Protein-Like Dynamics of Polycarbonate Polymers in Water - The

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Protein-Like Dynamics of Polycarbonate Polymers in Water Jernej Zidar, Geraldine Songlen Lim, Daniel Wee Loong Cheong, and Marco Klähn J. Phys. Chem. B, Just Accepted Manuscript • Publication Date (Web): 30 Nov 2014 Downloaded from http://pubs.acs.org on December 1, 2014

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The Journal of Physical Chemistry

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28 November 2014 – REVISION

Protein-Like Dynamics of Polycarbonate Polymers in Water Jernej Zidar,a,1 Geraldine S. Lim,a Daniel W. Cheong,a Marco Klähnb,2 a) Institute of High Performance Computing, Agency for Science, Technology and Research, 1 Fusionopolis Way, #16-16, 138632 Singapore, Rep. of Singapore b) Institute of Chemical and Engineering Sciences, Agency for Science, Technology and Research, 1 Pesek Road, Jurong Island, 627833, Rep. of Singapore

Corresponding authors: 1) [email protected] 2) [email protected]

Abstract The dynamics of amphiphilic peptide-mimicking polycarbonate polymers are investigated, considering variations in polymer length, monomer sequence, and monomer modification. The polymers are simulated in aqueous solution with atomistic molecular dynamics simulations and an empirical force field. Various structural polymer properties, interaction strengths and solvation free energies are derived. It is found that water is a less favorable solvent for these polymers than for peptides. Moreover, polymers readily adopt irreversibly a compact state that consists of a variety of distinct compact conformations that are adopted through frequent transitions. Furthermore, the polymers exhibit a strong propensity to form large aggregates. The driving forces for these processes appear to be a hydrophobic effect and more favorable polymer – solvent interactions of aggregates that overcome the otherwise strong mutual repulsion between the positively charged polymers. Replacing hydrophobic residues with polar side chains destabilize the compact conformations of the polymers. Our results also indicate that the monomer sequence has little effect on the overall solvation properties of the polymer molecule. However, the sequence influences flexibility and compactness of the monomer in solution. Overall, the

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results of this work confirm the protein-like characteristics of these polymers and elucidate the role of single residues in influencing the structure and aggregation in aqueous solution.

Keywords: polycarbonate, cationic, aggregation, molecular dynamics, polymer, solvation free energy, amphiphile

1. Introduction Antibiotics were discovered at the beginning of the 20th century and they are an effective means to fight many lethal diseases caused by bacteria. Classical antibiotics work by binding to different protein targets located either on the bacterial membrane or inside the bacterial cell. This in turn causes cell lysis or stops the bacterial replication.1-4 In the decades that followed their discovery, the widespread use and misuse of antibiotics led to the rise of multiresistant bacterial strains that do not respond to any antibiotics.5 This in turn, has prompted the search for alternative compounds with antimicrobial properties. The search for novel antimicrobial molecules that could replace antibiotics led to the discovery of antimicrobial peptides. Antimicrobial peptides are part of the innate immune system that complements the cell-mediated immune response.6,7 These peptides are able to swiftly kill a wide range of bacteria even before the cell-mediated immune response develops. All identified antimicrobial peptides share some common features: their net charge is positive, they contain both hydrophobic and hydrophilic residues and are able to disrupt the integrity of the plasma membrane.7,8 The mode of action appears to depend on the size of the peptide but the end result is always the disruption of the bacterial membrane and resulting death of the bacterial cell.1,9 Details on how exactly antimicrobial peptides exert their effects on bacterial cells are still scarce, which combined with their relatively short blood half life and high production price, non-specificity and the inability to enhance their specificity to be effective only against certain bacterial strains and/or species limit their widespread use as a viable alternative to conventional antibiotics.1,10 Another promising avenue of research is the application of various artificial polymer

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molecules that mimic such antimicrobial peptides. Polymer synthesis is relatively straightforward and the ability to tweak their properties and biocompatibility are only a few of the features that reveal the high potential of these peptide-mimicking polymers as alternative antimicrobials.11 Similarly to their protein counterparts, the polymers are amphipathic molecules. The antimicrobial polymer molecules that have been reported so far include guanidine-containing polymers, halogen polymers and polymers with quaternary nitrogen atoms.12 The mode of action of artificial antimicrobial polymers and naturally occurring peptides appears to be similar. Both are able to induce cell lysis by binding to the bacterial plasma membrane and causing its disruption.9,13,14 Moreover, the possibility to fine tune the polymer properties in order to achieve specific bactericidal activity by changing and modifying the constituting monomers provide additional opportunities to generate promising and highly specific antimicrobial compounds. One family of polymers that is being actively investigated is the polycarbonate family of polymers.15-17 Polycarbonate polymers are typically composed of two types of monomers that can be either charged or hydrophobic and are linked by a carbonate (i.e. -O-CO-O-) group. A polymer termed the triblock is one where the charged and hydrophobic residues are grouped together within the polymer molecule. These two sections are then linked together with a linker residue. If the polymer is composed of an arbitrary alternating sequence of charged and hydrophobic residues, the polymer is called a random polymer. Both types of polycarbonate polymer molecules can be synthesized in a very efficient manner.15,16 Polycarbonate polymers tend to form nanoparticles with an approximate size of 0.1 m that are able to kill Gram-positive bacteria and methicillin-resistant Staphylococcus aureus and fungi.15 These micelles can also be modified to release an active compound in an environment- or tissue-dependent manner.18 The observed antimicrobial activity of the polycarbonate polymers depends on the length of the polymer chain, the type of monomers used and their sequence. An alternating sequence of charged and hydrophobic units results in polymer molecules that readily self-assemble in solution but the resulting complexes are only transient and can easily disassemble under changing conditions.17 This property could be desirable as it may facilitate the disruption of the bacterial membrane. It has been observed that polycarbonate polymers in an aqueous environment can easily

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switch between the various different conformations that eventually leads to self-assembly of the observed nanoparticles. Depending on the type of monomeric units such complexes can be either transient or stable. The underlying molecular mechanisms that determine the structure of these polymers and their assemblies are experimentally often not directly accessible. Therefore, to gain insight into structure and dynamics of such polymers and the effect of solvation, molecular modeling techniques have been frequently applied. 19,20 By using all-atom molecular dynamics (MD) simulations it is possible to study one or several polymer molecules of varying composition and sequence in a well-defined environment. Recently, MD simulations were used to characterize the structural properties of solvated polymethacrylate polymers.21 The overall conformation depended heavily on the polymer composition. Polymers composed of only charged monomers adopted an extended helical conformation, which can be explained by the electrostatic repulsion of the charged side chains. Polymers with an alternating sequence of hydrophobic and charged units, however, tended to adopt either a crescent-like conformation or formed short segments of a helical turn. Overall, polymers with alternating units tended to adopt a less compact conformation, demonstrating the sensitivity of polymer structures in solution with respect to their monomer sequence. Furthermore, in the same study evidence was found that a flexible polymer backbone could improve biological activity rather than hindering it. 9,21 Bisphenol A polycarbonate22 was studied using the Dreiding force field. 23 MD simulations were able to reproduce both, the crystal structure of bisphenol A polycarbonate and X-ray scattering data, which indicated that the computational model was able to capture some of the most salient features that are observable in experiments. The same polymer was also simulated at the coarse-grain level, which significantly reduced the number of simulated particles, thus allowing for longer simulation times in a shorter amount of time. The main caveat of this approach, however, is that it may introduce artifacts in the polymer structure and dynamics. It was found, however, that such artifacts could be effectively removed by converting the system from a coarse-grained representation back to an all-atom model with subsequent equilibration.24

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In the present study we used all-atom MD to investigate the behavior of polycarbonate polymers with various chain lengths, different composition and two different residue sequences in an aqueous solution. Several structural and dynamic parameters were determined together with the free energy of solvation of the three shortest polymer molecules. Additionally, internal interactions within the polymers molecules were analyzed as well as interactions of polymers with other polymers and with surrounding water. Furthermore, polymer aggregation has been studied to provide an explanation for the experimentally observed aggregation propensity of this class of polymer molecules.

2. Methods 2.1 Monomer Nomenclature The polycarbonate polymers evaluated in this study are composed of four different monomers with the following IUPAC names: 3-(trimethylamino) propyl 2-(hydroxymethyl)-2methylsuccinate chloride (Fig. 1a), ethyl 2-(hydroxymethyl)-2-methylsuccinate (Fig. 1b), 2carbamoyl-1-carbonyloxy-3-hydroxy-2-methylpropane

(Fig.

1c)

and

1-carbonyloxy-2-

(hydroxymethyl)-2-methyl-3-oxo-4-phenylbutane (Fig. 1d). The monomers were chosen in such a way that the resulting polymer molecules were chemically the same as those used in experimental studies before.14,15 The side chains of the monomers resemble amino acids. This similarity was used to designate a shorthand notation that is used throughout this paper. The side chain shown in Figure 1a is similar to lysine, hence we designated it as ALY (Alike LYsine). The side chain shown in Figure 1b is similar to the side chain of the amino acid valine, hence the name AVA (Alike VAline). The third monomer is called AVN and is similar to monomer AVA, where the alkyl side chain was replaced by an amide group. The fourth monomer is called APH, because its side chain is similar to the side chain of the amino acid phenylalanine. The monomer AVN was added to the group of considered monomers to investigate the influence of the hydrophobic side chain of AVA. It is important that the chosen monomers are capable of constituting a cationic amphiphilic

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polymer molecule. The cationic part is in this case formed by the residues ALY, while the hydrophobic part is constituted by AVA and APH. The monomer AVN is weakly polar.

2.2 Force Field Parameterization of the Monomeric Units The initial monomer structures were generated in Molden.25 These initial structures were later further optimized using Gaussian 0926 with density functional theory (DFT) using the B3LYP hybrid functional and a 6-31G(d) basis set.27-31 The potential energy of the monomers was described using a standard functional form, such as shown e.g. in ref. 32. Atom types and corresponding bonded and non-bonded interaction parameters for bond, angle and dihedral potentials as well as partial charges and LennardJones parameters conforming to the CHARMM General Force Field (CGenFF 2b6, program version 0.9.1 beta) were assigned using the ParamChem web portal. 32-34 The assigned CHARMM atom types are available in the Supporting Information (SI) in Fig. S2. The ParamChem web portal assigns atom types and corresponding force field parameters according to deterministic rules that operate on the molecular graph. The degree of expected transferability of this assignment to the molecule in question is reflected in a penalty score that is associated with each assigned parameter, where parameters with large penalty values typically require further validation.33,34 The internal coordinates based on QM minimized geometries were added to the CHARMM topology entries. This enabled us to construct 3D structures of arbitrary polymer sequences using CHARMM’s model building facility. The CHARMM force field is available in the SI.

2.3 Building Systems of Solvated Polycarbonate Polymers Polycarbonate polymers that are laid out according to the general formula (ALY) n-(AVA)nAPH-(AVA)n-(ALY)n are called in the following triblock polymers. The unit is thus composed of two symmetrical units joined by the monomer APH. We generated a series of triblock polymers with n=1-5. A triblock polymer for n=2 is depicted in Figure 1a. For n=5 a second polymer molecule was constructed with the AVA residues being replaced by residues AVN.

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Also polymers with the sequence (ALY-AVA)n-APH-(AVA-ALY)n were simulated, which will be called “random” polymers in the following to distinguish the sequence from a sequence with successive same residues. The sequence of ALY and AVA monomers is alternating, followed by residue APH and another alternating sequence of residues ALY and AVA. A series of random polymers with n=2-5 was generated. A random polymer for n=2 is depicted in Figure 1b. For n=5 a second polymer molecule was constructed where the AVA residues were replaced by residues AVN. To further investigate the mutual interaction between polymer molecules a series of systems was constructed with two polymer molecules per unit cell for both the triblock and random sequences. A system with two polymer molecules was constructed by translating a copy of the original molecule along the y-axis for 2.0 nm. The overall distance between the two units is large enough to prevent any accidental contacts between the two units, which may limit their conformational freedom in subsequent MD simulations. In the next step, the polycarbonate polymer molecules were solvated with a 2.0 nm thick layer of TIPS3P 35 water molecules. Electroneutrality of the generated systems was achieved by adding a corresponding number of chlorine and sodium ions. These ions were added in excess to ensure a physiologically relevant concentration of NaCl (0.154 mol/L).

2.4 Specification of MD Simulations The equilibration of the systems was performed by a series of energy minimizations using the steepest descents method followed by MD simulations. In the first part of the energy minimization the solutes were fixed using position restraints set to 1000 kJ mol -1 nm2. For the second part those restraints were removed. Each equilibration consisted of an initial MD simulation in the isochoric – isothermal ensemble (NVT) and a successive simulation in the isobaric – isothermal ensemble (NPT). For both NVT and NPT simulations the number of steps was set to 500,000 with a time step of 2 fs, resulting in simulation lengths of 1 ns in total for initial equilibrations. Other technical aspects are listed in SI. Subsequently, simulations were continued for 50 ns using the same simulation parameters.

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During these simulations trajectory and energy data was collected every 1000 steps for analysis.

2.5 Analysis of Polymer Structure and Energetics Trajectories were analyzed by calculating the root mean square deviations (RMSD) for both the atoms of the polymer molecule backbone and for the whole polymer molecule. The RMSD was computed using the structure from the first step of the production run as a reference. End-to-end distances were calculated for the polymer molecules. The end-to-end distance was defined as the distance between atom O1T of the first ALY residue and atom O4T of the last ALY residue in the polymer sequence that represent the terminal atoms of the polymer molecules. A cluster analysis for simulated polymer structures was performed using the RMSD-based GROMOS algorithm implemented in GROMACS.36 The RMSD was measured between polymer backbone atoms after least-square translational and rotational fit. Structure neighbors were counted up to an RMSD cut-off of 0.3 nm. The cluster method was applied to the last 25 ns of the trajectories of triblock and random polymers for n=5, respectively. Solvent accessible surface areas (SAS) were computed for all the systems surveyed in this study. Atomic van der Walls radii used were based on corresponding atom types present in the force field. The contributions to the SAS were evaluated as well by splitting the system into a hydrophilic and a hydrophobic part, where atoms with a partial charge larger than 0.2 e were considered to be hydrophilic. For the calculation of solvation free energies the ChemSol 2.1 package was used that describes the solvent with Langevin dipoles.37,38 In the Langevin dipole model the solvent is approximated by polarizable dipoles fixed on a cubic grid and the solute is described by point charges within the grid of the Langevin dipoles. The parametrization is described elsewhere.37,38 The computed solvation energies includes not only the electrostatic solute8



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dipole interactions are considered but also hydrophobic effects, van der Waals interactions between solute and water, coupled with long range corrections and solvent polarization. Technical aspects are described in SI. Three sets of data were analyzed with ChemSol: (1) 50 structures for the system surveyed from the production run trajectory, (2) 1000 structures from a 20 ns simulation with parameters from the production run, where the terminal atoms (O1T and O4T, respectively) were fixed with a position restraint of 10 kJ mol -1nm2 and (3) 1000 structures from the last 20 ns of the production run.

2.6 Used Software The molecular modeling package CHARMM (version 36b)

39,40

was used to generate the

initial polymer models. MD simulations were performed using the freely-available molecular modeling package GROMACS (version 4.5.5). 41-45 GROMACS was also used for the preparation of the polymer systems; equilibration, production runs and its built-in tools were used to analyze the trajectories. The polymer systems were visualized using VMD (version 1.9.1).46

3. Results and Discussion Using all-atom molecular dynamics and the CHARMM General Force field we studied the conformational changes of several polycarbonate polymers in an aqueous solution. Polymer molecules of different lengths (example in Fig. 1), different composition and monomer sequence were generated as well as assemblies of several polymers. The aim was to identify through comparison the effect of these polymer variations on the overall polymer properties.

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3.1. Change of Polymer Structure Over Time RMSD (Fig. 2a) and end-to-end distance (Fig. 2b) were computed in order to determine when and if the system reaches an equilibrium state during the 50 ns production runs. RMSD plots for the backbone atoms indicate there is a distinct and fast conformational change in the first 10 ns of the production run, with fewer conformational changes occurring later in the simulation. RMSD values are also higher for longer polymers (n=3, 4, 5). Such behavior is expected because the conformational space is considerably larger for longer polymer molecules than it is for shorter polymers (i.e. n=1, 2). No major differences are observed between the random and triblock polymers at this point. It seems, however, that for larger n=4, 5 the RMSD for triblock polymers is larger than for random polymers. Average values for RMSD are reported in Table 1 and support this conclusion. While the average RMSD value increases with increasing chain length, the error associated with it decreases. The end-to-end distance corresponds to the distance between the atom O1T of the first ALY residue and atom O4T of the last ALY residue in the polymer chain. The results of the analysis suggest that there is little change of the end-to-end distance of the shortest polymer (i.e. n=1) throughout the 50-ns production run, while the end-to-end distance for the rest of the polymers appears to converge within 6 ns to values around 3 nm. This indicates that major and fast conformational changes occur during the simulations as indicated by both RMSD and end-to-end distance data. The conformational changes decrease the distance between the two terminal atoms significantly; a process that is similar to protein folding. Again, it seems that end-to-end distances of longer triblock polymers (n=4, 5) are larger than of random polymers. This suggests that random polymers are found in somewhat more compact structures. Average values for end-to-end distance are reported in Table 1 and show the same overall characteristics as the average RMSD values, which indicates that longer polymer molecules have greater conformational freedom than shorter polymers, with little difference between the triblock and random polymers. The measurements of the radius of gyration (Fig. 2c and average data in Table 1) further confirm the results obtained by the RMSD analysis and end-to-end measurements: the polymer molecules in aqueous solution quickly adopt compact conformations within about

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10 ns. The process appears to be fast and irreversible. The compact polymer state appeared to consist of an ensemble of distinct compact conformations that the polymer molecule can access throughout the simulations. This is indicated by fluctuating RMSD curves, end-to-end distances and radii of gyration towards the end of the simulations, i.e. conformational changes still occurred. To gain insights into the distribution of accessible compact conformations of the polymers, we performed a cluster analysis using the last 25 ns of the trajectories of triblock and random polymers for n=5, where compact structures were in both cases already adopted in solution. The method is specified in section 2.5. With an RMSD neighbor cut-off of 0.3 nm a total of 69 and 35 clusters were identified in triblock and random polymers, respectively. The structure population of these clusters is shown in Figure S3. The large used cut-off, the large number of identified clusters and the fact that structures are approaching a rather even distribution among these clusters indicate that the compact polymer states indeed consist of a larger number of well distinct compact conformations. Figure S3 also shows that the triblock polymer conformations are substantially more spread out in conformational space than the random polymer structures. In Figure S4 the transitions between clusters are shown during simulations. Frequent transitions especially of triblock polymers could be observed, while transitions of the random polymer were markedly less frequent, suggesting a reduced flexibility of compact random polymers. Several of the less populated clusters contain partially extended polymer conformations that can be adopted for a short time to transit from one compact state to another. It is also important to note that clusters were rarely re-visited during simulations, indicating the existence of a large number of accessible compact states. For the four most populated clusters the structure with the smallest average RMSD from all other structures in that cluster was determined and shown in Figure 3, respectively. These structures are representative conformations of triblock and random polymers, respectively, and illustrate the occurring conformational characteristics of the polymers that can be described as exhibiting a globular overall shape with embedded hydrophobic backbone and charged arginine residues orientated towards the solvent. It can also be observed that in random polymers the backbone was more tightly tied-up than in case of triblock polymers, which explains the reduced flexibility in solution and it is also consistent with the observations described above.

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Flory’s RIS model47,48 that connects the radius of gyration of a polymer with chain length, can be used to gain further insights into the polymer dynamics in aqueous solution according to the relation in Eq. 1: (1) The prefactor a is the effective length of the monomer and can be used as a measure for the stiffness of the polymer molecule, with large values indicating that the polymer is less flexible, i.e. stiffer. The exponent

is related to the solvation of the polymer. For good

solvents, with strong solvent – solute interactions, the value of about 1/3 indicates weak solvation; the experimental value of

is 3/5, while a value at

for proteins is 0.588.49

We used the average radius of gyration and number of monomers to compute both the prefactor a and the values of

(Table 2) by fitting Eq. 1 to this data. The low value of

for

both polymers indicates that the polymers are poorly solvated when compared to peptides. Moreover, triblock polymers are significantly better solvated than random polymers. This indicates that strong hydrophobic effects play an important role in the observed conformational changes of the polymer molecules. This effect is more pronounced in case of the random polymer. Furthermore, the results indicate that the random polymer is stiffer than the triblock polymer, due to the large value of a. These findings are fully consistent with our previous observations: it appears that the random polymer adopts a more compact structure that minimizes the contact with the polar solvent. The resulting compact structure is also less flexible compared to the better solvated triblock polymer. Stronger interactions with water appear to facilitate the transitions of the triblock polymer between the various compact conformations.

3.2 Surface Properties of Polymer Molecules During the conformational changes the molecular interface between the polymer and solvent drastically changes. Upon adopting the compact conformation/-s certain parts of the polymer molecule become inaccessible to the solvent. This can be best illustrated by

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measuring the SAS area of the molecule. Figure 4 and Table S1 report the results of this analysis. Short polymers have a very dynamic structure, which means they can easily and freely change conformations, without adopting any stable conformation. This result is in line with the RMSD data (Fig. 2a), end-to-end distance measurements (Fig. 4b) and radius of gyration calculations (Fig. 2c). For larger polymers (n>3) the changes in the SAS area are larger. The reason being that a long polymer has more degrees of freedom that allow shielding of hydrophobic parts of the polymer from water. Comparing the reduction of SAS for triblock and random polymers for n=4 and n=5 as a function of time reveals a difference in the rate of the initial conformational change. The triblock polymers appear to adopt the compact conformation at a slower pace than the polymers with a random sequence. This is not surprising, considering that the triblock polymer is better solvated, while the stronger hydrophobic effect in case of the random polymer stabilizes the compact state, thereby facilitating the process. The total SAS area can be further decomposed into contributions from either hydrophilic or hydrophobic atoms, according to the method described in section 2.5, and is depicted in Figures 4b and 4c, respectively. Hydrophilic atoms constitute the majority of the SAS area and belong to the carbonate groups linking the residues, atoms of the ester groups that link residue side chains to the backbone and the quaternary nitrogen atoms of residues ALY. All other groups contribute to the hydrophobic part of the SAS area. Fig. 4c displays a sharp decrease in the hydrophobic SAS area. The hydrophobic SAS area represents about one third of the total SAS area, thus the changes are more pronounced. After the initial decrease the value of the hydrophobic SAS area does not stabilize, which indicates the polymer molecule is still very flexible. The hydrophilic part of the SAS decreased as well, which can be attributed to the charged atoms that are not accessible to the solvent once the polymer adopts the compact conformation. Average values and standard deviations for total, hydrophilic and hydrophobic SAS areas are reported in Table S1. A large conformational change of the polymer molecule as observed in our simulations involves substantial reorganization of the surrounding solvent. Since we observe a profound contraction of the polymer molecule as indicated by the decrease of the SAS area (Fig. 4),

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major changes are also expected in the number of water molecule surrounding the polymer molecule. We counted the number of water molecules within 1.0 nm distance of the polymers as a function time, which is shown in Fig. 5. The respective average values are reported in Table S2. As expected, it is possible to observe a significant decrease in the number of water molecules of the polymer molecule during the simulation, a finding that is consistent with the decrease in SAS area reported in Fig. 4. Again, the observed decrease appears to occur faster for polymer molecules with the random monomer sequence, where the compact state also appears to be more stable as the comparably flat curves in Fig. 5a demonstrate, compared to the case of triblock polymers. A change in the number of water molecules around the polymer molecule leads also to changes in the hydrogen bonding patterns between solvent and the polymer molecules. Results of this analysis are shown in Fig. 5b and Table S2. The number of hydrogen bonds is decreasing, which is consistent with the trend observed for the SAS area. The biggest changes can be observed in the first 10-15 ns of the production run, with the number of hydrogen bonds decreasing faster in the case of the random polymer. Even after the initial conformational change of the polymer molecule the number of hydrogen bonds fluctuates substantially. This is consistent with both the dynamics of the water molecules around the polymer and the observed dynamics of the polymer molecule itself. The average number of hydrogen bonds of the compact states of triblock and random polymers with the solvent is found to be similar. The surprisingly small number of hydrogen bonds between water and the polymer molecule can be also be explained in the context of the decrease of the hydrophilic SAS, which indicates a decrease in the number of potential hydrogen bonding sites on the polymer molecule. Overall, the results of the hydrogen bonding analysis are in good agreement with the findings from Flory’s RIS because they confirm water is a relatively poor solvent for the type of polymer molecules surveyed in this study.

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3.3 Solvation Free Energy of Polymers The polymers in solution can adopt two distinct ensembles of conformations. At the beginning of the simulations the polymer is in an extended conformation. After only 10.015.0 ns of simulation the polymer molecules adopt a compact conformation. To gain better insight into this process we computed the free energy of solvation of the polymers in their compact and extended state. Derivation of the solvation free energies using the more commonly applied thermodynamic integration or free energy perturbation schemes was not attempted.50,51 These approaches rely on the assumption that simulations are sufficiently long to evaluate all energy and entropy changes related to gradually changing the interactions between solute and solvent. This, however, is not easily accomplished when very large solutes are considered, such as the polymers in this study, which cause massive reorganization of the surrounding solvent upon changes in the solute-solvent interactions. In fact, such computations are prohibitively expensive.

52,53

An alternative approach is offered

by the Langevin dipoles solvation model, that greatly simplifies the system and avoids the need for excessively long equilibration runs. In the first step we computed the time-dependent solvation free energies for the triblock and random polymers by taking fifty snapshots from the relevant production run trajectories. The plot of the solvation free energy as a function of time is displayed in Fig. S5. Our results indicate there is little difference in the solvation free energy between the polymers of same length, because the same groups are present in both types of polymer molecules surveyed in this study. Solvation free energies of triblock polymers were somewhat larger, thus suggesting more flexibility in solution as already observed before. The computed solvation free energy for the polymer molecules surveyed in this study strongly depends on the number of monomer units as expected due to differences in the contained total charge, while the dependency on residue sequence is only small. The solvation free energies barely vary for polymers with n=1, due to the restricted conformational space the short polymer can sample compared to longer polymers. In the next step we used the same method to estimate the difference in average solvation free energy between the non-compact polymer state and the compact state. Solvation free energies for these structures were again computed using Langevin dipoles and the averages

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of these energies together with changes of solvation free energy after the initial conformational transition are listed in Table 3. The transition from an extended conformation to a compact one is accompanied by improved solvation, which means that polymer transition is facilitated by the solvent that stabilizes the compact state of the polymer. Solvation of the compact polymer is more favorable, even though the polymer – solvent contact surface decreased (Fig. 4) and in turn the number of hydrogen bonds between polymer and water decreases as well (Fig. 5b). This, however, is more than compensated by favorable hydrophobic interactions, where non-polar polymer groups, such as the benzene group of APH and the ethyl group of AVA, are buried inside the polymer, while keeping polar groups and charged ALA exposed to the solvent, which induced an overall energetically more favorable solvent reorganization around the compact polymer molecule. The free energy increased steeply with increasing polymer length, which is not surprising considering that the polymers contained a total positive charge of Q = 2n·e, with e the elementary charge. A proportionality of the solvation free energies in Table 3 with ~Q2 can be observed. This can be explained with a simple physical model: in first approximation a compact polymer can be described as a sphere with constant surface charge density, due to its globular shape and positively charged ALA groups that are oriented towards the solvent. Since ALA groups avoid each other due to mutual Coulomb repulsion, the associated positive charges are more or less evenly distributed on the compact polymer surface, as can be seen in Figure 3. Applying Gauss’ law the electrostatic potential induced by such a sphere is equivalent to a point charge in the center of the sphere with a total charge Q. According to the Born solvation model, the solvation free energy for such an ion is proportional to ~Q2/a, where a is the radius of the sphere, thereby explaining the actually observed ~Q2 increase of the solvation free energy. The effective ion radius, a, increased only slightly with increasing polymer length, as can be seen from the radii of gyration in Table 1. Within the accuracy of the applied method, no significant difference in solvation free energy between triblock and random polymers could be found. This means that the monomer sequence did not seem to influence the solvation properties, neither of the compact nor of the extended state, according to values in Table 3.

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3.4 Analysis of Interaction Energies As seen in the previous section, solvation of the compact polymer state was significantly more favorable than the solvation of the extended state. To gain additional insights, we analyzed electrostatic and van der Waals contributions to the average interaction energies of polymers with the solvent as well as internal polymer interactions. Results are shown in Fig. 6. The Coulomb and Lenard-Jones contributions are displayed in Fig. S6 and S7. As expected, internal polymer energies were dominated by unfavorable strong Coulomb interactions (Fig. S6). During the first 10 ns of the production run they exhibit a large increase that is more pronounced for larger polymer molecules. The main cause for the observed repulsion are the positively charged trimethylammonium groups in the residues ALY and to a smaller extend due to polar ester groups of the residues ALY and AVA that link the side chains to the backbone. As the polymer molecule adopts a more compact conformation electrostatic repulsion increases because the average distances between charged trimethylammonium groups decreases. It also seems that the monomer sequence does not affect this repulsion significantly. This electrostatic repulsion within the polymer increases linearly with n and hence with Q, the total charge of the polymer. Also favorable polymer – water interactions increased linearly with Q, compensating the additional electrostatic repulsion for larger n.

We like to point out that chloride anions were not directly involved in the observed conformational transitions of the polymers. Most chloride ions remained solvated and basically homogenously distributed in the bulk phase of water throughout the entire simulations, as demonstrated by the radial distribution function (RDF) of polymer – chloride atom pairs shown in Figure S1. Small discontinuities of the RDFs at about 0.4 and 0.6 nm stemmed from weak transient coordination of chloride ions to polymer groups. The duration of these coordinations, however, were limited to a few picoseconds, in which also one or two water molecules remained located between chloride and polymer. Using the data presented so far it is possible to outline the mechanism for the observed

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protein-like conformational transition of the polymers. Fig. 7 depicts this process for the random polymer with n=5. At t=0 (Fig. 7a) the polymer molecule is in an extended conformation. At t=10 ns (Fig. 7b) the polymer molecule is already in a semi-compact state. Despite being in a semi-compact state the polymer molecule is still affected by thermal motion, allowing it to visit different conformations, as demonstrated by the fluctuations of the van der Waals interaction strength seen in Fig. S8. This process is facilitated by favorable polymer-solvent electrostatic interactions and a hydrophobic effect. The electrostatic repulsion caused by cationic ALY groups destabilizes the compact polymer conformations and facilitates the conformational transitions between the members of the ensemble of various compact states, as observed in the cluster analysis. While the polymer contracts, Lennard-Jones interactions within the polymer molecule become more favorable, which is caused by hydrophobic groups that move away from the solvent towards the polymer core, thereby increasing the number of internal polymer contacts. At t=20 ns (Fig. 7c) the polymer transition process is already complete and it merely switches between the various conformers, while keeping a generally compact shape (Fig. 7d-f). These fast transitions are facilitated by repulsive electrostatic interactions between positive polymer charges. The core of the compact polymer molecule is mostly composed of the hydrophobic AVA residues (red color in Fig. 7), shielded by hydrophilic ALY residues (blue color in Fig. 7), with charged side chains pointing towards the solvent and away from the hydrophobic polymer core.

3.5 Impact of Hydrophobic Side Chains on Polymer Conformation The results of our simulations indicate that hydrophobic interactions are one of the driving forces behind the observed folding-like behavior of the polymers in aqueous solution. The groups responsible for hydrophobic interactions are mainly the alkyl side chains of AVA residues. To investigate its role in determining the solution structure of the polymer, the residue was modified and its hydrophobic alkyl chain was replaced with a short and neutral amide group. Two polymer molecules with n=5 with triblock and random monomer sequence, respectively, were built as described previously. These new data were compared to results obtained for the original AVA-containing polymer molecules.

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After the simulations both AVN-containing polymers adopt a set of compact conformations, similar to the AVA-containing polymers with the same overall length and sequence. Looking at the RMSD data (Table S3 and Fig. S9a) we observe that the transition frequency between the various conformations in the compact polymer state containing AVN, i.e. its flexibility, increased substantially compared to the case of AVA-containing polymer molecules. The average RMSD data also indicate that the AVN-containing polymers deviate less from the initial structure, i.e. they adopt less compact structures. Interesting to note is also the observation that the random AVN polymer appears to revert back to a less compact state, as indicated by larger end-to-end distance as shown in Table S3 and Figure S9b. A comparison of the radius of gyration (Fig. S9c and Table S3) again confirms that AVN-containing polymers in aqueous solution are more flexible in the compact state than the original AVA polymers and exhibit more frequent conformational transitions. Substituting the hydrophobic alkyl side chain of residue AVA with a small hydrophobic amide group altered the polymer surface. This is evidenced by a small decrease of the total and hydrophobic SAS areas as well as an increase of the hydrophilic SAS area of the AVNcontaining polymers, as shown in Table S4 and Fig. S10. Especially for the random polymer it can be observed that after about 25 ns simulation the compact polymer adopts a partially extended conformation with a larger SAS area. Together with the increased frequency of conformational transitions this demonstrates that the hydrophobic alkyl chain of AVA contributes to a stabilization of the compact state of the polymer. The modification of the side chain of AVA impacts the water environment around the polymer molecules. Hence, we also determined the number of water molecules within 1 nm of the polymer and the number of hydrogen bonds between polymer atoms and the solvent. The results are shown in Fig. 8 and Table S5. Similar trends as before were observed, where the number of water molecules decreased, simultaneously decreasing the number of hydrogen bonds with the solvent as well. For the random polymer this trend was partially reversed after 25 ns, in line with the previous results. This suggests that the AVN containing polymer molecule goes through a folding-unfolding-like cycle, demonstrating again the reduced stability of the compact state. The average number of water molecules surrounding the polymer and the number of hydrogen bonds between polymer atoms and solvent as

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well as fluctuations of both are larger in AVN-containing polymers due to their less compact and less stable conformation. Moreover, the hydrophilic –CO-NH2 side chain in AVN is able to form additional hydrogen bonds, which contributes to the observed effects. The most drastic changes can be observed in internal interaction energies of the polymer molecules, as shown in Fig. 9a and Table S6. Replacing the side chain of AVA with AVN lowered internal electrostatic repulsion substantially, while Lennard-Jones interactions are less favorable than in the original AVA polymer. Both interaction changes are apparently a result of the reduced compactness of the AVN polymers. On the other hand, there is only little difference in the interaction energies between polymer molecules and water, as evidenced by data shown in Fig. 9b and Table S7. In general, in AVN-containing polymers the number of hydrophobic groups is reduced, thereby weakening the compact polymer state. Instead, the amide groups in the side chain of AVN form additional hydrogen bonds with water molecules, thereby stabilizing the extended state. While the compact state is energetically still more favorable, the compact state is less compact and more transient than in the case of AVA-containing polymers. This demonstrates the importance of the hydrophobic alkyl side chain of the residue AVA in stabilizing the compact polymer state.

3.6 Aggregation Propensity of Polycarbonate Polymers So far, we observed that hydrophobic interactions coupled with internal electrostatic repulsion within the polymer determined protein-like dynamics of polycarbonate polymers in aqueous solution. Experiments also indicate that these polymers exhibit a strong tendency to aggregate in solution.15 Such aggregation trends were surveyed by performing MD simulations of two solvated polymers with triblock sequence of varying length. Only results for triblock polymers that led to actual aggregation within simulation times are presented here. In order to better reproduce the experimental data we have considered polymer molecules with n ≤ 10. In some cases spontaneous aggregation was not observed because the polymer molecules

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coincidentally diffused into different directions without making initial contact within simulation times. In all other cases where initial contact did occur, aggregation proceeded rapidly and the resulting aggregates remained stable throughout the simulation. This finding can be confirmed by observing the distance between mass centers of the two aggregating polymer molecules as a function of simulation time (Fig. S13). These distances decreased initially during the first 20 ns of simulations, after which the distances converged to a small value for the remainder of the simulations. This indicates that formed aggregates remained indeed stable. This was further investigated by determining the overall SAS area of both polymers as well as the polymer – polymer contact area, as shown in Figure 10. A monotonous decrease of the overall solvent accessible surface area and an increase of the contact area were observed, which was more pronounced for longer polymer chains. This can be attributed to the larger accessible conformational space that enabled these longer polymers to find more suitable conformations that are capable of constituting energetically more favorable polymer dimers. By analyzing the time-dependent interaction energies within each polymer of the dimer it is possible to observe that each single molecule in this pair behaves similar to an isolated molecule of the same composition in solution (section 3.4 and Fig. 6). The results are shown in Fig. 11 and with further details on contributions in Figs. S14-S18, where average values are given in Tables S8-S12. While Coulomb interactions remain repulsive throughout simulations, Lennard-Jones interactions become increasingly more favorable as the simulation progresses. The longer the polymer chain is the more favorable the LennardJones interactions become during the simulation, which is also correlated with the distance between the polymer centers (Fig. S13). Also, longer polymer chains need more time to find an energetically favorable conformation during the aggregation process due to the larger conformational space that needs to be sampled. Interestingly, the aggregation of two polymers did not reduce the internal repulsive Coulomb interactions within neither polymer of the dimers. In fact, this interaction even appears to increase in the case of n=10. This means that after aggregation these polymers remain in a compact state or adopt an even more compressed conformation. Changes in the interaction energies between two polymers are displayed in Fig. S16c and

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Table S12. Lennard-Jones interactions became steadily stronger, as a result of an increasing contact area between the two polymers. The aggregation of the two polymers inevitably also shortened the distances between the charged ALY residues of the two polymers, thereby increasing the unfavorable electrostatic interactions between the two polymers. Thus it is important to note that aggregation was apparently not driven by mutual direct attraction of the polymers. In fact, direct polymer - polymer interactions are overall distinctively unfavorable. Therefore, the observed aggregation had to be caused by solventrelated effects. It appears that the same factors that induced transition of single polymers from an extended to a compact state in solution also at work during the observed polymer aggregation. Hydrophobic interactions strive to minimize the polymer – water interface area, where unfavorable interactions between non-polar polymer groups and polar water occur. This can be achieved by aggregate formation, where hydrophobic groups are buried within the core of the aggregate, while charged ALA residues point towards the solvent to maximize favorable interactions between cationic ALA and water, as illustrated in Fig. 12. While the aggregation process is driven by hydrophobic effects, it is still remarkable that these highly charged polymers readily aggregate considering that each polymer carries a total charge of Q = 2n·e. The Coulomb repulsion between these ionic polymers should at least impede aggregation, as indicated by the increasingly large positive internal interaction energies (Fig. 11a). Once aggregates formed, a large number of positive charges is concentrated within a rather small volume. Chloride counter ions, as mentioned before, basically did not coordinate with the polymers but remained solvated in the bulk of the solvent. According to Fig. 11b, increasingly more favorable polymer – water interactions during aggregation compensated unfavorable ALA – ALA repulsion for larger n. In section 3.3 we observed that with increasing n an improved solvation of single compact polymers could be achieved, as expressed by an increase of solvation free energy proportional to ~Q2. The more favorable polymer – water interactions after aggregation, despite of a substantially reduced polymer – water contact area, can be explained with the simple approximation used in section 3.3 as a fusion of two compact spherical polymers with radii a and constant surface charge Q into a single sphere with increased radius b and surface charge 2Q. Again,

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according to the Born model where the solvation free energy is proportional to ~Q2/a, the solvation free energy of the aggregate compared to two isolated solvated polymers would increase by a factor of 2a/b. The radius of the formed aggregate sphere should be smaller than twice the radius of a single polymer. Therefore, the solvation of the aggregate becomes overall more favorable. While this approximation is rather simple, it could explain qualitatively why polymer solvation becomes more favorable upon aggregate formation. This favorable solvation could act as a secondary effect to facilitate polymer aggregation next to the hydrophobic effect, however, further simulations will be necessary to corroborate and quantify this model.

4. Conclusion In the present work MD simulations were used to investigate the protein-like behavior of polycarbonate polymers in aqueous solutions. Monomers consisted of cationic ALY, hydrophobic AVA and non-polar linker APH units. Polymers with triblock monomer sequence and random sequence of varying length were evaluated. For polymers of sufficient length (n>1) a rapid (within 10-20 ns) transition to a more compact conformation was observed. This transition resulted in fewer contacts between non-polar polymer groups and the solvent, while at the same time leaving the charged and polar groups more exposed to the solvent. This indicates a hydrophobic effect as the driving force for the conformational change. After the transition into a compact polymer state, regular smaller transitions between distinct compact conformations were observed. These conformations were characterized by substantially shorter end-to-end distances, small radius of gyration, reduced SAS areas, and reduced contact areas with the solvent, which led to reduced hydrogen bonding between polymers and water. According to cluster analysis, polymer molecules with a random sequence adopted a slightly more compact structure than triblock polymers, which in turn led to a reduced flexibility of these polymers as indicated by markedly fewer transitions between different compact polymer structures. The results of the Flory RIS analysis based on calculated radii of gyration indicated that water 23


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is a significantly less favorable solvent for the polymer molecules than for typical peptides. The same analysis also showed that the solvation of compact random polymers is less favorable, with the polymer chains being somewhat less flexible than peptides. This indicates hydrophobic interactions play an important role in the conformational transition of polymer molecules. The same hydrophobic effect also facilitated stabilization of random polymers compared to triblock polymers. After replacing hydrophobic AVA with smaller hydrophilic AVN the frequency of transitions between different compact states increased. Removal of hydrophobic groups in the polymer led to a destabilization of the compact state to such an extent that random polymers were able to adopt a significantly less compact conformation. This demonstrates that hydrophobic side chain of monomer AVA plays an important role in stabilizing the compact polymers. During simulations the polymer molecules readily aggregated. In this process, unfavorable repulsive electrostatic interactions, mainly among positively charged ALY residues, dominated polymer – polymer interactions, hence direct overall attractive interactions between polymers were not present. Electrostatic interactions between polymers and water, however, became more favorable even though the polymer molecules were much less accessible to the solvent. A more favorable solvation of polymers after aggregation could be rationalized with the Born model. That model states that the solvation of two spheres with the same surface charge is less favorable than the solvation of a combination of these two spheres into a larger sphere, as long as the radius remains smaller than the radius of the two smaller spheres combined. Therefore, the improved solvation by fusion of charged polymer spheres could have supported the aggregation process. The polymer – water contact areas were minimized due to hydrophobic interactions, which in turn were found to be the probable driving force for aggregation, in a similar way as the hydrophobic effect induced the initial conformational changes of single polymers into compact structures. Overall, MD simulations were able to describe protein-like behavior of considered polycarbonate polymers and to identify the underlying factors governing the processes that determine structure and aggregation. Furthermore, the influence of specific polymer compositions on these processes was revealed. The molecular basis of the observed

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antimicrobial activity of this class of polymers should be addressed in the next step.

Acknowledgement We gratefully acknowledge the provision of computational facilities by the A*STAR Computational Resource Centre of Singapore (ACRC) and the Institute of High Performance Computing (IHPC) as well as the financial support from the Joint Council Office (JCO) of the Agency for Science, Technology and Research (A*STAR) of Singapore.

Supporting Information (a) Details on building the monomers; (b) Specifications of MD simulations; Table S1: SAS area of polymers; Table S2: Analysis of water structure around polymers; Table S3: RMSD, end-to-end distance and radius of gyration of AVA or AVN containing polymers; Table S4: SAS area of AVA or AVN containing polymers; Table S5: Analysis of water structure around polymers containing AVA or AVN; Table S6: Internal interaction strengths of polymers that contain AVA or AVN; Tables S7-S12: Internal polymer interactions and interactions of polymers with water; Figure S1: Radial distribution of chloride ions around triblock polymers; Figure S2: Assigned atom types; Figures S3-S4: Results from cluster analysis of polymer trajectories; Figures S5-S8: Structural and interaction energy data for single polymer molecules in solution; Figures S9-S12: Structural and interaction energy data for AVNcontaining polymers; Figures S13-S18: Structural and interaction energy data for two aggregating polymers.

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GROMACS: Fast, Flexible, and Free. J. Comput. Chem. 2005, 26, 1701–1718. (44) Hess, B.; Kutzner, C.; van der Spoel, D.; Lindahl, E. Gromacs 4: Algorithms for Highly Efficient, Load-Balanced, and Scalable Molecular Simulation. J. Chem. Theory Comput. 2008, 4, 435-447. (45) Pronk, S.; Páll, S.; Schulz, R.; Larsson, P.; Bjelkmar, P.; Apostolov, R.; Shirts, M. R.; Smith, J. C.; Kasson, P. M.; Van Der Spoel, D.; et al. GROMACS 4.5: a High-Throughput and Highly Parallel Open Source Molecular Simulation Toolkit. Bioinformatics 2013, 29, 845–854. (46) Humphrey, W.; Dalke, A.; Schulten, K. VMD: Visual Molecular Dynamics. J. Mol. Graphics 1996, 14, 33–38. (47) Flory, P. J. The Configuration of Real Polymer Chains. J. Chem. Phys. 1949, 17, 303310. (48) Flory, P. J. Statistical Mechanics of Chain Molecules, 1st ed.; Interscience, 1969. (49) Grosberg, A. Y.; Kuznetsov, D. V. Quantitative Theory of the Globule-to-Coil Transition. 1. Link Density Distribution in a Globule and Its Radius of Gyration. Macromolecules 1992, 25, 1970–1979. (50) Kirkwood, J. G. Statistical Mechanics of Fluid Mixtures. J. Chem. Phys. 1935, 3, 300313. (51) Zwanzig, R. W. High-Temperature Equation of State by a Perturbation Method. I. Nonpolar Gases. J. Chem. Phys. 1954, 22, 1420-1426. (52) Christ, C. D.; Mark, A. E.; van Gunsteren, W. F. Basic Ingredients of Free Energy Calculations: a Review. J. Comput. Chem. 2010, 31, 1569–1582. (53) Pohorille, A.; Jarzynski, C.; Chipot, C. Good Practices in Free-Energy Calculations. J. Phys. Chem. B 2010, 114, 10235–10253.

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Table of Contents Graphics

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Table 1: Average RMSD, End-to-end Distance and Radius of Gyration of Polymers.a Length n 1 2 3 4 5

RMSD Triblock Random 0.4 N/A (0.1) 0.9 0.7 (0.2) (0.1) 1.3 1.2 (0.1) (0.1) 1.9 1.4 (0.1) (0.1) 2.5 2.3 (0.1) (0.1)

D Triblock 1.3 (0.4) 1.6 (0.5) 1.9 (0.5) 2.2 (0.5) 2.6 (0.6)

rg Random N/A 1.4 (0.4) 1.7 (0.6) 1.6 (0.6) 1.8 (0.5)

a

Triblock 0.7 (0.1) 0.8 (0.1) 0.9 (0.1) 1.0 (0.1) 1.1 (0.1)

Random N/A 0.8 (0.6) 0.9 (0.0) 1.0 (0.0) 1.0 (0.1)

Values were averaged over the last 30 ns of simulations, with the standard deviation given in parentheses. All values are given in units of nm.

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Table 2: Flory Model Parameters of Hydrated Polymers.a,b Polymer type Triblock Random

a 0.384 (0.014) 0.420 (0.002)

0.348 (0.015) 0.294 (0.002)

a

Parameters were derived by fitting of Eq. 1 using polymer length and calculated radius of gyration. b An R-squared parameter of 0.99 for fitting the data using the model in Eq. 1 was found for both triblock and random polymers.

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Table 3: Solvation Free Energies of Polymers.a Length n 1 2 3 a

Uncompact -1042 (22) -3650 (62) -7186 (100)

Triblock Compact -1060 (21) -3802 (59) -7697 (54)

Difference -18 (43) -152 (120) -577 (155)

Uncompact N/A -3617 (57) -7239 (76)

Values are given in kJ/mol

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Random Compact N/A -3801 (33) -7718 (36)

Difference N/A -139 (91) -536 (112)


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Figure 1: Polycarbonate polymers for n=2: (a) Triblock polymer (ALY)2-(AVA)2-APH-(AVA)2(ALY)2, (b) random polymer (ALY-AVA)2-APH-(AVA-ALY)2 and (c) spatial structure of the triblock polymer before relaxation.

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Figure 2: Time-depended structural changes of the polymer molecule with varying length in either triblock or random configuration (left or right panels, respectively): a) RMSD, b) end-to-end distance and c) radius of gyration for one solvated polymer molecule. Key to colors: red line – n=1, green line – n=2, blue line – n=3, magenta line – n=4, cyan line – n=5.

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Figure 3: Most representative structures for the four most populated clusters found in (a) triblock and (b) random polymer trajectories. The most representative structure is the structure with the smallest average RMSD from all other structures in that cluster. The percentage of duration that the polymer was found in a respective cluster during simulations is added in the top left corner of each structure. The polymer backbone is emphasized and the display of hydrogen atoms was omitted for clarity.

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Figure 4: Time-dependent changes of solvent-accessible surface area of the polymer molecule of varying length in either triblock or random configuration (left or right panels, respectively): a) Total SAS area, b) hydrophobic SAS area and c) hydrophilic SAS area. Key to colors: red line – n=1, green line – n=2, blue line – n=3, magenta line – n=4, cyan line – n=5.

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Figure 5: Water environment around the triblock (left panels) and random (right panels) polymers as a function of time: a) Number of water molecules in the 1.0 nm shell around the polymer molecule and b) number of hydrogen bonds between the polymer molecule and water. Key to colors: red line – n=1, green line – n=2, blue line – n=3, magenta line – n=4, cyan line – n=5.

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Figure 6: Interaction energy data for triblock (full line) and random (broken line) polymer molecule. a) Intramolecular interaction. b) Polymer-water interaction. c) Water-water interaction. Key to colors: red line – n=1, green line – n=2, magenta line – n=3, ochre line – n=4, blue line – n=5.

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Figure 7: Snapshots of the random polymer n = 5 at different simulation times. A transition from an extended state (a) to a more compact intermediate conformation (b) and further to a series of ever more compact structures (c-f) can be observed. Key: blue – residue ALY, red – residue AVA, green – residue APH.

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Figure 8: Water environment around the AVN-containing polymer molecule with length n=5 and comparison with AVA-containing polymer: a) Number of waters and b) Number of hydrogen bonds. Key to colors: red line – AVA triblock, green line – AVA random, blue line – AVN triblock, magenta line – AVN random.

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Figure 9: Interaction energy for AVA-containing polymer (full line) molecule with length n=5 and comparison with AVN-containing polymer (broken line). a) Intramolecular interactions. b) Polymer-Water interactions. c) Water-Water interactions. Key: red line – triblock polymer, blue – random polymer.

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Figure 10: (a) Total SAS area of two polymers with triblock sequence and (b) their contact area during simulations. Key to colors: red line – n=3, green line – n=6, blue line – n=9, magenta line – n=10.

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Figure 11: Interaction energy between two aggregate-forming polymer molecules with a triblock sequence as a function of time. a) Intramolecular. b) Polymer-Water. c) Water-water. Key to colors: red line – n=3, green line – n=6, blue line – n=9, magenta line – n=10.

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Figure 12: Aggregate of two polymer molecules with length n=10 after 50 ns of simulation: a) all atoms are displayed and b) only backbone atoms are shown. Key to colors: red – polymer 1, blue – polymer 2, orange – residue APH.

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Protein-Like Dynamics of Polycarbonate Polymers in Water - The

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