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The stability of 3 transmembrane and 4 transmembrane human vitamin K epoxide reductase models

3 transmembrane and 4 transmembrane helices models are suggested for the human vitamin K epoxide reductase (VKOR). In this study, we investigate the stability of the human 3 transmembrane/4 transmembrane VKOR models employing a coarse-grained normal mode analysis and molecular dynamics simulation. Based on the analysis of the mobility of each transmembrane domain, we suggest that the 3 transmembrane human VKOR model is more stable than the 4 transmembrane human VKOR model.


I. INTRODUCTION
Human vitamin K epoxide reductase (VKOR) plays a critical role in generating gammacarboxyglutamate, one of the essential ingredient in blood coagulation cascade [1,2]. The amino acid sequence of human VKOR enzyme (163-residues) was identified [3,4]. Many biochemical experiments have been performed on the study of the human VKOR enzyme.
However, the X-ray crystal structure of the human VKOR enzyme is not known yet. In the absence of the X-ray crystal structure, two models for the topology of the human VKOR enzyme have been suggested: 3 transmembrane(TM) [5]/4 transmembrane(TM) [6,7] VKOR models. For the human 4TM VKOR model, it is derived from the bacterial VKOR homolog [8]. The initial TM domains of the human 4TM VKOR are defined as TM1: R12-A31, TM2:S81-L97, TM3:L105-V127, and TM4:C132-R151. On the other hand, for the human 3TM VKOR model, it is determined based on the biochemical experiments [9][10][11] and computer-aided program TOPCONS [12,13]. A schematic topology for the 3TM/4TM human VKOR models. The topology difference between the two models make the active sites, C132 and C135 (colored as yellow), locate in different positions within the lipid bilayer. The definitions of the TM domains for the human 3TM VKOR are determined as TM1: (G9-V29), TM2: (V104-L124), and TM3 (V127-W147). The most significant difference in the topology of the human 3TM/4TM VKOR models is that the N-terminus of the human 3TM VKOR model starts from the lumen while the C-terminus ends at the cytoplasm. On the other hand, for the human 4TM VKOR model, the N-terminus starts from the cytoplasm and the C-terminus ends at the cytoplasm. Figure 1 shows a schematic topology for the human 3TM/4TM VKOR model. The last two TM domains (2nd and 3rd TM domains in the human 3TM VKOR model and 3rd and 4th TM domains in the human 4TM VKOR model) show common feature in their membrane topology. The difference between the topology of the human 3TM/4TM VKOR models makes the two active sites, C132 and C135, locate in different positions inside the lipid bilayer.
Normal Mode Analysis (NMA) is an effective tool for analyzing the slowest motions of protein [14][15][16]. For the system in the equilibrium, the potential energy V can be expanded as Taylor series [17],  where η is a displacement from the equilibrium position, q=q 0 +η. 0 means the equilibrium position, q 0 in the generalized coordinate. For the oscillating system, the deviation can be expressed as where ω k is the angular frequency and δ k is the phase. And a ik is the component of the amplitude matrix A. Then, we can solve the equation in the matrix form.
A is the matrix of the oscillation amplitude.V is the matrix of the second derivatives of the potential energy, Hessian. λ is the eigenvalue matrix. The eigenvectors of the Hessian 2 correspond to normal modes. For accurate normal mode analysis for protein, it requires a full potential for all the atoms of the protein. However, it requires an expensive computational cost. To save the computational time, coarse-grained normal mode analysis (dealing with C α atoms) was developed [16]. The harmonic pair potential of the coarse-grained model, based on the elastic network model (ENM) [18], has a form where R 0 ij is the pair distance vector. And the spring constant k(r), function of the atomic pair distance, is obtained from the fitting to the Amber94 force field [19]. In this study, we analyze the mobility of TM helices of the two proposed models for the human VKOR using the normal mode analysis and molecular dynamics simulation.

A. Normal Mode Analysis
The translational movement along the axis, the rotational movement around the axis, the slide movement perpendicular to the axis towards/away from the center of the bundle, and the tilt perpendicular to the axis away from the center of bundle are defined in the web-application TMM@server [20] (insets in Figure 3). The axis of α-helix is defined as the principal axis of inertia of C α atoms. The projections are defined as [20]

B. Molecular Dynamics Simulation
We performed molecular dynamics simulation of the in-silico human 3TM/4TM VKOR model [5]. We employed the NAMD 2.8 package [21] with the CHARMM 27 force field [22] with the protein parameters incorporating the CMAP terms [5,23]. A palmitoyl-oleoylphosphatidylethanolamine lipid bilayer (POPE) was prepared with the dimension of 100Å× 100Åwith the TIP3P water model [24]. For physiological condition, we set the system to be 150 mM in NaCl environment. We performed an energy minimization over 20,000 steps by the conjugate gradient method. Subsequently, the system was heated to 310 K over 60 ps.
The particle mesh Ewald (PME) method [25] was used. Molecular dynamics simulation in the NPT ensemble (310 K, 1 atm) was performed for over 2 ns. Constant pressure (1atm) was maintained by using the Langevin piston Nose-Hoover method [26]. The MD simulation scheme was changed to the NPnTA ensemble for 60 ns simulation. and Leu108(TM2):Ile136(TM3) [12]. Figure 9 shows the hydrophobic interactions between leucine/isoleucine residues and their bond lengthes measured during 60 ns simulation. Up to 20 ns simulation, the bond lengths show dramatic changes, implying the dynamical equilibration process.

IV. CONCLUSIONS
The NMA analysis based on the elastic network model estimates the mobility of the TM helices in the translation, rotation, slide and tilt mode for the last snapshot of the 3TM /4TM VKOR models. In an alternative approach to NMA, the backbone RMSD the leucine/isoleucine residues than that of the 4TM human VKOR model.