biomolecules at interfaces

Vol. 5 BIOMOLECULES AT INTERFACES 285

BIOMOLECULES AT INTERFACES

Introduction

Many biomolecules are amphiphilic, that is, possess certain regions that inter-act favorably, and others that interact less favorably, with an aqueous solvent.As such, these biomolecules tend to reside at the interfacial region separatingan aqueous phase from another phase of matter. The process of interfacial at-tachment is referred to as “adsorption”; “adsorbed molecules” or “adsorbates”are terms describing molecules having undergone adsorption (qv). The princi-pal forces leading to adsorption have been identified; these are the ionic, vander Waals, hydrogen bonding, donor/acceptor, and solvation interactions (1). At-tachment by a chemical bond is also possible. Proteins, peptides, amino acids,polysaccharides, lipids, and nucleic acids are examples of biological moleculesknown to adsorb at solid–liquid, liquid–liquid, and/or liquid–vapor interfaces.To fully understand a biomolecule, one must understand its behavior at rele-vant interfaces, for it is the rare biomolecule not exhibiting a strong tendency toadsorb!

Many examples of biomolecules at interfaces come from nature. Membraneproteins—a term describing those spanning the cell membrane—actually reside attwo interfaces (intracellular matrix–cell membrane and extracellular matrix–cellmembrane) and serve to regulate transport into and out of cells. Plasma proteins—those existing in blood—attach to the surface of an unrecognized material andinitiate the clotting cascade. Other examples come from technological applications.The above-mentioned clotting process unfortunately occurs onto medical implantsas well. Interfacial adsorption is ubiquitous during bioprocessing applications; thiscan have the deleterious effects of vessel fouling and product structural alteration.Adsorption is one common mechanism by which bioseparations are conducted andbiocatalysts are immobilized. Adsorbed protein layers are known to have a stronginfluence on living cells; this effect is exploited in tissue engineering and cellularbioreactors. Finally, both the fabrication of, and detection using, biosensors involvebiomolecules residing at interfaces.

Encyclopedia of Polymer Science and Technology. Copyright John Wiley & Sons, Inc. All rights reserved.

286 BIOMOLECULES AT INTERFACES Vol. 5

The purpose of this article is to introduce, expand interest in, and growawareness of, the field of biomolecules at interfaces. Motivation for study in anyfield is typically driven by either application or curiosity. Workers investigatingbiomolecules at interfaces are fortunate in that numerous important technologi-cal applications exist together with several intriguing and perplexing (and for themost part unsolved!) intellectual curiosities. In most areas of science and engi-neering, important advances accompany the close interplay between theoreticalprediction and experimental measurement. Biomolecules at interfaces is no excep-tion, and a summary of key theoretical tools and experimental methods comprisesthe subsequent two sections. Note that no attempt is made toward an exhaustivecoverage of biomolecule/interface systems. The reader is also invited to consultother excellent reviews related to this topic (1–3).

Technological Applications

A number of important technological applications motivate the study ofbiomolecules at interfaces. In this section, discussion focuses on important ex-amples in two areas: biomaterials and biosensors.

Biomaterials. Biomaterials find important application as medical im-plants and tissue engineering substrates. In each case, clinical or scientific ef-fectiveness strongly depends on the behavior of interfacial biomolecules. Otherarticles in this encyclopedia discuss various aspects of biomaterials. In this sec-tion, 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 univer-sal problem concerns unwanted biological responses; these may be thrombogenic,inflammatory, immunological, or infectious (4–6). It is now well established thatprotein adsorption precedes and directs these unfavorable events. For example,it is the plasma protein fibrinogen that is thought to initiate thrombogenesis. Asmall conformational change in the adsorbed fibrinogen is now known to causeplatelet adhesion and subsequent aggregation; these events are followed by fibrinformation (6).

Not surprisingly, focus has been directed toward preventing protein adsorp-tion altogether or promoting adsorption of “passivating” proteins (ie those knownnot to trigger subsequent biological responses). A preeminent strategy for prevent-ing initial protein adsorption involves the grafting of hydrophilic polymer chainsto a material surface. Polyethylene oxide (PEO) is particularly effective in thiscapacity (7–17). The originally suggested mechanism by which PEO prevents pro-tein adsorption involved hydrodynamic currents due to the motion of the graftedchains (7). Subsequent theoretical work has shown that proteins residing withinreach of the polymeric brush reduce the conformational freedom of the graftedchains; the polymer layer thus provides an entropic barrier to adsorption (18–25).Very recent work has also demonstrated the importance of the conformationalfreedom of the individual PEO monomeric units to the prevention of protein ad-sorption (17).

An alternative to the complete prevention of protein adsorption is the con-trolled placement of certain biomolecules that act against thrombogenesis. One


natural choice is heparin, an anticoagulant. A number of studies suggest thatsurfaces with grafted heparin show a diminished thrombogenic response (26,27),but controversy remains as to whether the mechanism is due to heparin-catalyzedantithrombin deactivation of coagulation proteases (28) or to a suppressed adsorp-tion of cell adhesion proteins (29). In addition, although success has been achievedwith heparin-coated surfaces, results are not uniformly favorable (30).

Tissue Engineering Substrates. Tissue Engineering (qv) is a field ofbiomedical study in which techniques are sought to create functional replacementsfor diseased human tissues and organs (31–36). Successful tissue engineering of-fers the potential for considerable prolongation of the length and quality of humanlife. Additionally, it has been estimated that the availability of engineered tissuescould reduce expenses related to tissue loss and end-state organ failure by $400billion per year (31). The key issue in tissue engineering is the availability of mate-rials onto which cells attach, spread, grow, differentiate, and eventually organizeto form a desired tissue. Reasoning that the presence of an artificial materialwould tend to inhibit cellular activity, early efforts were directed toward develop-ing biologically inert materials. The current view, however, is one of a materialpossessing chemical/biological sequences and patterns capable of signaling andcontrolling the cellular response (32,37). Materials promoting a natural response,inducing a supernormal response, and/or inhibiting a naturally occurring (butunwanted) response are needed to engineer replacement human tissues.

Tissues or cells typically interact with a biomaterial indirectly through alayer of adsorbed protein. Certain matrix proteins are known to promote cellattachment and growth. One example is fibronectin, a large, extracellular gly-coprotein whose constituent modules contain binding sites for a wide range ofbiomolecules and biological units (38). Its cell-binding site, consisting of the tripep-tide amino acid sequence argenine–glycine–asperigine (RGD), is known to bindto the integrin proteins located within the cell membrane; this triggers eventsthat ultimately induce the adhesion, spreading, and growth of cells. Thus, onestrategy toward biomaterials for tissue engineering applications is to attach tothe biomaterial surface, either chemically or physically, a layer of matrix protein(39–48).

An important alternative to the surface placement of entire proteins is thedirect attachment of the cell-binding peptide sequences, such as the RGD sequencein fibronectin (32,37,49–59). This is an example of a “biomimetic” strategy, ie onethat mimics biology. Advantages over direct placement of proteins are the greaterdegree of control of peptide density, spatial arrangement, and orientation andthe diminished risk of the material triggering an immune response (37). Disad-vantages include the need for additional chemical surface modification (one mustgenerally attach the peptide units and grafted linear polymer chains such as PEOto ensure that proteins do not adsorb and cover the peptides) and the loss of biolog-ical signaling from other peptide sequences on the proteins. A number of successeshave been reported and it is safe to say that this is currently the most activelyresearched approach to develop biomaterials as tissue engineering substrates.

Biosensors. A biosensor is an analytical device for the detection of a tar-get biomolecule (60–63). Although many variations are possible, all biosensorscombine a detector, where a biological recognition event takes place, with a trans-ducer, which produces an output signal from the recognition event. A biosensor


must be selective for the target molecule in a mixture of structurally similarspecies. Robustness, cost, size, and real-time measurement capability are addi-tional factors governing the effectiveness of a given biosensing configuration. Anumber of clinical and biomedical applications are envisioned, but to date themost successful examples of commercialization are the glucose detectors used inthe management of diabetes. Other important applications are found in food pro-duction, 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 areoften themselves biomolecules. Detection involves an interaction between theseimmobilized molecules and biomolecules from solution that approach the detectorsurface. In this sense, both the fabrication of, and detection using, biosensorsinvolve biomolecules at interfaces.

Biosensor Fabrication. A crucial step in biosensor fabrication is the im-mobilization of chemical receptors. Chemical receptors may be of two types: cat-alytic or affinity. In both cases, the target molecule binds specifically to a chemicalreceptor. In the former, the binding event triggers a measurable change in thetransducer. In the latter, the specific binding event leads to a catalyzed chemicalreaction, often involving the target molecule itself. The presence of the catalyzedreaction product(s) then triggers a measurable change in the transducer. An im-portant example is the catalytic glucose sensor, in which an oxidation of glucosetakes place by immobilized glucose oxidase to gluconic acid and hydrogen perox-ide. 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 (covalentattachment) to the surface, (3) affinity binding to physically or chemically boundspecies, and (4) entrapment within a matrix. Since physical adsorption relies onrelatively weak forces (van der Waals, ionic, solvation, donor/acceptor), moleculesplaced in this way may detach over time and/or exhibit nonuniform biologicalactivity because of a distribution of surface orientations/conformations. However,this method is clearly the simplest of the four and therefore often finds use. Anexample is the popular enzyme-linked immunosorbent assay (ELISA) used inmedical diagnostics.

A more robust and controllable means of surface attachment is through acovalent bond. Large biomolecules such as proteins typically possess a numberof functional groups capable of chemical binding; these include amino, carboxyl,sulfhydryl, phenolic, thiol, and imidizol groups. The best choice for preservingbiological activity and optimizing accessibility of the receptor’s active site is of-ten a functional group far from the active site. Suitable complementary reactivegroups are available on some surfaces (for example, hydroxyl groups on silica), butin many cases, surface modification is needed. A popular means of surface mod-ification is to employ self-assembled monolayers (SAMs) (64). SAMs are closelypacked, (approximately) vertically aligned alkane chains residing at an interface.Through chemically functionalized termini, the tailoring of physical and chem-ical properties of the surface is possible. Chemical immobilization results froma reaction between a specific functional group at a SAM molecule terminus anda biomolecule. (In some cases, a bifunctional reagent is used to achieve the cou-pling.) A SAM may be placed onto a surface by the Langmuir–Blodget method


(65), via reaction of silanes with a metal oxide surface (66), or via reaction ofalkane thiols, alkane sulfides, or alkane disulfides with a metal surface (67,68).Another popular means of surface modification is through a grafted polysaccha-ride gel (69). Attachment occurs via straightforward chemistry, beginning with anEDC/NHS modification of the polysaccharide layer (70) followed by coupling of anamine, thiol, or aldehyde group on the protein with an NHS ester. The result is athree-dimensional film of receptor molecules.

Affinity binding offers a level of control over receptor molecule orientationand conformation that can significantly exceed that of either physical or chemicalattachment. Typically, monoclonal antibodies (IgGs) specific to a region of thereceptor molecule away from the active site are used. Binding constants are veryhigh, typically in the range of 109–1012 M − 1. The antibody itself may be attachedphysically, chemically, or via specific linkages between its Fc (constant) regionand a preadsorbed Protein A or G molecule (71). Additionally, the antibody maybe chemically modified via an attached biotin group; in this case, specific bindingoccurs between the biotin and a complementary site on a molecule of preadsorbedavidin or streptavidin (72,73).

Finally, biomolecules may be immobilized via entrapment within a polymergel matrix. A number of polymers may be used, eg cellulose acetate (74), poly(vinylalcohol) (75), and polypyrrole (76). Although high density biomolecule films arepossible, a drawback is gradual leakage. This may be alleviated somewhat bycross-linking the biomolecules via chemical reaction. In the case of proteins orpeptides, this may be achieved via glutaraldehyde, a reagent that couples withlysine amino acids.

Biosensor Detection. As mentioned above, detection occurs via a mea-surable change in the biosensor’s transducer. Binding of a target molecule toan immobilized chemical receptor may bring about measurable changes thatare electrochemical, electrical, thermal, magnetic, optical, or piezoelectric. Theprinciples behind some of these mechanisms are further described in the sectionentitled Experimental Methods. Additional information can be obtained from arecent review (62).

Intellectual Challenges

A number of experimental observations concerning biomolecules at interfaces areat first glance quite puzzling. Many of them stem from a tendency of these (typi-cally) large molecules to display an adsorptive behavior dependent on history. Oneexample from the literature concerns the adsorption of human serum albuminonto synthetic hydroxyapatite (77). In a series of experiments, the concentrationof bulk protein to which hydroxyapatite particles were exposed was varied andthe adsorbed amount measured. As shown in Figure 1, when the adsorbed densityversus concentration in solution (ie the adsorption isotherm) is plotted (Fig. 1), onefinds a significant dependence on the “concentration trajectory,” ie on the concen-trations to which the surface was exposed at earlier times. Another example is thestepwise adsorption of cellulose onto silica (78). In this experiment, a sample is al-ternately exposed to solutions of increasing or decreasing cellulose concentration(between each concentration, a rinse is conducted in cellulose-free solution). Asshown in Figure 2, it is found that the adsorption isotherm differs, depending


+

++

++

+

++

+

A

D

B

CI

0 200 400 600

Cb, µg/cm3

Cs,

µg/c

m2

0.1

0.2

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

0.4

0.3

0.2

0.1

00 75 150 225 300

Ads

orbe

d am

ount

, mg/

m2

Free FHEC concentration, ppm

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


upon whether the steps are of increasing or decreasing concentration. Infact, the adsorbed density increases with solution concentration only alongthe decreasing series. A final example is the multistep kinetic measurementof fibronectin onto silica–titania (79). As in the previous example, a surface isalternately exposed to a protein solution and an otherwise identical solutioncontaining no protein. As shown in Figure 3, when the time between the firstand second adsorption step is short, the rates of adsorption along both steps areroughly identical. However, when a longer time period separates the two steps,the rate of adsorption during the second step greatly exceeds—for a given amountof adsorbed protein—the rate during the initial step.

These features may be explained by considering two interesting featuresof biomolecular adsorption (features also exhibited by many synthetic macro-molecules): (1) the presence of irreversibility and (2) the presence of post-adsorption “relaxation” events on a time scale exceeding that of adsorption.Irreversibility is demonstrated in Figure 4, where the kinetics of cytochromeP450 adsorption to a lipid bilayer are shown (80). One sees that replacementof the protein solution by an identical solution without protein results in onlya fraction of the adsorbed molecules leaving the surface, the others being essen-tially irreversibly adsorbed. The insensitivity of isotherm D in Figure 1 to dilutioncan be explained by irreversible adsorption occurring at the initial (highest) con-centration. The history-dependent behavior observed in Figures 2 and 3 can beexplained by post-adsorption relaxation mechanisms. The decreasing nature ofthe ascending concentration branch of Figure 2 may be explained by the pres-ence of post-adsorption conformational changes. These changes lead to a flatter,more elongated adsorbed molecule and are favored when the rate of adsorptionis slow, as occurs when the bulk concentration is low. In contrast, when the rateof adsorption is high, relaxation to the flatter structure is sterically blocked bymolecules adsorbing at neighboring positions. If the same type of post-adsorptionevent occurred in the system whose kinetics are displayed in Figure 3, one wouldfind a decreased rate of adsorption during the second step because of the greatersurface area covered by the more conformationally altered molecules. Instead, theincreased second-step adsorption rate is caused by another type of post-adsorptionstructural change: clustering or aggregation among the adsorbed molecules. Thisevent opens up space on the surface in much the same way as clustering furniturein the corner of a room opens space for a social gathering.

The history dependence engendered by the slow rate, relative to that ofinitial attachment, of subsequent relaxation events (eg internal conformationalchanges, aggregation with other adsorbed molecules) renders challenging thetheoretical treatment of biomolecules (as well as many synthetic macromolecules)at interfaces. Nonequilibrium methods must generally be employed, but these areless well developed than their equilibrium counterparts. The quest for a theoret-ical description is therefore a daunting one; progress along this front is the topicof the next section.

Theoretical Approaches

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


0 500 1000 1500

0

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0.15

Sur

face

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sity

Γ,µ

g/cm

2

Time t, s

+

+

+++

+++++

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

curve shifted

a

b

a

× 10−3

0 0.05 0.1 0.15

Γ, µg/cm2

0

1

2

dΓ/d

t,µg

/cm

2 �s

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

(a)

0 1000 2000 3000

0

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face

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sity

Γ,µ

g/cm

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Time t, s

shifted curve

× 10−3

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Γ, µg/cm2

0

1

2

dΓ/d

t,µg

/cm

2 �s1

4000

0.2b

a

a

b

+++

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

(b)

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

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


a

b

×

×

××××××

×××××

×××××××× ××××××× ××××××××××××××××××××××××××××× ××××××××××××××××××××××××××××

0.4

0.2

0.00 2000 4000

t, s

M,µ

g/cm

2

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

a simple geometric object whose adsorption behavior is governed by a few lumpedphenomenological parameters. A third is the colloidal approach combining thesimple particle geometry with an explicit, continuum approach to the forces of in-teraction. A fourth is the polymer description, in which the chain-like structure ofmost biomolecules (linear sequence of amino acids in proteins and peptides, linearsequence of nucleic acids in DNA and RNA) is used to justify a treatment usingtheoretical methods developed for synthetic polymers. Finally, a fifth is the atom-istic description in which the detailed molecular architecture of the biomoleculeis taken into account. A molecular force field is invoked and the energy fromthe biomolecule–surface interactions is summed. (Solvent molecules are often im-plicit.) Of course, the level of detail within each of these approaches varies accord-ing to the system and the objectives of study. Generally, the particle descriptionis preferred for modeling systems of all but infinitely dilute surface densities.

Site Description. The adsorption of biomolecules at an interfacial regioncan be modeled as the filling of discrete surface sites. Although such models aremore appropriate for gas adsorption, their mathematical simplicity has madethem convenient and frequently used tools for modeling biomolecular adsorptionas well. The most well known is the Langmuir model, in which fully reversibleadsorption occurs onto noninteracting sites. The kinetic expression is

d�

dt= kacs

(1 − �

�max

)− kd� (1)

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 thedensity of adsorbed species when all surface sites are filled, and kd is the intrinsicrate of desorption. The solution to equation 1 is

�(t)�max

= Kcs

1+Kcs

[1 − e − (kacs/�max+kd)t] (2)

where K = ka/kd.


×

×

×

××

×××××××××××××××××××

0 0.1 0.2 0.3

2

1

0

M, µg/cm2

dM dt ,

ng/

cm2 �s

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 Langmuirapproach to most biomolecular systems. For one, the saturation is approachedmuch more slowly than the exponential behavior predicted by equation 2. Sec-ondly, by setting cs=0, equation 1 would predict a complete desorption during arinse. Instead, desorption of only a small fraction of the adsorbed molecules re-sults. Finally, equation 1 predicts a linear relationship between adsorption rateand 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 ina number of instances.

Extensions to account for experimentally observed features of biomolecu-lar adsorption have appeared. For example, the case of adsorption followed bysubsequent “spreading” has been treated in the context of a Langmuir approach(82,83). Other examples are models employing interactions between molecules onneighboring sites (or sets of sites in cases of multiple occupancy). Two-dimensionalprotein ordering or aggregation has been modeled using hexagons adsorbing to ahexagonal lattice (84) and tetramers adsorbing to a square lattice (85). A modeladditionally considering surface site heterogeneity has also appeared (86).

Particle Description. If the adsorption rate reflects the amount of avail-able surface for adsorption, then the nonmonotonic decrease in adsorption ratewith adsorbed density of Figure 5 may be interpreted as being due to the fillingof a continuous surface by geometric objects. This result is not surprising; whenone considers that the greater size of most biomolecules compared to the expecteddistance between surface attachment sites, adsorption essentially occurs onto acontinuum. Such an approach to biomolecular adsorption is called a particle de-scription and, through its more realistic treatment of surface exclusion effects,represents an improvement over a site description. At first thought, modeling a


complicated biological molecule as a simple geometric object (eg sphere, ellipsoid)seems a ridiculous oversimplification. After all, millennia of evolution have pro-duced biomolecules of exquisite complexity. However, unlike synthetic molecules,certain biomolecules (eg proteins) possess a unique folded three-dimensionalstructure (many are crystallizable!) and so long as the interfacial perturbationis not too great, may keep this structure and behave, to a first approximation, as arigid object. (Of course, a large interfacial perturbation may cause the biomoleculeto unfold to a degree where a polymer description becomes more appropriate.)In fact, the particle description is able to predict many interesting features ofbiomolecular adsorption (an important example of this is shown in Figure 5).

When adsorption is completely irreversible, the particle description reducesto the random sequential adsorption (RSA) model (87–89). An RSA process is onein which hard objects are added randomly and sequentially to a surface at a givenrate and in which any object placed in a position so as to overlap with anotherobject is immediately removed. The governing kinetic equation is

d�

dt= kacs� (3)

where � is the fractional surface available for adsorption. For line segments ad-sorbing to an infinite line, an analytical solution is available (90,91). In higherdimensions, analytical solutions have been elusive. However, exact theoreticaltreatment is possible in the limits of low and high surface coverage. At low sur-face coverage, � may be expressed as a power series in surface coverage (92):

� = 1+A1θ+A2θ2+· · · (4)

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

� = Ct − ν = (θ∞ − θ)ν

ν − 1 (5)

where C is a constant, θ∞ is the surface coverage approached as t → ∞, and ν isan exponent whose value depends on the particle geometry. For example, in thecase 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 theform of a Pade approximant (92):

�≈ (θ∞ − θ )ν

ν − 1

1+B1θ+B2θ2+· · · (6)

where the coefficients Bi are evaluated in terms of the known Ais by matching thefirst few terms in the θ expansion of equation 6 with those in the θ expansion ofequation 4.

Most biomolecular adsorption systems exhibit only partial irreversibility(see, eg, Fig. 4). The RSA model may be extended to include desorption and post-adsorption structural changes. In this case, one must write at least two kinetic


equations (one for each structure or “state” of the adsorbed molecule) (96–102):

d�α

dt= kacs�α − kd�α − ks�α�αβ (7)

d�β

dt= ks�α�αβ (8)

In equations 7 and 8, �α and �β are the adsorbed densities of molecules intheir initial and surface-altered structures, �α is the fractional available area foradsorbed molecules in their initial state, �αβ is the probability that an adsorbedmolecule in its initial state has available area around it sufficient to allow for aconversion to the surface-altered state, and ks is the intrinsic rate of structuralalteration. (Extensions are straightforward to cases of several adsorbed states.)Theoretical approximations to the functions �α and �αβ have been made in casesof (1) purely irreversible adsorption (kd = 0, no surface diffusion) using methodsanalogous to those used to derive equations 4–6 (97), and (2) high surface mo-bility using the equilibrium-scaled particle method (101,102). Simulations havealso been performed (96,98–100). Nonuniform or time-dependent rate constantshave also been incorporated in these expressions (99,100,103) and an extension ac-counting for protein clustering has been developed (104,105). A model combiningthe site and particle descriptions has been proposed (106). A complete descriptionof the adsorption process may be obtained by coupling equations 7 and 8 to bulktransport equations (107).

Another particle description is the molecular mean field treatment in whichthe free energy of a system of molecules near to an interfacial region is expressedas a functional of the density distribution (108). This approach was inspired by thesingle-chain mean-field method developed to study the behavior of grafted poly-mer layers. The equilibrium adsorbate density distribution is just that which min-imizes the free-energy functional subject to certain excluded volume constraints.The system’s dynamics may also be determined through a generalized diffusionequation; the diffusive flux is proportional to the chemical potential gradient, andthe position-dependent chemical potential is determined as the functional deriva-tive of the (nonequilibrium) free energy with respect to density. Although morecomputationally intensive than the particle methods discussed above, the majoradvantages of this method are the straightforward extensions to mixtures, mul-tiple conformational states, realistic intermolecular potentials, and the presenceof grafted polymer layers (20–25,109).

A brief mention is merited for models treating biomolecular (typically pro-tein) adsorption in the presence of tethered polymer chains. Early efforts uti-lized the Alexander–de Gennes theory to describe the steric repulsion felt byproteins near the polymer layer in its “brush” regime (18). Although results arequalitatively correct, this approach requires the chains to be longer than thoseused experimentally, so quantitative applicability is limited. A subsequent effortemployed a self-consistent field approach, but again only long chains were consid-ered (19). The treatment of systems with chain lengths closer to those of exper-iment became possible through the single-chain mean-field theory (20–25). Thistheory allows for the incorporation of detailed molecular structure for both poly-mer and protein and has been used to accurately predict the long- and short-timeadsorptive properties of biomaterials containing grafted polymer chains (24,110).


Colloidal Description. A colloidal approach combines the simple particlegeometry 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 Poissonequation,

∇2φ = − ρ(⇀r )ε

(9)

where φ is the electric potential, ρ is the charge density, and ε is the dielectricpermittivity. Within a solid adsorbent or a (assumed rigid) protein, the chargedensity distribution results from the presence of immobile charged species. Insolution, the charge density distribution results from dissolved ionic species, whichmay be assumed to be distributed in a Boltzmann manner,

ρi(⇀r ) = ρi,bulkzi exp

( − zieφ(⇀r )/kT

)(10)

where ρi,bulk is the bulk density of ionic species i, zi is its valence, e is the ele-mentary charge, k is the Boltzmann constant, and T is the absolute temperature.The resulting electric potential—which for all but the simplest geometries mustbe determined numerically—is used to calculate the total interaction energy

Uelec =∑

i

zieφ(⇀r i ) (11)

where the sum runs over all charges in the system. (The sum becomes an integralin 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 interactionsvary as distance to the minus sixth power. For protein/surface systems modeledvia a colloidal description, this 1/r6 dependence is integrated over the volumesof the interacting bodies. The result is the product of a Hamaker constant, whichdepends upon material properties, and a term dependent on the system’s geometry.In addition, forces related to solvation (114) and donor/acceptor (115) affects mayalso be included.

Although not amenable to predictions of irreversibility or conformationalchange, colloidal approaches have been successful in predicting qualitative trendsin—and, to a certain extent, quantitative values of—equilibrium constants in thecase of fully reversible adsorption at low surface coverage (116–120). In manycases, simple protein geometries and charge distributions suffice. In other cases,such as when adsorption is controlled by charged patches (121,122), more realisticmodels must be used. An accounting of protein–protein interactions to allow for afinite surface coverage has also been made (123–126).

The colloidal approach has also been applied to the adsorption of DNA on toa charged surface (127,128).

Polymer Description. A lattice model heteropolymer (129–131) providesa simple yet instructive description of a protein molecule. In general, the coarsegraining is such that each segment represents a portion of the protein (ie manyamino acids). In the simplest case, two types of segments are present; these maybe thought of as polar and hydrophobic (132–138). In other cases, a distribution


of segmental interactions is employed (139–143). The minimalist nature of thismodel allows for efficient sampling of conformational space via simulation (forchains of less than 20 segments, exact enumeration of all conformations is pos-sible). Despite its apparent simplicity, for a proper choice of segment–segmentnearest-neighbor interaction strength, this model is capable of exhibiting the es-sential physics of protein folding (eg coil–globule and globule–folded transitionsand the presence of a glass transition). Of particular importance have been 27 seg-ment 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 observationhas been the initial continuous transition of the model protein to an unfolded, fullyflattened state followed by an activated transition to a partially refolded, less-flattened state (145,146). Proteins modeled as shorter chains, where exact enu-meration 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 the-ory of Scheutjens and Fleer (150,151). This approach differs from previously posedstatistical theories for chain molecules in that the partition function is expressedin terms of the distribution of chain conformations rather than the distribution ofsegment densities. The equilibrium distribution of chain (ie model protein) con-formations is thus calculable. Quantities predicted using this approach includethe force between parallel plates coated with protein (152,153), the adsorptionisotherm (154,155), and the segmental density distribution (154–157).

A simple yet instructive model for determining general features of certainbiomolecules at interfaces is the random heteropolymer description (158–174).A random heteropolymer is defined as one whose sequence of monomers followsa statistical distribution. A collection of random heteropolymers is therefore anexample of a quenched–annealed system, that is, one in which certain degrees offreedom are fixed and follow a known distribution (in this case, the heteropolymersequence) and others equilibrate with respect to these fixed degrees of freedom(in this case, the spatial distribution of the segments). Special methods developedfor treating such systems (175) are therefore applicable and have been useful indetermining properties of single (160) and sets of (162,164) adsorbed chains.

Clearly, nucleic acids are also amenable to a polymer description. Theoret-ical (176) and simulation (177,178) methods have been used to determine thestructure, dynamics, and thermodynamics of nucleic acid chains on surfaces.

Atomistic Description. Molecular modeling at the atomistic level hasbecome commonplace. The dual challenges of accurate potential force field de-scription and efficient configurational sampling have been met to a degree wherepredictive capabilities now exist for many single- and multicomponent systemsof simple molecules. The extension of these methods to biomolecules, and morespecifically to biomolecules at interfaces, presents a challenge because of the sizeand complexity of these molecules. However, some attempts to calculate physicalproperties of atomistically modeled biomolecules at interfaces have appeared (seeMolecular modeling (structure, molec. graphics)).

Early efforts were essentially static calculations of the interaction energybetween a rigid protein and a surface (112,114,121,179–181). Pairwise atom-istic potential energy descriptions were used to calculate the van der Waals andelectrostatic contributions. In the case of hydrophobic surfaces, solvation energies


were estimated from partition coefficients of the individual amino acids betweenaqueous and organic phases (114,180). Some of these studies treated the elec-trostatic interactions in a colloidal manner (112,121). The calculated energies forvarious geometries were helpful in understanding chromatographic behavior. Sim-ilar calculations of individual amino acids on self-assembled monolayers have alsobeen conducted with the hope of uncovering trends useful for predicting behaviorof entire protein molecules (182).

Molecular dynamics (MD) is a method in which Newton’s equations of mo-tion 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 infor-mation on biomolecules at interfaces. Systems studied have included lysozymeand myoglobin on polyethylene glycol (183), cytochrome c on hydrophilic and hy-drophobic self-assembled monolayers (184), leucine enkephalin near a crystallinepolyethylene surface (185), thermal hysteresis proteins on ice (186), and lysozymeon polyvinylimidazole (187).

Experimental Methods

Progress in any field requires information on the state of well-defined systems asa function of conditions. Advancement is thus intimately linked to the availabilityof experimental probes capable of providing accurate and detailed information.Important metrics of biomolecules at interfaces include the interfacial composi-tion; distributions in molecular orientation, molecular spatial arrangement, andintramolecular conformation; and biological activity. In this section, several exper-imental techniques probing the physical properties of biomolecules at interfacesare introduced; these are grouped into optical, piezoelectric, and scanning probemethods. Further details can be found in other excellent reviews (62,188,189).

Optical Methods. Optical methods involve directing polarized monochro-matic light toward the solid–liquid interface and measuring a response, eg thepolarity or intensity of reflected or emitted light. Various schemes have been pro-posed, as described below, and these allow for the determination of adsorbed-layerthickness, density, and composition as well as information on internal conforma-tion. Principal advantages of optical experimental probes include nondestructive-ness and the capability of continuous, real-time measurements.

Reflection-based methods (190–194) involve measuring the reflection of po-larized light at the interface between two optical media. In fact, two reflectionsare measured: one for the electric field component perpendicular to the plane ofincidence (transverse electric or s-wave) and one for the electric field componentparallel to the plane of incidence (transverse magnetic or p-wave). At a certainangle of incidence (the Brewster angle), the p-wave reflection vanishes and aroundthis angle, the reflectivity, or square of the amplitude of the p-wave reflection, andellipticity, or ratio of p- and s-wave reflections, become very sensitive to interfacialheterogeneity, as brought about eg by adsorption of biomolecules. By assuming theadsorbed layer to be uniform in refractive index, both its thickness and refractiveindex may be determined. By further assuming a linear dependence of refractiveindex on concentration, the adsorbed density is calculable (195).


Optical waveguide methods (188,196–198) are based on the phase shift asso-ciated with multiple interfacial reflections: when either the s- or p-wave undergoesa total phase shift equal to an integral multiple of 2π upon one complete traversalof a planar, dielectric waveguide sandwiched between media of lower refractiveindex, a standing wave is excited in the waveguiding film. Because of their depen-dence on reflection, the phase shifts are sensitive to interfacial heterogeneity—andthe thickness, refractive index, and density of an adsorbed biomolecular layer canbe readily determined.

When light traversing an optically dense medium approaches an interfacewith 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 ex-ponentially decaying intensity penetrates the rarer medium. This phenomenon isat the heart of certain spectroscopic methods used to probe biomolecules at inter-faces (199). In total internal reflection fluorescence (TIRF) spectroscopy (200–202),the evanescent wave excites fluorescent probes attached to the biomolecules, anddetection of the emission associated with their decay provides information on thedensity, composition, and conformation of adsorbed molecules. In fourier trans-form infrared attenuated total reflection (FTIR-ATIR) spectroscopy (203,204), theevanescent wave excites certain molecular vibrational degrees of freedom, and thedetected loss in intensity due to these absorbances can provide quantitative dataon density, composition, and conformation.

Surface plasmon resonance (SPR) (205–209) is an optical method in whichthe p-wave of incident light excites a propagating, nonradiative charge densityoscillation at a metal–dielectric interface. The resonant condition is the matchingof the wave vector component of the p-wave parallel to the interface to the wavevector of the surface plasmon. The latter is sensitive to the optical properties of afluid or adlayer near the interface, so by monitoring changes in the angular dis-tribution of the intensity of reflected light, physical properties of adsorbed speciesmay be determined.

Piezoelectric Methods. A piezoelectric crystal is one in which a mechan-ical stress induces an electric current. Conversely, application of an alternatingvoltage to a piezoelectric crystal induces a vibration. The frequency of oscillationis extremely sensitive to the mass contacting the crystal, and it is the frequencyshift due to adsorption that is the basis for piezoelectric methods (210). A quartzcrystal microbalance (QCM) (211–214) consists of a thin disk of (piezoelectric) crys-talline quartz sandwiched between thin-film metal electrodes. Upon applicationof an alternating voltage, the crystal undergoes thickness shear mode vibration.The mass adsorbed to the electrode surface—here, unlike in the optical methodsdescribed above, the mass includes trapped solvent—is simply proportional to thefrequency shift. In addition, the dissipation of energy following voltage removal,as measured by the decay of the oscillation amplitude, is a sensitive measureof the viscoelastic properties of an adsorbed layer. QCM thus provides a valuablecomplement to optical methods through information concerning conformation (viathe amount of trapped solvent in an adsorbed film) and rigidity (via the film vis-coelastic response).

Scanning Probe Methods. Scanning probe methods (215–217) involveprobing a solid surface with a very sharp tip and measuring its deflection or otherphysical change in order to create a topographical image or to determine a sur-face force profile. Two common methods for imaging biomolecules at interfaces


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

Conclusions

Biomolecules at interfaces continues to be a challenging and important subjectof basic research and biotechnological development. Despite intense investiga-tion for several decades, a number of significant challenges remain, includingthe complete prevention of protein adsorption onto blood-contacting biomaterials,the controlled placement of biologically active molecules on sensing and tissueengineering substrates, and the quantitative prediction of events occurring asbiomolecules approach and reside at the interfacial region. Recent experimen-tal developments, particularly those in optical, scanning probe, and piezoelectricinstrumentation—and advances in statistical–mechanical modeling, interatomicforce field development, and computational power—are converging to provide newinsights, at an unparalleled rate, in order to meet these and other emerging chal-lenges.

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PAUL R. VAN TASSEL

Wayne State University

Vol. 5 BULK AND SOLUTION POLYMERIZATIONS REACTORS 307

BIOTECHNOLOGY APPLICATIONS. See Volume 1.

BLOCK COPOLYMERS. See Volume 1.

BLOCK COPOLYMERS, TERNARY TRIBLOCK. See Volume 1.

BLOWING AGENTS. See CELLULAR MATERIALS.

BLOW MOLDING. See Volume 1.

biomolecules at interfaces

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