INTRODUCTION

The human immunodeficiency virus (HIV) infects the cells of the immune system, leading to acquired immunodeficiency syndrome (AIDS). Mature (infectious) HIV is a spherical particle about 100 nm in diameter surrounded by a double-layered lipid membrane envelope, which is captured by the virus during the budding from the surface of an infected cell (Fig. 1a). The HIV genome is represented by two copies of the RNA molecule. The most conserved gene is the gag gene, which encodes the Gag polyprotein—the major structural protein of the virus. This polyprotein is involved in many stages of the viral life cycle, and constitutes approximately 50% of the mass of the entire viral particle [1, 2]. The Gag polyprotein is an N-terminally myristoylated polyprotein and consists of four major domains (matrix MA, capsid CA, nucleocapsid NC, and p6 domain), which are cleaved into separate proteins as the virus matures into an infectious active form, and two linker peptides (SP1 and SP2) (Fig. 1b) [2].

Fig. 1.
figure 1

(a) Schematic representation of the HIV particle; (b) schematic representation of structural elements of the Gag polyprotein.

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The matrix domain is responsible for Gag binding to the plasma membrane, where the assembly and budding of progeny virions occurs [2]. A number of studies have shown that the MA domain interacts electrostatically with the membrane via a highly basic region at its N-terminus. This region binds to the charged lipids phosphatidylserine (PS) and phosphatidylinositol 4,5-bisphosphate (PI(4,5)P2) on the inner side of the plasma membrane [3, 4]. Mutations in this region cause Gag to dissociate from the plasma membrane and relocate intracellularly in some cell types [5]. Thus, electrostatic interactions play an important role in the HIV pathogenesis [6]. In addition, studies have shown that the binding of the myristoylated MA domain to the membrane is impaired in the absence of PI(4,5)P2 suggesting a specific interaction between the protein and this lipid [7, 8]. In these works, the specificity of the interaction of Gag with PI(4,5)P2 is explained by two mechanisms: (i) it acts as an “anchor” to fix the protein in the lipid bilayer through electrostatic interactions, and (ii) it induces conformational changes in the myristoylated region of the protein that further retain Gag in the membrane through hydrophobic forces [9]. However, both PI(4,5)P2 and PS are negatively charged, and it remains unclear whether the surface charge provided by phosphatidylserine is involved in the specific membrane binding of Gag observed for PI(4,5)P2 [8].

Phosphatidylserine is abundant in various tissues of the body, and is involved in the “targeting” of proteins to cell membranes as a result of electrostatic lipid-protein interactions, which can significantly affect the physicochemical properties of the lipid bilayer [10]. Similar effects have been observed for the adsorption of certain multivalent cations with a high affinity for phosphatidylserine in membranes. For example, the binding of gadolinium cations (Gd3+) to PS alters the properties of the lipid matrix, making it more elastic during lateral compression of the monolayer, and more rigid during transmembrane compression of the bilayer [11, 12]. The simulation of membranes using molecular dynamics (MD) methods has revealed the coordination of multivalent cations with the polar heads of phospholipids, resulting in the association of 2–3 lipid molecules into nanoclusters [12]. MD methods have also shown that the binding of lysine molecules and lysine-based polypeptides to the surface of membranes containing anionic phospholipids significantly alters the network of hydrogen bonds between the phosphate groups of these lipids, which contribute to the elastic properties of the membranes [13]. It is natural to assume that both of these mechanisms can be realized when proteins bind to the membranes of living cells. The use of bioelectrochemical methods is advisable for the study of such effects, and their effectiveness has been demonstrated in the study of the interaction of many biologically active substances with lipid models of cell membranes [14].

The electrostatic nature of the adsorption of the HIV Gag protein onto lipid membranes containing phosphatidylserine has not been extensively studied. Some work has been done on individual Gag domains only. Surface plasmon resonance studies have shown that the efficiency of adsorption of MA domain onto the surface of a lipid bilayer depends on the presence of at least 20 mol % of anionic PS in the membrane [8]. Unexpectedly, not only the MA domain but also the NC domain, both free and complexed with nucleic acid, binds to the surface of membranes containing phosphatidylserine [15]. However, it is possible that results obtained for individual Gag domains do not fully reflect the membrane interactions of the entire full-length Gag polyprotein. For example, the membrane affinity of the MA domain dimer is several orders of magnitude higher than that of the monomer [6]. This suggests that the interaction of multiple Gag molecules with each other should enhance their adsorption to membranes due to the electrostatic attraction of the positively charged groups of the protein to the membrane anionic lipids [16, 17]. However, there are only a few studies that have used model systems to provide quantitative data on how Gag interacts with membranes in vitro [18, 19]. Furthermore, in all of these studies, only the role of PI(4,5)P2 has been investigated. Conflicting data on the contribution of phosphatidylserine and the possibility of Gag binding to neutral membranes have been ignored [20]. Thus, the question of the role of anionic and neutral phospholipids in Gag adsorption remains open and needs to be addressed by detailed studies of the protein interactions with membranes of different lipid compositions.

Electrostatic effects caused by the adsorption of molecules onto the surface of lipid membranes can be monitored by the classical method of electrokinetic measurements in a suspension of liposomes. This involves determining the value of the zeta potential in the hydrodynamic slipping plane [21]. Surface potential values obtained from these experiments can be compared with boundary potential measurements on flat lipid membranes of the same composition carried out by the inner field compensation (IFC) method [22]. This provides information on the thermodynamic constants of binding of molecules to the lipid bilayer, and allows the contribution of electrostatic effects to the efficiency of this interaction to be assessed [23]. For this purpose, in the present work we have chosen the approach described above to analyze the adsorption of the Gag polyprotein in a water-soluble form on neutral and phosphatidylserine-containing membranes. As a result, the binding constants of the protein with anionic phosphatidylserine and zwitterionic phosphatidylcholine were estimated, taking into account the influence of the bulk electrolyte ions on the adsorption process, and the stoichiometry of Gag binding to lipids was determined.

MATERIALS AND METHODS

Materials. Reagents used in experiments: KCl (Sigma-Aldrich, USA), HEPES (Helicon, Russia), EDTA (Life Technologies, USA), KOH (Reachem, Russia), HCl (Reachem, Russia), agar (Helicon, Russia), n-decane (Acros Organics, USA), lipids 1,2-diphytanoyl-sn-glycero-3-phosphocholine (DPhPC) and 1,2-diphytanoyl-sn-glycero-3-phosphoserine (DPhPS) (Avanti Polar Lipids, USA) in chloroform (99%, Merck, Germany) at a concentration of 10 mg/mL.

The Gag polyprotein was obtained as described in [24]. The protein lacks the myristoyl group at the N‑terminus and the p6 domain, making it water soluble. For experiments, Gag was dissolved in a buffer solution (10 mM KCl, 5 mM HEPES, and 0.1 mM EDTA, pH 7.2) immediately before each experiment, and stored at +4°C for maximum 72 h.

Formation of lipid membranes. Flat bilayer lipid membranes (BLMs) were formed at a 1 mm diameter round hole in a partition separating two chambers of a cell made of an inert hydrophobic material (Teflon) by the Müller–Rudin method [25]. In this work, uncharged BLMs were formed from DPhPC and charged BLMs were formed from a mixture of DPhPC : DPhPS 80 : 20 (mol %).

Each cell chamber was filled with a working buffer solution of 10 mM KCl, 5 mM HEPES, 0.1 mM EDTA, pH 7.2. A drop of a 15 mg/mL lipid solution in n-decane was applied to the hole in the cell to form BLM. Chloroform was first removed from the lipid stock solution under an argon stream for 30 min to form a thin film on the walls of the flask, and then the required amount of n-decane was added. Electrical measurements of the BLM were made using a pair of Ag/AgCl electrodes in contact with the working buffer in the cell chambers through salt bridges (plastic micropipette tips filled with a solution of 2% agar in 100 mM KCl). The resistance of the electrodes with the bridges did not exceed 40–50 kOhm. Membrane formation was monitored by the increase in its electrical capacitance. For electrical measurements, an AC voltage generator (output of the L780 DAC board, Lcard, Russia) was connected to the electrode on one side of the BLM, and a Keithley-427 current amplifier (Keithley, UK) was connected to the other side. The appearance of a capacitance of 1–3 nF, assuming that the membrane occupied the whole area of the hole, indicated that a bilayer membrane had been formed. During the experiment, a magnetic stirrer mixed the buffer solution in both chambers of the cell.

Liposomes were prepared using the lipid film hydration method [26]. A solution of lipids in chloroform was evaporated on a rotary evaporator (40 min at 40 mbar pressure) to obtain a thin film at the bottom of a round-bottomed glass flask. The film was then hydrated with a solution of 10 mM KCl in milli-Q water, pH 7.0, and vortexed on a BioVortex until the suspension was opalescent. The final concentration of lipids in the liposome suspension was 1 mg/mL.

Zeta potential of liposomes. The electrophoretic mobility of liposomes was measured by the dynamic light scattering using a Zetasizer II (Malvern Instruments, UK) with a PhotoCor SP correlator (USA) [23]. The electric field in the electrophoretic cell was generated by applying a voltage of 100–120 V between two platinised electrodes separated from the sample by a semi-permeable (colloidal particle-impermeable) membrane. The electric field strength was measured by briefly connecting of a pair of platinum electrodes located 5 cm apart inside the measuring cell. The polarity of the potential applied to the electrodes was changed at a frequency of 2 Hz to avoid their polarization. The electric potential in the hydrodynamic slipping plane (ζ-potential) was calculated using the Smoluchowski equation [21].

Inner field compensation method (IFC). The difference in the boundary potentials (Δφb) across the BLM was determined by the IFC method using the second harmonic of the capacitive current measured by the Stanford phase-sensitive amplifier (DSP lock-in amplifier, model SR830, USA) [22, 27]. The method is based on the ability of membranes to change their thickness in an electric field, thereby increasing their electrical capacitance. The value of the capacitance is minimal when the intramembrane field is zero, and the voltage at which it is reached is equal to the difference of boundary potentials across the BLM. In this case, the zero amplitude of the second harmonic of the capacitive current is recorded. The choice of this harmonic makes it possible to organize a feedback system that continuously monitors changes in the difference of boundary potentials and records the kinetics of adsorption of charged molecules onto one side of the membrane. All measurements were performed under low ionic strength conditions of a bulk electrolyte (10 mM KCl, 5 mM HEPES, 0.1 mM EDTA) to reduce the effects of surface charge screening and increase the resolution of the IFC method [28]. The influence of the buffer components on the ionic strength was assumed to be negligible in the calculations. In all experiments, Gag was added in a concentration range (CGag) from 10 to 200 nM to one of the two chambers of the cell, and the change in the difference of boundary potentials was monitored until a steady state was reached.

RESULTS AND DISCUSSION

Determining the Charge Density on the Membrane

We determined the charge density on the membrane (σ) consisting of charged and uncharged lipids to assess the contribution of phosphatidylserine to the total membrane surface charge. In the case of a symmetrical electrolyte, the relationship between the membrane charge density and the surface potential can be described by the Gouy–Chapman electrical double layer model [29, 30], according to equation (1). This model should be supplemented by the corresponding adsorption equation (2), as proposed by Stern [31], since ions of the bulk electrolyte can bind to the polar groups of the lipids. The following system of equations (1)–(4) for determining the membrane charge density from electrokinetic measurements can be obtained, assuming that the ion concentration near the membrane surface is described by the Boltzmann distribution (3), and the potential distribution near the charged membrane surface is described by equation (4):

$$\sigma = \sqrt {8kT\varepsilon {{\varepsilon }_{0}}C} \sinh \left( {\frac{{ze\varphi (0)}}{{2kT}}} \right),$$
(1)
$$\frac{\sigma }{{{{\sigma }_{{{\text{maxPS}}}}}}} = \frac{1}{{1 + {{K}_{{{\text{el}}}}}{{C}_{{{\text{el}}}}}(0)}},$$
(2)
$${{C}_{i}}(0) = {{C}_{i}}\exp \left( { - \frac{{{{z}_{i}}e\varphi (0)}}{{kT}}} \right),$$
(3)
$$\tanh \left( {\frac{{{{z}_{i}}e\varphi (x)}}{{4kT}}} \right) = \exp \left( { - \kappa x} \right)\tanh \left( {\frac{{{{z}_{i}}e\varphi (0)}}{{4kT}}} \right),$$
(4)

where σ is the charge density on the membrane surface, φ(0) is the membrane surface potential, φ(х) is the potential at a distance x from the membrane surface, Ci and Ci(0) are the bulk and surface concentrations of the electrolyte ions, respectively, \(\kappa = \sqrt {\frac{{2{{e}^{2}}C}}{{\varepsilon {{\varepsilon }_{0}}kT}}} \) is the reverse Debye screening length, Kel is the binding constant of potassium ions, σmaxPS is the maximum surface charge density on a membrane containing phosphatidylserine, Сel(0) is the surface concentration of potassium ions, ε and ε0 are dielectric constants in solution and in vacuum, respectively, zi is the charge number of electrolyte ions, е is the electron charge, k is the Boltzmann’s constant, Т is the absolute temperature.

The value of the membrane surface potential can be estimated from the results of the zeta potential in the hydrodynamic slipping plane by electrokinetic measurements. The distance x from the Helmholtz plane to the slipping plane, experimentally determined to be 0.2 nm for phospholipid membranes, is widely used for the quantitative analysis of electrokinetic measurements in liposome suspensions [21, 32]. For a suspension of multilamellar liposomes prepared from a mixture of DPhPC : DPhPS 80 : 20 (mol %), we determined the dependence of the ζ-potential on the ionic strength of the electrolyte. The surface potential values calculated from equation (4) are shown in Fig. 2. An approximation of the experimental data using equations (1)–(3) yielded the surface charge density of the liposomes (σ = –(2.5 ± 0.2) × 10–6 C/cm2) and the value of the binding constant for potassium ions of the bulk electrolyte (Kel = 1.00 ± 0.04 M–1). The values obtained are in agreement with the literature [32, 33].

Fig. 2.
figure 2

Dependence of the surface potential of liposomes from a mixture of DPhPC : DPhPS 80 : 20 (mol %) on the ionic strength of the KCl solution. The theoretical curve is plotted by combining equations (1)–(3).

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The charge density on the membrane was also determined by measuring the boundary potentials difference on a flat BLM with the same lipid composition. We formed a BLM on a hole in the partition of a Teflon cell in a 10 mM KCl solution, then gradually increased the ionic strength of the electrolyte on one side of the membrane by sequential addition of a 1 M KCl solution and recorded the boundary potentials difference using the IFC method. The dependence of the boundary potential difference on the increasing ionic strength of the electrolyte in one chamber of the cell is shown in Fig. 3a. This dependence was rearranged to calculate the surface charge density on the BLM as follows. The value of the boundary potentials difference for each KCl concentration was obtained by summing the effects of all previous salt additions to that chamber of the cell (Fig. 3b). Zero corresponded to the initial value of the surface potential (–64 mV) in the bulk electrolyte (10 mM KCl) before the ionic strength increase, obtained from electrokinetic measurements. From this dependence, the values of the surface potential on the BLM were calculated, and the charge density on the membrane was determined (Fig. 3c). An approximation of the experimental dependence of the surface potential on the electrolyte concentration by a combination of equations (1)–(3) gave the value σ = –(2.3 ± 0.1) × 10–6 C/cm2 and the potassium binding constant Kel = 1.0 ± 0.1 M–1. Figures 2 and 3 are the results of a single experiment performed three times independently to evaluate the parameters of the theoretical model and their errors. Thus, the results of the measurements obtained by the IFC method and the electrophoretic mobility of liposomes gave identical (within error) values for σ of membranes prepared from a mixture of phosphatidylserine and phosphatidylcholine. The values we obtained for the surface charge density of the membranes are consistent with those reported in literature for liposomes containing 20 mol % phosphatidylserine [33–35].

Fig. 3.
figure 3

Determination of the surface charge density of the BLM made from a mixture of DPhPC : DPhPS 80 : 20 (mol %). (a) Change of the boundary potential difference resulted from the sequential addition of 1 M KCl into the one of chambers of the experimental cell. The arrows (from left to right) correspond to changes in the ionic strength of the solution to 20, 30, 50, and 80 mM. (b) Dependence of the growth of the boundary potential difference at the BLM on the KCl concentration. (c) Dependence of the surface potential at the BLM on the KCl concentration. The theoretical curve is plotted by combining equations (1)–(3).

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Gag Adsorption onto Bilayer Lipid Membranes

The Gag polyprotein is in almost constant interaction with lipid membranes during the viral replication cycle [36]. Some researchers have suggested that this interaction occurs through the MA domain as a result of conformational rearrangements in the protein and incorporation of the N-terminal myristoyl group into the lipid bilayer [37]. However, a study of the adsorption kinetics of full-length Gag onto lipid membranes showed that the binding was possible regardless of the presence or absence of myristate, and that Gag adsorption was more effective on surfaces containing charged phospholipids [18]. This result confirms the dependence of protein affinity for membranes on electrostatic interactions. It is clear that the presence of a hydrocarbon chain in the structure of a protein molecule that can be immersed into the lipid bilayer, should not affect the electrostatic attraction. To answer the question of the physicochemical mechanisms of the Gag protein binding to lipid membranes, we carried out experiments to study the adsorption of this protein, lacking a myristoyl group, on lipid membranes of different compositions. The need to consume large amounts of protein to obtain data over a wide range of concentrations made it difficult to study the Gag binding to the lipid matrix in a suspension of multilamellar liposomes. Therefore, it was decided to further investigate the adsorption of Gag using the IFC method in a system with flat BLMs, which allows working with smaller amounts of the protein at a similar molar ratio of protein to lipids. During the development of the IFC method, the reliability of the results obtained has been demonstrated by analyzing the adsorption of small molecules and ions [23, 27, 38]. It has subsequently been shown to provide important results when studying the adsorption of different macromolecules [13, 35, 39].

Since an adsorbed charged protein alters the boundary potential of the lipid monolayer to which it is attached, any asymmetric addition of protein to the lipid bilayer also alters the transmembrane electric field. The resulting change in the transmembrane field can be measured by determining an external field that cancels out the asymmetry. The IFC method uses this principle to record the kinetics of the protein adsorption process. Addition of the Gag protein to one side of a planar phospholipid membrane results in a rapid increase in the membrane boundary potential difference (Δφb), with an initial slope proportional to the bulk protein concentration (Fig. 4). As the boundary potential difference reaches a steady state, the curve reflects the kinetics of Gag adsorption to the lipid bilayer.

Fig. 4.
figure 4

Kinetics of changes of the boundary potential difference across the BLM when Gag added to the one side of the membrane at time zero. BLM was made from DPhPC in the buffer solution of 10 mM KCl, 5 mM HEPES, 0.1 mM EDTA, pH 7.2. Gag bulk concentration is 100 nM (solid curve) and 200 nM (dashed curve).

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We constructed adsorption isotherms (Fig. 5) on charged and uncharged membranes in a biologically relevant concentration range (up to 500 nM in the cytoplasm of the cell [40]) based on the obtained dependencies of the change in the boundary potential difference on the bulk concentration of Gag. Each point on the plots corresponds to a steady-state value for a given concentration, averaged over 3–5 independent sets of experiments. With the addition of 10 to 200 nM Gag to one side of the zwitterionic DPhPC membrane, the boundary potential difference changed from 3 ± 2 to 23 ± 2 mV (Fig. 5, triangular symbols) with increasing bulk protein concentration (CGag). The data obtained indicate that the adsorption of Gag on an uncharged lipid membrane is in principle possible. In addition, positive values of the boundary potential difference indicate a positive charge of the protein molecule on the membrane. This suggests that the ability of Gag to bind to lipid bilayers goes beyond mere electrostatic attraction and that hydrophobic interactions play an important role.

Fig. 5.
figure 5

Growth of the boundary potential difference upon adsorption of the Gag protein onto the surface of a lipid membrane of DPhPC (triangles) and DPhPC : DPhPS 80 : 20 mol % (squares) measured by the IFC method. Each point corresponds to the steady-state value of the boundary potential difference. The range of the Gag concentrations in solution is from 10 to 200 nM. The measurement error was obtained as the standard deviation of 3–5 independent experiments.

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In infected cells, Gag targets to an inner monolayer of the plasma membrane that is enriched in negatively charged phosphatidylserine and PI(4,5)P2. Its MA domain is thought to interact with the membrane through electrostatic attraction, with possible specific protein-ligand binding to PI(4,5)P2 [41]. To date, full-length Gag protein adsorption to lipid bilayers containing PI(4,5)P2 has been well studied [18]. However, the electrostatic nature of the adsorption of Gag on lipid membranes containing phosphatidylserine but not PI(4,5)P2 has not been analyzed, and only a few data are available for an isolated MA domain [8]. At the same time, studies have shown that at least 20 mol % PS in the membrane allows this domain to bind effectively [8]. We obtained the adsorption isotherm of Gag on a lipid membrane from a mixture of DPhPC : DPhPS 80 : 20 mol % to evaluate the interaction of Gag with membranes containing phosphatidylserine (Fig. 5, square symbols). The experimental conditions and the range of Gag concentrations were similar to those described above for the DPhPC membrane. The difference in the boundary potentials varied from 3 ± 1 to 40 ± 9 mV depending on the bulk Gag concentration. The obtained Δφb values confirm that Gag binds more efficiently to the membrane containing the anionic lipid compared to the uncharged bilayer.

Our data were analyzed using the Langmuir model to determine the thermodynamic binding constants of Gag to each of the two types of phospholipids. This model has previously been used to describe the adsorption of the influenza A virus M1 protein at low concentrations [28], demonstrating the fundamental possibility of analyzing the adsorption of proteins with a simple model. The Gag adsorption isotherm on a phosphatidylcholine membrane is described by equation (5), which reflects the change in membrane surface charge during the protein adsorption.

$$\frac{\sigma }{{{{\sigma }_{{{\text{maxGag}}}}}}} = \frac{1}{{1 + {{K}_{{{\text{PC}}}}}{{C}_{{{\text{Gag}}}}}(0)}},$$
(5)

where KPC is the binding constant of Gag to phosphatidylcholine, σmaxGag is the maximum surface charge density generated by the adsorbed protein on phosphatidylcholine, СGag(0) is the surface concentration of Gag.

Only the difference in the membrane potential due to protein adsorption, but not the number of bound molecules, can be determined from experiments using the IFC method. According to the Gouy–Chapman model (1), the relationship between surface charge and potential can be considered linear if the change in potential due to protein adsorption is less than kT/e (approximately 25.4 mV). The potential measured in our experiments on DPhPC was less than this value over the whole range of Gag concentrations. The justification of the linear approximation can be easily calculated. If the hyperbolic sine argument is 0.5, the function exceeds the argument value by about 4%. This means that even at a potential of 25.4 mV, the error of the linear approximation does not exceed 5%. This value is within the accuracy of measurements using the IFC method. We therefore assumed that the measured boundary potential differences are directly proportional to the amount of protein adsorbed per unit membrane area. That is, we can take σ = A∆φb and σmaxGag = A∆φbmaxGag, where ∆φbmaxGag corresponds to the complete coverage of the membrane with protein, and A is some constant, and use ∆φb and ∆φbmaxGag instead of σ and σmaxGag, respectively, in equation (5).

For anionic lipid membranes, it is important to consider the possibility of bulk electrolyte ions adsorbing on binding sites. The Gouy–Chapman equation (1) considers the case of a symmetrical electrolyte. A more general dependence on the composition of the solution can be expressed using the Graham equation (6) [42]. This allows us to take into account the presence of different types of ions in the electrolyte.

$${{\sigma }^{2}} = 2kT\varepsilon {{\varepsilon }_{0}}{{\Sigma }_{i}}{{C}_{i}}\left[ {\exp \left( { - \frac{{{{z}_{i}}e\varphi (0)}}{{kT}}} \right) - 1} \right].$$
(6)

In this case, the Langmuir model equation with a stoichiometry of one adsorbate per lipid molecule takes the form of the competitive adsorption equation (7) [43] of the studied protein and the electrolyte monovalent cation.

$$\begin{gathered} \sigma = \frac{{\alpha {{\sigma }_{{{\text{maxPS}}}}}\left[ {\left( {{{z}_{{{\text{Gag}}}}} - 1} \right){{K}_{{{\text{PS}}}}}{{C}_{{{\text{Gag}}}}}(0) - 1} \right]}}{{1 + {{K}_{{{\text{el}}}}}{{C}_{{{\text{el}}}}}(0) + {{K}_{{{\text{PS}}}}}{{C}_{{{\text{Gag}}}}}(0)}} \\ + \,\,\frac{{\left( {1 - \alpha } \right){{\sigma }_{{{\text{maxGag}}}}}{{z}_{{{\text{Gag}}}}}{{K}_{{{\text{PC}}}}}{{C}_{{{\text{Gag}}}}}(0)}}{{1 + {{K}_{{{\text{PC}}}}}{{C}_{{{\text{Gag}}}}}(0)}}, \\ \end{gathered} $$
(7)

where α is the fraction of charged phospholipid in the membrane, σmaxPS is the maximum surface charge density on a membrane composed entirely of negatively charged phosphatidylserine, KPS is the binding constant of Gag to phosphatidylserine, zGag is the charge number of Gag.

It was therefore necessary to solve the system of equations (3), (6) and (7) in order to calculate the binding constants of the Gag protein with phosphatidylcholine and phosphatidylserine separately, taking into account the adsorption of potassium ions of the bulk electrolyte. The following parameters were selected. The maximum charge density (binding sites on the membrane) σmaxPS is assumed to be –11.5 × 10–6 C/cm2 for a 10 mM KCl solution. This is based on the calculation that for the membrane used in the experiment with 20 mol % DPhPS the value σ = –(2.3 ± 0.1) × 10‒6 C/cm2. The value of σmaxGag was determined as 0.9 × 10–6 C/cm2 according to equation (1) within the low potential approximation (φ(0) < kT/e) at ∆φbmaxGag = 37 ± 3 mV. The binding constant for the potassium ions of the bulk electrolyte is assumed to be 1 M–1. Since the charge number of Gag remains an unknown parameter, we considered several alternatives for zGag (from 1 to 3) and showed that only a value equal to 1 can better describe the experimental data (Fig. 6). The intrinsic binding constants of Gag with these parameters were found to be KPC = 8 × 106 M–1 for phosphatidylcholine and KPS = 3 × 106 M–1 for phosphatidylserine. The KPC value we obtained is in the order of magnitude of the results of previous studies for full-length Gag carried out on flat BLMs by recording the intensity of the second harmonic in the layer of adsorbed protein [18]. The effective binding constant to phosphatidylserine \(K_{{{\text{PS}}}}^{{{\text{eff}}}}\), taking into account the electrostatic contribution exp[eφ(0)/kT], was 37.2 × 106 M–1. This is also in good agreement with the value of the binding constant previously obtained for the MA domain of the Gag protein by surface plasmon resonance refractometry [8], but without attempting to assess the contribution of electrostatic interactions separately.

Fig. 6.
figure 6

The surface potential of the DPhPC : DPhPS 80 : 20 (mol %) membrane as a function of the Gag concentration, approximated by equations (3), (6) and (7). The theoretical curves are plotted for the Gag charge number (zGag) from 1 to 3.

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The values of the binding constants obtained were in the same order of magnitude, which led us to the conclusion that the adsorption of Gag onto the membrane was a complex process. It consists of a combination of electrostatic and hydrophobic interactions of the protein with the lipid matrix. It is important to note that in our studies we used the Gag protein lacking myristate at the N-terminus. However, the affinity of the protein for the uncharged membrane was found to be high. This suggests that, regardless of the presence of the myristoyl group, electrostatic and hydrophobic interactions contribute equally to the binding of the protein to the lipid matrix. We can conclude that the intrinsic binding constants of Gag to lipid membranes are determined by the area per lipid molecule, similar for phosphatidylcholine and phosphatidylserine [33], rather than a specific interaction with phosphatidylserine. In this case, the presence of a charge on the lipid contributes to an additional electrostatic attraction of the protein to the membrane, increasing the surface concentration of the protein near the negatively charged membrane, interpreted as a higher effective binding constant.

CONCLUSIONS

The Gag polyprotein is the major protein of the human immunodeficiency virus and is involved in several steps of the viral replication cycle. By interacting with the plasma membrane of an infected cell, Gag initiates the formation of new viral particles. In this work, we studied the binding of the Gag protein to model lipid membranes using electrochemical methods to better understand the physicochemical mechanisms of this interaction. Using the inner field compensation method, we obtained Gag adsorption isotherms on uncharged and negatively charged lipid membranes containing phosphatidylserine. The binding constants for zwitterionic phosphatidylcholine and anionic phosphatidylserine were calculated from the experimental data. The results of the boundary potential difference measurements showed that the presence of 20 mol % phosphatidylserine in the lipid bilayer enhances the interaction of Gag with the membrane compared to an uncharged bilayer. The fundamental possibility of Gag adsorption onto neutral bilayers indicates the role of hydrophobic forces in the protein-lipid interaction, in addition to specific and electrostatic forces. The contribution of hydrophobic interactions is confirmed by the values of the binding constants for both types of phospholipids. These were found to be almost identical. Thus, the binding of the Gag polyprotein to the lipid matrix is a complex process involving not only electrostatic forces of attraction, but also hydrophobic interactions determined by the area per lipid molecule. The surface charge of the membrane only affects the change in protein concentration in the vicinity of the membrane. Furthermore, the presence of myristate in the protein structure is not critical for such interactions as previously thought [3, 37].