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Counterion-release entropy governs the inhibition of serum proteins by polyelectrolyte drugs Xiao Xu, Qidi Ran, Pradip Dey, Rohit Nikam, Rainer Haag, Matthias Ballauff, and Joachim Dzubiella Biomacromolecules, Just Accepted Manuscript • DOI: 10.1021/acs.biomac.7b01499 • Publication Date (Web): 21 Dec 2017 Downloaded from http://pubs.acs.org on January 8, 2018

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Biomacromolecules

Counterion-release entropy governs the inhibition of serum proteins by polyelectrolyte drugs Xiao Xu,†,‡ Qidi Ran,†,¶,§ Pradip Dey,§,k Rohit Nikam,†,‡ Rainer Haag,¶,§ Matthias Ballauff,†,‡,¶ and Joachim Dzubiella∗,†,‡,¶ †Institut für Weiche Materie und Funktionale Materialien, Helmholtz-Zentrum Berlin, Hahn-Meitner-Platz 1, 14109 Berlin, Germany ‡Institut f¨ ur Physik, Humboldt-Universität zu Berlin, Newtonstr. 15, 12489 Berlin, Germany ¶Multifunctional Biomaterials for Medicine, Helmholtz Virtual Institute, Kantstrasse 55, 14513 Teltow-Seehof, Germany §Institut f¨ ur Chemie und Biochemie, Freie Universität Berlin, Takustrasse 3, 14195 Berlin, Germany kPolymer Science Unit, Indian Association for the Cultivation of Science, 2A & 2B Raja S. C. Mullick Road, 700032 Kolkata, India

E-mail: [email protected] Abstract Dendritic polyelectrolytes constitute high potential drugs and carrier systems for biomedical purposes, still their biomolecular interaction modes, in particular those determining the binding affinity to proteins, have not been rationalized. We study the interaction of the drug candidate dendritic polyglycerol sulfate (dPGS) with serum proteins using isothermal titration calorimetry (ITC) interpreted and complemented with molecular computer simulations. Lysozyme is first studied as a well-defined model protein to verify theoretical concepts, which are then applied to the important cell adhesion protein family of selectins. We demonstrate that the driving force of the strong

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complexation, leading to a distinct protein corona, originates mainly from the release of only a few condensed counterions from the dPGS upon binding. The binding constant shows a surprisingly weak dependence on dPGS size (and bare charge) which can be understood by colloidal charge-renormalization effects and by the fact that the magnitude of the dominating counterion-release mechanism almost exclusively depends on the interfacial charge structure of the protein-specific binding patch. Our findings explain the high selectivity of P- and L- selectins over E-selectin for dPGS to act as a highly anti-inflammatory drug. The entire analysis demonstrates that the interaction of proteins with charged polymeric drugs can be predicted by simulations with unprecedented accuracy. Thus, our results open new perspectives for the rational design of charged polymeric drugs and carrier systems.

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Introduction

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The rational design of polymeric drugs and nanocarriers has become a central task in

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medicine and pharmacy in the recent years. 1–3 A key challenge is the understanding of

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their interaction with proteins which is decisive for their metabolic fate and function in

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vivo 3–9 and can be limiting to the desired biomedical application. Calorimetry, in particular

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isothermal titration calorimetry (ITC), has become a central tool of these studies. 4,5,10,11

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It provides the binding affinity (binding constant), Kb , 12 if a suitable binding model for

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data analysis is applied and correctly interpreted. However, the major problem in this task,

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namely the quantitative rationalization of the complexation of such substances with various

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proteins relevant for the pharmaceutical problem, is often out of reach because of lack of

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molecular mechanistic insights. In general, the underlying interactions will be governed by

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a complex interplay between electrostatic, solvation, and steric effects, and theoretical and

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simulation concepts are in need that allow a quantitative assessment of these forces. 12–15

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Moreover, possible cooperative effects must be discussed if several ligands are bound to a

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given drug or carrier, 16 forming the protein corona. 4–7

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In particular, substances based on branched macromolecules have been increasingly used

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for a wide variety of purposes. Among those, dendritic polyglycerol terminated with sul-

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fate (dPGS) has received much attention because of its high anti-inflammatory potential

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by blocking selectins (cell adhesion proteins) during disordered immune response. 17–20 In

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addition, dPGS is presently discussed for the treatment of neurological 21 or cartilage disor-

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ders, 22 as an intrinsic tumor tracer in nanotherapeutics, 23 and as a drug delivery carrier. 24,25

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The anti-inflammatory potential of the highly anionic dPGS was traced back to its notable

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complexation with L- and P-selectin, but not E-selectin, 18,19,26 while electroneutral dPG

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exhibits a very different response and organic uptake. 27 It is known that P- and L-selectin

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have a characteristic region of positive electrostatic potential, not so distinctly developed

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in E-selectin, 28 that could lead to the observed differences. However, there is a lack of a

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quantitative understanding of the interaction of dPGS and a given protein that would allow

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us to design improved dPG-based therapeutics. Here, we present a major step forward in the understanding and prediction of the interaction of charged dendritic macromolecules such as dPGS with proteins. We analyze ITC data of dPGS-protein complexation and link the results to coarse-grained (CG) and atomistic computer simulations of dPGS of relevant generations, illustrated in Fig. 1A (chemical structure in SI Fig. S1). First, as a well-defined model protein, we study lysozyme that is available in large quantity with high purity. Here, ITC data interpretation faces the challenge to take into account the strong electrostatic cooperativity of the positively charged lysozyme that binds to the anionic dPGS in a multivalent fashion, cf. the simulation snapshot of the protein corona in Fig. 1B. In principle, dPGS is an excellent model system for such a study: Structural and charge properties are well characterized by experiments 29 and simulations, 30 where in particular the colloidal charge renormalization effect by counterion-condensation 31,32 was quantified in detail. In this work, we demonstrate that the latter effect governs the binding mechanisms of dPGS to a protein, as known already for strong linear polyelectrolytes: 33

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A few counterions condensed on the polyelectrolyte are liberated when the protein binds, whereupon an oppositely charged protein patch becomes a multivalent counterion for the polyelectrolyte. The resulting favorable (purely entropic) free energy in dependence of the salt concentration cs can be formulated as 34–38

∆GCR = −NCR kB T ln(cci /cs ),

(1)

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where cci (typically cs ) is the local concentration of condensed counterions and NCR de-

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notes the number of those released after binding. Eq. 1 follows from the pioneering consider-

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ations of Record and Lohman 39 in the realm of DNA-protein complexation that culminated

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in the leading-order expression for the binding constant purely from counterion release,

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d ln Kb /d ln cs = −NCR . Based on our combined calorimetric and simulation analysis we

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verify that this concept fully applies for dPGS-lysozyme complexation. We provide a quan-

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titative understanding of the underlying microscopic details, in particular explain the very

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weak generation dependence of the binding affinity. We finally calculate the binding affinity

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of dPGS to the pharmaceutically important selectin proteins yielding very good agreement

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with available experimental data, in particular elucidating the high selectivity among P, L

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and E-selectins in binding to dPGS.

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Methods

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dPGS molecules and Isothermal Titration Calorimetry (ITC)

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Dendritic polyglycerol (dPG) was synthesized by anionic ring opening polymerization of

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glycidol as reported before. 40,41 Gel permeation chromatography (GPC) was employed to

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measure the number averaged molecular weight of the core Mn,dPG and the polydispersity

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index (PDI). The synthesis led to samples of generations G2, G4, G4.5, and G5.5 with PDIs

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of 1.7, 1.7, 1.5, and 1.2, respectively. G4.5 and G5.5 have non-integer generation values be-

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Figure 1: (A) Schematic view of the simulated dPGS of generation n (Gn) in terms of their bare charge (left axis) and their effective diameter (right axis), 30 respectively. (B) Coarse-grained simulation snapshot of the complex G5-[lysozyme]4 , forming a protein ‘corona’. 4–7 The dPGS monomers as well as protein amino acids are represented as single beads. Electroneutral beads are colored white, positive beads are green, negative beads (such as the dPGS terminal sulfate groups and the acidic amino acids) are red. Also the surface layer of counterions (yellow beads, not to scale) is illustrated.

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cause the synthesis did not lead to complete outer branches. Afterwards, dPGS was prepared

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by the sulfation of dPG with SO3 -pyridine complex in dimethylformamide (DMF). 17,18 The

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degree of sulfation (DS) was determined by elemental analysis. Standard ITC measurements

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were performed with a VP-ITC instrument (MicroCal, GE Healthcare, Freiburg, Germany 42 )

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with a cell volume of 1.43 ml and a syringe volume of 280 µl. Lysozyme was titrated into

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dPGS in MOPS buffer at 37 ◦ C. The MOPS buffer at pH 7.4 with different ionic strengths

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was prepared by adding sodium chloride into 10 mM MOPS accordingly. For all generations

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at 10 mM ionic strength and T = 310 K the measurements were independently performed

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three times with the lysozyme concentration 0.2 g/L (first 7 µL injection followed by 30x9 µL

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injections), 0.5 g/L (first 6 µL injection followed by 34x8 µL injections), and 1 g/L (first

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3 µL injection followed by 55x5 µL injections) to balance the concentration error. At ionic

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strengths from 25 mM to 150 mM for G2, the lysozyme concentration increased from 1 g/L

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to 15 g/L, accordingly.

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5



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CG protein and dPGS models and simulations

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The CG force field for perfectly dendritic dPGS in explicit salt was derived from coarse-

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graining from all-atom explicit-water simulations as summarized in our previous work. 30

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Briefly, the CG beads represent the inner core C3 H5 , the repeating unit C3 H5 O, and terminal

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sulfate SO4 individually. Only the terminal segments are charged with -1 e, leading to the

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dPGS bare valency |Zn | = 6(2n+1 − 2n ) of generation n. The model is fully flexible and has

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bond and angular intra-bond potentials. The water is modeled as a dielectric continuum,

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while salt- and counterions are explicitly resolved. The CG force field for the proteins is

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derived from a structure-based model where every amino acid is represented by a single bead

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connected by a Go-model Hamiltonian 43 according to the structures from the Protein Data

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Bank: 2LZT for lysozyme, 44 3CFW for L-selectin, 45 and 1ESL for E-selectin. 46 The protein

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CG beads that correspond to basic and acidic amino acids were assigned a charge of +1 e and

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-1 e, respectively, approximating their dissociation state at pH = 7.4. Thus, the net charges

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of the simulated proteins were +8 e, 0 e, and -4 e for lysozyme, L-selectin, and E-selectin,

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respectively. Apart from the Coulomb interaction between all charged beads, the Lennard-

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Jones interaction acts between all CG beads. To approximate the van der Waals interaction

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energy between pairwise protein CG beads i and dPGS beads j with interaction diameter

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σij we take the Lifshitz-Hamaker approach 47 and use the same ij = 0.06 kB T for all protein-

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dPGS beads pairs, equivalent with a Hamaker constant of 9 kB T . 48 The CG simulation uses

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the stochastic dynamics (SD) integrator in GROMACS 4.5.4 49 as in previous work. 30,35 The

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PMF between protein and dPGS is attained by using steered Langevin Dynamics (SLD) 49

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as demonstrated before 35–38 with a steering velocity vp = 0.2 nm/ns and harmonic force

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constant K = 2500 KJ mol−1 nm−2 .

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Results and Discussion

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ITC experiments of dPGS-lysozyme complexation Table 1: Summary of experimental characteristics of dPGS of generation n (Gn)as well as fitting parameters of the ITC of dPGS-lysozyme complexation evaluated via the standard Langmuir binding model. Mn is the respective dPGS molecular weight and Zn the bare charge valency (defined by the number of terminal sulfate groups) both determined experimentally. Zeff is the effective charge valency due to charge renormalization and reff is the effective Debye-H¨ uckel radius interpolated from previous simulation work on perfect dendrimers. 30 The ITC fits via the Langmuir model yield the standard Gibbs binding free energy ∆G0 = −kB T ln Kb /v0 with the standard volume v0 = 1 liter/mol, enthalpy change ∆H, and stoichiometry N . The ITC was conducted at 10 mM salt concentration and T = 310 K.

dPGS Mn [kD] Zn [e] Zeff [e] reff [nm] ∆G0 [kB T ] ∆H [kB T ] N

G2 G4 G4.5 G5.5 5 18 24 47 -28 -102 -135 -266 -11 -19 -22 -28 1.9 2.8 3.2 3.6 -19.0± 0.4 -20.3 ± 0.2 -20.0± 0.3 -19.3 ± 0.1 -23.7± 0.7 -24.4± 0.6 -25.3± 0.5 -25.8±0.9 2.9± 0.5 8.1± 0.2 8.8± 0.7 13.9±1.4

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In the first step we evaluated lysozyme-dPGS complexation for the generations n = 2, 4, 4.5

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and 5.5 by ITC experiments. (Methods; SI Fig. S2 for raw ITC data). The released heat

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normalized by the number of injected proteins is plotted in Fig. 2A versus the molar ra-

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tio cLys /cdPGS . The data are satisfactorily fitted with a single set of identical binding sites

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(SSIS) model, that is, a standard Langmuir adsorption isotherm, 50 with fitting parameters

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summarized in Table 1. The resulting number of binding sites per dPGS, i.e., the stoichiom-

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etry N , increases from 2.9±0.5 for G2 to 13.9±1.4 for G5.5. Hence, binding is multivalent,

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with N significantly increasing with n due to the expanding dendrimer size. The standard

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Gibbs binding free energy, ∆G0 = −kB T ln Kb /v0 between −19 and −20 kB T , is large,

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however, stays surprisingly constant with n despite the one-order-of-magnitude variation of

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molecular weight and bare charge among the generations, cf. Table 1. Importantly, ITC-

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experiments on the salt concentration dependence of the lysozyme complexation with G2 7



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are plotted in Fig. 2B to scrutinize for counterion release effects according to the function

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d ln Kb /d ln cs = −NCR , cf. Eq. 1. The inset in Fig. 2B demonstrates that indeed a clear

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linear relationship, ln Kb ∝ ln cs , is found, except for the lowest ionic strength where stronger

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screened electrostatic (Debye-H¨ uckel) interactions come into play, discussed in detail below.

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ITC Evaluation of the slope indicates that NCR = 3.1±0.1 ions per protein are released, triggered

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by the complexation.

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The latter analysis strongly suggests that the dominating driving force for complexation

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originates from counterion-release entropy, cf. eq. 1, in particular for larger (physiological)

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salt concentrations. However, one has to be aware that the Langmuir assumption of non-

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interacting ligands is violated for our system where there exists a mutual Debye-H¨ uckel (DH)

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screened electrostatic repulsion among the charged proteins in the corona (cf. Fig. 1B). As

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a consequence of this electrostatic anti-cooperativity, the binding constant Kb depends on

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the coordination number i. This renders the interpretation of Kb difficult. In that respect,

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we should recall that the value of Kb in Fig. 2A is actually determined by the slope at the

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inflection point of the plotted differential heat curves. 42,51 From the integrated heat (SI Fig.

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S3), we thus find that the obtained Kb correspond, e.g., for n = 2, 4, and 5.5, to the binding

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at (mean) coordination i∗ = 2.7, 7.8, and 13.1, respectively, corresponding to large coverages

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θ∗ = i∗ /N = 0.93, 0.95, and 0.94. In our cooperative system we thus expect that the binding

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affinity determined at these large coordinations can be quite different to those of the first

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binding proteins, not captured by the simple Langmuir model.

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Binding affinity and interactions from CG simulations

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To further dissect and rationalize the experimental problem we employ coarse-grained (CG),

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but ion-resolved, computer simulations of lysozyme association with the perfect dendrimers

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G2, G3, G4, and G5 30 (cf. Methods). We focus on the case of 10 mM salt concentration where

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electrostatic cooperativity effects are strongest. The virtue of the simulations is that we can

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calculate the total binding free energy ∆Gsim b (i) of the ith lysozyme with the complex where 8


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A

0

B

0 108

-10 dQ/NLys [kJ/mol]

-10 dQ/NLys [kJ/mol]

-20 -30 -40 -50

G2 G4 G4.5 G5.5

-60 -70 0

5

10 cLys /cdPGS

15

107 106

-20

105

10

-30

100 cs [mM]

10 25 50 75 100 125 150

-40 -50 -60 -70

20

0

0.5

1

1.5

2 2.5 cLys /cdPGS

D -5

3 0 -3 -6

β∆Gsim ele

-10

2

i

4

6

8

10 12 14

∆GITC b,G2 ∆GITC b,G4 ∆GITC b,G5.5

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mM mM mM mM mM mM mM 3.5

4

G2 G4 G5

0

-15

β∆Gsim ele

β∆Gsim b

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Kb [M−1 ]

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-5 -10

1

-20

2

3 i

4

5

-25

G5

-30

0

0.2

0.4

0.6

0.8

1

θ

Figure 2: (A) ITC isotherms of the lysozyme-dPGS complexation ranging from generations 2 to 5.5 in MOPS buffer pH 7.4 at 310 K and 10 mM salt concentration. The solid lines correspond to the fits by the Langmuir model. (B) ITC isotherms of lysozyme-G2 complexation at different ionic strengths and fitted by the Langmuir model. The inset displays the salt dependence of the binding ITC = 3.1 ± 0.1 constant Kb on a log-log scale. According to Record-Lohman, 39 -d ln Kb /d ln cs = NCR counterions are released upon binding. (C) CG simulation results of the PMF, Vi (r), as a function of the center-of-mass distance r between G5 and lysozyme for the successive binding of i = 1 to 15 proteins in 10 mM salt concentration, color-coded according to the scale. Snapshots of the equilibrium complex for i = 1, 8, 13 proteins in the corona are shown. (D) The simulation binding sim for G2, G4, and G5, respectively, free energy ∆Gsim b (i) (symbols) plotted versus coverage θ = i/N read off from the global minimum of the PMFs, as such in (C). The large open circle, triangle and ∗ square symbols indicate the simulation-referenced Langmuir binding free energy ∆GITC b (i ), Eq. 2, ∗ ∗ for G2, G4, and G5.5 at their respective coverage θ = i /N ' 0.95. The insets present the total screened (DH) electrostatic interaction energy ∆Gsim ele (i) between ith ligand and the complex for G2 (lower inset) and G5 (upper inset), respectively.

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i − 1 proteins are already associated, i.e., we can stepwise investigate the assembly along i.

125

The binding free energy can be conveniently read off from the computed potential of mean

126

force (PMF) as a function of the pair separation distance, Vi (r), at hand of the difference

127

between the unbound (r = ∞) and the bound state at the PMF minimum at r = rb . The

128

PMFs for the example of G5 are plotted in Fig. 2C, along with snapshots of the growing

129

protein corona. The results for the free energy of binding, ∆Gsim b (i) = Vi (rb ), including those

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for G2 and G4, are presented in Fig. 2D versus the coverage θ = i/N sim . We find a strong

131

attraction that diminishes with rising i almost identically for all generations. The maximum

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coordination extracted from equilibrium simulations of the complex (see SI Fig. S4), N sim ,

133

for G5 is about 13±0.1, while for the smaller G4 and G2 we see maximally 9±0.2 and 4±0.1

134

ligands adsorbed, respectively. These calculated stoichiometries (N sim ) exceed the ones from

135

ITC (N ) only by about 1 ligand, cf. Table 1, which is a very satisfactory agreement.

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One reason for the decreasing attraction with i is the growing anti-cooperative DH repulsion

137

between ligand i and the complex (involving i − 1 proteins). The net DH interaction energy

138

between ligand i and the complex (for the calculation see SI) is plotted in the insets to Fig. 2D

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for the examples of G2 and G5: For low coordination i, an attractive DH interaction between

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the oppositely charged dPGS and proteins is observed, as expected. For increasing i, the

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DH interaction becomes much less attractive near saturation (i ' N sim ), due to additional

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protein-protein repulsion. The net DH interaction becomes even repulsive for G5, i.e., the

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complex shows a charge-reversal behavior, accompanied by repulsive barriers in the PMF,

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see Fig. 2C for large i ' N sim . The second reason for the decreasing attraction with rising

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coordination i, especially close to saturation, arises from the ligands’ steric packing near

146

saturation, or, in Langmuir terms, from the entropic penalty of filling up all possible binding

147

sites.

148

In order to compare the binding affinity obtained from ITC at coordination i∗ consistently

149

to the simulations, we need to define the simulation-referenced total Gibbs free energy cor-

10


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responding to the Langmuir model (see SI and related discussions in previous work 51 ), via

∗ 0 ∗ β∆GITC b (i ) = β∆G − ln(1 − i /N ) − ln(N v0 /Vb ),

(2)

151

where ∆G0 is the standard binding free energy from ITC, cf. Table 1, the second term on the

152

right hand side is the Langmuir entropic packing free energy, and the third term converts the

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standard reference state with binding volume v0 = l/mol to the simulation binding volume

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∗ Vb 12 (see SI Table S3). The results for ∆GITC b (i ) for generations n = 2, 4 and n = 5.5 are all

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very similar with 14-15 kB T and depicted by symbols at θ∗ in Fig. 2D. They match well the

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simulation free energies at coverages of θ ' 0.95, consistently right at the θ∗ values where

157

the ITC binding affinity was determined. Hence, our comparison on the total free energy

158

level shows full quantitative agreement between ITC and computer simulations, in particular

159

regarding the weak n-dependence of the determined complexation affinities.

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Counterion-release as main driving force

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The simulations enable us now to illuminate the details of the interactions driving the com-

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plexation of only the first protein, i = 1, (where no cooperative effects play a role) to dPGS

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of the various generations n. The PMFs are shown in Fig. 3A. The reasons for the weak n

164

dependence of the binding free energy, ranging from ' −26 kB T for G2 to ' −28 kB T for

165

G5, we find are twofold: First, the electrostatic screening (DH) part of the PMF, Vele (r),

166

plotted in the inset to Fig. 3A, is found to be relatively small. Corresponding contributions

167

are ' −9 to -4 kB T in the respective range of n = 2 to 5, apparently saturating already

168

for n > 3. The main cause for this is that dPGS exhibits a strong counterion condensation

169

and accompanying charge renormalization effect in the saturation regime, leading to a rel-

170

atively weakly n-dependent effective surface charge, up to one order of magnitude smaller

171

than the bare charge, 30 cf. Table 1. Thus, apart for G2, the DH contribution is of minor

172

importance and relatively constant with n. Second, a key consequence of the condensation

11



G3

G2

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G4

G5

Lysozyme

A

B

Figure 3: (A) The PMF, V1 (r), and (B) the number of released counterions, Nr (r), versus the center-of-mass separation distance r for the first lysozyme, i = 1, for G2 to G5 at 10 mM salt concentration from CG simulations. The lysozyme-dPGS complex (with snapshots on top) is stabilized at a distance rb (PMF minimum) where the binding free energy is ∆Gsim b (i = 1) := V1 (rb ) sim := N (r ). The and the number of released counterions (indicated by orange circles in (B)) is NCR r b insets in (A) depict the lysozyme binding patch (top inset, with positively charged beads in green), and the DH electrostatic interaction energy Vele (r) (bottom inset).

173

effect is the release of highly confined counterions from dPGS upon protein binding. Fig. 3B

174

presents the number of released counterions Nr (r) as a function of distance r, determined

175

by counting the ions within the dPGS condensed ion region 30 (see SI Fig. S6). The number

176

sim of released ions at the bound state is NCR := Nr (rb ) ' 3.3, 4.4, 4.5, and 4.8 for generations

177

G2, G3, G4, and G5, respectively. For G2 we reach a very good agreement with the number

178

ITC NCR = 3.1 ± 0.1 attained by the Record-Lohman analysis of the ITC data in Fig. 2B. The

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sim difference of NCR among the last three generations is quite minor. This is understandable

180

as the protein surface serves as a generation-independent ‘template’ that sets the number

12


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of replaceable counterions by the number of positive charges in the binding region (‘patch’),

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see the illustrative snapshot in the inset of Fig. 3A: Indeed several positively charged beads

183

(colored in green) cluster in the binding patch. Accordingly, for n & 3, where the dPGS

184

surface area is much larger than the binding patch, the dPGS size has a very weak influence

185

on the number of released ions.

186

For a more quantitative assessment we estimate that the condensed counterions are confined

187

3 in the dPGS shell with a local surface concentration cci ' 3Nci /[4π(reff − rd3 )], where reff − rd

188

defines the width of the interactive surface shell region (or ’Stern’ layer) between the diffusive

189

ionic double layer and the sulfate surface groups. 30 We find cci ' 2.43 M for G5 (for other

190

generations see SI Table S3), more than one or two orders of magnitude larger than typical

191

physiological or experimental bulk concentrations. According to Eq. 1, this can be translated

192

into the entropic benefit ∆GCR ' −5.5 kB T per counterion (SI Table S3) upon its release

193

into bulk at salt concentration cs = 10 mM. That amounts to the gross free energy gain

194

' −27 kB T exclusively arising from 4.8 released counterions for G5. Including the small

195

DH correction (' −4.5 kB T , cf. inset to Fig. 3A) the total estimate of about −31 kB T is

196

indeed close to the binding free energy for the first protein from the simulations, ∆Gsim b (i =

197

1) = −28 kB T . This good agreement, analogously derivable for the other generations,

198

demonstrates that the dPGS/protein association is indeed largely dominated by the release

199

of only a few ions.

200

dPGS-Selectin complexation

201

We finally applied our CG simulations to the biomedically important (E and L) selectin

202

proteins. Regarding the first ligand coordination, the PMF profiles, binding free energies,

203

released counterions as well as illustrative snapshots are presented in Fig. 4. A weak de-

204

pendence of the binding free energy on dPGS generation is revealed for L-selectin, where

205

∆Gsim b (i = 1) ' −21 kB T for G2 and ' −27 kB T for G5 (See Fig. 4A). This behavior

206

resembles that of lysozyme and is again accompanied by a relatively constant number of 13



A

E

C

B

L-Selectin

Page 14 of 28

E-Selectin

CG simulation

K113 K111

R97 K99

K87 K85

E

D

R46

K84

K8 R46

R14

K113 K111 K85

All atom simulation

R97 K99

K84

Figure 4: (A) The PMF V1 (r) (upper panel) and the corresponding number of released counterions Nr (r) (lower panel) for the first bound L-selectin at dPGS of generations 2 to 5 at 10 mM salt concentration from CG simulations. As a comparison, the inset shows the PMF between G4dPGS and E-selectin with the same simulation conditions and a snapshot of the E-selectin binding patch. (B, D) present snapshots of the L-selectin/G3-dPGS binding complex: CG versus all-atom simulations. Green colored beads or regions depict domains of positive charge. (C, E) show the corresponding snapshots of the L-selectin binding patch. The responsible basic amino acids shown to be interactive with dPGS are labeled and highlighted.

207

sim released counterions upon binding, being NCR ' 3 ∼ 4 for all generations. The correspond-

208

ing binding patch of L-selectin is found to accommodate a number of positively charged

209

groups, with complexation snapshots shown in Fig. 4B and the binding interface presented

210

in Fig. 4C. Furthermore, we conducted the CG simulation also for G3-dPGS and L-selectin

211

at near physiological salt concentration cs = 150 mM and temperature T = 293 K, for which

212

the experimental binding affinity from fluorescence measurements is available. 26 The simu-

213

lated result, ∆Gsim b (i = 1) = −14.3 kB T , (PMF in SI Fig. S8) is in good agreement with

214

−13.1 ± 1 kB T measured in the experiment for a 1:1 binding stoichiometry.

215

To further support the structural picture, the final G3-dPGS/L-selectin complex was studied

216

by standard, explicit-water all-atom (AA) molecular dynamics simulations (see SI). Com-

217

pared to the CG simulation, we find that the number of released counterions as well as the

218

structure of the complex is virtually the same, cf. Fig. 4D and E, regardless of the inclusion

219

of the explicit solvent and atomistic structure. We find 3.3 liberated counterions in the AA

14


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Biomacromolecules

220

simulation and 3.6 for the CG simulation. However, the CG model, where each amino acid

221

is replaced by a simple bead, to some extent brings small deviations to the surface geometry

222

as compared to the fully atomistic protein structure: we find that in the AA simulations

223

two more amino acids R14 and K8 of L-selectin can interact with the dPGS (see Fig. 4E).

224

Nevertheless, apparently this deviation in the binding interface does not much affect the

225

mean number of released ions.

226

Finally, as opposed to L-selectin, we find from the CG simulations that E-selectin has a much

227

weaker affinity to dPGS. The binding free energy (see the inset to Fig. 4 A) is only about

228

−1 kB T , suggesting a very unstable binding complex. Such an intriguing selective binding

229

behavior is in full agreement with the protein’s anti-inflammatory potency. 18 Interestingly,

230

the global features of the native structure of E-selectin are not so different from L-selectin.

231

For instance, 157 amino acids and -4 e net charge for E-selectin have to be compared to

232

156 amino acids and zero net charge for L-selectin. However, our findings clearly show that

233

the underlying difference of large ∼ 26 kB T in the binding free energy must be assigned to

234

local differences in protein interface structure, where a patch accommodating many positive

235

charge clusters as in lysozyme or L-selectin is less developed, 28 see also the inset to Fig. 4A.

236

Conclusions

237

We demonstrated that the complexation of proteins and highly charged dendritic macro-

238

molecules, especially at physiological ionic strength, is largely dominated by the entropic

239

counterion-release mechanism. The complexation weakly depends on the dendrimer genera-

240

tion (size and charge) mainly due to two effects: first, the relatively small effective surface

241

charge of dPGS in the charge renormalization saturation limit leads to a weak generation

242

dependence of the Debye-H¨ uckel interactions. Secondly, for the larger dendrimers the mag-

243

nitude of the dominating counterion contribution only depends on the protein-specific inter-

244

facial binding patch structure. With that the experimentally found weak generation depen-

15



245

dence of dPGS towards proteins and its high selectivity in the anti-inflammatory potential

246

can be fully understood. Our clear mechanistic picture behind the dPGS-protein complex-

247

ation as well as its predictive value for the calculation of binding affinities are important

248

for the rational optimization of dendritic polyelectrolytes as potential drugs and nanocar-

249

rier systems, which define their overall biological identity in vivo by their interactions and

250

coating with proteins. 4–7

251

Acknowledgement

252

Xiao Xu thanks the Chinese Scholar Council for financial support. The International Re-

253

search Training Group IRTG 1524 funded by the German Science Foundation as well as

254

the Helmholtz Virtual Institute for Multifunctional Biomaterials for Medicine are gratefully

255

acknowledged for financial support.

256

References

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399

Biomacromolecules

Graphical TOC Entry

Binding free energy

400

Released bound ions

23


Biomacromolecules 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

Page 24 of 28

Binding free energy


Released bound ions

Page 25 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

Biomacromolecules


B 0 10 Biomacromolecules -10 10

0

-30

G2 G4 G4.5 G5.5 10 cLys /cdPGS

15

-20

105

10

-30

100 cs [mM]

10 25 50 75 100 125 150

-40 -50 -60 -70

20

0

0.5

1

1.5

2 2.5 cLys /cdPGS

D -5

3 0 -3 -6

β∆Gsim ele

5

106

-10

2

i

4

6

8

10 12 14

∆GITC b,G2 ∆GITC b,G4 ITC ∆Gb,G5.5

3

mM mM mM mM mM mM mM 3.5

4

G2 G4 G5

0

-15

β∆Gsim ele

1 -40 2 -50 3 4-60 5-700 6 7 8 9 10 11 12 13 14 15

β∆Gsim b

dQ/NLys [kJ/mol]

7

-20

Page 26 of 28

Kb [M−1 ]

8

-10

dQ/NLys [kJ/mol]

A

-5 -10

1

-20

2

3 i

4

5

ACS Paragon Plus Environment -25 G5

-30

0

0.2

0.4

0.6 θ

0.8

1

Page 27 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

Biomacromolecules

G3

G2

G4

Lysozyme

A

B


G5

Biomacromolecules 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15


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Counterion-Release Entropy Governs the ... - ACS Publications

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