Interaction of Human Serum Albumin with shortPolyelectrolytes: A study by Calorimetry and

Computer Simulation

S. Yu,†,‡ X. Xu,¶ C. Yigit,¶,‡ M. van der Giet,§ W. Zidek,§ J. Jankowski,‖

J. Dzubiella,⊥,‡ and M. Ballauff∗,⊥,‡

Soft Matter and Functional Materials, Helmholtz-Zentrum Berlin, Hahn-Meitner Platz 1, 14109Berlin, Germany, and Helmholtz Virtual Institute "Multifunctional Biomaterials for Medicine",

Kantstr. 55, 14513 Teltow, Germany , Institut für Physik, Humboldt-Universität zu Berlin,Newtonstr. 15, 12489 Berlin, Germany, Soft Matter and Functional Materials,

Helmholtz-Zentrum Berlin, Hahn-Meitner Platz 1, 14109 Berlin, Germany, Medizinische Klinikfür Nephrologie, Charité , Hindenburgdamm 30, Charité -Campus Benjamin Franklin, 12203

Berlin, Institute for Molecular Cardiovascular Research IMCAR, RWTH Aachen, Pauvelsstr. 30,52074 Aachen, and Soft Matter and Functional Materials, Helmholtz-Zentrum Berlin,

Hahn-Meitner Platz 1, 14109 Berlin, Germany, and Helmholtz Virtual Institute "MultifunctionalBiomaterials for Medicine", Kantstr. 55, 14513 Teltow, Germany

E-mail: matthias.ballauff@helmholtz-berlin.de

∗To whom correspondence should be addressed†Soft Matter and Functional Materials, Helmholtz-

Zentrum Berlin, Hahn-Meitner Platz 1, 14109 Berlin, Ger-many, and Helmholtz Virtual Institute "Multifunctional Bio-materials for Medicine", Kantstr. 55, 14513 Teltow, Ger-many

‡Institut für Physik, Humboldt-Universität zu Berlin,Newtonstr. 15, 12489 Berlin, Germany

¶Soft Matter and Functional Materials, Helmholtz-Zentrum Berlin, Hahn-Meitner Platz 1, 14109 Berlin, Ger-many

§Charité - Universitätsmedizin Berlin‖RWTH Aachen⊥Soft Matter and Functional Materials, Helmholtz-

Zentrum Berlin, Hahn-Meitner Platz 1, 14109 Berlin, Ger-many, and Helmholtz Virtual Institute "Multifunctional Bio-materials for Medicine", Kantstr. 55, 14513 Teltow, Ger-many

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Abstract

We present a comprehensive study of the interaction of human serum albumin (HSA) withpoly(acrylic acid) (PAA; number average degree of polymerization: 25) in aqueous solution. Theinteraction of HSA with PAA is studied in dilute solution as the function of the concentration of addedsalt (20 - 100 mM) and temperature (25 - 37◦C). Isothermal titration calorimetry (ITC) is used toanalyze the interaction and to determine the binding constant and related thermodynamic data. It isfound that only one PAA chain is bound per HSA molecule. The free energy of binding ∆Gb increaseswith temperature significantly. ∆Gb decreases with increasing salt concentration and is dominated byentropic contributions due to the release of bound counterions. Coarse-grained Langevin computersimulations treating the counterions in an explicit manner are used study the process of binding indetail. These simulations demonstrate that the PAA chains are bound in the Sudlow II site of the HSA.Moreover, ∆Gb is calculated from the simulations and found to be in very good agreement with themeasured data. The simulations demonstrate clearly that the driving force of binding is the release ofcounterions in full agreement with the ITC-data.

IntroductionHuman Serum Albumin (HSA) is an importanttransport protein that interacts with substrates ase.g. fatty acids1,2 and pharmaceuticals in a spe-cific manner.3 Also, transport by HSA plays animportant role for renal clearance and the interac-tion of HSA with typical uremic toxins4 as e.g.phenylacetic acid, indoxyl sulfate, and p-cresylsulfate needs to be understood in detail.5 Ure-mic toxins play an essential role in the excessivecardiovascular mortality and all cause mortalityin patients with end stage renal disease. Elimi-nation of these substances is essential to reducethe high cardiovascular disease risk.6,7 The ob-vious biological importance of this transport hasled to a great number of studies of the interac-tion of HSA with various substrates, most no-tably by crystallography,8,9 electron paramagneticresonance spectroscopy,10 and isothermal titrationcalorimetry (ITC).11,12 Thus, it is well establishedthat the interaction of various substrates with HSAtakes place mainly on the Sudlow I and the Sud-low II site.13 ITC has been used to elucidate thethermodynamics of this interaction and by this thenumber of substrates adsorbed onto the surface ofthe protein.11,14–17

Charge-charge interaction plays an essential rolein the process of adsorption18–20 and a numberof ITC-studies explore the dependence of the ad-sorption constant on ionic strength.21–24 Recently,Jankowski and coworkers25,26 have demonstratedthat raising the ionic strength in the infusion fluid

leads to an improved clearance of protein-boundtoxins (PBT). Thus, raising the concentration ofNaCl to 600 mM led to a significantly better re-moval of of uremic toxins as e.g. phenylaceticacid. This result points clearly to the central im-portance of Coulombic interactions for the bind-ing strength of such toxins to HSA and to proteinsin general. Charged toxins as phenylacetic acidare difficult to remove by conventional dialysis andexploring their interaction is of central importancefor devising improved techniques for dialysis.25

Here we analyze the role of the interaction ofcharged substrates with HSA as the function ofionic strength and temperature. As a substrate wechose a short polyelectrolyte, namely poly(acrylicacid) (PAA) with 25 repeating units only. Thissubstrate allows us to explore the Coulombic in-teraction of HSA with charged molecules in gen-eral. In addition to this, synergetic effects of ad-jacent carboxyl groups onto the binding constantcan be elucidated. At the same time, PAA canbe regarded as a model of charged toxins withmolecular weight above 500 g/Mol.5 ITC is usedto obtain the binding constant and the number ofbound PAA-molecules per protein and the temper-ature is varied between 25◦C and 37◦C. A firststudy of the interaction of polyelectrolytes withproteins by ITC has been presented by Schaaf etal. who demonstrated the general suitability of thismethod for the study of protein-polyelectrolyte in-teraction.27

The interaction of long polyelectrolytes withproteins in aqueous solution has been the subject

2

of longstanding research that has led to an enor-mous literature.18,28,29 Proteins can form com-plex coacervates with polyelectrolyte of oppositecharge in aqueous solution and the strength of in-teraction is mediated by the ionic strength in thesystem.30 If the ionic strength of the system is lowenough, interaction may take place even on the“wrong side“ of the isoelectric point, that is, pro-teins associate with polyelectrolytes of like charge.In many cases the formation of complexes betweenthe protein and the polyelectrolyte is followed byprecipitation and phase separation that may alsolead to non-equilibrium states.23,28 Here we use avery short polyelectrolyte and low concentrationsto avoid multiple interactions and phase separa-tion. The results from the present experiments,however, may be directly utilized for a better un-derstanding of complex coacervates.

Evidently, protein crystallography cannot beused to elucidate the structure of the complex be-tween HSA and PAA. First of all, even in thebound state the non-bound segments of the poly-electrolyte will explore their conformational free-dom in solution and the entropic contribution de-riving therefrom will be an important part of theresulting change of free energy. Moreover, crystalsof HSA will certainly not accommodate substratesof the size of a polyelectrolyte having 25 units. Inorder to make progress on a detailed structural in-vestigation, we employ coarse-grained LangevinDynamics (LD) computer simulations with an im-plicit solvent whereas the co- and counterions aretreated in an explicit manner.31–33 The protein istreated within the Cα - Go model, that is, eachamino acid of HSA is modelled by a single beadbearing a charge or not. The polyelectrolyte PAAis also treated as a coarse-grained charged poly-mer. The combination of these models allows usto elucidate the details of the complex of PAA andHSA in solution with full structural resolution. Inaddition to this, LD-simulations allow us to calcu-late the free enthalpy of binding ∆Gb and to com-pare these data with measured values. Thus, thecombination of ITC with computer simulation canbe used to elucidate structural and thermodynamicdetails that are available by no other method.

ExperimentalMaterials. Polyacrylic acid (PAA) withMW =1800 g/mol was purchased from Sigma-Aldrich (Schnelldorf, Germany) and used afterseveral weeks of dialysis to match pH withoutchanging ionic strength in the system. HumanSerum Albumin (HSA) was also purchased fromSigma-Aldrich (lyophilized powder, Fatty acidfree, Globulin free, 99%) with molecular weightcalculated MW =66400 g/mol and its purity verifiedby sds-gelelectrophoresis. The buffer morpholin-N-oxide (MOPS) was purchased from Sigma-Aldrich and used as received.

Isothermal Titration CalorimetryITC experiments were performed using a VP-ITC instrument (Microcal, Northampton, MA).All samples were prepared in a pH 7.2 buffer so-lution using 10 mM MOPS and 10 mM, 40 mM,60 mM and 90 mM NaCl to adjust ionic strength.All samples were dialyzed against buffer solu-tion with according pH and degassed prior toexperiment. For dialysis, the dialysis-systemFloat-a-Lyzer by Spectrum Labs with molecularweight cut-off (MWCO) 500-1000 Da for PAAand MWCO 20 kDa for HSA were used respec-tively. The samples were thermostatted and the in-strument stabilized for 1 h to ensure thermal equi-librium and stability of the system. A total of298 µL PAA solution was titrated with 75 succes-sive 4 µL injections, stirring at 307 rpm and a timeinterval of 300-350 s between each injection intothe cell containing 1.4 mL protein solution. Theconcentration of PAA and HSA were 1.3 g/L and0.9 g/L respectively. We choose these low concen-trations in order to study the interaction of singlePAA-chains with only one HSA-molecule. More-over, possible complications by coacervate forma-tion are circumvented in this way. The experi-ments were performed at 25, 27.5, 30, 33, 37 oCand ionic strengths 20 mM, 50 mM, 70 mM and100 mM.

As a first step of the ITC data analysis, the inte-gration of the measured heat Q over time is carriedout to obtain the incremental heat ∆Q as a functionof the molar ratio x between polyelectrolyte andprotein. For each experiment, the heat of dilution

3

of PAA were measured separately by titrating theaccording polyelectrolyte into blank buffer solu-tion and subtracted from adsorption heats. Aftercorrection, the resulting binding isotherm are fittedusing a supplied module for Origin 7.0 (Microcal).

Data analysis.

For the analysis, we chose the single set of in-dependent binding sites (SSIS) model to fit alldata.34 This model is based on the Langmuir equa-tion, which assumes an equilibrium between theempty adsorption sites, the no. of proteins in solu-tion and the occupied adsorption sites. This leadsto the binding constant Kb:

Kb =Θ

(1−Θ)cPAA(1)

where Θ denotes the fraction of sites occupied bythe polyelectrolyte and cPAA the concentration offree polyelectrolyte. Since only the total concen-tration of PAA ctot

PAA in the solution is known, cPAAis connected to the ctot

PAA as follows:

ctotPAA = cPAA +NΘcprot (2)

where N is the number of free binding sites andcprot the total protein concentration in solution.Following these equations, the binding numberN, binding affinity Kb and the overall enthalpychange measured ∆HITC can be obtained by fittingthe isotherm. In the following, we will show thatonly one PAA is adsorbed onto HSA in all cases.Therefore the parameter N was fixed to unity forall subsequent fits. In this case the interaction ofPAA and HSA can be formulated as a conventionalchemical equilibrium:

Kb ≈cPAA−HSA

cPAA(ctotHSA− cPAA−HSA

) (3)

where ctotHSA denotes the total protein concentra-

tion in the solution and cPAA−HSA the concentrationof PAA-HSA complex. Furthermore, the bindingfree energy ∆Gb can be derived by

∆Gb =−RT · lnKb (4)

Furthermore using the following two equations,the entropy ∆Sb can be either calculated for onetemperature or extracted from its temperature de-pendence:

∆Gb = ∆HITC−T ∆S (5)

∂∆Gb

∂T=−∆Sb (6)

Theoretical MethodsComputer simulation model and parameters

In our simulations we employ an implicit-watercoarse-grained (CG) model, where each of theamino acids, PAA monomers, and salt ions is ex-plicitly represented by a single interaction bead.Hence, the water is modeled by a dielectric back-ground continuum while the salt is explicitly re-solved. The dynamics of each of the beads in oursimulations is governed by Langevin’s equation ofmotion35

mid2rrri

dt2 =−miξidrrri

dt+∇∇∇iU +RRRi(t) (7)

where mi and ξi are the mass and friction constantof the ith bead, respectively. U is the system po-tential energy and includes harmonic angular andbonded interactions between neighbouring beadsin HSA and PAA, dihedral potential in the case ofthe HSA, and interatomic Lennard-Jones (LJ) be-tween all non-neighbouring beads, including ions.Coulomb interactions govern the electrostatic pairpotential between all charged beads. The randomforce RRRi(t) is a Gaussian noise process and satis-fies the fluctuation-dissipation theorem

〈RRRi(t) ·RRR j(t ′)〉= 2miξikBT δ (t− t ′)δi j. (8)

The simulations are performed using the GRO-MACS 4.5.4 software package.36 A leap-frog al-gorithm with a time step of 2 fs is used to inte-grate the equations of motion. A cubic box withside lengths of L = 30 nm is employed and period-ically replicated to generate a quasi-infinite systemin the canonical ensemble. The Langevin frictionis ξi = 1.0 ps−1 that dissipates the energy at con-stant temperature T . Center of mass translation ofthe system is removed every 10 steps. The cutoff

4

radius is set to 3.0 nm to calculate the real-spaceinteractions while Particle-Mesh-Ewald37 (PME)is implemented to account for long-range elec-trostatics. The PME method is computed in thereciprocal space with a FFT grid of ∼ 0.12 nmspacing and a cubic interpolation of fourth-order.The solvent is modelled as a continuous mediumwith a static dielectric constant of εr = 73.4 and78.2 for temperatures T = 25◦C and 37◦C, respec-tively. All beads have mass mi = 1 amu, diameterσLJ = 0.4 nm, energy well εLJ = 0.1 kBT and in-teger charges q = 0, +1 or -1 e. The mass was cho-sen artificially low to enhance orientational fluctu-ations and sampling. Clearly, equilibrium proper-ties, as investigated in this work, are not affectedby any reasonable mass choices as long as the sim-ulations are ergodic.

The protein sequence for the HSA is providedby PDB databank: ID=1N5U.38 Every amino acidis described by a single bead positioned at its Cα

atom. The native structure of the protein is main-tained by a Go-model like force field as providedfrom the SMOG webtool for biomolecular simu-lations.39,40 All beads corresponding to basic andacidic amino acids are assigned a charge of +1eand -1e, according to their titration state at physi-ological pH = 7.4, that is, ARG and LYS residuesare assigned a charge +1e, while ASP and GLU are-1e, and HIS is neutral. With that the net charge ofthe simulated HSA is -14e.

A single flexible PAA polyelectrolyte is mod-eled in a coarse-grained fashion as a sequence ofNmon freely jointed beads. Each bead representsa monomer with a radius σLJ and carries an elec-tric charge of −1e. The PAA monomers are con-nected by a harmonic bond potential with an equi-librium bond length bmon = 0.4 nm and a forceconstant kmon = 4100 kJ mol−1 nm−2. The flex-ibility of the PAA chain is defined via a harmonicangle potential in which the angle between a tripletof monomer is φ = 120◦ and the force constant iskφ = 418.4 kJ mol−1 rad−2. As in the experimentswe consider short PAA chains with Nmon = 25monomers. The simulation box contains one HSA,while the amount of PAA and ions are character-ized by the molar ratio x = cPAA/cHSA, rangingfrom 1 to 10, and salt concentration csalt , rangingfrom 20 to 100 mM, respectively.

Binding and free energy calculations

The stoichiometry, in our case the average num-ber of bound PAA chains on one HSA, can be de-termined through a calculation of the normalizeddensity distribution function g(r) = c(r)/ctot

PAA,where r is the distance between the centers-of-mass (COM) coordinates of the HSA and PAA andctot

PAA is the PAA bulk concentration. Integrationof the g(r) further leads to the PAA coordinationnumber

n(r) = 4πctotPAA

∫ r

0g(r′)r′2dr′. (9)

which describes how many PAA chains are boundon average at a distance r. For each molar ratiowe simulated 120 ns in order to calculate the equi-librium coordination (binding) numbers of PAA toHSA. To quantify the number of bound and re-leased ions upon complexation, we count the av-erage number of ions Ni, i = ±1, that are bound(’condensed’) on the PAA chain or on the positiveprotein patches, respectively, and make a compari-son before and after PAA/HSA association. An ionis defined as ’condensed’ if it is located in the firstbinding layer, that is closer than a cut-off distancers = 0.5 nm from the charged bead, while double-counting in overlapping volumes is avoided. Theaverage is over long (ca. 30 ns) trajectories in thefully separated and stable bound states. To calcu-late the potential mean force (PMF) between theHSA and the PAA we employed steered LangevinDynamics simulations using the pull code as pro-vided by GROMACS.36 Here, the center of massof the PAA is restrained in space by an externaltime-dependent force. This force is applied asa constraint, i.e. harmonic potential, and movedwith a constant pulling velocity vp to steer the par-ticle in the prescribed direction.41 After severaltest runs, the pulling rate vp = 0.1 nm/ns was cho-sen and a harmonic force constant K = 2500 kJmol−1 nm−2. The simulations were performed for∼100 ns. Given the pulling speed above, this sim-ulation time is required to bring the two macro-molecules from a separated state (r ∼ 11 nm) to afinal state (r ∼ 1 nm). The standard deviation wascalculated by standard block averages to specifythe statistical error. The friction force F =−mξivpwas subtracted from the constraint force and the

5

result averaged within a specific interval of dis-crete spacing ∆r to obtain the mean force of theinteraction potential. According to the simulationsetup, the mean force was integrated backwards toget the potential of mean force (PMF). Becausethe CPPM were radially constraint in 3D space,the PMF has to be corrected for translational en-tropy42 by

G(r) = GI(r)−2kBTln(r), (10)

where GI(r) is the integrated mean force. Thebinding affinity of the PAA can then be defined as

the free energy value at the global minimum of thePMF in the stable complex as

∆Gsim = G(rmin)−G(∞), (11)

where the reference G(∞) is set to zero. How-ever, before making a comparison with the exper-iment, we had to consider that ∆Gexp

b provided bythe experiment is defined as a standard free en-ergy, which refers to the standard binding volumeV0 = 1/C0 of one liter per mol.43 Hence, the bind-ing constant Kb generated from experiment is for-

0 2 4 6 8 10

-2

0

2

4

0 100 200 300 400

0.0

0.2

0.4

0.6

Time (min)

µca

l/se

c

I=20 mM T=37°C

PAA dilution

HSA+PAA

n(PAA)/n(HSA)

kca

l/m

ole

of

PA

A

a)

0 2 4 6 8 10

-2.0

-1.6

-1.2

-0.8

-0.4

0 100 200 300 400

-0.20

-0.15

-0.10

-0.05

0.00

Time (min)µ

cal/sec

b)

I=50 mM T=37°C

PAA dilution

HSA+PAA

n(PAA)/n(HSA)

kcal/m

ole

of P

AA

7

6

5

4

3

2

1

0

Q in

kca

l/mol

of P

AA

1086420n(PAA)/n(HSA)

T=37°C I=20mM I=50mM SSIS Model Fit

c)

Figure 1: ITC data of adsorption of PAA upon HSA and the corresponding heats of dilution of PAA at pH=7.2, T=37◦Cand a) I=20 mM, b) I=50 mM. c) Binding isotherm corrected for the heat of dilution at 37◦C and I=20 mM & 50 mM.

Figure 2: Determination of the parameter N, i.e., the number of PAA molecules adsorbed on on HSA molecule isshown for one temperature 37◦C at a) I=20 mM and b) 50 mM. Each line shows a fit with different values of fixed Nmarked by different colors.

6

mulated as Kb = e−β∆GsimV0. In our simulations

we average the accessible volume Vb of the COMof the PAA in the bound state.

As a result, the standard binding free energyfrom the simulation can be obtained as43

∆Gsimb = ∆Gcorr +∆Gsim, (12)

with a term ∆Gcorr =−kBT ln(C0Vb) is the entropycorrection arising from the accessible volume ofthe COM of the PAA in the bound state.

Results and DiscussionWe performed a systematic series of ITC exper-iments comprising four ionic strengths and fivedifferent temperatures ranging from room tem-perature (25◦C) to the physiological temperature(37◦C). The experiments were performed at pH7.2 in buffer solution. This pH is well above theisoelectric point of the protein HSA used for thisexperiment leading to a net effective charge of -14.PAA is a weak acid with a pKa of 4.5 and hencea net charge of -25 at pH 7.2. Thus, we study theadsorption on the "wrong side" of the isoelectricpoint where both the protein as well as the poly-electrolyte is charged negatively.

ITC is certainly the method of choice for the de-termination of the adsorption constant of a givensubstrate to HSA.15,21,44 However, the concentra-tions of the protein and PAA are small and theevolved heat will be concomitantly small. Hence,all effects leading to spurious heat signals must beconsidered in detail and carefully excluded. Themain problem is the adjustment of the same pHand ionic strength in both the solution of the pro-tein and of the polyelectrolyte. This is done byextensive dialysis which turned out to be decisivefor obtaining meaningful ITC-data. Since the con-centrations of both PAA and HSA are low, all spu-rious effects leading to a heat signal must be con-sidered. Since PAA-solutions are added in smallportions to the solution of HSA, the heat of dilu-tion of PAA must be determined carefully and sub-tracted from the raw signal. Fig. 1 and Fig. S1 ofthe SI displays the raw ITC-signals of PAA ontoHSA (black curves and points) as well as the heatof dilution of PAA (green points). The signal is

weakly endothermic at I=20 mM but exothermicat I=50 mM (see Fig. 1). Dilutions are in all casesexothermic and the effect becomes stronger withincreasing salt content as expected (blue curvesand points). For higher ionic strength, the heat ofdilution has a dominant effect on the overall signaland determines the sign of the signal at I>20 mM.For data analysis, the heats of dilution are sub-tracted from the heats of adsorption prior to fitting.Here, special attention must be paid to this step, asfor some cases there remains a constant residue af-ter subtraction of the heat of dilution. Even thoughthis offset signal is very small and usually lessthan 0.1 kcal/mol, it cannot be neglected due to thesmall overall heat. We assign this offset to a slightmismatch of the pH or salt titrant and the solutionin the cell. In order to take this effect into account,a flat background was fitted to all isotherms afterthe first step of subtraction and used to correct thedata in the second step.

The panel on the right-hand side of Fig. 1 dis-plays a set of typical results thus obtained. Evi-dently, the heat of adsorption is positive and wefind this for all conditions under considerationhere. Hence, the driving force for the process ofadsorption must be entropic. This point will bediscussed in more detail below and is well borneout from the simulations, too.

In order to obtain the number N of PAA-molecules bound to one HSA-molecule, the datawere first fitted using the SSIS model as describedin Section 2.1.1. Fig. 2 shows a comparison of theparameter N for the two data sets as in Fig. 1. Thecolored curves showing different fixed values of Nreveal that the data clearly justify N = 1 as the bestchoice for fitting. This observation is true for anyother sets of data. Deviations from N = 1 are notsignificant and we can safely assume N = 1 in allsubsequent analysis (see eq. ?? in Section 2.1.1).

Strength of interaction as the functionof temperatureFig. 3 presents two series of temperature depen-dency studies for the ionic strengths I=20 mM and50 mM. For better clarity, only 3 temperaturesare displayed in these graphs. The data for twomore temperatures are displayed in Figure S1 ofthe Supporting Information. The data taken at both

7

1086420n(PAA)/n(HSA)

1.8

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.0

Q in

kca

l/mol

of P

AA

b)I=50mM

25°C 30°C 37°C

3.34x10-3

3.30x10-3

3.26x10-3

3.22x10-3

1/T in 1/K

104

105

Bin

ding

con

stan

t Kb

in m

ol-1

Figure 3: Effect of temperature. The integrated heats Q for adsorption of PAA on HSA at temperatures between 25◦Cand 37◦C for a) I=20 mM and b) I=50 mM and the according fits are displayed. For better clarity, only 3 temperaturesare displayed. c) Van’t Hoff analysis of the dependence of the adsorption constant on temperature. Data points arederived from the fits of the ITC-data shown in a) and b). The crosses correspond to I=20 mM and the empty squaresto I=50 mM.

ionic strength reveal a significant increase of en-thalpy with increasing temperature from 25◦C to37◦C. This effect is more pronounced for I=20 mMthan at I=50 mM. Additionally, the overall en-thalpy of adsorption becomes weaker with increas-ing salt content, which points directly to the im-portance of electrostatic interaction on the bind-ing of PAA onto HSA. All data are very well de-scribed by the model assuming N = 1. Data takenat higher salinity are more noisy but the raise ofthe signal with temperature is clearly discernible.Since there is no plateau in the ITC signal, the pa-rameter ∆HITC might be overestimated by the fits.

The results of these fits are listed in Table 1 with∆HITC and Kb as fitting parameters, N being fixedto unity (see above). The free energy of binding∆Gb was calculated from the fitting parameter Kbusing equation ??.

The temperature dependence of the binding cannow be analyzed according to van’t Hoff’s law:(

∂ lnKb

∂T−1

)p=−∆Hb

R(13)

Fig. 3 c) shows the resulting van’t Hoff plot. Alinear correlation between logarithm of the bind-ing constant Kb and the inverse temperature is seenwithin the limits of errors. The binding enthalpy∆Hb can be obtained from the slope of the lin-ear fit and ∆Sb from the intercept. The resultingdata are gathered in Table 1. In general, the values

of ∆HITC are larger than the data resulting fromthe van’t Hoff analysis. Similar finding have beenmade in a recent study of the interaction of pro-teins with charged microgels.45 Reasons may besought in additional processes as e.g. the hydra-tion of freed counterions that are not directly cou-pled to the process of binding (see below). Also,the heat of adsorption taken directly from the ITCdata might be slightly overestimated (see above).

Dependence on ionic strength.To study the dependence of the binding processon ionic strength, we carried out two more exper-iments at 37◦C and I=70 mM and 100 mM (seeFig. 4, raw data are shown in Figure S2). With in-creasing ionic strength, the measured enthalpy ap-proaches zero and the ITC method reaches its in-strumental limits. As described above, we fix theparameter N for both salt concentrations to unity.Table 1 gathers all data obtained from these exper-iments.

The data exhibit a very consistent decrease ofbinding constant Kb with increasing salt concen-tration (see Tab. 1). This observation combinedwith the fact that only about one PAA molecule isadsorbed on the HSA leads to the conclusion thatthe driving force of the interaction is an attractiveelectrostatic potential between the negative PAAwith patches of positive charge on the surface ofHSA molecule. These patches are known to actas multivalent counterions for the polyelectrolyte.

8

Table 1: Overview of thermodynamic parameters for all fitted isotherms for the temperature series between 25◦C-37◦C and ionic strengths between I = 20 mM - 100 mM. As discussed in Sec. 3, all data were fitted with fixed N = 1.∆Gexp

b , ∆Sb and ∆Hb were calculated according to eq. ??,?? and ?? respectively. Entropys for 70 mM and 100 mMwere calculated using eq. ?? at 37◦C.

Ionic Strength (mM) T (◦C) ∆HITC Kb ·104 ∆Gexpb ∆Sb ∆Hb

(kJ/mol) (mol−1) (kJ/mol) (kJ/mol/K) (kJ/mol)

25 16.4±0.3 7.7±0.5 -27.9±1.327.5 32.8±0.6 5.8±0.3 -27.4±1.4

20 30 34.0±0.5 6.9±0.3 -28.1±1.1 0.17±0.01 15±433 45.6±0.9 8.1±0.5 -28.8±1.637 53.4±1.0 8.3±0.5 -29.2±1.5

25 13.6±1.1 1.3±0.2 -23.4±0.527.5 14.4±0.9 1.6±0.2 -24.2±0.3

50 30 24.8±0.7 1.7±0.1 -24.6±0.1 0.27±0.02 44±833 27.6±0.9 1.8±0.2 -24.9±0.237 26.4±0.6 2.6±0.1 -26.2±0.1

70 37 21.9±0.7 1.0±0.1 -23.6±0.5 0.12 (37◦C)

100 37 35.5±11.6 0.3±0.1 -20.7±1.2 0.10 (37◦C)

Binding of such a polyelectrolyte to such a patchthus leads to a release of its counterions.45–47 This“counterion release force“ was considered manyyears ago by Record and Lohman who predicted alinear correlation between the logarithms of bind-ing constant and salt concentration48:

dlnKb

dlncsalt=−∆nion (14)

where Kb is the binding constant, csalt the salt con-centration and nion the number of counterion re-lease upon adsorption. This behavior is observedfor the present data as well if the ionic strengths isabove 20 mM (see Fig. 5). Application of eq. ??to the data in Fig. 5 yields ∆nion ≈ 2.9± 0.5, thatis, approximately 3 ions are released upon bind-ing of one PAA-molecule to a HSA molecule. Thedeviation from linearity for low ionic strength hasbeen observed as well by Dubin et al. for the in-teraction between Bovine Serum Albumin and thepolyanion Heparin at pH 6.8.22 Here, electrostaticinteractions become long-ranged and the relativecontributions of the counterion release mechanism

significantly decrease.Extrapolation of the linear fit reveals that inter-

action still persists at physiological ionic strengthsand temperature. At I=150 mM and 37◦C, wederive from our plot a finite binding free en-ergy of around -17 kJ/mol and it only decays tosmall values at around 750 mM. This concen-tration has been found to be necessary in dialy-sis to remove protein-bound uremic retention so-lutes.25 Evidently, there is still some binding un-der physiological conditions and much higher saltconcentrations are needed to remove the toxinsfrom the surface of HSA. These results show alsothat ITC-experiments can be deceptive when en-thalpies of different reaction in the system com-pensate in such a way that they vanish. Thus, inthe present case interaction still exists under phys-iological conditions but does not lead to measur-able enthalpies.

9

14121086420n(PAA)/n(HSA)

7

6

5

4

3

2

1

0

Q in

kca

l/mol

of P

AA

T= 37°C 20mM 50mM 70mM 100mM

Figure 4: Effect of ionic strength. Isotherms are shownfor a series of ionic strengths ranging from I=20 mM-100 mM at 37◦C. All fits have been done with N = 1.The thermodynamic data resulting from these fits arelisted in Table 1.

2 3 4 5 6 7 8 9100Ionic Strength in mM

103

104

105

Bin

ding

con

stan

t Kb

in m

ol-1

Figure 5: Linear dependence of the binding constantversus ionic strength as listed in Table 1 are depicted inlogarithmic scales according to eq.??.48

Comparison with computer sim-ulationsAll simulations presented in the following areusing an implicit-water coarse-grained (CG)structure-based model, where the CG proteinis held in its native structure by semi-empricialforce-fields.40 Here the amino acids, the PAAmonomers, and the salt ions are modelled explic-itly on a single bead level. Water is modelled bya dielectric background continuum while the saltions are explicitly resolved. Similar methods havebeen used repeatedly to study, e.g., protein fold-ing49 and the pair potential50 between proteins.

They provide a reasonable picture of the interac-tions of a given molecule with the amino acidslocalized at the surface of the protein because theyretain native structure, thermal motion, and ion-induced mechanisms in a well-resolved fashion.Hence, this type of simulations provides a full mi-croscopic picture of the interaction of PAA withHSA, in particular the identification of the siteswhere PAA docks on. Moreover, the simulationscan be used to obtain realistic free enthalpies ofbinding as will be further shown below. Our com-

FIG. 2: The snapshots of the binding configuration. The red and green beads refer to the negatively

and positively charged amino acids, respectively. The yellow monomers are the negatively charged

polyacrylic acids of the PAA chain. This color-scheme is used in all the figures. From left to right,

are configurations shot under condition of c = 20mM T = 25◦, c = 20mM T = 37◦, c = 50mM T =

25◦, c = 20mM T = 37◦, respectively.

simulation are very comparable, especially in low salt concentration c = 20mM . Only for

one condition (I=50mM T=37°C) deviation between theoretical and experimental results

grow slightly larger.

condition ∆Gsim[kBT ] Vb[nm3] ∆Gcorr[kBT ] ∆Gs[kBT ] ∆Gexp[kBT ]

20mM, 25◦ −10.0 ± 1.6 2.98 −0.6 −10.6 ± 1.6 −11.2

20mM, 37◦ −9.7 ± 1.4 5.91 −1.2 −10.9 ± 1.4 −11.8

50mM, 25◦ −6.5 ± 0.5 16 −2.3 −8.8 ± 0.5 −9.9

50mM, 37◦ −7.3 ± 0.2 7.48 −1.5 −8.8 ± 0.2 −10.7

TABLE II: The estimated binding free energy in comparison with the experimental ones in kbT.

Conditions ∆G′simb (kJ/mol) Vb (nm3) ∆Gcorr

b (kJ/mol) ∆Gsimb (kJ/mol) ∆Gexp

b (kJ/mol)

20mM, 25°C −24.8 ± 4 3 −1.5 −26.3 ± 4 −27.9 ± 0.2

20mM, 37°C −25.1 ± 3.6 5.9 −3.1 −28.2 ± 3.6 −29.2 ± 0.2

50mM, 25°C −16.1 ± 1 16 −5.7 −21.8 ± 1 −23.5 ± 0.5

50mM, 37°C −18.9 ± 0.5 7.5 −3.9 −22.8 ± 0.5 −26.2 ± 0.2

TABLE III: The estimated binding free energy in comparison with the experimental ones in kJ/mol.

10

Figure 6: (a) Representative computer simulation snap-shot of the total HSA-PAA complex. (b) Magnificationof the binding site: the PAA (yellow string of beads) isbound near the Sudlow II site. The amino acid beadsthat directly participate in the binding (defined by be-ing within 0.5 nm distance to the PAA on average) aredepicted by the opaque spheres. The rest of the HSAstructure is distinguished by a transparent surface plot.Electrostatically neutral HSA beads are colored white,positive beads are green, and negative beads are red.

puter simulations demonstrate that the HSA bindsonly one PAA chain, independent of temperature,salt concentration, and molar ratio in the consid-ered parameter ranges. Hence, it reconfirms the re-sult obtained previously by ITC. A representative

10

simulation snapshot of the bound complex withone PAA is presented in Fig. 6. From a thoroughscreening of our simulation trajectories it emergesthat this structure is highly reproducible and as-sumed in 80% of the simulation time. It is hencea highly stable and probable configuration. Ad-ditional analysis reveals that the PAA chain spansthe sub-domains II A, III A, and III B, involv-ing the Sudlow II binding site. As expected fora negatively charged polyelectrolyte we find thatit favorably binds positively charged amino acids,arginine (R) and lysine (K) at positions R410,R484, R485, R413, R538, K541, K199, K195, seealso the green opaque spheres in Fig. 6. This iscertainly a central result of the present analysisinasmuch as it defines the precise location of thebinding of a highly charged molecule as PAA.

0

1

2

3

4

5

0 2 4 6 8 10 12 14

n (r

)

r [nm]

c = 20 mM, T = 25°Cx = 1x = 2x = 6

x = 10

Figure 7: Running coordination number n(r) of the PAAchains around the HSA versus their centers-of-massdistance r at a temperature of 25◦ C, salt concentra-tion of 20 mM, and molar ratios x = cPAA/cHSA = 1, 2,6, and 10, see legend. In all cases roughly one PAAchain (horizontal black dotted line) is bound to HSA.

To demonstrate that only one PAA forms a com-plex with HSA, the running coordination numbern(r) of the PAA around HSA is shown in Fig. 7for molar ratios x = 1, 2, 6, and 10. The quan-tity n(r) is the total number of PAA-moleculesaround a given HSA as the function of distance.The plateau of the curves between separations ofr = 4 and 6 nm just above the average value ofthe HSA radius is a proof that the binding num-ber does not exceed one, irrespective of the molarratio. Only at larger distances n(r) is increasingbeyond unity since here the entire solution is ex-

plored. We find qualitatively similar results for theother investigated salt concentrations and temper-atures. This finding again is in direct agreementwith the results of the ITC-experiments (see alsothe normalized density profiles in Fig. S5).

It is furthermore interesting to see the temporalevolution of the complex of HSA with PAA. ThePAA chain slides along the Sudlow II site muchin a way of a threading through an orifice. A se-ries of snapshots combined with a movie can befound the in Fig. S4 of the supplementary infor-mation. At the one hand, this fact demonstratesthe strong binding of PAA by this side. On theother hand, the threading through this site leads toa strongly increased number of configurations ofthe complex and thus increases the entropy of thecomplex. This fact certainly leads to the bindingof the PAA-chain at the Sudlow II site and not onother positive patches on the surface of HSA.

Our simulations allow us to calculate the freeenergy profiles (potential of a mean force) alongthe HSA-PAA distance coordinate. Examples forthis interaction free energy G(r) between a sin-gle uncomplexed HSA and one PAA at two saltconcentrations is presented in Fig. 8. For largerdistances of approach, r ' 7 nm, a small repul-sive barrier can be observed stemming from themonopole charge repulsion which dominates forlarge separations as expected. The barrier de-creases and shifts slightly to shorter distances withhigher salt concentration. At about r ' 6 nmthe onset of a strong attraction takes place untila global minimum is observed at closer approachat about r = 2 nm. The onset of attraction hap-pens right at values comparable to half of the con-tour length of the PAA chain at which one of itsends is first able to get in contact with the HSAsurface. We never found a stable free energy min-imum for the adsorption of a second PAA. This isdue to a too strong monopole charge repulsion andthe covering of the high-potential binding spot bythe firstly bound PAA.

For the stable HSA/PAA complex, the bindingfree energy ∆Gsim can be calculated from the dif-ference of the global minimum and the referencefree energy at large distances (horizontal lines inFig. 8). The values of the simulation binding freeenergy, corrected to yield the standard free energyof binding from the simulations ∆Gsim

b (see Meth-

11

ods), are summarized in Table 2 for various saltconcentrations and temperatures. We find a verygood agreement for all systems with largest de-viation of only 13% for the case of 50 mM saltat 37◦ C temperature. As in the experiments, thebinding affinity decreases in the simulations withhigher salt concentrations and increases with ris-ing temperature. The highly quantitative descrip-tion by the simulations, however, is actually some-what surprising given the simplicity of the under-lying model and the neglect of hydration effectsand should be discussed with caution. However,we take it as a strong indication that relativelygeneric electrostatic interactions rule the complex-ation process and hydration contributions (such ashydrophobic or van der Waals (vdW) attractions)are rather small.

-12

-10

-8

-6

-4

-2

0

2 4 6 8 10

G(r

) [k

BT

]

r [nm]

c=20mM, T = 25°Cc=50mM, T = 25°C

Figure 8: Free energy profile (or potential of meanforce) G(r) between the PAA and the HSA versus theircenters-of-mass distance r at a temperature of 25◦ Cand for 20 mM (red) and 50 mM (blue) salt concentra-tions. The binding free energy ∆Gsim derived from thesimulation can be read off as the difference between thezero free energy reference state at far separation (hori-zontal black dotted line) and the global minimum repre-senting the bound state (horizontal blue and red dottedlines).

In order to test our hypothesis introduced abovethat the binding free energy is essentially domi-nated by the entropy of released counterions fromthe PAA chain and/or a positive patches on theHSA, we have counted the number of released ionsupon complexation. In brief, we define an ion as’condensed’ if it is located in the first bound layernear a charged HSA or PAA monomer, defined by

a cut-off radius of 0.5 nm. Hence, the number ofreleased ions is calculated as the difference of theaverage number of condensed ions in the fully sep-arated and the stable bound states (see Fig. S5).For a temperature of 25◦C and 20 mM and 50 mMsalt concentrations, our analysis shows that on av-erage indeed 2.5 condensed ions are diluted awayinto the bulk upon complexation. This is indeed ingood agreement with the Record-Lohman-analysisof the experiment data discussed above (cf. thediscussion of Fig. 5).

Deeper inspection shows that 2 of those ionscome from the PAA, at which they where boundin a high density state (see Fig. S6 for ionic pro-files around PAA monomers). If we now just con-sider the PAA-condensed ions and their averageconcentration in the bound state cdense ' 1.5±0.5 mol/l, this implies that a favorable entropy con-tributions of about' kBT ln(cdense/cs) = 4.3±0.4and 3.4± 0.4 kBT is gained per ion upon its re-lease into 20 mM and 50 mM bulk concentrations,respectively. The total release free energies es-timated by this analysis are thus roughly -21±2and -17±2 kJ/mol for 20 mM and 50 mM salt, re-spectively, which is close to the binding free en-ergies from both experimental data and from sim-ulations. Hence, the binding of PAA is to a greatpart ruled by a counterion release mechanism andentropy. We note, however, that the matching ofthese numbers may be fortunate since other non-negligible interactions such as (repulsive) chainentropy, vdW attractions, and multipolar chargeinteractions beyond the bound ion layer (that is,from screening ions), all present in both simula-tion and experiment, have been neglected in thissimple counterion release concept. The presentcomparison with experimental data, however, in-dicates that these contributions are of comparablemagnitude and cancel each other roughly for thepresent system.

Evidently, we obtained the leading contributionof the ions directly condensed on the PAA chain.Hence, the estimate of the entropy of counterionrelease given above should be considered a lowerbound for the absolute entropy contribution. Othercontributions not included in the theoretical anal-ysis apparently lead to experimental entropies thatare higher by a factor of 2-3 (see cf. Table 1). Thegood agreement between the measured and the cal-

12

Table 2: The calculated standard binding free energy from the simulations ∆Gsimb in comparison with the experimental

ones ∆Gexpb for various salt concentrations and temperatures in units of kJ/mol. ∆Gsim is the direct output from the

simulations which has to be corrected by ∆Gcorr for the binding volume Vb to obtain the standard free energy ofbinding (see Methods)

Conditions ∆Gsim (kJ/mol) Vb (nm3) ∆Gcorr (kJ/mol) ∆Gsimb (kJ/mol) ∆Gexp

b (kJ/mol)20 mM, 25◦C −24.8±4.0 3.0 −1.5 −26.3±4.0 −27.9±0.220 mM, 37◦C −25.1±3.6 5.9 −3.1 −28.2±3.6 −29.2±0.250 mM, 25◦C −16.1±1.0 16.0 −5.7 −21.8±1.0 −23.5±0.550 mM, 37◦C −18.9±0.5 7.5 −3.9 −22.8±0.5 −26.2±0.2

culated ∆Gb, however, demonstrates that these ad-ditional entropic contributions are canceled out byan enthalpic contribution of equal magnitude. This“enthalpy-entropy compensation“ is well-knownfor various processes as e.g. solute hydration,protein folding, or proteins association.27,44 Thepresent comparison of theory and experiment al-lows us to discern among these terms and the lead-ing contribution to ∆Gb.

ConclusionsWe presented a study of the binding of short PAAchains to HSA by combining calorimetry, that is,ITC and computer simulation. Both ITC experi-ments and simulation results show that there existsa strong attractive interaction between PAA andHSA at “the wrong side of pI“, where both arenegatively charged. Computer simulations demon-strate that the binding of the PAA takes place atthe Sudlow II site. ITC measurements for a se-ries of salt concentrations between 20 mM and100 mM show that the dependence of bindingaffinity ∆Gb on ionic strengths is mainly deter-mined by the counterion release mechanism andcan be described by the Record-Lohman relationsee eq. ?? (see Fig. 5). The binding affinity ∆Gbdecreases with high ionic strength, until it practi-cally vanishes at around 750 mM. Both the anal-ysis of the experimental data as well as the simu-lations find that approximately 3 ions are releasedin the binding process. The binding affinity ∆Gbcan be calculated from simulations with good ac-curacy. Combining simulations with calorimetryis hence a powerful tool to elucidate the interac-tion of proteins with given substrates or possibletoxins. Thus, this combination of theory and ex-

periment is now capable of solving biochemicalproblems of direct medical importance.

AcknowledgementThe Helmholtz Virtual Institute for Multifunc-tional Biomaterials for Medicine are gratefullyacknowledged for financial support. The au-thors thank the Helmholtz Association for fundingof this work through Helmholtz-Portfolio Topic"Technology and Medicine". X. Xu is sponsoredby the China Scholarship Council (CSC). In ad-dition, J. Jankowski was supported by the grant"NPORE" of the BMBF/IGSTC (01DQ13006A).

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Graphical TOC Entry

3 ions released

salt concentration

37°CPolyelectrolyte conc.

Bin

ding

Ent

halp

y

17