Ligand's Partition to the Lipid Bilayer Should Be Accounted for When Estimating Their Affinity to Proteins

Abstract

Ligand-protein interactions are usually studied in complex media that also contain lipids. This is particularly relevant for membrane proteins that are always associated with lipid bilayers, but also for water-soluble proteins studied in in vivo conditions. This work addresses the following two questions: (i) How does the neglect of the lipid bilayer influence the apparent ligand-protein affinity? (ii) How can the intrinsic ligand-protein affinity be obtained? Here we present a framework to quantitatively characterize ligand-protein interactions in complex media for proteins with a single binding site. The apparent affinity obtained when following some often-used approximations is also explored, to establish these approximations' validity limits and to allow the estimation of the true affinities from data reported in literature. It is found that an increase in the ligand lipophilicity or in the volume of the lipid bilayer always leads to a decrease in the apparent ligand-protein affinity, both for water-soluble and for membrane proteins. The only exceptions are very polar ligands (excluded from the lipid bilayer) and ligands whose binding affinity to the protein increases supralinearly with ligand lipophilicity. Finally, this work discusses which are the most relevant parameters to consider when exploring the specificity of membrane proteins.

Keywords: binding affinity; ligand exclusion; ligand sequestration; lipid-protein ratio; membrane proteins; partition coefficient; protein specificity.

Figure A1

Dependence of the amount of ligand associated with the lipid bilayer (plot (A)), in the aqueous medium (plot (B)), and bound to the protein (plot (C)), with the total ligand concentration. The system includes a water-soluble protein with M_W = 50 kDa and a total concentration of [P_T] = 10 μM (corresponding to V_P = 4.2 × 10⁻⁴V_T), to which the ligand binds with the intrinsic affinity for the protein ($K_{\mathrm{eq}}^{{\mathrm{L}}_{\mathrm{W}}}$) of 10⁶ M⁻¹ and for a ligand partition towards the lipid bilayer ($K_{\mathrm{PLb}}^{{\mathrm{L}}_{\mathrm{W}}}$) equal to 10³; in the absence of a lipid bilayer, and in the presence of increasing volumes of the lipid bilayer as indicated in the figure.

Figure A2

Effect of ligand lipophilicity on the equilibrium constants for the distribution between the aqueous phase, the lipid bilayer, and the membrane protein, assuming that the intrinsic affinity of the ligand to the protein is unchanged ($K_{\mathrm{eq}}^{{\mathrm{L}}_{\mathrm{W}}}$ = 10⁶ M⁻¹, left plots), that the relative affinity for the lipid bilayer and for the protein is unchanged ($K_{\mathrm{PP}}^{{\mathrm{L}}_{\mathrm{Lb}}}$ = 1, middle plots), or that the affinity for the protein increases supralinearly with ligand lipophilicity ($K_{\mathrm{PP}}^{{\mathrm{L}}_{\mathrm{W}}}={\left(K_{\mathrm{PLb}}^{{\mathrm{L}}_{\mathrm{W}}}\right)}^2$ = 1, right plots); for = 1 μM, M_W = 50 kDa, and different values of V_Lb: 0.1% (plots (A–C)), 1% (plots (D–F)), and 10% (plots (G–I)).

Figure 1

Kinetic schemes for the equilibrium distribution of the ligand between the aqueous medium, a protein soluble in the aqueous medium (case (I)) or in the lipid membrane (case (II)), and the membrane lipid bilayer. The association of the ligands to the protein is considered to occur to a single and well-defined binding site (saturable binding), while a partition (non-saturable) is considered for the association with the lipid bilayer.

Figure 2

Dependence of the protein saturation with ligand ([L_P]/[P_T]) with the total ligand concentration, for a protein soluble in the aqueous phase with M_W = 50 kDa and a total concentration [P_T] =10 μM (corresponding to V_P = 4.2 × 10⁻⁴ V_T, $K_{\mathrm{eq}}^{{\mathrm{L}}_{\mathrm{W}}}$ = 10⁶ M⁻¹, and $K_{\mathrm{PLb}}^{{\mathrm{L}}_{\mathrm{W}}}$ = 10³; in the absence of a lipid bilayer and in the presence of increasing lipid concentrations as indicated in the plots. The lines are the best fits neglecting the sequestration of the ligand by the lipid bilayer, considering either the concentration of ligand in the aqueous medium, Equation (6) (plot (A)) or the total ligand concentration, Equation (7) (plot (B)). The residuals of the best fit are shown in the bottom plots.

Figure 3

Dependence of the apparent binding affinity on the fractional volume of the lipid bilayer; when considering that the ligand is either in the aqueous medium or associated with the protein ($K_{\mathrm{eqApp}}^{{\mathrm{L}}_{\mathrm{W}}}$ Equation (6), plot (A), and when assuming large excess of ligand ($K_{\mathrm{eqApp}}^{{\mathrm{L}}_{\mathrm{T}}}$ Equation (7), plot (B). The parameters considered in the simulations were: $K_{\mathrm{eq}}^{{\mathrm{L}}_{\mathrm{W}}}$ = 10⁶ M⁻¹, and $K_{\mathrm{PLb}}^{{\mathrm{L}}_{\mathrm{W}}}$ = 10³, for different protein concentrations, as indicated in the plots. The line is the prediction from Equation (8).

Figure 4

Schematic representation of the ligand equilibrium distribution between the lipid bilayer and a membrane protein for the case of ligand-protein binding from the aqueous medium (IIa) or from the lipid bilayer (IIb). The equilibria indicated in black correspond to paths that may be followed by the ligand, while the equilibrium in grey results only from the impositions of the thermodynamic cycle.

Figure 5

Effect of the volume of the lipid bilayer on the equilibrium association of ligand with a protein with M_W = 50 kDa, P_T = 1 μM and $K_{\mathrm{eq}}^{{\mathrm{L}}_{\mathrm{W}}}$ = 10⁶ M⁻¹ for different ligand lipophilicity, as indicated in the figure. The variation of the apparent binding affinity is shown in the left plots (A,D,G), the fraction of ligand in the aqueous medium (continuous lines) and in the lipid bilayer (dashed lines) is shown in the middle plots (B,E,H), and the protein saturation with ligand is shown in the right plots (C,F,I); for [L_T] = 1 μM (light colors) and 10 μM (dark colors).

Figure 6

Effect of ligand lipophilicity on the equilibrium constants for the distribution between the aqueous phase, the lipid bilayer, and the membrane protein, assuming that the intrinsic affinity of the ligand to the protein is unchanged ($K_{\mathrm{eq}}^{{\mathrm{L}}_{\mathrm{W}}}$ = 10⁶ M⁻¹, plot (A)), that the relative affinity for the lipid bilayer and for the protein is unchanged ($K_{{\mathrm{P}}_{\mathrm{P}}}^{{\mathrm{L}}_{\mathrm{Lb}}}$ = 1, plot (B)), or that the affinity for the protein increases supralinearly with ligand lipophilicity ${\left(K_{{\mathrm{P}}_{\mathrm{P}}}^{\mathrm{LLw}}=\left(K_{\mathrm{PLb}}^{\mathrm{LLw}}\right)\right)}^2$ = 1, plot (C)); for P_T = 1 μM, M_W = 50 kDa, and V_Lb = 0.1%).

Figure 7

Effect of ligand lipophilicity ($K_{\mathrm{PLb}}^{{\mathrm{L}}_{\mathrm{W}}}$) on the apparent affinity ($K_{\mathrm{eqApp}}^{{\mathrm{L}}_{\mathrm{W}}}$) for different values of the intrinsic affinity ($K_{\mathrm{eq}}^{{\mathrm{L}}_{\mathrm{W}}}$) of binding to a protein in the presence of a lipid bilayer. The colored slabs correspond to a given value of $K_{\mathrm{eq}}^{{\mathrm{L}}_{\mathrm{W}}}$ (see scale on the right), the value that would be obtained for $K_{\mathrm{eqApp}}^{{\mathrm{L}}_{\mathrm{W}}}$ is the intercept of a horizontal line with the y-axis (exemplified by the dashed line at $K_{\mathrm{eqApp}}^{{\mathrm{L}}_{\mathrm{W}}}={10}^6$). The volume occupied by the protein was considered negligible, and the volume of the lipid phase was 0.1% (plot (A)), 1% (plot (B)), and 10% (plot (C)).