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 separating
an 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, van
der 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 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 rele-
vant 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.

286

BIOMOLECULES AT INTERFACES

Vol. 5

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 technologi-
cal applications exist together with several intriguing and perplexing (and for the
most part unsolved!) intellectual curiosities. In most areas of science and engi-
neering, important advances accompany the close interplay between theoretical
prediction and experimental measurement. Biomolecules at interfaces is no excep-
tion, 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 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. Other
articles 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 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 adsorp-

tion altogether or promoting adsorption of “passivating” proteins (ie those known
not to trigger subsequent biological responses). A preeminent strategy for prevent-
ing 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 pro-
tein 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 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

Vol. 5

BIOMOLECULES AT INTERFACES

287

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 adsorp-
tion 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 of-
fers 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 mate-
rials 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 develop-
ing 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 gly-
coprotein whose constituent modules contain binding sites for a wide range of
biomolecules and biological units (38). Its cell-binding site, consisting of the tripep-
tide 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). Disad-
vantages 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 biolog-
ical 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 tar-

get biomolecule (60–63). Although many variations are possible, all biosensors
combine a detector, where a biological recognition event takes place, with a trans-
ducer, which produces an output signal from the recognition event. A biosensor

288

BIOMOLECULES AT INTERFACES

Vol. 5

must be selective for the target molecule in a mixture of structurally similar
species. Robustness, cost, size, and real-time measurement capability are addi-
tional 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 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 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 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 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 im-
portant example is the catalytic glucose sensor, in which an oxidation of glucose
takes 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 (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 of-
ten 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 mod-
ification 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 chem-
ical 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 cou-
pling.) A SAM may be placed onto a surface by the Langmuir–Blodget method

Vol. 5

BIOMOLECULES AT INTERFACES

289

(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 polysaccha-
ride 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 10

9

–10

12

M

− 1

. The antibody itself may be attached

physically, chemically, or via specific linkages between its F

c

(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 mea-

surable 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 (typi-
cally) 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 concen-
trations 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 al-
ternately 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

290

BIOMOLECULES AT INTERFACES

Vol. 5

+

+

+

+

+

+

+

+

+

A

D

B

C

I

0

200

400

600

C

b

,

µg/cm

3

C

s

,µ

g/cm

2

0.1

0.2

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 solu-
tion. 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.

0.4

0.3

0.2

0.1

0

0

75

150

225

300

Adsorbed amount, mg/m

2

Free FHEC concentration, ppm

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.

Vol. 5

BIOMOLECULES AT INTERFACES

291

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 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 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 essen-
tially irreversibly adsorbed. The insensitivity of isotherm D in Figure 1 to dilution
can be explained by irreversible adsorption occurring at the initial (highest) con-
centration. 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 pres-
ence 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 theoret-
ical 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

292

BIOMOLECULES AT INTERFACES

Vol. 5

0

500

1000

1500

0

0.05

0.1

0.15

Surf

ace density

Γ

,µ

g/cm

2

Time t, s

+

+

+

+

++

++

++

++++

+++

+

+ +++

curve shifted

a

b

a

× 10

−3

0

0.05

0.1

0.15

Γ, µg/cm

2

0

1

2

dΓ

/d

t,

µ

g/cm

2

s

+

+++++

+

+

+

+

+

+

+

+

+

+

+

+

(a)

0

1000

2000

3000

0

0.05

0.1

0.15

Surf

ace density

Γ

,µ

g/cm

2

Time t, s

shifted curve

× 10

−3

0

0.1

0.2

Γ, µg/cm

2

0

1

2

dΓ

/d

t,

µ

g/cm

2

s

1

4000

0.2

b

a

a

b

+

+

+

+

++++

+

+

+

+

+ ++

(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

Vol. 5

BIOMOLECULES AT INTERFACES

293

a

b

×

×

×

×

××

××

××

×××

×××

×

×

×

×

× ×××

×××

× ×××××××××

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

×

×

0.4

0.2

0.0

0

2000

4000

t, s

M

,µ

g/cm

2

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 in-
teraction. 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 atom-
istic 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 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 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



dt

= k

a

c

s

1

−





max



− k

d



(1)

where

 is the adsorbed density, t is the time, k

a

is the intrinsic adsorption rate,

c

s

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 k

d

is the intrinsic

rate of desorption. The solution to equation 1 is

(t)



max

=

Kc

s

1

+Kc

s

1

− e

− (k

a

c

s

/ 

max

+k

d

)t



(2)

where K

= k

a

/k

d

.

294

BIOMOLECULES AT INTERFACES

Vol. 5

×

×

×

×

×

××

×××××××

××××××××××

0

0.1

0.2

0.3

2

1

0

M,

µg/cm

2

d

M

d

t

,

ng/cm

2

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 Langmuir

approach to most biomolecular systems. For one, the saturation is approached
much more slowly than the exponential behavior predicted by equation 2. Sec-
ondly, by setting c

s

=0, equation 1 would predict a complete desorption during a

rinse. Instead, desorption of only a small fraction of the adsorbed molecules re-
sults. 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 biomolecu-

lar 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 avail-

able 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 de-
scription and, through its more realistic treatment of surface exclusion effects,
represents an improvement over a site description. At first thought, modeling a

Vol. 5

BIOMOLECULES AT INTERFACES

295

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-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



dt

= k

a

c

s



(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 higher
dimensions, analytical solutions have been elusive. However, exact theoretical
treatment 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+A

1

θ+A

2

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

 = Ct

− ν

= (θ

∞

− θ)

ν

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):

≈

(

θ

∞

− θ)

ν

ν − 1

1

+B

1

θ+B

2

θ

2

+· · ·

(6)

where the coefficients B

i

are evaluated in terms of the known A

i

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 post-
adsorption structural changes. In this case, one must write at least two kinetic

296

BIOMOLECULES AT INTERFACES

Vol. 5

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

d



α

dt

= k

a

c

s



α

− k

d



α

− k

s



α



αβ

(7)

d



β

dt

= k

s



α



αβ

(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 k

s

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 (k

d

= 0, no surface diffusion) using methods

analogous to those used to derive equations 4–6 (97), and (2) high surface mo-
bility 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 ac-
counting 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 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 diffusion
equation; the diffusive flux is proportional to the chemical potential gradient, and
the position-dependent chemical potential is determined as the functional deriva-
tive 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, mul-
tiple 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 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 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 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). This
theory 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-time
adsorptive properties of biomaterials containing grafted polymer chains (24,110).

Vol. 5

BIOMOLECULES AT INTERFACES

297

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,

∇

2

φ = −

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,

ρ

i

(



r )

= ρ

i

,bulk

z

i

exp



− z

i

e

φ(



r )

/kT



(10)

where

ρ

i

,bulk

is the bulk density of ionic species i, z

i

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 must
be determined numerically—is used to calculate the total interaction energy

U

elec

=



i

z

i

e

φ(



r

i

)

(11)

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/r

6

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

298

BIOMOLECULES AT INTERFACES

Vol. 5

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 pos-
sible). Despite its apparent simplicity, for a proper choice of segment–segment
nearest-neighbor interaction strength, this model is capable of exhibiting the es-
sential physics of protein folding (eg coil–globule and globule–folded transitions
and 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 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, 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 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) con-
formations 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. Theoret-

ical (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 de-
scription 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 atom-
istic potential energy descriptions were used to calculate the van der Waals and
electrostatic contributions. In the case of hydrophobic surfaces, solvation energies

Vol. 5

BIOMOLECULES AT INTERFACES

299

were estimated from partition coefficients of the individual amino acids between
aqueous and organic phases (114,180). Some of these studies treated the elec-
trostatic interactions in a colloidal manner (112,121). The calculated energies for
various geometries were helpful in understanding chromatographic behavior. Sim-
ilar 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 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 lysozyme
and myoglobin on polyethylene glycol (183), cytochrome c on hydrophilic and hy-
drophobic 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 composi-
tion; distributions in molecular orientation, molecular spatial arrangement, and
intramolecular conformation; and biological activity. In this section, several exper-
imental 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 monochro-

matic light toward the solid–liquid interface and measuring a response, eg the
polarity or intensity of reflected or emitted light. Various schemes have been pro-
posed, as described below, and these allow for the determination of adsorbed-layer
thickness, 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 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).

300

BIOMOLECULES AT INTERFACES

Vol. 5

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 undergoes
a total phase shift equal to an integral multiple of 2

π 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 depen-
dence 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

(n

rare

/n

dens

), a total internal reflection occurs and an evanescent wave of ex-

ponentially decaying intensity penetrates the rarer medium. This phenomenon is
at 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, and
detection of the emission associated with their decay provides information on the
density, composition, and conformation of adsorbed molecules. In fourier trans-
form 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 dis-
tribution of the intensity of reflected light, physical properties of adsorbed species
may be determined.

Piezoelectric Methods.

A piezoelectric crystal is one in which a mechan-

ical 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) crys-
talline 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 vis-
coelastic 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 sur-
face force profile. Two common methods for imaging biomolecules at interfaces

Vol. 5

BIOMOLECULES AT INTERFACES

301

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 in-
formation 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 investiga-
tion 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 experimen-
tal 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 chal-
lenges.

BIBLIOGRAPHY

1. C. A. Haynes and W. Norde, Colloids Surf., B 2, 517 (1994).
2. M. Malmsten, J. Colloid Interface Sci. 207, 186 (1998).
3. M. Malmsten, ed., Biopolymers at Interfaces, Vol. 75, Surfactant Science Series, Mar-

cel Dekker, Inc., New York, 1998.

4. J. D. Andrade and V. Hlady, Adv. Polym. Sci. 79, 1 (1986).
5. L. P. Tang and J. W. Eaton, Am. J. Clin. Pathol. 103, 466 (1995).
6. W. J. Hu, J. W. Eaton, and L. P. Tang, Blood 98, 1231 (2001).
7. Y. Mori, S. Nagaoka, H. Takiuchi, T. Kikuchi, N. Noguchi, H. Tanzawa, and Y. Noishiki,

Trans. Am. Soc. Artifi. Intern. Organs 28, 459 (1982).

8. H. Jacobs, D. Grainger, T. Okano, and S. W. Kim, Artif. Organs 12, 506 (1988).
9. J. H. Lee, J. Kopecek, and J. D. Andrade, J. Biomed. Mater. Res. 23, 351 (1989).

10. M. Amiji and K. Park, Biomaterials 13, 682 (1992).
11. M. Amiji and K. Park, J. Biomater. Sci.—Polym. Ed. 4, 217 (1993).
12. J. M. Courtney, N. M. K. Lamba, S. Sundaram, and C. D. Forbes, Biomaterials 15, 737

(1994).

13. J. H. Lee, H. B. Lee, and J. D. Andrade, Prog. Polym. Sci. 20, 1043 (1995).
14. J. D. Andrade, V. Hlady, and S. I. Jeon, Hydrophilic Polymers: Performance with En-

vironmental Acceptance, American Chemical Society, Washington, D.C., 1996, p. 51.

302

BIOMOLECULES AT INTERFACES

Vol. 5

15. A. S. Hoffman, J. Biomater. Sci.—Polym. Ed. 10, 1011 (1999).
16. D. Leckband, S. Sheth, and A. Halperin, J. Biomater. Sci.—Polym. Ed. 10, 1125 (1999).
17. A. R. Halperin and D. E. Leckband, C. R. Acad. Sci. Ser. IV—Phys. Astrophys. 1, 1171

(2000).

18. S. I. Jeon, J. H. Lee, J. D. Andrade, and P. G. Degennes, J. Colloid Interface Sci. 142,

149 (1991).

19. G. Subramanian, D. R. M. Williams, and P. A. Pincus, Macromolecules 29, 4045 (1996).
20. I. Szleifer, Physica A 244, 370 (1997).
21. I. Szleifer, Curr. Opin. Solid State Mater. Sci. 2, 337 (1997).
22. I. Szleifer, Biophys. J. 72, 595 (1997).
23. M. A. Carignano and I. Szleifer, Colloids Surf., B— 18, 169 (2000).
24. J. Satulovsky, M. A. Carignano, and I. Szleifer, Proc. Natl. Acad. Sci. U.S.A. 97, 9037

(2000).

25. I. Szleifer and M. A. Carignano, Macromol. Rapid Commun. 21, 423 (2000).
26. M. Fukutomi, S. Kobayashi, K. Niwaya, Y. Hamada, and S. Kitamura, Artif. Organs

20, 767 (1996).

27. S. Svenmarker, E. Sandstrom, T. Karlsson, E. Jansson, S. Haggmark, R. Lindholm,

M. Appelblad, and T. Aberg, Eur. J. Cardio-Thorac. Surg. 11, 957 (1997).

28. J. Sanchez, G. Elgue, J. Riesenfeld, and P. Olsson, J. Biomed. Mater. Res. 29, 655

(1995).

29. N. Weber, H. P. Wendel, and G. Ziemer, Biomaterials 23, 429 (2002).
30. R. Blezer, B. Fouache, G. M. Willems, and T. Lindhout, J. Biomed. Mater. Res. 37, 108

(1997).

31. R. Langer and J. P. Vacanti, Science 260, 920 (1993).
32. J. A. Hubbell, Bio/Technology 13, 565 (1995).
33. J. Kohn, MRS Bull. 21, 18 (1996).
34. A. Curtis and M. Riehle, Phys. Med. Biol. 46, R47 (2001).
35. Y. Tabata, Drug Discov. Today 6, 483 (2001).
36. S. Lalan, I. Pomerantseva, and J. P. Vacanti, World J. Surg. 25, 1458 (2001).
37. J. A. Hubbell, Curr. Opin. Biotechnol. 10, 123 (1999).
38. J. R. Potts and I. D. Campbell, Matrix Biol. 15, 313 (1996).
39. J. G. Steele, B. A. Dalton, G. Johnson, and P. A. Underwood, Biomaterials 16, 1057

(1995).

40. M. Mrksich, C. S. Chen, Y. N. Xia, L. E. Dike, D. E. Ingber, and G. M. Whitesides,

Proc. Natl. Acad. Sci. U.S.A. 93, 10775 (1996).

41. C. D. Tidwell, S. I. Ertel, B. D. Ratner, B. J. Tarasevich, S. Atre, and D. L. Allara,

Langmuir 13, 3404 (1997).

42. C. H. Thomas, C. D. McFarland, M. L. Jenkins, A. Rezania, J. G. Steele, and K. E.

Healy, J. Biomed. Mater. Res. 37, 81 (1997).

43. A. J. Garcia, P. Ducheyne, and D. Boettiger, Tissue Eng. 3, 197 (1997).
44. K. Webb, K. Caldwell, and P. A. Tresco, Crit. Rev. Biomed. Eng. 28, 203 (2000).
45. G. Rainaldi, P. Filippini, A. Ferrante, P. L. Indovina, and M. T. Santini, J. Biomed.

Mater. Res. 55, 104 (2001).

46. R. Biran, K. Webb, M. D. Noble, and P. A. Tresco, J. Biomed. Mater. Res. 55, 1 (2001).
47. C. R. Nuttelman, D. J. Mortisen, S. M. Henry, and K. S. Anseth, J. Biomed. Mater.

Res. 57, 217 (2001).

48. M. Balcells and E. R. Edelman, J. Cell. Physiol. 191, 155 (2002).
49. W. G. Dai and W. M. Saltzman, Biotechnol. Bioeng. 50, 349 (1996).
50. S. P. Palecek, J. C. Loftus, M. H. Ginsberg, D. A. Lauffenburger, and A. F. Horwitz,

Nature 385, 537 (1997).

51. S. M. Cannizzaro, R. F. Padera, R. Langer, R. A. Rogers, F. E. Black, M. C. Davies, S.

J. B. Tendler, and K. M. Shakesheff, Biotechnol. Bioeng. 58, 529 (1998).

Vol. 5

BIOMOLECULES AT INTERFACES

303

52. K. M. Shakesheff, S. M. Cannizzaro, and R. Langer, J. Biomater. Sci.—Polym. Ed. 9,

507 (1998).

53. G. B. Fields, J. L. Lauer, Y. Dori, P. Forns, Y. C. Yu, and M. Tirrell, Biopolymers 47,

143 (1998).

54. N. Patel, R. Padera, G. H. W. Sanders, S. M. Cannizzaro, M. C. Davies, R. Langer, C.

J. Roberts, S. J. B. Tendler, P. M. Williams, and K. M. Shakesheff, FASEB J. 12, 1447
(1998).

55. J. L. Myles, B. T. Burgess, and R. B. Dickinson, J. Biomater. Sci.—Polym. Ed. 11, 69

(2000).

56. R. A. Quirk, W. C. Chan, M. C. Davies, S. J. B. Tendler, and K. M. Shakesheff, Bioma-

terials 22, 865 (2001).

57. R. A. Stile and K. E. Healy, Biomacromolecules 2, 185 (2001).
58. B. K. Mann, A. S. Gobin, A. T. Tsai, R. H. Schmedlen, and J. L. West, Biomaterials 22,

3045 (2001).

59. D. J. Irvine, A. V. G. Ruzette, A. M. Mayes, and L. G. Griffith, Biomacromolecules 2,

545 (2001).

60. C. R. Lowe, B. Hin, D. C. Cullen, S. E. Evans, L. D. G. Stephens, and P. Maynard, J.

Chromatogr. 510, 347 (1990).

61. M. P. Byfield and R. A. Abuknesha, Biosens. Bioelectron. 9, 373 (1994).
62. A. F. Collings and F. Caruso, Rep. Prog. Phys. 60, 1397 (1997).
63. P. J. O’Connell and G. G. Guilbault, Anal. Lett. 34, 1063 (2001).
64. T. Wink, S. J. vanZuilen, A. Bult, and W. P. vanBennekom, Analyst 122, R43 (1997).
65. G. G. Roberts and C. W. Pitt, Langmuir–Blodgett Films, Elsevier, Amsterdam,

1982/1983.

66. J. Sagiv, J. Am. Chem. Soc. 102, 92 (1980).
67. R. G. Nuzzo and D. L. Allara, J. Am. Chem. Soc. 105, 4481 (1983).
68. M. D. Porter, T. B. Bright, D. L. Allara, and C. E. D. Chidsey, J. Am. Chem. Soc. 109,

3559 (1987).

69. S. Howell, M. Kenmore, M. Kirkland, and R. A. Badley, J. Mol. Recognit. 11, 200

(1998).

70. J. M. Lee, H. H. L. Edwards, C. A. Pereira, and S. I. Samii, J. Mater. Sci.: Mater. Med.

7, 531 (1996).

71. J. Turkova, J. Chromatogr., B 722, 11 (1999).
72. P. S. Stayton, S. Freitag, L. A. Klumb, A. Chilkoti, V. Chu, J. E. Penzotti, R. To, D.

Hyre, I. Le Trong, T. P. Lybrand, and R. E. Stenkamp, Biomol. Eng. 16, 39 (1999).

73. P. S. Stayton, K. E. Nelson, T. C. McDevitt, V. Bulmus, T. Shimoboji, Z. Ding, and A.

S. Hoffman, Biomol. Eng. 16, 93 (1999).

74. H. Gunasingham, P. Y. T. Teo, Y. H. Lai, and S. G. Tan, Biosensors 4, 349 (1989).
75. J. H. Liu, M. Y. Chen, and M. T. Lin, J. Appl. Polym. Sci. 40, 2161 (1990).
76. Y. Kajiya, H. Sugai, C. Iwakura, and H. Yoneyama, Anal. Chem. 63, 49 (1991).
77. M. J. Mura-Galelli, J. C. Voegel, S. Behr, E. F. Bres, and P. Schaaf, Proc. Natl. Acad.

Sci. U.S.A. 88, 5557 (1991).

78. V. A. Rebar and M. M. Santore, Macromolecules 29, 6262 (1996).
79. C. Calonder, Y. Tie, and P. R. Van Tassel, Proc. Natl. Acad. Sci. U.S.A. 98, 10664 (2001).
80. J. J. Ramsden, Chem. Soc. Rev. 24, 73 (1995).
81. J. J. Ramsden, Phys. Rev. Lett. 71, 295 (1993).
82. I. Lundstrom, Prog. Colloid Polym. Sci. 70, 76 (1985).
83. M. Wahlgren, T. Arnebrant, and I. Lundstrom, J. Colloid Interface Sci. 175, 506 (1995).
84. V. P. Zhdanov and B. Kasemo, Proteins 40, 539 (2000).
85. P. Zhdanov, F. Hook, and B. Kasemo, Proteins 43, 489 (2001).
86. W. J. Ceyrolles, P. Viot, and J. Talbot, Langmuir 18, 1112 (2002).
87. J. W. Evans, Rev. Mod. Phys. 65, 1281 (1993).

304

BIOMOLECULES AT INTERFACES

Vol. 5

88. P. Schaaf, J. C. Voegel, and B. Senger, Ann. Phys. (Paris) 23, 1 (1998).
89. J. Talbot, G. Tarjus, P. R. Van Tassel, and P. Viot, Colloids Surf., A 165, 287 (2000).
90. A. Renyi, Publ. Math. Inst. Hung. Acad. Sci. 3, 109 (1958).
91. A. Renyi, Sel. Trans. Math. Stat. Prob. 4, 205 (1963).
92. P. Schaaf and J. Talbot, Phys. Rev. Lett. 62, 175 (1989).
93. Y. Pomeau, J. Phys. A: Math. Gen. 13 L193 (1980).
94. R. H. Swendsen, Phys. Rev. A 24, 504 (1981).
95. J. Talbot, G. Tarjus, and P. Schaaf, Phys. Rev. A 40, 4808 (1989).
96. P. R. Van Tassel, P. Viot, G. Tarjus, and J. Talbot, J. Chem. Phys. 101, 7064 (1994).
97. P. R. Van Tassel, J. Talbot, G. Tarjus, and P. Viot, Phys. Rev. E 53, 785 (1996).
98. P. R. Van Tassel, P. Viot, and G. Tarjus, J. Chem. Phys. 106, 761 (1997).
99. V. P. Zhdanov and B. Kasemo, Proteins 30, 177 (1998).

100. V. P. Zhdanov and B. Kasemo, J. Chem. Phys. 109, 6497 (1998).
101. A. P. Minton, Biophys. J. 76, 176 (1999).
102. M. A. Brusatori and P. R. Van Tassel, J. Colloid Interface Sci. 219, 333 (1999).
103. J. Talbot, Adsorpt.—J. Int. Adsorpt. Soc. 2, 89 (1996).
104. A. P. Minton, Biophys. Chem. 86, 239 (2000).
105. A. P. Minton, Biophys. J. 80, 1641 (2001).
106. X. Z. Jin, N. H. L. Wang, G. Tarjus, and J. Talbot, J. Phys. Chem. 97, 4256 (1993).
107. C. Calonder and P. R. Van Tassel, Langmuir 17, 4392 (2001).
108. F. Fang and I. Szleifer, Biophys. J. 80, 2568 (2001).
109. M. A. Carignano and I. Szleifer, Mol. Phys. 100, 2993 (2002).
110. T. McPherson, A. Kidane, I. Szleifer, and K. Park, Langmuir 14, 176 (1998).
111. K. A. Sharp and B. Honig, Annu. Rev. Biophys. Biophys. Chem. 19, 301 (1990).
112. B. J. Yoon and A. M. Lenhoff, J. Phys. Chem. 96, 3130 (1992).
113. C. M. Roth and A. M. Lenhoff, in M. Malmsten, ed., Biopolymers at Interfaces, Marcel

Dekker, Inc., New York, 1998, p. 89.

114. D. R. Lu, S. J. Lee, and K. Park, J. Biomater. Sci.—Polym. Ed. 3, 127 (1991).
115. C. Calonder, J. Talbot, and J. J. Ramsden, J. Phys. Chem. B 105, 725 (2001).
116. J. Stahlberg, B. Jonsson, and C. Horvath, Anal. Chem. 64, 3118 (1992).
117. C. M. Roth and A. M. Lenhoff, Langmuir 11, 3500 (1995).
118. J. Stahlberg and B. Jonsson, Anal. Chem. 68, 1536 (1996).
119. C. M. Roth, K. K. Unger, and A. M. Lenhoff, J. Chromatogr. A 726, 45 (1996).
120. N. BenTal, B. Honig, R. M. Peitzsch, G. Denisov, and S. McLaughlin, Biophys. J. 71,

561 (1996).

121. D. Asthagiri and A. M. Lenhoff, Langmuir 13, 6761 (1997).
122. C. J. van Oss, A. Docoslis, W. Wu, and R. F. Giese, Colloids Surf., B 14, 99 (1999).
123. M. R. Oberholzer, J. M. Stankovich, S. L. Carnie, D. Y. C. Chan, and A. M. Lenhoff, J.

Colloid Interface Sci. 194, 138 (1997).

124. M. R. Oberholzer, N. J. Wagner, and A. M. Lenhoff, J. Chem. Phys. 107, 9157 (1997).
125. M. R. Oberholzer and A. M. Lenhoff, Langmuir 15, 3905 (1999).
126. S. Ravichandran and J. Talbot, Biophys. J. 78, 110 (2000).
127. R. Menes, P. Pincus, R. Pittman, and N. Dan, Europhys. Lett. 44, 393 (1998).
128. C. Fleck, R. R. Netz, and H. H. von Grunberg, Biophys. J. 82, 76 (2002).
129. K. A. Dill, S. Bromberg, K. Z. Yue, K. M. Fiebig, D. P. Yee, P. D. Thomas, and H. S.

Chan, Protein Sci. 4, 561 (1995).

130. M. Karplus and A. Sali, Curr. Opin. Struct. Biol. 5, 58 (1995).
131. V. S. Pande, A. Y. Grosberg, and T. Tanaka, Rev. Mod. Phys. 72, 259 (2000).
132. H. S. Chan and K. A. Dill, Annu. Rev. Biophys. Biophys. Chem. 20, 447 (1991).
133. R. Miller, C. A. Danko, M. J. Fasolka, A. C. Balazs, H. S. Chan, and K. A. Dill, J. Chem.

Phys. 96, 768 (1992).

134. E. I. Shakhnovich and A. M. Gutin, Proc. Natl. Acad. Sci. U.S.A. 90, 7195 (1993).
135. H. S. Chan and K. A. Dill, J. Chem. Phys. 100, 9238 (1994).

Vol. 5

BIOMOLECULES AT INTERFACES

305

136. N. D. Socci and J. N. Onuchic, J. Chem. Phys. 101, 1519 (1994).
137. A. M. Gutin, V. I. Abkevich, and E. I. Shakhnovich, Proc. Natl. Acad. Sci. U.S.A. 92,

1282 (1995).

138. N. D. Socci and J. N. Onuchic, J. Chem. Phys. 103, 4732 (1995).
139. E. I. Shakhnovich and A. M. Gutin, Nature 346, 773 (1990).
140. E. Shakhnovich, G. Farztdinov, A. M. Gutin, and M. Karplus, Phys. Rev. Lett. 67, 1665

(1991).

141. D. K. Klimov and D. Thirumalai, Phys. Rev. Lett. 76, 4070 (1996).
142. D. K. Klimov and D. Thirumalai, Proteins 26, 411 (1996).
143. D. K. Klimov and D. Thirumalai, J. Chem. Phys. 109, 4119 (1998).
144. V. P. Zhdanov and B. Kasemo, Phys. Rev. E: stat. Phys., Plasmas, Fluids, Relat. Inter-

discip. Top. 56, 2306 (1997).

145. V. P. Zhdanov and B. Kasemo, Proteins 42, 481 (2001).
146. V. Castells, S. Yang, and P. R. Van Tassel, Phys. Rev. E: stat. Phys., Plasmas, Fluids,

Relat. Interdiscip. Top. 65, 031912 (2002).

147. R. E. Anderson, V. S. Pande, and C. J. Radke, J. Chem. Phys. 112, 9167 (2000).
148. M. R. Wattenbarger, H. S. Chan, D. F. Evans, V. A. Bloomfield, and K. A. Dill, J. Chem.

Phys. 93, 8343 (1990).

149. H. S. Chan, M. R. Wattenbarger, D. F. Evans, V. A. Bloomfield, and K. A. Dill, J. Chem.

Phys. 94, 8542 (1991).

150. J. M. H. M. Scheutjens and G. J. Fleer, J. Phys. Chem. 83, 1619 (1979).
151. J. M. H. M. Scheutjens and G. J. Fleer, J. Phys. Chem. 84, 178 (1980).
152. G. Belfort and C. S. Lee, Proc. Natl. Acad. Sci. U.S.A. 88, 9146 (1991).
153. E. Dickinson, V. J. Pinfield, D. S. Horne, and F. A. M. Leermakers, J. Chem. Soc.,

Faraday Trans. 93, 1785 (1997).

154. F. A. M. Leermakers, P. J. Atkinson, E. Dickinson, and D. S. Horne, J. Colloid Interface

Sci. 178, 681 (1996).

155. E. Dickinson, D. S. Horne, V. J. Pinfield, and F. A. M. Leermakers, J. Chem. Soc.,

Faraday Trans. 93, 425 (1997).

156. E. Dickinson, V. J. Pinfield, and D. S. Horne, J. Colloid Interface Sci. 187, 539 (1997).
157. J. M. P. van den Oever, F. A. M. Leermakers, G. J. Fleer, V. A. Ivanov, N. P. Shusharina,

A. R. Khokhlov, and P. G. Khalatur, Phys. Rev. E: stat. Phys., Plasmas, Fluids, Relat.
Interdiscip. Top. 65, 041708 (2002).

158. T. Cosgrove, N. A. Finch, and J. R. P. Webster, Macromolecules 23, 3353 (1990).
159. C. M. Marques and J. F. Joanny, Macromolecules 23, 268 (1990).
160. J. F. Joanny, J. Phys. II 4, 1281 (1994).
161. L. Gutman and A. K. Chakraborty, J. Chem. Phys. 101, 10074 (1994).
162. L. Gutman and A. K. Chakraborty, J. Chem. Phys. 103, 10733 (1995).
163. L. Gutman and A. K. Chakraborty, J. Chem. Phys. 105, 7842 (1996).
164. L. Gutman and A. K. Chakraborty, J. Chem. Phys. 104, 7306 (1996).
165. S. Srebnik, A. K. Chakraborty, and E. I. Shakhnovich, Phys. Rev. Lett. 77, 3157 (1996).
166. D. Bratko, A. K. Chakraborty, and E. I. Shakhnovich, Comput. Theor. Polym. Sci. 8,

113 (1998).

167. A. K. Chakraborty and D. Bratko, J. Chem. Phys. 108, 1676 (1998).
168. S. Srebnik, A. K. Chakraborty, and D. Bratko, J. Chem. Phys. 109, 6415 (1998).
169. A. J. Golumbfskie, V. S. Pande, and A. K. Chakraborty, Proc. Natl. Acad. Sci. U.S.A.

96, 11707 (1999).

170. X. Chatellier and J. F. Joanny, Eur. Phys. J. E 1, 9 (2000).
171. S. Srebnik, J. Chem. Phys. 112, 9655 (2000).
172. A. Naidenov and S. Nechaev, J. Phys. A: Math. Gen. 34, 5625 (2001).
173. V. A. Brazhnyi and S. Stepanow, Eur. Phys. J. B 27, 355 (2002).
174. S. Stepanow and A. L. Chudnovskiy, J. Phys. A: Math. Gen. 35, 4229 (2002).
175. S. F. Edwards and P. W. Anderson, J. Phys. F. 5, 965 (1975).

306

BIOMOLECULES AT INTERFACES

Vol. 5

176. R. R. Netz and J. F. Joanny, Macromolecules 32, 9013 (1999).
177. N. Pernodet, V. Samuilov, K. Shin, J. Sokolov, M. H. Rafailovich, D. Gersappe, and B.

Chu, Phys. Rev. Lett. 85, 5651 (2000).

178. Y. S. Velichko, K. Yoshikawa, and A. R. Khokhlov, Biomacromolecules 1, 459 (2000).
179. D. R. Lu and K. Park, J. Biomater. Sci.—Polym. Ed. 1, 243 (1990).
180. S. J. Lee and K. Park, J. Vac. Sci. Technol., A 12, 2949 (1994).
181. V. Noinville, C. Vidalmadjar, and B. Sebille, J. Phys. Chem. 99, 1516 (1995).
182. R. A. Latour and C. J. Rini, J. Biomed. Mater. Res. 60, 564 (2002).
183. K. Lim and J. N. Herron, in J. M. Harris, ed., Poly(ethylene glycol) Chemistry: Biotech-

nical and Biomedical Applications, Plenum Press, New York, 1992, p. 29.

184. D. J. Tobias, W. Mar, J. K. Blasie, and M. L. Klein, Biophys. J. 71, 2933 (1996).
185. A. M. Bujnowski and W. G. Pitt, J. Colloid Interface Sci. 203, 47 (1998).
186. J. D. Madura, K. Baran, and A. Wierzbicki, J. Mol. Recognit. 13, 101 (2000).
187. S. Ravichandran, J. D. Madura, and J. Talbot, J. Phys. Chem. B 105, 3610 (2001).
188. J. J. Ramsden, Q. Rev. Biophys. 27, 41 (1994).
189. P. B. Garland, Q. Rev. Biophys. 29, 91 (1996).
190. P. Schaaf, P. Dejardin, and A. Schmitt, Revue De Physique Appliquee 20, 631 (1985).
191. P. Schaaf, P. Dejardin, and A. Schmitt, Revue De Physique Appliquee 21, 741 (1986).
192. M. Malmsten, J. Colloid Interface Sci. 166, 333 (1994).
193. L. Heinrich, E. K. Mann, J. C. Voegel, and P. Schaaf, Langmuir 13, 3177 (1997).
194. H. Elwing, Biomaterials 19, 397 (1998).
195. J. A. de Feijter, J. Bejamins, and F. A. Veer, Biopolymers 17, 1759 (1978).
196. P. M. Nellen, K. Tiefenthaler, and W. Lukosz, Sens. Actuators 15, 285 (1988).
197. W. Lukosz, Sens. Actuators, B 29, 37 (1995).
198. J. Voros, J. J. Ramsden, G. Csucs, I. Szendro, S. M. De Paul, M. Textor, and N. D.

Spencer, Biomaterials 23, 3699 (2002).

199. N. J. Harrick, Internal Reflection Spectroscopy, John Wiley & Sons, Inc., New York,

1967.

200. N. L. Thompson and D. Axelrod, Biophys. J. 33, A183 (1981).
201. R. A. Vanwagenen and J. D. Andrade, Fed. Proc. 41, 1483 (1982).
202. B. K. Lok, Y. L. Cheng, and C. R. Robertson, J. Colloid Interface Sci. 91, 87 (1983).
203. K. K. Chittur, Biomaterials 19, 357 (1998).
204. A. R. Hind, S. K. Bhargava, and A. McKinnon, Adv. Colloid Interface Sci. 93, 91 (2001).
205. B. Liedberg, C. Nylander, and I. Lundstrom, Sens. Actuators 4, 299 (1983).
206. S. Lofas, M. Malmqvist, I. Ronnberg, E. Stenberg, B. Liedberg, and I. Lundstrom,

Sens. Actuators, B 5, 79 (1991).

207. B. Liedberg, C. Nylander, and I. Lundstrom, Biosens. Bioelectron. 10, R1 (1995).
208. J. Homola, S. S. Yee, and G. Gauglitz, Sens. Actuators, B 54, 3 (1999).
209. L. M. Lechuga, A. Calle, and F. Prieto, Quim. Anal. 19, 54 (2000).
210. G. Z. Sauerbrey, Z. Physics 155, 206 (1959).
211. M. Rodahl, F. Hook, A. Krozer, P. Brzezinski, and B. Kasemo, Rev. Sci. Instrum. 66,

3924 (1995).

212. M. Rodahl, F. Hook, and B. Kasemo, Anal. Chem. 68, 2219 (1996).
213. C. K. O’Sullivan and G. G. Guilbault, Biosens. Bioelectron. 14, 663 (1999).
214. C. K. O’Sullivan, R. Vaughan, and G. G. Guilbault, Anal. Lett. 32, 2353 (1999).
215. G. Binnig, C. F. Quate, and C. Gerber, Phys. Rev. Lett. 56, 930 (1986).
216. J. Jahanmir, B. G. Haggar, and J. B. Hayes, Scanning Microsc. 6, 625 (1992).
217. H. G. Hansma and L. Pietrasanta, Curr. Opin. Chem. Biol. 2, 579 (1998).

P

AUL

R. V

AN

T

ASSEL

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 C

ELLULAR

M

ATERIALS

.

BLOW MOLDING.

See Volume 1.