Mechanisms of Fibrinogen Adsorption on Mica - ACS Symposium

Chapter 5

Mechanisms of Fibrinogen Adsorption on Mica

Downloaded by UNIV OF ARIZONA on December 14, 2012 | http://pubs.acs.org Publication Date (Web): December 12, 2012 | doi: 10.1021/bk-2012-1120.ch005

Zbigniew Adamczyk,* Monika Wasilewska, Małgorzata Nattich-Rak, and Jakub Barbasz J.Haber Institute of Catalysis and Surface Chemistry, Polish Academy of Sciences, ul. Niezapominajek 8, 30-239 Cracow, Poland *E-mail: [email protected]. Phone: +4812 6395104. Fax: +4812 4251923

Analysis of experimental data obtained for fibrinogen solutions, obtained by DLS, microelectrophoretic and dynamic viscosity measurements, was performed in terms of the theoretical approach based on bead modeling. The presence of flexible side arms (Aα chains) in the fibrinogen molecule were explicitly considered in these calculations. Two main conformational states of the fibrinogen molecule were predicted, (i) the expanded, prevailing for pH < 4 and lower ionic strength and (ii) the semi collapsed existing under physiological conditions, i.e., pH = 7.4 and 0.15 M NaCl. The latter conformation is characterized by an intrinsic viscosity of 35 and a hydrodynamic radius of 10 nm. Additionally, the interaction energy between the arms and the body of the molecule was predicted to be – 4 kT units, confirming that they are oppositely charged under these conditions, in comparison to the central nodule. This confirms a highly heterogeneous charge distribution over the fibrinogen molecule with the positive charge mostly located at the ends of the Aα chains (for pH up to 9.7), and a negative charge located at the main body of the molecule. However, for pH below 4, the entire molecule becomes positively charged. These predictions were used to quantitatively interpret adsorption kinetics determined by AFM imaging of isolated fibrinogen molecules on mica and by the in situ streaming potential measurements. It was confirmed that fibrinogen adsorption for a coverage range below 0.3 proceeds irreversibly according to the side-on mechanism, both at pH 3.5 and 7.4.

© 2012 American Chemical Society In Proteins at Interfaces III State of the Art 2012; Horbett, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2012.


The anomalous adsorption at pH = 7.4 was explained in terms of heterogeneous charge distribution. Additionally, colloid deposition experiments (involving negatively charged latex particles) on fibrinogen monolayers were presented. These experiments confirmed the existence of transient states of fibrinogen molecules in the end-on orientation. Based on this hypothesis, a multistage ‘hopping’ mechanism of colloid particle deposition on fibrinogen monolayers was proposed. It consists of an irreversible immobilization of colloid particles by a few fibrinogen molecules excited to the end-on conformation. This mechanism can also be valid for bioparticle immobilization on fibrinogen monolayers leading to clotting and thrombus formation. Keywords: adsorption of fibrinogen on mica; bead model of fibrinogen; charge distribution over fibrinogen; conformations of fibrinogen molecule; fibrinogen molecule conformations; hydrodynamic radius of fibrinogen; mechanisms of fibrinogen adsorption

Introduction Adsorption of proteins is essential for their efficient separation and purification by chromatography, electrophoresis, filtration, biosensing, enzyme immobilization in bioreactors, immunological assays, etc. On the other hand, protein adsorption can be a highly undesirable process initiating biofouling cascades leading to membrane, artificial organ, and contact lense failure, plaque formation, thrombosis, etc. Numerous studies were devoted to fibrinogen because of its fundamental role in blood clotting, platelet adhesion, thrombosis, angiogenesis, wound healing and tumor growth (1–5). The early works (6–8) were focused on determining the molecular weight of fibrinogen by measuring its diffusion and sedimentation coefficients. Reliable data concerning fibrinogen’s geometrical dimensions and conformations stem from the electron microscopy studies of Hall and Slayter (9) and others (10–12). From the micrographs of fibrinogen adsorbed on mica, it was established that its molecule has a co-linear, trinodular shape with a total length of 47.5 nm. The two equal end domains are spherical having a diameter of 6.5 nm; the middle domain has a diameter of 5 nm. These domains are connected by cylindrical rods, having a diameter of 1.5 nm. A schematic view of the fibrinogen molecule derived from the Hall-Slayter model, hereafter referred to as the HS model is shown in Table 1. Interestingly, the HS model’s shape and dimensions of fibrinogen agree with the true crystallographic shape derived from X-ray diffraction (13), see Table 1. 98 In Proteins at Interfaces III State of the Art 2012; Horbett, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2012.


Table 1. Model shapes of the fibrinogen molecule. Reproduced with permission from Ref. (24). Copyright 2012 Elsevier

Similar shape and fibrinogen dimensions were confirmed by numerous studies carried out using atomic force microscopy (AFM) (14–20).

99 In Proteins at Interfaces III State of the Art 2012; Horbett, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2012.


As can be seen in Table 1, the fibrinogen molecule is highly anisotropic, characterized by considerable elongation (with the length to width ratio exceeding ten). It should be mentioned, however, that in these works the shape and dimensions of fibrinogen were determined under dry or vacuum conditions, where the molecule is likely to change its native conformations occurring in the electrolyte solutions, because of a considerable dehydration. Suggestions that such conformational changes can be essential stem from the chemical amino-acid sequence (primary structure) of fibrinogen determined in the eighties (21, 22). Thus, from the chemical point of view, the fibrinogen molecule is a symmetric dimer composed of three identical pairs of polypeptide chains, refereed to traditionally as Aα, Bβ and γ chains. They are coupled in the middle of the molecule through a few disulfide bridges and forming a central nodule (see Table 1). The longest Aα chain is composed of 610 aminoacids, the Bβ chain comprises 460 aminoacids and the γ chain 411 aminoacids. Accordingly, the molecular mass of the fibrinogen molecule equals to 337,897 D (21). Additionally, from the chemical structure one can deduce that major parts of the Aα chains extends from the core of the molecule forming two polar appendages each having a molecular mass equal to 42,300 D (5). These fragments of polypeptide Aα chains are not visible in the crystallographic structure of fibrinogen. Hence, it seems that these chains are collapsed under vacuum conditions. However, they can play an essential role in the hydrodynamic behavior of the molecule in electrolyte solutions because of charging effects. The essential role of the side ‘arms’ in determining hydrodynamic properties of the fibrinogen molecule was experimentally confirmed in Ref. (23). In this work systematic measurements of the diffusion coefficient and the dynamic viscosity of fibrinogen were performed. It was revealed that the diffusion coefficient of fibrinogen changed little with pH and ionic strength, whereas the dynamic viscosity exhibited large variations. These results were interpreted in terms of conformational changes of the fibrinogen molecule induced by increased charging for pH, deviating from the isoelectric point equal to 5.8 (23). By adopting the prolate spheroid model of the fibrinogen molecule, it was predicted that its effective length should be 80 nm for pH < 4 or pH > 7.4 (low ionic strength) and 65 - 68 nm for pH = 7.4 and I = 0.15 (this corresponds to physiological conditions). These estimations of the effective length were quantitatively confirmed in Ref. (24), where a more realistic bead model of the fibrinogen molecule was developed, which explicitly takes into account the presence of flexible side ‘arms’ (see Table 1). Knowing bulk fibrinogen properties, especially its conformations, one can attempt to properly interpret its mechanisms of adsorption on various substrates. There are abundant experimental studies of this type, mostly done by ellipsometry (14, 15, 25) and TIRF (19). A significant spread in the maximum coverage of fibrinogen was reported in these works with the lowest and highest value equal to 1.4 and 11 mg m–2, respectively. It seems that this discrepancy can be attributed to different adsorption 100 In Proteins at Interfaces III State of the Art 2012; Horbett, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2012.


mechanisms of fibrinogen on various substrates for various concentration range. For hydrophilic surfaces, and a low concentration regime, fibrinogen adsorption occurs according to the side-on mechanism with the maximum amount of adsorbed protein equal to 1.4 - 1.7 mg m-2, which was confirmed by recent theoretical results discussed in Ref. (26) For hydrophobic surfaces and higher fibrinogen concentrations, the end-on adsorption of the protein becomes feasible with the maximum coverage many times higher than for the side-on configuration. However, since the binding energy in the end-on configuration is much lower than for the side-on orientation, a partial reversibility of adsorption occurred, which can explain the source of the discrepancies. This adsorption regime was theoretically studied in Ref. (27) However, a deeper insight into the mechanism of fibrinogen adsorption and the structure of its monolayers on various substrates is hindered because few experimental methods are available working under wet, in situ conditions. One of few exemptions represent the electrokinetic methods, usually, the streaming potential or streaming current measurements. (28–30). Pioneering experiments of this kind were performed by Norde and Rouwendal (28). Later on Zembala and Dejardin (31) determined variations in the streaming potential of silica capillaries upon fibrinogen adsorption as a function of time for pH = 7.3 and the ionic strength of 10-2 M. A systematic increase in the negative potential of the substrate was observed upon fibrinogen adsorption, which was also negatively charged under these conditions. Thorough streaming potential measurements of fibrinogen adsorption on mica for various ionic strength and pH were reported in Ref. (32). The protein coverage was determined by direct AFM imaging of the adsorbed monolayers. Knowing the coverage, these experimental data were successfully interpreted in terms of the electrokinetic model developed for heterogeneous (particle covered) surfaces (33–35). The Gouy-Chapman model, based on the concept of a continuous charge distribution, was inadequate to interpret these results. Based on these measurements an irreversible side-on adsorption mechanism of fibrinogen was proposed. Anomalous adsorption of fibrinogen for pH = 7.4 was explained in terms of a heterogeneous charge distribution, characterized by the presence of positive charges on the side arms, and a negative charge on the core part of the molecule as predicted in Ref. (24). More detailed information about fibrinogen monolayers can be gathered using the in situ method developed in Refs. (36–39) based on the unspecific deposition of colloid particles. The technique, referred to as the colloid enhancement (CE) (38, 39), enables one to determine a unique functional relationship between the amount of adsorbed protein and the amount of adsorbed colloid, which can be quantitatively assessed via optical microscope imaging under wet conditions. Using the colloid deposition method, in conjunction with thorough electrokinetic characteristics of protein covered substrates, one can determine the dynamic behavior of protein monolayers. The goal of this work is to discuss results pertinent to fibrinogen adsorption on solid substrates, concerning both the theoretical modeling and experimental results acquired by DLS electrophoresis, dynamic viscosity, streaming potential and AFM measurements. Based on an analysis of these data, a unified view 101 In Proteins at Interfaces III State of the Art 2012; Horbett, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2012.

of fibrinogen adsorption mechanisms and monolayer behavior is formulated. In particular, when exploiting the CE measurements, a ‘hopping’ mechanism of colloid particle deposition on fibrinogen monolayers is proposed, having significance for bioparticle, e.g., platelet or red blood cell immobilization on protein monolayers.

Theoretical Modeling of Fibrinogen Adsorption


Calculating Bulk Hydrodynamic Properties of the Fibrinogen Molecule Because of the complicated shape of the fibrinogen molecule, which has no symmetry axis (see Table 1), calculations of its hydrodynamic mobility matrix or intrinsic viscosity, which convey information about the molecule conformations, are not feasible. Therefore, in Ref. (26) a bead model of the fibrinogen molecule was proposed to describe adsorption kinetics on solid surfaces. The model, hereafter referred to as Model A, is shown schematically in Table 1. As can be seen, the fibrinogen molecule is approximated as an array of touching beads of various size forming a co-linear conformation. The two external beads have the size of d1, the central bead has the size of d2 and the 2n remaining, equal-sized beads have the dimension of d3. For calculations presented in Ref. (26), it was assumed that d1 = 6.7 nm, d2 = 5.3 nm, d3 = 1.5 and 2n = 20. This gives the overall length of the fibrinogen molecule equal to 48.7 nm. This is slightly larger than in the HS and crystallographic model, due to presence of tightly bound water (hydration effect). Accordingly the volume of the fibrinogen molecule in Model A, νA, equals to 428 nm3. This slightly exceeds the molecular volume given by

where Mw is the molecular mass of fibrinogen, Aν is the Avogadro number, ρf is the specific density of fibrinogen and is the specific molar volume of fibrinogen. For the molecular weight Mw = 337,817 derived from the amino acid sequence (see Table 1) and ρf = 1.38 g cm-3 (32) one obtains = 0.72 cm-3 g-1 and the fibrinogen molecule volume of 405 nm3. Model A, due to its simplicity, proved advantageous for performing time consuming MC simulations of fibrinogen adsorption on solid substrates under various orientations (26, 27). However, a limitation of this model is the negligence of side arms in the fibrinogen molecule, which can exert essential influence on its bulk hydrodynamic properties. Therefore, in ref. (24) a more realistic model, hereafter referred to as Model B was developed (see Table 2), where the presence of these arms is explicitly considered by introducing two straight sequences of ns beads of equal size, having the diameter of d4. These arms form the angle φ with the main body of the fibrinogen molecule. Both the number of beads ns and the angle φ are variable parameters, which can were optimized in calculations presented in Ref. (24). Obviously, for ns = 0, Model B is reduced to Model A, previously described. 102 In Proteins at Interfaces III State of the Art 2012; Horbett, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2012.


Table 2. Hydrodynamic radii and intrinsic viscosities for model shapes of the fibrinogen molecule. Adapted with permission from Ref. (24). Copyright 2012 Elsevier

The volume of the fibrinogen molecule for the Model B is given by the expression

where is the volume of one bead in the side arm. According to Model B, the fibrinogen molecule has two planes of symmetry, but no symmetry axis, which complicates the hydrodynamic calculations due to the appearance of the coupling between translational and rotational motion. 103 In Proteins at Interfaces III State of the Art 2012; Horbett, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2012.


Using this Model B, extensive calculations were performed in Ref. (24) in which the average hydrodynamic mobility and the intrinsic viscosity [η] (also called the viscosity increment) were determined for various side arm lengths (number of small beads ns). The hydrodynamic mobility is a relevant quantity for predicting fibrinogen adsorption kinetics, because it is connected with the orientation averaged translational diffusion coefficient D through the Einstein dependence

where k is the Boltzmann constant and T is the absolute temperature. However, since D is dependent on the temperature (in contrast to the hydrodynamic mobility) and the solvent viscosity, it is often useful to introduce the hydrodynamic radius of a molecule RH defined by the constitutive relationship

RH is a quantity of primary importance because it solely depends on the shape and size of molecules being independent not only of temperature and the viscosity but also particle density and other parameters characterizing the solvent. Physically RH corresponds to the radius of an equivalent sphere having the same hydrodynamic mobility as the molecule of an arbitrary shape. For the fibrinogen molecule, RH is rather insensitive to its conformations depending mostly on the contour length. In this respect, the intrinsic viscosity [η] is more sensitive to conformational changes of the molecules. It is defined as the second virial coefficient in the expansion of the suspension dynamic viscosity against the concentration of the solute (molecules) (40). This can be mathematically formulated as

where ηs is the solvent dynamic viscosity and c is the concentration of the solute. Using this definition, [η]c can be defined as (41)

for It should be mentioned that confusion may arise because the solute concentration can be expressed using various concentrations. In Ref. (24) the hydrodynamic radius and the intrinsic viscosity of fibrinogen were calculated as a function of the angle φ and the number of the beads in the side arms ns keeping a fixed value of n = 10. The multipole expansion method was used to solve the linear Stokes equation with no-slip boundary conditions on the molecule surface. Values of RH and [η] were calculated in a quasi-continuous form 104 In Proteins at Interfaces III State of the Art 2012; Horbett, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2012.


for various conformations of the fibrinogen molecule and ns ranging between zero (Model A) and 12. In the latter case the length of each arm equals to 18 nm. Results obtained in these calculations for some limiting conformations are collected in Table 2. As can be seen, the presence of side arms exerts only a limiting influence on RH, which increases from 8.54 nm (no arms) through 10.8 nm (ns = 12, φ = 90°) to 11 nm for the fully extended molecule conformation (ns = 12, φ = 180°). Note that the theoretical values of RH predicted if the molecule shape is approximated by a spheroidal or cylindrical shape are much lower than those derived from Model B (see Table 2). In contrast to hydrodynamic radius, variations in the intrinsic viscosity with fibrinogen conformations are much more significant. Thus, for model A (no arms), [η] = 27.1 (Table 2), for ns = 12, φ = 90°, [η] = 43.6 and for the fully extended conformation ns = 12, φ = 180°, [η] = 62.3. Using these values, in Ref. (24) the average hydrodynamic radii and intrinsic viscosities of the fibrinogen molecule were calculated in the thermodynamic limit, i.e., assuming that the probability of a given conformation of side arms is governed by the Boltzmann statistics. In the case of zero interaction energy between the arms and the central nodule the following values of intrinsic viscosity, hydrodynamic radius and the orientation angle are predicted (for ns = 12):

These parameters correspond, therefore, to the situation where electrostatic interactions within the fibrinogen molecule are absent. It was also shown that in the presence of repulsive interaction these values increase monotonically with the magnitude and the effective range of the interaction energy . On the other hand, in the presence of attractive interactions between the arms and the central nodule, the average angle decreases significantly, thus becomes closer to 10 nm and [η] closer to 30. Hence, by comparing these theoretical predictions with experimental data one can estimate the interaction energy between arms and the central nodule of the molecule, which is mostly governed by electrostatic interactions (24). Reliable values of the hydrodynamic radius of fibrinogen can be acquired by the dynamic light scattering (DLS) measurements. The primary parameter derived from these measurements is the autocorrelation function converted to the average translational diffusion coefficient. Knowing the diffusion coefficient the hydrodynamic radius can be calculated using Eq. (4). Such measurements done for various pH and ionic strength were reported in Ref. (23). For pH = 7.4, I = 0.15 M NaCl (physiological conditions) it was determined that D = 2.15 x 10-7 cm2 s-1 (RH = 10 nm). For pH = 3.5, I = 10-3 M, D = 2.01 x 10-7 cm2 s-1, (RH = 10.7 nm).


As seen, for pH = 7.4, the hydrodynamic radius of fibrinogen assumes lower values than the previous estimate for the neutral molecule (10.5 nm). This may confirm the existence of attractive interactions at this pH. However, more unequivocal estimations of the interaction energy can be derived from the viscosity measurements done in Ref. (24) for the same set of physicochemical parameters. The intrinsic viscosity values are: [η] = 35 for pH = 7.4, I = 0.15 M, and [η] = 50 for pH = 3.5, I = 10-3 M. Comparing these data with experimental predictions it was predicted that for pH = 7.4 and I = 0.15 M, the


= – 4 kT. interaction energy On the other hand for pH = 3.5, I = 10-3 M it was predicted that there appears electrostatic repulsion between the arms and the body characterized by the energy of

= 4 kT.

Knowing one can estimate the number of effective (uncompensated) charges on the arms and the central nodule of the fibrinogen molecule. It was determined in Ref. (23) that at pH = 7.4 and I = 0.15 M the overall number of elementary (positive) charges is 6 (3 per each arm) and the number of elementary charges (negative) on the central nodule is -6. Considering additionally that the net charge of the fibrinogen molecule under these conditions is -8 elementary charges (23), one can predict the charge distribution over the fibrinogen molecule as shown in Table 3.

Table 3. Predicted conformations of the fibrinogen molecule. Adapted with permission from Ref. (24). Copyright 2012 Elsevier



These estimates are quite significant because the presence of positive charges at the ends of the flexible arms explains anomalous adsorption of fibrinogen at negatively charged surfaces such as mica (42) modified glass (43) or polystyrene latex particles (44) at pH = 7.4. These aspects are discussed in more detail later on. On the other hand, for pH = 3.5, I = 10-3 M, the following charge distribution over the fibrinogen molecule was predicted. There are 5 positive charges per each arm, 4 positive charges at the central nodule and 12 additional positive charges distributed over the rest of the molecule (see Table 3). Because the entire molecule is positively charged, one can deduce that fibrinogen adsorption on negatively charged surfaces should proceed irreversibly at this pH. Indeed, in Ref. (27) it was predicted that the for this charge distribution, the energy minimum for the fibrinogen/mica interactions in the side-on configuration equals to -34.8 kT. Accordingly, the characteristic relaxation time for the fibrinogen molecule desorption is 109 seconds (ca. 11.000 days), which is practically infinite from the experimental point of view. It can also be concluded from this analysis that the fibrinogen model B, in which the presence of flexible arms is considered, properly reflects the available experimental data such as the diffusion coefficient (hydrodynamic radius) and the intrinsic viscosity. By exploiting these findings two main conformational states of the fibrinogen molecule can be distinguished. For a physiological conditions, pH = 7.4, I = 0.15 M NaCl, a semi-collapsed conformation dominates, characterized by the angle = 56°, intrinsic viscosity of 35 and the hydrodynamic radius of 10.0 nm. On the other hand, for pH 3.5 and I < 10-3 M, an expanded conformation exists, characterized by a high intrinsic viscosity of 50, a hydrodynamic radius of 10.7 nm and the angle < φ> = 115° (see Table 3).

Fibrinogen Adsorption Kinetics Knowing the hydrodynamic radius and diffusion coefficient of the fibrinogen molecule one can predict adsorption kinetics at initial stages where the surface blocking effects, stemming from particles accumulated at interfaces, remain negligible. On the other hand, to describe adsorption kinetics for higher coverages, information is required about the maximum amount of adsorbed particles (called the jamming coverage) and the blocking function, referred to as the available surface function (ASF) (45–48). This kind of information can be derived using the above models of fibrinogen and performing the Brownian-dynamics (BD) or Monte-Carlo (RSA) simulations, which are more universal and efficient (26, 27, 45–51). The general rules of the Monte-Carlo simulation scheme, based on the random sequential adsorption concept, are (45–51): (i) a particle is created, whose position and orientation is selected at random within prescribed limits defining the adsorption domain, 107 In Proteins at Interfaces III State of the Art 2012; Horbett, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2012.


(ii) if the particle fulfills prescribed criteria it becomes deposited and its position remains unchanged during the entire simulation process (postulate of an irreversible adsorption), (iii) if the deposition criteria are violated, a new attempt is made uncorrelated with previous attempts.

There are usually two major deposition criteria (i) no overlapping of any previously adsorbed particles and (ii) a contact with the bare interface. Despite the simplicity of the governing rules, the RSA method is a powerful tool for generating adsorbed molecule populations of the number Np exceeding 106 particles. The primary parameter characterizing such particle populations is the dimensionless coverage defined as

where Sg is the characteristic cross-section area of a molecule and ΔS is the surface area of the simulation plane. Once a monolayer configuration or an ensemble of configurations at fixed Θ are generated, they can be statistically analyzed to determine, for example, the surface blocking function BΘ defined as the probability of adsorbing an additional particle on the interface already covered by Np particles (45–50). In simulations BΘ is calculated as the average number of attempts to deposit the particle, from the formula

where Natt is the number of attempts at depositing the particle and < > means the ensemble average. Using the blocking function concept one can define the jamming coverage Θ∞, which is a quantity of vital significance

Thus, by definition, at the jamming state, there is no space available for adsorption of particles of a given size and shape. In the case of hard sphere adsorption on planar surfaces Θ∞ = 0.547 as determined by (49). It is interesting to note that this value is markedly smaller than the maximum hexagonal packing of hard spheres in 2D, equal to or the regular packing, equal to . Jamming coverages were also determined for non-spherical particles of elongated shape such as spheroids, cylinders and spherocylinders (46). For spherocylinder characterized by the axis ratio 2:1, Θ∞ = 0.583 and for the axis ratio 15:1, Θ∞ = 0.445 (47). However, these results were obtained for convex particles of regular geometrical shapes. Therefore, they cannot be directly applied for 108 In Proteins at Interfaces III State of the Art 2012; Horbett, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2012.


predicting the jamming coverage of molecules approximated by the bead model. Calculations for such a case were recently performed for the fibrinogen Model A adsorbing side - on at a planar interface of infinite extension (26). The equivalent aspect ratio for this shape is 14.6, i.e., very similar to the spherocylinder. It was determined that the jamming coverage for the side-on adsorption of such a model fibrinogen molecule was 0.291, which is a lower value than the above obtained for the spherocylinder having a convex shape (0.445). It is interesting to mention that the jamming coverages are universal quantities, independent of the size of molecules. However, for practical applications one is more interested in experimentally accessible parameters such as the surface concentration N∞, defined as the number of particles or molecules per unit surface area of the interface. It can be calculated from Eq. (8) rearranged as

In practice N∞ is often expressed as the number of molecules (particles) per a square μm. Thus, the above value of Θ∞= 0.291 for fibrinogen corresponds to N∞= 2.27x103 μm-2 considering that Sg for the Model A molecule in the side-on orientation equals to 128 nm2 (26). However, N∞ is a specific parameter depending not only on the particle shape but also its size. The interesting case of the end-on adsorption of fibrinogen on surfaces pre-covered by the jammed side-on monolayer was considered in Ref. (27). The jamming coverage for the end–on configuration,

was 0.216, which

6.13x103

corresponds to the surface concentration of μm-2. This is higher than before because the cross-section area of Model A fibrinogen molecule in the end-on orientation is only 35 nm2 (27). The RSA calculations performed according to the above scheme can also be used in determining surface blocking functions, which have essential significance for analyzing adsorption kinetics of fibrinogen. From calculations performed in Ref. (26), the following expression for the blocking function was derived for the side-on adsorption of fibrinogen,

where is the normalized coverage for the side-on orientation a1 = - 0.727, a2 = -2.01 and a3 = 1.882. For not too high coverage range, Eq. (12) can be approximated by the second order series expansion

where C1 = 16.3 and C2 = 82 (side-on adsorption). 109 In Proteins at Interfaces III State of the Art 2012; Horbett, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2012.

On the other hand, for Θ approaching the jamming coverage, the blocking function assumes the form (46)


where C∞ = 0.0653. For the end-on adsorption of fibrinogen on surfaces pre-covered by the side-on monolayer, the blocking functions is given by (27).

where B0 = 0.130, is the normalized coverage for the end-on orientation and a1 = - 0.851, a2 = - 0.566, a3 = 0.609. It is worthwhile mentioning that these results were obtained within the framework of the standard RSA model, whose application requires no adjustable parameters. Knowing the jamming coverage and the blocking functions one can quantitatively analyze the kinetics of fibrinogen adsorption and desorption using the phenomenological approach based on the continuity (mass-balance) equations (35, 45). The advantage of this approach is the possibility of studying long-lasting adsorption processes (103 - 106 seconds) for broad range of bulk protein concentration. This makes such calculations useful for interpreting a variety of experimental data concerning fibrinogen adsorption. Such phenomenological descriptions involve the formulation of the constitutive equation describing the flux of protein molecules at the edge of the adsorption layer, which is as follows (26, 27, 45)

where ja is the net adsorption/desorption flux, t is the adsorption time, is the generalized blocking function, ka, kd are the adsorption and desorption constants, and n(δa) is the concentration of particles at the adsorption boundary layer of the thickness δa. To describe the net adsorption kinetics, Eq. (16) is used as the boundary condition for the bulk mass transfer equations formulated for various transport can be mechanisms. For most applications, the general blocking function approximated by the above discussed RSA blocking functions B(Θ). Moreover, the kinetic adsorption and desorption constant occurring in Eq. (16) can be expressed in terms of physical parameters characterizing the transport conditions, such as the protein diffusion coefficient, the specific energy distribution governed by the depth of the primary minimum

, the energy barrier height

, etc. (26,



27, 45). This allows one to determine the depth of the energy minimum (binding energy) by comparing theoretical predictions derived from the phenomenological models with experimental results. Eq. (16) is nonlinear and it is coupled with the bulk transport equation. Therefore, it cannot be analytically solved in the general case. However, limiting analytical solutions of vital significance can be derived (26). For example, under equilibrium conditions, where the adsorption flux vanishes, Eq. (16) reduces to the isotherm equation

where Θe is the equilibrium coverage of the protein, Ka = ka / kd is the equilibrium adsorption constant and ne is the equilibrium concentration of particles in the bulk. The adsorption isotherm, i.e., the dependence of Θe on nb, can be derived by a numerical inversion of this equation. Another limiting analytical solution can be derived from Eq. (16) in the case of a quasi-stationary transport, where the particle concentration n(δa) is in a local equilibrium with the surface coverage. This stems from the fact that the relaxation time of the bulk transport is usually much longer than the characteristic time of the surface coverage variations. Under such conditions the constitutive expression for the adsorption flux, Eq. (16) becomes (27)

where K = ka / kc are the dimensionless coupling constants, is the dimensionless desorption constant, and kc is the bulk transfer rate constant, known in analytical form for many types of flows and interface configurations (45, 46). In order to obtain an explicit dependence of the coverage on time, Eq. (18) can be integrated, which yields

where Θ0 is the initial coverage of particles, tch = 1 / Sg kc nb is the characteristic time of particle monolayer formation under convection transport conditions and τ = t / tch is the dimensionless time. Eq. (19), with the blocking functions given by Eq. (12) or Eq. (15), represents a general solution for particle adsorption/desorption kinetics under convection driven transport. However, it can only be evaluated by numerical integration methods as done in Ref. (26) for the irreversible (Kd = 0), side-on adsorption of fibrinogen. 111 In Proteins at Interfaces III State of the Art 2012; Horbett, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2012.


A more complicated situation arises in the case of diffusion-controlled adsorption of the protein. In this case the constitutive expression for the flux, Eq. (16), cannot be integrated directly because the flux from the bulk to the interface and the concentration n(δa) remain non-stationary for all times. In this case, to explicitly evaluate particle adsorption kinetics, one has to solve the non-stationary bulk diffusion equation with Eq. (16) serving as the boundary condition (26, 27, 45). For sake of convenience it is transformed to a dimensionless form involving the adsorption and desorption constants given by

where tch, L are the characteristic time and the length scale, respectively, defined as

As can be noticed, the characteristic monolayer formation time increases rapidly for diluted suspensions, proportionally to nb-2 analogously as the dimensionless desorption constant

. On the other hand, the dimensionless

increases proportionally to nb-1. As a result, these two adsorption constant parameters become very large for diluted protein solutions, often met under experimental conditions. Hence, for the above discussed case of fibrinogen (26), the characteristic adsorption time for the bulk protein concentration of 1 ppm (nb = 1.78x1012 cm-3) is 9.27x105 seconds and the adsorption constant

= 3x105.

For nb = 100 ppm (nb = 1.78x1014 cm-3), tch is reduced to 93 seconds and = 3x103. Using these data calculation were performed in Ref. (26) for the irreversible, side-on adsorption of fibrinogen controlled by diffusion. It was shown that for such high values of typical for fibrinogen adsorption for low concentration rages (1 to 10 ppm), adsorption kinetics remains linear in respect to (t/tch)1/2 until the coverage approaches 0.9 of the jamming coverage. In this case the surface concentration of adsorbed fibrinogen molecules is governed by the formula

where nb is the number concentration of fibrinogen molecules in the bulk. 112 In Proteins at Interfaces III State of the Art 2012; Horbett, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2012.

Experimental Evidences


Fibrinogen Adsorption

In Ref. (32), measurements for the fibrinogen/mica system were performed with the aim of unequivocally elucidating adsorption mechanisms for such a model hydrophilic substrate. In order to properly interpret these experimental data, thorough characteristics of fibrinogen solutions and mica were done. The electrophoretic mobility of fibrinogen as a function of pH and the ionic strength was determined using the micro-electrophoretic method. It was calculated from these measurements that the zeta potential of fibrinogen ζf for pH < 5.8 was positive, equal to 24 and 28 mV for pH = 3.5 and the ionic strength of 10-2 and 10-3 M, respectively. On the other hand, for pH = 7.4, ζf became negative, equal to - 19 and – 21 mV for the ionic strength of 10-2 and 10-3 M, respectively. Accordingly from the electrophoretic mobility measurements, the isoelectric point of fibrinogen (pH value where its electrophoretic mobility and zeta potential vanished) was pH = 5.8. The corresponding charge distribution over fibrinogen derived from these measurements and the above theoretical calculations is shown in Table 3. Zeta potential of the mica substrate was determined via the streaming potential measurements according to the procedure described in Refs. (35, 53, 54). For the ionic strength of 10-3 M, zeta potential of mica was – 63 mV for pH = 3.5 and – 112 mV at pH = 7.4. For the ionic strength of 10-2 M, zeta potential of mica was less negative, equal to – 52 mV for pH = 3.5 and – 80 mV for pH = 7.4. Fibrinogen adsorption experiments were conducted in Ref. (32) under diffusion-controlled transport and the number of adsorbed molecules was determined by AFM imaging (semi-contact mode, air) of the monolayers. The topology of fibrinogen monolayers on mica acquired in these experiments (pH = 3.5, I = 10-2 M NaCl) is shown in Figure 1. For comparison, a monolayer of the same coverage derived from numerical simulations using Model A, is also shown. As can be seen, fibrinogen molecules appear as isolated entities, which facilitates their enumeration by AFM. Therefore, using this counting procedure the kinetics of fibrinogen adsorption on mica can be quantitatively evaluated. In Figure 1 (Part b), the kinetics is shown as the dependence of the reduced surface concentration of fibrinogen N/cb on the square root of the adsorption time t1/2 (cb is the fibrinogen bulk concentration in ppm connected with the number concentration nb via the dependence cb = nb106Mw/Aν). As can be seen, the experimental data in Figure 1b are in agreement with theoretical results (depicted by the solid line) stemming from Eq. (22), pertinent to an irreversible, diffusion-controlled adsorption mechanism (26, 27). It is worthwhile observing that results shown in Figure 1b have interesting practical implications because one can conveniently determine the unknown bulk concentration of fibrinogen by plotting N vs. the square root of adsorption time, t1/ 2. As discussed in Ref. (32) one can accurately determine fibrinogen concentration of 0.1 ppm and less. 113 In Proteins at Interfaces III State of the Art 2012; Horbett, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2012.


Figure 1. Part “a”. Experimental (l.h.s. of the picture) and simulated (MC-RSA method, r.h.s. of the picture) monolayers of fibrinogen on mica at the coverage of 0.67%. Part “b”. The dependence of the reduced surface concentration of fibrinogen N/cb [µm-2 ppm-1] on the square of adsorption time t1/2, I = 10-3 M. The full points denote experimental results obtained by a direct AFM enumeration for pH = 3.5 (various bulk concentration of fibrinogen) and the hollow points denote results obtained for pH = 7.4. The solid line shows exact theoretical results obtained using the RSA model. Adapted with permission from Ref. (39). Copyright 2011 Elsevier. 114 In Proteins at Interfaces III State of the Art 2012; Horbett, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2012.


Table 4. Mechanisms of fibrinogen adsorption on hydrophilic surfaces and immobilization of colloid particle on its monolayers

The results shown in Figure 1b suggest that fibrinogen adsorption on mica for pH = 3.5 was irreversible and bulk transport controlled with negligible surface transport resistance. This seems quite natural considering the strong attraction between fibrinogen molecules and the oppositely charged mica substrate. Under these circumstances the fibrinogen molecules could adsorb side-on as schematically shown in Table 4. 115 In Proteins at Interfaces III State of the Art 2012; Horbett, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2012.


However, identical adsorption kinetics of fibrinogen was also observed in the case of pH = 7.4 (see Figure 1b), where the average (mean-field) zeta potential of fibrinogen and mica were both negative. It should be mentioned that such anomalous fibrinogen adsorption at pH = 7.4 was previously observed by Zembala and Dejardin (31), Malmsten (25), Ortega-Vinuesa et al. (14, 15), Toscano and Santore (19) and Kalasin and Santore (43). This anomalous adsorption can be explained in terms of a heterogeneous charge distribution over the fibrinogen molecule above predicted (see Table 3). Thus, the molecules could efficiently adsorb in the side-on orientation with the arms touching the interface and the main body levitating above the surface. The distance between the molecule and the interface can be changed by regulating the ionic strength. Thus, it can exceed 10 nm for ionic strength of 10-3 M and below. Such an adsorption mechanism is shown schematically in Table 4. However, the AFM measurements alone cannot furnish a decisive proof of this hypothesis. This can be achieved via the in situ measurements done under wet conditions using the streaming-potential and colloid deposition methods.

Figure 2. The dependence of the zeta potential of mica ζ on the coverage of fibrinogen Θf. The points denote experimental results obtained from the streaming potential measurements for 1. pH = 3.5, 2. pH = 7.4, I = 10-2 M NaCl. The solid lines represent exact theoretical results calculated according to the electrokinetic model developed in Refs. (33, 35).



Streaming Potential Measurements

Streaming potential measurements were carried out using a home-made apparatus exploiting the parallel-plate channel flow, according to the procedure previously described (32, 35, 52–54). Two series of experiments were carried out for pH = 3.5 and 7.4. The dependence of the streaming potential on the coverage of fibrinogen adsorbed in situ under diffusion transport was systematically studied. From these measurements the zeta potential of fibrinogen covered mica ζ was calculated using the Smoluchowski equation. The dependencies of ζ on the fibrinogen coverage for pH = 3.5 and 7.4 are shown in Figure 2. As seen, pH = 3.5, where Fb is positively charged, a steep, quasi-linear increase in the zeta potential of mica is observed for Θf < 0.1. Then, for Θf > 0.16 (inversion point), the zeta potential of mica becomes positive and it approached the saturation value, which is markedly lower than the bulk zeta potential of fibrinogen (equal to 24 mV for this pH). At pH = 7.4 (lower curve, Figure 2) the mica zeta potential also increased monotonically with the fibrinogen coverage but it remained negative, attaining the value of -20 mV for higher coverage. This is close to being bulk value of fibrinogen at this pH (-19 mV). It was additionally confirmed in separate desorption experiments (32) that no changes in the fibrinogen covered mica zeta potential were observed upon flushing the cell with pure electrolyte over a prolonged time period. These experiments proved, therefore, that fibrinogen adsorbed irreversibly on mica surface both at pH = 3.5 and 7.4, which agrees with previous observations shown in Figure 1b. More refined analysis of this behavior was carried out in terms of the electrokinetic model developed in Refs. (33–35), which considers a uniform 3D distribution of charge over adsorbed protein molecules. This model was successfully applied for interpreting the zeta potential of surfaces covered by colloid particles (55) and polyelectrolytes (37). As seen in Figure 2, for pH = 3.5, theoretical results derived from this model, where a side-on adsorption of fibrinogen was assumed, quantitatively agree with experimental data for the entire range of coverage. This is a quite interesting because such a unique, functional dependence enables a precise determination, via the streaming potential measurements, of the coverage of fibrinogen under wet, in situ conditions. This also implies that the bulk concentration of fibrinogen can be precisely measured by this method. Given the large slope of the zeta vs. fibrinogen coverage dependence one can expect that this method is more robust, than others, chemical type, methods. As observed in Figure 2, the theoretical model also works for pH = 7.4 (lower curve). However, in this case, agreement with experiments is attained using the effective zeta potential of adsorbed fibrinogen molecules of – 30 mV, which is considerably more negative than in the bulk (-19 mV). This observation supports the side-on adsorption mechanism of fibrinogen shown in Table 4, where the positively charged arms form bonds with the substrate and the more negative body of the molecule is exposed to the flow. 117 In Proteins at Interfaces III State of the Art 2012; Horbett, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2012.


Colloid Deposition on Fibrinogen Layers Additional information about the dynamic behavior of fibrinogen monolayers on mica can be acquired via the colloid deposition method. In Ref. (39) systematic experiments of this kind involving negative and positive polystyrene latex particles (referred to as the L800 sample) were performed. In the first step of these experiments fibrinogen monolayers of desired coverages were produced and fully characterized by the streaming potential measurements. Afterwards, latex deposition was carried out in a thermostated cell under diffusion over time period of 24 hours. The number of latex particle adsorbed as a function of deposition time was determined by optical microscope imaging under wet conditions and independently by AFM imaging in air. An advantage of the optical microscopy is that it enables measurements to be carried out under wet conditions, where particle positions over the substrate surface remain undisturbed. This allows one to reliably determine the coverage of particles and their distributions over bare and fibrinogen covered substrates. These measurements enabled one to determine unique functional dependencies between the fibrinogen coverage Θf and the maximum coverage of latex particles deposited after long period of time ΘL. Such dependency obtained for a negative polystyrene latex, having the zeta potential of -105 mV at pH = 3.5, I = 10-2 M is plotted in Figure 3. The inset shows the latex particle monolayer at the maximum coverage Θmax = 0.48, which was used as a normalization variable in Figs. 3 - 5. As can be seen, ΘL/Θmax increases abruptly with the fibrinogen coverage, attaining 0.9 for Θf = 0.1 and almost 1 (a saturated latex monolayer coverage) for Θf = 0.16. These results are rather unexpected given the negative zeta potential both of the latex and mica covered by fibrinogen (see Figure 2). Indeed, the classical DLVO theory, based on the concept of mean-field zeta potential, predicts a negligible latex deposition for this range of fibrinogen coverage (dashed line in Figure 3a). As discussed in Ref. (39) this deviation of experimental results from the DLVO theory is direct proof of a heterogeneous charge distribution over mica induced by fibrinogen coverage fluctuations. Because fibrinogen molecules exhibited a net positive zeta potential at pH = 3.5, a local increase in their concentration at mica could lead to formation of favorable adsorption sites, capable of immobilizing latex particles. This effect was analyzed in terms of the fluctuation theory developed to interpret particle deposition on surfaces covered by polyelectrolytes (35–37) and fibrinogen molecules (39). The basic assumption of the charge fluctuation approach is that particle adsorption occurs at sites formed by nf fibrinogen molecules adsorbed close to each other. Depending on the number of molecules forming a site population, they differ in the binding strength of colloid particles. The sites are assumed to be randomly distributed over the substrate surface (39) Accordingly, the coverage of sites formed by nf fibrinogen molecules is governed by the Poisson statistics, i.e.,



With this assumption, using the RSA theory of site covered surfaces (56), one can calculate the latex coverage on fibrinogen monolayers from the analytical expression

where and λ2 is the ratio of the latex to fibrinogen cross-section area, equal to 3.93x103 in this case. As can be seen in Figure 3, theoretical results predicted from Eq. (24) properly reflect experimental data if nf = 2 is assumed (see curve 2). On the other hand, theoretical results calculated for nf = 1 (curve 1 in Figure 3a) considerably overestimate the experimental data. This means that an efficient latex particle immobilization is only possible on sites formed by two fibrinogen molecules adsorbed close to each other. This is an essential finding which provides valuable hints concerning mechanisms of colloid particle deposition on fibrinogen monolayers. Therefore, in Refs. (39, 57) extensive measurements were performed, where the role of pH and ionic strength in latex particle deposition on fibrinogen monolayers was systematically studied. In Figure 3b such dependencies of ΘL/Θmax on Θf acquired for various pH (equal to 3.5, 7.4, 9.7 and 11) at a fixed ionic strength of 10-2 M are presented. As observed, in contrast to previously shown dependence for pH = 3.5 (Figure 3a), the results obtained for pH = 7.4 and 9.7 can be well accounted for by the theoretical model, given by Eq. (24), if nf = 3 is assumed. This means that an efficient latex particle immobilization at this pH occurred on sites formed by three fibrinogen molecules. On the other hand, for pH = 11 there was practically no deposition of latex on fibrinogen covered mica. Additional series of experiments were also performed in Ref. (57) to elucidate the role of the ionic strength at a fixed pH = 4. The results of these experiments are shown in Figure 4. As shown, all results obtained for ionic strength within the range 0.15 to 10-3 M are practically the same (within experimental error bounds) and can be well described by the theoretical model assuming nf = 2. However, for lower ionic strength, the latex deposition efficiency (expressed as the ΘL/Θmax on Θf dependencies) abruptly decreases, and vanishes for I = 3x10-4 M. It is interesting to mention that analogous results were previously reported in Ref. (36) where kinetics of deposition of negatively charged polystyrene latex particles on a cationic polyelectrolyte monolayers (poly allylamine hydrochloride, PAH) pre-adsorbed on mica was studied. Ionic strength in these experiments was either 10-2 or 10-3 M, NaCl. It was demonstrated that the increase in the maximum coverage of latex with the PAH coverage could be properly reflected by Eq. (24) assuming that the efficient adsorption site is formed by four closely spaced PAH molecules. 119 In Proteins at Interfaces III State of the Art 2012; Horbett, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2012.


Figure 3. Part “a”. The dependence of the normalized coverage of latex particles, ΘL/Θmax on the fibrinogen coverage Θf The points (▲) denote the averaged experimental results obtained by optical microscopy and AFM, for ionic strength 10-2 M, pH = 3.5, T = 293 K. The solid lines 1-2 denote theoretical 120 In Proteins at Interfaces III State of the Art 2012; Horbett, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2012.


prediction derived from the fluctuation theory, Eqs. (23, 24) for the adsorption site composed of one and two fibrinogen molecules, respectively (23, 24). The dashed line denotes the theoretical results derived from the mean-field DLVO theory. The inset shows the latex monolayer deposited on fibrinogen monolayer for ΘL = Θmax = 0.48 Part “b”, The dependence of the normalized coverage of latex particles, ΘL/Θmax on the fibrinogen coverage Θf. The points denote the averaged experimental results obtained for ionic strength of 10-2 M and various pH: (▲), pH = 3.5, (●), pH = 7.4, (□), pH = 9.7, ((), pH = 11. The solid line denotes theoretical prediction derived from the fluctuation theory, Eqs. (23, 24) for the adsorption site composed of two (curve 2) and three (curve 3) fibrinogen molecules.

Figure 4. The dependence of the normalized coverage of latex particles, ΘL/Θmax on the fibrinogen coverage Θf The points denote the averaged experimental results obtained by optical microscopy and AFM for pH = 3.5 – 4, (■), ionic strength 0.15 M; (▲), ionic strength 10-2 M; (●), ionic strength 10-3 M; (♦), ionic strength 8x10-4 M; (▼), ionic strength 3x10-4 M. The solid line denotes theoretical prediction derived from the fluctuation theory, Eqs. (23, 24) for the adsorption site composed of two fibrinogen molecules. 121 In Proteins at Interfaces III State of the Art 2012; Horbett, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2012.


Figure 5. The dependence of the normalized coverage of L800 latex particles, ΘL/Θmax on the minimum approach distance h*.The points denote the averaged experimental results obtained by optical microscopy and AFM for pH = 3.5 - 4 and the solid line is the non-linear fit of experimental data.

A quantitative interpretation of these results requires a thorough analysis of the interaction energy profile of the latex particle with the mica substrate covered by the protein for various ionic strength and pH (57). Briefly speaking, because of the highly negative zeta potential of latex and mica under these experimental conditions, there appears a considerable repulsion extending over distances many times larger than the electrical double-layer thickness (ε is the dielectric permittivity of the liquid, e is the elementary charge). It was estimated in Ref. (57) that the minimum approach distance of latex particles to the mica interface h* equals to 6 κ-1. This means that for I = 10-2 M, h* = 18.3 nm, for I = 10-3 M, h* = 54.3 nm and for I = 6x10-4 M (pH = 4), h* = 74.4 nm. Thus, latex particles practically cannot approach the mica substrate at distances closer than h*. This excludes the possibility that they can deposit directly on fibrinogen molecules, because their diameter is 6.7 nm (see Table 1). Therefore, latex deposition becomes only possible if they contact the arms protruding from the fibrinogen molecule. However, as stated above, the length of these arms is 18 nm, thus latex deposition for ionic strength below 10-3 M would not be possible. This contradicts experimental observations which are presented in Figure 5 122 In Proteins at Interfaces III State of the Art 2012; Horbett, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2012.


as the dependence of the normalized latex coverage ΘL/Θmax (for Θf = 0.1) on the minimum approach distance h*. As can be seen in Figure 5, the threshold value (which is defined as the value where ΘL/Θmax falls to 0.5) is 75 nm. This considerably exceeds not only the diameter of the fibrinogen molecule but also its length of 49 nm (see Table 1). However, this threshold distance is quite close to the length of the molecule with fully extended arms, equal to 67 nm. Hence, the most probable mechanism which accounts for these experimental findings is the ‘hopping’ mechanism shown schematically in Figure 6 (57). Accordingly, latex deposition on fibrinogen monolayers is a multistage process consisting of following steps:

(i) One of a few closely separated fibrinogen molecules adsorbed in the sideon configuration is activated due to natural fluctuations and transferred into the transient end-on configuration. (ii) Latex particle is immobilized on the end of the arm and a transient fibrinogen/latex complex is formed. (iii) The immobilized latex particle forms additional contact with the next fibrinogen molecule activated into the end-on configuration. The binding energy is increased twice.

Obviously step (iii) can be repeated since additional bonds between the interface and the latex particle can be formed via fibrinogen molecules, with the binding energy increasing in a quantum-like fashion ( i.e., two-, three-, etc. times). This ensures irreversible immobilization of latex. It was shown in Ref. (57) by performing calculations of the probability of the appearance of the transient state of fibrinogen and the fibrinogen/latex complex that it is sufficiently high to irreversibly immobilize latex particles over the time of 24 hours. It was also shown that the for low pH, where the fibrinogen molecule is strongly charged, two bonds formed between the arm and the latex particles are sufficient to irreversibly capture a single latex particle. On the other hand, for pH = 7.4 and above, because of the decreased charge of the arms, three bonds are needed. For pH > 9.7, the charge of the amidine groups stemming from lysine and arginine amino acids vanishes, which prohibits latex deposition. Although these results were obtained for the model system mica/ fibrinogen/latex, it is expected that a similar mechanism can explain bioparticle immobilization on fibrinogen monolayers leading to clotting and thrombus formation. It is also interesting to mention that the proposed hopping mechanism can be used to explain above mentioned results concerning latex deposition on PAH monolayers (36). A decisive argument to support this conclusion is that the hydrated diameter of the PAH molecule is only 1.13 nm (36), whereas the minimum approach distance of latex particles varies between 18.3 and 54.3 nm for I = 10-2 and 10-3 123 In Proteins at Interfaces III State of the Art 2012; Horbett, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2012.


M, respectively, as above discussed. Thus, the only possibility to form an efficient contact between a latex particle and adsorbed PAH molecules is if the latter are activated into the end-on conformations forming tails or loops.

Figure 6. A schematic view of the colloid deposition mechanism of fibrinogen monolayers. 124 In Proteins at Interfaces III State of the Art 2012; Horbett, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2012.


Conclusions Analysis of experimental data obtained by DLS, microelectrophoretic and dynamic viscosity measurements, in terms of theoretical approaches based on bead modeling, revealed a highly heterogeneous charge distribution over the fibrinogen molecule. The positive charge, (up to pH = 9.7), is located at ends of the Aα chains, and the negative charge is mainly located at the main body of the molecule. However, for pH close to 4, the entire molecule is positively charged. The highly anisotropic charge distribution predicted for pH 7.4 - 9.7 explains anomalous adsorption of fibrinogen at negatively charged surfaces such as mica at this pH range determined by AFM enumeration of isolated fibrinogen molecules and in situ streaming potential measurements. It was also confirmed that fibrinogen adsorption for a coverage range below 0.3 proceeds irreversibly according to the side-on mechanism. Colloid deposition experiments confirmed, however, the existence of dynamic transient state of fibrinogen molecules in the end-on orientations. Based on this hypothesis a multistage ‘hopping’ mechanism of colloid particle deposition on fibrinogen monolayers was proposed. The essential point is that particles are immobilized on the end part of the arms forming a transient fibrinogen/latex complex. An irreversible immobilization of colloid particles is finally achieved if two or more additional bonds are formed with closely separated fibrinogen molecules. This also explains ‘quantum’ effects experimentally observed in latex deposition on fibrinogen monolayers. Although these results were obtained for the model system mica/fibrinogen/ latex, it is expected that the above mechanism is quite universal explain also deposition of colloid or bioparticles on polyelectrolyte monolayers formed on solid substrates.

Acknowledgments This work was partially supported by the MNiSZW Grant No.: N N204 026438.

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Mechanisms of Fibrinogen Adsorption on Mica - ACS Symposium

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