The adsorption of prothrombin to phosphatidylserine multilayers quantitated by ellipsometry

We investigated by means of an automated ellipso-meter the adsorption of prothrombin from a buffer solution by multilayers of L4z0/L4zO-and 18:1/18:1-phosphatidylserine (PS) stacked on chromium slides. In this instrument thickness and refractive index of the adsorbed phospholipid and proteins are monitored continuously. T\no equations are derived to relate the mass of stacked phospholipids and the mass of protein adsorbed to the thickness and refractive index. These equations are based upon the Lorentz-Lorenz relation among the molar refractivities, refractive indices, and the densities of binarSr rnixtures.

The Adsorption of Prothrombin to Phosphatidylserine Multilayqrs Quantitated by Ellipsometry* (Received for publication, July 6, 1982) Peter A. cu5pers$, Jan w. corsel, Marie P. Janssen, Jos M. M. Kop, wim Th.Hermens, and H. Coenraad Hemker$ !rym the Depqrtrnent of Biophysics and the $Department of Biochemistry, [Jniuersity of Limburg, M aastr icht, T he N etherlands We investigated by means of an automated ellipsometer the adsorption of prothrombin from a buffer solution by multilayers of L4z0/L4zOand 18:1/18:1phosphatidylserine (PS) stacked on chromium slides.In this instrument thickness and refractive index of the adsorbed phospholipid and proteins are monitored continuously.
T\no equations are derived to relate the mass of stacked phospholipids and the mass of protein adsorbed to the thickness and refractive index.These equations are based upon the Lorentz-Lorenz relation among the molar refractivities, refractive indices, and the densities of binarSr rnixtures.
Experimental validation of these equations is performed by measuring stacked multilayers of known mass of phosphatidylserine and the adsorption of [r25I] albumin and [slllprothrombin on these multilayerJ.
-Using these equations we measured the dissociation constants Ka and the number of binding sites za of prothrombin.Values of Ka -0.15 x 10-8 u arrd,nb = !22molecules of PS,/molecule of prothrombin were observed for di Cra,o PS and values of K6 = 0.45 x l0-8 rvr and n6 = 54 molecules of PS/molecule of prothrombin for di Crs,r PS.These data compare well to data obtained by other methods available in the Eterature.
Several crucial steps in the activation sequence of blood coagulation occur at phospholipid-water interfaces (1).In order to allow a quantitative description ofthese reactions it is essential to know the binding parameters of the enz5,'rnes and proenz5rmes involved at these phospholipid surfaces.To determine these protein-lipid interactions different techniques have been used, such as gel filtration, light scattering, fluorescence quenching, and measurement of surface radioactivity (2)(3)(4)(5)(6).
In this paper we present quantitative automatic ellipsometry as a new technique by which the adsorption process of proteins on phospholipid surfaces can be studied.As a model for the phospholipid surfaces we use phospholipid monoor multilayers which are stacked on a reflecting chromium surface by the dipping technique of Blodgett-Langmuir (7).The optical constants ofthese layers are measured before, during, and afber the interaction with the proteins.From these measurements the amount and density of the protein and lipid in the protein-lipid complex can be calculated directly.
* The costs of publication of this article were defrayed in part by the payment of page charges.This article must therefore be hereby marked "aduertisemenl" in accordance with 18 U.S.C.Section 1734 solely to indicate this fact.
Staching of Monolayers or Multilayers-Stacking was done with a preparative Langmuir trough (Lauda, Type FW-1) according to the method of Blodgett and Langmuir (7).Unless mentioned otherwise the trough was filled with double distilled water and 5 pnr CaCIz.On this aqueous subphase a monomolecular fiLm of phospholipids is spread by adding 100 pl of a solution containing =2 mg of phospholipid/ml of chloroform and the surface pressure is held constant at 40 dyne/cm.A chromium-coated glass slide is mechanically dipped into this trough and subsequently redrawn at a speed of 2 mm,/min.A double layer of phospholipid is deposited on the slide at each repeated dip.The surface arealmolecule of phospholipid was determined on this trough at collapse pressure.The exact quantity of phospholipid spread on the trough was determined by phosphorus analysis (11).In this way it was possible to stack phospholipid layers with an exactly known mass.
Validation of the Lorentz-Lorenz Equations-This validation was performed by using stacked phospholipid layers of known mass and by using radioactive proteins.The phospholipid layers were measured in air and in buffer.The validation using the proteins was performed in the following way.Chromium-coated glass slides were stacked with phospholipid multilayers and placed in a cuvette fiIled with buffer.The protein was added to the cuvette.After adsorption the cuvette was repeatedly rinsed with a volume of buffer 10 times that of the cuvette in order to avoid errors due to radioactive proteins in the adhering water.The cuvette was removed and the protein was desorbed from the slide with a 1 nr HCI solution and the amount of radioactivity was counted.Adsorptions of [3H]prothrombin and [r25[ albumin to di Cra,o PS1 were performed at pH 5 to avoid desorption during the change of the content of the cuvette.With di Cre,, PS, protein desorption was sufficiently slow to allow measurement at pH 7.5.

Deterntination of the Equilibrium
Constanf-To study the adsorption of prothrombin on di Cu,o PS, we stacked a double layer of di Cra,o PS on the chromium slide.This slide was put in the cuvette filled with 0.05 na Tris-HCl buffer, pH 7.5, and 10 mrvr Ca2*, 0.1 u NaCI.In order to obtain maximal adsorption of prothrombin, the slides had to be conditioned at 40-50 oC for a few minutes.Prothrombin was adsorbed at 37 "C.The protein concentrations used varied between 0.1 and a0 p.g,/rnl.The adsorption of prothrombin to di Cra,r PS was done under the same conditions as for di Crn,o PS except for the conditioning, which"in this case had no influence on the amount of prothrombin adsorbed.

Ellipsometra-The
ellipsometer is an optical instrument that measures the changes in the polarization oflight due to reflection (cf, Fig. 1).These changes are influenced by the presence of a thin film Jf substance on the reflecting surface.The refractive index z and thickness d of, for instance, an adsorbing layer of protein can be measured at short intervals (1-10 s) because the positions of the polarizer and analyzer are monitored.The instrument used is a modified Rudoloh & Sons ellipsometer Type 43303-200 E. The instrument is automated by computer-controlled stepping motors on the two polarizers indicated in Fig. 1 as the polarizer (P) and the analyzer (A).The measurement consists of finding the positions ofp and A correspond_ ing to minimal transmission of light to the photodiode.A complete description of the instrument is given in Refs.12 and 18.The method of computation is based on Refs.14 and 1b.It can be summarized as follows.The ratio ftp/.R", where Ro is the reflection coefficient for light polarized parallel to the plane ofincidence and.R" is the reflection coefficient for light polarized perpendicular to the plane of incidence, is given by Rp/ R" : tan ip.exp(lA) ( where f and A can be directly determined from the readings o{ respectively, A and, P and r : r/-1.n and d of phospholipid layers stacked on chromium slides were analyzed according to the system presented in Fig. 2. The reflection coefficients.Ro and rR" are depend_ ent upon the angle of incidence dr, the wavelength of light I, the refractive indicas r?.y h2, and 23, and the thickness dz.In fact Equation I can be written (16) as where C1, Cz, and Ce are complex functions of the refractive indices.
V and A and D: -4rinz J= @ril;6,/Ad"t^ (B) The value of zr is determined by refractometry and the (complex) value of zs is determined ellipsometrically for the chromium slide in buffer, before it is coated with phospholipid.Substituting these values, and an arbitrary (real) value for n2, in Equation 2 wil glneraly yield a complex value for dz.The correct value for dz must however be real, so Equation 3 is solved by an iterative procedure in which z: is adjusted such that the complex part of d.z is minimized.
Proteins adsorbed on phospholipid were analyzed according to the system presented in Fig. 3. Equations 2 and B remain valid 6ut the complex functions Ct Cz, and G now also depend upon D3 and d:.Values of nz and.d,a are determined by ellipsometric measurement before the protein is added to the cuvette.
Calculation of the Adsorbed Mass frotn the Refractiue Ind.ex and Thickness of an Adsorbed Layer-The Lorentz-Lorenz relation for the refractive index z of a mixture of substances can be written as (17) f(n): n+nb GT u@P + r\ From Formula 6 it follows that the molecular weight, the mblar refractivity, and the partial specific volume ofthe adsoibed or stacked molecular species have to be known in order to obtain m from d and o":M.N-Mn2-r ' An'+2 Molar Refractiuity-The molar refractivity of a molecular species can in principle be obtained from the known data of its constituent material.Using the different values of the molar refractivities of the atoms or atom groups (Table I), we calculated the molar refractivities of the different compounds that are used from their molecular structures (17).Knowing this molar refractivity it is easy to calculate the M/A or A/M vaJtes for the mass formulas.In order to calcr:late the M/A for the proteins, we first calculated the M/A values of the different amino acids and then calculated t}re M/A values of the proteins by taking the weighted average of their amino acids.If part of the protein consisted of carbohydrate we included their calculated M/A vahtes in our calculations.Calculated values of the M/A values of proteins were checked with data on albumin solutions of different densities and refractive indices known from the literature (19).The M/A for albumin thus calculated was 4.12, whereas the value calcu-Iated from data in the literature was 4.14.No data are available on the refractive index as a function of prothrombin concentration because of the large quantities that are needed for such experiments; so for prothrombin we calculated M/A : 4.23 from the amino acid composition (20).
Partial Spectfic Volumes-The values of the partial specific volumes of the proteins were taken from the literature (Table I).For phospholipids only a few data are available (21) and we determined the partial specific volumes in the following way.From the change in area of the monomolecular film on the Langmuir trough the quantity of adsorbed phospholipid per cm' was calculated.The thickness of this layer was measured in air by ellipsometry and, based on the high refractive index of the layers, we assumed that the water content of these stacked phospholipid layers on chromium in air was too low to influence the thickness significantly.This assumption is supported by the validity of the one-component formula (ci below) and also by direct observations that stacked lipid layers in air do not contain any water (22).The partial specific volume was calculated according to the following relation thickness v2o:;;t;ff The thicknesses of these stacked layers are given in Table III.The calculated partial specific volumes are shown in Table II.
Accuracy of Ellipsornetric Measurernents and Mass Calculation-In Fig. 4 the registration of ellipsometer readings during a prothrombin adsorption on 4 layers of di Crs,r PS on chromium is shown.The total change in analyzer and polarizer values during protein adsorption is about 0.9" for the polarizer and 0.6o for the analyzer.These changes correspond to an adsorbed mass of about 0.30 1tg/cm".
As illustrated in Fig. 5 Frc. 5.The thickness, the refractive index, and the mass of the adsorption of Fig. 4 as a function of time. of 0.02-0.04" in polarizel and analyzer readings (cf FiS. 4) results in considerable variation in calculated thickness and refractive index.However, this is not a random scatter.A high incidental value of calculated thickness corresponds with a low value of the refractive index and vice versa.This explains why the adsorbed mass of protein can be calculated with much mote accr.rracy then either refractive index or thickness (cf Fig. 5).This sensitivity of calculated values of  All values given are mean t standard deviation.Phospholipid layers are stacked as described under ..Materials and Methods'" Buffer, 0.05 rvr tis-HCl, pH 7.5, 10 mnr CaClr, 0.1 il Naol.prothrombin adsorption on 8layers of di Cra'o PS: prothrombin concentration, 26 t s/m1,0.05!r Hepes, prr s. protruo---lL adsorption on g layers of d1cre,r lj;i:..j-T*11^""i"^",11.,11:"?gl_c-lj1.0.bb^y rTs-.H^cl_;n_?i,ib -.; c;Ai;, 0.1 u riacr.Arbumin adsorption on 8 layers of di Cu,o: albumin concentration, 20 p4/rnl, O.OS r ff"f]"q pH-S.thickness and refractive index to experimental scatter in p and, A readings is dependent on the specific optical properties of the system under study.It is much less, for instanci, in eipeiiments with stacked multilayers of PS alone.

_
Calculation of Adsorbed Mass from the Amount of di Cu1 PS and di CBi PS Deposited-Total adsorbed *u." *u, calculated for 12 stacked monolayers of di Cra,o pS and di Cre,r PS and compared with the quantities of phospholipid dis;: pearing from the Langmuir trough.The results are shown in Table III.Values of the refractive index, the thickness per layer, the mass calculated by the two-component formula, and the-mass calculated by the one-component formula are given as the mean values + standard deviation.If we compare the values of the phospholipid layers measured in air with the val.ues measured in buffer we observe an increase in thickness and a decrease in refractive index for both phospholipids when they are in buffer, indicating swelling by penetiation of water.
The results of the mass calculation with the different mass formulas show that for the layers measured in air the results obtained with the one-component formula correspond best with the directly determined mass measured on the trough, _ Frc. 7. Scatchard plot.Ratio for the equilibrium values ofprothrombin surface concentration micromoles/cm, to its free corrcenirution micromoles/cm3 against the surface concentration micromoles/ cm'.Lines through the data points are least squares lines.O, di Crer PS; *, di Cra,o PS. whereas the layers measured in buffer are better calculated by the two-component formula.

Quantitation
of [r2slJAlbumin and fHJprothrombin-Calculations of adsorbed mass of protein based on the onecomponent and the two-component formulas were compared with direct estimates of adsorbed radioactivity.
Adsorptions of [3H]prothrombin on 8 layers of di Cra.oPS and 8 layers of di Cre,r PS and adsorption of 1125l1dbumin on 8 layers of di Cra,o PS are shown in Table III.This table shows a considerable variation in refractive index and thickness among differ-bound 1o-6 pmoilcm2 ent experiments.If we look at the results of thertwo formulas we see that the mass in some of the experiments should be calculated by the one-component formula and in other experiments by the two-component formula.To find criteria for using one of these formulas, the calculated mass divided by the directly determined mass is presented in Fig. 6 as a function of the refractive index.This figure shows that ihe mass should be calculated by the two-component forrnula if the refractive index value is between buffer values n : 1.3335 and z : 1.5-1.6,depending on the substance adsorbed' For refractive indices higher than z : 1.5-1.6 we have to use the one-component formula.
Adsorption of Prothrombin to di Cun PS and di Cre,r PS-To determine the dissociation constant and the number of binding sites of prothrombin to di Crn,o PS and di Cie,r PS we adsorbed prothrombin to these layers (0.1-40 pglml) at different concentrations.Fig. 7 presents the Scatchard plot of prothrombin adsorptions.We obtain two different sets of data depending upon the phospholipid used.This results in a Ka of prothrombin for di Cra,o PS of Ka : 0.15 x-10-" mol/liter and number of binding sites n : 3.08 X 10-o pmol,/cm', which corresponds to 122 mol of PS,/mol of prothrombin' The values for the di Cre,r PS-prothrombin interaction axe Ka: 0.45 x 10-e mol/liter and number of binding sites n : 5.2 x 10-6 p.mol/cm2, which corresponds to 54 mol of PS,/mol of prothrombin.

DISCUSSION AND CONCLUSIONS
Calculation of Adsorbed Mass-Calculations of adsorbed mass of protein should be done by two different formulas depending on the value ofthe refoactive index.As long as the refractive index ofthe adsorbed layer is between the value of pure buffer and pure protein or pure phospholipid we have to use the formula derived for the mixtures.The one-component formula shoutd be used however if we are dealing with pure substances.This formula also is applicable for values of the refractive index which are higher than calculated for the pure substance.The existence of these high refractive indices can only partly be explained by the experimental scatter in the measruements (see "Materials and Methods").These inaccuracies cannot explain discrepancies like a refractive index of n : I.46 + 0.02 for adsorption of prothrombin on di Cre,r PS and a refractive index of n :1.90 + 0.20 for adsorption of prothrombin on di Cu,o PS.It is presently assumed that refractive indices that are higher than the refractive index of the pure components indicate interactions between the adsorbant and the adsorbing molecules that are more complicated than simple apposition' One might think of penetration of the protein into the lipid, sMnking or swelling of the lipid layers, etc.The validation of the formulas also shows that the assumption of ideal behavior of the protein solution, even for very high concentrations, is justified.This result was previously found for solutions with protein concentration as high as 40Vo p.t9t"--(23, 24') n iefractive index and density studies.This ideal behavior also means that the refractive index increment of these proteins is a constant at all concentrations.The good correlation between calculated mass and the radioactive labeling protein mass for prothrombin and albumin justifies the calculation of the value Zt Ut,a.from the amino acid composition.As shown in Table III.the refractive index ofthe stacked phospholipids is lower in buffer than in air.This indicates that water molecu-Ies penetrate the phospholipid layer' In stacked phospholipid iuy"tt " water gradient was found with fluorescent probes (22).Tine good results of the mass calculation mean that it is also possible to determine the partial specific volume of the adsorbed or stacked substances by ellipsometry'  (25), the two areas are the same magnitude, suggesting a monolayer.As di Cre'r PS has a lower surface charge than di Ctr'o PS these differences found indicate that the negative charge is probably not the only factor that is responsible for the prothrombin phosphatidylserine interaction.
In the present study binding experiments with prothrombin were performed on pu-re PS phospholipid layers and in the concentration range between 0.1-40 1t'g/rr:i of prothrombin.Our method is advantageous in that the binding of prothrombin to phospholipid using light scattering (3,4) cannot be performed in the lower range of these protein concentrations and cannot be studied for pure PS because of aggregation of vesicles in the presence of Ca2+.In contrast, it is not possible to measure prothrombin adsorption at concentrations exceeding =5 pglml with the Langmuir trough technique with radiolabeled proteins (5) because the phospholipid layer is solubilized at higher prothrombin concentrations.
Achnouleclgnrents-We are indebted to Dr' G. Willems for his mathematical support and to Jose Govers for her prothrombin preparations.

Frc. 6 .
Mass calculated, with the one-component formula a1d the two-component formula, divided by the direct determined psss measured on the Langmuir trough or by radioactivity presented as a function of the reftactive indei.*. one_ component formula; O, two-component formula.
Adsorption of Prothrombin to Phosphatidylserine by Ellipsonxetry Binding Parameters of Prothrornbin-Direct comparison of our data with those found in the literature is impossible because our results are obtained with s5mthetic prrre compounds whereas binding parameters found in the literature are obtained with mixtures of s1'nthetic compounds or inhomogeneous biological preparations, and in systems in which protein adsorption onto micelles is measured in the presence of Ca2*, where PS cannot be used because of aggregation of the micelles.The adsorption of prothrombin to di Cte,t PS gives results comparable with the results of Lecompte and Miller (5) who used ox brain PS which is mainly composed of di Cre,r PS and found values of n : 6.2 x 10-12 mol/cm2 and Ka: 0.I2 x 10-7 to 0.8 x 10-8 mol/liter.In the concentration range of0.1-40 pg/rnl, no indication for a biphasic adsorption as suggested by Lecompte and Miller was found however.To obtain maximal adsorption of prothrombin on di Cra,o PS Iayers, the stacked layers had to be heated in buffer for several minutes at 50 oC.This heating was not necessary for the adsorption on di Cra,r PS.A possible explanation for this discrepancy can be the fact that di Cre,r PS layers are stacked above the phase transition temperature whereas the di Cra,o PS layers are stacked below this temperature.On heating di Cra,o PS layers in the buffer, a change in-the layers is observed at about 38 oC depending on pH and Ca'* concentration.Even after conditioning the slides, adsorption ofprothrombin to di Cuo PS is only 6OVo of ttre amount adsorbed on the di Cre,r PS surface.If we compare the number of phospholipid molecules,/ prothrombin molecule we find n : 122 di C14 0 PS/prothrombin and n:54 di Cre,r PS/prothrombin.These values give an area/prothrombin molecule of 5300 A' and 3200 4'z, respectively.Comparing the areas occupied with the cross-sectional area of the prothrombin molecule