This paper is published as part of a PCCP Themed Issue on: Coarse-grained modeling of soft condensed matter

Guest Editor: Roland Faller (UC Davis)

Editorial

Coarse-grained modeling of soft condensed matter Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b903229c

Perspective

Multiscale modeling of emergent materials: biological and soft matter Teemu Murtola, Alex Bunker, Ilpo Vattulainen, Markus Deserno and Mikko Karttunen, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b818051b

Communication

Dissipative particle dynamics simulation of quaternary bolaamphiphiles: multi-colour tiling in hexagonal columnar phases Martin A. Bates and Martin Walker, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b818926a

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Adsorption of peptides (A3, Flg, Pd2, Pd4) on gold and palladium surfaces by a coarse-grained Monte Carlo simulation R. B. Pandey, Hendrik Heinz, Jie Feng, Barry L. Farmer, Joseph M. Slocik, Lawrence F. Drummy and Rajesh R. Naik, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b816187a

A coarse-graining procedure for polymer melts applied to 1,4-polybutadiene T. Strauch, L. Yelash and W. Paul, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b818271j

Anomalous waterlike behavior in spherically-symmetric water models optimized with the relative entropy Aviel Chaimovich and M. Scott Shell, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b818512c

Coarse-graining dipolar interactions in simple fluids and polymer solutions: Monte Carlo studies of the phase behavior B. M. Mognetti, P. Virnau, L. Yelash, W. Paul, K. Binder, M. Müller and L. G. MacDowell, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b818020m

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Improved simulations of lattice peptide adsorption Adam D. Swetnam and Michael P. Allen, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b818067a

Curvature effects on lipid packing and dynamics in liposomes revealed by coarse grained molecular dynamics simulations

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Self-assembling dipeptides: conformational sampling in solvent-free coarse-grained simulation Alessandra Villa, Christine Peter and Nico F. A. van der Vegt, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b818144f

Self-assembling dipeptides: including solvent degrees of freedom in a coarse-grained model Alessandra Villa, Nico F. A. van der Vegt and Christine Peter, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b818146m

Computing free energies of interfaces in self-assembling systems Marcus Müller, Kostas Ch. Daoulas and Yuki Norizoe, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b818111j

Anomalous ductility in thermoset/thermoplastic polymer alloys Debashish Mukherji and Cameron F. Abrams, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b818039c

A coarse-grained simulation study of mesophase formation in a series of rod–coil multiblock copolymers Juho S. Lintuvuori and Mark R. Wilson, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b818616b

Simulations of rigid bodies in an angle-axis framework Dwaipayan Chakrabarti and David J. Wales, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b818054g

Effective force coarse-graining Yanting Wang, W. G. Noid, Pu Liu and Gregory A. Voth, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b819182d

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Molecular dynamics study of the effect of cholesterol on the properties of lipid monolayers at low surface tensions Cameron Laing, Svetlana Baoukina and D. Peter Tieleman, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b819767a

On using a too large integration time step in molecular dynamics simulations of coarse-grained molecular models Moritz Winger, Daniel Trzesniak, Riccardo Baron and Wilfred F. van Gunsteren, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b818713d

The influence of polymer architecture on the assembly of poly(ethylene oxide) grafted C60 fullerene clusters in aqueous solution: a molecular dynamics simulation study Justin B. Hooper, Dmitry Bedrov and Grant D. Smith, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b818971d

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Adsorption of peptides (A3, Flg, Pd2, Pd4) on gold and palladium

surfaces by a coarse-grained Monte Carlo simulation

R. B. Pandey,*a Hendrik Heinz,b Jie Feng,b Barry L. Farmer,c Joseph M. Slocik,c

Lawrence F. Drummycand Rajesh R. Naik

c

Received 16th September 2008, Accepted 16th December 2008

First published as an Advance Article on the web 26th January 2009

DOI: 10.1039/b816187a

Monte Carlo simulations are performed to study adsorption and desorption of coarse-grained

peptide chains on generic gold and palladium surfaces in the presence of solvent. The atomistic

structural details are ignored within the amino acid residues; however, their specificity and

hydrophobicity are incorporated via an interaction matrix guided by atomistic simulation.

Adsorption probabilities of the peptides A3, Flg, Pd2, Pd4, Gly10, Pro10 on gold and palladium

surfaces are studied via analysis of the mobility of each residue, the interaction energy with the

surface, profiles of the proximity to the surface, the radius of gyration, and comparisons to

homopolymers. In contrast to the desorption of Gly10 and Pro10 (with faster global dynamics),

peptides Pd2, Pd4, Flg, and A3 exhibit various degrees of adsorption on gold and palladium

surfaces (with relatively slower dynamics). Adsorption on both gold and palladium occurs

through aromatic anchoring residues Tyr2 and Phe12 in A3, Tyr2 in Flg, Phe2, His10 and His12 in

Pd2, and His6 and His11 in Pd4. A lower (more negative) surface-interaction energy of these

residues and lower mobility on palladium lead us to conclude that they are slightly more likely to

be adsorbed on palladium surfaces than on gold.

1. Introduction

Short peptides with specific sequences of residues are increas-

ingly important as a building block in emerging hybrid

materials as well as in understanding ways to incorporate

large proteins at desired targets.1–7 Insight into how to inte-

grate short peptide chains in a matrix of multi-component

systems (inorganic compounds, composites, polymer, and

solvent) is therefore crucial and involves processes such as

thermodynamic equilibration and secondary structure relaxa-

tions. Peptides can also be attached to many surfaces in

biological environments, and preventive measures may be of

interest to enhance the longevity of such surfaces. From a

basic scientific viewpoint, understanding the selective adsorp-

tion of peptides to specific surfaces is desirable within the

broader quest for biomimetic materials.

A number of experiments8–10 are often carried out to assess

the possibility of adsorption of peptides on such surfaces.

Identifying the probability of adsorption or desorption of a

peptide chain with a specific sequence is a laborious experi-

mental task, and it can be difficult to eliminate uncertainties

such as the surface structure or the influence of additional

solutes. It is also challenging to identify how a peptide binds to

specific surfaces, apart from identifying the affinity of certain

residues inside a longer chain. Computer simulation experi-

ments would be valuable not only to complement the experi-

mental efforts but also in predicting the probability of

adsorption of peptides or peptide subunits at different length

scales.

Designing advanced materials from functionalized nano-

particles with specific properties has been the subject of intense

interest in recent years,10 primarily due to the potential for

interesting material and medical applications. Using current

technical advances, surfaces of nanoparticles can be modified

with relative ease to tailor their characteristics in order to

assemble them in a desired morphology for optimal perfor-

mance. However, the incorporation of such nanostructured

materials with functionalized nanoparticles in practical devices

is still a challenge10 due to the difficulty of preserving and

exploiting their unique characteristics. Peptides are excellent

candidates to attach to the surface of a nanoparticle to intro-

duce specific characteristics. They possess unique recognition

motifs with well-defined structures controlled by the sequence

of residues, and interactions with constituents of multi-component

hybrid materials can be modulated through choice of specific

solvents. Of particular interest8–10 are bio-functionalized gold

and palladium nanoparticles for a range of applications

such as sensing, catalysis, bio-transport, and bio-recognition.

Understanding of dynamics and structural stability of

appropriate peptides (e.g. A3, Flg, Pd2, Pd4, Gly10, Pro10)

on gold and palladium surfaces is therefore highly desirable.

In regards to computer simulation and modeling, a peptide

is a short protein with a relatively small number of amino acid

groups. There are two main coarse-grained computer simula-

tion approaches to model a protein chain: on- and off-lattice.

aDepartment of Physics and Astronomy, University of SouthernMississippi, Hattiesburg, MS, 39406, USA

bDepartment of Polymer Engineering, University of Akron, Akron,Ohio 44325, USA

cAir Force Research Laboratory, Materials and ManufacturingDirectorate, AFRL/RXBP, Wright-Patterson AFB, Ohio 45433,USA

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Off-lattice approaches (including all-atomic methods)11–15 are

often used to probe such specific configurations as a-helices andb-sheets, especially in the folding of small proteins.16–18 Large

degrees of freedom are very important in probing the structural

fluctuations around known stable structures. The multi-scale

dynamics and related relaxation pathways from one structure to

another, however, are severely limited in proteins due to long

relaxation time when atomistic details are included. In order to

reproduce known characteristics (information-based approach),

some constraints are usually invoked, e.g. peptide group dipole

interaction,19 in addition to standard interactions and con-

straints. The bond-fluctuation (BF) model on a discrete lattice

is a further coarse-grained simplification but has been used to

study the conformational relaxation of a protein chain into the

native structure20 for a general HP (Hydrophobic Polar) protein

chain, a HPE (Hydrophobic, Polar, Electrostatic) protein

model,21 and even for a specific protein, sensory rhodopsin I22

without severe constraints. The main advantages of this

approach over the methods used in probing the structural

dynamics with all-atom descriptions are higher computational

efficiency, coverage of large scales, and avoidance of unphysical

constraints beyond the coarse-grained description on a discrete

lattice; the disadvantage is the lack of atomistic details. Attempts

have been made recently to incorporate specificity of each amino

acid in studying the segmental structure and stochastic mobility

of each residue of an HIV-I protease (1DIFA).23 We would like

to employ BF description here to examine the adsorption and

desorption of a set of peptides on gold and palladium surfaces.

The model is presented in section 2, followed by results and

discussion in section 3, and conclusions in section 4.

2. Model

A peptide (small protein) chain of size M is a specific sequence

of amino acid (AA) residues from a set of twenty. A typical

amino acid group has a central carbon atom (Ca) covalently

bonded by an amino group (NH2), a carboxyl group (COOH),

a hydrogen atom, and a side group (RL) (see Fig. 1). Differ-

ences in the side group distinguish one residue from the other.

The consecutive covalent (peptide) bond between the carboxyl

group of one residue and the amino group of the next

constitutes the peptide chain. Twisting and turning around

the central carbon (Ca) along with the segmental rearrange-

ment of the side groups provides stable structures such as

a-helices, b-sheets, and a whole host of mixed secondary struc-

tures in large polypeptides. A part of computational protein

modeling11–15 is focused on understanding such structures.

One of the major challenges with such modeling is to capture

relevant details and extend it to long time scales to draw

meaningful conclusions and gain useful insights into func-

tional characteristics of the protein. In all bonding (covalent

and non-covalent), electronic densities of states and their

distributions are involved in which the quantum descriptions

are particularly crucial in understanding electronic excitations

and related kinetics. However, it is not feasible to incorporate

such electronic structural details in exploring the long-time

physical properties of a peptide chain. Therefore, coarse-

graining is hard to bypass, i.e. ignoring some microscopic

details but capturing its relevant characteristics via approx-

imate interaction potentials has become a common practice in

modeling such a complex system.

In the so-called ‘all-atomic’ model,11–15 one usually consid-

ers all intra-structural details of an amino acid residue (see

Fig. 1) beyond the mesoscopic scales in the framework of a

coarse-grained description; it involves extensive force field

parameters derived from experiment, exploratory simulations

on smaller sub-systems, or a combination thereof. This ap-

proach has enormous advantages in capturing the microscopic

details, especially for short-time properties. However, it is

often not feasible to carry out simulations long enough to

sample the relevant portions of conformational and dynamical

phase space. Therefore, it is highly desirable to look for

alternative approaches that may still be coarse-grained but

computationally efficient to probe long-time properties, in

concert with all-atomic simulation. Such a coarse-grained

modeling approach is presented here with the bond-fluctuation

method for the chain24,25 that incorporates ample degrees of

freedom and the specificity23 of the residues while maintaining

the computational efficiency of a discrete lattice.

2.1 Coarse-grained lattice

We use a three-dimensional discrete (cubic) lattice as the host

matrix. An amino acid residue is represented by a particle or

node, i.e. the internal structural details of the amino acid

(Fig. 1) are ignored but its specific characteristics are in-

corporated (see below). A poly-peptide is a set of residues

(represented by particles or nodes) tethered together in a

flexible chain in a specific sequence. The peptide chain with

the covalently bonded nodes is represented by the bond-

fluctuation model on a lattice with a cubic grid. A node is

represented by a unit cube (by occupying its eight lattice sites)

and the bond length between consecutive nodes can vary

(fluctuate) between 2 and O10 with an exception of O8 in

units of the lattice constant. Such a bond-fluctuation descrip-

tion is known to capture the computational efficiency while

incorporating ample degrees of freedom in complex polymer

systems24,25 and multi-component nanocomposites.26–29 Thus,

a peptide is represented as a chain of unique nodes (amino

acids) in a specific sequence.

Since each node represents a specific residue, it is essential to

capture their specificity or uniqueness. Amino acids can be

divided into three broad categories:21 hydrophobic (H),

hydrophilic or polar (P) and electrostatic (E). An amino acid

within each group is further distinguished23 by its relative

hydrophobicity, polar, or electrostatic strength as shown in

Table 1. In addition to peptide chains, there is a substrate (S)Fig. 1 Amino acid.

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at the bottom and mobile solvent (water, W) particles each

with the size of a peptide node. This constitutes five main

components, H, P, E, S, and W in which there are three sub-

groups to characterize specificity of each residue: eight hydro-

phobic (H1, H2 . . . H8), eight polar (P1, P2 . . . P8), and four

electrostatic (E1, E2, E3, E4) (see Table 1). A set of pheno-

menological interactions (see below) among these components

are used to execute the stochastic movement of each node and

solvent particle with the Metropolis algorithm.

2.2 Interaction matrix

Interaction among five main components (H, P, E, W, S) can

be represented by a 5 � 5 matrix (see Table 2). The interaction

strength between two elements at sites i and j separated by a

distance rij is represented by the standard Lennard-Jones (LJ)

potential

Uij ¼ f eijsrij

� �12

�"

srij

� �6#; rijorc

where rc is the cut-off range and feij is the interaction strength

with an arbitrary parameter f that can be varied and s= 1. On

a cubic lattice the distance between two sites are discrete and

measured in units of the lattice constant. A variation of the LJ

potential with the distance is shown in Fig. 2 which shows how

it falls off quickly after the minimum distance r between the

two particles (nodes or solvent) is reached. Note that the

minimum distance between two neighboring particles is two

in units of the lattice constant (e.g. r2 = 4) below which the LJ

potential goes to infinity at r o 2. It is worth pointing out that

although the variation of the LJ potential in a continuum host

space is smoother than that on the cubic lattice (Fig. 2), the

general form remains similar. Since the potential falls of very

quickly, we limit the range of the interaction potential to rc2 = 8

which includes as many as 60 neighboring lattice sites. The

depth of the LJ potential is controlled by the magnitude of

the pair interaction strength feij which is relatively large. The

number of the pair-interaction matrix elements is reduced

somewhat due to symmetries, e.g. eij = eji.The magnitude of each interaction element is based on the

insight gained from all-atomistic description and general

characteristics. The structural details from atomic scale in-

cluding covalent bond and non-covalent interaction are gen-

erally considered in an all-atomic description. Ghiringhelli and

Delle Site30 have recently analyzed the structure of an amino

acid, i.e. phenylalanine near inorganic surfaces including

Au(111) and pointed out that both the atomic interaction

and flexibility of the molecule are important in predicting its

stable conformation. Heinz et al. have examined the adsorp-

tion energy of all 20 amino acids (see Table 1) on such surfaces

including Au(111) as shown in Fig. 3.31,32

Note that the amino acids (Phe, Trp, Tyr, His) with

aromatic groups have the largest adsorption energy followed

by the adsorption energy of electrostatic and polar residues.

The adsorption energy of the hydrophobic residues is lowest

among all the amino acids. Accordingly we assume a typical

Table 1 Amino acids and their hydrophobic, polar, and electrostatic strengths; the relative strength is assigned in each group (H, P, E) separately(ref: http://en.wikipedia.org/wiki/Amino_acid)

Amino Acid Hydrophobic/ polar/ electrostatic Relative weight: H/ P/ E

Ile (I): H1 4.5 1.00Val (V): H2 4.2 0.93Leu (L): H3 3.8 0.84Phe (F): H4 2.8 0.62Cys (C): H5 2.5 0.56Met (M): H6 1.9 0.42Ala (A): H7 1.8 0.40Gly (G): H8 �0.4 0.09

Thr (T): P1 �0.7 0.20Ser (S): P2 �0.8 0.23Trp (W): P3 �0.9 0.26Tyr (Y): P4 �1.3 0.37Pro (P): P5 �1.6 0.46His (H): P6 �3.2 0.91Gln (Q): P7 �3.5 1.00Asn (N): P8 �3.5 1.00

Asp (D): E1 �3.5 0.78Glu (E): E2 �3.5 0.78Lys (K): E3 �3.9 0.87Arg (R): E4 �4.5 1.00

Table 2 Interaction matrix among H, P, E, S and W components

H P E W S

H eHH eHP eHE eHW eHS

P ePH ePP ePE ePW ePSE eEH eEP eEE eEW eESW eWH eWP eWE eWW eWS

S eSH eSP eSE eSW eSS

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set of values of the interaction matrix presented in Table 3 to

capture the specific characteristics of these amino acids.

Surface interactions with gold and palladium are different:

for gold, eHS = 0.0, ePS = �0.2, eES =�0.2 and for palladium

eHS = 0.0, ePS = �0.27, eES = �0.27. Interactions among the

electrostatic residues are: e11 = e12 = e22 = e33 = e34 = e44 =0.1, e13 = e14 = e23 = e24 = �0.4. Among the hydrophobic

and polar groups, there are four residues (Phe (H4), Trp (P3),

Tyr (P4), His (P6)) with aromatic groups with strong surface

interaction (see Fig. 3) strength eAS = �0.7 with Au and

eAS = �0.9 with Pd. We have used f = 50 as the inter-

action energy factor for gold and palladium to accentuate the

differences in adsorption probabilities for different peptides.

Incorporating the specificity of each amino acid group for a

particular system enhances the size of the interaction matrix.

For example, the interaction energy of the polar group with

the gold surface is given by eP(i)S = Wp(i) � ePS where the

relative weight of each polar residue Wp(1) = 0.20 (Thr),

Wp(2) = 0.23 (Ser), Wp(3) = 0.26 (Trp), . . ., Wp(8) = 1.00

(Asn) (see Table 1). It is worth pointing out that despite these

specified values of the interaction matrix element, there is

ample room for varying the interaction strength including

relative magnitude without altering the qualitative results

significantly. For example, the qualitative result for the prob-

ability of adsorption of these peptides on the substrates can be

distinguished for a range of interaction strength f and a

specific value of f (=50) is selected to see these relative

differences as mentioned above. Thus, the choice of the matrix

elements presented here is primarily to illustrate how to

predict the relative adsorption of a set of peptide groups on

gold and palladium surfaces with a coarse-grained model with

the phenomenological interaction. This approach can be easily

extended to other surfaces and many polypeptides and pro-

teins. Most of our findings seem consistent with experimental

observations8,10 and molecular dynamics simulations with

‘all-atomic’ model32 qualitatively (see below). The main draw-

back is the lack of quantitative comparison. The efficiency of

our coarse-grained approach provides an alternate method to

investigate and predict the relative adsorption of different

polypeptides on gold and palladium substrates.

2.3 Stochastic movement

Each residue and solvent particle executes their stochastic

movement based on the Metropolis algorithm as follows. A

particle (node or solvent) at a site i and one of its 26

neighboring sites, say j, are selected randomly. If site j is

empty, then an attempt is made to move the particle from site

i to site j. If the particle attempted to move is a peptide node, it

is ensured that the length of the bond resulting from such a

move is within the specified limit. Provided the excluded

volume condition is satisfied, the energy in the old (Ei) and

the new configuration (Ej) is compared and the particle is

moved from site i to j with probability exp(�DEij/T), where

DEij = Ej � Ei, the temperature T is in units of the Boltzmann

constant and the interaction energy. Attempts to move each

node and solvent particle once defines one Monte Carlo step

Fig. 2 Variation of the Lennard-Jones potential with r2 (=rij2) with

s = 1, feij = 1 on a cubic lattice in unit of lattice constant.

Fig. 3 Adsorption energy of each amino acid in aqueous solution on an Au {111} surface with an all-atom model (consistent valence force field

(CVFF) with recent parameters for fcc metals, pH = 7, see ref. 31 and 32).

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(MCS) time. Simulation is performed for a sufficiently long

time to achieve the equilibration. A number of physical

quantities are evaluated during the simulation including the

energy of each residue, their mobility, their neighboring

components (substrate, solvent, and residues), and the

mean square displacement of the center of mass of the peptide

chains. Based on the analysis of these quantities along with

the visual analysis of the snapshots, we predict the

relative probability of adsorption of specific residues and

of the corresponding polypeptides on gold and palladium

substrates.

3. Results and discussion

Simulations are performed on different lattice sizes primarily

to check for severe finite size effects on the qualitative varia-

tion of the physical quantities. All data presented here are

generated on a 643 lattice, as no significant finite size effects are

detected that warrant change in our conclusions. Each simula-

tion consists of 10 copies of each peptide chain brought onto

the substrate with the solvent concentration cw = 0.05. 100

independent samples are used to estimate the average values of

the physical quantities. Animations are used to complement

our conclusions based on data analysis. Initially peptide

chains are dropped on the substrate and their structure,

dynamics, and distributions and dispersion are monitored as

they equilibrate.

In Table 4, coarse-grained descriptions are used to study the

adsorption of following peptide chains on the gold and

palladium surfaces.

Note that the different values of the matrix elements

(eHS, ePS, eES) for the interactions between the residues of

these peptide chains and the substrates distinguishes between

gold and palladium (see section 2).

Snapshots of some of these peptide chains at the end of

simulations are presented in Fig. 4. At a first glance, we see

that A3 and Pd2 are adsorbed on both gold and palladium

while Pro10 is desorbed. Most of the aromatic groups seem to

bind both surfaces. It is difficult to distinguish the degree of

adsorption of A3 and Pd2 on gold and palladium surfaces

from a snapshot at the end of simulation. Therefore, a closer

examination of adsorption is necessary by quantitative

analysis of the energy of each residue, their mobility, and

surrounding profiles as follows.

The energy of each residue with gold and palladium sub-

strates is presented in Fig. 5 and 6 respectively. Note that the

total energy of a residue includes its interaction with other

residues of the same peptide and that of its neighboring

peptides, surrounding solvent, and the substrate. There is a

considerable change in energy from one residue to another in

the same peptide chain as well as among different peptide

chains. The comparison of Fig. 5 and 6 shows no change in

pattern in samples with gold and palladium apart from minor

differences in the magnitude. Residues with low energy in both

Figures include Pro11 of A3, Asp4 and Lys8 of Flg, Pro6 and

Arg7 of Pd2, Asn3, Thr8, and His11 of Pd4. Despite the overall

low energy, one cannot tell which peptide has higher adsorp-

tion probability to these substrates (Au, Pd) or which residue

anchors them. Based on purely non-covalent interaction thermo-

dynamics, the stability of equilibrium (and subsequent

structure) is dictated by low energy. The peptide (homopolymer)

chains Gly and Pro possess very little cohesive energy; the

residue energy in these peptides is too large in comparison to

low-energy residues in rest of the peptides, e.g. A3, Flg, Pd2

and Pd4.

In order to assess the adsorption of the peptides and identify

the specific residues that may bind to the substrate, it is

important to analyze their profiles of surface-interaction

(adsorption) energies. Unlike the total energy of each residue

described above (Fig. 5 and 6), only the interaction energy of

each residue with the substrate within the range of interaction

of the surface sites constitutes the surface-interaction energy.

Table 3 A typical interaction matrix among H, P, E, S and W components

H P E W S

H 0.0 0.0 0.0 0.1 eHS

P 0.0 �0.2 �0.2 �0.2 ePSE 0.0 �0.2 eEE �0.3 eESW 0.1 �0.2 �0.3 �0.1 0.0S eSH eSP eSE 0.0 0.0

Table 4 Peptide chain details

Peptide chain Amino acids

A3 Ala–Tyr–Ser–Ser–Gly–Ala–Pro–Pro–Met–Pro–Pro–Phe[H7–P4–P2–P2–H8–H7–P5–P5–H6–P5–P5–H4]

Flg Asp–Tyr–Lys–Asp–Asp–Asp–Asp–Lys[E1–P4–E3–E1–E1–E1–E1–E3]

Pd2 Asn–Phe–Met–Ser–Leu–Pro–Arg–Leu–Gly–His–Met–His[P8–H4–H6–P2–H3–P5–E4–H3–H8–P6–H6–P6]

Pd4 Thr–Ser–Asn–Ala–Val–His–Pro–Thr–Leu–Arg–His–Leu[P1–P2–P8–H7–H2–P6–P5–P1–H3–E4–P6–H3]

Pro10 Pro–Pro–. . .–Pro[P5–P5–. . .– P5]

Gly10 Gly-Gly–. . .–Gly[H8–H8–. . .–H8]

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Fig. 7 and 8 show the profiles of the surface-interaction

energy of each residue in all peptide chains with gold and

palladium surfaces, respectively. The residues in each peptide

with low (e.g. large negative) surface-interaction energy can be

easily identified. Peptide A3 has two residues, Tyr2 and Phe12,

with very low surface-interaction energy on both substrates

(Au and Pd). Both residues are aromatic and have potential to

anchor A3 on the substrates. The surface-interaction energy of

these residues is comparatively lower at the palladium surface.

Therefore, the probability of adsorption of A3 on the palla-

dium substrate is higher than on the gold substrate. Similarly,

the peptide Flg is anchored by an aromatic residue Tyr2 on

both surfaces and the probability of adsorption is higher on

palladium. The probability of adsorption of the peptides Pd2

and Pd4 is also higher on the palladium substrate in compar-

ison to gold. Binding residues are Phe2, His10 and His12 for

Pd2 and His10 and His11 for Pd4; these residues are also

aromatic. The peptides Gly and Pro possess only very minor

negative surface interaction energy and do not adsorb on

either substrate.

Since the interaction potential and matrix in our coarse-

grained description (presented above) are phenomenological,

Fig. 4 Snapshots of A3, Pd2 and Pro on gold (Au, top row) and palladium (Pd, bottom row) surfaces are shown at the end of simulations

(105 MCS time) on a 643 lattice. (green (H), gold (P), blue (E), pink (A), grey (W), dirty gold (substrate)).

Fig. 5 Profile of the total energy of each residue of each peptide on a gold substrate. Statistics: sample size 643, 10 peptides in each of 100

independent samples, with 105 time steps.

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one may question the validity of conclusions based on the

specificity of the residues and their sequences. To test the

sensitivity of the role of amino acids in a specific sequence, we

have examined the physical properties of analogous homo-

polymers of each residue in some of these peptides. As an

example, Flg appears suitable as it contains only three differ-

ent amino acids, i.e. Asp, Tyr, and Lys which lead to three

homopolymer chains25 Asp8, Tyr8, and Lys8, each with eight

nodes of the respective residue. The adsorption energy of each

monomer segment in these three homopolymers on the palla-

dium surface is presented in Fig. 9 along with that of the

peptide Flg. We notice the contrast in adsorption energy

among the homopolymers and the peptide. Despite the same

characteristics of each monomer in a homopolymer (e.g. Asp8

and Lys8), there is a considerable difference in surface-

interaction energy from one node (segment) to another. This

implies that the conformation of the chain at the surface and

steric constraints play a significant role in adsorption and

Fig. 6 Profile of the total energy of each residue of each peptide on a palladium substrate. Statistics: sample size 643, 10 peptides in each of 100

independent samples, with 105 time steps.

Fig. 7 Surface-interaction energy Ens of each residue of each peptide with the gold substrate. Statistics: sample size 643, 10 peptides in each of 100

independent samples, with 105 time steps.

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anchoring (strong adsorption). The lowest surface-interaction

energy of Tyr2 in Flg, however, is due to its interaction with

the Pd surface. Anchoring of Flg by Tyr2 leads to a different

conformation than that of corresponding homopolymers,

e.g. Tyr8.

The mobility of each residue is evaluated from their average

number of successful moves per unit time step. Fig. 10 and 11

show the mobility profiles of each residue in all peptide chains

with gold and palladium surfaces, respectively. The mobility of

Tyr2 is the lowest among all residues of peptide A3 on gold

substrate. Despite the low surface-interaction energy of Phe12

of A3 (Fig. 7), it is more mobile on gold (Fig. 10). We conclude

that the adsorption of A3 on gold is for the most part

mediated by Tyr2 and not by Phe12. The mobility of Tyr2 of

A3 is much lower on palladium than that on gold (see Fig. 10

and 11). Therefore, Tyr2 is the major anchoring residue for A3

on palladium as well. The mobility of Phe12 of A3 on

palladium is higher than Tyr2 but it is still low in comparison

Fig. 8 Surface-interaction energy Ens of each residue of each peptide with the palladium substrate. Statistics: sample size 643, 10 peptides in each

of 100 independent samples, with 105 time steps.

Fig. 9 Surface-interaction energy Ens of each residue in various homopolymers (Asp8, Lys8, Tyr8) and peptide Flg on a palladium substrate.

Statistics: sample size 643, 10 peptides in each of 100 independent samples, with 105 time steps.

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to Phe12 and comparable to Tyr2 on gold. Thus, Phe12 is an

additional anchor for the adsorption of A3 on palladium due

to both low surface-interaction energy (Fig. 8) and low

mobility (Fig. 11). Residue Tyr2 of Flg is of lowest mobility

on both gold and palladium surfaces (Fig. 10 and 11) and

anchors the adsorption of Flg. It should be pointed out the

contributions of residues Lys3 and Asp5 in anchoring (at least

partially) the peptide Flg for its adsorption cannot be ruled

out due to their relatively low mobility and low surface energy.

Low mobility of Phe2, His10, and His12 of Pd2 and His6 and

His11 of Pd4 along with their low surface-interaction energy on

both gold and palladium substrates (Fig. 7–11), with lower

Fig. 10 Mobility Mn of each residue of all 10 peptide chains on the gold substrate; mobility (y-axis) of each residue per peptide chain should be

divided by 10. Statistics: sample size 643, 10 peptides in each of 100 independent samples, with the 105 time steps.

Fig. 11 MobilityMn of each residue of all 10 peptide chains on the palladium substrate; mobility (y-axis) of each residue per peptide chain should

be divided by 10. Statistics: sample size 643, 10 peptides in each of 100 independent samples, with 105 time steps.

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surface-interaction energy on the latter, show that these

residues most strongly anchor the peptides Pd2 and Pd4. All

residues of Gly and Pro are relatively more mobile and offer

little probability of adsorption or anchoring.

Local structural profiles are also examined by monitoring

the number of different components (residue groups, solvent,

substrate) within the range of interaction of each residue in all

peptide with both gold and palladium surfaces. The profile for

the number of surface sites (Ns) within the range of interaction

of each residue may be most relevant, especially for assessing

the adsorption of peptides and their anchoring residues.

Fig. 12 and 13 show such surface-interaction profiles. The

closer a residue is to the substrate, the larger a value Ns would

have and therefore the higher its adsorption probability. High

numbers of surface-interaction sites (Ns) are found for Tyr2

and Phe12 of peptide A3, Tyr2 of peptide Flg, Phe2, His10, and

His12 of peptide Pd2, and His6 and His11 of peptide Pd4 on

both gold and palladium substrates (Fig. 12 and 13). Structural

profiles near surfaces support our above analysis in identifying

the residues that anchor the peptides to the surface and

are consistent with the above analysis based on their low

surface-interaction energy and low mobility.

Note that the molecular weight of all peptide chains is not

the same (the smallest is Flg with eight residues) and the size of

each chain is too small to analyze the scaling of the radius of

gyration with the molecular weight. The radius of gyration

(Rg) can be calculated, nevertheless, and its magnitude can be

compared in the sample with the gold surface to the sample

with the palladium surface. The equilibrium value of the

radius of gyration hRgi of each peptide chain is different in

both samples. Estimates of hRgi for each peptide chain are

presented in Table 5. We see that hRgi is generally lower in the

sample with the palladium substrates. Of particular note is the

difference in the magnitude of hRgi of A3 which is reduced by

about 70% on the palladium surface in comparison to its value

on the gold surface. In general, palladium is found to be more

adsorbing than gold.

Finally, the overall dynamics of the peptide chains can be

studied by analyzing the variation of the root mean square

(RMS) displacement of the chains with the number of time

steps. Variations of the RMS displacement of the center of

mass of the peptide chains and its components (x, y, z) as a

function of time steps (number of Monte Carlo moves) are

presented in Fig. 14 and 15 with gold and palladium sub-

strates, respectively. The collective dynamics of the peptides

appears very similar in the samples with gold (Fig. 14) and

palladium surfaces (Fig. 15). However, there are marked

differences in the dynamics between the individual peptides

on the surfaces. For example, the rate of change of the RMS

displacement (R) of the peptide Pd2 is the lowest followed by

Pd4, A3, and Flg while that of the peptides Gly and Pro

(homopolymers) is the highest. Peptides Gly and Pro are most

mobile and have the lowest probability of adsorption on both

substrates. The motion of the remaining peptide chains

(A3, Flg, Pd2, Pd4) is considerably slower due to their adsorption

on the substrates. Further the differences in motion of peptides

along different directions (x, y, and z) should be pointed

out. The metallic substrates considered here lie in the

zx-plane normal to y, the vertical direction (see Fig. 4).

The motion of peptide chains along the longitudinal (y)

direction is constrained by their adsorption on the substrates

as seen from the y-component of the RMS displacement of

the center of mass of peptide chains. In transverse directions

(z and x), there is no such constraint and chains diffuse freely.

These differences in the dynamics of each peptide along the

longitudinal and transverse directions are clearly seen in

Fig. 12 Number of surface sites (Ns) in the vicinity of each residue of each peptide on the gold substrate. Statistics: sample size 643, 10 peptides in

each of 100 independent samples, with the 105 time steps.

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Fig. 14 and 15 from the rate of change of corresponding RMS

displacements.

4. Summary and conclusions

A coarse-grained computer simulation model is introduced to

study the adsorption of the peptides A3, Flg, Pd2, Pd4, Gly10,

Pro10 on gold and palladium surfaces. With the simplicity of

the model and computational efficiency it is possible to predict

the probability of adsorption of peptides and their specific

binding (anchoring) residues. A peptide is represented by a

specific set of residues (represented by particles or nodes)

tethered together by fluctuating bonds in a flexible chain of

a specific sequence. Although the internal structural details of

each residue are ignored, their specific characteristics are

captured via an interaction matrix for the coefficients of a LJ

potential; the relative magnitude of the interaction matrix

elements are based on the all-atomic analysis31,32 of each

residue.

The adsorption probability of each peptide chain is deter-

mined by analyzing a number of global and local quantities

including the energy of each peptide chain and that of each

residue in their unique sequence position, the interaction

energy of each residue with the surface, their neighborhood

profiles, their mobility, the radius of gyration of the peptides

on the different surfaces, and the variation of the root mean

square displacement of the peptide chains as a function of the

number of simulation steps. In addition, visual inspection is

also used to assess the degree of adsorption of each peptide.

We find that peptides A3, Flg, Pd2, and Pd4 are more likely

to be adsorbed on both gold and palladium surfaces with

various degrees while Pro10 and Gly10 are desorbed. These

observations, though speculative, seem consistent with the

experimental observation (SEM images of bi-metallic nano-

particles in presence of A3 and Flg and their dimers and

surface coverage of Au and Pd,9 as well as with TEM micro-

graphs10 of the aggregation of spherical gold nanoparticles

with A3 and Flg). There are many residues with lower

(negative) surface-interaction energy and lower mobility in

A3, Flg, Pd2, and Pd4 than those in Gly10 and Pro10. Slightly

negative surface-interaction energy does not necessarily indi-

cate higher adsorption probability. Such residues include Ser4,

Pro8, Pro11 in peptide A3, Asp4 and Lys8 in Flg, Pro6 and Arg7

in Pd2, Asn3, Thr8 and His11 in Pd4 and Pro10 in Pro. Residues

with significantly negative surface-interaction energy and thus

strong adsorption with both gold and palladium surfaces, on

the other hand, are Tyr2 and Phe12 in A3, Tyr2 in Flg, Phe2,

His10, and Phe12 in Pd2, and His6 and His11 in Pd4. Mobility is

also low for these residues on both gold and palladium

surfaces with an exception, i.e. Phe12 in A3 with gold. This

means that the conformational entropy (physical constraints

on the shape) plays a more important role for the peptide than

for a small molecule such as a single amino acid,30 in concert

with the energy in anchoring the peptide chains to the surface.

The number of surrounding substrate sites of residues in the

peptide chains (surface-interaction profiles) confirm the

Fig. 13 Number of surface sites (Ns) in the vicinity of each residue of each peptide on the palladium substrate. Statistics: sample size 643,

10 peptides in each of 100 independent samples, with 105 time steps.

Table 5 Radius of gyration (Rg) of peptides on gold and palladiumsurfaces

Peptide hRgi on Au hRgi on Pd % difference

A3 4.484 � 0.031 2.619 � 0.024 71.2Flg 3.240 � 0.019 3.194 � 0.016 1.4Pd2 4.480 � 0.033 2.804 � 0.027 37.4Pd4 4.486 � 0.032 2.702 � 0.035 39.8Gly 4.086 � 0.025 2.249 � 0.028 44.9Pro 3.951 � 0.020 2.190 � 0.025 44.6

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adsorption of these peptides onto gold and palladium surfaces

and help identify likely ‘‘anchoring’’ residues of the peptides.

A relatively lower (more strongly negative) surface-interaction

energy of these residues and lower mobility on palladium in

comparison to gold lead us to conclude that they are slightly

more likely to be adsorbed on palladium surfaces than on gold

surfaces. Unfortunately such specific detail as the binding

mechanism for the adsorption of peptides is not (yet) available

from laboratory measurements.

The radius of gyration of peptide chains conforms to lower

values with palladium substrates for all peptides with an

exception of Flg which is comparable in its size at both

Fig. 15 Variation of the root mean square (RMS) displacement (R) of the center of mass of the peptide chains and its components (x, y, and z) as

a function of time steps in samples with palladium substrate. Statistics: same as Fig. 13.

Fig. 14 Variation of the root mean square (RMS) displacement (R) of the center of mass of the peptide chains and its components (x, y, and z) as

a function of time steps in samples with the gold substrate. Statistics: same as Fig. 13).

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(gold and palladium) surfaces. The global dynamics of peptide

based on the variation of the RMS displacement of peptide

chains show that Gly and Pro move fast after desorption from

the substrates while A3, Flg, Pd2, and Pd4 remains slow.

These findings seem consistent with all-atomic simulations32

and laboratory observations.8–10

The model and the results presented here certainly leave

room for improvement. The interaction matrix selected for the

phenomenological interaction potential is one of our early

attempts which can be fine-tuned in coordination with labora-

tory data. Moreover, the combination with bioinformatics

approaches in the future might provide interesting opportu-

nities for in silico screening of the huge number of potential

peptides to control binding properties to a given surface.

Acknowledgements

Support from the Materials and Manufacturing Directorate of

the Air Force Research Laboratory, the Air Force Office of

Scientific Research (AFOSR) is gratefully acknowledged.

H. H. and J. F. acknowledge further support from the University

of Akron and from the Ohio Supercomputing Center.

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