ABSTRACT The thermodynamics and kinetics of protein adsorption are studied using a molecular theoretical approach. The cases studied include competitive adsorption from mixtures and the effect of conformational changes upon adsorption. The kinetic theory is based on a generalized diffusion equation in which the driving force for motion is the gradient of chemical potentials of the proteins. The time-dependent chemical potentials, as well as the equilibrium behavior of the system, are obtained using a molecular mean-field theory. The theory provides, within the same theoretical formulation, the diffusion and the kinetic (activated) controlled regimes. By separation of ideal and nonideal contributions to the chemical potential, the equation of motion shows a purely diffusive part and the motion of the particles in the potential of mean force resulting from the intermolecular interactions. The theory enables the calculation of the time-dependent surface coverage of proteins, the dynamic surface tension, and the structure of the adsorbed layer in contact with the approaching proteins. For the case of competitive adsorption from a solution containing a mixture of large and small proteins, a variety of different adsorption patterns are observed depending upon the bulk composition, the strength of the interaction between the particles, and the surface and size of the proteins. It is found that the experimentally observed Vroman sequence is predicted in the case that the bulk solution is at a composition with an excess of the small protein, and that the interaction between the large protein and the surface is much larger than that of the smaller protein. The effect of surface conformational changes of the adsorbed proteins in the time-dependent adsorption is studied in detail. The theory predicts regimes of constant density and dynamic surface tension that are long lived but are only intermediates before the final approach to equilibrium. The implications of the findings to the interpretation of experimental observations is discussed.
INTRODUCTION
Protein adsorption plays a major role in a variety of important technological and biological processes (Clerc and Lukosz, 1997; Denizli et al., 2000; Ghose and Chase, 2000; Hlady and Buijs, 1996; Montdargent and Letourneur, 2000; Shi and Ratner, 2000; Slomkowski, 1998; Topoglidis et al., 1998). For example, blood proteins tend to adsorb into surfaces of foreign materials. This is the first step on surface-induced thrombosis (Andrade and Hlady, 1986; Horbett, 1993; E. F. and S. 1993; Tanaka et al. 2000). A large number of biotechnological devices include surface-bound proteins, e.g., biosensors (Nyquist et al., 2000; Slomkowski et al., 1996; Sukhishvili and Granick, 1999; Zhou et al., 2000). Separation of proteins by chromatography involves the competitive adsorption of the particles (Wang 1993). The understanding of the fundamental factors that determine protein adsorption are imperative to improve our ability to design biocompatible materials and biotechnological devices. Moreover, protein adsorption is a very important fundamental problem that involves large competing energy scales and conformational statistics that may result in reversible and irreversible processes.
The adsorption of proteins on surfaces is a complex process. The adsorbing particles are large, and, thus, the surface-protein interactions are usually long range and the strength is many times the thermal energy. Further, due to the large size and the shape of the particles, the interactions between the adsorbed particles on the surface are nontrivial and can be strongly influentiated by the fact that the particles may undergo conformational changes upon adsorption (Billsten et al., 1995; Ishihara et al., 1998; Kondo and Fukuda, 1998; Nasir and McGuire, 1998; Norde and Giacomelli, 1999, 2000; Tan and Martic, 1990; Van Tassel et al., 1998; Gidalevitz et al., 1999). Actually, the kinetics and thermodynamics of protein conformational changes on the surface is a very complex subject and their understanding is at its early stages. The idea behind the work presented here is an attempt to formulate a molecular theoretical approach that can be applied to study both the equilibrium and the kinetic behavior of protein adsorption.
On experimental studies (Green et al., 1999; Malmsten, 1997), it has been observed that, when two or more kinds of proteins are present in solution, such as in blood plasma, the adsorption is the result of the competition between the time scale to reach the surface and the strength of the surface-- protein interaction. For example, in blood plasma solutions of albumin, immunoglobulin-G (IgG) and fibrinogen (Fgn) in contact with a polystyrene surface, the initial adsorption is dominated by the smaller protein (albumin), which are also at larger concentrations in the bulk, to be later replaced by the larger proteins like IgG and Fgn. This sequential adsorption is called the Vroman sequence. In other experiments (Lassen and Malmsten, 1997), different adsorption patterns are observed when the surfaces are changed. On the hydrophobic PP-HMDSO (hexamethyldisiloxane), surface albumin and IgG dominate the adsorption. However, on hydrophilic PP-DACH (1,2-diaminocyclohexane) and PP-AA (acrylic acid) surfaces, Fgn is almost exclusively found on the surface. These experimental observations demonstrate that the incorporation of the solution conditions and the protein-surface interactions have to be considered for the proper understanding and description of the adsorption process.
One of the most important contributions to the understanding of the kinetics of protein adsorption is the random sequential adsorption (RSA) model (Feder and Giaever, 1980; Schaaf and Talbot, 1989). In this approach, the proteins are assumed to be rigid particles that interact only through excluded volume interactions. The particles are assumed to irreversibly adsorb to the surface, and, thus, they do not have translational degrees of freedom or desorption on the surface. This model has been very useful in understanding why the kinetics of protein adsorption do not follow the Langmuir predictions. Furthermore, the model has been extended to consider conformational changes, desorption, and the treatment of mixtures (Van Tassel et al., 1994, 1996, 1998). The main limitation of this model is that it is hard to include detailed molecular information of the proteins and the formulation is based on a kinetic approach.
Some other studies have assumed that the adsorption kinetics is determined by the diffusion of the proteins to the surface (Iordanskii et al., 1996), whereas others assume that the dominant regime is the one controlled by a kinetic (activated) process (Chatelier and Minton, 1996; Minton, 1999). In a recent study, Cho et al. (1997) formulated a model in which both the diffusion and kinetic processes were included. Olson and Talbot (2000) studied the equilibrium and kinetics of adsorption of a polydisperse mixture. Each of these models has provided important insights toward the understanding of the adsorption process. However, none of them can describe both the equilibrium and kinetics of the adsorption process within the same molecular approach that can be applied for a large variety of experimental systems.
The theory that we use in this paper is based on the formulation of the free energy of the system. The minimization of the free energy provides the equilibrium state of the system, and, thus, we can study the protein adsorption isotherms. Furthermore, the free energy formulation enables the study of possible conformational changes of the protein on the surface. The equilibrium version of the theory for protein adsorption was originally formulated to study the ability of grafted polymer layers to prevent, or reduce, protein adsorption (Szleifer, 1997b). The predictions of the theory were shown to be in excellent quantitative agreement with experimental observations for the equilibrium adsorption isotherms of lysozyme on surfaces with grafted polyethylene oxide layers (McPherson et al., 1998; Satulovsky et al., 2000). The theory was later generalized to study the kinetics of the adsorption process in the same systems (Satulovsky et al., 2000). The basic idea in the dynamic version of the theory is to start with an equilibrium bulk system that, at time zero, is put in contact with a surface. The presence of the surface induces a distance dependent chemical potential of the proteins. The free energy of the new system is formulated, but instead of minimizing to obtain the new equilibrium state in the presence of the surface, the time evolution of the density of proteins is evolved with a diffusion-like equation, with the driving force being the gradient of chemical potentials arising from the sudden presence of the surface. These chemical potentials are obtained as derivatives of the time-dependent free energy with respect to the local density of proteins. Similar approaches were used for the adsorption of surfactants (Diamant and Andelman, 1996) and polymers (Fraaije, 1993; Hasegawa and Doi, 1997). Recently, it has been shown that this kind of dynamic equations can be derived for the time dependence of the density from density functional theory (Marconi and Tarazona, 1999).
In this paper, we are interested in using the same theoretical approach but to the study of protein adsorption on bare surfaces. The idea is to understand what are the parameters that determine the different dynamic regimes. Further, we are interested in studying in detail the effect of conformational changes on the kinetics of adsorption and also the adsorption of proteins mixtures.
The paper is organized as follows: the next section contains a description of the theoretical methodology, including a detailed presentation of the way the equations are solved. The following section present a variety of representative results. Finally, the last section includes our conclusions.
THEORETICAL APPROACH
In this section, we present our theoretical approach to study the equilibrium and kinetic properties of the adsorption of proteins to planar surfaces. We will present a general theoretical framework for the determination of equilibrium adsorption isotherms in the case of protein mixtures. The treatment explicitly includes the possibility that the proteins have many different configurations. The second part of this section presents the dynamic theory that we use to study the kinetics of protein adsorption.
After the presentation of the general thermodynamic and kinetic approaches, we will show the specific cases for which we present explicit calculations below. Namely, the adsorption of proteins that are assumed to have a single configuration in the bulk but that can undergo conformational changes upon contact with the surface and those assumed to be a mixture of proteins of different sizes for a variety of different bulk conditions and surfaces. Following the model, we present details on the numerical methodology used in solving the equilibrium and kinetic equations.
Equilibrium free energy
CONCLUSIONS
We have presented a general theoretical approach to study the thermodynamic and kinetic behavior of adsorbing proteins on solid surfaces. We have derived the theory in its most general form for both the equilibrium and kinetic studies. The theory was then applied to simple cases to study the effect of size, composition, surface-protein interactions, and protein conformational changes to the adsorption isotherms and the kinetics of protein adsorption.
The formulation of the theory does not require the specific introduction of the kinetic pathways that may happen through the adsorption process, but it predicts them. For example, adsorption and desorption will be predicted if the local thermodynamic environment is optimal for that process. Further, the kinetic version of the theory is formulated such that the system will eventually reach thermodynamic equilibrium. However, the theory is capable of predicting some kind of irreversible adsorption for cases of very slow dynamic processes. The theory describes the adsorption process from the bulk solution to the surface, including a detailed description of the region in the vicinity of the surface. Further, although the theory was presented here assuming that the only inhomogeneous direction is that perpendicular to the surface, it can be easily extended to treat inhomogeneous three-dimensional systems (Seok et al. 2000). The theory enables the study of the changes of the structure of the adsorbed layer, with molecular detail, as a function of time. This molecular description allows the understanding of the factors that determine the different kinetic regimes.
The theory requires, as input, the intermolecular and surface-protein interactions, and the possible conformations of the proteins. The intrinsic rate of transformation from one conformation to another also needs to be given. These are very difficult quantities to obtain, and, therefore, we applied the theory to simple systems to study the main factors determining the adsorption behavior. Although the application of the theory was done for simple geometries for the proteins, the real configuration of the protein could be included if they are known. As more microscopic understanding of the structure and conformational properties of proteins are learned, they can be incorporated into the theoretical framework. Actually, the lack of knowledge of the conformational properties of proteins may be one of the most important limitations in the application of the theory.
The complete understanding of the adsorption process should optimally permit description of the dynamic changes from the nanosecond time scale, which is the time scale for local conformational changes, to hours, which is the time scale of the whole adsorption process. Clearly, this is an impossible computational task with current methodologies and hardware. Note that atomistic simulations can be run for a single solvated small protein for nanoseconds. The theory presented here is aimed at bridging the gap between microseconds and hours. We hope, in the future, to be able to introduce the input necessary for the theory from molecular dynamic simulations of single proteins and, thus, bridge the gap between the atomistic time scale to the macroscopic one. It is important to emphasize that, to describe the very large range of time scales that the theory can treat, one needs to compromise in atomistic detail. Thus, the description of the solvent and basic elements forming the proteins are coarse grained. The level of coarse graining depends upon the level of detail that is of interest and the time scale of the overall process.
It is important also to emphasize the limitations of the approach presented here. First, although the theory has shown the ability to quantitatively predict the adsorption isotherms of lysozyme and fibrinogen on hydrophobic surfaces with grafted PEO (McPherson. et al., 1998; Satulovsky et al., 2000), it is still a mean-field theory with all its limitations, in particular with respect to the lateral interactions. The applicability of the theory can be improved by considering inhomogeneous densities in all three dimensions, (see, e.g., Seok et al., 2000). However, even though some correlations will be accounted for, the theory will remain, in essence, a mean-field approach. Second, for the kinetic behavior, we have assumed that the diffusion in the plane of the surface is much faster than the motion perpendicular to it. Although Brownian Dynamics simulations (Ravichandran and Talbot, 2000) show that this is a valid approximation for layers that are not very dense, we cannot predict a priori whether this is going to be the case generally. Again, this limitation may partially be overcome by considering the motion in all three directions. However, this will require an extremely large computational effort. Third, the theory requires, as input, the information on the molecular details of the proteins. This information has to be coarse grained to be able to integrate the equations of motion. Therefore, some of the detailed structural information is lost. Fourth, the theory assumes that there is a separation of time scales between the diffusion of the proteins (slow motion) and the rearrangement of the solvent molecules (fast motion). Although this is generally a reasonable approximation, it may have important consequences, in particular regarding solvent rearrangements upon conformational changes of the protein. Atomistic studies of single proteins in solvents may shed light on the cases in which this approximation breaks down. Fifth, we have assumed that the diffusion constant of the protein does not change with composition. Further, the approach assumes that there are no flow effects.
The advantages of the theory, such as the ability to study kinetic processes over many orders of magnitude in time, the ability to follow the adsorption with a large degree of molecular detail, and the wide range of applicability of the approach, should be balanced against its limitations to apply this approach in the appropriate cases where the theory is valid. The conclusions presented here are kept within that context, and we believe that the generic behaviors that we have found are applicable in a large range of systems in which adsorption of proteins takes place.
We have found that the competitive adsorption of proteins from solution can show a variety of different behaviors depending upon the protein-surface interactions, the composition of the bulk solution, and the ratio of sizes between the proteins. We found, in agreement with experimental observations, that the Vroman sequence is obtained when the large proteins have a much stronger attractive interaction with the surface than the smaller ones and the bulk solution is rich in the small proteins. Changing the composition of the bulk solutions puts the large proteins at a larger concentration on the surface at all times. The results presented here show the different conditions under which one can temporarily and thermodynamically control the adsorption of proteins on surfaces. Thus, they can serve as one of the building blocks in the design of optimal surfaces for protein separations. Our findings on the plateau of the dynamic surface tension suggest that changing the bulk composition of the protein mixture may be a good indicator of whether the system has achieved thermodynamic equilibrium. The equilibrium value of the surface tension will depend upon bulk composition, whereas the dynamic plateau will not.
The ability of the protein molecules to change their conformation upon adsorption has dramatic effects on the kinetics of protein adsorption. Depending upon the intrinsic rate of conformational change compared to protein diffusion, one can observe different adsorption patterns that are determined also by the intermolecular interactions. These interactions, in turn, depend on the population of different conformers on the surface. Our findings suggest that measurements of dynamic surface tension versus time may give an indication of possible conformational changes upon adsorption. Slow conformational changes seem to be associated with changes in the slope of the dynamic surface tension versus time. Further, the intermolecular interactions play a key role in the rate of conformational transformation once a certain density threshold of proteins is found on the surface. These results may lead to ways of surface modification that can be used to selectively adsorb proteins in a given configuration.
To summarize, the work presented here is one more step toward the systematic understanding of the molecular factors that determine the adsorption of proteins on surfaces. The complexity in the dynamic and equilibrium behavior calculated even for our simple protein models are comparable to those observed experimentally. Further, it demonstrates that explicit incorporation of the size, shape, composition, and strength of the intermolecular and surface interactions are necessary for the proper description of these complex systems. For example, the complex and timedependent shape of the potentials of mean force demonstrate that the kinetics of adsorption is a process associated with multiple relaxation times that are strongly dependent upon the size and shape of the molecules.
We are currently working on simple detailed models of proteins that will enable us to include more molecular and conformational detail as input to the theory. In parallel, we plan to compare the predictions of the theory with available experimental data to build up a database of useful models of proteins with which the theory can predict the behavior of real systems.
We thank Drs. M. A. Carignano and J. Satulovsky for very enlightening discussions. The work presented here is supported by the National Science Foundation. LS. is a Camille Dreyfus Teacher-Scholar.
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[Author Affiliation]
Fang Fang and Igal Szleifer
Department of Chemistry, Purdue University, West Lafayette, Indiana 47907 USA
[Author Affiliation]
Address reprint requests to Igal Szleifer, Purdue University, Dept. of Chemistry, Brown Building 1393, West Lafayette, IN 47907-1393. Tel.: 765-494-5255; Fax: 765-494-0239; E-mail: igal@purdue.edu.
