Human Fibrinogen Adsorption on Positively Charged Latex Particles

Aug 26, 2014 - These experimental data reveal a new, side-on adsorption mechanism of fibrinogen on positively charged surfaces and confirmed the decis...
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Human Fibrinogen Adsorption on Positively Charged Latex Particles Paulina Ż eliszewska,† Anna Bratek-Skicki,*,† Zbigniew Adamczyk,*,† and Michał Cieśla‡ †

J. Haber Institute of Catalysis and Surface Chemistry, Polish Academy of Sciences, Niezapominajek 8, 30-239 Cracow, Poland M. Smoluchowski Institute of Physics, Jagiellonian University, Reymonta 4, 30-059 Cracow, Poland

‡

ABSTRACT: Fibrinogen (Fb) adsorption on positively charged latex particles (average diameter of 800 nm) was studied using the microelectrophoretic and the concentration depletion methods based on AFM imaging. Monolayers on latex were adsorbed from diluted bulk solutions at pH 7.4 and an ionic strength in the range of 10−3 to 0.15 M where fibrinogen molecules exhibited an average negative charge. The electrophoretic mobility of the latex after controlled fibrinogen adsorption was systematically measured. A monotonic decrease in the electrophoretic mobility of fibrinogen-covered latex was observed for all ionic strengths. The results of these experiments were interpreted according to the three-dimensional electrokinetic model. It was also determined using the concentration depletion method that fibrinogen adsorption was irreversible and the maximum coverage was equal to 0.6 mg m−2 for ionic strength 10−3 M and 1.3 mg m−2 for ionic strength 0.15 M. The increase of the maximum coverage was confirmed by theoretical modeling based on the random sequential adsorption approach. Paradoxically, the maximum coverage of fibrinogen on positively charged latex particles was more than two times lower than the maximum coverage obtained for negative latex particles (3.2 mg m−2) at pH 7.4 and ionic strength of 0.15 M. This was interpreted as a result of the side-on adsorption of fibrinogen molecules with their negatively charged core attached to the positively charged latex surface. The stability and acid base properties of fibrinogen monolayers on latex were also determined in pH cycling experiments where it was observed that there were no irreversible conformational changes in the fibrinogen monolayers. Additionally, the zeta potential of monolayers was more positive than the zeta potential of fibrinogen in the bulk, which proves a heterogeneous charge distribution. These experimental data reveal a new, side-on adsorption mechanism of fibrinogen on positively charged surfaces and confirmed the decisive role of electrostatic interactions in this process. Initial information concerning fibrinogen’s dimensions was obtained by Hall, Slayter,5 and others.6−8 They established that the molecule is linear, and has a trinodular shape. The total length of the molecule was 47.5 nm. The two end nodules are spherical and their diameter was equal to 6.5 nm. The domain in the middle has a diameter of 5 nm. These three nodules are connected by rods, which have a diameter of 1.5 nm. Similar fibrinogen molecule dimensions were observed in numerous atomic force microscopy (AFM) studies.9−15 From these experimental data it was shown that the fibrinogen molecule is anisotropic. The length-to-width ratio of the molecule exceeds 10 and is related to its biological function as an important polymerization compound in the blood clotting process initiated by thrombin.16−20 It is important to mention that in these studies the dimensions of the Fb molecule were obtained under vacuum or dry conditions. Under these conditions the molecule changes its conformation to a collapsed one. Indeed, in the recent work21 it was experimentally and theoretically confirmed using the bead model that the fibrinogen molecule assumes various conformations in electrolyte solutions at different pH and ionic strengths. At an ionic strength of 0.15 M and pH 7.4 it was established that the molecule had a semicollapsed

1. INTRODUCTION The adsorption of proteins to a charged surface is an essential aspect of the cascade of biological reactions, which take place at the surface between a synthetic material and the biological environment. Definitely, impact studies of whole blood or plasma proteins with surfaces of artificial materials, which is of vital interest in a variety of biomedical applications, would be the most valuable. In biological systems a mixture of proteins, which are typically encountered, are too complicated to enable definite conclusions to be drawn. Since this is experimentally not feasible, an alternative approach is to untangle the general adsorption mechanism, separate the components involved, and to examine the simpler systems obtained this way. Therefore, understanding protein adsorption is necessary for the development of efficient analytical methods and advanced drug delivery systems. One of the most important proteins is human plasma fibrinogen. This protein has received much attention because of its important biological role in the regulation of thrombosis, and hemeostasis.1,2 The fibrinogen molecule consists of three polypeptide chains: Aα, Bβ, and γ. These chains are connected in the middle through disulfide bridges which form a central nodule. The Aα chain consists of 610 amino acids, the Bβ chain contains 460 amino acids, and the γ chain has 411 amino acids. The molecular mass of the fibrinogen molecule is equal to 338 kDa.1−3 Detailed primary chemical and crystallographic structures of fibrinogen have been recently discussed in ref 4. © 2014 American Chemical Society

Received: June 30, 2014 Revised: August 20, 2014 Published: August 26, 2014 11165

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2. MATERIALS AND METHODS

conformation. The molecule has a heterogeneous charge distribution with the negative charge mainly located at the core part of the molecule and the positive charge located at the end part of the Aα chains. Because of its significance the adsorption of fibrinogen onto various solid/electrolyte interfaces has been investigated by a variety of experimental methods such as ellipsometry,22 TIRF,23 AFM,24 WDS, QCM,25 streaming potential,26 etc. However, there are only a few experiments concerning fibrinogen adsorption on colloid particles.27,28 This is in contrast to the vast number of literature data pertinent to analogous problems of albumins, immunoglobulins (antibodies), and other protein adsorption on polymeric particles.29−38 For example in ref,39 the role of ionic strength in the adsorption of fibrinogen on polystyrene latex particles at pH 7.4 was systematically studied as a function of ionic strength. The electrophoretic mobility measurements were performed to control the progress of protein adsorption under in situ conditions. The coverage of the protein was determined by AFM measurements using the depletion concentration method without the centrifuging step. It was revealed that the maximum coverage of fibrinogen on latex determined by this method varied between 1.9 and 3.2 mg m−2 for 10−3 and 0.15 M NaCl concentrations, respectively. Adsorption of fibrinogen on positively charged colloid particles has not been studied in the literature; however, the work of Brash et al.40 is worth mentioning. This work investigated the dynamic aspects of the interactions between fibrinogen molecules and the tree-model polyelectrolyte complex (one neutral, one negatively charged, and one positively charged) formed on glass tube surfaces. The authors used radiolabeled proteins to monitor the adsorption process. They observed that in the plateau region of the isotherm, the exchange between the interface and the solution takes place at two different rates. It was explained that in the adsorption process, three populations of fibrinogen have to be taken into account: rapidly exchanging, slowly exchanging, and nonexchanging. For positively charged surfaces it was shown that the percentage of fast and slow exchanging molecules is oppositely different than for adsorption on the neutral and negatively charged surfaces. This behavior was explained as a result of two markedly different relaxation times. However, no quantitative studies concerning the mechanism of fibrinogen adsorption were presented. Therefore, the main goal of this paper is to systematically evaluate fibrinogen adsorption on positively charged latex particles at pH 7.4. Most attention was given to quantitatively determine the maximum coverage as a function of ionic strength. The progress of protein adsorption was observed by the electrophoretic mobility measurements. The coverage of adsorbed Fb molecules was determined by AFM measurements of its residual concentration. The experimental data were interpreted according to the random sequential adsorption model generalized to account for the lateral electrostatic interactions between adsorbed molecules. In this way, one can unequivocally confirm the purely side-on adsorption mechanism of fibrinogen that has not been observed before. This has a significance for basic science. A practical aspect of this work is the possibility of developing a method for preparing stable fibrinogen monolayers of a wellcontrolled coverage and a specific orientation of the molecules. This side-on orientation allows one to study interactions of immobilized fibrinogen molecules with other proteins (antibodies) and low molecular weight ligands.

2.1. Experimental Section. Human blood plasma fibrinogen (fraction I, type IV) was purchased from Sigma (F4753). The powder contains 65% protein, 25% sodium chloride, and 15% sodium citrate. The purity of the fibrinogen solution was checked by using the dynamic surface tension method. The concentration of fibrinogen was determined by using Bicinchoninic acid (BCA) Protein Assays.41 By diluting the stock solution various concentrations of fibrinogen solutions (0.1−5 mg L−1) were prepared. Usually the ionic strength was changed by the addition of NaCl, and the pH was regulated by the addition of NaOH or HCl. To avoid specific adsorption of ions, buffers were not used. The MiliporeElix 5 instrument was employed to purify water used in the experiments. Remaining reagents used in the experiment were not purified and were purchased from Sigma−Aldrich. The temperature at which the experiment was performed was equal to 298 ± 0.1 K. A positively charged, surfactant free, amidine latex used in our experiments was purchased from Invitrogen. This latex had a nominal size of 800 nm and a concentration equal to 3.7%. Mica, which was used as a substrate for the fibrinogen absorption was purchased from Continental Trade. The dynamic light scattering (DLS) method was used to determine the diffusion coefficient of latex particles and fibrinogen molecules. The laser doppler velocimetry (LDV) technique was used to determine the microelectrophoresis of bare latex particles, fibrinogen, and fibrinogen-covered latex particles. The margin of error of these measurements was ±2% for fibrinogen solutions and ±5% for latex particles covered by various amounts of fibrinogen. The concentration depletion method described previously42 was used to determine the residual concentration of Fb after adsorption on latex. This method was proven to be accurate and it was used because the spectrophotometric method becomes insensitive for fibrinogen concentrations below 5 mg L−1. This method consists of a few steps: fibrinogen-covered latex particles suspension, after the adsorption process, is transferred to the diffusion cell. Next, a few mica sheets are vertically immersed in the suspension. The adsorption time was 30 min. Afterward, the fibrinogen-covered mica are rinsed a few times (usually for 30 seconds) using an electrolyte of the same pH and ionic strength as was used for fibrinogen adsorption on latex particles. The mica sheets with the adsorbed fibrinogen molecules are observed by the atomic force microscopy. The number of fibrinogen molecules are counted from 10 to 20 equal-sized areas chosen randomly. The count precision was more than 95% and the total number of fibrinogen molecules was between 500 and 1000. Precise variance tests were also performed to prove that the surface concentration of adsorbed molecules was uniform over the entire surface area of mica. 2.2. Theoretical Modeling. The theoretical modeling of fibrinogen monolayer formation on latex particles was performed according to the random sequential adsorption (RSA) approach developed in refs 43 and 44 for quantifying irreversible adsorption proteins (ferritin) on flat interfaces. In these calculations the specific interactions among protein molecules were neglected, and their shape was approximated by a circular disk. Afterward, the RSA model was used for calculating the kinetics, the maximum (jamming) coverage, and the monolayer structure of anisotropic particles.45−47 In recent publications,48,49 RSA calculations were also applied for predicting the jamming coverage of fibrinogen under various orientations. However, in none of these works were the effect of the curvature of the interface and the lateral interactions among adsorbed particles considered. The basic rules of the Monte Carlo simulation scheme based on the RSA approach are as follows: (i) a virtual particle (molecule) is created, and its position and orientation are selected randomly with a probability depending on the interaction energy, (ii) if the particle fulfills the predefined adsorption criteria, it deposits irreversibly and its position is not changed during the simulation process, (iii) if the deposition criteria are violated, a new, uncorrelated attempt is made. 11166

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Table 1. Electrophoretic Mobilities, Zeta Potentials (Calculated from the Henry’s Model) and Charge Densities of Latex and Human Serum Fibrinogen, pH 7.4a

a

Footnotes, d1 = 6.7 nm, d2 = 5.3 nm, d3 = d4, φ = 56o (pH = 7.4). The values for σ0 and Nc were determined from the equations:

σ0 =

⎛ eζ ⎞ (8εkTnb)1/2 ⎟, sinh⎜ ⎝ 2kT ⎠ 0.1602

Nc =

3πη df μ 0.1602 e

Typically, two deposition criteria are defined: (i) there should be no overlapping of the virtual particle and there should not be any previously adsorbed particles and (ii) there should be a physical contact of the particle with the interface. The RSA method despite its simplicity is a very useful tool for efficiently producing populations of a high number of molecules Np (often exceeding 105). Additionally, this method is efficient for molecules of anisotropic shapes having various geometry. In this work, adsorption of fibrinogen on latex particles was theoretically studied using the bead model B (see Table 1), previously used for describing adsorption at flat and negatively charged interfaces.26 In this approach, the fibrinogen molecule is approximated by a string of 23 colinear spheres having various diameters. The two external spheres have diameters of 6.7 nm and the central sphere has a diameter of 5.3 nm. This gives the cross-section area of the core part of the molecule in the side-on orientation equal to 128 nm2. The side arms are approximated as straight sequences of 12 beads of equal size, and their diameter is 1.5 nm. These arms form the angle φ with the core part of the fibrinogen molecule. Partial charges denoted by q1, q2, q3 are attributed to various parts of the fibrinogen molecule (see Table 1). These charges are calculated on the basis of the electrophoretic mobility measurements as discussed later on. The model molecules were adsorbed according to the above RSA scheme on a homogeneous sphere whose diameter exactly matched the dimension of the latex particles used in adsorption experiments. The lateral interactions among molecules were accounted for by using the Yukawa (screened Coulomb) pair potential, summing up contributions from various spheres. On the other hand, the electrostatic interactions of the protein with the latex surface were assumed to be of the square well (perfect sink) type.

Typically, in one simulation run, 1500 molecules were generated. Therefore, to improve the statistics, averages from ca. 50 independent runs were taken, with the total number of particles exceeding 70000. This ensures the relative precision of the simulation at better than 99.5%. The primary parameter derived from these simulations was the average number of molecules adsorbed on latex particles calculated as a function of time. By extrapolating this dependence to infinite time using the procedure previously described49,50 one obtains the maximum number of molecules adsorbed on the latex particles. Consequently, the surface concentration of the protein is Np/ΔS (where ΔS = πdl2/4 is the surface area of the latex particle of the diameter dl) and the dimensionless coverage is calculated from the equation

Θ = SgNp/ΔS

(1)

where Sg is the characteristic cross-section area of the protein molecule. Knowing Np, commonly used for the interpretation of experimental data dimensional coverage is calculated from the dependence

Γf = (M w /Av)Np

(2)

where Mw is the molar mass of fibrinogen and Av is the Avogadros’s constant.

3. RESULTS AND DISCUSSION 3.1. Latex and Fibrinogen Characteristics in the Bulk. The diffusion coefficient of the latex particles for various ionic strengths was determined by DLS as described above. On the basis of the diffusion coefficient values the hydrodynamic 11167

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diameter of particles was calculated using the Stokes-Einstein dependence. It was 860 ±15 nm, for 10−3 M, 830 ±10 nm for 10−2 M and 815 ±10 nm for 0.15 M. The electrophoretic mobility of latex particles μe was measured using the LDV microelectrophoretic technique as described above, and the zeta potential was calculated using the Henry’s equation. It was determined that the zeta potential of latex at pH 7.4 was 67, 80, and 32 mV for NaCl concentration of 10−3, 10−3, and 0.15 M, respectively. Moreover, as can be seen in Figure 1, the zeta potential of latex remains positive for pH up to 10.5, hence no isoelectric point is observed.

Figure 2. Dependence of the electrophoretic mobility and zeta potential (right axis) of human serum fibrinogen on pH: (1) I = 10−3 M, (2) I = 10−2 M, (3) I = 0.15 M. The solid lines denote the fits of experimental data.

where η is the dynamic viscosity of the solvent (water). The number of electrokinetic charges per molecule Nc can be calculated by knowing Q, and considering e to be 1.602 × 10‑19 C. It this way it was calculated that at pH 7.4, Nc = −11, −7, and −4, for NaCl concentrations of 10−3, 10−2, and 0.15 M, respectively (see Table 1). It should be mentioned that lower values of −17, −12, and −7 were previously reported in ref 42 for the bovine fibrinogen at the same pH of 7.4. 3.2. Fibrinogen Adsorption on Latex Particles. Adsorption of fibrinogen was studied by monitoring changes in the electrophoretic mobility (zeta potential) of latex particles induced by this process. The experimental procedure was as follows:39 (i) zeta potential of bare latex particles in suspensions whose concentration cl was equal to 40 and 60 mg L−1 was measured, (ii) fibrinogen covered latex particles were formed in situ by filling the cell with the fibrinogen suspension whose concentration cf was between 0.1 and 5 mg L−1 (usually for 600 seconds), (iii) the latex suspension was purified by using a filtration membrane and the electrophoretic mobility of fibrinogen covered latex was measured using the microelectrophoretic method. This procedure was proved to be reproducible, and it enables a direct determination of the zeta potential changes as a function of the concentration of fibrinogen added to the latex suspension. The nominal coverage of fibrinogen adsorbed on latex particles is calculated by using the following formula

Figure 1. Dependence of the electrophoretic mobility and zeta potential (right axis) of the A800 latex on pH: (1) I = 10−2 M, (2) I = 10−3 M, (3) I = 0.15 M. The solid lines denote the fits of experimental data.

Knowing the zeta potential, the electrokinetic charge of latex particles σ0 is calculated from the Gouy−Chapman relationship.51,52 In this way one obtains σ0 = 0.040, 0.17, and 0.21 e nm−2 for the NaCl concentrations of 10−3, 10−2, and 0.15 M, respectively, where e is the elementary charge equal to 1.602 × 10‑19 C. These data are collected in Table 1. The DLS and microelectrophoretic techniques were also used for measuring the diffusion coefficient and the electrophoretic mobility of fibrinogen molecules. For pH 7.4 and the range of ionic strength listed above, the average diffusion coefficient of fibrinogen molecules at the bulk concentration of 500 mg L−1 was 2.2 × 10−7 cm2 s−1 (for T = 298 K). This gives 22 nm as the hydrodynamic diameter of fibrinogen denoted by df that was calculated using the Stokes−Einstein dependence. Additionally, the electrophoretic mobility μe of the fibrinogen molecules was measured as a function of pH for fixed values of ionic strength. These results are shown in Figure 2. As can be seen, the isoelectric point of fibrinogen (defined as the pH value where its electrophoretic mobility vanishes) is 5.8 which agrees with previous data reported in the literature.42 Accordingly, for pH > 5.8, the electrophoretic mobility of fibrinogen becomes negative, assuming −0.944 μm cm (Vs)−1, −0.565 μm cm (Vs)−1 and −0.302 μm cm (Vs)−1 for NaCl concentrations of 10−3, and 0.15 M, respectively, and pH 7.4. These values correspond to the zeta potential of fibrinogen molecules equal to −17, −9.8, and −4.5 mV, respectively (calculated using the Henry’s model). Knowing the electrophoretic mobility, the electrokinetic charge per molecule Q (expressed in Coulombs) can be calculated from the Lorenz−Stokes equation Q = 3πηdf μe

Γf = 10−3vsc f /S l

(2)

where Γf is the coverage of fibrinogen on latex particles expressed in mg m−2, vs is the volume of the suspension mixture, cf is the initial concentration of fibrinogen in the suspension after mixing with the latex, and Sl is the surface area of latex expressed in m2, given by Sl = 6clvs /dlρl, where ρl is the latex density equal to 1.05 × 103 kg m−3. In this way, one can analyze adsorption runs expressed as the dependence of the latex zeta potential ζ on the nominal fibrinogen coverage, Γf calculated from eq 2. Experimental results obtained in this way are shown in Figure 3 for pH 7.4 and NaCl concentrations of 0.15 M. As can be seen, ζ abruptly decreases with the nominal fibrinogen coverage Γf attaining values close to zero at Γf > 1 mg m−2. Afterward, for fibrinogen coverage above 1.5 mg m−2 the changes in the zeta potential of latex become practically

(1) 11168

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this method. Specifically, in these measurements, one determines by a direct counting procedure the average number of fibrinogen molecules per unit area of mica Nfm at images acquired from AFM. It should be mentioned that the deposition of latex particles on mica during the time of this experiment (15 min) is negligible because of their low concentrations and low diffusion coefficients compared to the fibrinogen molecules. Under diffusion transport conditions, for a fixed adsorption time, the fibrinogen surface concentration Nfm increases proportionally to the bulk concentration of the fibrinogen in the suspension cf according to the formula28,42 Nfm = 2(Dt /π )1/2 c fr = C c fr

(3)

where cfr is the concentration of fibrinogen in the suspension and C = (Dt/π)1/2 is the constant, which can be calculated because the adsorption time and diffusion coefficient of fibrinogen are known. As shown in refs 28 and 42 eq 3 is valid for a broad range of Nfm up to 1000 μm−2. Therefore, by measuring Nfm, one can calculate from eq 3 the fibrinogen concentration in the suspension after adsorption on the latex particles. Knowing this and the initial fibrinogen concentration before adsorption cf, one can calculate the maximum coverage of fibrinogen on latex particles Γmx from the dependence

Figure 3. Dependencies of the zeta potential of latex ζ on the fibrinogen coverage Γf [mg m−2] and the surface concentration of fibrinogen Nf [μm−2] (upper axis).The points denote experimental results obtained for pH 7.4, ionic strengths of 0.15 M, and the A800 latex concentration of 60 mg L−1 (●) and 40 mg (△). The solid lines show the theoretical results calculated from the 3D electrokinetic model. The dashed−dotted line shows the theoretical results calculated from the Gouy−Chapman model.

negligible. This limiting value is a quite accurate estimate of the limiting fibrinogen coverage on the positive latex particles. In an analogous way, the limiting coverage for the NaCl concentration of 10−3 and 10−2 M were determined to be 0.8 and 1.2 mg m−2, respectively. The experimental results shown in Figure 3 were interpreted according to the three-dimensional (3D) electrokinetic model previously used for the interpretation of nanoparticle deposition on latex particles,52 albumin,53 and fibrinogen adsorption at negatively charged latex particles.28 Physically, in this model, described in ref 54, the ion flux from the doublelayer near the interface and adsorbed molecules is quantitatively evaluated via numerical solutions of the governing Stokes equation. This allows one to uniquely express the zeta potential changes of interfaces (latex particles) in terms of the molecule coverage. These functional dependencies have been previously given in ref 4. As can be seen in Figure 3, the theoretical results obtained from this electrokinetic model (depicted by the solid line) adequately reflect the experimental data for the entire range of the fibrinogen coverage Γf in contrast to the results derived from the mean-field Gouy−Chapman model. In this model the adsorbed molecules are treated as two-dimensional flat objects, and as one can see in Figure 3 (dashed line), the experimental data completely deviate from this model. This indicates that the 3D elctrokinetic model is more adequate, allowing for a robust determination of the fibrinogen coverage on latex particles via the direct measurement of the electrophoretic mobility. However, the primary electrokinetic data shown in Figure 3 are rather limited in their precision for higher coverage ranges because of the small slope of the dependence of ζ on Γf. Therefore, in order to precisely determine the maximum coverage, a complementary method developed in ref 28 was used. It is based on determining the residual concentration of fibrinogen in the suspension after the adsorption step via a direct AFM imaging of single protein molecules adsorbed on mica. The adsorption of fibrinogen is carried out under diffusion transport using the native latex suspension without applying any filtration or centrifugation. This considerably increases the reliability and reproducibility of

Γmx = 10−3vs(c f − c fr)/S l = 10−3vs(c f − Nfm/C)/S l

(4)

where Γmx is expressed in mg m−2. Typical results of measurements performed according to this method are shown in Figure 4 for NaCl concentrations of 0.15 M and a latex concentration of 60 mg L−1.

Figure 4. Dependence of the surface concentration of fibrinogen on mica N fm determined by AFM imaging on the fibrinogen concentration in the suspension after mixing cf and the corresponding fibrinogen coverage Γf (lower axis), ionic strength 0.15, pH 7.4, bulk latex concentration after mixing cl = 60 mg L−1. The solid line 1 shows the reference results predicted for diffusion-controlled transport of fibrinogen (calculated from eq 3) and the dashed line 2 shows the linear fits of experimental data.

The reference data predicted for fibrinogen solutions without latex particles (having the same concentration as for adsorption experiments) are presented as the solid line 1. As can be seen, there is a range of fibrinogen concentration in the initial solution cf in which the Nfm remains negligible. Only for cf exceeding the break-through value of 0.6 mg L−1, did there appear a linear increase in Nfm with the slope identical to the reference case. This behavior indicates, according to eq 4, that 11169

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Γmx remains constant for a wide range of cf and is equal to 1.3 mg m−2. This confirms that fibrinogen adsorption is irreversible under these conditions (pH 7.4, 0.15 M, NaCl). As can be noticed, this value is considerably more precise (charged with the error of ±0.1 mg m−2) than what was previously derived from the primary microelectrophoretic measurements (that was equal to 1.5 mg m−2). Analogously, it was determined that the maximum coverage of fibrinogen on latex particles was 0.6 and 1.2 mg m−2 for 10−3, 10−2 M, NaCl. These data are compared with those previously obtained39 for negatively charged latex particles of the same size and pH 7.4 in Table 2.

In order to calculate the net interaction between aggregates, the pair potentials given by eq 5 were evaluated over the interaction area, significantly exceeding the double-layer thickness (by excluding interaction of the beads belonging to the same fibrinogen molecule). Calculations were performed using the symmetric charge distribution on the fibrinogen molecule shown in Table 1. The partial charges q1, q2, q3 on the external spheres, the central sphere, and the arms, respectively, were calculated from the net charge Q derived from the microelectrophoretic mobility measurements as described above. Additionally, it was assumed that the charge distribution in the present case of the human serum fibrinogen is analogous to what was previously determined for the bovine fibrinogen from the dynamic viscosity measurements and modeling.21 In this way, definite charges were attributed to various fibrinogen domains (see Table 3).

Table 2. Maximum Coverage of Fibrinogen on Negatively and Positively Charged Latex Particles Expressed in mg m−2 vs the Ionic Strength, pH 7.4 maximum fibrinogen coverage on latexes [mg m−2] ionic strength [M]

κdf/2

negative latex*

positive latex

positive latex, theoretical soft RSA modeling

10−3 10−2 0.15

1.27 3.51 13.6

1.9 ± 0.2 2.7 ± 0.2 3.2 ± 0.1

0.60 ± 0.1 1.2 ± 0.1 1.3 ± 0.1

0.650 1.12 1.29

Table 3. Charge Distribution over the Fibrinogen Molecule (Bead Model B) vs. the Ionic Strength at pH 7.4 ionic strength [M] 10−3 10−2 0.15

*previous data from ref 39

Q [e] * −11 −7 −4

q1 [e]** q2 [e]** q3 [e]** −7 −6 −4

−4 −3 −2

+4 +4 +3

*net charge derived from microelectrophoresis **postulated charge distribution

It can be noticed that the charge distribution is heterogeneous with the core part of the molecule exhibiting a negative charge of −10, −15, and −18 e for 0.15, 10−2, and 10−3 M, NaCl, respectively. The side arms, forming the angle of 56 degrees with the core part of the molecule (as previously determined in ref 21), are positively charged exhibiting 3, 4, and 4 e charges each for the above range of ionic strength. It should be mentioned that this charge distribution explains the postulated side-on adsorption mechanism of fibrinogen on positive latex. It also prohibits the end-on adsorption possibility because of an electrostatic repulsion of the positively charged side arms with the latex surface. Using these charge distributions, theoretical calculations were performed aimed at determining the maximum coverage of fibrinogen on latex as a function of ionic strength. Additionally, the role of the charge distribution (by keeping the net charge constant) was systematically studied for 0.15 M, NaCl. Owing to complicated topology and heterogeneous charge distributions, these calculations required a significant computational effort. Snapshots of fibrinogen monolayers on latex particles derived from these simulations are shown in Figure 5 for the ionic strength 10−3, 10−2, and 0.15 M, NaCl. As can be seen in all cases, fibrinogen molecules adsorb side-on exposing the positively charged side arms into the electrolyte solution. Additionally, due to the lateral electrostatic repulsion among the beads forming the core part of molecules, the monolayer obtained for 10−3 M, NaCl is characterized by a considerably smaller density compared to 0.15 M NaCl. Quantitatively, the maximum coverage for each ionic strength was obtained by extrapolation of the data obtained for long (but finite) adsorption times. In this way, the maximum coverage derived from these calculations was 0.650, 1.12, and 1.29 mg m−2 for the NaCl concentration of 10−3,

Contrary to what one could intuitively expect, the maximum coverage of fibrinogen (negatively charged at this pH) in the present case of the positive latex is more than two times smaller for all ionic strengths compared to the case of negative latex. Moreover, the maximum coverage obtained for the positive latex in the limit of high ionic strength agrees well with the theoretical modeling performed in ref 49 assuming the side-on adsorption of fibrinogen. However, in these calculations the simpler Model A of fibrinogen was used where the presence of the side arms was neglected as well as the electrostatic interactions among adsorbed molecules. These facts suggest that fibrinogen adsorption on positive latex particles occurs solely according to the side-on mechanisms. This hypothesis is also consistent with the experimentally observed increase in the maximum coverage of fibrinogen on latex for higher ionic strength that is due to the reduced range of the lateral electrostatic interactions among adsorbed molecules. To quantitatively verify this postulate, extensive theoretical modeling of fibrinogen adsorption was performed according to the RSA algorithm described above. The bead model B of fibrinogen shown in Table 1 was applied in these calculations. The lateral electrostatic interactions between adsorbed aggregates were accounted for by using the Yukawa (screened Coulomb) pair potential given by qiqj ϕ(rij) = e−κ(rij − di /2 − dj /2) 4πεrij (5) where qi and qj are the effective (electrokinetic) charges of the two beads i and j, rij is the distances between the bead centers having the diameters di, di, and κ−1 = (εkT/2e2I)1/2 is the electrical double-layer thickness, ε is the permittivity of the medium, k is the Boltzmann constant, T is the absolute temperature, and I is the ionic strength. 11170

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Figure 6. Dependence of normalized hydrodynamic diameter of fibrinogen df/do on the time: (△) 0.15 M, Γf = 1.3 mg m−2, (●) 10−3 M, Γf = 0.6 mg m−2.

Figure 5. Topology of fibrinogen molecules (approximated by the bead model B) on the positive latex particles derived from the RSA simulations for various electrolyte concentrations: (a) 10−3 M, 0.6 mg m−2 coverage; (b) 10−2 M, 1.1 mg m−2 coverage; (c) 0.15 M, 1.3 mg m−2 coverage). Figure 7. Dependence of normalized electrophoretic mobility of fibrinogen μe /μeo on the time: (△) 0.15 M, Γf = 1.3 mg m−2; (●)10−3 M, Γf = 0.6 mg m−2.

−2

10 , and 0.15 M, respectively. In the latter case, it was also shown that the variation in the partial charges q1, q2, influenced the maximum coverage only by 0.01 mg m−2 which is well within the error boundaries. As can be noticed, the theoretical results coincide (within experimental error boundaries) with the experimental results collected in Table 2. This agreement supports the postulated side-on mechanism of fibrinogen adsorption on positively charged surfaces. Therefore, these fibrinogen monolayers are considerably more homogeneous than the monolayers adsorbed at negatively charged surfaces studied in ref 24 and negatively charged latex particles.28 Additionally, because the binding with positive latex occurs via the negative charge of the core part of the fibrinogen molecule rather than via the positively charged arms, the depth of the energy minimum is expected to be considerably larger. This suggests that the stability of fibrinogen monolayers is higher for positively charged surfaces than for the negatively charged surfaces where changes in molecule orientations were observed.24 To prove this hypothesis, additional series of experiments were performed with the aim of determining fibrinogen monolayer stability in pH cycling experiments. 3.3. Stability of Fibrinogen Monolayers on Latex Particles. In this series of experiments the stability of fibrinogen-covered latex particles was checked by measuring the hydrodynamic diameter and the electrophoretic mobility of fibrinogen-covered latex as a function of time. The results are presented in Figures 6 and 7, where the dependencies of df/dfo (where dfo is the initial hydrodynamic diameter of latex particles covered by fibrinogen) on the storage time are shown for NaCl concentrations of 10−3 and 0.15 M.

Simultaneously, the corresponding variations in the normalized mobility of latex particles μe/μeo are plotted (where μeo is the initial electrophoretic mobility of the fibrinogen covered latex). As can be seen, no measurable variations were observed in the normalized hydrodynamic diameter or the zeta potential of latex. The experiments were performed for a time period up to 40 h. The stability of fibrinogen covered latex particles was also determined in experiments involving cyclic pH variations of the suspension carried out according to the following procedure: (a) a fibrinogen monolayer of a well-defined coverage is adsorbed on latex particles at pH 7.4 and NaCl concentrations of 0.15 M (b) the pH is varied in a discrete (step-by-step) manner by the appropriate addition of HCl (pH decrease) and after reaching pH 3.5 by the addition of NaOH (the ionic strength change induced by this process was negligible compared to the initial ionic strength) (c) after the stabilization of pH, the electrophoretic mobility of latex was measured (d) the entire sequence was reversed three times varying pH between 3.5 and 9 Using this procedure, the acid−base characteristics of fibrinogen monolayers on the positive latex particles are acquired. Results of these measurements obtained for the monolayer coverage of 1.3 mg m−2 and 0.15 M, NaCl are shown in Figure 8 (points fitted by the solid line 1). 11171

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Such an adsorption mechanism of fibrinogen, unique for positively charged surfaces, has not been reported before in the literature. The stability and acid base properties of these side-on monolayers on latex were also determined in pH cycling experiments. It was confirmed that there were no orientational or irreversible conformational changes in the fibrinogen molecules. Therefore, it can be concluded that the stability of fibrinogen monolayers on positively charged surfaces is much higher than for negatively charged surfaces where changes in molecule orientations were observed. A practical aspect of this work is the possibility of preparing stable fibrinogen monolayers of a well-controlled coverage and a specific orientation of the molecules allowing for efficient interactions with other proteins (antibodies) and low molecular weight ligands.

Figure 8. Dependence of the zeta potential of the fibrinogen monolayer (points) on pH. The monolayer of the coverage Γf = 1.3 mg m−2 was formed by fibrinogen adsorption on the positive latex at pH 7.4 and ionic strength of 0.15 M. Afterward, pH was cycled between 3.5 and 9.5 (three cycles were made at ionic strength of 0.15 M). Curve 1 represents the fit of the experimental data, curve 2 shows the normalized results for fibrinogen in the bulk, and curve 3 shows the results obtained for the fibrinogen monolayer on the negative latex (Γf = 1.3 mg m−2).

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Tel.: +48 126395 104. Fax. +48 12 4251923. Notes

One can see that the differences between the first and the third cycles are negligible. This suggests that no irreversible conformation or orientation changes in the fibrinogen monolayers were observed upon pH cycling. It should also be mentioned that the zeta potential of the monolayer is much more positive than the normalized zeta potential of the fibrinogen in the bulk (fitted by the solid line 2). Even at pH of 9.5 the fibrinogen monolayer on the positive latex exhibited a slightly positive charge. This behavior also significantly deviates from the fibrinogen monolayer acid−base characteristic at negative latex (see line 3 in Figure 8) where a clearly defined isoelectric point is observed at pH 4.5 (solid line 3). All these results are consistent with the proposed side-on fibrinogen adsorption mechanism where the positively charged side arms are exposed to the solution, and the negatively charged core of the molecule is firmly attached to the latex. As a result, the zeta potential of fibrinogen on the positive latex is considerably higher than the bulk zeta potential of fibrinogen and the zeta potential of fibrinogen on negative latex where the negative core part is exposed to the solution.39

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

This work was financially supported by the NCN Grant UMO2012/07/B/ST4/00559.

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4. CONCLUSIONS Electrokinetic measurements supplemented by AFM determination of residual protein concentration enabled a quantitative analysis of fibrinogen adsorption on positively charged latex at pH 7.4 and various ionic strengths. It was confirmed that the adsorption was irreversible and the maximum coverage of the protein increased with ionic strength attaining 1.3 mg m−2 for 0.15 M, NaCl which is significantly smaller than the maximum coverage obtained for negative latex particles at the same pH (3.2 mg m−2). This was interpreted as a result of the side-on adsorption mechanism of fibrinogen whose negatively charged core faced the positively charged latex surface. This adsorption mechanism predicted from experiments was confirmed by the theoretical calculations performed using the random sequential adsorption model pertinent to soft particles interacting via the screened Yukawa potential. 11172

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