Membrane Association of the PTEN Tumor Suppressor: Molecular Details of the Protein-Membrane Complex from SPR Binding Studies and Neutron Reflection

The structure and function of the PTEN phosphatase is investigated by studying its membrane affinity and localization on in-plane fluid, thermally disordered synthetic membrane models. The membrane association of the protein depends strongly on membrane composition, where phosphatidylserine (PS) and phosphatidylinositol diphosphate (PI(4,5)P2) act pronouncedly synergistic in pulling the enzyme to the membrane surface. The equilibrium dissociation constants for the binding of wild type (wt) PTEN to PS and PI(4,5)P2 were determined to be Kd∼12 µM and 0.4 µM, respectively, and Kd∼50 nM if both lipids are present. Membrane affinities depend critically on membrane fluidity, which suggests multiple binding sites on the protein for PI(4,5)P2. The PTEN mutations C124S and H93R show binding affinities that deviate strongly from those measured for the wt protein. Both mutants bind PS more strongly than wt PTEN. While C124S PTEN has at least the same affinity to PI(4,5)P2 and an increased apparent affinity to PI(3,4,5)P3, due to its lack of catalytic activity, H93R PTEN shows a decreased affinity to PI(4,5)P2 and no synergy in its binding with PS and PI(4,5)P2. Neutron reflection measurements show that the PTEN phosphatase “scoots" along the membrane surface (penetration <5 Å) but binds the membrane tightly with its two major domains, the C2 and phosphatase domains, as suggested by the crystal structure. The regulatory C-terminal tail is most likely displaced from the membrane and organized on the far side of the protein, ∼60 Å away from the bilayer surface, in a rather compact structure. The combination of binding studies and neutron reflection allows us to distinguish between PTEN mutant proteins and ultimately may identify the structural features required for membrane binding and activation of PTEN.

: Structure of HC18. Standard SPR reflectivity curves are plots of the reflectivity as a function of incidence angle in degrees. As our SPR uses a fan-design, it samples a range of incidence angles simultaneously. 1 However, the angles are reported as pixels on the detector and a conversion fac-tor from pixels to degrees needs to be calculated for comparison of our data to the literature. This was accomplished by using glycerol:water mixtures of known refractive index on slides of known gold and chromium thickness thereby allowing for a comparison between the SPR minimum in pixels (experimental) and the SPR minimum in degrees (theoretical). 2 While the refractive index of glycerol:water mixtures are commonly tabulated in the literature and in handbooks, we were unable to find any corresponding to λ = 763.8 nm, the wavelength used in our SPR. Weighting the refractive index of water and glycerol by the respective volume fractions has been shown to be a bad estimate of the refractive index of the mixture. 3 Instead, we resorted to weighting the water and glycerol components by their respective mass fractions. At λ = 763.8 nm, the refractive index of pure glycerol is 1.46716 (Ref. 4) and that of water is 1.32972. 5 Glycerol:water mixtures were prepared ranging from 0% glycerol (by volume) to 10% glycerol in 1% increments. The mass-weighted refractive indices of these mixtures are given in Table S1.

II. Calibration of SPR Instrument
Using the Fresnel model, we can fit the SPR reflectivity curve to obtain the refractive index and thickness of each layer of dielectric medium on the glass prism. For the substrate used in this calibration measurement, the parameters are given in Table S2.  From the data given in Tables S1 and S3, we obtain the following conversion relation: This gives a relation connecting the change in refractive index and the corresponding SPR minimum in degrees. In order to calculate the conversion factor between refractive index change and the SPR minimum in pixels, we performed 3 calibration experiments detailed in Ta    From Table S4 we obtain: ∆ 1 pixel = (6.11 ± 0.08) × 10 −5 ∆n (Eq. S2) From Table S5 we obtain: ∆ 1 pixel = (6.47 ± 0.06) × 10 −5 ∆n (Eq. S3) From Table S6 we obtain: Averaging Eqns. S2, S3 and S4, we obtain the relation: From Eqns. S1 and S5, we obtain the relation: Given an SPR minimum in pixels, we calculate the absolute SPR minimum in degrees as: SPR Minimum (deg) = (63.97 ± 0.03) + (0.0067 ± 0.0001) × SPR minimum (pixels) (Eq. S7)

Relation between SPR Minimum Change and Protein Layer Thickness and Surface Density
The Fresnel model can be used to fit the refractive index and thickness of a lipid bilayer atop the thin gold film on the glass slide. However, fitting a protein layer atop a bilayer atop a substrate has sufficiently high number of parameters such that an accurate fit of the parameters is nearly impossible.
Instead, it is easier to calculate a conversion factor between SPR minimum change and protein thickness (or surface density) as observed by comparing the reflectivity curve corresponding to the bilayer with that for the bilayer with protein.
The relation between protein thickness and surface density is given by where Γ is the surface density, dprotein is the thickness of the protein layer, nprotein is the refractive index of the protein, nbulk is the refractive index of the bulk buffer and dn/dc is the change in refractive index of the protein as a function of protein concentration.
The standard value for nprotein is 1.41, for nlipid is 1.5 and for nbulk is 1.33. dn/dc = 0.187 ± 0.003 ml/g was calculated for Bovine Serum Albumin (BSA). 6 Plugging these values into Eq. S8, we obtain: where dprotein is in Å.
We can assume the same substrate parameters as in Table S2. There are at least three distinct ways to model a tethered bilayer lipid membrane (tBLM) in a slab model: 1. Single slab model: We can consider the "tether layer" (which actually contains the EOn tether and βME), plus the lipid chains and headgroups as one single slab with a thickness of d = 55 Å and index, n = 1.5.
2. Double slab model: Treat the "tether layer" and the lipid chains as a slab of d = 45 Å and n = 1.5, and the distal headgroups as a slab of d = 10 Å and n = 1.417 (assuming 50% lipid and 50% water by volume).
3. Triple slab model: Treat the "tether layer" as a slab of d = 15 Å and n = 1.442 (65% PEG and 35% water), the lipid chains as a slab of d = 30 Å and n = 1.5 and the distal headgroups as a slab of d = 10 Å and n = 1.417 (assuming 50% lipid and 50% water by volume). For each model, we plot a theoretical curve of the neat bilayer and then add increasing amounts of protein (n = 1.41). We then plot the SPR minimum as a function of protein layer thickness. We did this for all three models and also for model 1 (assuming 30 nm of gold instead of the standard 45 nm) to test the effect of gold thickness (see Fig. S1).
In all four cases, the slope obtained was approximately 20 nm/deg. This means that a change in the SPR minimum of the reflectivity profile between the bilayer and (bilayer + protein) corresponds to the addition of a 20 nm protein layer. Given the conversion relation between pixels and degrees (Eq. S7), we obtain: i.e., a 1 pixel increase in the SPR minimum corresponds to the addition of 0.134 nm of (homogeneously distributed) protein.
∆dprotein = 1 nm ⇒ ∆(SPR minimum) = 7.5 pixels (Eq. S11) i.e., the addition of a 1 nm layer of protein corresponds to an increase in the SPR minimum by 7.5 pixels.

III. Estimate of the K d from Insufficient SPR Data. Example for the Binding of the Truncated PTEN Mutant to PS-Containing Membranes
The equilibrium binding constant (Kd) can be determined with high precision if the highest concentration of protein used in the SPR experiment is sufficiently greater than the Kd. For binding of the truncated PTEN to PS containing membranes, we were limited to a maximum protein concentration of 3 µM due to aggregation. However, this concentration appeared to be sufficiently close to the Kd that we were able to develop a criterion to estimate its value and define confidence limits. Figure S3: Fits to an SPR Data Set with Insufficient Data. SPR data sets for with high protein concentrations are not available were evaluated by estimating the possible range of Kd and Bmax values. In this example, the SPR minimum change for a fictitious data point at a protein concentration of 10 µM was varied between 30 and 100 pixels (grey arrow). Two fits assuming a Langmuir adsorption isotherm shown in blue and red represent these extremal values of the fictitious data point.
The 3 µM concentration corresponds to an experimentally measured change in the SPR reflectivity minimum of 34.0 ± 0.2 pixels (as compared to the baseline bilayer signal). We added a fictitious data point at 10 µM and varied its position on the ordinate from 30 pixels to 100 pixels, both significantly larger than the 0.2 pixel standard deviation in 1 pixel increments. We then fitted each data set (that now consisted of 5 experimentally determined points and 1 fictitious data point) to determine the Kd and the quality of the fit, χ 2 (see Fig. S4).
To account for the uncertainties in protein concentration and pixel change associated with the experimental data points, a Monte-Carlo resampling method was used. 7 From the error bars for each data point, 1000 statistically independent data sets were generated any of which could have occurred given the statistical uncertainties. For each of the 1000 data sets, we varied the pixel change for the 10 µM concentration from 30 pixels to 100 pixels and calculated the Kd and χ 2 . Figure S4 shows the averaged Kd and χ 2 values for a given pixel change at 10 µM protein concentration across all 1000 fits and their uncertainties (68% confidence limits). The smallest χ 2 of 10.7 corresponds to a Kd of 3.3 µM. Again using one standard deviation, we determine bounds on Kd of 2.5 µM to 4.9 µM.     * nSLD of Cr bonding layers is found typically above the bulk value of 3.03 10 -6 Å -2 due to interdiffusion of Cr and Au. # In some cases a inter-diffusion of SiOx and Permalloy is observed, which is best described by an elevated nSLD of the SiOx. ** This value is computed from a combination of fit parameters.