Molecular Insight into the Protein–Polymer Interactions in N-Terminal

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Cite This: J. Phys. Chem. B XXXX, XXX, XXX−XXX

Molecular Insight into the Protein−Polymer Interactions in N‑Terminal PEGylated Bovine Serum Albumin Aravinda Munasinghe,†,∥,⊥,# Akash Mathavan,†,‡,∥,# Akshay Mathavan,†,‡,∥ Ping Lin,†,∥,⊥ and Coray M. Colina*,†,§,∥,⊥ Department of Chemistry, ‡Department of Biomedical Engineering, §Department of Materials Science and Engineering, ∥George & Josephine Butler Polymer Research Laboratory, and ⊥Center for Macromolecular Science & Engineering, University of Florida, Gainesville, Florida 32611, United States

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S Supporting Information *

ABSTRACT: Therapeutic proteins have increasingly been used in modern medical applications, but their effectiveness is limited by factors such as stability and blood circulation time. Recently, there has been significant research into covalently linking polyethylene glycol polymer chains (PEG) to proteins, known as PEGylation, to mitigate these issues. In this work, an atomistic molecular dynamics study of N-terminal conjugated PEG-BSA (bovine serum albumin) was conducted with varying PEG molecular weights (2, 5, 10, and 20 kDa) to probe PEGBSA interactions and evaluate the effect of polymer length on dynamics. It was found that the affinity of PEG toward the protein surface increased as a function of PEG molecular weight and that a certain weight (around 10 kDa) was required to promote protein−polymer interactions. Additionally, preferential interactions were monitored through formed contacts and hotspots were identified. PEG chains coordinating in looplike conformations were found near lysine residues. Also, it was found that hydrophobic interactions played an important role in promoting PEG-BSA interactions as the PEG molecular weight increased. The results provide insight into underlying mechanisms behind transitions in PEG conformations and will aid in future design of effective PEGylated drug molecules.

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ficiency, chronic hepatitis C, and renal anemia, respectively).7 Also, it is often found that only PEGylation with a specific polymer molecular weight, architecture, and conjugation chemistry can produce effective therapeutic applications. These applications emphasize the importance of understanding how polymers interact with biomolecules and, furthermore, predicting how polymers interact with proteins. One of the primary approaches to investigating protein− PEG interactions is to characterize the structure and shape of the bioconjugate. A strong favorable protein−PEG interaction may lead to a shroud-like conformation, while a strong unfavorable interaction may lead to a dumbbell-like conformation. In 2011, Pai et al.6 carried out small-angle neutron scattering (SANS) studies on mono-PEGylated lysozyme and mono-PEGylated human growth hormone and found that conjugated PEG with a molecular weight of 20 kDa acts as a random coil adjacent to the protein. However, a similar study performed in 2015 by Le Coeur et al. showed that the polymer conformation in di-PEGylated hemoglobin depends on the molecular weight of the conjugated PEG chain.10 They demonstrated that the shroud-like conformation is favored

INTRODUCTION Proteins are highly efficient in carrying out biological activities; however, the effectiveness and potency of administered therapeutic proteins are challenged by a variety of factors (e.g., stability, blood circulation time, specificity). Studies have shown that some limitations of these therapeutic proteins can be overcome by making bioconjugates via covalently linking polymers to proteins.1 These bioconjugates can be synthesized in a synergistic manner,2,3 where desirable properties from both components may be preserved. Proteins are delicate, and many functions are based on their unique tertiary structure. Hence, upon chemical modification, a protein’s tertiary structure and its active site should not change in a way that affects its integrity. Among many polymer types, polyethylene glycol (PEG) is widely used in the synthesis of bioconjugates.3−6 This is mainly due to the biocompatibility of PEG and its ability to help native protein overcome challenges of a hostile environment.7 The attachment of PEG chains to protein surfaces, known as PEGylation, serves a fundamental role in a variety of applications, such as in pH-dependent drug delivery, sitespecific functionalization, and shielding.8,9 As of 2015, the USF Food and Drug Administration (FDA) has approved 12 PEGylated protein conjugate drugs (e.g., Adagen, Oncaspar, and Somarvert for treatment of severe combined immunode© XXXX American Chemical Society

Received: December 20, 2018 Revised: March 4, 2019

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DOI: 10.1021/acs.jpcb.8b12268 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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potentially be used to investigate the mechanism underlying the increased blood circulation time of PEGylated interferon therapeutics.28 Settanni et al. employed extensive atomistic MD simulations using short PEG chains (4 and 7 monomers).34 They found that PEG molecules tend to accumulate around nonpolar residues. The authors proposed a methodology to predict total PEG/water accumulation near a protein using the sum of contributions from each residue type weighted by solvent accessible surface area (SASA). Short PEG chains were used due to the associated computational cost when studying higher molecular weight PEG in solutions within the scope of their work. Though the usage of short PEG chains was justified, as the persistence length of PEG is small, use of 4 or 7 monomer PEG chains may not sufficiently translate to protein−PEG interactions in longer PEG chain models. Exploring how higher molecular weight PEG chains conjugated to BSA interact with the protein at the atomistic scale will increase our understanding of how PEGylation enhances certain properties of a model therapeutic protein when compared to its native state. In this work, we present an atomistic MD study of N-terminal conjugated PEG-BSA systems, with linear PEG chains of varying molecular weights. Specifically, results provide molecular insight on how the polymer interacts with regions of the protein surface and the effect of polymer length on conformation and interaction. We hope this work will assist in constructing effective bioconjugates for delivery purposes as well as in utilization of PEGylation for other applications, such as protein shielding.

when the PEG molecular weight is higher than 10 kDa. Several other studies have been carried out to understand which configuration of PEG is favored when conjugated to proteins,11−16 yet a definite molecular picture has not clearly emerged. Over the protein−polymer conjugates that have been considered for development as therapeutic agents, serum albumins have been increasingly assessed as viable targets for PEGylation. Serum albumin is a 67 kDa transport protein and one of the most abundant proteins in mammalian plasma, thereby serving as an appropriate protein to model potential bioconjugates. Human serum albumins are known to have multiple binding pockets for different molecules, including (i) seven sites for medium and long chain fatty acids (FA), (ii) four additional sites for small chain FAs, (iii) two main sites for drugs, (iv) one site for bilirubin where heme binds in primates as well, (v) five sites for thyroxin, and (vi) several sites for selective single-ligand binding.17 Within currently identified serum albumins, human serum albumin (HSA), which can be found within humans, and bovine serum albumin (BSA), which can be derived from cows, have been extensively studied. PEG-BSA conjugates have been studied by several research groups due to their pharmaceutical importance, as there is close homology in both structure and function between BSA and HSA.18−21 In addition to conjugates, BSA and free PEG derivatives in solution have also been extensively studied.22−25 Recent work by Ferebee et al. on mono- and multi-PEGylated BSA revealed that solubility of the conjugate increased as the molecular weight of the PEG increased. 20 Also, they demonstrated that as solubility increased, structural transition of the conjugate may have occurred via changing of the polymer shape from a dumbbell-like conformation to a shroudlike conformation. The transition occurred within 10 kDa conjugates. However, according to their published data, the relationship between PEG molecular weight and conformation is not clearly resolved for low molecular weight PEG conjugates. A different study from Plesner et al. in 2011 showed that, upon PEGylation of linear PEG chains of 5, 10, 20, 30, 40, and 60 kDa, sodium dodecyl sulfate’s (SDS) affinity toward two high affinity and one low affinity binding sites was not retained compared to SDS’s ability to bind to two high affinity sites and six low affinity sites in native BSA, independent of the conjugated PEG molecular weight.25 SDS’s accessibility to the aforementioned sites may have been limited due to the PEG chain’s steric hindrance resulting from PEG interactions with the nearby protein surface. However, without information at the atomistic level, such observations might not be able to be purely resolved based on experimental studies alone. To address the lack of information at the atomistic level, several computational studies have shed light upon unresolved protein−polymer interactions in other conjugate systems. An atomistic molecular dynamics (MD) study by Yang et al. in 2011 on PEGylated insulin used root-mean-square-deviation (RMSD) and secondary structure calculations to show that PEGylation could enhance the structural stability of the protein.26 Atomistic MD simulations have also been utilized to screen several PEGylated proteins to evaluate benefits and drawbacks of PEGylation.13,27−33 These studies have shown that PEGylation could be utilized not only to increase blood circulation time, but also to increase the stability of the secondary structure of the conjugated protein. Recent work by Xu et al. showed that atomistic MD simulations could

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METHODOLOGY The crystallographic structure of the BSA protein was taken from the RCSB Protein Data Bank (ID: 4F5S).35 The Reduce code36 within the AMBER16 software tools was used to assign the protonation state of each amino acid residue in BSA. PEG polymer chains for each conjugate were constructed using the PySimm software.37 The protein was modeled using the CHARMM C36m force field. BSA was PEGylated via an oxime link (Figure S1) and the linker molecule was modeled using the CGenFF force field, while the PEG chain was modeled using the CHARMM ether force field.38,39 The psfgen tool within the Visual Molecular Dynamics (VMD) software was used to generate corresponding topology and coordinate files of BSA and PEG-BSA conjugates.40 Each conjugate was then solvated with TIP3P water molecules in a orthorhombic box and the initial buffering distance between any edges of the conjugate (including protein and PEG) and the edge of the box was set to 14 Ålarge enough to avoid periodic images of BSA having an effect on PEG-BSA interactions in the central unit cell. Simulation system sizes for each of the conjugates are reported in Table S1. Na+ and Cl− ions were added to neutralize each system and mimic physiological concentration (0.15 M). Due to rising complexity of the conformational space explored by the PEG chain as its molecular weight increased, ten different initial configurations of PEG conjugated to the protein were generated to increase the sampling of the polymer around the protein surface. PEG end-to-end vectors in each initial structure were evenly distributed over the accessible protein surface (Figure S2). In other words, each initial configuration had its PEG chain covering a different region of the surface of BSA. PEG chains for each corresponding molecular weight (Mw) were also simulated in explicit water by B

DOI: 10.1021/acs.jpcb.8b12268 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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RESULTS AND DISCUSSION Conformation of PEG-BSA Bioconjugates. One of the primary focuses and often-asked questions of protein-PEG bioconjugates revolve around the determination of the structure of the PEGylated protein. There are numerous speculations toward the conformation that PEG adopts relative to the protein. It is believed that the strength of the protein− polymer interaction determines the overall conformation, or “shape”, of bioconjugates. Some of the most commonly described shapes include a dumbbell-like conformation, where the grafted PEG chain dangles away from the protein, and a shroud-like/“core−shell” conformation, where the PEG chain collapses onto or wraps around the protein surface. Unfavorable interactions between protein and PEG will keep PEG in water and away from the protein’s surface, leading to the dumbbell-like conformation. On the other hand, strong attractive interactions between protein and PEG will, if able to overcome entropy loss due to reduction in PEG’s mobility, enable PEG to wrap around the protein, forming the shroudlike conformation. In Figure 1, snapshots taken from MD simulations of PEG-BSA conjugates illustrate some of the possible conformations expected for bioconjugates with PEG chains of different Mw. While free PEG in solution may have characteristics of ideal chains,38 conjugation of the PEG chain to a protein may alter the behavior of the polymer based on the protein−polymer interactions. To evaluate this, experimental studies generally use SANS, small-angle X-ray scattering (SAXS), dynamic light scattering (DLS), and static light scattering (SLS) techniques. While most of these techniques can be used to probe dynamics of the whole conjugate, SANS can be used to study dynamics of a grafted PEG chain alone by contrast matching. However, the interpretation of the data can be difficult as it often requires strong assumptions about the overall structure and fitting data with corresponding mathematical models. When there exist many different forms of conjugates with varying conformations, it becomes difficult to develop a correct model using SANS alone. The points mentioned above, as well as other

themselvesthroughout this paper, these are referred to as free PEG, while PEG within conjugates will be referred to as grafted PEG. MD simulations were conducted using the NAMD 2.12 software package.41 The conjugate gradient algorithm within NAMD 2.12 was used to perform energy minimizations. Minimization was carried out in two phases. Initially, the protein backbone was restrained and minimized for 10 000 steps followed by another 10 000 steps with restraints on the protein backbone removed. Heating of each system was carried out under the following conditions: 50 K increments and a 20 ps interval in the NVT ensemble was used until the system reached the desired temperature of 300 K. Following heating, each system was subjected to an additional 500 ps NVT ensemble simulation time period before switching to NPT simulations at 1 bar. NPT simulations were conducted with a cutoff of 12 Å and a force switching function was applied at 10 Å. Long-range electrostatic interactions were incorporated via Particle Mesh Ewald summation. To maintain the system temperature at 300 K, the Langevin thermostat with a 1.0 ps−1 collision frequency was used. The SETTLE algorithm was used to constrain bond lengths involving hydrogen atoms, allowing a 2 fs time step.42 Simulation lengths for each conjugate are reported in Table 1. All analyses (see eqs S1 and S2) and visualizations were carried out using the VMD software40 and TCL and python scripts. Table 1. Summary of Simulations Performed in This Work for Each PEG-BSA Conjugate PEG molecular weight

PEG length

(Da)

(# of monomers)

2 000 5 000 10 000 20 000

45 113 227 454

simulation time (ns) conjugate

free polymer

× × × ×

300 300 300 300

10 10 10 10

150 150 150 150

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Figure 1. Observed conformations of PEG-BSA bioconjugates for different Mw of PEG (left to right: 2, 5, 10, 20 kDa). Blue and red circles represent average pervaded volume of BSA and PEG, respectively, using arrows to show Rg as the radius. The green arrow represents the distance between the centers of mass of PEG and BSA (DCOM PEG,BSA). C

DOI: 10.1021/acs.jpcb.8b12268 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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Through analysis of an MD simulation of free BSA, the Rg of the native protein was determined to be 27.5 ± 0.2 Å. Upon PEGylation, the Rg of BSA was not changed. However, as Mw of PEG increased from 2 to 20 kDa, the distance between the two centers of mass continued to decrease. In 2 kDa PEGylated BSA, the distance between the two centers of mass was 53.6 Å. This was significantly larger than the sum of the Rg values of free PEG and free BSA of 42.9 Å, consistent with a dumbbell-like conformation. For 5 and 10 kDa PEGylated BSA, the distance between two centers of mass was 44.4 and 41.0 Å, larger than the Rg of PEG but smaller than the sum of the Rg values of free PEG and free BSA of 49.1 and 56.1 Å, suggesting a partial coverage of the protein surface by PEG. At 20 kDa, the distance between the two centers of mass was 39.2 Å, smaller than the sum of the Rg values of free PEG and free BSA of 77.2 Å, and the Rg of grafted PEG was similar to that of free PEG, suggesting a shroud-like conformation for the conjugate. Therefore, when the Mw of grafted PEG increases from 2 kDa to 5 and 10 kDa, the Rg of grafted PEG becomes significantly larger than that of free PEG of the corresponding Mw. Furthermore, as the Mw of PEG reaches 20 kDa, the Rg of the grafted PEG becomes slightly smaller than that of free PEG. Such changes are consistent with a transition from little coverage to partial coverage to extended coverage of the protein by PEG. When there is little interaction between protein and PEG, grafted PEG behaves as free PEG, as seen in the case of 2 kDa PEGylated BSA. When PEG is partially covering the protein, the PEG chain’s dynamics are affected by the inaccessible volume occupied by protein, and the overall shape may be distorted due to interaction with the protein surface, leading to larger grafted PEG Rg, as seen in the case of 5 and 10 kDa PEG conjugates. When PEG is long enough to potentially wrap around the protein surface, the Rg of the grafted PEG is determined by the Rg of the protein and the thickness of the PEG polymer on the protein surface, which can be smaller than that of the free PEG, as seen in the case of 20 kDa PEG conjugates. If the interaction between the PEG polymer and the protein remains strong as the Mw of PEG continues to increase, it is expected that the Rg of the grafted PEG will become smaller than that of free PEG until all of the protein surface in which there is favorable interaction with PEG is covered. Such findings are consistent with a recent light scattering study.20 Although not specific to N-terminal conjugation, the study suggested that a structural change from dumbbell-like to shroud-like conformation is seen as the Mw of PEG increases in PEGylated BSA, and the transition occurs at 10 kDa Mw. It was also noticed that the standard deviation of Rg values for PEG and for the distance between the two centers of mass was significant, suggesting a very dynamic interaction between PEG and the protein in the conjugates. Local PEG density calculations around BSA, in which PEG density is larger than one-tenth of the highest density in each conjugate (Figure S7), also suggest higher protein surface coverage as the Mw of PEG increases. These calculations of the PEG density around the protein provide a direct view of the distribution of the PEG polymer around BSA for each of the bioconjugates. It was noticed that increased contact between the protein surface and PEG often led to higher PEG density in those regions, which could effectively reduce the accessibility of both the covered protein surface as well as nearby patches of the protein surface through a barrier/blocking layer.

issues present while characterizing bioconjugates, have been extensively discussed in recent work by Russell et al.43 Regardless of the adopted conformation of the PEG chain, PEGylation of a protein should ideally not disrupt its secondary structure, but rather promote conformational stability. However, effects of PEGylation widely vary; PEGylation has been shown to have positive, negative, or no effects on protein stability.25−33 Previous MD work by Lawrence et al. revealed that no specific secondary structure motif was more responsive to PEG induced stabilization than another, and no substantial change in secondary structure was reported.33 Furthermore, induced stabilization was found to be greatly dependent on PEG’s orientation. Other MD studies have likewise shown that PEGylation did not significantly change protein secondary structure.26,31 As a preliminary analysis to ensure system validity and to measure protein stability, RMSD values for the protein backbone and each domain of BSA were calculated and averaged across the ten simulations (Table S2). Results were compared between the varying PEG Mw systems and to an MD simulation (350 ns) of free BSA (no PEGylation), conducted with conditions similar to those described in the methodology section. RMSD analysis showed that, upon conjugation, deviation of the protein structure from the crystallographic structure was low. This observation was consistent throughout subdomains as well. Additionally, VMD’s STRIDE algorithm was employed to measure changes in secondary structure of BSA over time as a function of PEG Mw.44 Comparison of results for the varying PEG Mw systems and free BSA again showed no overall substantial changes in secondary structure (Figures S3 and S4). Radius of gyration and end-to-end distance of PEG polymers were also calculated as a function of time (Figures S5 and S6). Results show fluctuations and variability between samples, likely due to varying initial orientations, and indicate there is no single equilibration state. Thus, using many trajectories allows for analysis of multiple stable “states” of the conjugate with the shroud conformation. In MD simulations, one method for estimating the overall structure of the bioconjugate involves tracking and comparing the radius of gyration (Rg) of the protein and PEG, together or individually, with the distance between the centers of mass of the protein and PEG (DCOM PEG,BSA), as shown in Figure 1. For the dumbbell-like conformation to be favorable, the average distance is expected to be approximately equal to or greater than the summation of the Rg values of free PEG and free protein. For the shroud-like conformation, the average distance is expected to be less than the sum of Rg values of free PEG and free protein. In Table 2, Rg values of free PEG and grafted PEG are listed as well as the DCOM PEG,BSA for each bioconjugate. Table 2. Radius of Gyration for Free PEG and Grafted PEG, and Distance between Centers of Mass of PEG and BSA a (DCOM PEG,BSA) in Conjugates average radius of gyration (Å) PEG Mw (Da) 2 000 5 000 10 000 20 000

free PEG 15.4 21.6 28.6 49.7

(3.1) (4.7) (5.0) (7.4)

grafted PEG 14.9 25.7 34.1 48.6

(3.2) (6.6) (8.6) (8.9)

DCOM PEG,BSA (Å) 53.6 44.4 41.0 39.2

(9.4) (19.4) (16.6) (17.5)

a

Error bars shown in parentheses. D

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Figure 2. Contact timeline for 2, 5, 10, and 20 kDa PEGylated BSA trajectories. The color bar to the left represents the domain and subdomain to which the corresponding residue belongsIA (purple), IB (red), IIA (green), IIB (cyan), IIIA (brown), and IIIB (gray). Color map intensity (right) reflects how many atoms in each residue were in contact with the PEG polymer (within 5 Å).

Figure 3. Cartoon representation of BSA with the heatmap coloring scheme showing the interacting regions of 2 (a), 5 (b), 10 (c), and 20 (d) kDa PEGylated BSA conjugates. Images were generated with contact times scaled to 0−1 in a white-red scheme (white is 0 contact time and red is 1 contact time). N-terminals (cyan) of each protein are situated in the middle of their mirror images. Labels for BSA domains are provided in the first cartoon.

Determination of Preferential Interactions. Trajectories from MD simulations can serve as a rich source of information on the interactions between protein and PEG. This is important when one considers current discussions on the conformation of PEGylated proteins, especially the impact of Mw of PEG and numbers of grafted PEG on protein dynamics, that lead to speculation toward the exact cause of a specific conformation. Analysis of MD trajectories was conducted in the context of finding contacts between protein and PEG to possibly determine the cause for specific protein− PEG conformations being favored. A “contact” was recorded when the distance between atoms of BSA and the PEG chain was less than 5 Å (excluding hydrogen atoms in both selections). These contacts were monitored as a function of time for each conjugate. Data was collected over the entire 1.5 μs of simulation time for each corresponding Mw. As previously discussed, ten configurations of PEG of each Mw were

constructed to improve sampling of PEG interactions with the protein’s surface, whereby the end-group of the PEG chain was oriented toward different directions to facilitate contact exploration with as many different parts of BSA’s surface as possible. The time evolution of the contacts for each residue was measured for trajectories of every PEG-BSA conjugate and is presented in Figure 2. The color map shows how many atoms in each residue were in contact with the PEG polymer for a given time. In the case of 2 kDa PEGylated BSA, very limited interactions between BSA and PEG were seen, and even those few contacts did not last for more than 40 ns. Furthermore, interactions formed by 2 kDa grafted PEG were mainly localized near the N-terminal to which the polymer was grafted. When Mw of PEG increased to 5 kDa, significant contacts between residues in domain III and PEG were seen in two trajectories, and stable interactions with residues in E

DOI: 10.1021/acs.jpcb.8b12268 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry B Table 3. Unique Residues with Top Ten Maximum Residence Times for Each Mw PEGylated Systema 2 kDa PEG

5 kDa PEG

residue

time (ns)

Lys4

His9

32.7 8.8 28.1 6.2 25.2

Lys12

10 kDa PEG

20 kDa PEG

time (ns)

residue

time (ns)

residue

time (ns)

Lys20

146.5

Lys556

Lys136

150.0

Asn482

123.0

Lys180

150.0 81.7 109.3

Phe133

112.6

Lys131

107.3

Lys350

87.4

Lys12

9.6

Lys544

104.2

Lys544

Val54

Arg81 Glu45 Lys41 Thr2 Arg10

8.6 8.1 7.9 6.4 6.2

Lys350 Lys12 Val481 Leu397 Met547

91.6 75.4 62.9 56.6 52.9

Leu397 Asn404 Cys486 Met547 Phe553

Lys537 Pro492 Glu125 Leu115 Cys486

Glu63

6.1

Asn404

42.1

Phe501

55.7 41.6 54.5 49.3 48.9 43.1 42.4 39.6 39.6

112.2 64.6 57.9 50.6 49.1 41.6 46.4 36.4 36.2

Gln33

35.8

His3

residue

a

Residence time is reported as continuous time periods of contact for any given simulation (multiple residence time segments included separately).

low affinity sites.25 A previous study has also shown that out of the seven FA binding sites in HSA, two sites are located in domain III while a third site is located between domains I and II.45 Due to similarity between albumins, as well as similarity between SDS and FAs,35 dominant interactions between PEG and domains I and III, as observed in this study, may have limited the accessibility of SDS toward high affinity binding sites in BSA. In addition to FAs, domain III was identified as an important site for binding of several other substrates (catechins and small, anionic aromatic compounds).46,47 Therefore, providing detailed dynamics of PEGylated BSA could assist in designing potent drug carriers.39 To characterize the stability of observed PEG-BSA interactions, maximum residence times of PEG near each residue of BSA’s surface was measured. Residence time was defined as a continuous segment of time during which atoms of PEG (excluding hydrogen) resided within 5 Å of atoms in each amino acid residue (excluding hydrogen). Because residence time is reported as continuous time periods of contact for any given simulation and ten simulations were performed for each PEG Mw, one residue within BSA for a given PEG Mw could have multiple residence times. Therefore, Table 3 presents unique residues of BSA which formed stable interactions with PEG (top ten maximum residence times shown) for each Mw. For readability, the number of residence time segments for any given residue that fell within the top ten was limited to two. The top maximum residence times for residues in the 2 kDa PEGylated systems were observed to be much lower in magnitude when compared to other PEG Mw conjugate systems. This relates with the lower number of contacts seen in 2 kDa PEG systems and agrees with the observation that 2 kDa grafted PEG most likely behaves like free PEG. In other words, the resulting low residence times near the protein surface likely means PEG chains were in dumbbell-like conformations, dangling away from the protein. As Mw of PEG increases, top maximum residence times for residues likewise increase. Again, PEG’s transition into covering more of the protein’s surface area and assuming a shroud-like conformation explain these observations. Interestingly, it was found that the highest residence times of PEG were observed mainly near lysine residues. Upon investigation of lysine residues that formed favorable

domain I were seen in one of the trajectories. In trajectories for 10 and 20 kDa PEGylated BSA, a similar contact timeline between PEG and residues in domain I and increased interactions at residues in domain III were identified. Initial structures with PEG near domain II, on the other hand, often had reduced contacts between PEG and BSA after 100 ns. Consequently, there is a resulting lower density of PEG near domain II of BSA for all conjugates studied in this work. Further contact analyses were performed by measuring normalized contact time per residue of BSA for each conjugate to gain insight toward any preferred PEG−amino acid interactions as a function of PEG Mw. Results showed that the total time in which PEG is in contact with any given amino acid increases as a function of PEG Mw, corroborating the previous discussion (Figure S8). Additionally, while there is variation in peak locations for the distributions, certain regions become more favorable in forming protein−polymer interactions, such as patches of residues in domain III. To explore regions and identify amino acid residues of BSA with which PEG polymers established preferential interactions, scaled heatmaps of PEG-BSA contact times for each corresponding Mw were generated (Figure 3). For purposes of comparison, grafted sites (N terminal) of the visualized BSA proteins were excluded from the heatmap scheme. The highest contact time (seen in 20 kDa Pegylated BSA) was set to 1, and all other contact times were normalized with respect to it. For all PEG Mw except 20 kDa PEG, contacts were highest at the grafting site (N terminal). For 20 kDa PEGylated BSA, contacts were still predominant near the grafted site, with the residue of highest contact time being Val53, in domain I. As PEG Mw increased, more patches of increasing contact time began to appear near domain I and III, establishing “hotspots” on the BSA surface. According to Figure 3 and Figure S7, it was observed that domains I and III formed strong interactions with PEG chains as there was a higher density of PEG near these two domains. Localization of PEG near domain I and III could sterically hinder the accessibility of those substrates to other molecules which may have higher affinity for these domains. This may explain the experimentally observed changes in the binding profile of PEGylated BSA, where SDS was only able to bind with five low affinity sites out of the available two high and six F

DOI: 10.1021/acs.jpcb.8b12268 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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Figure 4. Snapshot of the looplike arrangement of PEG near lysine residues of a 10 kDa PEGylated system. Hydrogen atoms of the PEG chain are not shown for visualization purposes. Relevant PEG monomers and lysine residues (Lys180 and Lys556) are shown in CPK representation. Residues surrounding lysine are also shown in CPK representation and colored based on chemical nature: hydrophobic (yellow) and all others (purple).

Figure 5. Solvent accessible surface area for (a) hydrophobic residues and (b) total residues of BSA as a function of grafted PEG Mw. “Free”, on the x axis, refers to free BSA in the solution (without PEGylation).

from this figure that the environment is predominantly hydrophobic. To explore the effect of the chemical environment of lysine residues and resulting residence time, the hydrophobic surface area surrounding each lysine residue (within 5 Å) was calculated and is reported in Table S3. When considering residence time calculations, and the chemical nature of the region near the lysine residues, it was observed that maximum residence times of PEG were higher when residues surrounding lysine were hydrophobic. Therefore, while PEG−lysine interactions are favored due to hydrogen bonding, the stability of the looplike conformation depends on the chemical environment surrounding the lysine residues. Increased hydrophobicity around a lysine residue would allow PEG to favorably interact with both hydrophilic (hydrogen bonding between PEG’s oxygens and lysine’s hydrogens), and hydrophobic residues (via the carbon backbone in PEG and hydrophobic residues) on the protein’s surface. While the maximum residence times for PEG near hydrophobic residues were lower than that of PEG near lysine residues, the simultaneous hydrophobic interactions were clear when considering the collective interaction between PEG and protein. Figure 5 shows the SASA for both hydrophobic residues and all residues of BSA as a function of grafted PEG Mw. Consideration of SASA for hydrophobic residues showed that as the PEG Mw increased, solvent accessible hydrophobic surface area decreased. Also, results from calculations of total

interactions with PEG, it was found that PEG formed a stable looplike structure near those lysine residues. While the lifetime of the looplike conformation was not quantified, the shape was seen near many of the lysine residues that were in contact with PEG. A selected configuration of PEG illustrating looplike structures near lysine residues (Lys180 and Lys556) of a 10 kDa PEGylated system is shown in Figure 4. Arrangement of PEG around lysine allows oxygens in PEG to form hydrogen bonds with the residue. A previous purine crystallographic study has revealed that PEG has the capability to form interactions with polar lysine residues by making these looplike conformations, leaving the rest of the chain to dangle in the solution.48 Upon studying several other crystallographic structures (i.e., 4F5V, 3V08, 3VO9, 4JK4, 4ORO) from the Protein Data Bank, similar PEG conformations were found near lysine residues. Moreover, not all lysine residues presented preferred interaction sites for PEG. Within the simulation time of this work, lysine residues which interacted with PEG were observed to be mainly in domain I and III. Hence, while PEG−lysine interactions seem to be important, a lysine residue by itself may not provide strong enough interactions to keep PEG bound to the protein surface. Specifically, PEG-lysine stability depends on the surrounding chemical environment of the lysine residue which interacts with PEG. For example, Figure 4 presents the chemical nature of the residues surrounding lysine as either hydrophobic (yellow) or all others (purple). It can be observed G

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The Journal of Physical Chemistry B SASA show that as PEG Mw increased, there is an optimal Mw that allowed maximum protein surface coverage (around 10 kDa PEG), beyond which further coverage of the protein surface was not likely. This agrees with Yang’s previous MD study on PEGylation of insulin, which showed that PEG’s ability to shield the protein surface from water depended on the PEG chain length only up to a limitbeyond 4 kDa, increasing PEG length did not produce additional changes.26 Information from these MD simulations about the interplay of hydrophilic and hydrophobic interactions provides insight toward the specific conformations of PEG-BSA bioconjugates. In the case of shroud-like conformations, not all of the PEG chain forms close contacts with the protein surface. As the Mw of grafted PEG increases, several protein-PEG contacts are formed, which bring other parts of the polymer closer to the protein while the rest protrudes away (seen qualitatively in Figures 1 and S7). This behavior of PEG chains has been reported in previous experimental studies on PEGylated hemoglobin, human growth hormone, and lysozyme using SANS and SAXS methods.6,49 PEG can transform between different conformations with only a small energy barrier to overcome, and different conformations can bind preferentially to hydrophobic or hydrophilic atomic groups. Therefore, when the shroud-like conformation is formed, part of the protein surface is solvent accessible regardless of polymer Mw. This can be seen in a previous experimental study which found that only five out of eight binding sites in native BSA were retained upon mono-PEGylation of six linear PEG polymers between 5 and 60 kDa, irrespective of the specific PEGylated Mw.25 The atomistic insight toward PEG-BSA interactions can not only aid our understanding of the underlying mechanism behind PEG conformation transition with increasing Mw but also assist in the design of effective PEGylated drug molecules. Utilization of different initial conformations along with experimental data allowed probing of the BSA surface by PEG on a microsecond time scale to gain a better understanding of how PEG interacts with BSA. We also observed that the simulation time required to achieve an adequate sample of polymer conformation space increased dramatically as the Mw of the grafted polymer increased. Therefore, application of enhanced sampling methodologies50−52 and coarse-grained molecular dynamics simulations53−58 are needed to sufficiently explore the free energy landscape and conformational space for protein−polymer conjugates.

proteins will no longer be available for substrate binding while the rest will still be accessible. Concerning PEG-BSA interactions, lysine residues were found to play a dominant role due to the unique ability of PEG to coordinate around the residue and form looplike conformations. Measurement of maximum residence times, total contact times, and the hydrophobic SASA around lysine residues showed that, in addition to hydrogen bonding between PEG and lysine, the chemical environment surrounding the lysine residues served an important role in increasing the contact time of PEG. Analysis also showed that PEG-BSA interactions do not substantially change protein stability, with secondary structure generally being maintained.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.8b12268.

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Schematic of oxime linking molecule; initial structures of PEGylated systems; RMSD calculations for the protein backbone and each domain of BSA for 2, 5, 10, and 20 kDa PEGylated BSA conjugates as well as for free BSA; secondary structure analyses for PEGylated and native BSA systems (all residues and domain I); density visualizations of PEGylated BSA systems; normalized contact time distributions; lysine residue residence times and hydrophobic SASA values (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]fl.edu. Phone: +1 (352) 294-3488. ORCID

Ping Lin: 0000-0002-6141-5424 Coray M. Colina: 0000-0003-2367-1352 Author Contributions #

Aravinda Munasinghe and Akash Mathavan contributed equally to this work.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge the financial assistance given by the University of Florida Preeminence Initiative and the US National Science Foundation, SI2 program, Grant: 1613155. University of Florida Research Computing is also acknowledged for providing computational support that have contributed to the research results reported in this publication.

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CONCLUSION In this work, the dynamics of N-terminal mono-PEGylated BSA conjugates were studied, using atomistic simulations, as a function of grafted PEG Mw to understand how PEG interacts with BSA. Simulation data was analyzed to explore dynamics of the PEG chain and to investigate interactions between PEG and the protein surface. While Rg analyses could not definitively differentiate dynamics of free and grafted PEG, DCOM PEG,BSA calculations and trajectory visualization showed that as PEG Mw increased, the level of PEG-BSA interactions increased with the PEG shape transitioning from a dumbbelllike conformation to a shroud-like conformation around 10 kDa. Additionally, it was observed that BSA has PEG hotspots on domains I and III, while the remainder of the PEG chain protrudes away from the protein surface. This offers a possible explanation for previous observations showing that, irrespective of the grafted PEG Mw, some binding sites on PEGylated

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REFERENCES

(1) Duncan, R. The Dawning Era of Polymer Therapeutics. Nat. Rev. Drug Discovery 2003, 2, 347−360. (2) Heredia, K. L.; Maynard, H. D. Synthesis of Protein−polymer Conjugates. Org. Biomol. Chem. 2007, 5 (1), 45−53. (3) Pelegri-O’Day, E. M.; Lin, E.-W.; Maynard, H. D. Therapeutic Protein−Polymer Conjugates: Advancing Beyond PEGylation. J. Am. Chem. Soc. 2014, 136 (41), 14323−14332. (4) Dozier, K. J.; Distefano, D. M. Site-Specific PEGylation of Therapeutic Proteins. Int. J. Mol. Sci. 2015, 16 (10), 25831−25864. (5) Kolate, A.; Baradia, D.; Patil, S.; Vhohra, I.; Kore, G.; Misra, A. PEG  A Versatile Conjugating Ligand for Drugs and Drug Delivery Systems. J. Controlled Release 2014, 192, 67−81. H

DOI: 10.1021/acs.jpcb.8b12268 J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B (6) Pai, S. S.; Hammouda, B.; Hong, K.; Pozzo, D. C.; Przybycien, T. M.; Tilton, R. D. The Conformation of the Poly(Ethylene Glycol) Chain in Mono-PEGylated Lysozyme and Mono-PEGylated Human Growth Hormone. Bioconjugate Chem. 2011, 22 (11), 2317−2323. (7) Turecek, P. L.; Bossard, M. J.; Schoetens, F.; Ivens, I. A. PEGylation of Biopharmaceuticals: A Review of Chemistry and Nonclinical Safety Information of Approved Drugs. J. Pharm. Sci. 2016, 105 (2), 460−475. (8) Wu, H.; Zhu, L.; Torchilin, V. P. PH-Sensitive Poly(Histidine)PEG/DSPE-PEG Co-Polymer Micelles for Cytosolic Drug Delivery. Biomaterials 2013, 34 (4), 1213−1222. (9) Patri, A. K.; Majoros, I. J.; Baker, J. R. Dendritic Polymer Macromolecular Carriers for Drug Delivery. Curr. Opin. Chem. Biol. 2002, 6 (4), 466−471. (10) Le Cœur, C.; Combet, S.; Carrot, G.; Busch, P.; Teixeira, J.; Longeville, S. Conformation of the Poly(Ethylene Glycol) Chains in DiPEGylated Hemoglobin Specifically Probed by SANS: Correlation with PEG Length and in Vivo Efficiency. Langmuir 2015, 31 (30), 8402−8410. (11) Oishi, M.; Hayashi, H.; Itaka, K.; Kataoka, K.; Nagasaki, Y. PHResponsive PEGylated Nanogels as Targetable and Low Invasive Endosomolytic Agents to Induce the Enhanced Transfection Efficiency of Nonviral Gene Vectors. Colloid Polym. Sci. 2007, 285 (9), 1055−1060. (12) Fee, C. J.; Van Alstine, J. M. Prediction of the Viscosity Radius and the Size Exclusion Chromatography Behavior of PEGylated Proteins. Bioconjugate Chem. 2004, 15 (6), 1304−1313. (13) Manjula, B. N.; Tsai, A.; Upadhya, R.; Perumalsamy, K.; Smith, P. K.; Malavalli, A.; Vandegriff, K.; Winslow, R. M.; Intaglietta, M.; Prabhakaran, M.; et al. Site-Specific PEGylation of Hemoglobin at Cys-93(β): Correlation between the Colligative Properties of the PEGylated Protein and the Length of the Conjugated PEG Chain. Bioconjugate Chem. 2003, 14 (2), 464−472. (14) Cattani, G.; Vogeley, L.; Crowley, P. B. Structure of a PEGylated Protein Reveals a Highly Porous Double-Helical Assembly. Nat. Chem. 2015, 7, 823−828. (15) Lam, C. N.; Chang, D.; Wang, M.; Chen, W.-R.; Olsen, B. D. The Shape of Protein-Polymer Conjugates in Dilute Solution. J. Polym. Sci., Part A: Polym. Chem. 2016, 54 (2), 292−302. (16) He, L.; Wang, H.; Garamus, V. M.; Hanley, T.; Lensch, M.; Gabius, H.-J.; Fee, C. J.; Middelberg, A. Analysis of MonoPEGylated Human Galectin-2 by Small-Angle X-Ray and Neutron Scattering: Concentration Dependence of PEG Conformation in the Conjugate. Biomacromolecules 2010, 11 (12), 3504−3510. (17) Liu, Z.; Chen, X. Simple Bioconjugate Chemistry Serves Great Clinical Advances: Albumin as a Versatile Platform for Diagnosis and Precision Therapy. Chem. Soc. Rev. 2016, 45 (5), 1432−1456. (18) Sahu, R. K.; Nacharaju, P.; Manjula, B. N.; Acharya, S. A. Induced Plasma Expander-like Properties as a Function of PEGChains on Extension Arm Facilitated PEGylation of Albumin: “Mushroom to Brush-Like” Conformational Transition of the PEGAlbumin Conjugate. Artif. Cells, Blood Substitutes, Biotechnol. 2009, 37 (6), 245−256. (19) Fee, C. J. Size Comparison between Proteins PEGylated with Branched and Linear Poly(Ethylene Glycol) Molecules. Biotechnol. Bioeng. 2007, 98 (4), 725−731. (20) Ferebee, R.; Hakem, I. F.; Koch, A.; Chen, M.; Wu, Y.; Loh, D.; Wilson, D. C.; Poole, J. L.; Walker, J. P.; Fytas, G.; et al. Light Scattering Analysis of Mono- and Multi-PEGylated Bovine Serum Albumin in Solution: Role of Composition on Structure and Interactions. J. Phys. Chem. B 2016, 120 (20), 4591−4599. (21) Mehtala, J. G.; Kulczar, C.; Lavan, M.; Knipp, G.; Wei, A. Cys34-PEGylated Human Serum Albumin for Drug Binding and Delivery. Bioconjugate Chem. 2015, 26 (5), 941−949. (22) Yu, M.; Ding, Z.; Jiang, F.; Ding, X.; Sun, J.; Chen, S.; Lv, G. Analysis of Binding Interaction between Pegylated Puerarin and Bovine Serum Albumin by Spectroscopic Methods and Dynamic Light Scattering. Spectrochim. Acta, Part A 2011, 83 (1), 453−460.

(23) Rawat, S.; Raman Suri, C.; Sahoo, D. K. Molecular Mechanism of Polyethylene Glycol Mediated Stabilization of Protein. Biochem. Biophys. Res. Commun. 2010, 392 (4), 561−566. (24) Bekale, L.; Agudelo, D.; Tajmir-Riahi, H. A. The Role of Polymer Size and Hydrophobic End-Group in PEG−Protein Interaction. Colloids Surf., B 2015, 130, 141−148. (25) Plesner, B.; Free, C. J.; Westh, P.; Nielsen, A. D. Effects of PEG Size on Structure, Function and Stability of PEGylated BSA. Eur. J. Pharm. Biopharm. 2011, 79 (2), 399−405. (26) Yang, C.; Lu, D.; Liu, Z. How PEGylation Enhances the Stability and Potency of Insulin: A Molecular Dynamics Simulation. Biochemistry 2011, 50 (13), 2585−2593. (27) Mu, Q.; Hu, T.; Yu, J. Molecular Insight into the Steric Shielding Effect of PEG on the Conjugated Staphylokinase: Biochemical Characterization and Molecular Dynamics Simulation. PLoS One 2013, 8 (7), e68559. (28) Xu, D.; Smolin, N.; Shaw, R. K.; Battey, S. R.; Tao, A.; Huang, Y.; Rahman, S. E.; Caylor, M. L. Molecular Insights into the Improved Clinical Performance of PEGylated Interferon Therapeutics: A Molecular Dynamics Perspective. RSC Adv. 2018, 8 (5), 2315−2322. (29) Lawrence, P. B.; Gavrilov, Y.; Matthews, S. S.; Langlois, M. I.; Shental-Bechor, D.; Greenblatt, H. M.; Pandey, B. K.; Smith, M. S.; Paxman, R.; Torgerson, C. D.; et al. Criteria for Selecting PEGylation Sites on Proteins for Higher Thermodynamic and Proteolytic Stability. J. Am. Chem. Soc. 2014, 136 (50), 17547−17560. (30) Pandey, B. K.; Smith, M. S.; Price, J. L. Cys i − Lys i + 3 − Lys i + 4 Triad: A General Approach for PEG-Based Stabilization of αHelical Proteins. Biomacromolecules 2014, 15 (12), 4643−4647. (31) Hamed, E.; Xu, T.; Keten, S. Poly(Ethylene Glycol) Conjugation Stabilizes the Secondary Structure of α-Helices by Reducing Peptide Solvent Accessible Surface Area. Biomacromolecules 2013, 14 (11), 4053−4060. (32) Jain, A.; Ashbaugh, H. S. Helix Stabilization of Poly(Ethylene Glycol)−Peptide Conjugates. Biomacromolecules 2011, 12 (7), 2729− 2734. (33) Lawrence, P. B.; Price, J. L. How PEGylation Influences Protein Conformational Stability. Curr. Opin. Chem. Biol. 2016, 34, 88−94. (34) Settanni, G.; Zhou, J.; Suo, T.; Schöttler, S.; Landfester, K.; Schmid, F.; Mailänder, V. Protein Corona Composition of Poly(Ethylene Glycol)- and Poly(Phosphoester)-Coated Nanoparticles Correlates Strongly with the Amino Acid Composition of the Protein Surface. Nanoscale 2017, 9 (6), 2138−2144. (35) Bujacz, A. Structures of Bovine, Equine and Leporine Serum Albumin. Acta Crystallogr., Sect. D: Biol. Crystallogr. 2012, 68 (10), 1278−1289. (36) Word, J. M.; Lovell, S. C.; Richardson, J. S.; Richardson, D. C. Asparagine and Glutamine: Using Hydrogen Atom Contacts in the Choice of Side-Chain Amide Orientation. J. Mol. Biol. 1999, 285 (4), 1735−1747. (37) Fortunato, M. E.; Colina, C. M. Pysimm: A Python Package for Simulation of Molecular Systems. SoftwareX 2017, 6, 7−12. (38) Lee, H.; Venable, R. M.; MacKerell, A. D.; Pastor, R. W. Molecular Dynamics Studies of Polyethylene Oxide and Polyethylene Glycol: Hydrodynamic Radius and Shape Anisotropy. Biophys. J. 2008, 95 (4), 1590−1599. (39) Mayne, C. G.; Saam, J.; Schulten, K.; Tajkhorshid, E.; Gumbart, J. C. Rapid Parameterization of Small Molecules Using the Force Field Toolkit. J. Comput. Chem. 2013, 34 (32), 2757−2770. (40) Humphrey, W.; Dalke, A.; Schulten, K. VMD: Visual Molecular Dynamics. J. Mol. Graphics 1996, 14 (1), 33−38. (41) Phillips, J. C.; Braun, R.; Wang, W.; Gumbart, J.; Tajkhorshid, E.; Villa, E.; Chipot, C.; Skeel, R. D.; Kalé, L.; Schulten, K. Scalable Molecular Dynamics with NAMD. J. Comput. Chem. 2005, 26 (16), 1781−1802. (42) Miyamoto, S.; Kollman, P. A. SETTLE: An Analytical Version of the SHAKE and RATTLE Algorithm for Rigid Water Molecules. J. Comput. Chem. 1992, 13, 952−962. I

DOI: 10.1021/acs.jpcb.8b12268 J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B (43) Russell, A. J.; Baker, S. L.; Colina, C. M.; Figg, C. A.; Kaar, J. L.; Matyjaszewski, K.; Simakova, A.; Sumerlin, B. S. Next Generation Protein-Polymer Conjugates. AIChE J. 2018, 64 (9), 3230−3245. (44) Heinig, M.; Frishman, D. STRIDE: A Web Server for Secondary Structure Assignment from Known Atomic Coordinates of Proteins. Nucleic Acids Res. 2004, 32, 500−502. (45) Simard; Jeffrey, R.; Zunszain, P. A.; Hamilton, J. A.; Curry, S. Location of High and Low Affinity Fatty Acid Binding Sites on Human Serum Albumin Revealed by NMR Drug-Competition Analysis. J. Mol. Biol. 2006, 361, 336−351. (46) Li, Y.; An, L.; Huang, Q. Replica Exchange Monte Carlo Simulation of Human Serum Albumin−Catechin Complexes. J. Phys. Chem. B 2014, 118 (35), 10362−10372. (47) Hajduk, P. J.; Mendoza, R.; Petros, A. M.; Huth, J. R.; Bures, M.; Fesik, S. W.; Martin, Y. C. Ligand Binding to Domain-3 of Human Serum Albumin: A Chemometric Analysis. J. Comput.-Aided Mol. Des. 2003, 17 (2), 93−102. (48) Sinha, S. C.; Krahn, J.; Shin, B. S.; Tomchick, D. R.; Zalkin, H.; Smith, J. L. The Purine Repressor of Bacillus Subtilis: A Novel Combination of Domains Adapted for Transcription Regulation. J. Bacteriol. 2003, 185 (14), 4087−4098. (49) Svergun, D. I.; Ekström, F.; Vandegriff, K. D.; Malavalli, A.; Baker, D. A.; Nilsson, C.; Winslow, R. M. Solution Structure of Poly(Ethylene) Glycol-Conjugated Hemoglobin Revealed by SmallAngle X-Ray Scattering: Implications for a New Oxygen Therapeutic. Biophys. J. 2008, 94 (1), 173−181. (50) Bernardi, R. C.; Melo, M. C. R.; Schulten, K. Enhanced Sampling Techniques in Molecular Dynamics Simulations of Biological Systems. Biochim. Biophys. Acta, Gen. Subj. 2015, 1850 (5), 872−877. (51) Kasahara, K.; Sakuraba, S.; Fukuda, I. Enhanced Sampling of Molecular Dynamics Simulations of a Polyalanine Octapeptide: Effects of the Periodic Boundary Conditions on Peptide Conformation. J. Phys. Chem. B 2018, 122 (9), 2495−2503. (52) Paul, W.; Müller, M. Enhanced Sampling in Simulations of Dense Systems: The Phase Behavior of Collapsed Polymer Globules. J. Chem. Phys. 2001, 115 (2), 630−635. (53) Peng, J.; Zhang, Z. Simulating Large-Scale Conformational Changes of Proteins by Accelerating Collective Motions Obtained from Principal Component Analysis. J. Chem. Theory Comput. 2014, 10 (8), 3449−3458. (54) Stanzione, F.; Jayaraman, A. Hybrid Atomistic and CoarseGrained Molecular Dynamics Simulations of Polyethylene Glycol (PEG) in Explicit Water. J. Phys. Chem. B 2016, 120 (17), 4160− 4173. (55) Lee, H.; de Vries, A. H.; Marrink, S.-J.; Pastor, R. W. A CoarseGrained Model for Polyethylene Oxide and Polyethylene Glycol: Conformation and Hydrodynamics. J. Phys. Chem. B 2009, 113 (40), 13186−13194. (56) Wang, Q.; Keffer, D. J.; Nicholson, D. M. A Coarse-Grained Model for Polyethylene Glycol Polymer. J. Chem. Phys. 2011, 135 (21), 214903. (57) Prasitnok, K.; Wilson, M. R. A Coarse-Grained Model for Polyethylene Glycol in Bulk Water and at a Water/Air Interface. Phys. Chem. Chem. Phys. 2013, 15 (40), 17093. (58) Ramezanghorbani, F.; Lin, P.; Colina, C. M. Optimizing Protein−Polymer Interactions in a Poly(Ethylene Glycol) CoarseGrained Model. J. Phys. Chem. B 2018, 122 (33), 7997−8005.

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