretical and Experimental Biology in One’ (Lin and Lapointe, 2013). However, the crystal structures present only single conformation under particular set of conditions. Likewise, to really understand the action principle of CK-1 isoforms, we should consider not only the static structures concerned but also the dynamical information. To realize this, the MD simulation is one of the feasible tools. The three systems (i.e. aCK1-M, dCK1-M and eCK1-M) used for MD simulation, attained temperature of 300 K and pressure of 1 bar during equilibration. The RMSD and Rg analyses were carried out to estimate the stability of each trajectory throughout simulation period.

3.2.1. Flexibility of CK1 isoforms The RMSD and RMSF profiles of each of three kinases are shown in Figs. 1 and 2 in order to depict their flexibility. For each trajectory, RMSD was calculated with reference to their respective initial structures. Though RMSD for each trajectory achieved stability within first 1.25 ns yet we excluded values of first two ns thus all analyses were carried out for last 18 ns. The RMSD profile of each trajectory clearly displays two distinct plateaus (Fig. 1). The first plateau in RMSD profile of aCK1-M extends up to sixth ns of the trajectory, for dCK1-M it spreads until eighth ns of trajectory whereas for eCK1-M it ends a bit earlier by fifth ns of trajectory. The second plateau in RMSD profiles of aCK1-M, dCK1-M and eCK1-M span between 9 and 20 ns, 12 and 20 ns and 8 and 20 ns respectively. Fig. 1 also reveals that two plateaus are separated by a distance of 1.0 Å, 0.5 Å and 1.25 Å in RMSD profile of aCK1-M, dCK1-M and eCK1-M respectively. This RMSD profile led us to infer that CK1 isoforms dynamically exist in two well separated microstates. Root mean square fluctuations (RMSF) were computed for each trajectory and averaged over per alpha-carbon residue (Cα) of respective isoform. Throughout the simulation time RMSF values are significantly small 0.5–1.0 Å (Fig. 2(C)), except the N- and the

Fig. 1. Root mean square deviation of backbone atoms. Two different plateaus are clearly visible in the RMSD profile of aCK1- M (black), dCK1-M (red) and eCK1-M (green). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)


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Fig. 2. (A) Multiple sequence alignment (MSA) of three isoforms of CK1 superimposed with secondary structures. ClustalX program was used for MSA and secondary structures were obtained from pdbsum. (available at: http://www.ebi.ac.uk/pdbsum/). The highlighted regions in MSA correspond to regions of high fluctuation in RMSF profile. (B) Cartoon representation of all three Isoforms of CK1 using PyMol Delano, 2002. aCK1-M, dCK1-M and eCK1-M are represented in green, cyan and hotpink colors respectively. The blue colored regions represent the high fluctuating regions and labeled as in Table 2. The ATP binding residue (i.e. K46 of aCK1-M and K38 of dCK1-M and eCk1-M) is shown in orange sticks while proton acceptor residue (i.e. D136 of aCK1-M and D128 of dCK1-M and eCK1-M) is shown in wheat sticks. (C) Atomistic fluctuations for Cα atoms of aCK1-M (black), dCK1-M (red) and eCK1-M (green). Colored bars placed at bottom represent the fluctuations of interest (details in Suppl. Table 2) and discussed in text. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

C- terminal regions; which constitute random coils and thus are free for random movements. Moreover, the RMSF profile shows six regions of high fluctuations, sequence of high fluctuation regions are highlighted in Fig. 2(B) and summarized in Table 2, which are further discussed below in detail. The first region of high fluctuation corresponds to ATP binding loop which is located between I23–I31 of aCK1-M and I15–I23 of dCK1-M and eCK1-M. This loop is responsible for holding ATP to the enzyme active site, thus the fluctuation in this loop is important for the functioning of enzyme. The second distribution of high fluctuation extends for seven residues, for aCK1-M stretching between A34 and G40 and for dCK1-M and eCK1-M it is in between G28 and G34. During this region of high fluctuation all the three isoforms, do not reveal any structural change, but interestingly all undergo a small translational shift. The third distribution of high fluctuation is positioned between residues L47 and L58 for aCK1-M while for dCK1-M and eCK1-M; it is between residues L39 and H50. In this region some structural changes are visible inasmuch as the aCK1-M shows transition from α-helix to random coil at Q56, while the dCK1-M isoform shows change from a helix to coil at Glu42 and eCK1-M shows change of helix to coil at residues Q50 and L51. The fourth distribution of high fluctuation extends between residues G145

Table 2 Details of five distributions of interest in RMSF profile. Distribution

Maximum fluctuation (Å)

Sequence

1


3.0 2.9 3.1

IGSGSFGDI IGSGSFGDI IGSGSFGDI

2


2.1 3.4 2.4

AINITNG GTDIAAG GANIASG

3


2.8 4.0 3.5

LESQKARHPQLL LECVKTKHPQLH LECVKTKHPQLH

4


2.7 4.9 3.4

GIGRHC GLGKKG GLGKKG

5


3.6 2.9 3.6

ADNRTRQHIP RDARTHQ RDARTHQ

6


5.4 3.1 4.0

WQGLKAATKKQK WQGLKAATKRQK WQGLKAATKRQK


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and C150 for aCK1-M, whereas for dCK1-M and eCK1-M, it is between residues G139 and G144; interestingly, in this region the aCK1-M shows very small fluctuation of 1.2 Å while dCK1-M and eCK1-M show high fluctuations of 4.9 Å and 3.4 Å respectively, which seem to correlate well with the transition of α-helix to loop between K142 and G144. The fifth distribution of high fluctuation spreads between residues R165 and P174 for aCK1-M and residues

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R159 and Q165 for dCK1-M and eCK1-M. This region forms a loop in all the three isoforms and apparently very stable without undergoing any structural change; however it is free to wobble and thus contribute a high fluctuation in all isoforms (viz. 3.2 Å, 2.9 Å and 3.6 Å for aCK1-M dCK1-M and eCK1-M respectively). The sixth and last distribution of high fluctuation in RMSF profile is located between residues W221 and K232 for aCK1-M and

Table 3 Active site residue of three isoforms of CK1. Lysine present in the active site is shown here in solid and in Fig. 2(A) by orange sticks. Name

Active site residues

aCK1-M

Gly-26, Ser-27, Gly-29, Asp-30, Lys-46, Leu-47, Glu-48, Gln-56, Leu-57

dCK1-M

Gly-18, Ser-19, Phe-20, Asp-22, Lys-38, Leu-39, Glu-40, Gln-48 Leu-49, Glu-52

eCK1-M

Gly-18, Ser-19, Ile-23, Ala-36, Lys-38, Tyr-56, Glu-83, Gly-86, Pro-87, Ser-88

Fig. 3. The temporal changes in per residue secondary structure by the DSSP method. The DSSP profile for aCK1-M, dCK1-M and eCK1-M are represented by A–C correspondingly. Legends of secondary structures are shown at the bottom of the picture.


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between residues W215 and K226 for dCK1-M and eCK1-M; once again the RMSF values for this region is very high (viz. 6.5 Å, 3.1 Å and 4.0 Å for aCK1-M, dCK1-M and eCK1-M respectively). The high fluctuation associated with the sixth distribution involves secondary structural changes. During this distribution, the isoform aCK1-M shows a change of loop to helix at K229, while similar change can be recognized at the corresponding residue in dCK1-M isoform (i.e. at K223). In eCK1-M isoform, it gets inversed i.e. a helix is being converted to loop at K223. In order to reveal significant structural changes during dynamics of each isoform, we compared the initial structure of each isoform with the corresponding average structure from the respective trajectory which was verified from secondary structure analysis. RMSF data led us to conclude that the high fluctuations of Cα are either contributed by structural changes or free motions in the mainchain of the protein. Such fluctuations are of great functional importance. Motions of the loop L1 together with L3 govern the movement of H1 helix (Fig. 2(A)) which ultimately regulates the opening of active site that posses a lysine residue (shown in orange color in Fig. 2(A) K46 of aCK1-M and K38 of d/eCK1-M). Motions of loop L5 and L6 (Fig. 2(A)) regulate the substrate protein binding site which posses a highly conserved aspartate residue (shown in wheat color in Fig. 2(A)) moreover the motions of L6 governs the movement in H11 helix. Thus we conclude that the binding of ATP and substrate protein to various isoforms of CK1 is powered by rhythmic motions of four loops (i.e. L1, L3, L5 and L6) and two helices H1 and H11. The active site for each isoform was

predicted by FTsite server (http://www.ftsite.bu.edu) and is tabulated in Table 3, moreover, above mentioned lysine residue (i.e. K46, and K38 for aCK1-M and d/eCK1-M) is conserved in all and thus is very important for drug design and mutagenesis experiments (Chou, 2004; Chou et al., 1999; Zhang et al., 2002). The secondary structural changes in these highly fluctuating regions can be observed in Suppl. Table 1. Conformational changes associated with these high fluctuating regions can also be observed in the secondary structures analyses of trajectories.

3.2.2. Secondary structure, radius of gyration and hydrophobicity analyses Temporal changes in secondary structural elements during the evolution of each trajectory were adjudged by DSSP program which strongly suggested that all the three isoforms of CK-1 have comparable secondary structures (Fig. 3). Further, DSSP analysis of each trajectory on the basis of per residue secondary structure transformations (i.e. changes in contribution of each residue to the local secondary structures such as loop, α-helix and β-sheet) showed good agreement with the RMSF analytics discussed above. Rg of a system is widely used to discuss its dimensions; it is computed as root mean square distance between the center of mass and the ends of the system. A comparative illustration of Rg for all the three isoforms, during evolution of their respective trajectories clearly displayed the center of mass of all the three systems are stable and compact throughout the simulation period with an overall fluctuation

Fig. 4. (A) Radius of gyration (Rg) as a function of time for all the three trajectories. (B) Variations of hydrophobic contact area, as a function of simulation time, for all the three isoforms of CK1. (C) The Solvent accessible surface area (SASA) of all the isoforms of CK1. SASA profile is in strong correlate with Rg and Hydrophobic contact. Data in black, red and green is for aCK1-M, dCK1-M and eCK1-M respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)


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of only 0.5–1.0 Å (Fig. 4(a)). The temporal changes in the hydrophobic surface area were computed for all the three independent trajectories (Fig. 4(b)). Variations in hydrophobic surface area clearly indicate that aCK1-M and dCK1-M have almost static hydrophobic surface area during the entire simulation period. Interestingly however, eCK1-M with respect to hydrophobic surface area, a noticeable jump during initial first five ns of trajectory, was observed followed by stability towards the end of simulation time without any significant variations. The temporal changes in hydrophobic surface area were in good agreement with the Rg analytics. The Rg provides a way to estimate the compactness of structures of biomolecules, which also depends upon its hydrophobicity. The hydrophobic contacts are crucially important for the compact protein tertiary structures and have been reported by Hong (2009). Notably, the solvent accessible surface area (SASA) profile of each isoform is similar to Rg and hydrophobic contacts (Fig. 4(c)). 3.3. Essential dynamics Covariance matrix of each trajectory was diagonalized, and the corresponding eigenvalues in decreasing order were obtained (shown

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in Suppl. Fig. 2). The scree plot (Fig. 5), represents the percent contribution of first twenty eigenvectors to the total variance, this clearly shows that first PC from each trajectory strongly dominates (i.e. the first principal component contributes 41%, 46% and 52% of the total variance for aCK1-M, dCK1-M and eCK1-M, respectively). Further, it also shows that the top twenty PCs capture approximately 85% of internal motions. A careful appraisal reveals that the internal motion, in all the three molecular systems, is prominently associated with 1st and 3rd principal components. The internal motions with respect to 2nd PC are suggestive of its modest contribution to collective motion (i.e. it merely is responsible for trembling of N and C terminals whereas most of protein remains almost stable). Linear regression analysis, considered as the measure of relatedness, between first PC of each trajectory and its RMSDs was performed to find any relationship, this revealed a strong negative correlation between them and an excellent correlation coefficient (r) was obtained for all the three trajectories (i.e. 0.96, 0.73 and 0.89 for aCK1-M dCK1-M and eCK1-M respectively) (Suppl. Fig. 3). This analysis suggests that thermal diffusion motion in the protein along the first PC regulates the cooperative motion represented by the MD trajectories (Maisuradze et al., 2009).

Fig. 5. Scree plot of first twenty eigenvectors for trajectories of aCK1-M (A), dCK1-M (B) and eCK1-M (C). First 20 principal components contribute approximately 85% of total variance.


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The essential dynamics partitions the conformational spaces into an essential subspace with a few degrees of freedom in such a way that could describe the overall functional motion in the molecule. Perhaps kinases are the most important proteins that undergo large conformational changes in order to regulate various cellular processes. Conformational alterations of CK1 isoforms, directly linked to their structural fluctuations and functions, allow them to preferentially interact with their binding partners at different times or locations (Frauenfelder et al., 1991; Grant, 2010; Berendsen, 2000). Dynamics of these kinases regulates spatiotemporal modulation of function which allows the eukaryotic cells to manage so many essential cellular processes with limited number of proteins. Kinases are ubiquitous enzymes which function as the conformational switches and regulators, and are fueled by ATP binding and hydrolysis (Chou et al., 1999;

Fig. 6. Principal component analysis of MD trajectories. A 2D projection, for the trajectory of aCK1-M (A), dCK1-M (B) and eCK1-M (C) shows two conformational substates in the dynamics of each system.

Sinha and Smith-Gill, 2002; Frauenfelder et al., 2007). The essential dynamics sampling was performed with two major PCs (i.e. PC1 and PC3) to find the conformational subspaces during dynamics Fig. 6. Each distribution of dots represents the conformational subspace sampled by respective molecule (Caves et al., 1998). In analogy with RMSD profile, here essential dynamics sampling of aCK1-M (A) and eCK1-M (B) trajectories yield well defined two distinct conformational substates (CSs) (viz. first CS is constituted up to the 5th ns of simulation time and second CS exists until end of simulation), whereas the first CS of dCK1-M (b) is very broad and in itself consists of two micro-substates (viz. the first micro-substate exists up to 5th ns of simulation time, and the second micro-substate occurs between 7th and 10th ns of trajectory) the second CS is apparent and regular which appears to be similar with that of a/eCK1-M. Thus it is inferred that the conformational changes in three isoforms of CK1 are similar. Furthermore, we also conclude that the specific internal motions in the

Fig. 7. The contour map of potential energy surface along the two principal components (viz. PC1 and PC3) for the trajectories of aCK1-M (A) dCK1-M (B) and eCK1-M (C). CSs in each landscape are separated by potential energy barrier; the high energy substate (maxima) is presented by yellow color whereas the low energy substate is shown in deep blue color. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)


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proteins empower them for their biological functions. Such internal motions are responsible for different conformational changes that allow the proteins to bind with their substrates with high specificity (Stein et al., 2006). In order to validate the conformational subspaces during dynamics of CK1 isoforms, we performed potential energy surface (PES) study for each trajectory (Fig. 7). The PES is a hypersurface of potential energy of proteins as a function of conformational coordinates. At any given time point, each protein molecule exists in a specific CS and it jumps to another CS exploring the energy landscape (Frauenfelder et al., 1991). The motions of proteins, considered as soft matter can be elucidated by drawing analogy with non-biological systems, like glass (Stillinger and Weber, 1984). Since the simulation was run at room temperature (i.e. 300 K), considering the protein function is directly related to its internal motions, it is expected that protein should move through its CSs. The PES shows two clearly distinguishable CSs (viz. first corresponds to the maxima and second corresponds to the minima) in each isoform, moreover, it also authenticates that the first CS of dCK1-M is very broad and has two maxima in the PES while its second CS has only one minima analogous to a/eCK1-M. The PES indicates conformations at different simulation times have unequal potential energies and thus their stability is also different. Further, the internal motions of kinases have been recognized as essential for its functions such as biomolecular recognitions and ligand binding. It is presumed that the binding of high energy molecule (viz. ATP) to these kinases depends upon the conformational shifts. The two CS during MD simulation of these kinases are surmised as two different conformations that may exist during pre- and postphosphorylation events.

4. Conclusion The tridimensional structure of CK1-α isoform was constructed and incomplete structures of CK1-δ and CK1-ε isoforms were repaired through homology modeling. All the modeled structures were refined by energy minimization and the quality of these structures was ensured on the basis of Ramachandran plot and Z-score analytics. Based on MD simulations and PCA, we have shown that isoforms of CK1 undergo large conformational changes. Moreover, it reveals that these kinases have an intrinsic capability to sample multiple conformational subspaces despite of the bound nucleotide (i.e. ATP); meaning that, the ligand binding does not directly induce the conformational change rather shifts the pre-existing conformations. Since each substate of a protein represents its specific functional microstate, thus two major conformational substates of these isoforms are assumed to be responsible for their kinase action. Dynamics and the conformation analysis of three isoforms of CK-1 discussed can further be very useful for therapeutic benefits for the treatment of cancers of multiple origins.

Uncited references Grant et al. (2010) and Berendsen and Hayward (2000).

Acknowledgment Authors are grateful for the financial support (Grant 41-980/ 2012(SR)) to University Grant Commission (UGC), New Delhi110002, INDIA. SPS is also thankful to Dr. Bipin Singh (CCNSB, IIIT Hyderabad) for the critical reading of the manuscript and valuable suggestions.

9

Appendix A. Supporting information Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.jtbi.2015.01.032.

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