duca 1999 modelling

Molecular modeling of polymers18. Molecular dynamics simulation of poly(acrylic acid) copolymer

analogs. Capture of calcium ions as a function of monomer structure,sequence and flexibility

J.S. Duca, A.J. Hopfinger*

Laboratory of Molecular Modeling and Design, M/C 781, College of Pharmacy, University of Illinois at Chicago, 833 South Wood St., Chicago,IL 60612-7231, USA

Received 1 December 1998; received in revised form 3 February 1999; accepted 3 February 1999

Abstract

The behavior of four derivative copolymers of poly(acrylic acid) were modeled in dilute aqueous polymer solutions with calciumcounterions. Molecular dynamics simulations of negatively charged copolymer models in the presence of different Ca21 ion concentrationsat 300 K, using an effective molecular dielectric constant of 3.5, were performed. Analyses of the dependence of the total potential energy,the counterion binding energy and the time average chain segment length of each of the copolymer models on Ca21 ion concentration wasperformed. One of the copolymer models was predicted to have the greatest propensity to capture the calcium counterions. Unusually strongbinding interactions between the copolymer and Ca21 counterions were identified for this copolymer. Structure-binding analysis led to theidentification of a specific Ca21 binding site sequence and geometry as being responsible for the strong counterion binding. The events thattake place during the calcium capturing process at this binding-site are discussed in terms of intramolecular dynamics and intermolecularelectrostatic interactions. The existence of this specific Ca21 binding sequence is a clear example of how property optimization studies in thelaboratory mimic breakthrough outcomes realized in natural evolution.q 1999 Elsevier Science Ltd. All rights reserved.

Keywords:Poly(acrylic acid) copolymer; Molecular dynamics simulations; Polyacrylates

1. Introduction and background

The presence of free radical calcium ions can be aproblem to many industrial chemical processes, thus requir-ing the use of Ca21 complexing agents and/or dispersants. Inthe presence of carbonate ions, for example, polyacrylatesact as dispersants and the formation of macroscopic CaCO3precipitation is inhibited. Thus, polyacrylates are used toprevent scaling, or residue buildup in many aqueous chemi-cal and thermal operations where it is difficult to avoid thepresence of calcium ions.

The utilization of polyacrylates as dispersant agentsbegan about twenty years ago [1] because the high concen-tration of COO2 groups along the polymer chain cancapture Ca21 ions and effectively rid the system of thesefree ions. The design idea behind this capturing of freeCa21 ions is based more on establishing a high local concen-tration of carboxyl groups, and less upon how these groups

can be spatially deployed (molecular structure) relative toone another.

Once the Ca21 binding capacity of a polyacrylate actingas a dispersant is exceeded, it will form an insoluble calciumsalt complex and contribute to scaling/residue buildup. Theformation of an insoluble polyacrylate-Ca21 salt complexgenerally occurs at higher Ca21 ion concentrations in thepresence of carbonate ions [2]. Obviously, the higher theCa21 binding capacity of the polyacrylate, the better willbe its performance as Ca21 ion dispersant. In terms of mole-cular design, maximizing counterion binding capacity istreated in terms of modifying the chemical structure ofthe polyacrylate. Modifications of polyacrylate structureare realized by using different compositions of differentmonomers.

In many ways this synthetic approach to the optimizationof Ca21 ion binding is an example of mans way of mimick-ing natural evolution. Within this context, the purpose ofthis article is to demonstrate that each polyacrylate copoly-mer studied has specific local three-dimensional (3D)geometries in much the same way as each amino residue

Computational and Theoretical Polymer Science 9 (1999) 227244

CTPS 88

1089-3156/99/$ - see front matterq 1999 Elsevier Science Ltd. All rights reserved.PII: S1089-3156(99)00009-4

* Corresponding author.

sequence of a polypeptide chain (protein) leads to a distinctset of conformational states. Moreover, the local copolymermolecular geometries have distinct Ca21 ion bindingpropensities. One of these local copolymer moleculargeometries, by chance, is ideally suited to selectively andstrongly bind Ca21 ions. This binding site is highly remi-niscent of the specific ion binding sites found in the crystalstructures of ion-binding proteins.

Polyacrylates have been studied extensively [3,4].Conformational transition studies of poly(acrylic acid)(PAA) have been performed using potentiometric [5],spectroscopic [6,7], viscosimetric [8], and conductometric[9] methodologies that have demonstrated that thetransitions are characteristic of classical polyelectrolyte-counterion systems, and not too highly dependent on choiceof solvent. The properties of the conformational changes ofPAA have been studied for a range of dielectric-solventmedia. Tanaka et al. [10] have shown that even in deionizedwater, the formation of cooperative hydrogen bonds ishighly probable. These studies surmise that intramolecularattractions prevail in spite of strong charge repulsions, butthe nature of the solvent can play a role in details of thetransitions.

The most commonly studied counterion is sodium (Na1)[36]. Some work has been done on both lithium ion (Li1)[6,8,11] and calcium ion (Ca21) [12,13] polyelectrolytesystems. It also appears that the conformational transitionproperties of PAA are independent of chain tacticity. Someinvestigators have not specified chain tacticity in theirreports, with the implication being that atactic sampleswere used in the experiments.

Recently, molecular modeling studies on the conforma-tional transitions of both PAA and poly(methacrylic acid)(PMA) were performed in our laboratory with a strongemphasis on transition behavior as a function of the degreeof ionization and the presence of Na1 and Ca21 counterions[1416]. In these modeling studies, the thermodynamic andgeometric nature of the transitions of PAA/PMA and PAA/PMA-counterion systems have been elucidated.

With respect to the interactions between PAA and Ca21

ions, it is well-known that neutralized carboxylic acids havea substantial tendency to interact with Ca21 ions. This char-acteristic feature extends over different processes belongingto both biological systems and industrial processes.

Dilute polymer solution molecular dynamics simulations(MDS) of four atactic PAA derivatives at various calciumcounterion concentrations are reported here. Conforma-tional transitions, as well as the role of long-range inter-actions on the flexibility of these copolymers and thecorresponding implications on calcium capturing capabil-ities were investigated. An analysis of the MDS trajectoriesreveals information aboutspecificevents occurring duringthe calcium capturing process as a function of copolymerchemical structure and geometry.

2. Methods

The four copolymers used in this study are derivatives ofPAA obtained by a specific synthetic pathway [17]. Thecopolymer composition and corresponding nomenclaturefor each chain-segment model investigated are reported in

J.S. Duca, A.J. Hopfinger / Computational and Theoretical Polymer Science 9 (1999) 227244228

Table 1(a) The monomers used in the construction of each chain-segment copolymer model for the MDS studies; (b) Copolymer chain-segment model compositionexpressed in monomer percentages

Part (a)

Part (b)Copolymerchain-segmentmodel,ak

AA AM lm

Poly9 90 10 0Poly8 82 10 8Poly7 72 20 8Poly6 62 30 8

Table 1. Fifty monomer chain segment models wereconstructed to simulate each of the four copolymers. Themodels were constructed using the polymer builder ofCHEMLAB-II [18]. Five different monomer sequences,consistent with composition, were assigned to each copoly-mer model, and for each of these sequences the monomertacticities were randomly chosen to achieve overall, atacticchains. The AM1/RHF [19] semiempirical methodologywas used to assign partial charges to each copolymerchain-segment model.

The final step to prepare each copolymer chain-segmentmodel for MDS was to carry out a static molecularmechanics (MM) geometry optimization with an energyconvergence of 0.5 kcal/mol for each degree of freedom.The force field parameters used to perform the optimizationswere obtained from the extended Allinger MM2 force fieldas implemented in the MOLSIM MDS program [20]. TheMOLSIM MM minimization algorithm was used to performthe geometry optimization.

Full Cartesian MDS using MOLSIM MDS were carriedout on the chain-segment models of the four atactic PAAcopolymer derivatives. The AM1/RHF partial atomiccharges were utilized for computing the electrostatic poten-tial energy using a Coulomb-like potential function [18].The Ca21 ions were assigned two-unit positive charges.The MDS were performed at 300 K.

The MDS studies were divided into two sets of simula-tions, as in an earlier polymer simulation study [15]:

MDS were performed on neutral and completely chargedcopolymer chain-segment models. This was done in theabsence of counterions to establish the range of chain-segment dimensions that could be expected in the simu-lation modeling.

MDS were performed in the presence of Ca21 ions togener-ate data about the energetics of the polymer-counterion

interactions and the role of chain conformational flex-ibility on these interactions.

The simulation data must be independent of chain tacti-city and counterion distribution. The MDS were checked toestablish these independent features. One spatial measurefor the characterization of the neutral and charged chainmodels is the distance,RH-T(ak), from the head to the tailof the copolymer chain-segment model.ak , is a symbolused to reference a particular copolymer chain-segmentmodel. The term folding is used in this study and isdefined as the ratio of the averageRH-T(ak ) length of themodel chain segment to its corresponding maximum[extended] RH-T(ak) value. Thus, folding incorporatessome component measure of chain conformational flexibil-ity (entropy) as being a direct spatial measure.

In order to characterize the copolymercounterion inter-action energetics, three energy measures were computedfrom the MD trajectories.ET(CI,ak) is the total potentialenergy of the simulation system at counterion concentrationCI (the number of Ca

21 ions present/number of ionizablemonomer units in the chain-segment model). Thus,CI is arelative concentration measure made relative to the numberof ionizable groups on the polymer chain. The total potentialenergy of the system includes intramolecular chain-segment, polymercounterion and counterioncounterioninteractions. The second energy measure considered isET(CI,ak)/CINM, whereNM is the number of charged mono-mer units in the chain-segment model. Accordingly,ET(CI,ak)/CINM measures the total potential energy perunit of counterion-charge. The final interaction energymeasure considered isEC(CI,ak)/CINM which is the sumof the polymercounterion and counterioncounterioninteraction energies per unit of counterion-charge.

3. Results

The five different tacticity distributions listed in Table 2were used to define the fifty-unit copolymer chain-segmentmodels poly6, poly7, poly8 and poly9 whose monomercompositions are given in Table 1. In addition, for eachatactic model five different randomly selected seed numberswere used in order to generate trajectories independent ofthe sets of initial velocities for each MDS.

During the first phase of the study, the MDS were focusedon poly8 and poly9 models, both in neutral, and the

J.S. Duca, A.J. Hopfinger / Computational and Theoretical Polymer Science 9 (1999) 227244 229

Table 2Tacticity distributions of the chain-segment copolymer models poly6,poly7, poly8 and poly9 (Ssyndiolinkage, Iiso linkage)

Model No. Tacticity distribution

1 SIIISSISSSISSSSSISSISISSSSIISSIISSISSIISSSSISISSSI2 SSSISSISISSISSSISSSSSISSISISISSSSIISSIISISSIISSSSS3 ISSISISSISSSISISSISSSSSSISSISSISISIISSISSIISISSIIS4 IISSISSSISSISSISSSISISSISISSSSSISISSISISISISIISSII5 SISSSISISSISSSIISSSISSSSISISISSISISSSSISSIISSISSSS

Table 3Average values forRH-T(ak ,1) determined during the last 10 ps of the MDS for the neutral and negative charged models of poly8 and poly9

Molecular dielectric,1 RH-T(poly8, 1) (A) RH-T(poly9, 1) (A)Neutral Charged Neutral Charged

3.5 15.8^ 4.4 78.8^ 6.8 17.8^ 5.8 72.2^ 6.810 21.8^ 7.4 57.0^ 9.2 25.2^ 7.0 54.4^ 7.615 20.4^ 9.8 44.8^ 11.6 18.4 6.4 46.8^ 8.220 28.4^ 9.0 43.6^ 10.6 27.4 8.8 53.4^ 9.2


Fig. 1. Dependence of the average values ofRH-T(ak ,1) listed in Table 3 on the molecular dielectric,1 .

Fig. 2. RepresentativeRH-T(ak ,1) trajectories of neutral models of poly8 and poly9.


Tab

le4

The

aver

age

valu

esan

dR

MS

devi

atio

nsin

both

ET(C

I,ak)/

50C

Ian

dE

C(C

I,ak)/

50C

Ifo

rdi

ffere

ntco

poly

mer

mod

el-c

ount

erio

nco

ncen

trat

ions

,beg

inni

ngw

ithco

mpl

etel

yne

gativ

ely

char

ged

copo

lym

erm

odel

s.T

heen

ergi

esar

ein

kcal

/mol

/cha

rge-

unit

CIN

ME

T(C

I,ak)/

50C

IE

C(C

I,a

k)/

50C

I

Pol

y6P

oly7

Pol

y8P

oly9

Pol

y6P

oly7

Pol

y8P

oly9

240

2^

3254

2^

3748

4^

962

7^

222

173.

3^

21.6

213

2.9^

37.5

220

4.2^

6.7

220

4^

186

21.

4^

14.1

11.9

38.6

24.

2^

19.6

4.1^

16.1

214

1.8^

6.5

214

3.1^

25.4

216

3.6^

16.5

219

2.2^

9.1

102

116.

2^

20.1

210

6.3^

20.0

211

6.4^

13.7

211

0.2^

19.1

214

3.5^

13.2

215

0.5^

13.1

216

0.9^

12.3

217

4.8^

15.7

202

198.

1^

14.4

219

6.8^

11.7

217

4.7^

10.2

219

2.3^

20.6

215

7.4^

13.4

216

3.0^

9.7

214

5.5^

9.1

216

5.4^

16.2

30(a

)a2

185.

8^

14.3

218

2.8^

16.6

216

4.7^

2.9

218

5.2^

11.9

213

3.7^

11.8

213

4^

132

119^

22

138.

1^

10.3

40(b

)a2

169.

5^

17.2

216

5.6^

9.7

215

6.3^

13.1

211

8.4^

14.5

211

6.5^

8.1

211

3.3^

10.3

502

147.

3^

6.1

214

9.6^

5.1

299

.7^

4.7

210

3.5^

4.6

56(c

)a2

136.

2^

5.5

213

5.7^

6.7

291

.4^

4.7

291

.5^

5.9

aB

eyon

dth

issi

teoc

cupa

ncy

limit,

itis

not

poss

ible

toco

ntin

uead

ding

Ca

21co

unte

rions

to:

(a)

the

poly

6m

odel

;(b

)th

epo

ly7

mod

el;

(c)

the

poly

8an

dpo

ly9

mod

els.


Fig. 3. Average total energy,Etotal, dependence on Ca21 concentration for: (a) the poly6 model, (b) the poly7 model, (c) the poly8 model, and (d) the poly9

model.


Fig. 3. (continued)

completely negatively charged states. MDS were carried outfor different values of the molecular dielectric,1 3.5, 10,15, 20. Each MDS was run for 55 ps. The first 5 ps wereused to equilibrate the system, and the next 50 ps used togenerate an approximate ensemble profile for property esti-mation. The last 10 ps trajectory of each MDS was used tocompute average property values.

Table 3 contains the average values ofRH-T(ak ,1 ) forpoly8 and poly9 in both the charged and neutral statesafter the entire set (five atactic models and five initial setsof velocities) of 25 MDS were carried out for each model ata given molecular dielectric. TheRH-T(ak ,1 ) values of Table3 suggest that there are no significant differences in thespatial properties of poly8 and poly9. Another importantfinding is that the sizes of the copolymer chain-segmentmodels being used are adequate because the average spatialvalues are independent of the tacticity of each model.RH-T(ak) is ca. 125 Afor both poly9 and poly8 when each iscompletely extended. Thus, the degree of folding isabout 88% for the neutral models and 44% for the chargedmodels. Fig. 1 shows the average values ofRH-T(ak ,1 ) forthe MDS reported in Table 3. As expected, changes inRH-T(ak ,1 ) are more dependent on the molecular dielectric forthe charged models than for the neutral ones. Neutralmodels are clearly more flexible than the correspondingnegatively charged ones due to the lack of chargechargeintramolecular repulsions.

Neutral poly8 and poly9, and negatively charged poly8and poly9, have, respectively, similar conformational beha-viors over their MDS trajectories. Hence, poly8 and poly9should be expected to have similar inherent backbone flex-ibility and ability to capture counterions. However, a differ-ent viewpoint results ifRH-T(ak ,1 ) is traced through theentire MDS trajectory. This tracing was done for everyMDS run for both poly8 and poly9. Fig. 2 displays repre-sentativeRH-T(ak ,1) trajectories of neutral models of poly8and poly9. Fig. 2 indicates that even when the averagetrajectory values ofRH-T(ak ,1) are very similar for neutralchain-segment models of poly8 and poly9, the MDS ensem-bles from which these average values are reached showdifferent behaviors. Poly8 converges to a constantRH-T(ak ,1 ) value much more slowly (10 ps longer) thanpoly9. Both the chain-segment models exhibit a largedegree of folding, but poly9 is more flexible than poly8.This difference in conformational flexibility is due to thepresence of the cyclic imide moiety in poly8.

Once the dimensional range and stability of the MDSwere established, MDS were carried out for interactingcopolymercounterion systems. The general simulationconditions were chosen from the initial neutral chain studiesin order to detect small changes in either intermolecularinteractions (binding capability) or intramolecular chain-segment dimensions (intrinsic flexibility). A low moleculardielectric of 3.5, and fully ionized copolymers were selectedin order to realize high initial rigidity and extension of thechains (lower degree of folding). These fully ionized initial

conditions permitted us to directly observe how increasingthe counterion concentrations influence both folding andchain flexibility.

The MDS were run at 300 K for the various chargedcopolymer Ca21 ion models of poly6, poly7, poly8 andpoly9. Table 4 contains the average values ofET(CI,ak)/CINM and EC(CI,ak)/CINM for the entire collection of 50MDS (five atactic models five initial sets of velocitiestwo counterion distribution) considered at a givenCI Ca

21

ion concentration.The average deviations in the energy measures reported

in Table 4 reflect the variance in the energetics as a functionof MDS trajectory sampling, atactic chain model and differ-ent distributions of the counterions over the length of acopolymer chain-segment model. The data of Table 4 arealso plotted in Figs. 3 and 4 for each copolymer chain-segment model. The total potential energy,ET(CI,ak )/CINM, decreases with increasingCI for the four copolymersystems studied. The greatest rate of decrease inET(CI,ak)/CINM occurs for counterion concentrations in the rangebetween 0 and 0.50 where the polymercounterion attrac-tive interaction terms prevail. This situation is reversed athigher counterion concentrations (CI . 1.0), where the totalenergy becomes slightly higher because of repulsive coun-terioncounterion interactions near the polymer.

The plots ofEC(CI,ak )/CINM show both similarities anddifferences among the chain-segment models. The poly8and poly9 systems exhibit a steady increase in bindingenergy untilCI is close to one, and the standard deviationsin the binding energies remain almost a constant over thisrange ofCI. That is, there is a net destabilization in the directbinding of Ca21 ions, even though the total system energy issignificantly stabilized. In contrast, for poly7 stabilization inthe binding energy occurs for values ofCI less than 0.6, andthere is a subsequent increase in binding energy as the coun-terion concentration is increased above 0.6. Poly6 exhibits arelatively constant, slightly stabilizing binding energy up toa CI value of 0.65.

A comparison of the absolute binding energies revealsthat poly9 has more negative values (ca. 20 kcal/mol) thanpoly8 for values ofCI less than 0.7. Apparently, a Ca

21 ionseems to be more comfortable in a poly9 environmentthan near poly8 in this Ca21 concentration regime. Poly7has stabilizing interactions with Ca21 ions in this concentra-tion range, and the binding energies are quite similar tothose of the poly9 system. Poly6 is least able to captureCa21 ions, and correspondingly has the most positive bind-ing energies. However, at higher counterion concentrations,poly6 interacts more favorably with the counterions thanboth poly8 and poly9. Overall, the order of capturingCa21 ions at concentration values up to 0.7 is poly7.poly9 poly6 . poly8. At higher Ca21 concentrations,the capturing order changes to poly7. poly6 . poly9 poly8.

Intramolecular repulsions among the carboxylate groupsin the ionized form of each of these copolymer models



Fig. 4. Average binding energy,Ebind, dependence on Ca21 concentration for: (a) the poly6 model, (b) the poly7 model, (c) the poly8 model, and (d) the poly9

model.


Fig. 4. (continued)

destabilize the electrostatic potential energy and limits theconformational flexibility. This behavior is reflected in thetotal energy of the system which is larger (less stable) at lowcounterion concentrations than for the correspondingneutral systems. A divalent cation, like Ca21, prefers toassociate with at least two charged-carboxyl groups.Owing to their diminished conformational flexibility, theionized copolymers are not readily able to accommodatethe short-range (more folded) interactions needed for effec-tive Ca21 binding to two carboxylates, and simultaneouslyminimize the counterioncounterion interactions. Thus,with increasing Ca21 concentration, the binding energiesbecome more positive (less stable).

Table 5 lists the averageRH-T(ak ,CI) for the entire collec-tion of 50 MDS as a function of Ca21 ion concentration. Thegraphical representation of the data in Table 5 is presentedin Fig. 5 for each copolymer chain-segment model consid-ered. Poly9 exhibits a significant conformational flexibility,especially in the range of Ca21 concentrations between 0.15and 0.5, where 20% folding occurs. With increasingcounterion concentration flexibility is lost, mainly due tocounterioncounterion repulsive interactions. Poly8 isclearly a more rigid copolymer than poly9. The ensembleaverage values of the headtail distances for poly8 modelslie largely in the range of 6080 A . This rigid chain beha-vior could be predicted from an analysis of the trajectoriesof the corresponding neutral models. Poly7 has an inter-mediate level of flexibility compared to poly8 and poly9.The values ofRH-T(ak ,CI) vary from 50 to 65 A for thecomplete range of Ca21 concentrations. Conformationalfolding is most extensive for values ofCI less than 0.6.Poly6 is the most flexible copolymer, and the average valuesof RH-T(ak ,CI) are in the range of 4050 A .

Flexibility of the copolymer models under study can besignificantly characterized in terms of intramolecular attrac-tive interactions and repulsions. As discussed before, poly8and poly9 exhibit their difference in flexibility due to thepresence of a low monomer percentage of the rigid cyclicimide structure, Im, in poly8. This small structural

difference between poly8 and poly9 is sufficient to establisha clear preference in calcium counterion capturing ability.However, both systems are far from the ideal Ca21 ionscapturing copolymer because the large number of carbox-ylate groups produce large intramolecular repulsions. Incontrast, poly6 and poly7 (that have the same percentageof Im as poly8) have less intrinsic rigidity owing to repul-sive carboxyl interactions because of their greater percen-tages of AM monomer. Even though increasing the amountof AM corresponds to a loss in the number of carboxyl sitesto capture Ca21 ions, this situation can be preferablebecause of the gain in conformational flexibility. Thecopolymer chain-segment model that best balances theconcentration of carboxyl groups and conformationalflexibility is poly7.

One general feature of these copolymercounterionsimulations is that after about 10 ps of MDS, most of theCa21 ions are bound to localized pairs of carboxylategroups. These negative-charge pairs are often not separatedalong the chain by more than two monomers. Only rarelyare counterions found binding to three (or even four)carboxylate groups. This situation is only found for poly9when the value ofCI is in the range of 0.150.50, and is alsoresponsible for the relatively high degree of folding foundfor poly9. However, this behavior cannot occur at highcalcium concentrations because of the repulsive interactionsbetween the counterions.

Fig. 6 schematically describes the process of calciumpositioning near COO2 groups, and illustrates the type ofpolymercounterion interactions commonly found in theMDS trajectories. It was possible to perform MDS studiesat high calcium concentrations in terms of the interactionsgiven in Fig. 6. The Ca21 ions were initially positioned nearthe COO2 groups at an average distance from one oxygen tocalcium, R(CaO), of 2.09 A and a OCaO bond angleof ca. 1008. Under these conditions, the Ca21 ion is symme-trically located with respect to the COO2 groups carbon ata bond distance, R(CaC), of ca. 1.955 A . This metho-dology of Ca21 ion positioning was found to be the best toefficiently reach high Ca21 ion concentrations (CI . 1.33),which are higher than those generated in our previous work[15]. The relative distribution of the Ca21 ions over thebackbone was also varied to make the results independentof the model chain-segment tacticity.

There exists a Ca21 counterion concentration limitbeyond which it is not possible to continue adding counter-ions to the copolymer model. This limit is established withinthe framework of Mannings counterion condensationtheory [21,22]. In accordance with this theory, a divalentcation, like Ca21, will bind to the charged-carboxyl groupsof a PAA analog model up to approximately 82% chargeneutralization at 298 K in an aqueous environment. For theMDS conditions of this study, it was possible to add up to65% more Ca21 ions (beyond the upper limit of condensa-tion theory) into the charged poly8 and poly9 copolymersystems because of the extraordinary rigidity of both


Table 5Time average values forRH-T(ak ,CI) determined during the last 10 ps of theMDS for the negatively charged models of poly6, poly7, poly8 and poly9

CINM RH-T(ak ,CI) (A)Poly6 Poly7 Poly8 Poly9

2 55^ 13 63.7^ 12.8 62.7 12.4 61.8 12.56 41.5^ 8.7 55.9^ 9.2 53.5^ 12.9 60.6 6.510 41.6^ 14.5 54.7 14.9 63.6 5.2 46.7^ 15.320 36.4^ 12.8 46.2 10.3 64.0 10.5 45.9 16.130(a)a 40.2^ 11.3 64.2 16.9 80.8 10.4 63^ 1540(b)a 58.8^ 16.2 65.8 9.3 77.0^ 11.650 76.9^ 8.7 80.6^ 9.256(c)a 70.2^ 9.1 77^ 14

a Beyond this site occupancy limit, it is not possible to continue addingCa21 counterions to: (a) the poly6 model; (b) the poly7 model; (c) the poly8and poly9 models.


Fig. 5. AverageRH-T dependence on Ca21 concentration for: (a) the poly6 model, (b) the poly7 model, (c) the poly8 model, and (d) the poly9 model.


Fig. 5. (continued)

chain-segment models. However, no extra Ca21 ion couldbe added once the condensation limit was reached. Allexcess cations left the vicinity of the polymercounter-ion complex preferring distances over 2030 A away fromthe copolymer chain-segment. For poly6 and poly7, theexcess Ca21 over that predicted by condensation theorywas 18% and 35%, respectively.

An aim of this study was to characterize the Ca21 coun-terion binding behavior from very low to very high counter-ion concentrations. Thus, the space-time behavior ofcounterions near the carboxylate groups was monitoredover the MDS. Table 6 contains data from this analysis.The average distance between a carboxylate carbon and aCa21 ion, kR(CCa)l, was determined during the last 10 psof the MDS. This analysis identified the existence of threedifferent classes of attractive side chain-counterion interac-tions taking place in the model copolymercounterionsystems:

Normal interactionsfound in all four of the modelcopolymer systems. These interactions are responsiblefor the net attraction between one Ca21 ion and twocarboxylate groups. The attractive term of the intermo-lecular potential charge energy is ca.2100 to2200 kcal/mol, and the average value ofkR(CCa)l is (2.5^ 0.1) Ausing a molecular dielectric of 3.5.

Strong interactionsfound only in the poly7 and poly9chain-segment models. These interactions involve oneCa21 ion and three carboxylate groups, and are predomi-nantly found in the poly7-counterion system. Poly9 onlyexhibits these strong interactions for values ofCIbetween 0.15 and 0.50. The attractive energy terms are

in the range of2 300 to 2 400 kcal/mol (1 3.5). Thevalue ofkR(CCa)l is (2.24^ 0.01) A.

Very strong interactionsthat can only be detected inthe poly7-counterion system. The attractive energy termis in the range of2 400 to 2 500 kcal/mol (1 3.5),and the correspondingkR(CCa)l is (2.14^ 0.03) A.

The identification of strong attractive copolymercounter-ion interactions for chain-segment models which can undergohigh degrees of folding clearly indicates that the ability ofthese PAA analogs to capture Ca21 ions is directly related tothe existence of preferred intrinsic geometric bindingpatterns. In the case of poly7, it was possible to determinea structure counterion-binding pattern responsible for stronginteractions in almost 40% of the randomly generated atacticsequences. This finding, in turn, led to the identification of aspecific 3D binding site which can capture a Ca21 ion. Thebinding site is realized after about 20 ps of MDS, startingfrom a completely extended model, and its schematic struc-ture is shown in Fig. 7. As can be seen in Fig. 7, the bindingsite is composed of eight monomer units, and has a verysimilar monomer composition as poly7: 63% AA, 25% AMand 12% Im. The counterion concentration is 0.8 for theMDS used to generate the binding site model shown in Fig. 7.

There are different interaction zones in Fig. 7 thatmust be explained. From left to right, the first two carbox-ylate groups are interacting with one Ca21 ion and theirrelative stereochemistry is not important. The next twomonomers are an AM-Im sequence with a specifictransstereo orientation. This sequence is followed by anothermonomer with a carboxylatesyn to the Im monomer. Thiscarboxylate plays a central binding role, and is shown in Fig.7. The sequence of the next three monomers is (trans)AA(syn)AM(trans)AA which is responsible for capturing thesecond Ca21 counterion.

Thirty picosecond MDS of this binding site sequence,located in the middle of an atactic 20-monomer chain-segment model, were carried out in a separate set of MDSstudies. The results are in complete agreement with thosepreviously found for the full poly7 system. The same attrac-tive potential energy and binding geometry were found in allMDS, indicating the intrinsic structure, stability and bindingcapacity of this unique binding site. Fig. 8 shows the initialand final states of a MDS trajectory of the monomersequence binding leading to the specific Ca21 binding sitegeometry.

As shown in Fig. 8, the final binding site geometry has theshape of a pocket, but the Ca21 ions are located on theoutside of this pocket. The structure also possesses ahigh degree of folding, mainly because of the presence ofthe cyclic imide monomer unit. This rigid moiety is respon-sible for allowing the side-chain groups of AM and acarboxylate (in the box) to interact in an electrostatic/H-bond like fashion (see Fig. 7). The boxed COO2 isalso involved in another H-bond interaction with the nextavailable AM group (see Fig. 7), to yield an inflexible


Fig. 6. Schematic representations of the dominant carboxyl-Ca21 complex-ing states observed in the MDS.

Table 6MDS ensemble average distanceskR(CCal and kR(OCa)l betweencalcium counterions and the center carbon, or oxygen atom of the nearestcarboxylate group as a function of the magnitude of the attractive energyterms. The ensemble averaging is based on the last 10 ps of the MDS

Energy range (kcal/mol) kR(CCa)l (A) kR(OCa)l (A)

2400/2500 2.14^ 0.03 1.46 0.042300/2400 2.24^ 0.01 1.75 0.022100/2300 2.5^ 0.1 1.55^ 0.08

pocket, highly stabilized by electrostatic and H-bond intra-chain interactions. This optimal geometry leaves the fourCOO2 groups nearly naked and without any externalrepulsive interactions to interfere with the process of coun-terion capturing. These types of interactions and the foldedchain geometry is reminiscent of charged residue side chainconformation observed in some rigidb -turn peptide confor-mations of proteins [23,24].

Considering the remarkable capacity of this binding sitesequence to capture the Ca21 ions, one could think of it as asuper monomer unit which is able to form a super Ca21

ion capturing polymer, with a final monomer compositionquite similar to that of poly7.

4. Discussion

PoissonBoltzmann treatment of counterion binding inpolyelectrolyte systems predicts that the condensed counter-ions remain closer to the polyion than the free ions [25]. Thespace-time MDS study reported here is in agreement withthese predictions. The MDS indicate that, on the average,the bound counterions are never more than 5 A away fromthe polyion chain. In contrast, the free ions are much fartheraway, usually more than 25 A .

By definition, a hyperbolic dependency ofET(CI,ak)/CINM on CI is expected for the charged form of the copoly-mer models. Thus, the shape of the total energy vs. Ca21

concentration plots shown in Fig. 5 are not unexpected.Interestingly, the maximum rate of decrease inET as a func-tion of increasingCI occurs in the counterion concentrationregion where the most significant changes in chain dimen-sions take place. This behavior can be understood in termsof a large flexibility of the polymercounterion system atCIvalues where intramolecular COO2/COO2 repulsion arereduced by the presence of bound Ca21 ions, and repulsionsdue to the bound Ca21 ions interacting with one another arenot predominant factors to stiffen the copolymer chain.

TheEC(CI,ak )/CINM, which by definition should becomeless stable with increasingCI, appears to behave as expectedfor the chain-segment models poly6, poly8 and poly9.However, poly7 shows counterion binding stabilizationprevailing over intramolecular repulsions forCI values up

to 0.70, i.e. near the theoretical limit for polymercounter-ion condensation [21]. The reason why the overall bindingenergy decreases with increasingCI up to 0.70 for poly7 isdue to the cooperative interactions between Ca21 ions andmore than two carboxylate groups, as well as the highlyfavorable binding of Ca21 ions to the site specific sequences.These latter extraordinary strong polymercounterion inter-actions are dominant in poly7.

The conformational flexibility of each copolymer chain-segment model, measured in terms ofRH-T and its standarddeviation over the MDS, also plays a relevant role in theintrinsic capacity of a copolymer to capture counterions.Plots ofRH-T vs. Ca

21 concentration in Fig. 9 indicate thatthe relative order of flexibility at different values ofCI arepredicted to be: {CI , 0.7: poly7 . poly9 poly6 .poly8}. { CI . 0.7: poly7 . poly6 . poly9 poly8}.


Fig. 7. Schematic structure of the specific Ca21 binding site found for the poly7 models.

Fig. 8. Initial and final states of the MDS trajectory of the specific bindingsite monomer sequence schematically shown in Fig. 7.

This relative ordering of chain flexibility reflects the ther-modynamic compromise between the number of internalbackbone repulsions which increases with both the numberof COO2 and the number of AM monomers, but decreaseswith the number of available sites to bind the Ca21 ions.

Figs. 9 and 10 summarize the counterion and spatial beha-vior of the four-copolymer PAA chain-segment modelsinvestigated. Fig. 9 illustrates the dependence of the timeaverage distance,RH-T, on both bound counterion calciumconcentration and polymer composition. Instead ofCI, themagnitudeCINM is used, i.e. the number of occupied coun-terion-binding sites. Fig. 10 is the same type of plot as Fig.9, but in this caseEC is plotted rather thanRH-T. Fig. 9 bestillustrates the effect of the cyclic amide moiety on the flex-ibility of poly8 compared to the other three copolymermodels.

From Figs. 9 and 10, it is clear that the best PAA copo-lymer analog to capture Ca21 counterions is poly7.At highcounterion site occupancy only poly7 provides a net stabi-lizing polymercounterion interaction comparable to thatof poly9 at very low counterion site occupancy. This usefulbinding behavior of poly7 is due to a balance between aflexible backbone and a strong counterion binding energy.

The specific Ca21 binding site sequence discovered forpoly7 presents an extra, and unique, source of counterionbinding stability that contributes to the strong stabilizationof the poly7- Ca21 counterion system. This specific Ca21

binding site sequence represents a highly function-specificstructure generated as a result of a largely random monomersequence synthesis from an initial fixed monomer composi-tion. The identification of sequence functional specificitydoes not appear to have been described for other syntheticpolymer, or polymercounterion models. However, thefinding of structure-function specificity in this studysuggests the opportunity to discover distinctive molecularstructures and properties using molecular modeling that, atthe macroscopic level, are not discernable. Finally, thisspecific binding site sequence could be used as a supermonomer to build up super copolymers possessinghigh efficiency in the process of removing calcium fromsolutions.

It is interesting to compare the combined analog synthesisand modeling studies to natural evolution of biologicalmolecules, and in particular proteins. The synthesis andtesting of calcium counterion binding of the four PAAanalogs reported here indicates that the analogs having the


Fig. 9. Dependence ofRH-T on both bound counterion concentration and polymer composition for the poly6, poly7, poly8 and poly9 models.

poly7 composition are unusually good Ca21 binderswithoutknowing why poly7 binds Ca21 better than the other analogsmade and tested. Nature does identically the same synthesisand testing optimization procedure. However, naturelearns the structural source of the better property or func-tion by having the luxury of making and comparingvast numbers of analogs over long periods of times notavailable to researchers. Nonetheless, the modeling studyreported in this paper suggests that molecular modelingmay provide a shortcut to learn the structural sourcesof the unusually good properties and/or functions of semi-randomly synthesized copolymers which are onlyconstrained by monomer chemical structure and polymercomposition. Molecular modeling takes the place oflongtimesandlarge numbers of analogsinherent to evolutionaryoptimization.

The counterion binding sites in proteins are, in overallstructure, the reverse of the specific Ca21 binding site ofpoly7 [26]. In proteins, the binding site (b-turn) has thecarboxyl groups, and other ligand groups to the counterion,and are able to form a pocket around the counterionwhen it is bound. This would include calcium bindingpeptides and proteins of which calcitonin, essential formuscle contraction and membrane function, is perhaps,

the prime example [26]. Again, the poly7 binding site hascarboxyl groups on the outside of such a pocket, not onthe inside and around the counterion. A plausible reasonfor this structural difference between the specific bindinggeometries is due to the protein wanting to bind one specificcounterion. Poly7 is evaluated in terms of the maximumnumber of calcium counterions.

In some ways, this work parallels many of the studies ofconformational transition behavior of ionizable biopoly-mers as a function of counterion concentration done in the60s and 70s [27,28]. Interestingly, none of these earlystudies lead to the suggestion of possible stable local bind-ing geometries in the synthetic biopolymers made andtested. The lack of modern computational chemistrycapabilities may have prevented the exploration and identi-fication of local stable binding sites similar to that discov-ered in this study.

Acknowledgements

We appreciate the financial support of the Nalco Chemi-cal Company. Drs. D. Johnson, P. Young and V. Narutis, allof Nalco, made many helpful suggestions and comments to


Fig. 10. Binding energy dependence,Ebind, on bound calcium counterion concentration and polymer composition for the poly6, poly7, poly8 and poly9 models.

us during the course of this study. Resources of both theNalco Chemical Company and of the Laboratory of Mole-cular Modeling and Design at UIC were used to perform thiswork.

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