1 INTRODUCTION

Peripheral membrane proteins (PMPs) are temporarily coupled to the surface of a membrane, penetrating into the lipid layer, and can transfer from the surface of the membrane to a solution and back. The study of PMPs is important because of the pharmacological importance of many members of this family such as phospholipases [1, 2], cytochrome C [3], lipid carrying proteins [4, 5], lipoxygenases [6, 7], and acetylcholinesterases [8–10].

The formation of a PMP/membrane complex is a decisive stage of the formation of these proteins [11]. However, the study of formed complexes is complicated because coupling is temporal. In particular, well-developed methods of structural biology such as high-resolution NMR spectroscopy [12] and cryo-electron microscopy [13] are efficient for integral membrane proteins but not for PMPs. For this reason, to obtain information on the interaction of PMPs with the membrane, one should use a complex of experimental approaches [14], mass spectroscopy [15] and molecular dynamics [16] methods, and physical models [17, 18]. No one of the methods cannot provide the total picture of the interaction of PMPs with the membrane.

Molecular changes in lipids of the membrane upon its coupling with PMPs are insufficiently studied. In this work, we study how conformations of hydrophobic chains of lipids change upon the coupling of a peripheral protein on the surface of the membrane.

2 MATERIALS AND METHODS

We studied palmitoyl-oleoyl-phosphatidylcholine (POPC) lipid and secretory phospholipase А2Footnote 1 (sPLA2), which is a classical peripheral membrane protein [23]. Contacting with the membrane, sPLA2 behaves itself as all PMPs; i.e., it is coupled to the surface through a network of ion and hydrogen bonds and hydrophobic interactions. Coupling leads to the displacement of polar heads of phospholipids from the region of contact with the protein. A hydrophobic spot is formed under the protein molecule, and the bilayer in the contact region becomes thinner [24].

In this work, the data were obtained by the molecular dynamics simulation of the interaction of sPLA2 protein with the bilayer of their POPC. The structure of the protein was obtained from the Protein Data Bank (PDB identifier 1POC). Previously, we verified the molecular dynamics data experimentally: (i) the state of the membrane correlated with fluorescent spectroscopy data [24] and (ii) the orientation of the protein molecule on the surface of the membrane correlated with atomic force microscopy data [22]. The simulation was performed in two successive stages: coarse grain (CG) and full-atom simulation.

Calculations in the first stage were performed with the Gromacs package using the Martini 2.2 force field for the protein and standard lipid topology [25]. The resin bond scheme was used to hold the protein structure when generating its topology [26]. The simulation was carried out for 295 K with the parameters recommended for the calculation of protein–membrane systems with the Martini 2.2 force field [27], and the integration step was reduced to 20 fs to obtain correct data for the dynamics of aromatic groups of the protein. The aim of the first stage was to develop a molecular dynamics model of the protein coupled to the surface of the lipid membrane.

The behavior of the resulting bound state was examined in the second stage in the full atomic approximation using the Gromacs molecular dynamics package [28] with the Amber-14SB force field parameters for proteins [29], the Slipids parameterization of lipid molecules [30], and the TIP3P water model [31]. The duration of the trajectory was 500 ns. The simulation cell contained 450 POPC molecules (225 molecules in one layer) and one sPLA2 molecule.

In this work, we used the concept of sets of conformations [32], where a set of identical molecules, in this case, POPC molecules, is separated into individual sets each characterizing by the key conformation. We consider two sets. The first and second sets consist of POPC molecules contacting and non-contacting with the protein, respectively. For each POPC molecule, we considered conformations of hydrophobic chains lipids, i.e., sequences of dihedral angles that can have the trans and gosh configurations. All dihedral angles in acyl chains of lipids were calculated for all frames on the molecular dynamics trajectory. The dihedral angles in the regions of 30°–90°, 150°–210°, and 270°–330° were attributed to the gosh+, trans, and gosh– conformations, respectively. The data were averaged over the entire molecular dynamics trajectory.

3 RESULTS AND DISCUSSIONS

3.1 Coupling of sPLA2 to the Surface of the Membrane

The POPC lipid bilayer with the ferment molecule adsorbed on it is shown in Fig. 1 presenting the frame of the molecular dynamics trajectory. It is seen that the protein divaricates the polar heads of lipids. As a result, the hydrophobic spot screened from water by the protein molecule is formed on the surface of the membrane in the contact region. The interfacial binding site of the protein directly contacts with hydrophobic chains of lipids. The bilayer becomes thinner in the contact region.

Fig. 1.
figure 1

(Color online) Molecular dynamics results for the protein adsorbed on the surface of the membrane. (a) Side view. (b) Top view. (c) Top view with a hidden protein molecule. The protein is shown in green, lipid molecules are drawn in black, and phosphor atoms in lipid molecules are given in orange.

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3.2 Conformations of Hydrophobic Chains

Lipid molecules can interact or not interact with the protein. The molecules that directly contact and not contact with the protein belong to the first, I, and second, N, sets, respectively. Each element of the set N or I is an individual conformation of the chain.

For phosphatidylcholines, e.g., POPC, the number of possible conformations of the polar heads is much smaller than the number of conformations of the hydrophobic chain. For this reason, we consider below only changes in conformations of the hydrophobic chain. Hydrophobic chains of POPC are palmitic and oleic acid residues with 13 dihedral angles and 12 dihedral angles and a double bond at the middle of the chain, respectively (see Fig. 2a). Dihedral angles in hydrophobic chains of lipids can be in gosh–, gosh+, and trans configurations. The energy difference between trans and gosh configurations is 2 kJ/mol [33].

Fig. 2.
figure 2

(Color online) (a) Molecular structure of palmitoyl-oleoyl-phosphatidylcholine (POPC) and the numbering of dihedral angles in the palmitic and oleic chains. (b) Graphic representation of key conformations, i.e., the fractions of trans configurations in the (solid lines) palmitic and (dotted lines) oleic chains of the lipid. The key conformations Nk and Ik, i.e., the fractions of trans configurations in chains of lipids non-contacting and contacting with the protein are given in black and orange, respectively.

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Since trans, gosh+, and gosh– configurations are transformed to each other, the configuration of the ith dihedral angle in the ensemble of chains can be represented as the fraction fi of trans configurations of the ith dihedral angle among all hydrophobic chains in all molecules, i.e., the number of dihedral angles in the trans configuration divided by the total number of molecules in the set. Then, the set of all conformations of molecules in the set can be simply represented as the key (average) conformation. The key conformation is the sequence of the fractions fi for all dihedral angles of the lipid chain:

$$\begin{array}{*{20}{c}} 1&2&3&{...}&k \\ {{{f}_{1}}}&{{{f}_{2}}}&{{{f}_{3}}}&{...}&{{{f}_{{\text{k}}}}} \end{array}.$$

Both sets I and N are represented in the form of the respective ley conformations Ik and Nk.

The energy Econf of one key conformation, which is the energy of one hydrophobic chain averaged over the entire set N or I, can be determined by the formula

$${{E}_{{{\text{conf}}}}} = \sum\limits_i (1 - {{f}_{i}}){{E}_{{{\text{t}} \to {\text{g}}}}},$$
(1)

where Et → g ~ 2 kJ/mol is the energy of the trans–gosh transition. Since the POPC molecule consists of the palmitic and oleic hydrophobic chains, the total energy of the molecule is the sum of the energies of conformations of chains:

$${{E}_{{{\text{mol}}}}} = {{E}_{{{\text{palm}}}}} + {{E}_{{{\text{ole}}}}}.$$
(2)

The notion of the key conformation allows the comparison of the energies of lipids contacting and non-contacting with the membrane protein. The energy difference between the molecule in the contact region and that beyond it is

$$\Delta E = {{E}_{{{\text{mol}}{\kern 1pt} N}}} - {{E}_{{{\text{mol}}{\kern 1pt} I}}}.$$
(3)

The key conformations for the palmitic and oleic chains of POPC in the membrane contacting with the protein are presented in Fig. 2.

It is seen that the fraction of trans configurations decreases in the contact region. This decrease is different for different chains and different dihedral angles. The largest decrease in the fraction of trans configurations for the palmitic acid residue occurs in the middle of the chain from the fifth to the ninth dihedral angle. The fraction of trans configurations in the beginning of the chain (angles from the first to the fourth) and in its end (the twelve and thirteenth angles) is independent of the presence of the protein. The picture for the oleic acid residue is generally similar: the fraction of trans configurations decreases for chains of lipids contacting with the protein. However, the character of changes is different: the largest decrease in the fraction of trans configurations is observed in the region from the eighth to the eleventh dihedral angle.

The gosh configuration has a higher energy than the trans configuration. The decrease in the fraction of trans configurations and the increase in the fraction of gosh configurations result in the increase in the energy of the chain. The data in Fig. 2 indicate an increase in the fraction of trans configurations up to 2% in the segment of the chain.

The calculated energies of conformations of chains and molecules in the contact region of the protein with the membrane and beyond it, as well as ΔE, are summarized in Table 1.

Table 1. Conformation energies of chains in units of kilojoule per mole
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According to Table 1, the energy difference between lipid molecules inside and outside the contact region of the protein with the membrane is 0.0976 kJ/mol. In this case, the energy of the molecule inside the contact region is higher. Thus, the binding of the protein leads to the appearance of conformations with an increased energy. The difference ΔE is small. However, since several lipids are in contact with the protein, the conformation contribution to the interaction energy is the product of ΔE and the number of lipid molecules in contact with the protein, as follows from the molecular dynamics trajectory (see Fig. 3a).

Fig. 3.
figure 3

(Color online) (а) Number of lipid molecules in contact with the protein molecule along the molecular dynamics trajectory. The actual number of molecules at a given time, the mean number over the entire trajectory, and the standard deviation are shown in black, red, and orange, respectively. (b) Energy of the molecule versus the distance from the center of mass of the protein for the molecules (orange) in the membrane monolayer contacting with the protein and (black) in the monolayer opposite to the protein.

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It is seen in Fig. 3a that the number of lipid molecules in contact with the protein is \(22.3 \pm 2.5\). Correspondingly, the conformation contribution to the interaction energy of the protein with the membrane is estimated as 1.9–2.4 kJ/mol; i.e., it is comparable with kBT.

To estimate the conformation contribution to the interaction energy, we performed averaging over all lipids in the sets I and N. However, the energy of conformations of an individual molecule depends on the distance of this molecule from the protein (see Fig. 3b). Figure 3b indicates that the energy of the conformation of the lipid molecule increases noticeably in the contact region of the protein with the membrane. At the same time, the energy of the conformation hardly changes in the opposite monolayer non-contacting with the protein. The effect decreases rapidly: the energies of the conformation of molecules in both monolayers become equal already at a distance of 15 Å from the center of the protein (see Fig. 3b).

The energy of change in conformations of hydrophobic chains a part of perturbations introduced by the protein to the membrane. Other such perturbations are a change in the orientation of polar heads, breaking and formation of ion and hydrogen bonds, and rearrangement of dipole contacts. The interaction with the protein in hydrophobic chains increases the fraction of gosh configurations and thereby the energy of the chains. The binding of the PMP to the membrane, which is generally determined by the hydrophobic and electrostatic interactions, is energetically favorable. Consequently, the energy of conformations is opposite to the energy of the interaction of the protein with the membrane; i.e., the energy should be spent to change conformations. A part of the interaction energy of the PMPs with the membrane is really spent to change conformations of lipid chains. Theoretically, the resistance of the membrane is described by its elastic modulus. A change in e conformations of chains is a part of molecular mechanisms responsible for the elastic modulus of membranes. In terms of molecular biology, the energy stored in conformations of chains can be spent to the desorption of the protein from the surface of the membrane, which explains in the molecular level why the interaction of the PMP with the membrane is temporal.

4 CONCLUSIONS

Hydrophobic chains of lipids can have numerous different conformations. This property determines the capability of a lipid membrane to adapt to external impacts such as the coupling of peripheral proteins to its surface. The coupling of peripheral membrane proteins is accompanied by a change in conformations of hydrophobic chains of lipids so that the fraction of trans configurations of dihedral angles in the region of contact of the protein with the membrane decreases and, correspondingly, the energy of the chain increases.