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BIOMOLECULES AT INTERFACES Introduction Many biomolecules are amphiphilic, that is, possess certain regions that interact favorably, and others that interact less favorably, with an aqueous solvent. As such, these biomolecules tend to reside at the interfacial region separating an aqueous phase from another phase of matter. The process of interfacial attachment is referred to as “adsorption”; “adsorbed molecules” or “adsorbates” are terms describing molecules having undergone adsorption (qv). The principal forces leading to adsorption have been identified; these are the ionic, van der Waals, hydrogen bonding, donor/acceptor, and solvation interactions (1). Attachment by a chemical bond is also possible. Proteins, peptides, amino acids, polysaccharides, lipids, and nucleic acids are examples of biological molecules known to adsorb at solid–liquid, liquid–liquid, and/or liquid–vapor interfaces. To fully understand a biomolecule, one must understand its behavior at relevant interfaces, for it is the rare biomolecule not exhibiting a strong tendency to adsorb! Many examples of biomolecules at interfaces come from nature. Membrane proteins—a term describing those spanning the cell membrane—actually reside at two interfaces (intracellular matrix–cell membrane and extracellular matrix–cell membrane) and serve to regulate transport into and out of cells. Plasma proteins— those existing in blood—attach to the surface of an unrecognized material and initiate the clotting cascade. Other examples come from technological applications. The above-mentioned clotting process unfortunately occurs onto medical implants as well. Interfacial adsorption is ubiquitous during bioprocessing applications; this can have the deleterious effects of vessel fouling and product structural alteration. Adsorption is one common mechanism by which bioseparations are conducted and biocatalysts are immobilized. Adsorbed protein layers are known to have a strong influence on living cells; this effect is exploited in tissue engineering and cellular bioreactors. Finally, both the fabrication of, and detection using, biosensors involve biomolecules residing at interfaces. Encyclopedia of Polymer Science and Technology. Copyright John Wiley & Sons, Inc. All rights reserved.

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The purpose of this article is to introduce, expand interest in, and grow awareness of, the field of biomolecules at interfaces. Motivation for study in any field is typically driven by either application or curiosity. Workers investigating biomolecules at interfaces are fortunate in that numerous important technological applications exist together with several intriguing and perplexing (and for the most part unsolved!) intellectual curiosities. In most areas of science and engineering, important advances accompany the close interplay between theoretical prediction and experimental measurement. Biomolecules at interfaces is no exception, and a summary of key theoretical tools and experimental methods comprises the subsequent two sections. Note that no attempt is made toward an exhaustive coverage of biomolecule/interface systems. The reader is also invited to consult other excellent reviews related to this topic (1–3).

Technological Applications A number of important technological applications motivate the study of biomolecules at interfaces. In this section, discussion focuses on important examples in two areas: biomaterials and biosensors. Biomaterials. Biomaterials find important application as medical implants and tissue engineering substrates. In each case, clinical or scientific effectiveness strongly depends on the behavior of interfacial biomolecules. Other articles in this encyclopedia discuss various aspects of biomaterials. In this section, important aspects dealing with adsorbed biomolecules are briefly presented. Medical Implants. The insertion of medical implants serving as teeth, bones, skin, blood vessels, and even organs has become commonplace. A universal problem concerns unwanted biological responses; these may be thrombogenic, inflammatory, immunological, or infectious (4–6). It is now well established that protein adsorption precedes and directs these unfavorable events. For example, it is the plasma protein fibrinogen that is thought to initiate thrombogenesis. A small conformational change in the adsorbed fibrinogen is now known to cause platelet adhesion and subsequent aggregation; these events are followed by fibrin formation (6). Not surprisingly, focus has been directed toward preventing protein adsorption altogether or promoting adsorption of “passivating” proteins (ie those known not to trigger subsequent biological responses). A preeminent strategy for preventing initial protein adsorption involves the grafting of hydrophilic polymer chains to a material surface. Polyethylene oxide (PEO) is particularly effective in this capacity (7–17). The originally suggested mechanism by which PEO prevents protein adsorption involved hydrodynamic currents due to the motion of the grafted chains (7). Subsequent theoretical work has shown that proteins residing within reach of the polymeric brush reduce the conformational freedom of the grafted chains; the polymer layer thus provides an entropic barrier to adsorption (18–25). Very recent work has also demonstrated the importance of the conformational freedom of the individual PEO monomeric units to the prevention of protein adsorption (17). An alternative to the complete prevention of protein adsorption is the controlled placement of certain biomolecules that act against thrombogenesis. One

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natural choice is heparin, an anticoagulant. A number of studies suggest that surfaces with grafted heparin show a diminished thrombogenic response (26,27), but controversy remains as to whether the mechanism is due to heparin-catalyzed antithrombin deactivation of coagulation proteases (28) or to a suppressed adsorption of cell adhesion proteins (29). In addition, although success has been achieved with heparin-coated surfaces, results are not uniformly favorable (30). Tissue Engineering Substrates. Tissue Engineering (qv) is a field of biomedical study in which techniques are sought to create functional replacements for diseased human tissues and organs (31–36). Successful tissue engineering offers the potential for considerable prolongation of the length and quality of human life. Additionally, it has been estimated that the availability of engineered tissues could reduce expenses related to tissue loss and end-state organ failure by $400 billion per year (31). The key issue in tissue engineering is the availability of materials onto which cells attach, spread, grow, differentiate, and eventually organize to form a desired tissue. Reasoning that the presence of an artificial material would tend to inhibit cellular activity, early efforts were directed toward developing biologically inert materials. The current view, however, is one of a material possessing chemical/biological sequences and patterns capable of signaling and controlling the cellular response (32,37). Materials promoting a natural response, inducing a supernormal response, and/or inhibiting a naturally occurring (but unwanted) response are needed to engineer replacement human tissues. Tissues or cells typically interact with a biomaterial indirectly through a layer of adsorbed protein. Certain matrix proteins are known to promote cell attachment and growth. One example is fibronectin, a large, extracellular glycoprotein whose constituent modules contain binding sites for a wide range of biomolecules and biological units (38). Its cell-binding site, consisting of the tripeptide amino acid sequence argenine–glycine–asperigine (RGD), is known to bind to the integrin proteins located within the cell membrane; this triggers events that ultimately induce the adhesion, spreading, and growth of cells. Thus, one strategy toward biomaterials for tissue engineering applications is to attach to the biomaterial surface, either chemically or physically, a layer of matrix protein (39–48). An important alternative to the surface placement of entire proteins is the direct attachment of the cell-binding peptide sequences, such as the RGD sequence in fibronectin (32,37,49–59). This is an example of a “biomimetic” strategy, ie one that mimics biology. Advantages over direct placement of proteins are the greater degree of control of peptide density, spatial arrangement, and orientation and the diminished risk of the material triggering an immune response (37). Disadvantages include the need for additional chemical surface modification (one must generally attach the peptide units and grafted linear polymer chains such as PEO to ensure that proteins do not adsorb and cover the peptides) and the loss of biological signaling from other peptide sequences on the proteins. A number of successes have been reported and it is safe to say that this is currently the most actively researched approach to develop biomaterials as tissue engineering substrates. Biosensors. A biosensor is an analytical device for the detection of a target biomolecule (60–63). Although many variations are possible, all biosensors combine a detector, where a biological recognition event takes place, with a transducer, which produces an output signal from the recognition event. A biosensor

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must be selective for the target molecule in a mixture of structurally similar species. Robustness, cost, size, and real-time measurement capability are additional factors governing the effectiveness of a given biosensing configuration. A number of clinical and biomedical applications are envisioned, but to date the most successful examples of commercialization are the glucose detectors used in the management of diabetes. Other important applications are found in food production, environmental monitoring, and defense/security. A biosensor’s detector typically consists of chemical receptors attached or “immobilized” to a material surface (typically the transducer surface). These are often themselves biomolecules. Detection involves an interaction between these immobilized molecules and biomolecules from solution that approach the detector surface. In this sense, both the fabrication of, and detection using, biosensors involve biomolecules at interfaces. Biosensor Fabrication. A crucial step in biosensor fabrication is the immobilization of chemical receptors. Chemical receptors may be of two types: catalytic or affinity. In both cases, the target molecule binds specifically to a chemical receptor. In the former, the binding event triggers a measurable change in the transducer. In the latter, the specific binding event leads to a catalyzed chemical reaction, often involving the target molecule itself. The presence of the catalyzed reaction product(s) then triggers a measurable change in the transducer. An important example is the catalytic glucose sensor, in which an oxidation of glucose takes place by immobilized glucose oxidase to gluconic acid and hydrogen peroxide. Hybrid biosensors, in which both catalytic and affinity receptors are utilized, are also possible. The principal methods for the immobilization of chemical receptors are (1) physical adsorption to a solid surface, (2) chemical adsorption (covalent attachment) to the surface, (3) affinity binding to physically or chemically bound species, and (4) entrapment within a matrix. Since physical adsorption relies on relatively weak forces (van der Waals, ionic, solvation, donor/acceptor), molecules placed in this way may detach over time and/or exhibit nonuniform biological activity because of a distribution of surface orientations/conformations. However, this method is clearly the simplest of the four and therefore often finds use. An example is the popular enzyme-linked immunosorbent assay (ELISA) used in medical diagnostics. A more robust and controllable means of surface attachment is through a covalent bond. Large biomolecules such as proteins typically possess a number of functional groups capable of chemical binding; these include amino, carboxyl, sulfhydryl, phenolic, thiol, and imidizol groups. The best choice for preserving biological activity and optimizing accessibility of the receptor’s active site is often a functional group far from the active site. Suitable complementary reactive groups are available on some surfaces (for example, hydroxyl groups on silica), but in many cases, surface modification is needed. A popular means of surface modification is to employ self-assembled monolayers (SAMs) (64). SAMs are closely packed, (approximately) vertically aligned alkane chains residing at an interface. Through chemically functionalized termini, the tailoring of physical and chemical properties of the surface is possible. Chemical immobilization results from a reaction between a specific functional group at a SAM molecule terminus and a biomolecule. (In some cases, a bifunctional reagent is used to achieve the coupling.) A SAM may be placed onto a surface by the Langmuir–Blodget method

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(65), via reaction of silanes with a metal oxide surface (66), or via reaction of alkane thiols, alkane sulfides, or alkane disulfides with a metal surface (67,68). Another popular means of surface modification is through a grafted polysaccharide gel (69). Attachment occurs via straightforward chemistry, beginning with an EDC/NHS modification of the polysaccharide layer (70) followed by coupling of an amine, thiol, or aldehyde group on the protein with an NHS ester. The result is a three-dimensional film of receptor molecules. Affinity binding offers a level of control over receptor molecule orientation and conformation that can significantly exceed that of either physical or chemical attachment. Typically, monoclonal antibodies (IgGs) specific to a region of the receptor molecule away from the active site are used. Binding constants are very high, typically in the range of 109 –1012 M − 1 . The antibody itself may be attached physically, chemically, or via specific linkages between its Fc (constant) region and a preadsorbed Protein A or G molecule (71). Additionally, the antibody may be chemically modified via an attached biotin group; in this case, specific binding occurs between the biotin and a complementary site on a molecule of preadsorbed avidin or streptavidin (72,73). Finally, biomolecules may be immobilized via entrapment within a polymer gel matrix. A number of polymers may be used, eg cellulose acetate (74), poly(vinyl alcohol) (75), and polypyrrole (76). Although high density biomolecule films are possible, a drawback is gradual leakage. This may be alleviated somewhat by cross-linking the biomolecules via chemical reaction. In the case of proteins or peptides, this may be achieved via glutaraldehyde, a reagent that couples with lysine amino acids. Biosensor Detection. As mentioned above, detection occurs via a measurable change in the biosensor’s transducer. Binding of a target molecule to an immobilized chemical receptor may bring about measurable changes that are electrochemical, electrical, thermal, magnetic, optical, or piezoelectric. The principles behind some of these mechanisms are further described in the section entitled Experimental Methods. Additional information can be obtained from a recent review (62).

Intellectual Challenges A number of experimental observations concerning biomolecules at interfaces are at first glance quite puzzling. Many of them stem from a tendency of these (typically) large molecules to display an adsorptive behavior dependent on history. One example from the literature concerns the adsorption of human serum albumin onto synthetic hydroxyapatite (77). In a series of experiments, the concentration of bulk protein to which hydroxyapatite particles were exposed was varied and the adsorbed amount measured. As shown in Figure 1, when the adsorbed density versus concentration in solution (ie the adsorption isotherm) is plotted (Fig. 1), one finds a significant dependence on the “concentration trajectory,” ie on the concentrations to which the surface was exposed at earlier times. Another example is the stepwise adsorption of cellulose onto silica (78). In this experiment, a sample is alternately exposed to solutions of increasing or decreasing cellulose concentration (between each concentration, a rinse is conducted in cellulose-free solution). As shown in Figure 2, it is found that the adsorption isotherm differs, depending

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0.2

C

D

+ +

C s, µg/cm2

B

I

+

+

+

+

0.1 + + +

A

0

200

400 C b,

600

µg/cm3

Fig. 1. The concentration of human serum albumin adsorbed to hydroxyapatite particles versus bulk protein concentration along several concentration “trajectories.” Curve A: a gradual increase in bulk protein concentration via flow of 0.066 g/L protein solution into chamber of particles. Curve B: a gradual decrease in bulk protein concentration via flow of buffer solution without protein. Curve C: a protein concentration of 0.695 g/L for 30 min followed by a gradual decrease in bulk protein concentration via flow of buffer solution. Curve D: a protein concentration of 0.858 g/L for 8 h followed by a gradual decrease in bulk protein concentration via flow of buffer solution. Curve I: Protein concentrations corresponding to the horizontal axis for 8 h. Taken with permission from Ref. 77.

Adsorbed amount, mg/m2

0.4

0.3

0.2

0.1

0 0

75

225 150 Free FHEC concentration, ppm

300

Fig. 2. The density of hydroxyethylcellulose adsorbed to silica versus bulk concentration for a series of alternating 40-min exposures to pure buffer and biopolymer solutions. Curves representing progressively increasing (squares) and decreasing (triangles) concentrations are shown. Taken with permission from Ref. 78.

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upon whether the steps are of increasing or decreasing concentration. In fact, the adsorbed density increases with solution concentration only along the decreasing series. A final example is the multistep kinetic measurement of fibronectin onto silica–titania (79). As in the previous example, a surface is alternately exposed to a protein solution and an otherwise identical solution containing no protein. As shown in Figure 3, when the time between the first and second adsorption step is short, the rates of adsorption along both steps are roughly identical. However, when a longer time period separates the two steps, the rate of adsorption during the second step greatly exceeds—for a given amount of adsorbed protein—the rate during the initial step. These features may be explained by considering two interesting features of biomolecular adsorption (features also exhibited by many synthetic macromolecules): (1) the presence of irreversibility and (2) the presence of postadsorption “relaxation” events on a time scale exceeding that of adsorption. Irreversibility is demonstrated in Figure 4, where the kinetics of cytochrome P450 adsorption to a lipid bilayer are shown (80). One sees that replacement of the protein solution by an identical solution without protein results in only a fraction of the adsorbed molecules leaving the surface, the others being essentially irreversibly adsorbed. The insensitivity of isotherm D in Figure 1 to dilution can be explained by irreversible adsorption occurring at the initial (highest) concentration. The history-dependent behavior observed in Figures 2 and 3 can be explained by post-adsorption relaxation mechanisms. The decreasing nature of the ascending concentration branch of Figure 2 may be explained by the presence of post-adsorption conformational changes. These changes lead to a flatter, more elongated adsorbed molecule and are favored when the rate of adsorption is slow, as occurs when the bulk concentration is low. In contrast, when the rate of adsorption is high, relaxation to the flatter structure is sterically blocked by molecules adsorbing at neighboring positions. If the same type of post-adsorption event occurred in the system whose kinetics are displayed in Figure 3, one would find a decreased rate of adsorption during the second step because of the greater surface area covered by the more conformationally altered molecules. Instead, the increased second-step adsorption rate is caused by another type of post-adsorption structural change: clustering or aggregation among the adsorbed molecules. This event opens up space on the surface in much the same way as clustering furniture in the corner of a room opens space for a social gathering. The history dependence engendered by the slow rate, relative to that of initial attachment, of subsequent relaxation events (eg internal conformational changes, aggregation with other adsorbed molecules) renders challenging the theoretical treatment of biomolecules (as well as many synthetic macromolecules) at interfaces. Nonequilibrium methods must generally be employed, but these are less well developed than their equilibrium counterparts. The quest for a theoretical description is therefore a daunting one; progress along this front is the topic of the next section.

Theoretical Approaches The ultimate objective in any physical science is often to understand a system or phenomenon quantitatively, that is, within the framework of a mathematical

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curve shifted

b

+ × 10−3

0.1 dΓ/dt, µg/cm2
s

Surface density Γ, µg/cm2

0.15

0.05

2 1

++++ + + ++++++++++++

0

a

0

0.05

0.15

0.1

Γ, µg/cm2

0 0

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b

b

shifted curve

0.2

1500

1000 Time t, s (a)

0.15 × 10−3 dΓ/dt, µg/cm2
s1

Surface density Γ, µg/cm2

a

0.1

0.05

2 1

++++ +++++++ + +++

0 0

a 0 0

1000

2000 Time t, s

0.1 Γ, µg/cm2 3000

0.2

4000

(b)

Fig. 3. The density of fibronectin adsorbed to silica–titania versus time for a multistep experiment in which exposure to a flowing solution of 0.05 g/L protein concentration is interrupted by exposure to a flowing solution without protein. (a) A short initial adsorption step and rinse. (b) A longer initial adsorption step and rinse. Taken with permission from Ref. 79.

model. Attempts to model biomolecules at interfaces—where, as mentioned above, history-dependent behavior is rampant—fall principally along five lines. The first and simplest is the site description in which interfacial behavior is modeled as the filling of discrete adsorption sites at the interface. Borrowing heavily from theories on gas adsorption, many closed-form mathematical models are available. A second is the particle description in which the biomolecule is approximated by

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×××××××××××××××××××××××××××××××× ××××××××××××××××××××× ××××××××× ××××××× × × ××× × ×× ×× b × × × ×

a

M, µg/cm2

0.4

0.2

× × 0.0

0

2000

4000

t, s

Fig. 4. The density of cytochrome P450 adsorbed to a lipid bilayer versus time. Points A and B denote the onset and termination of exposure to the protein solution and the dashed line represents the expected curve assuming first-order kinetics and fully reversible adsorption. Taken with permission from Ref. 80.

a simple geometric object whose adsorption behavior is governed by a few lumped phenomenological parameters. A third is the colloidal approach combining the simple particle geometry with an explicit, continuum approach to the forces of interaction. A fourth is the polymer description, in which the chain-like structure of most biomolecules (linear sequence of amino acids in proteins and peptides, linear sequence of nucleic acids in DNA and RNA) is used to justify a treatment using theoretical methods developed for synthetic polymers. Finally, a fifth is the atomistic description in which the detailed molecular architecture of the biomolecule is taken into account. A molecular force field is invoked and the energy from the biomolecule–surface interactions is summed. (Solvent molecules are often implicit.) Of course, the level of detail within each of these approaches varies according to the system and the objectives of study. Generally, the particle description is preferred for modeling systems of all but infinitely dilute surface densities. Site Description. The adsorption of biomolecules at an interfacial region can be modeled as the filling of discrete surface sites. Although such models are more appropriate for gas adsorption, their mathematical simplicity has made them convenient and frequently used tools for modeling biomolecular adsorption as well. The most well known is the Langmuir model, in which fully reversible adsorption occurs onto noninteracting sites. The kinetic expression is
 d  − kd  = ka cs 1 − (1) dt max where  is the adsorbed density, t is the time, ka is the intrinsic adsorption rate, cs is the concentration of adsorbing species in solution at the surface,  max is the density of adsorbed species when all surface sites are filled, and kd is the intrinsic rate of desorption. The solution to equation 1 is  (t) Kcs 1 − e − (ka cs / max +kd )t = max 1+Kcs where K = ka /kd .

(2)

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×

dM , ng/cm2
s dt

2

× 1 × ×

0

0

0.1

0.2

×

××

××× ××× ×××××××××× × 0.3

M, µg/cm2

Fig. 5. The rate of adsorption of transferrin onto silica–titania versus adsorbed amount. Taken with permission from Ref. 81.

A consideration of Figure 4 demonstrates the inadequacy of the Langmuir approach to most biomolecular systems. For one, the saturation is approached much more slowly than the exponential behavior predicted by equation 2. Secondly, by setting cs =0, equation 1 would predict a complete desorption during a rinse. Instead, desorption of only a small fraction of the adsorbed molecules results. Finally, equation 1 predicts a linear relationship between adsorption rate and adsorbed amount. In fact, most systems demonstrate a nonlinear relationship. An example is shown in Figure 5 for transferrin adsorption onto silica–titania (81). Despite these and other drawbacks, the Langmuir model continues to find use in a number of instances. Extensions to account for experimentally observed features of biomolecular adsorption have appeared. For example, the case of adsorption followed by subsequent “spreading” has been treated in the context of a Langmuir approach (82,83). Other examples are models employing interactions between molecules on neighboring sites (or sets of sites in cases of multiple occupancy). Two-dimensional protein ordering or aggregation has been modeled using hexagons adsorbing to a hexagonal lattice (84) and tetramers adsorbing to a square lattice (85). A model additionally considering surface site heterogeneity has also appeared (86). Particle Description. If the adsorption rate reflects the amount of available surface for adsorption, then the nonmonotonic decrease in adsorption rate with adsorbed density of Figure 5 may be interpreted as being due to the filling of a continuous surface by geometric objects. This result is not surprising; when one considers that the greater size of most biomolecules compared to the expected distance between surface attachment sites, adsorption essentially occurs onto a continuum. Such an approach to biomolecular adsorption is called a particle description and, through its more realistic treatment of surface exclusion effects, represents an improvement over a site description. At first thought, modeling a

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complicated biological molecule as a simple geometric object (eg sphere, ellipsoid) seems a ridiculous oversimplification. After all, millennia of evolution have produced biomolecules of exquisite complexity. However, unlike synthetic molecules, certain biomolecules (eg proteins) possess a unique folded three-dimensional structure (many are crystallizable!) and so long as the interfacial perturbation is not too great, may keep this structure and behave, to a first approximation, as a rigid object. (Of course, a large interfacial perturbation may cause the biomolecule to unfold to a degree where a polymer description becomes more appropriate.) In fact, the particle description is able to predict many interesting features of biomolecular adsorption (an important example of this is shown in Figure 5). When adsorption is completely irreversible, the particle description reduces to the random sequential adsorption (RSA) model (87–89). An RSA process is one in which hard objects are added randomly and sequentially to a surface at a given rate and in which any object placed in a position so as to overlap with another object is immediately removed. The governing kinetic equation is d = ka cs  dt

(3)

where  is the fractional surface available for adsorption. For line segments adsorbing to an infinite line, an analytical solution is available (90,91). In higher dimensions, analytical solutions have been elusive. However, exact theoretical treatment is possible in the limits of low and high surface coverage. At low surface coverage,  may be expressed as a power series in surface coverage (92):  = 1+A1 θ+A2 θ 2 +· · ·

(4)

where θ is the fraction of the surface covered by the vertically projected area of the particles. At high surface coverage, the time evolution of the size distribution of isolated regions of empty space may be deduced and related to the overall rate of adsorption. This gives ν

 = Ct − ν = (θ ∞ − θ ) ν − 1

(5)

where C is a constant, θ ∞ is the surface coverage approached as t → ∞, and ν is an exponent whose value depends on the particle geometry. For example, in the case of a disk, ν = 3/2 (93,94); while for an elongated, convex 2-D object, ν = 4/3 (95). A reasonable approximate expression for  valid at all times is found in the form of a Pade approximant (92): ν

≈

(θ ∞ − θ ) ν − 1 1+B1 θ +B2 θ 2 +· · ·

(6)

where the coefficients Bi are evaluated in terms of the known Ai s by matching the first few terms in the θ expansion of equation 6 with those in the θ expansion of equation 4. Most biomolecular adsorption systems exhibit only partial irreversibility (see, eg, Fig. 4). The RSA model may be extended to include desorption and postadsorption structural changes. In this case, one must write at least two kinetic

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equations (one for each structure or “state” of the adsorbed molecule) (96–102): dα = ka cs α − kd α − ks α αβ dt

(7)

dβ = ks α αβ dt

(8)

In equations 7 and 8,  α and  β are the adsorbed densities of molecules in their initial and surface-altered structures, α is the fractional available area for adsorbed molecules in their initial state,  αβ is the probability that an adsorbed molecule in its initial state has available area around it sufficient to allow for a conversion to the surface-altered state, and ks is the intrinsic rate of structural alteration. (Extensions are straightforward to cases of several adsorbed states.) Theoretical approximations to the functions α and  αβ have been made in cases of (1) purely irreversible adsorption (kd = 0, no surface diffusion) using methods analogous to those used to derive equations 4–6 (97), and (2) high surface mobility using the equilibrium-scaled particle method (101,102). Simulations have also been performed (96,98–100). Nonuniform or time-dependent rate constants have also been incorporated in these expressions (99,100,103) and an extension accounting for protein clustering has been developed (104,105). A model combining the site and particle descriptions has been proposed (106). A complete description of the adsorption process may be obtained by coupling equations 7 and 8 to bulk transport equations (107). Another particle description is the molecular mean field treatment in which the free energy of a system of molecules near to an interfacial region is expressed as a functional of the density distribution (108). This approach was inspired by the single-chain mean-field method developed to study the behavior of grafted polymer layers. The equilibrium adsorbate density distribution is just that which minimizes the free-energy functional subject to certain excluded volume constraints. The system’s dynamics may also be determined through a generalized diffusion equation; the diffusive flux is proportional to the chemical potential gradient, and the position-dependent chemical potential is determined as the functional derivative of the (nonequilibrium) free energy with respect to density. Although more computationally intensive than the particle methods discussed above, the major advantages of this method are the straightforward extensions to mixtures, multiple conformational states, realistic intermolecular potentials, and the presence of grafted polymer layers (20–25,109). A brief mention is merited for models treating biomolecular (typically protein) adsorption in the presence of tethered polymer chains. Early efforts utilized the Alexander–de Gennes theory to describe the steric repulsion felt by proteins near the polymer layer in its “brush” regime (18). Although results are qualitatively correct, this approach requires the chains to be longer than those used experimentally, so quantitative applicability is limited. A subsequent effort employed a self-consistent field approach, but again only long chains were considered (19). The treatment of systems with chain lengths closer to those of experiment became possible through the single-chain mean-field theory (20–25). This theory allows for the incorporation of detailed molecular structure for both polymer and protein and has been used to accurately predict the long- and short-time adsorptive properties of biomaterials containing grafted polymer chains (24,110).

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Colloidal Description. A colloidal approach combines the simple particle geometry with an explicit, continuum approach to the forces of interaction (111– 113). At the heart of this approach is a treatment of electrostatics via the Poisson equation, ∇ 2φ = −

 ρ( r ) ε

(9)

where φ is the electric potential, ρ is the charge density, and ε is the dielectric permittivity. Within a solid adsorbent or a (assumed rigid) protein, the charge density distribution results from the presence of immobile charged species. In solution, the charge density distribution results from dissolved ionic species, which may be assumed to be distributed in a Boltzmann manner,     ρi ( r ) = ρi,bulk zi exp − zi eφ( r )/kT

(10)

where ρ i,bulk is the bulk density of ionic species i, zi is its valence, e is the elementary charge, k is the Boltzmann constant, and T is the absolute temperature. The resulting electric potential—which for all but the simplest geometries must be determined numerically—is used to calculate the total interaction energy Uelec =



 zi eφ( r i )

(11)

i

where the sum runs over all charges in the system. (The sum becomes an integral in the case of a continuous charge distribution.) Colloidal approaches also frequently account for van der Waals interactions, ie interactions due to fluctuating dipoles. For atomic species, these interactions vary as distance to the minus sixth power. For protein/surface systems modeled via a colloidal description, this 1/r6 dependence is integrated over the volumes of the interacting bodies. The result is the product of a Hamaker constant, which depends upon material properties, and a term dependent on the system’s geometry. In addition, forces related to solvation (114) and donor/acceptor (115) affects may also be included. Although not amenable to predictions of irreversibility or conformational change, colloidal approaches have been successful in predicting qualitative trends in—and, to a certain extent, quantitative values of—equilibrium constants in the case of fully reversible adsorption at low surface coverage (116–120). In many cases, simple protein geometries and charge distributions suffice. In other cases, such as when adsorption is controlled by charged patches (121,122), more realistic models must be used. An accounting of protein–protein interactions to allow for a finite surface coverage has also been made (123–126). The colloidal approach has also been applied to the adsorption of DNA on to a charged surface (127,128). Polymer Description. A lattice model heteropolymer (129–131) provides a simple yet instructive description of a protein molecule. In general, the coarse graining is such that each segment represents a portion of the protein (ie many amino acids). In the simplest case, two types of segments are present; these may be thought of as polar and hydrophobic (132–138). In other cases, a distribution

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of segmental interactions is employed (139–143). The minimalist nature of this model allows for efficient sampling of conformational space via simulation (for chains of less than 20 segments, exact enumeration of all conformations is possible). Despite its apparent simplicity, for a proper choice of segment–segment nearest-neighbor interaction strength, this model is capable of exhibiting the essential physics of protein folding (eg coil–globule and globule–folded transitions and the presence of a glass transition). Of particular importance have been 27 segment models in which certain sequences fold into a unique 3 × 3 × 3 cubic structure (134,136–143). Recently, uniquely folding sequences have been studied at liquid– solid (99,144–146) and liquid–liquid (147) interfaces. An interesting observation has been the initial continuous transition of the model protein to an unfolded, fully flattened state followed by an activated transition to a partially refolded, lessflattened state (145,146). Proteins modeled as shorter chains, where exact enumeration is possible, have also been studied at the liquid–solid interface (148,149). Other lattice polymer efforts have been based on the self-consistent field theory of Scheutjens and Fleer (150,151). This approach differs from previously posed statistical theories for chain molecules in that the partition function is expressed in terms of the distribution of chain conformations rather than the distribution of segment densities. The equilibrium distribution of chain (ie model protein) conformations is thus calculable. Quantities predicted using this approach include the force between parallel plates coated with protein (152,153), the adsorption isotherm (154,155), and the segmental density distribution (154–157). A simple yet instructive model for determining general features of certain biomolecules at interfaces is the random heteropolymer description (158–174). A random heteropolymer is defined as one whose sequence of monomers follows a statistical distribution. A collection of random heteropolymers is therefore an example of a quenched–annealed system, that is, one in which certain degrees of freedom are fixed and follow a known distribution (in this case, the heteropolymer sequence) and others equilibrate with respect to these fixed degrees of freedom (in this case, the spatial distribution of the segments). Special methods developed for treating such systems (175) are therefore applicable and have been useful in determining properties of single (160) and sets of (162,164) adsorbed chains. Clearly, nucleic acids are also amenable to a polymer description. Theoretical (176) and simulation (177,178) methods have been used to determine the structure, dynamics, and thermodynamics of nucleic acid chains on surfaces. Atomistic Description. Molecular modeling at the atomistic level has become commonplace. The dual challenges of accurate potential force field description and efficient configurational sampling have been met to a degree where predictive capabilities now exist for many single- and multicomponent systems of simple molecules. The extension of these methods to biomolecules, and more specifically to biomolecules at interfaces, presents a challenge because of the size and complexity of these molecules. However, some attempts to calculate physical properties of atomistically modeled biomolecules at interfaces have appeared (see Molecular modeling (structure, molec. graphics)). Early efforts were essentially static calculations of the interaction energy between a rigid protein and a surface (112,114,121,179–181). Pairwise atomistic potential energy descriptions were used to calculate the van der Waals and electrostatic contributions. In the case of hydrophobic surfaces, solvation energies

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were estimated from partition coefficients of the individual amino acids between aqueous and organic phases (114,180). Some of these studies treated the electrostatic interactions in a colloidal manner (112,121). The calculated energies for various geometries were helpful in understanding chromatographic behavior. Similar calculations of individual amino acids on self-assembled monolayers have also been conducted with the hope of uncovering trends useful for predicting behavior of entire protein molecules (182). Molecular dynamics (MD) is a method in which Newton’s equations of motion are solved for a molecular system obeying a differentiable potential function. A few efforts at modeling proteins at interfaces using MD have appeared (183– 187). Obviously, these studies provide dynamic as well as thermodynamic information on biomolecules at interfaces. Systems studied have included lysozyme and myoglobin on polyethylene glycol (183), cytochrome c on hydrophilic and hydrophobic self-assembled monolayers (184), leucine enkephalin near a crystalline polyethylene surface (185), thermal hysteresis proteins on ice (186), and lysozyme on polyvinylimidazole (187).

Experimental Methods Progress in any field requires information on the state of well-defined systems as a function of conditions. Advancement is thus intimately linked to the availability of experimental probes capable of providing accurate and detailed information. Important metrics of biomolecules at interfaces include the interfacial composition; distributions in molecular orientation, molecular spatial arrangement, and intramolecular conformation; and biological activity. In this section, several experimental techniques probing the physical properties of biomolecules at interfaces are introduced; these are grouped into optical, piezoelectric, and scanning probe methods. Further details can be found in other excellent reviews (62,188,189). Optical Methods. Optical methods involve directing polarized monochromatic light toward the solid–liquid interface and measuring a response, eg the polarity or intensity of reflected or emitted light. Various schemes have been proposed, as described below, and these allow for the determination of adsorbed-layer thickness, density, and composition as well as information on internal conformation. Principal advantages of optical experimental probes include nondestructiveness and the capability of continuous, real-time measurements. Reflection-based methods (190–194) involve measuring the reflection of polarized light at the interface between two optical media. In fact, two reflections are measured: one for the electric field component perpendicular to the plane of incidence (transverse electric or s-wave) and one for the electric field component parallel to the plane of incidence (transverse magnetic or p-wave). At a certain angle of incidence (the Brewster angle), the p-wave reflection vanishes and around this angle, the reflectivity, or square of the amplitude of the p-wave reflection, and ellipticity, or ratio of p- and s-wave reflections, become very sensitive to interfacial heterogeneity, as brought about eg by adsorption of biomolecules. By assuming the adsorbed layer to be uniform in refractive index, both its thickness and refractive index may be determined. By further assuming a linear dependence of refractive index on concentration, the adsorbed density is calculable (195).

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Optical waveguide methods (188,196–198) are based on the phase shift associated with multiple interfacial reflections: when either the s- or p-wave undergoes a total phase shift equal to an integral multiple of 2π upon one complete traversal of a planar, dielectric waveguide sandwiched between media of lower refractive index, a standing wave is excited in the waveguiding film. Because of their dependence on reflection, the phase shifts are sensitive to interfacial heterogeneity—and the thickness, refractive index, and density of an adsorbed biomolecular layer can be readily determined. When light traversing an optically dense medium approaches an interface with a more optically rare medium at an angle exceeding a critical value, θ crit = sin − 1 (nrare /ndens ), a total internal reflection occurs and an evanescent wave of exponentially decaying intensity penetrates the rarer medium. This phenomenon is at the heart of certain spectroscopic methods used to probe biomolecules at interfaces (199). In total internal reflection fluorescence (TIRF) spectroscopy (200–202), the evanescent wave excites fluorescent probes attached to the biomolecules, and detection of the emission associated with their decay provides information on the density, composition, and conformation of adsorbed molecules. In fourier transform infrared attenuated total reflection (FTIR-ATIR) spectroscopy (203,204), the evanescent wave excites certain molecular vibrational degrees of freedom, and the detected loss in intensity due to these absorbances can provide quantitative data on density, composition, and conformation. Surface plasmon resonance (SPR) (205–209) is an optical method in which the p-wave of incident light excites a propagating, nonradiative charge density oscillation at a metal–dielectric interface. The resonant condition is the matching of the wave vector component of the p-wave parallel to the interface to the wave vector of the surface plasmon. The latter is sensitive to the optical properties of a fluid or adlayer near the interface, so by monitoring changes in the angular distribution of the intensity of reflected light, physical properties of adsorbed species may be determined. Piezoelectric Methods. A piezoelectric crystal is one in which a mechanical stress induces an electric current. Conversely, application of an alternating voltage to a piezoelectric crystal induces a vibration. The frequency of oscillation is extremely sensitive to the mass contacting the crystal, and it is the frequency shift due to adsorption that is the basis for piezoelectric methods (210). A quartz crystal microbalance (QCM) (211–214) consists of a thin disk of (piezoelectric) crystalline quartz sandwiched between thin-film metal electrodes. Upon application of an alternating voltage, the crystal undergoes thickness shear mode vibration. The mass adsorbed to the electrode surface—here, unlike in the optical methods described above, the mass includes trapped solvent—is simply proportional to the frequency shift. In addition, the dissipation of energy following voltage removal, as measured by the decay of the oscillation amplitude, is a sensitive measure of the viscoelastic properties of an adsorbed layer. QCM thus provides a valuable complement to optical methods through information concerning conformation (via the amount of trapped solvent in an adsorbed film) and rigidity (via the film viscoelastic response). Scanning Probe Methods. Scanning probe methods (215–217) involve probing a solid surface with a very sharp tip and measuring its deflection or other physical change in order to create a topographical image or to determine a surface force profile. Two common methods for imaging biomolecules at interfaces

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are contact-mode and tapping-mode atomic force microscopy. In the former, the tip is scanned over the surface while remaining essentially in contact with the surface or adsorbed species. In the latter, the probe oscillates as it scans and only in the “valley” of each oscillation does it contact the substrate. An advantage to the tapping-mode method is the elimination of shear forces capable of damaging soft samples (eg biomolecules) that can diminish image resolution. Atomic force microscopy in force–distance mode provides information on the intramolecular, intermolecular, and molecule–surface forces. The experiment involves directing the tip (often coated with biomolecules) toward the surface and measuring the resulting force as a function of tip–surface distance. The capability to extract information from individual molecules is the principal advantage to scanning probe methods; in contrast, optical and piezoelectric methods give information on the collective properties of an adsorbed layer.

Conclusions Biomolecules at interfaces continues to be a challenging and important subject of basic research and biotechnological development. Despite intense investigation for several decades, a number of significant challenges remain, including the complete prevention of protein adsorption onto blood-contacting biomaterials, the controlled placement of biologically active molecules on sensing and tissue engineering substrates, and the quantitative prediction of events occurring as biomolecules approach and reside at the interfacial region. Recent experimental developments, particularly those in optical, scanning probe, and piezoelectric instrumentation—and advances in statistical–mechanical modeling, interatomic force field development, and computational power—are converging to provide new insights, at an unparalleled rate, in order to meet these and other emerging challenges.

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PAUL R. VAN TASSEL Wayne State University

Vol. 5

BULK AND SOLUTION POLYMERIZATIONS REACTORS

BIOTECHNOLOGY APPLICATIONS. BLOCK COPOLYMERS.

See Volume 1.

See Volume 1.

BLOCK COPOLYMERS, TERNARY TRIBLOCK. BLOWING AGENTS. BLOW MOLDING.

307

See CELLULAR MATERIALS.

See Volume 1.

See Volume 1.