Membrane Fluidity

The fatty acid (FA) panel considered 12 fatty acids, representative of the main building blocks of the RBC membrane glycerophospholipids and of the three FA families: SFAs, palmitic acid (C16:0); stearic acid (C18:0); MUFAs, palmitoleic acid (C16:1;9c); oleic acid (C18:1; 9c); cis-vaccenic acid (C18:1; 11c); n-3 PUFAs, (eicosapentaenoic acid (EPA): C20:5; docosahexaenoic acid (DHA): C20:6); n-6 PUFAs, linoleic acid (LA): C18:2; dihomo-gamma-linolenic acid (DGLA): C20:3; arachidonic acid (AA): C20:4; trans isomers, considering elaidic acid (C18: 1; 9t) and mono-trans arachidonic acid isomers (mono trans-C20:4; n-6).
Considering these fatty acids, different indexes were calculated [34 (link)]: Membrane fluidity index or saturation index (SI) (%SFA/%MUFA), inflammatory risk index (%Omega 6/%Omega 3), cardiovascular risk index (%EPA + %DHA) [35 (link)], PUFA balance ((%EPA + %DHA)/total PUFA × 100) [36 (link)], Free radical stress index (sum of trans-18:1 + Σ monotrans 20:4 isomers), Unsaturation Index (UI) ((%MUFA × 1) + (%LA × 2) + (%DGLA × 3) + (%AA × 4) + (% EPA × 5) + (%DHA × 6), and Peroxidation Index (PI) ((%MUFA × 0.025) + (%LA × 1) + (%DGLA × 2) + (%AA × 4) + (% EPA × 6) + (%DHA × 8)). Additionally, the enzymatic indexes of elongase and desaturase enzymes, the two classes of enzymes of the MUFA and PUFA biosynthetic pathways, were estimated by calculating the product/precursor ratio of the involved FAs.

The erythrocyte membrane ordering parameter was estimated by using a steady—state fluorescent polarization technique. The suspension of erythrocytes (2 ml of 0.05% hematocrit in 0.9% NaCl) was labelled with a fluorescent probe (DPH or TMA-DPH, respectively) at a concentration of 1 μM (10 min, 37 °C). The fluorescence measurements were carried out at 37 °C using a Perkin-Elmer LS-55 (Perkin-Elmer, UK) spectrofluorometer equipped with a fluorescence polarization device. The readings were taken at intervals of 2 s. Changes in membrane fluidity after addition of tannins in the concentration range of 2–10 µM were determined based on polarization values of the samples (r).
The polarization values (r) were calculated by the fluorescence data manager program using the Jablonski equation: $$r=\frac{I_{\mathit{VV}}-G{I}_{\mathit{VH}}}{I_{\mathit{VV}}+2G{I}_{\mathit{VH}}}$$ where I_VV and I_VH are the vertical and horizontal fluorescence intensities, respectively to the vertical polarization of the excitation light beam. The factor G = I_HV/I_HH (grating correction factor) corrects the polarizing effects of the monochromator. The excitation wavelengths were 348 nm (DPH) and 340 nm (TMA-DPH) and the fluorescence emission was measured at 426 nm for DPH and 430 nm for TMA-DPH^{78 (link)}.
Based on the data obtained, the membrane ordering parameter was calculated using the equation⁴⁷ : $$S=\frac{\sqrt{\left[1-2\left(\frac{r}{r_0}\right)+5{\left(\frac{r}{r_0}\right)}^2\right]}-1+\frac{r}{r_0}}{2\left(\frac{r}{r_0}\right)}$$ where r₀ is the fluorescence anisotropy of DPH or TMA-DPH in the absence of any rotational motion of the probe. The theoretical value of r₀ of DPH and TMA-DPH is 0.4.

The membrane fluidity of SH-SY5Y cells was measured using the lipophilic pyrene probe pyrene decanoate (PDA) in the Membrane Fluidity Kit (ab189819, Marker Gene Technologies, Inc., Eugene, OR, USA). SH-SY5Y cells were seeded onto collagen-coated 96-well black plates at 1 × 10⁶ cells/mL; treated with Aβo, Aβo + curcumin, or Aβo + GT863 for 3 h; and then stained with a fluorescent lipid reagent containing PDA. When PDA forms excimers from monomers in spatial motion, the emission spectrum of PDA shifts to red. The ratio of fluorescence emission at 400 and 470 nm from 360 nm excitation (monomer-to-excimer ratio) was measured using a Spectra Max i3 (Molecular Devices) and was used as an estimate of membrane fluidity.

The hydropathy of the guest molecule is described by considering a periodic potential of mean force $U\left(z\right)$ such as the one depicted in Figure 1b (we show only one periodicity), which corresponds to the equation
$$U\left(z\right)=\left\{\begin{array}{cc}\Delta U\hfill & \mathrm{if}\left|z\right|\le l-h\hfill \\ \Delta U+8\frac{\Delta U_b-\Delta U}{h^2}{\left(l-h-\left|z\right|\right)}^2\hfill & \mathrm{if} l-h<\left|z\right|\le l-\frac{3}{4}h\hfill \\ \Delta U_b-8\frac{\Delta U_b-\Delta U}{h^2}{\left(l-\frac{1}{2}h-\left|z\right|\right)}^2\hfill & \mathrm{if} l-\frac{3}{4}h<\left|z\right|\le l-\frac{1}{2}h\hfill \\ \Delta U_b-8\frac{\Delta U_b}{h^2}{\left(l-\frac{1}{2}h-\left|z\right|\right)}^2\hfill & \mathrm{if} l-\frac{1}{2}h<\left|z\right|\le l-\frac{1}{4}h\hfill \\ 8\frac{\Delta U_b}{h^2}{\left(l-\left|z\right|\right)}^2\hfill & \mathrm{if} l-\frac{1}{4}h<\left|z\right|\le l\hfill \\ 0\hfill & \mathrm{if} l<\left|z\right|\le \frac{a}{2}\hfill \end{array}\right..$$
In the previous formula, a is the lattice parameter, l is the total length of a lipid within the bilayer, and h is the size of the lipid head (see Figure 1). In order to set reasonable values for these parameters, we considered $a=6.65$ nm, which corresponds to fully-hydrated $L_{\alpha }$ lamellar mesophases obtained by water/dipalmitoylphosphatidylcholine mixtures at 43 °C [46 ]. Moreover, we also set $l=2.365$ nm and $h=1$ nm based on the electron-density profile computed in Ref. [47 ] for the same mixture. As for the energy parameters, $\Delta U$ is the free-energy difference between the plateaus corresponding to the lipid tails and the water region. Therefore, $\Delta U>0$ for hydrophilic molecules (such as in Figure 1b), while $\Delta U<0$ in the case of hydrophobicity. The parameter $\Delta U_b$ introduces a barrier in correspondence with the lipid heads, which can mimic the kinetic barriers associated with the permeability of the membrane; moreover, $\Delta U_b$ can be employed to introduce depletion of molecules from the lipid heads ( $\Delta U_b>0$ ) or the tendency to sit at the water/lipid interface typical of amphiphilic molecules, which is the case for many proteins ( $\Delta U_b<0$ ) [48 ]. The use of parabolic fragments in Equation (1) allows for tuning the potential between $0, \Delta U$ and $\Delta U_b$ , while ensuring that both $U\left(z\right)$ and its derivative are continuous throughout space (see Figure 1b), which avoids undesirable numerical instabilities in the simulations.
A similar approach was used to account for heterogeneity in molecular transport. To this aim, we introduced a space-dependent diffusion coefficient $D\left(z\right)$ (Figure 1c): $$D\left(z\right)=\left\{\begin{array}{cc}{D}_{lip}\hfill & \mathrm{if}\left|z\right|\le l\hfill \\ D_{lip}+2\frac{D_{wat}-D_{lip}}{w^2}{\left(l-\left|z\right|\right)}^2\hfill & \mathrm{if} l<\left|z\right|\le l+\frac{1}{2}w\hfill \\ D_{wat}-2\frac{D_{wat}-D_{lip}}{w^2}{\left(l+w-\left|z\right|\right)}^2\hfill & \mathrm{if} l+\frac{1}{2}w<\left|z\right|\le l+w\hfill \\ D_{wat}\hfill & \mathrm{if} l+w<\left|z\right|\le \frac{1}{2}a\hfill \end{array}\right..$$
In the previous formula, $D_{wat}$ and $D_{lip}$ correspond to the diffusion coefficients of the guest molecule when considered in pure water and in the lipid bilayer, respectively, while w is the thickness of the water layer in which the continuous change between $D_{lip}$ and $D_{wat}$ takes place; therefore, w accounts for the reduced mobility of water molecules in the vicinity of the lipid heads [44 (link)].
Typical values of $D_{wat}$ for nanoscopic objects are found in the range ${10}^{-10}–{10}^{-9}$ m²/s. For instance, at 25 °C, one has $D_{wat}=0.7-0.9\times {10}^{-9}$ m²/s for amino acids [49 ,50 ,51 (link),52 ,53 ], and $D_{wat}=0.5,0.7,0.8\times {10}^{-9}$ m²/s for ibuprofen [54 (link)], aspirin [55 (link)], and paracetamol [56 (link)], respectively. The value of $D_{wat}$ is expected to be dependent on temperature, T. When small temperature differences are considered (such as estimation of $D_{wat}$ at physiological temperature starting from room-temperature measurements), a simple yet effective approach to estimate the effect of T is to assume a Stokes–Einstein relation $D_{wat}=k_{B}T/\left(6\pi \eta \left(T\right)R\right)$ , where $k_B$ is Boltzmann’s constant, R is the size of the particle, and $\eta \left(T\right)$ is the temperature-dependent viscosity of water. This approach has enabled accurate predictions of transport of glucose molecules in monolinolein-based cubic phases [57 (link)]. Unless stated otherwise, in our simulations, we consider $D_{wat}=0.7\times {10}^{-9}$ m²/s.
As for the diffusion coefficient in the lipid phase, $D_{lip}$ , one expects its value to be significantly smaller than $D_{wat}$ due to the lower fluidity of the lipid membrane as compared to water. For instance, the three-dimensional self-diffusion of lipids for various monoacylglycerols with cubic symmetry has been reported to be $1.1–1.3\times {10}^{-11}$ m²/s [26 (link)], which gives values in the range $1.7–2\times {10}^{-11}$ m²/s for the lateral diffusion coefficient when accounting for the geometric constraint imposed by the minimal surface at the mid-plane of the lipid bilayer [58 (link)]. Amino acids and drugs such as the ones mentioned above are smaller than lipid molecules, so that $D_{lip}$ is expected to be somewhat larger for them. Here, we fix $D_{lip}=0.09D_{wat}$ , based on molecular dynamics simulations of paracetamol in DPPC [47 ].
Finally, the parameter w was set in accordance with experimental evidence and molecular dynamics simulations, which point to the existence of 3–4 layers of water with reduced mobility in proximity of the lipid heads [8 (link),40 ,44 (link)]. The specific value of this thickness was selected to be $w=0.96$ nm (Figure 1c), in order to ensure that $D_{wat}$ is reached exactly at $z=a/2$ , thus avoiding a discontinuity in the derivative of $D\left(z\right)$ , which would have occurred for larger values of w.